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lemma(1, [], ap(gap_a, []): (i(a1, b2c2);i(b2, a1c1))). lemma(2, [i(a1, b2c2)], ap(gap_b, []): (i(b1, a2c2);i(c2, a1b1))). lemma(3, [i(b1, a2c2), i(a1, b2c2)], ap(gap_c, []): (i(c1, a2b2);i(a2, b1c1))). lemma(4, [i(c1, a2b2), i(b1, a2c2), i(a1, b2c2)], ap(t1in2, [i(a1, b2c2), i(b1, a2c2), i(c1, a2b2)]):goal). lemma(5, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ia1b1, []):i(a1, a1b1)). lemma(6, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ib1a1, []):i(b1, a1b1)). lemma(7, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ia2b2, []):i(a2, a2b2)). lemma(8, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ib2a2, []):i(b2, a2b2)). lemma(9, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ia1c1, []):i(a1, a1c1)). lemma(10, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ic1a1, []):i(c1, a1c1)). lemma(11, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ia2c2, []):i(a2, a2c2)). lemma(12, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ic2a2, []):i(c2, a2c2)). lemma(13, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ic1b1, []):i(c1, b1c1)). lemma(14, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ib1c1, []):i(b1, b1c1)). lemma(15, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ic2b2, []):i(c2, b2c2)). lemma(16, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ib2c2, []):i(b2, b2c2)). lemma(17, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(iooa, []):i(o, oa)). lemma(18, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ioob, []):i(o, ob)). lemma(19, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(iooc, []):i(o, oc)). lemma(20, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ia1oa, []):i(a1, oa)). lemma(21, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ia2oa, []):i(a2, oa)). lemma(22, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ib1ob, []):i(b1, ob)). lemma(23, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ib2ob, []):i(b2, ob)). lemma(24, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ic1oc, []):i(c1, oc)). lemma(25, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ic2oc, []):i(c2, oc)). lemma(26, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ibc1, []):i(bc, b1c1)). lemma(27, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ibc2, []):i(bc, b2c2)). lemma(28, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(iac1, []):i(ac, a1c1)). lemma(29, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(iac2, []):i(ac, a2c2)). lemma(30, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(iab1, []):i(ab, a1b1)). lemma(31, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(iab2, []):i(ab, a2b2)). lemma(32, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(a1, b2c2), [i(a1, b2c2)]):p(a1, a1)). lemma(33, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(b1, a2c2), [i(b1, a2c2)]):p(b1, b1)). lemma(34, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(a2, b1c1), [i(a2, b1c1)]):p(a2, a2)). lemma(35, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(b2, a2b2), [8]):p(b2, b2)). lemma(36, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(c1, a1c1), [10]):p(c1, c1)). lemma(37, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(c2, a2c2), [12]):p(c2, c2)). lemma(38, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(o, oa), [17]):p(o, o)). lemma(39, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(bc, b1c1), [26]):p(bc, bc)). lemma(40, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(ac, a1c1), [28]):p(ac, ac)). lemma(41, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pref(ab, a1b1), [30]):p(ab, ab)). lemma(42, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lref(a1, b2c2), [i(a1, b2c2)]):l(b2c2, b2c2)). lemma(43, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lref(b1, a2c2), [i(b1, a2c2)]):l(a2c2, a2c2)). lemma(44, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lref(a2, b1c1), [i(a2, b1c1)]):l(b1c1, b1c1)). lemma(45, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lref(a1, a1b1), [5]):l(a1b1, a1b1)). lemma(46, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lref(a2, a2b2), [7]):l(a2b2, a2b2)). lemma(47, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lref(a1, a1c1), [9]):l(a1c1, a1c1)). lemma(48, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lref(o, oa), [17]):l(oa, oa)). lemma(49, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lref(o, ob), [18]):l(ob, ob)). lemma(50, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lref(o, oc), [19]):l(oc, oc)). lemma(51, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(b1, a2, a2c2, b1c1), [i(b1, a2c2), 14, 11, i(a2, b1c1)]): (p(b1, a2);l(a2c2, b1c1))). lemma(52, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(b1, a2), [p(b1, a2)]):p(a2, b1)). lemma(53, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(b1, a2, a2b2), [p(b1, a2), 7]):i(b1, a2b2)). lemma(54, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(b1, a2, oa), [p(b1, a2), 21]):i(b1, oa)). lemma(55, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(a2, b1, a1b1), [52, 6]):i(a2, a1b1)). lemma(56, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(a2, b1, ob), [52, 22]):i(a2, ob)). lemma(57, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(a1, b1, a1b1, oa), [5, 20, 6, 54]): (p(a1, b1);l(a1b1, oa))). lemma(58, [p(a1, b1), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(a1, b1), [p(a1, b1)]):p(b1, a1)). lemma(59, [p(a1, b1), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(a2, b1, a1), [52, 58]):p(a2, a1)). lemma(60, [p(a1, b1), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(notaa, [59]):false). lemma(61, [p(a1, b1), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [60]):goal). lemma(62, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a1b1, oa), [l(a1b1, oa)]):l(oa, a1b1)). lemma(63, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(o, oa, a1b1), [17, 62]):i(o, a1b1)). lemma(64, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(ab, a1b1, oa), [30, l(a1b1, oa)]):i(ab, oa)). lemma(65, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(b1, o, a1b1, ob), [6, 22, 63, 18]): (p(b1, o);l(a1b1, ob))). lemma(66, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(b1, o), [p(b1, o)]):p(o, b1)). lemma(67, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(a2, b1, o), [52, p(b1, o)]):p(a2, o)). lemma(68, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(a2, o), [67]):p(o, a2)). lemma(69, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(b1, o, oc), [p(b1, o), 19]):i(b1, oc)). lemma(70, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(a2, b1, oc), [52, 69]):i(a2, oc)). lemma(71, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(o, b1, a2c2), [66, i(b1, a2c2)]):i(o, a2c2)). lemma(72, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(o, b1, b1c1), [66, 14]):i(o, b1c1)). lemma(73, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(o, b1, a2b2), [66, 53]):i(o, a2b2)). lemma(74, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(b1, c2, a2c2, oc), [i(b1, a2c2), 69, 12, 25]): (p(b1, c2);l(a2c2, oc))). lemma(75, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(b1, c2), [p(b1, c2)]):p(c2, b1)). lemma(76, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(a2, b1, c2), [52, p(b1, c2)]):p(a2, c2)). lemma(77, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(a2, c2), [76]):p(c2, a2)). lemma(78, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(o, b1, c2), [66, p(b1, c2)]):p(o, c2)). lemma(79, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(o, c2), [78]):p(c2, o)). lemma(80, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(b1, c2, b2c2), [p(b1, c2), 15]):i(b1, b2c2)). lemma(81, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(a2, b1, b2c2), [52, 80]):i(a2, b2c2)). lemma(82, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(triangle2(b2c2), [81, 16, 15]):false). lemma(83, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [82]):goal). lemma(84, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a2c2, oc), [l(a2c2, oc)]):l(oc, a2c2)). lemma(85, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(c1, oc, a2c2), [24, 84]):i(c1, a2c2)). lemma(86, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(ac, a2c2, oc), [29, l(a2c2, oc)]):i(ac, oc)). lemma(87, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(b1, c1, a2c2, b1c1), [i(b1, a2c2), 14, 85, 13]): (p(b1, c1);l(a2c2, b1c1))). lemma(88, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(b1, c1), [p(b1, c1)]):p(c1, b1)). lemma(89, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(a2, b1, c1), [52, p(b1, c1)]):p(a2, c1)). lemma(90, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(a2, c1), [89]):p(c1, a2)). lemma(91, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(o, b1, c1), [66, p(b1, c1)]):p(o, c1)). lemma(92, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(o, c1), [91]):p(c1, o)). lemma(93, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(b1, c1, a1c1), [p(b1, c1), 10]):i(b1, a1c1)). lemma(94, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(triangle1(a1c1), [9, 93, 10]):false). lemma(95, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [94]):goal). lemma(96, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a2c2, b1c1), [l(a2c2, b1c1)]):l(b1c1, a2c2)). lemma(97, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(oc, a2c2, b1c1), [84, l(a2c2, b1c1)]):l(oc, b1c1)). lemma(98, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(oc, b1c1), [97]):l(b1c1, oc)). lemma(99, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(c2, a2c2, b1c1), [12, l(a2c2, b1c1)]):i(c2, b1c1)). lemma(100, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(bc, b1c1, a2c2), [26, 96]):i(bc, a2c2)). lemma(101, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(bc, b1c1, oc), [26, 98]):i(bc, oc)). lemma(102, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(ac, a2c2, b1c1), [29, l(a2c2, b1c1)]):i(ac, b1c1)). lemma(103, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(b1, ab, a1b1, a2b2), [6, 53, 30, 31]): (p(b1, ab);l(a1b1, a2b2))). lemma(104, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(b1, ab), [p(b1, ab)]):p(ab, b1)). lemma(105, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(a2, b1, ab), [52, p(b1, ab)]):p(a2, ab)). lemma(106, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(a2, ab), [105]):p(ab, a2)). lemma(107, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(o, b1, ab), [66, p(b1, ab)]):p(o, ab)). lemma(108, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(o, ab), [107]):p(ab, o)). lemma(109, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(ab, b1, a2c2), [104, i(b1, a2c2)]):i(ab, a2c2)). lemma(110, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(goal_normal(a2c2), [43, 100, 29, 109]):goal). lemma(111, [l(a1b1, a2b2), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(notab, [l(a1b1, a2b2)]):false). lemma(112, [l(a1b1, a2b2), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [111]):goal). lemma(113, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(103), [110, 112]):goal). lemma(114, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(87), [95, 113]):goal). lemma(115, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(74), [83, 114]):goal). lemma(116, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a1b1, ob), [l(a1b1, ob)]):l(ob, a1b1)). lemma(117, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(oa, a1b1, ob), [62, l(a1b1, ob)]):l(oa, ob)). lemma(118, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(oa, ob), [117]):l(ob, oa)). lemma(119, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(a1, a1b1, ob), [5, l(a1b1, ob)]):i(a1, ob)). lemma(120, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(b2, ob, a1b1), [23, 116]):i(b2, a1b1)). lemma(121, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(b2, ob, oa), [23, 118]):i(b2, oa)). lemma(122, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(ab, a1b1, ob), [30, l(a1b1, ob)]):i(ab, ob)). lemma(123, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(a1, b2, b2c2, a1b1), [i(a1, b2c2), 5, 16, 120]): (p(a1, b2);l(b2c2, a1b1))). lemma(124, [p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(a1, b2), [p(a1, b2)]):p(b2, a1)). lemma(125, [p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(a1, b2, a2b2), [p(a1, b2), 8]):i(a1, a2b2)). lemma(126, [p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(b2, a1, a1c1), [124, 9]):i(b2, a1c1)). lemma(127, [p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(a1, b1, a1b1, a2b2), [5, 125, 6, 53]): (p(a1, b1);l(a1b1, a2b2))). lemma(128, [p(a1, b1), p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(a1, b1), [p(a1, b1)]):p(b1, a1)). lemma(129, [p(a1, b1), p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(a2, b1, a1), [52, 128]):p(a2, a1)). lemma(130, [p(a1, b1), p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(notaa, [129]):false). lemma(131, [p(a1, b1), p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [130]):goal). lemma(132, [l(a1b1, a2b2), p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(notab, [l(a1b1, a2b2)]):false). lemma(133, [l(a1b1, a2b2), p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [132]):goal). lemma(134, [p(a1, b2), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(127), [131, 133]):goal). lemma(135, [l(b2c2, a1b1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(b2c2, a1b1), [l(b2c2, a1b1)]):l(a1b1, b2c2)). lemma(136, [l(b2c2, a1b1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(oa, a1b1, b2c2), [62, 135]):l(oa, b2c2)). lemma(137, [l(b2c2, a1b1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(oa, b2c2), [136]):l(b2c2, oa)). lemma(138, [l(b2c2, a1b1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(ob, a1b1, b2c2), [116, 135]):l(ob, b2c2)). lemma(139, [l(b2c2, a1b1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(ob, b2c2), [138]):l(b2c2, ob)). lemma(140, [l(b2c2, a1b1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(b1, a1b1, b2c2), [6, 135]):i(b1, b2c2)). lemma(141, [l(b2c2, a1b1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(a2, b1, b2c2), [52, 140]):i(a2, b2c2)). lemma(142, [l(b2c2, a1b1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(triangle2(b2c2), [141, 16, 15]):false). lemma(143, [l(b2c2, a1b1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [142]):goal). lemma(144, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(123), [134, 143]):goal). lemma(145, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(65), [115, 144]):goal). lemma(146, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(57), [61, 145]):goal). lemma(147, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a2c2, b1c1), [l(a2c2, b1c1)]):l(b1c1, a2c2)). lemma(148, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(c2, a2c2, b1c1), [12, l(a2c2, b1c1)]):i(c2, b1c1)). lemma(149, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(c1, b1c1, a2c2), [13, 147]):i(c1, a2c2)). lemma(150, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(bc, b1c1, a2c2), [26, 147]):i(bc, a2c2)). lemma(151, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(ac, a2c2, b1c1), [29, l(a2c2, b1c1)]):i(ac, b1c1)). lemma(152, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(c1, ac, a1c1, b1c1), [10, 13, 28, 151]): (p(c1, ac);l(a1c1, b1c1))). lemma(153, [p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(c1, ac), [p(c1, ac)]):p(ac, c1)). lemma(154, [p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(ac, c1, oc), [153, 24]):i(ac, oc)). lemma(155, [p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(c2, bc, a2c2, b2c2), [12, 15, 150, 27]): (p(c2, bc);l(a2c2, b2c2))). lemma(156, [p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(c2, bc), [p(c2, bc)]):p(bc, c2)). lemma(157, [p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(bc, c2, oc), [156, 25]):i(bc, oc)). lemma(158, [p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(c2, ac, a2c2, oc), [12, 25, 29, 154]): (p(c2, ac);l(a2c2, oc))). lemma(159, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(c2, ac), [p(c2, ac)]):p(ac, c2)). lemma(160, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(c1, ac, c2), [p(c1, ac), 159]):p(c1, c2)). lemma(161, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(c1, c2), [160]):p(c2, c1)). lemma(162, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(notcc, [161]):false). lemma(163, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [162]):goal). lemma(164, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a2c2, oc), [l(a2c2, oc)]):l(oc, a2c2)). lemma(165, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(b1c1, a2c2, oc), [147, l(a2c2, oc)]):l(b1c1, oc)). lemma(166, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(b1c1, oc), [165]):l(oc, b1c1)). lemma(167, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(b1, a2c2, oc), [i(b1, a2c2), l(a2c2, oc)]):i(b1, oc)). lemma(168, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(a2, b1c1, oc), [i(a2, b1c1), 165]):i(a2, oc)). lemma(169, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(o, oc, a2c2), [19, 164]):i(o, a2c2)). lemma(170, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(o, oc, b1c1), [19, 166]):i(o, b1c1)). lemma(171, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(b1, o, a2c2, ob), [i(b1, a2c2), 22, 169, 18]): (p(b1, o);l(a2c2, ob))). lemma(172, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(b1, o), [p(b1, o)]):p(o, b1)). lemma(173, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(b1, o, oa), [p(b1, o), 17]):i(b1, oa)). lemma(174, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(o, b1, a1b1), [172, 6]):i(o, a1b1)). lemma(175, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(b1, a2, a2c2, oa), [i(b1, a2c2), 173, 11, 21]): (p(b1, a2);l(a2c2, oa))). lemma(176, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(b1, a2), [p(b1, a2)]):p(a2, b1)). lemma(177, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(o, b1, a2), [172, p(b1, a2)]):p(o, a2)). lemma(178, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(o, a2), [177]):p(a2, o)). lemma(179, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(b1, a2, a2b2), [p(b1, a2), 7]):i(b1, a2b2)). lemma(180, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(o, b1, a2b2), [172, 179]):i(o, a2b2)). lemma(181, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(a2, b1, a1b1), [176, 6]):i(a2, a1b1)). lemma(182, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(a2, b1, ob), [176, 22]):i(a2, ob)). lemma(183, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(a1, b1, a1b1, oa), [5, 20, 6, 173]): (p(a1, b1);l(a1b1, oa))). lemma(184, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(a1, b1), [p(a1, b1)]):p(b1, a1)). lemma(185, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(o, b1, a1), [172, 184]):p(o, a1)). lemma(186, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(o, a1), [185]):p(a1, o)). lemma(187, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(a2, b1, a1), [176, 184]):p(a2, a1)). lemma(188, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(notaa, [187]):false). lemma(189, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [188]):goal). lemma(190, [l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a1b1, oa), [l(a1b1, oa)]):l(oa, a1b1)). lemma(191, [l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(ab, a1b1, oa), [30, l(a1b1, oa)]):i(ab, oa)). lemma(192, [l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(unique(b1, ab, a1b1, a2b2), [6, 179, 30, 31]): (p(b1, ab);l(a1b1, a2b2))). lemma(193, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(b1, ab), [p(b1, ab)]):p(ab, b1)). lemma(194, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(o, b1, ab), [172, p(b1, ab)]):p(o, ab)). lemma(195, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(o, ab), [194]):p(ab, o)). lemma(196, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ptra(a2, b1, ab), [176, p(b1, ab)]):p(a2, ab)). lemma(197, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(psym(a2, ab), [196]):p(ab, a2)). lemma(198, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(ab, b1, a2c2), [193, i(b1, a2c2)]):i(ab, a2c2)). lemma(199, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(goal_normal(a2c2), [43, 150, 29, 198]):goal). lemma(200, [l(a1b1, a2b2), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(notab, [l(a1b1, a2b2)]):false). lemma(201, [l(a1b1, a2b2), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [200]):goal). lemma(202, [l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(192), [199, 201]):goal). lemma(203, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(183), [189, 202]):goal). lemma(204, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a2c2, oa), [l(a2c2, oa)]):l(oa, a2c2)). lemma(205, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(b1c1, a2c2, oa), [147, l(a2c2, oa)]):l(b1c1, oa)). lemma(206, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(b1c1, oa), [205]):l(oa, b1c1)). lemma(207, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(oc, a2c2, oa), [164, l(a2c2, oa)]):l(oc, oa)). lemma(208, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(oc, oa), [207]):l(oa, oc)). lemma(209, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(c2, a2c2, oa), [12, l(a2c2, oa)]):i(c2, oa)). lemma(210, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(pcon(bc, c2, oa), [156, 209]):i(bc, oa)). lemma(211, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(c1, b1c1, oa), [13, 205]):i(c1, oa)). lemma(212, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(triangle1(oa), [20, 173, 211]):false). lemma(213, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [212]):goal). lemma(214, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(175), [203, 213]):goal). lemma(215, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a2c2, ob), [l(a2c2, ob)]):l(ob, a2c2)). lemma(216, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(b1c1, a2c2, ob), [147, l(a2c2, ob)]):l(b1c1, ob)). lemma(217, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(b1c1, ob), [216]):l(ob, b1c1)). lemma(218, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(oc, a2c2, ob), [164, l(a2c2, ob)]):l(oc, ob)). lemma(219, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(oc, ob), [218]):l(ob, oc)). lemma(220, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(a2, b1c1, ob), [i(a2, b1c1), 216]):i(a2, ob)). lemma(221, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lcon(c2, a2c2, ob), [12, l(a2c2, ob)]):i(c2, ob)). lemma(222, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(triangle2(ob), [220, 23, 221]):false). lemma(223, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [222]):goal). lemma(224, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(171), [214, 223]):goal). lemma(225, [p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(158), [163, 224]):goal). lemma(226, [l(a2c2, b2c2), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a2c2, b2c2), [l(a2c2, b2c2)]):l(b2c2, a2c2)). lemma(227, [l(a2c2, b2c2), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(b1c1, a2c2, b2c2), [147, l(a2c2, b2c2)]):l(b1c1, b2c2)). lemma(228, [l(a2c2, b2c2), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(notbc, [227]):false). lemma(229, [l(a2c2, b2c2), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [228]):goal). lemma(230, [p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(155), [225, 229]):goal). lemma(231, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a1c1, b1c1), [l(a1c1, b1c1)]):l(b1c1, a1c1)). lemma(232, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(ltra(a2c2, b1c1, a1c1), [l(a2c2, b1c1), 231]):l(a2c2, a1c1)). lemma(233, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(lsym(a2c2, a1c1), [232]):l(a1c1, a2c2)). lemma(234, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(notac, [233]):false). lemma(235, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(false_ind(goal), [234]):goal). lemma(236, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(152), [230, 235]):goal). lemma(237, [i(a2, b1c1), i(b1, a2c2), i(a1, b2c2)], ap(or_elim(51), [146, 236]):goal). lemma(238, [i(b1, a2c2), i(a1, b2c2)], ap(or_elim(3), [4, 237]):goal). lemma(239, [i(c2, a1b1), i(a1, b2c2)], ap(gap_c, []): (i(c1, a2b2);i(a2, b1c1))). lemma(240, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ia1b1, []):i(a1, a1b1)). lemma(241, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ib1a1, []):i(b1, a1b1)). lemma(242, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ia2b2, []):i(a2, a2b2)). lemma(243, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ib2a2, []):i(b2, a2b2)). lemma(244, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ia1c1, []):i(a1, a1c1)). lemma(245, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ic1a1, []):i(c1, a1c1)). lemma(246, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ia2c2, []):i(a2, a2c2)). lemma(247, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ic2a2, []):i(c2, a2c2)). lemma(248, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ic1b1, []):i(c1, b1c1)). lemma(249, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ib1c1, []):i(b1, b1c1)). lemma(250, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ic2b2, []):i(c2, b2c2)). lemma(251, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ib2c2, []):i(b2, b2c2)). lemma(252, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(iooa, []):i(o, oa)). lemma(253, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ioob, []):i(o, ob)). lemma(254, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(iooc, []):i(o, oc)). lemma(255, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ia1oa, []):i(a1, oa)). lemma(256, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ia2oa, []):i(a2, oa)). lemma(257, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ib1ob, []):i(b1, ob)). lemma(258, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ib2ob, []):i(b2, ob)). lemma(259, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ic1oc, []):i(c1, oc)). lemma(260, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ic2oc, []):i(c2, oc)). lemma(261, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ibc1, []):i(bc, b1c1)). lemma(262, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ibc2, []):i(bc, b2c2)). lemma(263, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(iac1, []):i(ac, a1c1)). lemma(264, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(iac2, []):i(ac, a2c2)). lemma(265, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(iab1, []):i(ab, a1b1)). lemma(266, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(iab2, []):i(ab, a2b2)). lemma(267, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(a1, b2c2), [i(a1, b2c2)]):p(a1, a1)). lemma(268, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(c2, a1b1), [i(c2, a1b1)]):p(c2, c2)). lemma(269, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(c1, a2b2), [i(c1, a2b2)]):p(c1, c1)). lemma(270, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(b1, a1b1), [241]):p(b1, b1)). lemma(271, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(a2, a2b2), [242]):p(a2, a2)). lemma(272, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(b2, a2b2), [243]):p(b2, b2)). lemma(273, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(o, oa), [252]):p(o, o)). lemma(274, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(bc, b1c1), [261]):p(bc, bc)). lemma(275, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(ac, a1c1), [263]):p(ac, ac)). lemma(276, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pref(ab, a1b1), [265]):p(ab, ab)). lemma(277, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lref(a1, b2c2), [i(a1, b2c2)]):l(b2c2, b2c2)). lemma(278, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lref(c2, a1b1), [i(c2, a1b1)]):l(a1b1, a1b1)). lemma(279, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lref(c1, a2b2), [i(c1, a2b2)]):l(a2b2, a2b2)). lemma(280, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lref(a1, a1c1), [244]):l(a1c1, a1c1)). lemma(281, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lref(a2, a2c2), [246]):l(a2c2, a2c2)). lemma(282, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lref(c1, b1c1), [248]):l(b1c1, b1c1)). lemma(283, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lref(o, oa), [252]):l(oa, oa)). lemma(284, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lref(o, ob), [253]):l(ob, ob)). lemma(285, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lref(o, oc), [254]):l(oc, oc)). lemma(286, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c2, b2c2, a1b1), [i(a1, b2c2), 240, 250, i(c2, a1b1)]): (p(a1, c2);l(b2c2, a1b1))). lemma(287, [p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c2), [p(a1, c2)]):p(c2, a1)). lemma(288, [p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, c2, a2c2), [p(a1, c2), 247]):i(a1, a2c2)). lemma(289, [p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, c2, oc), [p(a1, c2), 260]):i(a1, oc)). lemma(290, [p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, a1c1), [287, 244]):i(c2, a1c1)). lemma(291, [p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, oa), [287, 255]):i(c2, oa)). lemma(292, [p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, ac, a1c1, a2c2), [244, 288, 263, 264]): (p(a1, ac);l(a1c1, a2c2))). lemma(293, [p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, ac), [p(a1, ac)]):p(ac, a1)). lemma(294, [p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, ac), [287, p(a1, ac)]):p(c2, ac)). lemma(295, [p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, ac), [294]):p(ac, c2)). lemma(296, [p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, b2c2), [293, i(a1, b2c2)]):i(ac, b2c2)). lemma(297, [p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, a1b1), [293, 240]):i(ac, a1b1)). lemma(298, [p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, oa), [293, 255]):i(ac, oa)). lemma(299, [p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, oc), [293, 289]):i(ac, oc)). lemma(300, [p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c1, a1c1, oc), [244, 289, 245, 259]): (p(a1, c1);l(a1c1, oc))). lemma(301, [p(a1, c1), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c1), [p(a1, c1)]):p(c1, a1)). lemma(302, [p(a1, c1), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, c1), [287, p(a1, c1)]):p(c2, c1)). lemma(303, [p(a1, c1), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(notcc, [302]):false). lemma(304, [p(a1, c1), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [303]):goal). lemma(305, [l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1c1, oc), [l(a1c1, oc)]):l(oc, a1c1)). lemma(306, [l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(o, oc, a1c1), [254, 305]):i(o, a1c1)). lemma(307, [l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, o, a1c1, oa), [244, 255, 306, 252]): (p(a1, o);l(a1c1, oa))). lemma(308, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, o), [p(a1, o)]):p(o, a1)). lemma(309, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, o), [287, p(a1, o)]):p(c2, o)). lemma(310, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, o), [309]):p(o, c2)). lemma(311, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(ac, a1, o), [293, p(a1, o)]):p(ac, o)). lemma(312, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(ac, o), [311]):p(o, ac)). lemma(313, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, o, ob), [p(a1, o), 253]):i(a1, ob)). lemma(314, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, ob), [287, 313]):i(c2, ob)). lemma(315, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, ob), [293, 313]):i(ac, ob)). lemma(316, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, b2c2), [308, i(a1, b2c2)]):i(o, b2c2)). lemma(317, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, a1b1), [308, 240]):i(o, a1b1)). lemma(318, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, a2c2), [308, 288]):i(o, a2c2)). lemma(319, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, b2, b2c2, ob), [i(a1, b2c2), 313, 251, 258]): (p(a1, b2);l(b2c2, ob))). lemma(320, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, b2), [p(a1, b2)]):p(b2, a1)). lemma(321, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, b2), [287, p(a1, b2)]):p(c2, b2)). lemma(322, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, b2), [321]):p(b2, c2)). lemma(323, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(ac, a1, b2), [293, p(a1, b2)]):p(ac, b2)). lemma(324, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(ac, b2), [323]):p(b2, ac)). lemma(325, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, b2), [308, p(a1, b2)]):p(o, b2)). lemma(326, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, b2), [325]):p(b2, o)). lemma(327, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, b2, a2b2), [p(a1, b2), 243]):i(a1, a2b2)). lemma(328, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, a2b2), [287, 327]):i(c2, a2b2)). lemma(329, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(triangle2(a2b2), [242, 243, 328]):false). lemma(330, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [329]):goal). lemma(331, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, ob), [l(b2c2, ob)]):l(ob, b2c2)). lemma(332, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b1, ob, b2c2), [257, 331]):i(b1, b2c2)). lemma(333, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(bc, b2c2, ob), [262, l(b2c2, ob)]):i(bc, ob)). lemma(334, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, b1, b2c2, a1b1), [i(a1, b2c2), 240, 332, 241]): (p(a1, b1);l(b2c2, a1b1))). lemma(335, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, b1), [p(a1, b1)]):p(b1, a1)). lemma(336, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, b1), [287, p(a1, b1)]):p(c2, b1)). lemma(337, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, b1), [336]):p(b1, c2)). lemma(338, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(ac, a1, b1), [293, p(a1, b1)]):p(ac, b1)). lemma(339, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(ac, b1), [338]):p(b1, ac)). lemma(340, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, b1), [308, p(a1, b1)]):p(o, b1)). lemma(341, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, b1), [340]):p(b1, o)). lemma(342, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, b1, b1c1), [p(a1, b1), 249]):i(a1, b1c1)). lemma(343, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(triangle1(b1c1), [342, 249, 248]):false). lemma(344, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [343]):goal). lemma(345, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, a1b1), [l(b2c2, a1b1)]):l(a1b1, b2c2)). lemma(346, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(ob, b2c2, a1b1), [331, l(b2c2, a1b1)]):l(ob, a1b1)). lemma(347, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(ob, a1b1), [346]):l(a1b1, ob)). lemma(348, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b2, b2c2, a1b1), [251, l(b2c2, a1b1)]):i(b2, a1b1)). lemma(349, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(bc, b2c2, a1b1), [262, l(b2c2, a1b1)]):i(bc, a1b1)). lemma(350, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(goal_normal(a1b1), [278, 349, 297, 265]):goal). lemma(351, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(334), [344, 350]):goal). lemma(352, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(319), [330, 351]):goal). lemma(353, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1c1, oa), [l(a1c1, oa)]):l(oa, a1c1)). lemma(354, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(oc, a1c1, oa), [305, l(a1c1, oa)]):l(oc, oa)). lemma(355, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(oc, oa), [354]):l(oa, oc)). lemma(356, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(c1, a1c1, oa), [245, l(a1c1, oa)]):i(c1, oa)). lemma(357, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(a2, oa, a1c1), [256, 353]):i(a2, a1c1)). lemma(358, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(a2, oa, oc), [256, 355]):i(a2, oc)). lemma(359, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(c1, a2, a2b2, a1c1), [i(c1, a2b2), 245, 242, 357]): (p(c1, a2);l(a2b2, a1c1))). lemma(360, [p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(c1, a2), [p(c1, a2)]):p(a2, c1)). lemma(361, [p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c1, a2, a2c2), [p(c1, a2), 246]):i(c1, a2c2)). lemma(362, [p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a2, c1, b1c1), [360, 248]):i(a2, b1c1)). lemma(363, [p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c1, a1c1, a2c2), [244, 288, 245, 361]): (p(a1, c1);l(a1c1, a2c2))). lemma(364, [p(a1, c1), p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c1), [p(a1, c1)]):p(c1, a1)). lemma(365, [p(a1, c1), p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, c1), [287, p(a1, c1)]):p(c2, c1)). lemma(366, [p(a1, c1), p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(notcc, [365]):false). lemma(367, [p(a1, c1), p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [366]):goal). lemma(368, [l(a1c1, a2c2), p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(notac, [l(a1c1, a2c2)]):false). lemma(369, [l(a1c1, a2c2), p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [368]):goal). lemma(370, [p(c1, a2), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(363), [367, 369]):goal). lemma(371, [l(a2b2, a1c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a2b2, a1c1), [l(a2b2, a1c1)]):l(a1c1, a2b2)). lemma(372, [l(a2b2, a1c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(oc, a1c1, a2b2), [305, 371]):l(oc, a2b2)). lemma(373, [l(a2b2, a1c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(oc, a2b2), [372]):l(a2b2, oc)). lemma(374, [l(a2b2, a1c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(oa, a1c1, a2b2), [353, 371]):l(oa, a2b2)). lemma(375, [l(a2b2, a1c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(oa, a2b2), [374]):l(a2b2, oa)). lemma(376, [l(a2b2, a1c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b2, a2b2, a1c1), [243, l(a2b2, a1c1)]):i(b2, a1c1)). lemma(377, [l(a2b2, a1c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(triangle2(a1c1), [357, 376, 290]):false). lemma(378, [l(a2b2, a1c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [377]):goal). lemma(379, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(359), [370, 378]):goal). lemma(380, [l(a1c1, oc), p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(307), [352, 379]):goal). lemma(381, [p(a1, ac), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(300), [304, 380]):goal). lemma(382, [l(a1c1, a2c2), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(notac, [l(a1c1, a2c2)]):false). lemma(383, [l(a1c1, a2c2), p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [382]):goal). lemma(384, [p(a1, c2), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(292), [381, 383]):goal). lemma(385, [l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, a1b1), [l(b2c2, a1b1)]):l(a1b1, b2c2)). lemma(386, [l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b1, a1b1, b2c2), [241, 385]):i(b1, b2c2)). lemma(387, [l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b2, b2c2, a1b1), [251, l(b2c2, a1b1)]):i(b2, a1b1)). lemma(388, [l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(bc, b2c2, a1b1), [262, l(b2c2, a1b1)]):i(bc, a1b1)). lemma(389, [l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(ab, a1b1, b2c2), [265, 385]):i(ab, b2c2)). lemma(390, [l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(b1, bc, a1b1, b1c1), [241, 249, 388, 261]): (p(b1, bc);l(a1b1, b1c1))). lemma(391, [p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(b1, bc), [p(b1, bc)]):p(bc, b1)). lemma(392, [p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(bc, b1, ob), [391, 257]):i(bc, ob)). lemma(393, [p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(b1, b2, a1b1, ob), [241, 257, 387, 258]): (p(b1, b2);l(a1b1, ob))). lemma(394, [p(b1, b2), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(b1, b2), [p(b1, b2)]):p(b2, b1)). lemma(395, [p(b1, b2), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(notbb, [394]):false). lemma(396, [p(b1, b2), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [395]):goal). lemma(397, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1b1, ob), [l(a1b1, ob)]):l(ob, a1b1)). lemma(398, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(b2c2, a1b1, ob), [l(b2c2, a1b1), l(a1b1, ob)]):l(b2c2, ob)). lemma(399, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, ob), [398]):l(ob, b2c2)). lemma(400, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(a1, b2c2, ob), [i(a1, b2c2), 398]):i(a1, ob)). lemma(401, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(c2, a1b1, ob), [i(c2, a1b1), l(a1b1, ob)]):i(c2, ob)). lemma(402, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(o, ob, a1b1), [253, 397]):i(o, a1b1)). lemma(403, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(o, ob, b2c2), [253, 399]):i(o, b2c2)). lemma(404, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(ab, a1b1, ob), [265, l(a1b1, ob)]):i(ab, ob)). lemma(405, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, o, b2c2, oa), [i(a1, b2c2), 255, 403, 252]): (p(a1, o);l(b2c2, oa))). lemma(406, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, o), [p(a1, o)]):p(o, a1)). lemma(407, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, o, oc), [p(a1, o), 254]):i(a1, oc)). lemma(408, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, a1c1), [406, 244]):i(o, a1c1)). lemma(409, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c2, b2c2, oc), [i(a1, b2c2), 407, 250, 260]): (p(a1, c2);l(b2c2, oc))). lemma(410, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c2), [p(a1, c2)]):p(c2, a1)). lemma(411, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, c2), [406, p(a1, c2)]):p(o, c2)). lemma(412, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, c2), [411]):p(c2, o)). lemma(413, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, c2, a2c2), [p(a1, c2), 247]):i(a1, a2c2)). lemma(414, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, a2c2), [406, 413]):i(o, a2c2)). lemma(415, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, a1c1), [410, 244]):i(c2, a1c1)). lemma(416, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, oa), [410, 255]):i(c2, oa)). lemma(417, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(b2, ab, a2b2, b2c2), [243, 251, 266, 389]): (p(b2, ab);l(a2b2, b2c2))). lemma(418, [p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(b2, ab), [p(b2, ab)]):p(ab, b2)). lemma(419, [p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c1, a1c1, oc), [244, 407, 245, 259]): (p(a1, c1);l(a1c1, oc))). lemma(420, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c1), [p(a1, c1)]):p(c1, a1)). lemma(421, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, c1), [406, p(a1, c1)]):p(o, c1)). lemma(422, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, c1), [421]):p(c1, o)). lemma(423, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, c1), [410, p(a1, c1)]):p(c2, c1)). lemma(424, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(notcc, [423]):false). lemma(425, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [424]):goal). lemma(426, [l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1c1, oc), [l(a1c1, oc)]):l(oc, a1c1)). lemma(427, [l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(ac, a1c1, oc), [263, l(a1c1, oc)]):i(ac, oc)). lemma(428, [l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, ac, a1c1, a2c2), [244, 413, 263, 264]): (p(a1, ac);l(a1c1, a2c2))). lemma(429, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, ac), [p(a1, ac)]):p(ac, a1)). lemma(430, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, ac), [406, p(a1, ac)]):p(o, ac)). lemma(431, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, ac), [430]):p(ac, o)). lemma(432, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, ac), [410, p(a1, ac)]):p(c2, ac)). lemma(433, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, ac), [432]):p(ac, c2)). lemma(434, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, b2c2), [429, i(a1, b2c2)]):i(ac, b2c2)). lemma(435, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(goal_normal(b2c2), [277, 262, 434, 389]):goal). lemma(436, [l(a1c1, a2c2), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(notac, [l(a1c1, a2c2)]):false). lemma(437, [l(a1c1, a2c2), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [436]):goal). lemma(438, [l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(428), [435, 437]):goal). lemma(439, [p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(419), [425, 438]):goal). lemma(440, [l(a2b2, b2c2), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a2b2, b2c2), [l(a2b2, b2c2)]):l(b2c2, a2b2)). lemma(441, [l(a2b2, b2c2), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(a1b1, b2c2, a2b2), [385, 440]):l(a1b1, a2b2)). lemma(442, [l(a2b2, b2c2), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(notab, [441]):false). lemma(443, [l(a2b2, b2c2), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [442]):goal). lemma(444, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(417), [439, 443]):goal). lemma(445, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, oc), [l(b2c2, oc)]):l(oc, b2c2)). lemma(446, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(a1b1, b2c2, oc), [385, l(b2c2, oc)]):l(a1b1, oc)). lemma(447, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1b1, oc), [446]):l(oc, a1b1)). lemma(448, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(ob, a1b1, oc), [397, 446]):l(ob, oc)). lemma(449, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(ob, oc), [448]):l(oc, ob)). lemma(450, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b1, a1b1, oc), [241, 446]):i(b1, oc)). lemma(451, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(triangle1(oc), [407, 450, 259]):false). lemma(452, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [451]):goal). lemma(453, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(409), [444, 452]):goal). lemma(454, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, oa), [l(b2c2, oa)]):l(oa, b2c2)). lemma(455, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(a1b1, b2c2, oa), [385, l(b2c2, oa)]):l(a1b1, oa)). lemma(456, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1b1, oa), [455]):l(oa, a1b1)). lemma(457, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(ob, a1b1, oa), [397, 455]):l(ob, oa)). lemma(458, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(ob, oa), [457]):l(oa, ob)). lemma(459, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(c2, a1b1, oa), [i(c2, a1b1), 455]):i(c2, oa)). lemma(460, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b1, a1b1, oa), [241, 455]):i(b1, oa)). lemma(461, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(pcon(bc, b1, oa), [391, 460]):i(bc, oa)). lemma(462, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b2, b2c2, oa), [251, l(b2c2, oa)]):i(b2, oa)). lemma(463, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(triangle2(oa), [256, 462, 459]):false). lemma(464, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [463]):goal). lemma(465, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(405), [453, 464]):goal). lemma(466, [p(b1, bc), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(393), [396, 465]):goal). lemma(467, [l(a1b1, b1c1), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1b1, b1c1), [l(a1b1, b1c1)]):l(b1c1, a1b1)). lemma(468, [l(a1b1, b1c1), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(ltra(b2c2, a1b1, b1c1), [l(b2c2, a1b1), l(a1b1, b1c1)]):l(b2c2, b1c1)). lemma(469, [l(a1b1, b1c1), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, b1c1), [468]):l(b1c1, b2c2)). lemma(470, [l(a1b1, b1c1), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(notbc, [469]):false). lemma(471, [l(a1b1, b1c1), l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [470]):goal). lemma(472, [l(b2c2, a1b1), i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(390), [466, 471]):goal). lemma(473, [i(c1, a2b2), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(286), [384, 472]):goal). lemma(474, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ia1b1, []):i(a1, a1b1)). lemma(475, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ib1a1, []):i(b1, a1b1)). lemma(476, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ia2b2, []):i(a2, a2b2)). lemma(477, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ib2a2, []):i(b2, a2b2)). lemma(478, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ia1c1, []):i(a1, a1c1)). lemma(479, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ic1a1, []):i(c1, a1c1)). lemma(480, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ia2c2, []):i(a2, a2c2)). lemma(481, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ic2a2, []):i(c2, a2c2)). lemma(482, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ic1b1, []):i(c1, b1c1)). lemma(483, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ib1c1, []):i(b1, b1c1)). lemma(484, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ic2b2, []):i(c2, b2c2)). lemma(485, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ib2c2, []):i(b2, b2c2)). lemma(486, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(iooa, []):i(o, oa)). lemma(487, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ioob, []):i(o, ob)). lemma(488, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(iooc, []):i(o, oc)). lemma(489, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ia1oa, []):i(a1, oa)). lemma(490, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ia2oa, []):i(a2, oa)). lemma(491, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ib1ob, []):i(b1, ob)). lemma(492, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ib2ob, []):i(b2, ob)). lemma(493, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ic1oc, []):i(c1, oc)). lemma(494, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ic2oc, []):i(c2, oc)). lemma(495, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ibc1, []):i(bc, b1c1)). lemma(496, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ibc2, []):i(bc, b2c2)). lemma(497, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(iac1, []):i(ac, a1c1)). lemma(498, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(iac2, []):i(ac, a2c2)). lemma(499, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(iab1, []):i(ab, a1b1)). lemma(500, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(iab2, []):i(ab, a2b2)). lemma(501, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(a1, b2c2), [i(a1, b2c2)]):p(a1, a1)). lemma(502, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(c2, a1b1), [i(c2, a1b1)]):p(c2, c2)). lemma(503, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(a2, b1c1), [i(a2, b1c1)]):p(a2, a2)). lemma(504, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(b1, a1b1), [475]):p(b1, b1)). lemma(505, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(b2, a2b2), [477]):p(b2, b2)). lemma(506, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(c1, a1c1), [479]):p(c1, c1)). lemma(507, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(o, oa), [486]):p(o, o)). lemma(508, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(bc, b1c1), [495]):p(bc, bc)). lemma(509, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(ac, a1c1), [497]):p(ac, ac)). lemma(510, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pref(ab, a1b1), [499]):p(ab, ab)). lemma(511, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lref(a1, b2c2), [i(a1, b2c2)]):l(b2c2, b2c2)). lemma(512, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lref(c2, a1b1), [i(c2, a1b1)]):l(a1b1, a1b1)). lemma(513, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lref(a2, b1c1), [i(a2, b1c1)]):l(b1c1, b1c1)). lemma(514, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lref(a2, a2b2), [476]):l(a2b2, a2b2)). lemma(515, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lref(a1, a1c1), [478]):l(a1c1, a1c1)). lemma(516, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lref(a2, a2c2), [480]):l(a2c2, a2c2)). lemma(517, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lref(o, oa), [486]):l(oa, oa)). lemma(518, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lref(o, ob), [487]):l(ob, ob)). lemma(519, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lref(o, oc), [488]):l(oc, oc)). lemma(520, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c2, b2c2, a1b1), [i(a1, b2c2), 474, 484, i(c2, a1b1)]): (p(a1, c2);l(b2c2, a1b1))). lemma(521, [p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c2), [p(a1, c2)]):p(c2, a1)). lemma(522, [p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, c2, a2c2), [p(a1, c2), 481]):i(a1, a2c2)). lemma(523, [p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, c2, oc), [p(a1, c2), 494]):i(a1, oc)). lemma(524, [p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, a1c1), [521, 478]):i(c2, a1c1)). lemma(525, [p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, oa), [521, 489]):i(c2, oa)). lemma(526, [p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, ac, a1c1, a2c2), [478, 522, 497, 498]): (p(a1, ac);l(a1c1, a2c2))). lemma(527, [p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, ac), [p(a1, ac)]):p(ac, a1)). lemma(528, [p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, ac), [521, p(a1, ac)]):p(c2, ac)). lemma(529, [p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, ac), [528]):p(ac, c2)). lemma(530, [p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, b2c2), [527, i(a1, b2c2)]):i(ac, b2c2)). lemma(531, [p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, a1b1), [527, 474]):i(ac, a1b1)). lemma(532, [p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, oa), [527, 489]):i(ac, oa)). lemma(533, [p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, oc), [527, 523]):i(ac, oc)). lemma(534, [p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c1, a1c1, oc), [478, 523, 479, 493]): (p(a1, c1);l(a1c1, oc))). lemma(535, [p(a1, c1), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c1), [p(a1, c1)]):p(c1, a1)). lemma(536, [p(a1, c1), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, c1), [521, p(a1, c1)]):p(c2, c1)). lemma(537, [p(a1, c1), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(notcc, [536]):false). lemma(538, [p(a1, c1), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [537]):goal). lemma(539, [l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1c1, oc), [l(a1c1, oc)]):l(oc, a1c1)). lemma(540, [l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(o, oc, a1c1), [488, 539]):i(o, a1c1)). lemma(541, [l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, o, a1c1, oa), [478, 489, 540, 486]): (p(a1, o);l(a1c1, oa))). lemma(542, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, o), [p(a1, o)]):p(o, a1)). lemma(543, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, o), [521, p(a1, o)]):p(c2, o)). lemma(544, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, o), [543]):p(o, c2)). lemma(545, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(ac, a1, o), [527, p(a1, o)]):p(ac, o)). lemma(546, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(ac, o), [545]):p(o, ac)). lemma(547, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, o, ob), [p(a1, o), 487]):i(a1, ob)). lemma(548, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, ob), [521, 547]):i(c2, ob)). lemma(549, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, ob), [527, 547]):i(ac, ob)). lemma(550, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, b2c2), [542, i(a1, b2c2)]):i(o, b2c2)). lemma(551, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, a1b1), [542, 474]):i(o, a1b1)). lemma(552, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, a2c2), [542, 522]):i(o, a2c2)). lemma(553, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, b2, b2c2, ob), [i(a1, b2c2), 547, 485, 492]): (p(a1, b2);l(b2c2, ob))). lemma(554, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, b2), [p(a1, b2)]):p(b2, a1)). lemma(555, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, b2), [521, p(a1, b2)]):p(c2, b2)). lemma(556, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, b2), [555]):p(b2, c2)). lemma(557, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(ac, a1, b2), [527, p(a1, b2)]):p(ac, b2)). lemma(558, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(ac, b2), [557]):p(b2, ac)). lemma(559, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, b2), [542, p(a1, b2)]):p(o, b2)). lemma(560, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, b2), [559]):p(b2, o)). lemma(561, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, b2, a2b2), [p(a1, b2), 477]):i(a1, a2b2)). lemma(562, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, a2b2), [521, 561]):i(c2, a2b2)). lemma(563, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(triangle2(a2b2), [476, 477, 562]):false). lemma(564, [p(a1, b2), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [563]):goal). lemma(565, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, ob), [l(b2c2, ob)]):l(ob, b2c2)). lemma(566, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b1, ob, b2c2), [491, 565]):i(b1, b2c2)). lemma(567, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(bc, b2c2, ob), [496, l(b2c2, ob)]):i(bc, ob)). lemma(568, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, b1, b2c2, a1b1), [i(a1, b2c2), 474, 566, 475]): (p(a1, b1);l(b2c2, a1b1))). lemma(569, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, b1), [p(a1, b1)]):p(b1, a1)). lemma(570, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, b1), [521, p(a1, b1)]):p(c2, b1)). lemma(571, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, b1), [570]):p(b1, c2)). lemma(572, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(ac, a1, b1), [527, p(a1, b1)]):p(ac, b1)). lemma(573, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(ac, b1), [572]):p(b1, ac)). lemma(574, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, b1), [542, p(a1, b1)]):p(o, b1)). lemma(575, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, b1), [574]):p(b1, o)). lemma(576, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, b1, b1c1), [p(a1, b1), 483]):i(a1, b1c1)). lemma(577, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(triangle1(b1c1), [576, 483, 482]):false). lemma(578, [p(a1, b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [577]):goal). lemma(579, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, a1b1), [l(b2c2, a1b1)]):l(a1b1, b2c2)). lemma(580, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(ob, b2c2, a1b1), [565, l(b2c2, a1b1)]):l(ob, a1b1)). lemma(581, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(ob, a1b1), [580]):l(a1b1, ob)). lemma(582, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b2, b2c2, a1b1), [485, l(b2c2, a1b1)]):i(b2, a1b1)). lemma(583, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(bc, b2c2, a1b1), [496, l(b2c2, a1b1)]):i(bc, a1b1)). lemma(584, [l(b2c2, a1b1), l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(goal_normal(a1b1), [512, 583, 531, 499]):goal). lemma(585, [l(b2c2, ob), p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(568), [578, 584]):goal). lemma(586, [p(a1, o), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(553), [564, 585]):goal). lemma(587, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1c1, oa), [l(a1c1, oa)]):l(oa, a1c1)). lemma(588, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(oc, a1c1, oa), [539, l(a1c1, oa)]):l(oc, oa)). lemma(589, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(oc, oa), [588]):l(oa, oc)). lemma(590, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(c1, a1c1, oa), [479, l(a1c1, oa)]):i(c1, oa)). lemma(591, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(a2, oa, a1c1), [490, 587]):i(a2, a1c1)). lemma(592, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(a2, oa, oc), [490, 589]):i(a2, oc)). lemma(593, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a2, c1, b1c1, oa), [i(a2, b1c1), 490, 482, 590]): (p(a2, c1);l(b1c1, oa))). lemma(594, [p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a2, c1), [p(a2, c1)]):p(c1, a2)). lemma(595, [p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c1, a2, a2b2), [594, 476]):i(c1, a2b2)). lemma(596, [p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c1, a2, a2c2), [594, 480]):i(c1, a2c2)). lemma(597, [p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c1, a1c1, a2c2), [478, 522, 479, 596]): (p(a1, c1);l(a1c1, a2c2))). lemma(598, [p(a1, c1), p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c1), [p(a1, c1)]):p(c1, a1)). lemma(599, [p(a1, c1), p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, c1), [521, p(a1, c1)]):p(c2, c1)). lemma(600, [p(a1, c1), p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(notcc, [599]):false). lemma(601, [p(a1, c1), p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [600]):goal). lemma(602, [l(a1c1, a2c2), p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(notac, [l(a1c1, a2c2)]):false). lemma(603, [l(a1c1, a2c2), p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [602]):goal). lemma(604, [p(a2, c1), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(597), [601, 603]):goal). lemma(605, [l(b1c1, oa), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b1c1, oa), [l(b1c1, oa)]):l(oa, b1c1)). lemma(606, [l(b1c1, oa), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(a1c1, oa, b1c1), [l(a1c1, oa), 605]):l(a1c1, b1c1)). lemma(607, [l(b1c1, oa), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1c1, b1c1), [606]):l(b1c1, a1c1)). lemma(608, [l(b1c1, oa), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(oc, a1c1, b1c1), [539, 606]):l(oc, b1c1)). lemma(609, [l(b1c1, oa), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(oc, b1c1), [608]):l(b1c1, oc)). lemma(610, [l(b1c1, oa), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(a1, a1c1, b1c1), [478, 606]):i(a1, b1c1)). lemma(611, [l(b1c1, oa), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(triangle1(b1c1), [610, 483, 482]):false). lemma(612, [l(b1c1, oa), l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [611]):goal). lemma(613, [l(a1c1, oa), l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(593), [604, 612]):goal). lemma(614, [l(a1c1, oc), p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(541), [586, 613]):goal). lemma(615, [p(a1, ac), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(534), [538, 614]):goal). lemma(616, [l(a1c1, a2c2), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(notac, [l(a1c1, a2c2)]):false). lemma(617, [l(a1c1, a2c2), p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [616]):goal). lemma(618, [p(a1, c2), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(526), [615, 617]):goal). lemma(619, [l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, a1b1), [l(b2c2, a1b1)]):l(a1b1, b2c2)). lemma(620, [l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b1, a1b1, b2c2), [475, 619]):i(b1, b2c2)). lemma(621, [l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b2, b2c2, a1b1), [485, l(b2c2, a1b1)]):i(b2, a1b1)). lemma(622, [l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(bc, b2c2, a1b1), [496, l(b2c2, a1b1)]):i(bc, a1b1)). lemma(623, [l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(ab, a1b1, b2c2), [499, 619]):i(ab, b2c2)). lemma(624, [l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(b1, bc, a1b1, b1c1), [475, 483, 622, 495]): (p(b1, bc);l(a1b1, b1c1))). lemma(625, [p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(b1, bc), [p(b1, bc)]):p(bc, b1)). lemma(626, [p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(bc, b1, ob), [625, 491]):i(bc, ob)). lemma(627, [p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(b1, b2, a1b1, ob), [475, 491, 621, 492]): (p(b1, b2);l(a1b1, ob))). lemma(628, [p(b1, b2), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(b1, b2), [p(b1, b2)]):p(b2, b1)). lemma(629, [p(b1, b2), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(notbb, [628]):false). lemma(630, [p(b1, b2), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [629]):goal). lemma(631, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1b1, ob), [l(a1b1, ob)]):l(ob, a1b1)). lemma(632, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(b2c2, a1b1, ob), [l(b2c2, a1b1), l(a1b1, ob)]):l(b2c2, ob)). lemma(633, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, ob), [632]):l(ob, b2c2)). lemma(634, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(a1, b2c2, ob), [i(a1, b2c2), 632]):i(a1, ob)). lemma(635, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(c2, a1b1, ob), [i(c2, a1b1), l(a1b1, ob)]):i(c2, ob)). lemma(636, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(o, ob, a1b1), [487, 631]):i(o, a1b1)). lemma(637, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(o, ob, b2c2), [487, 633]):i(o, b2c2)). lemma(638, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(ab, a1b1, ob), [499, l(a1b1, ob)]):i(ab, ob)). lemma(639, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, o, b2c2, oa), [i(a1, b2c2), 489, 637, 486]): (p(a1, o);l(b2c2, oa))). lemma(640, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, o), [p(a1, o)]):p(o, a1)). lemma(641, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, o, oc), [p(a1, o), 488]):i(a1, oc)). lemma(642, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, a1c1), [640, 478]):i(o, a1c1)). lemma(643, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c2, b2c2, oc), [i(a1, b2c2), 641, 484, 494]): (p(a1, c2);l(b2c2, oc))). lemma(644, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c2), [p(a1, c2)]):p(c2, a1)). lemma(645, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, c2), [640, p(a1, c2)]):p(o, c2)). lemma(646, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, c2), [645]):p(c2, o)). lemma(647, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(a1, c2, a2c2), [p(a1, c2), 481]):i(a1, a2c2)). lemma(648, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(o, a1, a2c2), [640, 647]):i(o, a2c2)). lemma(649, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, a1c1), [644, 478]):i(c2, a1c1)). lemma(650, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(c2, a1, oa), [644, 489]):i(c2, oa)). lemma(651, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(b2, ab, a2b2, b2c2), [477, 485, 500, 623]): (p(b2, ab);l(a2b2, b2c2))). lemma(652, [p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(b2, ab), [p(b2, ab)]):p(ab, b2)). lemma(653, [p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, c1, a1c1, oc), [478, 641, 479, 493]): (p(a1, c1);l(a1c1, oc))). lemma(654, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, c1), [p(a1, c1)]):p(c1, a1)). lemma(655, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, c1), [640, p(a1, c1)]):p(o, c1)). lemma(656, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, c1), [655]):p(c1, o)). lemma(657, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, c1), [644, p(a1, c1)]):p(c2, c1)). lemma(658, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(notcc, [657]):false). lemma(659, [p(a1, c1), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [658]):goal). lemma(660, [l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1c1, oc), [l(a1c1, oc)]):l(oc, a1c1)). lemma(661, [l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(ac, a1c1, oc), [497, l(a1c1, oc)]):i(ac, oc)). lemma(662, [l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(unique(a1, ac, a1c1, a2c2), [478, 647, 497, 498]): (p(a1, ac);l(a1c1, a2c2))). lemma(663, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(a1, ac), [p(a1, ac)]):p(ac, a1)). lemma(664, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(o, a1, ac), [640, p(a1, ac)]):p(o, ac)). lemma(665, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(o, ac), [664]):p(ac, o)). lemma(666, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ptra(c2, a1, ac), [644, p(a1, ac)]):p(c2, ac)). lemma(667, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(psym(c2, ac), [666]):p(ac, c2)). lemma(668, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(ac, a1, b2c2), [663, i(a1, b2c2)]):i(ac, b2c2)). lemma(669, [p(a1, ac), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(goal_normal(b2c2), [511, 496, 668, 623]):goal). lemma(670, [l(a1c1, a2c2), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(notac, [l(a1c1, a2c2)]):false). lemma(671, [l(a1c1, a2c2), l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [670]):goal). lemma(672, [l(a1c1, oc), p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(662), [669, 671]):goal). lemma(673, [p(b2, ab), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(653), [659, 672]):goal). lemma(674, [l(a2b2, b2c2), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a2b2, b2c2), [l(a2b2, b2c2)]):l(b2c2, a2b2)). lemma(675, [l(a2b2, b2c2), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(a1b1, b2c2, a2b2), [619, 674]):l(a1b1, a2b2)). lemma(676, [l(a2b2, b2c2), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(notab, [675]):false). lemma(677, [l(a2b2, b2c2), p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [676]):goal). lemma(678, [p(a1, c2), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(651), [673, 677]):goal). lemma(679, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, oc), [l(b2c2, oc)]):l(oc, b2c2)). lemma(680, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(a1b1, b2c2, oc), [619, l(b2c2, oc)]):l(a1b1, oc)). lemma(681, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1b1, oc), [680]):l(oc, a1b1)). lemma(682, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(ob, a1b1, oc), [631, 680]):l(ob, oc)). lemma(683, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(ob, oc), [682]):l(oc, ob)). lemma(684, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b1, a1b1, oc), [475, 680]):i(b1, oc)). lemma(685, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(triangle1(oc), [641, 684, 493]):false). lemma(686, [l(b2c2, oc), p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [685]):goal). lemma(687, [p(a1, o), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(643), [678, 686]):goal). lemma(688, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, oa), [l(b2c2, oa)]):l(oa, b2c2)). lemma(689, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(a1b1, b2c2, oa), [619, l(b2c2, oa)]):l(a1b1, oa)). lemma(690, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1b1, oa), [689]):l(oa, a1b1)). lemma(691, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(ob, a1b1, oa), [631, 689]):l(ob, oa)). lemma(692, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(ob, oa), [691]):l(oa, ob)). lemma(693, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(c2, a1b1, oa), [i(c2, a1b1), 689]):i(c2, oa)). lemma(694, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b1, a1b1, oa), [475, 689]):i(b1, oa)). lemma(695, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(pcon(bc, b1, oa), [625, 694]):i(bc, oa)). lemma(696, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lcon(b2, b2c2, oa), [485, l(b2c2, oa)]):i(b2, oa)). lemma(697, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(triangle2(oa), [490, 696, 693]):false). lemma(698, [l(b2c2, oa), l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [697]):goal). lemma(699, [l(a1b1, ob), p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(639), [687, 698]):goal). lemma(700, [p(b1, bc), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(627), [630, 699]):goal). lemma(701, [l(a1b1, b1c1), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(a1b1, b1c1), [l(a1b1, b1c1)]):l(b1c1, a1b1)). lemma(702, [l(a1b1, b1c1), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(ltra(b2c2, a1b1, b1c1), [l(b2c2, a1b1), l(a1b1, b1c1)]):l(b2c2, b1c1)). lemma(703, [l(a1b1, b1c1), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(lsym(b2c2, b1c1), [702]):l(b1c1, b2c2)). lemma(704, [l(a1b1, b1c1), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(notbc, [703]):false). lemma(705, [l(a1b1, b1c1), l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(false_ind(goal), [704]):goal). lemma(706, [l(b2c2, a1b1), i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(624), [700, 705]):goal). lemma(707, [i(a2, b1c1), i(c2, a1b1), i(a1, b2c2)], ap(or_elim(520), [618, 706]):goal). lemma(708, [i(c2, a1b1), i(a1, b2c2)], ap(or_elim(239), [473, 707]):goal). lemma(709, [i(a1, b2c2)], ap(or_elim(2), [238, 708]):goal). lemma(710, [i(b2, a1c1)], ap(gap_b, []): (i(b1, a2c2);i(c2, a1b1))). lemma(711, [i(b1, a2c2), i(b2, a1c1)], ap(gap_c, []): (i(c1, a2b2);i(a2, b1c1))). lemma(712, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ia1b1, []):i(a1, a1b1)). lemma(713, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ib1a1, []):i(b1, a1b1)). lemma(714, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ia2b2, []):i(a2, a2b2)). lemma(715, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ib2a2, []):i(b2, a2b2)). lemma(716, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ia1c1, []):i(a1, a1c1)). lemma(717, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ic1a1, []):i(c1, a1c1)). lemma(718, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ia2c2, []):i(a2, a2c2)). lemma(719, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ic2a2, []):i(c2, a2c2)). lemma(720, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ic1b1, []):i(c1, b1c1)). lemma(721, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ib1c1, []):i(b1, b1c1)). lemma(722, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ic2b2, []):i(c2, b2c2)). lemma(723, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ib2c2, []):i(b2, b2c2)). lemma(724, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(iooa, []):i(o, oa)). lemma(725, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ioob, []):i(o, ob)). lemma(726, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(iooc, []):i(o, oc)). lemma(727, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ia1oa, []):i(a1, oa)). lemma(728, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ia2oa, []):i(a2, oa)). lemma(729, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ib1ob, []):i(b1, ob)). lemma(730, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ib2ob, []):i(b2, ob)). lemma(731, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ic1oc, []):i(c1, oc)). lemma(732, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ic2oc, []):i(c2, oc)). lemma(733, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ibc1, []):i(bc, b1c1)). lemma(734, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ibc2, []):i(bc, b2c2)). lemma(735, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(iac1, []):i(ac, a1c1)). lemma(736, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(iac2, []):i(ac, a2c2)). lemma(737, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(iab1, []):i(ab, a1b1)). lemma(738, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(iab2, []):i(ab, a2b2)). lemma(739, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(b2, a1c1), [i(b2, a1c1)]):p(b2, b2)). lemma(740, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(b1, a2c2), [i(b1, a2c2)]):p(b1, b1)). lemma(741, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(c1, a2b2), [i(c1, a2b2)]):p(c1, c1)). lemma(742, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(a1, a1b1), [712]):p(a1, a1)). lemma(743, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(a2, a2b2), [714]):p(a2, a2)). lemma(744, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(c2, a2c2), [719]):p(c2, c2)). lemma(745, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(o, oa), [724]):p(o, o)). lemma(746, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(bc, b1c1), [733]):p(bc, bc)). lemma(747, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(ac, a1c1), [735]):p(ac, ac)). lemma(748, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pref(ab, a1b1), [737]):p(ab, ab)). lemma(749, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lref(b2, a1c1), [i(b2, a1c1)]):l(a1c1, a1c1)). lemma(750, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lref(b1, a2c2), [i(b1, a2c2)]):l(a2c2, a2c2)). lemma(751, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lref(c1, a2b2), [i(c1, a2b2)]):l(a2b2, a2b2)). lemma(752, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lref(a1, a1b1), [712]):l(a1b1, a1b1)). lemma(753, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lref(c1, b1c1), [720]):l(b1c1, b1c1)). lemma(754, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lref(c2, b2c2), [722]):l(b2c2, b2c2)). lemma(755, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lref(o, oa), [724]):l(oa, oa)). lemma(756, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lref(o, ob), [725]):l(ob, ob)). lemma(757, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lref(o, oc), [726]):l(oc, oc)). lemma(758, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(b2, c1, a1c1, a2b2), [i(b2, a1c1), 715, 717, i(c1, a2b2)]): (p(b2, c1);l(a1c1, a2b2))). lemma(759, [p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(b2, c1), [p(b2, c1)]):p(c1, b2)). lemma(760, [p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b2, c1, b1c1), [p(b2, c1), 720]):i(b2, b1c1)). lemma(761, [p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b2, c1, oc), [p(b2, c1), 731]):i(b2, oc)). lemma(762, [p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(c1, b2, b2c2), [759, 723]):i(c1, b2c2)). lemma(763, [p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(c1, b2, ob), [759, 730]):i(c1, ob)). lemma(764, [p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(c1, bc, b1c1, b2c2), [720, 762, 733, 734]): (p(c1, bc);l(b1c1, b2c2))). lemma(765, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(c1, bc), [p(c1, bc)]):p(bc, c1)). lemma(766, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(b2, c1, bc), [p(b2, c1), p(c1, bc)]):p(b2, bc)). lemma(767, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(b2, bc), [766]):p(bc, b2)). lemma(768, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(bc, c1, a2b2), [765, i(c1, a2b2)]):i(bc, a2b2)). lemma(769, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(bc, c1, a1c1), [765, 717]):i(bc, a1c1)). lemma(770, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(bc, c1, oc), [765, 731]):i(bc, oc)). lemma(771, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(bc, c1, ob), [765, 763]):i(bc, ob)). lemma(772, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(c1, b1, b1c1, ob), [720, 763, 721, 729]): (p(c1, b1);l(b1c1, ob))). lemma(773, [p(c1, b1), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(c1, b1), [p(c1, b1)]):p(b1, c1)). lemma(774, [p(c1, b1), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(b2, c1, b1), [p(b2, c1), p(c1, b1)]):p(b2, b1)). lemma(775, [p(c1, b1), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(notbb, [774]):false). lemma(776, [p(c1, b1), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [775]):goal). lemma(777, [l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(b1c1, ob), [l(b1c1, ob)]):l(ob, b1c1)). lemma(778, [l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(o, ob, b1c1), [725, 777]):i(o, b1c1)). lemma(779, [l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(c1, o, b1c1, oc), [720, 731, 778, 726]): (p(c1, o);l(b1c1, oc))). lemma(780, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(c1, o), [p(c1, o)]):p(o, c1)). lemma(781, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(b2, c1, o), [p(b2, c1), p(c1, o)]):p(b2, o)). lemma(782, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(b2, o), [781]):p(o, b2)). lemma(783, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(bc, c1, o), [765, p(c1, o)]):p(bc, o)). lemma(784, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(bc, o), [783]):p(o, bc)). lemma(785, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(c1, o, oa), [p(c1, o), 724]):i(c1, oa)). lemma(786, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b2, c1, oa), [p(b2, c1), 785]):i(b2, oa)). lemma(787, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(bc, c1, oa), [765, 785]):i(bc, oa)). lemma(788, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, c1, a2b2), [780, i(c1, a2b2)]):i(o, a2b2)). lemma(789, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, c1, a1c1), [780, 717]):i(o, a1c1)). lemma(790, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, c1, b2c2), [780, 762]):i(o, b2c2)). lemma(791, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(b2, a1, a1c1, oa), [i(b2, a1c1), 786, 716, 727]): (p(b2, a1);l(a1c1, oa))). lemma(792, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(b2, a1), [p(b2, a1)]):p(a1, b2)). lemma(793, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(c1, b2, a1), [759, p(b2, a1)]):p(c1, a1)). lemma(794, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(c1, a1), [793]):p(a1, c1)). lemma(795, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(bc, c1, a1), [765, 793]):p(bc, a1)). lemma(796, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(bc, a1), [795]):p(a1, bc)). lemma(797, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, c1, a1), [780, 793]):p(o, a1)). lemma(798, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, a1), [797]):p(a1, o)). lemma(799, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b2, a1, a1b1), [p(b2, a1), 712]):i(b2, a1b1)). lemma(800, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(c1, b2, a1b1), [759, 799]):i(c1, a1b1)). lemma(801, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(triangle1(a1b1), [712, 713, 800]):false). lemma(802, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [801]):goal). lemma(803, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1c1, oa), [l(a1c1, oa)]):l(oa, a1c1)). lemma(804, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a2, oa, a1c1), [728, 803]):i(a2, a1c1)). lemma(805, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ac, a1c1, oa), [735, l(a1c1, oa)]):i(ac, oa)). lemma(806, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(b2, a2, a1c1, a2b2), [i(b2, a1c1), 715, 804, 714]): (p(b2, a2);l(a1c1, a2b2))). lemma(807, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(b2, a2), [p(b2, a2)]):p(a2, b2)). lemma(808, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(c1, b2, a2), [759, p(b2, a2)]):p(c1, a2)). lemma(809, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(c1, a2), [808]):p(a2, c1)). lemma(810, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(bc, c1, a2), [765, 808]):p(bc, a2)). lemma(811, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(bc, a2), [810]):p(a2, bc)). lemma(812, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, c1, a2), [780, 808]):p(o, a2)). lemma(813, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, a2), [812]):p(a2, o)). lemma(814, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b2, a2, a2c2), [p(b2, a2), 718]):i(b2, a2c2)). lemma(815, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(triangle2(a2c2), [718, 814, 719]):false). lemma(816, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [815]):goal). lemma(817, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1c1, a2b2), [l(a1c1, a2b2)]):l(a2b2, a1c1)). lemma(818, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(oa, a1c1, a2b2), [803, l(a1c1, a2b2)]):l(oa, a2b2)). lemma(819, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(oa, a2b2), [818]):l(a2b2, oa)). lemma(820, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a1, a1c1, a2b2), [716, l(a1c1, a2b2)]):i(a1, a2b2)). lemma(821, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ac, a1c1, a2b2), [735, l(a1c1, a2b2)]):i(ac, a2b2)). lemma(822, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(goal_normal(a2b2), [751, 768, 821, 738]):goal). lemma(823, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(806), [816, 822]):goal). lemma(824, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(791), [802, 823]):goal). lemma(825, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(b1c1, oc), [l(b1c1, oc)]):l(oc, b1c1)). lemma(826, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(ob, b1c1, oc), [777, l(b1c1, oc)]):l(ob, oc)). lemma(827, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(ob, oc), [826]):l(oc, ob)). lemma(828, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(b1, b1c1, oc), [721, l(b1c1, oc)]):i(b1, oc)). lemma(829, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c2, oc, b1c1), [732, 825]):i(c2, b1c1)). lemma(830, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c2, oc, ob), [732, 827]):i(c2, ob)). lemma(831, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(b1, c2, a2c2, b1c1), [i(b1, a2c2), 721, 719, 829]): (p(b1, c2);l(a2c2, b1c1))). lemma(832, [p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(b1, c2), [p(b1, c2)]):p(c2, b1)). lemma(833, [p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b1, c2, b2c2), [p(b1, c2), 722]):i(b1, b2c2)). lemma(834, [p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(c2, b1, a1b1), [832, 713]):i(c2, a1b1)). lemma(835, [p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(c1, b1, b1c1, b2c2), [720, 762, 721, 833]): (p(c1, b1);l(b1c1, b2c2))). lemma(836, [p(c1, b1), p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(c1, b1), [p(c1, b1)]):p(b1, c1)). lemma(837, [p(c1, b1), p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(b2, c1, b1), [p(b2, c1), p(c1, b1)]):p(b2, b1)). lemma(838, [p(c1, b1), p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(notbb, [837]):false). lemma(839, [p(c1, b1), p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [838]):goal). lemma(840, [l(b1c1, b2c2), p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(notbc, [l(b1c1, b2c2)]):false). lemma(841, [l(b1c1, b2c2), p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [840]):goal). lemma(842, [p(b1, c2), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(835), [839, 841]):goal). lemma(843, [l(a2c2, b1c1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2c2, b1c1), [l(a2c2, b1c1)]):l(b1c1, a2c2)). lemma(844, [l(a2c2, b1c1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(ob, b1c1, a2c2), [777, 843]):l(ob, a2c2)). lemma(845, [l(a2c2, b1c1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(ob, a2c2), [844]):l(a2c2, ob)). lemma(846, [l(a2c2, b1c1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(oc, b1c1, a2c2), [825, 843]):l(oc, a2c2)). lemma(847, [l(a2c2, b1c1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(oc, a2c2), [846]):l(a2c2, oc)). lemma(848, [l(a2c2, b1c1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a2, a2c2, b1c1), [718, l(a2c2, b1c1)]):i(a2, b1c1)). lemma(849, [l(a2c2, b1c1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(triangle2(b1c1), [848, 760, 829]):false). lemma(850, [l(a2c2, b1c1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [849]):goal). lemma(851, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(831), [842, 850]):goal). lemma(852, [l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(779), [824, 851]):goal). lemma(853, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(772), [776, 852]):goal). lemma(854, [l(b1c1, b2c2), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(notbc, [l(b1c1, b2c2)]):false). lemma(855, [l(b1c1, b2c2), p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [854]):goal). lemma(856, [p(b2, c1), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(764), [853, 855]):goal). lemma(857, [l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1c1, a2b2), [l(a1c1, a2b2)]):l(a2b2, a1c1)). lemma(858, [l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a2, a2b2, a1c1), [714, 857]):i(a2, a1c1)). lemma(859, [l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a1, a1c1, a2b2), [716, l(a1c1, a2b2)]):i(a1, a2b2)). lemma(860, [l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ac, a1c1, a2b2), [735, l(a1c1, a2b2)]):i(ac, a2b2)). lemma(861, [l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ab, a2b2, a1c1), [738, 857]):i(ab, a1c1)). lemma(862, [l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(a1, ab, a1b1, a1c1), [712, 716, 737, 861]): (p(a1, ab);l(a1b1, a1c1))). lemma(863, [p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(a1, ab), [p(a1, ab)]):p(ab, a1)). lemma(864, [p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(ab, a1, oa), [863, 727]):i(ab, oa)). lemma(865, [p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(a2, ac, a2b2, a2c2), [714, 718, 860, 736]): (p(a2, ac);l(a2b2, a2c2))). lemma(866, [p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(a2, ac), [p(a2, ac)]):p(ac, a2)). lemma(867, [p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(ac, a2, oa), [866, 728]):i(ac, oa)). lemma(868, [p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(a2, ab, a2b2, oa), [714, 728, 738, 864]): (p(a2, ab);l(a2b2, oa))). lemma(869, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(a2, ab), [p(a2, ab)]):p(ab, a2)). lemma(870, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(a1, ab, a2), [p(a1, ab), 869]):p(a1, a2)). lemma(871, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(a1, a2), [870]):p(a2, a1)). lemma(872, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(notaa, [871]):false). lemma(873, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [872]):goal). lemma(874, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2b2, oa), [l(a2b2, oa)]):l(oa, a2b2)). lemma(875, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(a1c1, a2b2, oa), [l(a1c1, a2b2), l(a2b2, oa)]):l(a1c1, oa)). lemma(876, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1c1, oa), [875]):l(oa, a1c1)). lemma(877, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(b2, a1c1, oa), [i(b2, a1c1), 875]):i(b2, oa)). lemma(878, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c1, a2b2, oa), [i(c1, a2b2), l(a2b2, oa)]):i(c1, oa)). lemma(879, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(o, oa, a2b2), [724, 874]):i(o, a2b2)). lemma(880, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(o, oa, a1c1), [724, 876]):i(o, a1c1)). lemma(881, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(b2, o, a1c1, ob), [i(b2, a1c1), 730, 880, 725]): (p(b2, o);l(a1c1, ob))). lemma(882, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(b2, o), [p(b2, o)]):p(o, b2)). lemma(883, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b2, o, oc), [p(b2, o), 726]):i(b2, oc)). lemma(884, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, b2, b2c2), [882, 723]):i(o, b2c2)). lemma(885, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(b2, c1, a1c1, oc), [i(b2, a1c1), 883, 717, 731]): (p(b2, c1);l(a1c1, oc))). lemma(886, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(b2, c1), [p(b2, c1)]):p(c1, b2)). lemma(887, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, b2, c1), [882, p(b2, c1)]):p(o, c1)). lemma(888, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, c1), [887]):p(c1, o)). lemma(889, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b2, c1, b1c1), [p(b2, c1), 720]):i(b2, b1c1)). lemma(890, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, b2, b1c1), [882, 889]):i(o, b1c1)). lemma(891, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(c1, b2, b2c2), [886, 723]):i(c1, b2c2)). lemma(892, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(c1, b2, ob), [886, 730]):i(c1, ob)). lemma(893, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(unique(c1, bc, b1c1, b2c2), [720, 891, 733, 734]): (p(c1, bc);l(b1c1, b2c2))). lemma(894, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(c1, bc), [p(c1, bc)]):p(bc, c1)). lemma(895, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(b2, c1, bc), [p(b2, c1), p(c1, bc)]):p(b2, bc)). lemma(896, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(b2, bc), [895]):p(bc, b2)). lemma(897, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, b2, bc), [882, 895]):p(o, bc)). lemma(898, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, bc), [897]):p(bc, o)). lemma(899, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(bc, c1, a2b2), [894, i(c1, a2b2)]):i(bc, a2b2)). lemma(900, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(goal_normal(a2b2), [751, 899, 860, 738]):goal). lemma(901, [l(b1c1, b2c2), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(notbc, [l(b1c1, b2c2)]):false). lemma(902, [l(b1c1, b2c2), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [901]):goal). lemma(903, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(893), [900, 902]):goal). lemma(904, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1c1, oc), [l(a1c1, oc)]):l(oc, a1c1)). lemma(905, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(a2b2, a1c1, oc), [857, l(a1c1, oc)]):l(a2b2, oc)). lemma(906, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2b2, oc), [905]):l(oc, a2b2)). lemma(907, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(oa, a2b2, oc), [874, 905]):l(oa, oc)). lemma(908, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(oa, oc), [907]):l(oc, oa)). lemma(909, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a2, a2b2, oc), [714, 905]):i(a2, oc)). lemma(910, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(triangle2(oc), [909, 883, 732]):false). lemma(911, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [910]):goal). lemma(912, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(885), [903, 911]):goal). lemma(913, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1c1, ob), [l(a1c1, ob)]):l(ob, a1c1)). lemma(914, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(a2b2, a1c1, ob), [857, l(a1c1, ob)]):l(a2b2, ob)). lemma(915, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2b2, ob), [914]):l(ob, a2b2)). lemma(916, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(oa, a2b2, ob), [874, 914]):l(oa, ob)). lemma(917, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(oa, ob), [916]):l(ob, oa)). lemma(918, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c1, a2b2, ob), [i(c1, a2b2), 914]):i(c1, ob)). lemma(919, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a2, a2b2, ob), [714, 914]):i(a2, ob)). lemma(920, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(pcon(ac, a2, ob), [866, 919]):i(ac, ob)). lemma(921, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a1, a1c1, ob), [716, l(a1c1, ob)]):i(a1, ob)). lemma(922, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(triangle1(ob), [921, 729, 918]):false). lemma(923, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [922]):goal). lemma(924, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(881), [912, 923]):goal). lemma(925, [p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(868), [873, 924]):goal). lemma(926, [l(a2b2, a2c2), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2b2, a2c2), [l(a2b2, a2c2)]):l(a2c2, a2b2)). lemma(927, [l(a2b2, a2c2), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(a1c1, a2b2, a2c2), [l(a1c1, a2b2), l(a2b2, a2c2)]):l(a1c1, a2c2)). lemma(928, [l(a2b2, a2c2), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(notac, [927]):false). lemma(929, [l(a2b2, a2c2), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [928]):goal). lemma(930, [p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(865), [925, 929]):goal). lemma(931, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1b1, a1c1), [l(a1b1, a1c1)]):l(a1c1, a1b1)). lemma(932, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(ltra(a2b2, a1c1, a1b1), [857, 931]):l(a2b2, a1b1)). lemma(933, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2b2, a1b1), [932]):l(a1b1, a2b2)). lemma(934, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(notab, [933]):false). lemma(935, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [934]):goal). lemma(936, [l(a1c1, a2b2), i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(862), [930, 935]):goal). lemma(937, [i(c1, a2b2), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(758), [856, 936]):goal). lemma(938, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ia1b1, []):i(a1, a1b1)). lemma(939, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ib1a1, []):i(b1, a1b1)). lemma(940, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ia2b2, []):i(a2, a2b2)). lemma(941, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ib2a2, []):i(b2, a2b2)). lemma(942, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ia1c1, []):i(a1, a1c1)). lemma(943, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ic1a1, []):i(c1, a1c1)). lemma(944, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ia2c2, []):i(a2, a2c2)). lemma(945, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ic2a2, []):i(c2, a2c2)). lemma(946, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ic1b1, []):i(c1, b1c1)). lemma(947, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ib1c1, []):i(b1, b1c1)). lemma(948, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ic2b2, []):i(c2, b2c2)). lemma(949, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ib2c2, []):i(b2, b2c2)). lemma(950, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(iooa, []):i(o, oa)). lemma(951, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ioob, []):i(o, ob)). lemma(952, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(iooc, []):i(o, oc)). lemma(953, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ia1oa, []):i(a1, oa)). lemma(954, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ia2oa, []):i(a2, oa)). lemma(955, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ib1ob, []):i(b1, ob)). lemma(956, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ib2ob, []):i(b2, ob)). lemma(957, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ic1oc, []):i(c1, oc)). lemma(958, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ic2oc, []):i(c2, oc)). lemma(959, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ibc1, []):i(bc, b1c1)). lemma(960, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ibc2, []):i(bc, b2c2)). lemma(961, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(iac1, []):i(ac, a1c1)). lemma(962, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(iac2, []):i(ac, a2c2)). lemma(963, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(iab1, []):i(ab, a1b1)). lemma(964, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(iab2, []):i(ab, a2b2)). lemma(965, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(b2, a1c1), [i(b2, a1c1)]):p(b2, b2)). lemma(966, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(b1, a2c2), [i(b1, a2c2)]):p(b1, b1)). lemma(967, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(a2, b1c1), [i(a2, b1c1)]):p(a2, a2)). lemma(968, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(a1, a1b1), [938]):p(a1, a1)). lemma(969, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(c1, a1c1), [943]):p(c1, c1)). lemma(970, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(c2, a2c2), [945]):p(c2, c2)). lemma(971, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(o, oa), [950]):p(o, o)). lemma(972, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(bc, b1c1), [959]):p(bc, bc)). lemma(973, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(ac, a1c1), [961]):p(ac, ac)). lemma(974, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pref(ab, a1b1), [963]):p(ab, ab)). lemma(975, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lref(b2, a1c1), [i(b2, a1c1)]):l(a1c1, a1c1)). lemma(976, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lref(b1, a2c2), [i(b1, a2c2)]):l(a2c2, a2c2)). lemma(977, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lref(a2, b1c1), [i(a2, b1c1)]):l(b1c1, b1c1)). lemma(978, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lref(a1, a1b1), [938]):l(a1b1, a1b1)). lemma(979, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lref(a2, a2b2), [940]):l(a2b2, a2b2)). lemma(980, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lref(c2, b2c2), [948]):l(b2c2, b2c2)). lemma(981, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lref(o, oa), [950]):l(oa, oa)). lemma(982, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lref(o, ob), [951]):l(ob, ob)). lemma(983, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lref(o, oc), [952]):l(oc, oc)). lemma(984, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(b1, a2, a2c2, b1c1), [i(b1, a2c2), 947, 944, i(a2, b1c1)]): (p(b1, a2);l(a2c2, b1c1))). lemma(985, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(b1, a2), [p(b1, a2)]):p(a2, b1)). lemma(986, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b1, a2, a2b2), [p(b1, a2), 940]):i(b1, a2b2)). lemma(987, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b1, a2, oa), [p(b1, a2), 954]):i(b1, oa)). lemma(988, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(a2, b1, a1b1), [985, 939]):i(a2, a1b1)). lemma(989, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(a2, b1, ob), [985, 955]):i(a2, ob)). lemma(990, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(a1, b1, a1b1, oa), [938, 953, 939, 987]): (p(a1, b1);l(a1b1, oa))). lemma(991, [p(a1, b1), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(a1, b1), [p(a1, b1)]):p(b1, a1)). lemma(992, [p(a1, b1), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(a2, b1, a1), [985, 991]):p(a2, a1)). lemma(993, [p(a1, b1), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(notaa, [992]):false). lemma(994, [p(a1, b1), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [993]):goal). lemma(995, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1b1, oa), [l(a1b1, oa)]):l(oa, a1b1)). lemma(996, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(o, oa, a1b1), [950, 995]):i(o, a1b1)). lemma(997, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ab, a1b1, oa), [963, l(a1b1, oa)]):i(ab, oa)). lemma(998, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(b1, o, a1b1, ob), [939, 955, 996, 951]): (p(b1, o);l(a1b1, ob))). lemma(999, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(b1, o), [p(b1, o)]):p(o, b1)). lemma(1000, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(a2, b1, o), [985, p(b1, o)]):p(a2, o)). lemma(1001, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(a2, o), [1000]):p(o, a2)). lemma(1002, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b1, o, oc), [p(b1, o), 952]):i(b1, oc)). lemma(1003, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(a2, b1, oc), [985, 1002]):i(a2, oc)). lemma(1004, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, b1, a2c2), [999, i(b1, a2c2)]):i(o, a2c2)). lemma(1005, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, b1, b1c1), [999, 947]):i(o, b1c1)). lemma(1006, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, b1, a2b2), [999, 986]):i(o, a2b2)). lemma(1007, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(b1, c2, a2c2, oc), [i(b1, a2c2), 1002, 945, 958]): (p(b1, c2);l(a2c2, oc))). lemma(1008, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(b1, c2), [p(b1, c2)]):p(c2, b1)). lemma(1009, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(a2, b1, c2), [985, p(b1, c2)]):p(a2, c2)). lemma(1010, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(a2, c2), [1009]):p(c2, a2)). lemma(1011, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, b1, c2), [999, p(b1, c2)]):p(o, c2)). lemma(1012, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, c2), [1011]):p(c2, o)). lemma(1013, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b1, c2, b2c2), [p(b1, c2), 948]):i(b1, b2c2)). lemma(1014, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(a2, b1, b2c2), [985, 1013]):i(a2, b2c2)). lemma(1015, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(triangle2(b2c2), [1014, 949, 948]):false). lemma(1016, [p(b1, c2), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1015]):goal). lemma(1017, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2c2, oc), [l(a2c2, oc)]):l(oc, a2c2)). lemma(1018, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c1, oc, a2c2), [957, 1017]):i(c1, a2c2)). lemma(1019, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ac, a2c2, oc), [962, l(a2c2, oc)]):i(ac, oc)). lemma(1020, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(b1, c1, a2c2, b1c1), [i(b1, a2c2), 947, 1018, 946]): (p(b1, c1);l(a2c2, b1c1))). lemma(1021, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(b1, c1), [p(b1, c1)]):p(c1, b1)). lemma(1022, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(a2, b1, c1), [985, p(b1, c1)]):p(a2, c1)). lemma(1023, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(a2, c1), [1022]):p(c1, a2)). lemma(1024, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, b1, c1), [999, p(b1, c1)]):p(o, c1)). lemma(1025, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, c1), [1024]):p(c1, o)). lemma(1026, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b1, c1, a1c1), [p(b1, c1), 943]):i(b1, a1c1)). lemma(1027, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(triangle1(a1c1), [942, 1026, 943]):false). lemma(1028, [p(b1, c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1027]):goal). lemma(1029, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2c2, b1c1), [l(a2c2, b1c1)]):l(b1c1, a2c2)). lemma(1030, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(oc, a2c2, b1c1), [1017, l(a2c2, b1c1)]):l(oc, b1c1)). lemma(1031, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(oc, b1c1), [1030]):l(b1c1, oc)). lemma(1032, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c2, a2c2, b1c1), [945, l(a2c2, b1c1)]):i(c2, b1c1)). lemma(1033, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(bc, b1c1, a2c2), [959, 1029]):i(bc, a2c2)). lemma(1034, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(bc, b1c1, oc), [959, 1031]):i(bc, oc)). lemma(1035, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ac, a2c2, b1c1), [962, l(a2c2, b1c1)]):i(ac, b1c1)). lemma(1036, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(b1, ab, a1b1, a2b2), [939, 986, 963, 964]): (p(b1, ab);l(a1b1, a2b2))). lemma(1037, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(b1, ab), [p(b1, ab)]):p(ab, b1)). lemma(1038, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(a2, b1, ab), [985, p(b1, ab)]):p(a2, ab)). lemma(1039, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(a2, ab), [1038]):p(ab, a2)). lemma(1040, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, b1, ab), [999, p(b1, ab)]):p(o, ab)). lemma(1041, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, ab), [1040]):p(ab, o)). lemma(1042, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(ab, b1, a2c2), [1037, i(b1, a2c2)]):i(ab, a2c2)). lemma(1043, [p(b1, ab), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(goal_normal(a2c2), [976, 1033, 962, 1042]):goal). lemma(1044, [l(a1b1, a2b2), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(notab, [l(a1b1, a2b2)]):false). lemma(1045, [l(a1b1, a2b2), l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1044]):goal). lemma(1046, [l(a2c2, b1c1), l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1036), [1043, 1045]):goal). lemma(1047, [l(a2c2, oc), p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1020), [1028, 1046]):goal). lemma(1048, [p(b1, o), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1007), [1016, 1047]):goal). lemma(1049, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1b1, ob), [l(a1b1, ob)]):l(ob, a1b1)). lemma(1050, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(oa, a1b1, ob), [995, l(a1b1, ob)]):l(oa, ob)). lemma(1051, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(oa, ob), [1050]):l(ob, oa)). lemma(1052, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a1, a1b1, ob), [938, l(a1b1, ob)]):i(a1, ob)). lemma(1053, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(b2, ob, a1b1), [956, 1049]):i(b2, a1b1)). lemma(1054, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(b2, ob, oa), [956, 1051]):i(b2, oa)). lemma(1055, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ab, a1b1, ob), [963, l(a1b1, ob)]):i(ab, ob)). lemma(1056, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(b2, a1, a1c1, ob), [i(b2, a1c1), 956, 942, 1052]): (p(b2, a1);l(a1c1, ob))). lemma(1057, [p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(b2, a1), [p(b2, a1)]):p(a1, b2)). lemma(1058, [p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(a1, b2, a2b2), [1057, 941]):i(a1, a2b2)). lemma(1059, [p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(a1, b2, b2c2), [1057, 949]):i(a1, b2c2)). lemma(1060, [p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(a1, b1, a1b1, a2b2), [938, 1058, 939, 986]): (p(a1, b1);l(a1b1, a2b2))). lemma(1061, [p(a1, b1), p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(a1, b1), [p(a1, b1)]):p(b1, a1)). lemma(1062, [p(a1, b1), p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(a2, b1, a1), [985, 1061]):p(a2, a1)). lemma(1063, [p(a1, b1), p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(notaa, [1062]):false). lemma(1064, [p(a1, b1), p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1063]):goal). lemma(1065, [l(a1b1, a2b2), p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(notab, [l(a1b1, a2b2)]):false). lemma(1066, [l(a1b1, a2b2), p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1065]):goal). lemma(1067, [p(b2, a1), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1060), [1064, 1066]):goal). lemma(1068, [l(a1c1, ob), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1c1, ob), [l(a1c1, ob)]):l(ob, a1c1)). lemma(1069, [l(a1c1, ob), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(a1b1, ob, a1c1), [l(a1b1, ob), 1068]):l(a1b1, a1c1)). lemma(1070, [l(a1c1, ob), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1b1, a1c1), [1069]):l(a1c1, a1b1)). lemma(1071, [l(a1c1, ob), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(oa, a1b1, a1c1), [995, 1069]):l(oa, a1c1)). lemma(1072, [l(a1c1, ob), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(oa, a1c1), [1071]):l(a1c1, oa)). lemma(1073, [l(a1c1, ob), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(b1, a1b1, a1c1), [939, 1069]):i(b1, a1c1)). lemma(1074, [l(a1c1, ob), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(triangle1(a1c1), [942, 1073, 943]):false). lemma(1075, [l(a1c1, ob), l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1074]):goal). lemma(1076, [l(a1b1, ob), l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1056), [1067, 1075]):goal). lemma(1077, [l(a1b1, oa), p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(998), [1048, 1076]):goal). lemma(1078, [p(b1, a2), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(990), [994, 1077]):goal). lemma(1079, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2c2, b1c1), [l(a2c2, b1c1)]):l(b1c1, a2c2)). lemma(1080, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c2, a2c2, b1c1), [945, l(a2c2, b1c1)]):i(c2, b1c1)). lemma(1081, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c1, b1c1, a2c2), [946, 1079]):i(c1, a2c2)). lemma(1082, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(bc, b1c1, a2c2), [959, 1079]):i(bc, a2c2)). lemma(1083, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ac, a2c2, b1c1), [962, l(a2c2, b1c1)]):i(ac, b1c1)). lemma(1084, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(c1, ac, a1c1, b1c1), [943, 946, 961, 1083]): (p(c1, ac);l(a1c1, b1c1))). lemma(1085, [p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(c1, ac), [p(c1, ac)]):p(ac, c1)). lemma(1086, [p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(ac, c1, oc), [1085, 957]):i(ac, oc)). lemma(1087, [p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(c2, bc, a2c2, b2c2), [945, 948, 1082, 960]): (p(c2, bc);l(a2c2, b2c2))). lemma(1088, [p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(c2, bc), [p(c2, bc)]):p(bc, c2)). lemma(1089, [p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(bc, c2, oc), [1088, 958]):i(bc, oc)). lemma(1090, [p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(c2, ac, a2c2, oc), [945, 958, 962, 1086]): (p(c2, ac);l(a2c2, oc))). lemma(1091, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(c2, ac), [p(c2, ac)]):p(ac, c2)). lemma(1092, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(c1, ac, c2), [p(c1, ac), 1091]):p(c1, c2)). lemma(1093, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(c1, c2), [1092]):p(c2, c1)). lemma(1094, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(notcc, [1093]):false). lemma(1095, [p(c2, ac), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1094]):goal). lemma(1096, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2c2, oc), [l(a2c2, oc)]):l(oc, a2c2)). lemma(1097, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(b1c1, a2c2, oc), [1079, l(a2c2, oc)]):l(b1c1, oc)). lemma(1098, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(b1c1, oc), [1097]):l(oc, b1c1)). lemma(1099, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(b1, a2c2, oc), [i(b1, a2c2), l(a2c2, oc)]):i(b1, oc)). lemma(1100, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a2, b1c1, oc), [i(a2, b1c1), 1097]):i(a2, oc)). lemma(1101, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(o, oc, a2c2), [952, 1096]):i(o, a2c2)). lemma(1102, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(o, oc, b1c1), [952, 1098]):i(o, b1c1)). lemma(1103, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(b1, o, a2c2, ob), [i(b1, a2c2), 955, 1101, 951]): (p(b1, o);l(a2c2, ob))). lemma(1104, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(b1, o), [p(b1, o)]):p(o, b1)). lemma(1105, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b1, o, oa), [p(b1, o), 950]):i(b1, oa)). lemma(1106, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, b1, a1b1), [1104, 939]):i(o, a1b1)). lemma(1107, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(b1, a2, a2c2, oa), [i(b1, a2c2), 1105, 944, 954]): (p(b1, a2);l(a2c2, oa))). lemma(1108, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(b1, a2), [p(b1, a2)]):p(a2, b1)). lemma(1109, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, b1, a2), [1104, p(b1, a2)]):p(o, a2)). lemma(1110, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, a2), [1109]):p(a2, o)). lemma(1111, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(b1, a2, a2b2), [p(b1, a2), 940]):i(b1, a2b2)). lemma(1112, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(o, b1, a2b2), [1104, 1111]):i(o, a2b2)). lemma(1113, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(a2, b1, a1b1), [1108, 939]):i(a2, a1b1)). lemma(1114, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(a2, b1, ob), [1108, 955]):i(a2, ob)). lemma(1115, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(a1, b1, a1b1, oa), [938, 953, 939, 1105]): (p(a1, b1);l(a1b1, oa))). lemma(1116, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(a1, b1), [p(a1, b1)]):p(b1, a1)). lemma(1117, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, b1, a1), [1104, 1116]):p(o, a1)). lemma(1118, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, a1), [1117]):p(a1, o)). lemma(1119, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(a2, b1, a1), [1108, 1116]):p(a2, a1)). lemma(1120, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(notaa, [1119]):false). lemma(1121, [p(a1, b1), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1120]):goal). lemma(1122, [l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1b1, oa), [l(a1b1, oa)]):l(oa, a1b1)). lemma(1123, [l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(ab, a1b1, oa), [963, l(a1b1, oa)]):i(ab, oa)). lemma(1124, [l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(unique(b1, ab, a1b1, a2b2), [939, 1111, 963, 964]): (p(b1, ab);l(a1b1, a2b2))). lemma(1125, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(b1, ab), [p(b1, ab)]):p(ab, b1)). lemma(1126, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(o, b1, ab), [1104, p(b1, ab)]):p(o, ab)). lemma(1127, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(o, ab), [1126]):p(ab, o)). lemma(1128, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ptra(a2, b1, ab), [1108, p(b1, ab)]):p(a2, ab)). lemma(1129, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(psym(a2, ab), [1128]):p(ab, a2)). lemma(1130, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(ab, b1, a2c2), [1125, i(b1, a2c2)]):i(ab, a2c2)). lemma(1131, [p(b1, ab), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(goal_normal(a2c2), [976, 1082, 962, 1130]):goal). lemma(1132, [l(a1b1, a2b2), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(notab, [l(a1b1, a2b2)]):false). lemma(1133, [l(a1b1, a2b2), l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1132]):goal). lemma(1134, [l(a1b1, oa), p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1124), [1131, 1133]):goal). lemma(1135, [p(b1, a2), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1115), [1121, 1134]):goal). lemma(1136, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2c2, oa), [l(a2c2, oa)]):l(oa, a2c2)). lemma(1137, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(b1c1, a2c2, oa), [1079, l(a2c2, oa)]):l(b1c1, oa)). lemma(1138, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(b1c1, oa), [1137]):l(oa, b1c1)). lemma(1139, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(oc, a2c2, oa), [1096, l(a2c2, oa)]):l(oc, oa)). lemma(1140, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(oc, oa), [1139]):l(oa, oc)). lemma(1141, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c2, a2c2, oa), [945, l(a2c2, oa)]):i(c2, oa)). lemma(1142, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(pcon(bc, c2, oa), [1088, 1141]):i(bc, oa)). lemma(1143, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c1, b1c1, oa), [946, 1137]):i(c1, oa)). lemma(1144, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(triangle1(oa), [953, 1105, 1143]):false). lemma(1145, [l(a2c2, oa), p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1144]):goal). lemma(1146, [p(b1, o), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1107), [1135, 1145]):goal). lemma(1147, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2c2, ob), [l(a2c2, ob)]):l(ob, a2c2)). lemma(1148, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(b1c1, a2c2, ob), [1079, l(a2c2, ob)]):l(b1c1, ob)). lemma(1149, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(b1c1, ob), [1148]):l(ob, b1c1)). lemma(1150, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(oc, a2c2, ob), [1096, l(a2c2, ob)]):l(oc, ob)). lemma(1151, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(oc, ob), [1150]):l(ob, oc)). lemma(1152, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(a2, b1c1, ob), [i(a2, b1c1), 1148]):i(a2, ob)). lemma(1153, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lcon(c2, a2c2, ob), [945, l(a2c2, ob)]):i(c2, ob)). lemma(1154, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(triangle2(ob), [1152, 956, 1153]):false). lemma(1155, [l(a2c2, ob), l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1154]):goal). lemma(1156, [l(a2c2, oc), p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1103), [1146, 1155]):goal). lemma(1157, [p(c2, bc), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1090), [1095, 1156]):goal). lemma(1158, [l(a2c2, b2c2), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2c2, b2c2), [l(a2c2, b2c2)]):l(b2c2, a2c2)). lemma(1159, [l(a2c2, b2c2), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(b1c1, a2c2, b2c2), [1079, l(a2c2, b2c2)]):l(b1c1, b2c2)). lemma(1160, [l(a2c2, b2c2), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(notbc, [1159]):false). lemma(1161, [l(a2c2, b2c2), p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1160]):goal). lemma(1162, [p(c1, ac), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1087), [1157, 1161]):goal). lemma(1163, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a1c1, b1c1), [l(a1c1, b1c1)]):l(b1c1, a1c1)). lemma(1164, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(ltra(a2c2, b1c1, a1c1), [l(a2c2, b1c1), 1163]):l(a2c2, a1c1)). lemma(1165, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(lsym(a2c2, a1c1), [1164]):l(a1c1, a2c2)). lemma(1166, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(notac, [1165]):false). lemma(1167, [l(a1c1, b1c1), l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(false_ind(goal), [1166]):goal). lemma(1168, [l(a2c2, b1c1), i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(1084), [1162, 1167]):goal). lemma(1169, [i(a2, b1c1), i(b1, a2c2), i(b2, a1c1)], ap(or_elim(984), [1078, 1168]):goal). lemma(1170, [i(b1, a2c2), i(b2, a1c1)], ap(or_elim(711), [937, 1169]):goal). lemma(1171, [i(c2, a1b1), i(b2, a1c1)], ap(gap_c, []): (i(c1, a2b2);i(a2, b1c1))). lemma(1172, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ia1b1, []):i(a1, a1b1)). lemma(1173, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ib1a1, []):i(b1, a1b1)). lemma(1174, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ia2b2, []):i(a2, a2b2)). lemma(1175, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ib2a2, []):i(b2, a2b2)). lemma(1176, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ia1c1, []):i(a1, a1c1)). lemma(1177, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ic1a1, []):i(c1, a1c1)). lemma(1178, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ia2c2, []):i(a2, a2c2)). lemma(1179, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ic2a2, []):i(c2, a2c2)). lemma(1180, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ic1b1, []):i(c1, b1c1)). lemma(1181, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ib1c1, []):i(b1, b1c1)). lemma(1182, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ic2b2, []):i(c2, b2c2)). lemma(1183, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ib2c2, []):i(b2, b2c2)). lemma(1184, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(iooa, []):i(o, oa)). lemma(1185, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ioob, []):i(o, ob)). lemma(1186, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(iooc, []):i(o, oc)). lemma(1187, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ia1oa, []):i(a1, oa)). lemma(1188, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ia2oa, []):i(a2, oa)). lemma(1189, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ib1ob, []):i(b1, ob)). lemma(1190, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ib2ob, []):i(b2, ob)). lemma(1191, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ic1oc, []):i(c1, oc)). lemma(1192, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ic2oc, []):i(c2, oc)). lemma(1193, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ibc1, []):i(bc, b1c1)). lemma(1194, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ibc2, []):i(bc, b2c2)). lemma(1195, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(iac1, []):i(ac, a1c1)). lemma(1196, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(iac2, []):i(ac, a2c2)). lemma(1197, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(iab1, []):i(ab, a1b1)). lemma(1198, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(iab2, []):i(ab, a2b2)). lemma(1199, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(b2, a1c1), [i(b2, a1c1)]):p(b2, b2)). lemma(1200, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(c2, a1b1), [i(c2, a1b1)]):p(c2, c2)). lemma(1201, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(c1, a2b2), [i(c1, a2b2)]):p(c1, c1)). lemma(1202, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(a1, a1b1), [1172]):p(a1, a1)). lemma(1203, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(b1, a1b1), [1173]):p(b1, b1)). lemma(1204, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(a2, a2b2), [1174]):p(a2, a2)). lemma(1205, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(o, oa), [1184]):p(o, o)). lemma(1206, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(bc, b1c1), [1193]):p(bc, bc)). lemma(1207, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(ac, a1c1), [1195]):p(ac, ac)). lemma(1208, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pref(ab, a1b1), [1197]):p(ab, ab)). lemma(1209, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lref(b2, a1c1), [i(b2, a1c1)]):l(a1c1, a1c1)). lemma(1210, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lref(c2, a1b1), [i(c2, a1b1)]):l(a1b1, a1b1)). lemma(1211, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lref(c1, a2b2), [i(c1, a2b2)]):l(a2b2, a2b2)). lemma(1212, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lref(a2, a2c2), [1178]):l(a2c2, a2c2)). lemma(1213, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lref(c1, b1c1), [1180]):l(b1c1, b1c1)). lemma(1214, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lref(c2, b2c2), [1182]):l(b2c2, b2c2)). lemma(1215, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lref(o, oa), [1184]):l(oa, oa)). lemma(1216, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lref(o, ob), [1185]):l(ob, ob)). lemma(1217, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lref(o, oc), [1186]):l(oc, oc)). lemma(1218, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(b2, c1, a1c1, a2b2), [i(b2, a1c1), 1175, 1177, i(c1, a2b2)]): (p(b2, c1);l(a1c1, a2b2))). lemma(1219, [p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(b2, c1), [p(b2, c1)]):p(c1, b2)). lemma(1220, [p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(b2, c1, b1c1), [p(b2, c1), 1180]):i(b2, b1c1)). lemma(1221, [p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(b2, c1, oc), [p(b2, c1), 1191]):i(b2, oc)). lemma(1222, [p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(c1, b2, b2c2), [1219, 1183]):i(c1, b2c2)). lemma(1223, [p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(c1, b2, ob), [1219, 1190]):i(c1, ob)). lemma(1224, [p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(c1, bc, b1c1, b2c2), [1180, 1222, 1193, 1194]): (p(c1, bc);l(b1c1, b2c2))). lemma(1225, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(c1, bc), [p(c1, bc)]):p(bc, c1)). lemma(1226, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(b2, c1, bc), [p(b2, c1), p(c1, bc)]):p(b2, bc)). lemma(1227, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(b2, bc), [1226]):p(bc, b2)). lemma(1228, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(bc, c1, a2b2), [1225, i(c1, a2b2)]):i(bc, a2b2)). lemma(1229, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(bc, c1, a1c1), [1225, 1177]):i(bc, a1c1)). lemma(1230, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(bc, c1, oc), [1225, 1191]):i(bc, oc)). lemma(1231, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(bc, c1, ob), [1225, 1223]):i(bc, ob)). lemma(1232, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(c1, b1, b1c1, ob), [1180, 1223, 1181, 1189]): (p(c1, b1);l(b1c1, ob))). lemma(1233, [p(c1, b1), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(c1, b1), [p(c1, b1)]):p(b1, c1)). lemma(1234, [p(c1, b1), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(b2, c1, b1), [p(b2, c1), p(c1, b1)]):p(b2, b1)). lemma(1235, [p(c1, b1), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(notbb, [1234]):false). lemma(1236, [p(c1, b1), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1235]):goal). lemma(1237, [l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(b1c1, ob), [l(b1c1, ob)]):l(ob, b1c1)). lemma(1238, [l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(o, ob, b1c1), [1185, 1237]):i(o, b1c1)). lemma(1239, [l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(c1, o, b1c1, oc), [1180, 1191, 1238, 1186]): (p(c1, o);l(b1c1, oc))). lemma(1240, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(c1, o), [p(c1, o)]):p(o, c1)). lemma(1241, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(b2, c1, o), [p(b2, c1), p(c1, o)]):p(b2, o)). lemma(1242, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(b2, o), [1241]):p(o, b2)). lemma(1243, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(bc, c1, o), [1225, p(c1, o)]):p(bc, o)). lemma(1244, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(bc, o), [1243]):p(o, bc)). lemma(1245, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(c1, o, oa), [p(c1, o), 1184]):i(c1, oa)). lemma(1246, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(b2, c1, oa), [p(b2, c1), 1245]):i(b2, oa)). lemma(1247, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(bc, c1, oa), [1225, 1245]):i(bc, oa)). lemma(1248, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(o, c1, a2b2), [1240, i(c1, a2b2)]):i(o, a2b2)). lemma(1249, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(o, c1, a1c1), [1240, 1177]):i(o, a1c1)). lemma(1250, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(o, c1, b2c2), [1240, 1222]):i(o, b2c2)). lemma(1251, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(b2, a1, a1c1, oa), [i(b2, a1c1), 1246, 1176, 1187]): (p(b2, a1);l(a1c1, oa))). lemma(1252, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(b2, a1), [p(b2, a1)]):p(a1, b2)). lemma(1253, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(c1, b2, a1), [1219, p(b2, a1)]):p(c1, a1)). lemma(1254, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(c1, a1), [1253]):p(a1, c1)). lemma(1255, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(bc, c1, a1), [1225, 1253]):p(bc, a1)). lemma(1256, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(bc, a1), [1255]):p(a1, bc)). lemma(1257, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(o, c1, a1), [1240, 1253]):p(o, a1)). lemma(1258, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(o, a1), [1257]):p(a1, o)). lemma(1259, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(b2, a1, a1b1), [p(b2, a1), 1172]):i(b2, a1b1)). lemma(1260, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(c1, b2, a1b1), [1219, 1259]):i(c1, a1b1)). lemma(1261, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(triangle1(a1b1), [1172, 1173, 1260]):false). lemma(1262, [p(b2, a1), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1261]):goal). lemma(1263, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a1c1, oa), [l(a1c1, oa)]):l(oa, a1c1)). lemma(1264, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(a2, oa, a1c1), [1188, 1263]):i(a2, a1c1)). lemma(1265, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(ac, a1c1, oa), [1195, l(a1c1, oa)]):i(ac, oa)). lemma(1266, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(b2, a2, a1c1, a2b2), [i(b2, a1c1), 1175, 1264, 1174]): (p(b2, a2);l(a1c1, a2b2))). lemma(1267, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(b2, a2), [p(b2, a2)]):p(a2, b2)). lemma(1268, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(c1, b2, a2), [1219, p(b2, a2)]):p(c1, a2)). lemma(1269, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(c1, a2), [1268]):p(a2, c1)). lemma(1270, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(bc, c1, a2), [1225, 1268]):p(bc, a2)). lemma(1271, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(bc, a2), [1270]):p(a2, bc)). lemma(1272, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(o, c1, a2), [1240, 1268]):p(o, a2)). lemma(1273, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(o, a2), [1272]):p(a2, o)). lemma(1274, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(b2, a2, a2c2), [p(b2, a2), 1178]):i(b2, a2c2)). lemma(1275, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(triangle2(a2c2), [1178, 1274, 1179]):false). lemma(1276, [p(b2, a2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1275]):goal). lemma(1277, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a1c1, a2b2), [l(a1c1, a2b2)]):l(a2b2, a1c1)). lemma(1278, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(oa, a1c1, a2b2), [1263, l(a1c1, a2b2)]):l(oa, a2b2)). lemma(1279, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(oa, a2b2), [1278]):l(a2b2, oa)). lemma(1280, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(a1, a1c1, a2b2), [1176, l(a1c1, a2b2)]):i(a1, a2b2)). lemma(1281, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(ac, a1c1, a2b2), [1195, l(a1c1, a2b2)]):i(ac, a2b2)). lemma(1282, [l(a1c1, a2b2), l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(goal_normal(a2b2), [1211, 1228, 1281, 1198]):goal). lemma(1283, [l(a1c1, oa), p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1266), [1276, 1282]):goal). lemma(1284, [p(c1, o), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1251), [1262, 1283]):goal). lemma(1285, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(b1c1, oc), [l(b1c1, oc)]):l(oc, b1c1)). lemma(1286, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(ob, b1c1, oc), [1237, l(b1c1, oc)]):l(ob, oc)). lemma(1287, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(ob, oc), [1286]):l(oc, ob)). lemma(1288, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(b1, b1c1, oc), [1181, l(b1c1, oc)]):i(b1, oc)). lemma(1289, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(c2, oc, b1c1), [1192, 1285]):i(c2, b1c1)). lemma(1290, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(c2, oc, ob), [1192, 1287]):i(c2, ob)). lemma(1291, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(c2, b1, a1b1, oc), [i(c2, a1b1), 1192, 1173, 1288]): (p(c2, b1);l(a1b1, oc))). lemma(1292, [p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(c2, b1), [p(c2, b1)]):p(b1, c2)). lemma(1293, [p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(b1, c2, a2c2), [1292, 1179]):i(b1, a2c2)). lemma(1294, [p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(b1, c2, b2c2), [1292, 1182]):i(b1, b2c2)). lemma(1295, [p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(c1, b1, b1c1, b2c2), [1180, 1222, 1181, 1294]): (p(c1, b1);l(b1c1, b2c2))). lemma(1296, [p(c1, b1), p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(c1, b1), [p(c1, b1)]):p(b1, c1)). lemma(1297, [p(c1, b1), p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(b2, c1, b1), [p(b2, c1), p(c1, b1)]):p(b2, b1)). lemma(1298, [p(c1, b1), p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(notbb, [1297]):false). lemma(1299, [p(c1, b1), p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1298]):goal). lemma(1300, [l(b1c1, b2c2), p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(notbc, [l(b1c1, b2c2)]):false). lemma(1301, [l(b1c1, b2c2), p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1300]):goal). lemma(1302, [p(c2, b1), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1295), [1299, 1301]):goal). lemma(1303, [l(a1b1, oc), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a1b1, oc), [l(a1b1, oc)]):l(oc, a1b1)). lemma(1304, [l(a1b1, oc), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(b1c1, oc, a1b1), [l(b1c1, oc), 1303]):l(b1c1, a1b1)). lemma(1305, [l(a1b1, oc), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(b1c1, a1b1), [1304]):l(a1b1, b1c1)). lemma(1306, [l(a1b1, oc), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(ob, b1c1, a1b1), [1237, 1304]):l(ob, a1b1)). lemma(1307, [l(a1b1, oc), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(ob, a1b1), [1306]):l(a1b1, ob)). lemma(1308, [l(a1b1, oc), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(a1, a1b1, oc), [1172, l(a1b1, oc)]):i(a1, oc)). lemma(1309, [l(a1b1, oc), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(triangle1(oc), [1308, 1288, 1191]):false). lemma(1310, [l(a1b1, oc), l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1309]):goal). lemma(1311, [l(b1c1, oc), l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1291), [1302, 1310]):goal). lemma(1312, [l(b1c1, ob), p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1239), [1284, 1311]):goal). lemma(1313, [p(c1, bc), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1232), [1236, 1312]):goal). lemma(1314, [l(b1c1, b2c2), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(notbc, [l(b1c1, b2c2)]):false). lemma(1315, [l(b1c1, b2c2), p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1314]):goal). lemma(1316, [p(b2, c1), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1224), [1313, 1315]):goal). lemma(1317, [l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a1c1, a2b2), [l(a1c1, a2b2)]):l(a2b2, a1c1)). lemma(1318, [l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(a2, a2b2, a1c1), [1174, 1317]):i(a2, a1c1)). lemma(1319, [l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(a1, a1c1, a2b2), [1176, l(a1c1, a2b2)]):i(a1, a2b2)). lemma(1320, [l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(ac, a1c1, a2b2), [1195, l(a1c1, a2b2)]):i(ac, a2b2)). lemma(1321, [l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(ab, a2b2, a1c1), [1198, 1317]):i(ab, a1c1)). lemma(1322, [l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(a1, ab, a1b1, a1c1), [1172, 1176, 1197, 1321]): (p(a1, ab);l(a1b1, a1c1))). lemma(1323, [p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(a1, ab), [p(a1, ab)]):p(ab, a1)). lemma(1324, [p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(ab, a1, oa), [1323, 1187]):i(ab, oa)). lemma(1325, [p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(a2, ac, a2b2, a2c2), [1174, 1178, 1320, 1196]): (p(a2, ac);l(a2b2, a2c2))). lemma(1326, [p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(a2, ac), [p(a2, ac)]):p(ac, a2)). lemma(1327, [p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(ac, a2, oa), [1326, 1188]):i(ac, oa)). lemma(1328, [p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(a2, ab, a2b2, oa), [1174, 1188, 1198, 1324]): (p(a2, ab);l(a2b2, oa))). lemma(1329, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(a2, ab), [p(a2, ab)]):p(ab, a2)). lemma(1330, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(a1, ab, a2), [p(a1, ab), 1329]):p(a1, a2)). lemma(1331, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(a1, a2), [1330]):p(a2, a1)). lemma(1332, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(notaa, [1331]):false). lemma(1333, [p(a2, ab), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1332]):goal). lemma(1334, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a2b2, oa), [l(a2b2, oa)]):l(oa, a2b2)). lemma(1335, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(a1c1, a2b2, oa), [l(a1c1, a2b2), l(a2b2, oa)]):l(a1c1, oa)). lemma(1336, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a1c1, oa), [1335]):l(oa, a1c1)). lemma(1337, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(b2, a1c1, oa), [i(b2, a1c1), 1335]):i(b2, oa)). lemma(1338, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(c1, a2b2, oa), [i(c1, a2b2), l(a2b2, oa)]):i(c1, oa)). lemma(1339, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(o, oa, a2b2), [1184, 1334]):i(o, a2b2)). lemma(1340, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(o, oa, a1c1), [1184, 1336]):i(o, a1c1)). lemma(1341, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(b2, o, a1c1, ob), [i(b2, a1c1), 1190, 1340, 1185]): (p(b2, o);l(a1c1, ob))). lemma(1342, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(b2, o), [p(b2, o)]):p(o, b2)). lemma(1343, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(b2, o, oc), [p(b2, o), 1186]):i(b2, oc)). lemma(1344, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(o, b2, b2c2), [1342, 1183]):i(o, b2c2)). lemma(1345, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(b2, c1, a1c1, oc), [i(b2, a1c1), 1343, 1177, 1191]): (p(b2, c1);l(a1c1, oc))). lemma(1346, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(b2, c1), [p(b2, c1)]):p(c1, b2)). lemma(1347, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(o, b2, c1), [1342, p(b2, c1)]):p(o, c1)). lemma(1348, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(o, c1), [1347]):p(c1, o)). lemma(1349, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(b2, c1, b1c1), [p(b2, c1), 1180]):i(b2, b1c1)). lemma(1350, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(o, b2, b1c1), [1342, 1349]):i(o, b1c1)). lemma(1351, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(c1, b2, b2c2), [1346, 1183]):i(c1, b2c2)). lemma(1352, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(c1, b2, ob), [1346, 1190]):i(c1, ob)). lemma(1353, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(unique(c1, bc, b1c1, b2c2), [1180, 1351, 1193, 1194]): (p(c1, bc);l(b1c1, b2c2))). lemma(1354, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(c1, bc), [p(c1, bc)]):p(bc, c1)). lemma(1355, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(b2, c1, bc), [p(b2, c1), p(c1, bc)]):p(b2, bc)). lemma(1356, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(b2, bc), [1355]):p(bc, b2)). lemma(1357, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ptra(o, b2, bc), [1342, 1355]):p(o, bc)). lemma(1358, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(psym(o, bc), [1357]):p(bc, o)). lemma(1359, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(bc, c1, a2b2), [1354, i(c1, a2b2)]):i(bc, a2b2)). lemma(1360, [p(c1, bc), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(goal_normal(a2b2), [1211, 1359, 1320, 1198]):goal). lemma(1361, [l(b1c1, b2c2), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(notbc, [l(b1c1, b2c2)]):false). lemma(1362, [l(b1c1, b2c2), p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1361]):goal). lemma(1363, [p(b2, c1), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1353), [1360, 1362]):goal). lemma(1364, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a1c1, oc), [l(a1c1, oc)]):l(oc, a1c1)). lemma(1365, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(a2b2, a1c1, oc), [1317, l(a1c1, oc)]):l(a2b2, oc)). lemma(1366, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a2b2, oc), [1365]):l(oc, a2b2)). lemma(1367, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(oa, a2b2, oc), [1334, 1365]):l(oa, oc)). lemma(1368, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(oa, oc), [1367]):l(oc, oa)). lemma(1369, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(a2, a2b2, oc), [1174, 1365]):i(a2, oc)). lemma(1370, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(triangle2(oc), [1369, 1343, 1192]):false). lemma(1371, [l(a1c1, oc), p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1370]):goal). lemma(1372, [p(b2, o), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1345), [1363, 1371]):goal). lemma(1373, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a1c1, ob), [l(a1c1, ob)]):l(ob, a1c1)). lemma(1374, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(a2b2, a1c1, ob), [1317, l(a1c1, ob)]):l(a2b2, ob)). lemma(1375, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a2b2, ob), [1374]):l(ob, a2b2)). lemma(1376, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(oa, a2b2, ob), [1334, 1374]):l(oa, ob)). lemma(1377, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(oa, ob), [1376]):l(ob, oa)). lemma(1378, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(c1, a2b2, ob), [i(c1, a2b2), 1374]):i(c1, ob)). lemma(1379, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(a2, a2b2, ob), [1174, 1374]):i(a2, ob)). lemma(1380, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(pcon(ac, a2, ob), [1326, 1379]):i(ac, ob)). lemma(1381, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lcon(a1, a1c1, ob), [1176, l(a1c1, ob)]):i(a1, ob)). lemma(1382, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(triangle1(ob), [1381, 1189, 1378]):false). lemma(1383, [l(a1c1, ob), l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1382]):goal). lemma(1384, [l(a2b2, oa), p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1341), [1372, 1383]):goal). lemma(1385, [p(a2, ac), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1328), [1333, 1384]):goal). lemma(1386, [l(a2b2, a2c2), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a2b2, a2c2), [l(a2b2, a2c2)]):l(a2c2, a2b2)). lemma(1387, [l(a2b2, a2c2), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(a1c1, a2b2, a2c2), [l(a1c1, a2b2), l(a2b2, a2c2)]):l(a1c1, a2c2)). lemma(1388, [l(a2b2, a2c2), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(notac, [1387]):false). lemma(1389, [l(a2b2, a2c2), p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1388]):goal). lemma(1390, [p(a1, ab), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1325), [1385, 1389]):goal). lemma(1391, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a1b1, a1c1), [l(a1b1, a1c1)]):l(a1c1, a1b1)). lemma(1392, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(ltra(a2b2, a1c1, a1b1), [1317, 1391]):l(a2b2, a1b1)). lemma(1393, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(lsym(a2b2, a1b1), [1392]):l(a1b1, a2b2)). lemma(1394, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(notab, [1393]):false). lemma(1395, [l(a1b1, a1c1), l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(false_ind(goal), [1394]):goal). lemma(1396, [l(a1c1, a2b2), i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1322), [1390, 1395]):goal). lemma(1397, [i(c1, a2b2), i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1218), [1316, 1396]):goal). lemma(1398, [i(a2, b1c1), i(c2, a1b1), i(b2, a1c1)], ap(t2in1, [i(a2, b1c1), i(b2, a1c1), i(c2, a1b1)]):goal). lemma(1399, [i(c2, a1b1), i(b2, a1c1)], ap(or_elim(1171), [1397, 1398]):goal). lemma(1400, [i(b2, a1c1)], ap(or_elim(710), [1170, 1399]):goal). lemma(1401, [], ap(or_elim(1), [709, 1400]):goal). 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