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val it : (string * thm) list = [("0 ", |- ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) ==> a /\ b /\ c); ("00 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- a /\ b /\ c); ("000 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- a); ("0000 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c), ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- a); ("00000 ", ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c), (b = c) ==> a /\ b /\ c |- a); ("000000 ", ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c), (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c |- a); ("0000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- a); ("00000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c = a); ("000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c ==> a); ("0000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a); ("00000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a = b); ("000000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a ==> b); ("0000000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- b); ("00000000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c = a); ("000000000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c ==> a); ("0000000000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("000000000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a ==> c); ("0000000000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c); ("00000000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, a /\ b /\ c |- b); ("000000000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, b /\ c |- b); ("0000000000000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, b |- b); ("000000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- b ==> a); ("0000000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- a); ("00000000000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b = c); ("000000000001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b ==> c); ("0000000000010000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- c); ("000000000001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- c ==> b); ("0000000000010010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b); ("00000000000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b, a /\ b /\ c |- a); ("000000000001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b, a |- a); ("00000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a /\ b /\ c |- a); ("000000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- a ==> c); ("0000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- c); ("00000000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- b = c); ("000000001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- b ==> c); ("0000000010000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- c); ("00000000100000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a = b); ("000000001000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a ==> b); ("0000000010000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- b); ("000000001000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- b ==> a); ("0000000010000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a); ("00000000100001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, a /\ b /\ c |- c); ("000000001000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, b /\ c |- c); ("0000000010000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, c |- c); ("000000001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- c ==> b); ("0000000010010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- b); ("00000000100100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c = a); ("000000001001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c ==> a); ("0000000010010000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- a); ("000000001001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- a ==> c); ("0000000010010010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("00000000100101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, a /\ b /\ c |- b); ("000000001001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, b /\ c |- b); ("0000000010010100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, b |- b); ("00000000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, a /\ b /\ c |- c); ("000000001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b /\ c |- c); ("0000000010100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("00000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a /\ b /\ c |- a); ("000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- a); ("001 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- b /\ c); ("0010 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- b); ("00100 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c), ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- b); ("001000 ", ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c), (b = c) ==> a /\ b /\ c |- b); ("0010000 ", ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c), (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c |- b); ("00100000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- b); ("001000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c = a); ("0010000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c ==> a); ("00100000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a); ("001000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a = b); ("0010000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a ==> b); ("00100000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- b); ("001000000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c = a); ("0010000000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c ==> a); ("00100000000000000", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("0010000000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a ==> c); ("00100000000000010", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c); ("001000000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, a /\ b /\ c |- b); ("0010000000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, b /\ c |- b); ("00100000000000100", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, b |- b); ("0010000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- b ==> a); ("00100000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- a); ("001000000000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b = c); ("0010000000001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b ==> c); ("00100000000010000", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- c); ("0010000000001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- c ==> b); ("00100000000010010", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b); ("001000000000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b, a /\ b /\ c |- a); ("0010000000001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b, a |- a); ("001000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a /\ b /\ c |- a); ("0010000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("0010000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- a ==> c); ("00100000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- c); ("001000000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- b = c); ("0010000001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- b ==> c); ("00100000010000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- c); ("001000000100000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a = b); ("0010000001000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a ==> b); ("00100000010000000", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- b); ("0010000001000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- b ==> a); ("00100000010000010", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a); ("001000000100001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, a /\ b /\ c |- c); ("0010000001000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, b /\ c |- c); ("00100000010000100", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, c |- c); ("0010000001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- c ==> b); ("00100000010010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- b); ("001000000100100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c = a); ("0010000001001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c ==> a); ("00100000010010000", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- a); ("0010000001001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- a ==> c); ("00100000010010010", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("001000000100101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, a /\ b /\ c |- b); ("0010000001001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, b /\ c |- b); ("00100000010010100", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, b |- b); ("001000000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, a /\ b /\ c |- c); ("0010000001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b /\ c |- c); ("00100000010100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("001000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a /\ b /\ c |- b); ("0010000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, b /\ c |- b); ("00100000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, b |- b); ("0011 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- c); ("00110 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c), ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- c); ("001100 ", ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c), (b = c) ==> a /\ b /\ c |- c); ("0011000 ", ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c), (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c |- c); ("00110000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c); ("001100000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c = a); ("0011000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c ==> a); ("00110000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a); ("001100000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a = b); ("0011000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a ==> b); ("00110000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- b); ("001100000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c = a); ("0011000000000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c ==> a); ("00110000000000000", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("0011000000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a ==> c); ("00110000000000010", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c); ("001100000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, a /\ b /\ c |- b); ("0011000000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, b /\ c |- b); ("00110000000000100", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, b |- b); ("0011000000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- b ==> a); ("00110000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- a); ("001100000000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b = c); ("0011000000001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b ==> c); ("00110000000010000", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- c); ("0011000000001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- c ==> b); ("00110000000010010", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b); ("001100000000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b, a /\ b /\ c |- a); ("0011000000001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b, a |- a); ("001100000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a /\ b /\ c |- a); ("0011000000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("0011000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- a ==> c); ("00110000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- c); ("001100000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- b = c); ("0011000001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- b ==> c); ("00110000010000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- c); ("001100000100000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a = b); ("0011000001000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a ==> b); ("00110000010000000", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- b); ("0011000001000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- b ==> a); ("00110000010000010", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a); ("001100000100001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, a /\ b /\ c |- c); ("0011000001000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, b /\ c |- c); ("00110000010000100", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, c |- c); ("0011000001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- c ==> b); ("00110000010010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- b); ("001100000100100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c = a); ("0011000001001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c ==> a); ("00110000010010000", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- a); ("0011000001001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- a ==> c); ("00110000010010010", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("001100000100101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, a /\ b /\ c |- b); ("0011000001001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, b /\ c |- b); ("00110000010010100", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, b |- b); ("001100000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, a /\ b /\ c |- c); ("0011000001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b /\ c |- c); ("00110000010100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("001100001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a /\ b /\ c |- c); ("0011000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, b /\ c |- c); ("00110000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- c)] (* filtering safe linear steps *) val it : (string * thm) list = [("0 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- a /\ b /\ c); ("00 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- a); ("000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c = a); ("0000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a); ("00000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a = b); ("000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- b); ("0000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c = a); ("00000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("00000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c); ("0000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, b |- b); ("000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- a); ("0000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b = c); ("00000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- c); ("00000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b); ("0000011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b, a |- a); ("00001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("0001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- c); ("00010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- b = c); ("000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- c); ("0001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a = b); ("00010000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- b); ("00010001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a); ("0001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, c |- c); ("000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- b); ("0001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c = a); ("00010100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- a); ("00010101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("0001011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, b |- b); ("00011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- a); ("01 ", ((b = c) ==> a /\ b /\ c) /\ ((c = a) ==> a /\ b /\ c) /\ ((a = b) ==> a /\ b /\ c) |- b /\ c); ("010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- b); ("0100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c = a); ("01000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a); ("010000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a = b); ("0100000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- b); ("01000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c = a); ("010000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("010000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c); ("01000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, b |- b); ("0100001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- a); ("01000010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b = c); ("010000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- c); ("010000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b); ("01000011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b, a |- a); ("010001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("01001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- c); ("010010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- b = c); ("0100100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- c); ("01001000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a = b); ("010010000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- b); ("010010001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a); ("01001001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, c |- c); ("0100101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- b); ("01001010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c = a); ("010010100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- a); ("010010101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("01001011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, b |- b); ("010011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("0101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, b |- b); ("011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c); ("0110 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c |- c = a); ("01100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a); ("011000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- a = b); ("0110000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- b); ("01100000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c = a); ("011000000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("011000001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- c); ("01100001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a, b |- b); ("0110001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- a); ("01100010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b = c); ("011000100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- c); ("011000101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b |- b); ("01100011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, b, a |- a); ("011001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c, a |- a); ("01101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- c); ("011010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a |- b = c); ("0110100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- c); ("01101000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a = b); ("011010000 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- b); ("011010001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b |- a); ("01101001 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, b, c |- c); ("0110101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- b); ("01101010 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c = a); ("011010100 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- a); ("011010101 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("01101011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c, b |- b); ("011011 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, a, c |- c); ("0111 ", (b = c) ==> a /\ b /\ c, (a = b) ==> a /\ b /\ c, (c = a) ==> a /\ b /\ c, c |- c)]