TSTP Solution File: GRP440-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP440-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:15:00 EDT 2023
% Result : Unsatisfiable 14.44s 14.79s
% Output : CNFRefutation 14.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : GRP440-1 : TPTP v8.1.2. Released v2.6.0.
% 0.03/0.15 % Command : toma --casc %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 21:15:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 14.44/14.79 % SZS status Unsatisfiable
% 14.44/14.79 % SZS output start Proof
% 14.44/14.79 original problem:
% 14.44/14.79 axioms:
% 14.44/14.79 inverse(multiply(A, multiply(B, multiply(multiply(inverse(B), C), inverse(multiply(D, multiply(A, C))))))) = D
% 14.44/14.79 goal:
% 14.44/14.79 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 14.44/14.79 To show the unsatisfiability of the original goal,
% 14.44/14.79 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 14.44/14.79 Here is an equational proof:
% 14.44/14.79 0: inverse(multiply(X0, multiply(X1, multiply(multiply(inverse(X1), X2), inverse(multiply(X3, multiply(X0, X2))))))) = X3.
% 14.44/14.79 Proof: Axiom.
% 14.44/14.79
% 14.44/14.79 1: X4 = inverse(multiply(X5, multiply(X1, multiply(multiply(inverse(X1), multiply(multiply(inverse(X5), X6), inverse(multiply(X7, multiply(X4, X6))))), X7)))).
% 14.44/14.79 Proof: A critical pair between equations 0 and 0.
% 14.44/14.79
% 14.44/14.79 2: X3 = inverse(multiply(X0, multiply(multiply(X4, multiply(X5, multiply(multiply(inverse(X5), X6), inverse(multiply(X7, multiply(X4, X6)))))), multiply(multiply(X7, X2), inverse(multiply(X3, multiply(X0, X2))))))).
% 14.44/14.79 Proof: A critical pair between equations 0 and 0.
% 14.44/14.79
% 14.44/14.79 3: X9 = inverse(multiply(X5, multiply(X1, multiply(multiply(inverse(X1), multiply(multiply(inverse(X5), multiply(multiply(inverse(X9), X10), inverse(multiply(X11, multiply(X8, X10))))), X11)), X8)))).
% 14.44/14.79 Proof: A critical pair between equations 1 and 0.
% 14.44/14.79
% 14.44/14.79 10: multiply(X9, multiply(X10, multiply(multiply(inverse(X10), X11), inverse(multiply(X12, multiply(X9, X11)))))) = inverse(multiply(X5, multiply(X1, multiply(multiply(inverse(X1), multiply(multiply(inverse(X5), multiply(multiply(X12, X13), inverse(multiply(X14, multiply(X8, X13))))), X14)), X8)))).
% 14.44/14.79 Proof: A critical pair between equations 1 and 2.
% 14.44/14.79
% 14.44/14.79 15: X9 = multiply(X9, multiply(X10, multiply(multiply(inverse(X10), X11), inverse(multiply(inverse(X9), multiply(X9, X11)))))).
% 14.44/14.79 Proof: Rewrite equation 3,
% 14.44/14.79 lhs with equations []
% 14.44/14.79 rhs with equations [10].
% 14.44/14.79
% 14.44/14.79 18: inverse(multiply(X5, multiply(X1, multiply(multiply(inverse(X1), multiply(multiply(inverse(X5), multiply(multiply(inverse(X15), X13), inverse(multiply(X14, multiply(X8, X13))))), X14)), X8)))) = X15.
% 14.44/14.79 Proof: A critical pair between equations 10 and 15.
% 14.44/14.79
% 14.44/14.79 22: X3 = inverse(multiply(X12, multiply(X1, multiply(multiply(inverse(X1), multiply(X13, multiply(multiply(inverse(X13), X14), inverse(multiply(inverse(X12), multiply(X12, X14)))))), inverse(multiply(X3, X12)))))).
% 14.44/14.79 Proof: A critical pair between equations 0 and 15.
% 14.44/14.79
% 14.44/14.79 26: X3 = inverse(multiply(X0, multiply(X1, multiply(inverse(X1), inverse(multiply(X3, multiply(X0, multiply(X13, multiply(multiply(inverse(X13), X14), inverse(multiply(inverse(inverse(X1)), multiply(inverse(X1), X14)))))))))))).
% 14.44/14.79 Proof: A critical pair between equations 0 and 15.
% 14.44/14.79
% 14.44/14.79 28: X3 = inverse(multiply(inverse(X1), multiply(X1, multiply(inverse(X1), inverse(multiply(X3, inverse(X1))))))).
% 14.44/14.79 Proof: A critical pair between equations 26 and 15.
% 14.44/14.79
% 14.44/14.79 29: multiply(X9, multiply(X10, multiply(multiply(inverse(X10), X11), inverse(multiply(inverse(X18), multiply(X9, X11)))))) = X18.
% 14.44/14.79 Proof: A critical pair between equations 10 and 18.
% 14.44/14.79
% 14.44/14.79 35: X3 = inverse(multiply(X16, multiply(X1, multiply(multiply(inverse(X1), multiply(X13, multiply(multiply(inverse(X13), multiply(multiply(inverse(X16), X17), inverse(multiply(X18, multiply(inverse(X16), X17))))), X18))), inverse(multiply(X3, X16)))))).
% 14.44/14.79 Proof: A critical pair between equations 22 and 0.
% 14.44/14.79
% 14.44/14.79 51: X18 = multiply(X19, multiply(X10, multiply(multiply(inverse(X10), multiply(X20, multiply(multiply(inverse(X20), X21), inverse(multiply(inverse(X22), multiply(X19, X21)))))), inverse(multiply(inverse(X18), X22))))).
% 14.44/14.79 Proof: A critical pair between equations 29 and 29.
% 14.44/14.79
% 14.44/14.79 52: X18 = multiply(inverse(X10), multiply(X10, multiply(X26, inverse(multiply(inverse(X18), X26))))).
% 14.44/14.79 Proof: A critical pair between equations 51 and 29.
% 14.44/14.79
% 14.44/14.79 56: X3 = inverse(multiply(X0, multiply(X1, multiply(X22, inverse(multiply(X3, multiply(X0, multiply(X20, multiply(multiply(inverse(X20), X21), inverse(multiply(inverse(X22), multiply(inverse(X1), X21)))))))))))).
% 14.44/14.79 Proof: A critical pair between equations 0 and 29.
% 14.44/14.79
% 14.44/14.79 61: X18 = multiply(X23, multiply(X10, multiply(multiply(inverse(X10), multiply(X20, multiply(multiply(inverse(X20), multiply(inverse(X23), inverse(multiply(X24, inverse(X23))))), X24))), inverse(multiply(inverse(X18), X23))))).
% 14.44/14.79 Proof: A critical pair between equations 51 and 28.
% 14.44/14.79
% 14.44/14.79 64: X3 = inverse(multiply(inverse(X27), multiply(X27, multiply(X29, inverse(multiply(X3, X29)))))).
% 14.44/14.79 Proof: A critical pair between equations 56 and 52.
% 14.44/14.79
% 14.44/14.79 65: X27 = multiply(inverse(X10), multiply(X10, multiply(multiply(X27, multiply(X28, inverse(multiply(inverse(X29), X28)))), inverse(X29)))).
% 14.44/14.79 Proof: A critical pair between equations 52 and 52.
% 14.44/14.79
% 14.44/14.79 67: X27 = multiply(X27, multiply(X10, multiply(multiply(inverse(X10), multiply(X28, inverse(multiply(inverse(X29), X28)))), inverse(X29)))).
% 14.44/14.79 Proof: A critical pair between equations 29 and 52.
% 14.44/14.79
% 14.44/14.79 76: X3 = inverse(multiply(X16, multiply(X1, multiply(inverse(X1), inverse(multiply(X3, X16)))))).
% 14.44/14.79 Proof: A critical pair between equations 35 and 67.
% 14.44/14.79
% 14.44/14.79 78: X18 = multiply(X23, multiply(X10, multiply(inverse(X10), inverse(multiply(inverse(X18), X23))))).
% 14.44/14.79 Proof: A critical pair between equations 61 and 67.
% 14.44/14.79
% 14.44/14.79 80: X30 = multiply(inverse(X10), multiply(X10, multiply(multiply(X30, multiply(X31, inverse(multiply(X32, X31)))), X32))).
% 14.44/14.79 Proof: A critical pair between equations 52 and 64.
% 14.44/14.79
% 14.44/14.79 83: X27 = multiply(X27, multiply(X10, multiply(multiply(inverse(X10), multiply(multiply(X30, multiply(X31, inverse(multiply(X32, X31)))), X32)), inverse(X30)))).
% 14.44/14.79 Proof: A critical pair between equations 67 and 64.
% 14.44/14.79
% 14.44/14.79 85: X27 = multiply(inverse(X10), multiply(X10, multiply(multiply(X27, multiply(multiply(X30, multiply(X31, inverse(multiply(X32, X31)))), X32)), inverse(X30)))).
% 14.44/14.79 Proof: A critical pair between equations 65 and 64.
% 14.44/14.79
% 14.44/14.79 94: X18 = multiply(X20, multiply(X10, multiply(multiply(inverse(X10), multiply(inverse(X20), inverse(multiply(X21, inverse(X18))))), X21))).
% 14.44/14.79 Proof: A critical pair between equations 29 and 76.
% 14.44/14.79
% 14.44/14.79 96: X30 = inverse(multiply(inverse(X27), multiply(X27, multiply(multiply(X31, multiply(inverse(X31), inverse(multiply(X32, X30)))), X32)))).
% 14.44/14.79 Proof: A critical pair between equations 64 and 76.
% 14.44/14.79
% 14.44/14.79 98: X30 = multiply(inverse(inverse(multiply(X30, multiply(X31, inverse(multiply(multiply(X34, inverse(multiply(inverse(X35), X34))), X31)))))), X35).
% 14.44/14.79 Proof: A critical pair between equations 80 and 52.
% 14.44/14.79
% 14.44/14.79 108: X33 = multiply(X33, multiply(X10, multiply(multiply(inverse(X10), multiply(multiply(X34, multiply(inverse(X34), inverse(multiply(X35, X36)))), X35)), X36))).
% 14.44/14.79 Proof: A critical pair between equations 29 and 96.
% 14.44/14.79
% 14.44/14.79 115: X33 = multiply(X33, multiply(multiply(X34, multiply(inverse(X34), inverse(multiply(multiply(X38, inverse(multiply(inverse(X39), X38))), X36)))), multiply(X39, X36))).
% 14.44/14.79 Proof: A critical pair between equations 108 and 52.
% 14.44/14.79
% 14.44/14.79 117: X27 = multiply(X27, multiply(multiply(X30, multiply(X31, inverse(multiply(multiply(X34, inverse(multiply(inverse(X35), X34))), X31)))), multiply(X35, inverse(X30)))).
% 14.44/14.79 Proof: A critical pair between equations 83 and 52.
% 14.44/14.79
% 14.44/14.79 124: multiply(inverse(X43), X43) = multiply(inverse(X40), X40).
% 14.44/14.79 Proof: A critical pair between equations 94 and 115.
% 14.44/14.79
% 14.44/14.79 125: inverse(multiply(inverse(X40), X40)) = inverse(multiply(inverse(X36), X36)).
% 14.44/14.79 Proof: A critical pair between equations 96 and 117.
% 14.44/14.79
% 14.44/14.79 126: X27 = multiply(X27, multiply(X10, multiply(inverse(X10), inverse(multiply(inverse(X40), X40))))).
% 14.44/14.79 Proof: A critical pair between equations 83 and 117.
% 14.44/14.79
% 14.44/14.79 127: X36 = multiply(inverse(X10), multiply(X10, multiply(X36, inverse(multiply(inverse(X40), X40))))).
% 14.44/14.79 Proof: A critical pair between equations 85 and 117.
% 14.44/14.79
% 14.44/14.79 137: X27 = multiply(X27, multiply(inverse(multiply(inverse(X40), X40)), multiply(inverse(X45), X45))).
% 14.44/14.79 Proof: A critical pair between equations 126 and 124.
% 14.44/14.79
% 14.44/14.79 139: X18 = multiply(X23, multiply(inverse(multiply(inverse(X18), X23)), multiply(inverse(X45), X45))).
% 14.44/14.79 Proof: A critical pair between equations 78 and 124.
% 14.44/14.79
% 14.44/14.79 141: multiply(inverse(X43), X43) = multiply(inverse(multiply(inverse(X45), X45)), multiply(inverse(X44), X44)).
% 14.44/14.79 Proof: A critical pair between equations 124 and 125.
% 14.44/14.79
% 14.44/14.79 142: multiply(inverse(X43), X43) = inverse(multiply(X45, multiply(inverse(X45), inverse(multiply(inverse(X46), X46))))).
% 14.44/14.79 Proof: A critical pair between equations 124 and 126.
% 14.44/14.79
% 14.44/14.79 143: inverse(inverse(multiply(inverse(X40), X40))) = multiply(inverse(X10), multiply(X10, multiply(inverse(X45), X45))).
% 14.44/14.79 Proof: A critical pair between equations 127 and 124.
% 14.44/14.79
% 14.44/14.79 144: X36 = multiply(inverse(inverse(multiply(X36, inverse(multiply(inverse(X40), X40))))), multiply(inverse(X45), X45)).
% 14.44/14.79 Proof: A critical pair between equations 127 and 124.
% 14.44/14.79
% 14.44/14.79 147: inverse(multiply(X10, multiply(inverse(X10), inverse(multiply(inverse(X40), X40))))) = multiply(inverse(X45), X45).
% 14.44/14.79 Proof: A critical pair between equations 126 and 124.
% 14.44/14.79
% 14.44/14.79 148: X46 = multiply(X46, multiply(inverse(X48), X48)).
% 14.44/14.79 Proof: A critical pair between equations 139 and 141.
% 14.44/14.79
% 14.44/14.79 149: multiply(inverse(X45), X45) = multiply(inverse(X49), X49).
% 14.44/14.79 Proof: A critical pair between equations 147 and 142.
% 14.44/14.79
% 14.44/14.79 152: X18 = multiply(X23, inverse(multiply(inverse(X18), X23))).
% 14.44/14.79 Proof: A critical pair between equations 139 and 139.
% 14.44/14.79
% 14.44/14.79 153: X27 = multiply(X27, inverse(multiply(inverse(X40), X40))).
% 14.44/14.79 Proof: A critical pair between equations 137 and 139.
% 14.44/14.79
% 14.44/14.79 156: multiply(inverse(X43), X43) = inverse(multiply(inverse(X49), X49)).
% 14.44/14.79 Proof: A critical pair between equations 142 and 141.
% 14.44/14.79
% 14.44/14.79 159: inverse(inverse(multiply(inverse(X40), X40))) = multiply(inverse(X48), X48).
% 14.44/14.79 Proof: A critical pair between equations 143 and 139.
% 14.44/14.79
% 14.44/14.79 162: X36 = multiply(inverse(X10), multiply(X10, X36)).
% 14.44/14.79 Proof: Rewrite equation 127,
% 14.44/14.79 lhs with equations []
% 14.44/14.79 rhs with equations [153].
% 14.44/14.79
% 14.44/14.79 186: X30 = multiply(inverse(inverse(multiply(X30, multiply(X31, inverse(multiply(X35, X31)))))), X35).
% 14.44/14.79 Proof: Rewrite equation 98,
% 14.44/14.79 lhs with equations []
% 14.44/14.79 rhs with equations [152].
% 14.44/14.79
% 14.44/14.79 191: X36 = inverse(inverse(X36)).
% 14.44/14.79 Proof: Rewrite equation 144,
% 14.44/14.79 lhs with equations []
% 14.44/14.79 rhs with equations [153,148].
% 14.44/14.79
% 14.44/14.79 192: multiply(inverse(X40), X40) = multiply(inverse(X48), X48).
% 14.44/14.79 Proof: Rewrite equation 159,
% 14.44/14.79 lhs with equations [191]
% 14.44/14.79 rhs with equations [].
% 14.44/14.79
% 14.44/14.79 201: multiply(inverse(X43), X43) = inverse(multiply(X45, inverse(X45))).
% 14.44/14.79 Proof: Rewrite equation 142,
% 14.44/14.79 lhs with equations []
% 14.44/14.79 rhs with equations [153].
% 14.44/14.79
% 14.44/14.79 202: multiply(inverse(X40), X40) = inverse(multiply(X45, inverse(X45))).
% 14.44/14.79 Proof: Rewrite equation 143,
% 14.44/14.79 lhs with equations [191]
% 14.44/14.79 rhs with equations [201,162].
% 14.44/14.79
% 14.44/14.79 205: multiply(inverse(X40), X40) = multiply(X49, inverse(X49)).
% 14.44/14.79 Proof: A critical pair between equations 192 and 191.
% 14.44/14.79
% 14.44/14.79 207: multiply(inverse(X45), X45) = multiply(X50, inverse(X50)).
% 14.44/14.79 Proof: A critical pair between equations 149 and 191.
% 14.44/14.79
% 14.44/14.79 211: inverse(X37) = multiply(X23, inverse(multiply(X37, X23))).
% 14.44/14.79 Proof: A critical pair between equations 152 and 191.
% 14.44/14.79
% 14.44/14.79 219: X30 = multiply(multiply(X30, inverse(X35)), X35).
% 14.44/14.79 Proof: Rewrite equation 186,
% 14.44/14.79 lhs with equations []
% 14.44/14.79 rhs with equations [211,191].
% 14.44/14.79
% 14.44/14.79 228: inverse(multiply(X45, inverse(X45))) = multiply(X50, inverse(X50)).
% 14.44/14.79 Proof: Rewrite equation 207,
% 14.44/14.79 lhs with equations [202]
% 14.44/14.79 rhs with equations [].
% 14.44/14.79
% 14.44/14.79 235: multiply(inverse(X43), X43) = inverse(multiply(X49, inverse(X49))).
% 14.44/14.79 Proof: Rewrite equation 156,
% 14.44/14.79 lhs with equations []
% 14.44/14.79 rhs with equations [205].
% 14.44/14.79
% 14.44/14.79 247: X51 = multiply(inverse(multiply(X52, inverse(X52))), X51).
% 14.44/14.79 Proof: A critical pair between equations 219 and 228.
% 14.44/14.79
% 14.44/14.79 260: X51 = multiply(multiply(inverse(X54), X54), X51).
% 14.44/14.79 Proof: A critical pair between equations 247 and 235.
% 14.44/14.79
% 14.44/14.79 279: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 14.44/14.79 Proof: Rewrite lhs with equations [260]
% 14.44/14.79 rhs with equations [].
% 14.44/14.79
% 14.44/14.79 % SZS output end Proof
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