TSTP Solution File: GRP556-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP556-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n004.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 01:15:20 EDT 2023
% Result : Unsatisfiable 2.58s 2.91s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP556-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 02:12:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.58/2.91 % SZS status Unsatisfiable
% 2.58/2.91 % SZS output start Proof
% 2.58/2.91 original problem:
% 2.58/2.91 axioms:
% 2.58/2.91 divide(divide(A, inverse(divide(B, divide(A, C)))), C) = B
% 2.58/2.91 multiply(A, B) = divide(A, inverse(B))
% 2.58/2.91 goal:
% 2.58/2.91 multiply(a(), b()) != multiply(b(), a())
% 2.58/2.91 To show the unsatisfiability of the original goal,
% 2.58/2.91 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 2.58/2.91 Here is an equational proof:
% 2.58/2.91 0: divide(divide(X0, inverse(divide(X1, divide(X0, X2)))), X2) = X1.
% 2.58/2.91 Proof: Axiom.
% 2.58/2.91
% 2.58/2.91 1: multiply(X0, X1) = divide(X0, inverse(X1)).
% 2.58/2.91 Proof: Axiom.
% 2.58/2.91
% 2.58/2.91 2: X1 = divide(divide(divide(X3, inverse(divide(X4, divide(X3, X5)))), inverse(divide(X1, X4))), X5).
% 2.58/2.91 Proof: A critical pair between equations 0 and 0.
% 2.58/2.91
% 2.58/2.91 3: divide(X3, inverse(divide(X4, divide(X3, divide(X0, X2))))) = divide(divide(X0, inverse(X4)), X2).
% 2.58/2.91 Proof: A critical pair between equations 0 and 0.
% 2.58/2.91
% 2.58/2.91 4: X1 = divide(X7, inverse(divide(X1, X7))).
% 2.58/2.91 Proof: A critical pair between equations 2 and 0.
% 2.58/2.91
% 2.58/2.91 5: X6 = divide(divide(divide(X7, inverse(X6)), X8), divide(X7, X8)).
% 2.58/2.91 Proof: A critical pair between equations 0 and 3.
% 2.58/2.91
% 2.58/2.91 8: divide(divide(X0, inverse(X4)), X2) = divide(divide(X5, inverse(divide(X6, divide(X5, divide(X0, X2))))), inverse(divide(X4, X6))).
% 2.58/2.91 Proof: A critical pair between equations 3 and 0.
% 2.58/2.91
% 2.58/2.91 9: divide(X6, inverse(divide(X7, divide(X6, X8)))) = divide(divide(divide(X3, inverse(divide(X8, divide(X3, X5)))), inverse(X7)), X5).
% 2.58/2.91 Proof: A critical pair between equations 2 and 0.
% 2.58/2.91
% 2.58/2.91 14: divide(divide(X0, inverse(X4)), X2) = divide(divide(divide(X6, inverse(divide(X7, divide(X6, divide(X0, X2))))), inverse(divide(X9, X7))), inverse(divide(X4, X9))).
% 2.58/2.91 Proof: A critical pair between equations 3 and 2.
% 2.58/2.91
% 2.58/2.91 20: X6 = divide(divide(multiply(X7, X6), X8), divide(X7, X8)).
% 2.58/2.91 Proof: Rewrite equation 5,
% 2.58/2.91 lhs with equations []
% 2.58/2.91 rhs with equations [1].
% 2.58/2.91
% 2.58/2.91 21: X1 = multiply(X7, divide(X1, X7)).
% 2.58/2.91 Proof: Rewrite equation 4,
% 2.58/2.91 lhs with equations []
% 2.58/2.91 rhs with equations [1].
% 2.58/2.91
% 2.58/2.91 23: X1 = divide(multiply(multiply(X3, divide(X4, divide(X3, X5))), divide(X1, X4)), X5).
% 2.58/2.91 Proof: Rewrite equation 2,
% 2.58/2.91 lhs with equations []
% 2.58/2.91 rhs with equations [1,1].
% 2.58/2.91
% 2.58/2.91 24: divide(multiply(X0, X4), X2) = multiply(multiply(multiply(X6, divide(X7, divide(X6, divide(X0, X2)))), divide(X9, X7)), divide(X4, X9)).
% 2.58/2.91 Proof: Rewrite equation 14,
% 2.58/2.91 lhs with equations [1]
% 2.58/2.91 rhs with equations [1,1,1].
% 2.58/2.91
% 2.58/2.91 27: multiply(X6, divide(X7, divide(X6, X8))) = divide(multiply(multiply(X3, divide(X8, divide(X3, X5))), X7), X5).
% 2.58/2.91 Proof: Rewrite equation 9,
% 2.58/2.91 lhs with equations [1]
% 2.58/2.91 rhs with equations [1,1].
% 2.58/2.91
% 2.58/2.91 28: divide(multiply(X0, X4), X2) = multiply(multiply(X5, divide(X6, divide(X5, divide(X0, X2)))), divide(X4, X6)).
% 2.58/2.91 Proof: Rewrite equation 8,
% 2.58/2.91 lhs with equations [1]
% 2.58/2.91 rhs with equations [1,1].
% 2.58/2.91
% 2.58/2.91 32: multiply(X6, divide(divide(X12, X10), divide(X6, X10))) = X12.
% 2.58/2.91 Proof: A critical pair between equations 27 and 23.
% 2.58/2.91
% 2.58/2.91 33: divide(X10, X9) = divide(divide(X10, X8), divide(X9, X8)).
% 2.58/2.91 Proof: A critical pair between equations 20 and 21.
% 2.58/2.91
% 2.58/2.91 34: divide(multiply(X9, X10), X11) = multiply(divide(X9, X11), X10).
% 2.58/2.91 Proof: A critical pair between equations 21 and 20.
% 2.58/2.91
% 2.58/2.91 41: divide(multiply(X12, X4), X13) = multiply(divide(multiply(X12, X14), X13), divide(X4, X14)).
% 2.58/2.91 Proof: A critical pair between equations 24 and 28.
% 2.58/2.91
% 2.58/2.91 43: divide(divide(X12, inverse(X4)), X13) = divide(divide(divide(X12, inverse(divide(X4, X14))), inverse(X14)), X13).
% 2.58/2.91 Proof: Rewrite equation 41,
% 2.58/2.91 lhs with equations [1]
% 2.58/2.91 rhs with equations [1,34,34,1].
% 2.58/2.91
% 2.58/2.91 50: divide(X6, inverse(divide(X12, X6))) = X12.
% 2.58/2.91 Proof: Rewrite equation 32,
% 2.58/2.91 lhs with equations [33,1]
% 2.58/2.91 rhs with equations [].
% 2.58/2.91
% 2.58/2.91 51: X1 = divide(divide(divide(X3, inverse(divide(X4, divide(X3, X5)))), inverse(divide(X1, X4))), X5).
% 2.58/2.91 Proof: Rewrite equation 23,
% 2.58/2.91 lhs with equations []
% 2.58/2.91 rhs with equations [1,1].
% 2.58/2.91
% 2.58/2.91 66: divide(divide(X18, inverse(X16)), X16) = X18.
% 2.58/2.91 Proof: A critical pair between equations 43 and 51.
% 2.58/2.91
% 2.58/2.91 84: divide(multiply(X18, X16), X16) = X18.
% 2.58/2.91 Proof: Rewrite equation 66,
% 2.58/2.91 lhs with equations [1]
% 2.58/2.91 rhs with equations [].
% 2.58/2.91
% 2.58/2.91 91: multiply(X6, divide(X12, X6)) = X12.
% 2.58/2.91 Proof: Rewrite equation 50,
% 2.58/2.91 lhs with equations [1]
% 2.58/2.91 rhs with equations [].
% 2.58/2.91
% 2.58/2.91 109: multiply(X19, X20) = multiply(X20, X19).
% 2.58/2.91 Proof: A critical pair between equations 91 and 84.
% 2.58/2.91
% 2.58/2.91 140: divide(X19, inverse(X20)) = divide(X20, inverse(X19)).
% 2.58/2.91 Proof: Rewrite equation 109,
% 2.58/2.91 lhs with equations [1]
% 2.58/2.91 rhs with equations [1].
% 2.58/2.91
% 2.58/2.91 146: multiply(a(), b()) = multiply(b(), a()).
% 2.58/2.91 Proof: Rewrite lhs with equations [1,140]
% 2.58/2.91 rhs with equations [1].
% 2.58/2.91
% 2.58/2.91 % SZS output end Proof
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