TSTP Solution File: GRP598-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP598-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n003.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 01:15:28 EDT 2023
% Result : Unsatisfiable 1.04s 1.33s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP598-1 : TPTP v8.1.2. Released v2.6.0.
% 0.03/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 01:56:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.04/1.33 % SZS status Unsatisfiable
% 1.04/1.33 % SZS output start Proof
% 1.04/1.33 original problem:
% 1.04/1.33 axioms:
% 1.04/1.33 double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(inverse(C), B))))) = C
% 1.04/1.33 multiply(A, B) = inverse(double_divide(B, A))
% 1.04/1.33 goal:
% 1.04/1.33 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 1.04/1.33 To show the unsatisfiability of the original goal,
% 1.04/1.33 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 1.04/1.33 Here is an equational proof:
% 1.04/1.33 0: double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(double_divide(inverse(X2), X1))))) = X2.
% 1.04/1.33 Proof: Axiom.
% 1.04/1.33
% 1.04/1.33 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.04/1.33 Proof: Axiom.
% 1.04/1.33
% 1.04/1.33 2: X2 = double_divide(double_divide(double_divide(inverse(X2), X4), inverse(double_divide(inverse(X5), X4))), inverse(X5)).
% 1.04/1.33 Proof: A critical pair between equations 0 and 0.
% 1.04/1.33
% 1.04/1.33 3: X2 = double_divide(X5, inverse(double_divide(double_divide(X3, X4), inverse(double_divide(inverse(X2), inverse(double_divide(X3, inverse(double_divide(inverse(X5), X4))))))))).
% 1.04/1.33 Proof: A critical pair between equations 0 and 0.
% 1.04/1.33
% 1.04/1.33 5: X2 = double_divide(X9, inverse(double_divide(double_divide(double_divide(X7, X8), inverse(double_divide(X7, inverse(double_divide(inverse(inverse(X2)), X8))))), inverse(X9)))).
% 1.04/1.33 Proof: A critical pair between equations 3 and 3.
% 1.04/1.33
% 1.04/1.33 6: X2 = double_divide(X5, inverse(double_divide(double_divide(double_divide(inverse(X5), X7), inverse(double_divide(inverse(X8), X7))), inverse(double_divide(inverse(X2), inverse(X8)))))).
% 1.04/1.33 Proof: A critical pair between equations 3 and 0.
% 1.04/1.33
% 1.04/1.33 12: X2 = double_divide(double_divide(X9, inverse(double_divide(inverse(X5), inverse(double_divide(double_divide(X7, X8), inverse(double_divide(inverse(X9), inverse(double_divide(X7, inverse(double_divide(inverse(inverse(X2)), X8))))))))))), inverse(X5)).
% 1.04/1.33 Proof: A critical pair between equations 2 and 3.
% 1.04/1.33
% 1.04/1.33 15: X2 = double_divide(X9, inverse(double_divide(inverse(X2), inverse(X9)))).
% 1.04/1.33 Proof: Rewrite equation 5,
% 1.04/1.33 lhs with equations []
% 1.04/1.33 rhs with equations [0].
% 1.04/1.33
% 1.04/1.33 16: X5 = double_divide(double_divide(X13, inverse(X13)), inverse(X5)).
% 1.04/1.33 Proof: A critical pair between equations 12 and 3.
% 1.04/1.33
% 1.04/1.33 17: X2 = double_divide(double_divide(inverse(X11), inverse(inverse(X2))), inverse(X11)).
% 1.04/1.33 Proof: A critical pair between equations 15 and 15.
% 1.04/1.33
% 1.04/1.33 22: X2 = double_divide(double_divide(X11, inverse(double_divide(inverse(X5), inverse(double_divide(inverse(X11), inverse(inverse(X2))))))), inverse(X5)).
% 1.04/1.33 Proof: A critical pair between equations 2 and 15.
% 1.04/1.33
% 1.04/1.33 29: double_divide(inverse(X5), inverse(inverse(X13))) = double_divide(X13, inverse(X5)).
% 1.04/1.33 Proof: A critical pair between equations 2 and 17.
% 1.04/1.33
% 1.04/1.33 35: X2 = double_divide(double_divide(inverse(X5), inverse(double_divide(inverse(double_divide(X14, inverse(X14))), inverse(inverse(X2))))), inverse(X5)).
% 1.04/1.33 Proof: A critical pair between equations 22 and 16.
% 1.04/1.33
% 1.04/1.33 39: X2 = double_divide(double_divide(inverse(X8), inverse(inverse(X13))), inverse(double_divide(X13, inverse(double_divide(inverse(X2), inverse(X8)))))).
% 1.04/1.33 Proof: A critical pair between equations 6 and 17.
% 1.04/1.33
% 1.04/1.33 42: X2 = double_divide(inverse(X5), inverse(inverse(double_divide(inverse(X5), inverse(double_divide(inverse(double_divide(X14, inverse(X14))), inverse(inverse(X2)))))))).
% 1.04/1.33 Proof: Rewrite equation 35,
% 1.04/1.33 lhs with equations []
% 1.04/1.33 rhs with equations [29].
% 1.04/1.33
% 1.04/1.33 49: X2 = double_divide(inverse(X11), inverse(inverse(double_divide(inverse(X11), inverse(inverse(X2)))))).
% 1.04/1.33 Proof: Rewrite equation 17,
% 1.04/1.33 lhs with equations []
% 1.04/1.33 rhs with equations [29].
% 1.04/1.33
% 1.04/1.33 56: inverse(inverse(X15)) = X15.
% 1.04/1.33 Proof: A critical pair between equations 39 and 15.
% 1.04/1.33
% 1.04/1.33 78: X2 = double_divide(inverse(X11), double_divide(inverse(X11), X2)).
% 1.04/1.33 Proof: Rewrite equation 49,
% 1.04/1.33 lhs with equations []
% 1.04/1.33 rhs with equations [56,56].
% 1.04/1.33
% 1.04/1.33 87: X2 = inverse(double_divide(inverse(double_divide(X14, inverse(X14))), X2)).
% 1.04/1.33 Proof: Rewrite equation 42,
% 1.04/1.33 lhs with equations []
% 1.04/1.33 rhs with equations [56,56,78].
% 1.04/1.33
% 1.04/1.33 94: double_divide(inverse(X5), X13) = double_divide(X13, inverse(X5)).
% 1.04/1.33 Proof: Rewrite equation 29,
% 1.04/1.33 lhs with equations [56]
% 1.04/1.33 rhs with equations [].
% 1.04/1.33
% 1.04/1.33 95: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 1.04/1.33 Proof: Rewrite lhs with equations [1,1,94,87]
% 1.04/1.33 rhs with equations [].
% 1.04/1.33
% 1.04/1.33 % SZS output end Proof
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