TSTP Solution File: GRP537-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP537-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n017.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 01:15:16 EDT 2023
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP537-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 00:50:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 original problem:
% 0.19/0.52 axioms:
% 0.19/0.52 divide(divide(A, B), divide(divide(A, C), B)) = C
% 0.19/0.52 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.19/0.52 inverse(A) = divide(divide(B, B), A)
% 0.19/0.52 identity() = divide(A, A)
% 0.19/0.52 goal:
% 0.19/0.52 multiply(inverse(a1()), a1()) != multiply(inverse(b1()), b1())
% 0.19/0.52 To show the unsatisfiability of the original goal,
% 0.19/0.52 it suffices to show that multiply(inverse(a1()), a1()) = multiply(inverse(b1()), b1()) (skolemized goal) is valid under the axioms.
% 0.19/0.52 Here is an equational proof:
% 0.19/0.52 1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.19/0.52 Proof: Axiom.
% 0.19/0.52
% 0.19/0.52 2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.19/0.52 Proof: Axiom.
% 0.19/0.52
% 0.19/0.52 3: identity() = divide(X0, X0).
% 0.19/0.52 Proof: Axiom.
% 0.19/0.52
% 0.19/0.52 4: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.19/0.52 Proof: Rewrite equation 1,
% 0.19/0.52 lhs with equations []
% 0.19/0.52 rhs with equations [3].
% 0.19/0.52
% 0.19/0.52 5: inverse(X0) = divide(identity(), X0).
% 0.19/0.52 Proof: Rewrite equation 2,
% 0.19/0.52 lhs with equations []
% 0.19/0.52 rhs with equations [3].
% 0.19/0.52
% 0.19/0.52 18: multiply(inverse(a1()), a1()) = multiply(inverse(b1()), b1()).
% 0.19/0.52 Proof: Rewrite lhs with equations [5,4,3]
% 0.19/0.52 rhs with equations [5,4,3].
% 0.19/0.52
% 0.19/0.52 % SZS output end Proof
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