TSTP Solution File: GRP538-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP538-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n019.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 01:15:17 EDT 2023
% Result : Unsatisfiable 0.19s 0.62s
% 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
% 0.00/0.12 % Problem : GRP538-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon Aug 28 21:48:13 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.62 % SZS status Unsatisfiable
% 0.19/0.62 % SZS output start Proof
% 0.19/0.62 original problem:
% 0.19/0.62 axioms:
% 0.19/0.62 divide(divide(A, B), divide(divide(A, C), B)) = C
% 0.19/0.62 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.19/0.62 inverse(A) = divide(divide(B, B), A)
% 0.19/0.62 identity() = divide(A, A)
% 0.19/0.62 goal:
% 0.19/0.62 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 0.19/0.62 To show the unsatisfiability of the original goal,
% 0.19/0.62 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.19/0.62 Here is an equational proof:
% 0.19/0.62 0: divide(divide(X0, X1), divide(divide(X0, X2), X1)) = X2.
% 0.19/0.62 Proof: Axiom.
% 0.19/0.62
% 0.19/0.62 1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.19/0.62 Proof: Axiom.
% 0.19/0.62
% 0.19/0.62 2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.19/0.62 Proof: Axiom.
% 0.19/0.62
% 0.19/0.62 3: identity() = divide(X0, X0).
% 0.19/0.62 Proof: Axiom.
% 0.19/0.62
% 0.19/0.62 4: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.19/0.62 Proof: Rewrite equation 1,
% 0.19/0.62 lhs with equations []
% 0.19/0.62 rhs with equations [3].
% 0.19/0.62
% 0.19/0.62 5: inverse(X0) = divide(identity(), X0).
% 0.19/0.62 Proof: Rewrite equation 2,
% 0.19/0.62 lhs with equations []
% 0.19/0.62 rhs with equations [3].
% 0.19/0.62
% 0.19/0.62 12: X2 = divide(divide(X0, divide(X0, X2)), identity()).
% 0.19/0.62 Proof: A critical pair between equations 0 and 3.
% 0.19/0.62
% 0.19/0.62 13: X2 = divide(identity(), divide(divide(X3, X2), X3)).
% 0.19/0.62 Proof: A critical pair between equations 0 and 3.
% 0.19/0.62
% 0.19/0.62 16: X4 = divide(divide(X3, divide(divide(X3, X5), X4)), X5).
% 0.19/0.62 Proof: A critical pair between equations 0 and 0.
% 0.19/0.62
% 0.19/0.62 18: X5 = divide(X5, identity()).
% 0.19/0.62 Proof: A critical pair between equations 12 and 0.
% 0.19/0.62
% 0.19/0.62 21: X4 = divide(divide(X6, divide(identity(), X4)), X6).
% 0.19/0.62 Proof: A critical pair between equations 16 and 3.
% 0.19/0.62
% 0.19/0.62 23: divide(divide(X4, X5), X4) = divide(identity(), divide(X5, identity())).
% 0.19/0.62 Proof: A critical pair between equations 13 and 13.
% 0.19/0.62
% 0.19/0.62 34: divide(divide(X4, X5), X4) = inverse(X5).
% 0.19/0.62 Proof: Rewrite equation 23,
% 0.19/0.62 lhs with equations []
% 0.19/0.62 rhs with equations [18,5].
% 0.19/0.62
% 0.19/0.62 35: X4 = inverse(inverse(X4)).
% 0.19/0.62 Proof: Rewrite equation 21,
% 0.19/0.62 lhs with equations []
% 0.19/0.62 rhs with equations [5,34].
% 0.19/0.62
% 0.19/0.62 36: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.19/0.62 Proof: Rewrite equation 4,
% 0.19/0.62 lhs with equations []
% 0.19/0.62 rhs with equations [5].
% 0.19/0.62
% 0.19/0.62 39: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 0.19/0.62 Proof: Rewrite lhs with equations [36,3,36,5,35]
% 0.19/0.62 rhs with equations [].
% 0.19/0.62
% 0.19/0.62 % SZS output end Proof
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