TSTP Solution File: GRP524-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP524-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n029.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 01:18:46 EDT 2023
% Result : Unsatisfiable 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP524-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 21:17:11 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.38 Command-line arguments: --no-flatten-goal
% 0.14/0.38
% 0.14/0.38 % SZS status Unsatisfiable
% 0.14/0.38
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.14/0.40 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.14/0.40 Axiom 3 (single_axiom): divide(X, divide(Y, divide(Z, divide(X, Y)))) = Z.
% 0.14/0.40
% 0.14/0.40 Lemma 4: divide(X, inverse(Y)) = multiply(X, Y).
% 0.14/0.40 Proof:
% 0.14/0.40 divide(X, inverse(Y))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 divide(X, divide(divide(Z, Z), Y))
% 0.14/0.40 = { by axiom 2 (multiply) R->L }
% 0.14/0.40 multiply(X, Y)
% 0.14/0.40
% 0.14/0.40 Lemma 5: inverse(divide(X, multiply(Y, X))) = Y.
% 0.14/0.40 Proof:
% 0.14/0.40 inverse(divide(X, multiply(Y, X)))
% 0.14/0.40 = { by lemma 4 R->L }
% 0.14/0.40 inverse(divide(X, divide(Y, inverse(X))))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 inverse(divide(X, divide(Y, divide(divide(Z, Z), X))))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 divide(divide(Z, Z), divide(X, divide(Y, divide(divide(Z, Z), X))))
% 0.14/0.40 = { by axiom 3 (single_axiom) }
% 0.14/0.40 Y
% 0.14/0.40
% 0.14/0.40 Lemma 6: multiply(divide(X, X), Y) = inverse(inverse(Y)).
% 0.14/0.40 Proof:
% 0.14/0.40 multiply(divide(X, X), Y)
% 0.14/0.40 = { by lemma 4 R->L }
% 0.14/0.40 divide(divide(X, X), inverse(Y))
% 0.14/0.40 = { by axiom 1 (inverse) R->L }
% 0.14/0.40 inverse(inverse(Y))
% 0.14/0.40
% 0.14/0.40 Lemma 7: divide(X, divide(Y, Y)) = multiply(X, divide(Z, Z)).
% 0.14/0.40 Proof:
% 0.14/0.40 divide(X, divide(Y, Y))
% 0.14/0.40 = { by lemma 5 R->L }
% 0.14/0.40 divide(X, inverse(divide(W, multiply(divide(Y, Y), W))))
% 0.14/0.40 = { by lemma 6 }
% 0.14/0.40 divide(X, inverse(divide(W, inverse(inverse(W)))))
% 0.14/0.40 = { by lemma 6 R->L }
% 0.14/0.40 divide(X, inverse(divide(W, multiply(divide(divide(Z, Z), divide(Z, Z)), W))))
% 0.14/0.40 = { by lemma 5 }
% 0.14/0.40 divide(X, divide(divide(Z, Z), divide(Z, Z)))
% 0.14/0.40 = { by axiom 1 (inverse) R->L }
% 0.14/0.40 divide(X, inverse(divide(Z, Z)))
% 0.14/0.40 = { by lemma 4 }
% 0.14/0.40 multiply(X, divide(Z, Z))
% 0.14/0.40
% 0.14/0.40 Lemma 8: inverse(inverse(multiply(X, divide(Y, Y)))) = X.
% 0.14/0.40 Proof:
% 0.14/0.40 inverse(inverse(multiply(X, divide(Y, Y))))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 inverse(divide(divide(Y, Y), multiply(X, divide(Y, Y))))
% 0.14/0.40 = { by lemma 5 }
% 0.14/0.40 X
% 0.14/0.40
% 0.14/0.40 Lemma 9: multiply(X, divide(Y, Y)) = X.
% 0.14/0.40 Proof:
% 0.14/0.40 multiply(X, divide(Y, Y))
% 0.14/0.40 = { by lemma 8 R->L }
% 0.14/0.40 inverse(inverse(multiply(multiply(X, divide(Y, Y)), divide(Z, Z))))
% 0.14/0.40 = { by lemma 7 R->L }
% 0.14/0.40 inverse(inverse(divide(multiply(X, divide(Y, Y)), divide(inverse(multiply(X, divide(Y, Y))), inverse(multiply(X, divide(Y, Y)))))))
% 0.14/0.40 = { by lemma 4 }
% 0.14/0.40 inverse(inverse(divide(multiply(X, divide(Y, Y)), multiply(inverse(multiply(X, divide(Y, Y))), multiply(X, divide(Y, Y))))))
% 0.14/0.40 = { by lemma 5 }
% 0.14/0.40 inverse(inverse(multiply(X, divide(Y, Y))))
% 0.14/0.40 = { by lemma 8 }
% 0.14/0.40 X
% 0.14/0.40
% 0.14/0.40 Lemma 10: divide(X, divide(multiply(Y, X), Y)) = divide(Z, Z).
% 0.14/0.40 Proof:
% 0.14/0.40 divide(X, divide(multiply(Y, X), Y))
% 0.14/0.40 = { by lemma 5 R->L }
% 0.14/0.40 divide(X, divide(multiply(Y, X), inverse(divide(X, multiply(Y, X)))))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 divide(X, divide(multiply(Y, X), divide(divide(Z, Z), divide(X, multiply(Y, X)))))
% 0.14/0.40 = { by axiom 3 (single_axiom) }
% 0.14/0.40 divide(Z, Z)
% 0.14/0.40
% 0.14/0.40 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.14/0.40 Proof:
% 0.14/0.40 multiply(a, b)
% 0.14/0.40 = { by axiom 3 (single_axiom) R->L }
% 0.14/0.40 multiply(divide(multiply(b, a), divide(b, divide(a, divide(multiply(b, a), b)))), b)
% 0.14/0.40 = { by lemma 10 }
% 0.14/0.40 multiply(divide(multiply(b, a), divide(b, divide(X, X))), b)
% 0.14/0.40 = { by lemma 7 }
% 0.14/0.40 multiply(divide(multiply(b, a), multiply(b, divide(Y, Y))), b)
% 0.14/0.40 = { by lemma 9 }
% 0.14/0.40 multiply(divide(multiply(b, a), b), b)
% 0.14/0.40 = { by axiom 3 (single_axiom) R->L }
% 0.14/0.40 divide(multiply(b, a), divide(b, divide(multiply(divide(multiply(b, a), b), b), divide(multiply(b, a), b))))
% 0.14/0.40 = { by lemma 10 }
% 0.14/0.40 divide(multiply(b, a), divide(Z, Z))
% 0.14/0.40 = { by lemma 7 }
% 0.14/0.40 multiply(multiply(b, a), divide(W, W))
% 0.14/0.40 = { by lemma 9 }
% 0.14/0.40 multiply(b, a)
% 0.14/0.40 % SZS output end Proof
% 0.14/0.40
% 0.14/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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