TSTP Solution File: GRP593-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP593-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n012.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 01:19:02 EDT 2023
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% 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 : GRP593-1 : TPTP v8.1.2. Released v2.6.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 01:53:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.42 Command-line arguments: --flatten
% 0.21/0.42
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.21/0.43 Axiom 2 (single_axiom): inverse(double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(Z, Y)))))) = Z.
% 0.21/0.43
% 0.21/0.43 Lemma 3: multiply(multiply(multiply(X, Y), Z), double_divide(Z, X)) = Y.
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(multiply(multiply(X, Y), Z), double_divide(Z, X))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 multiply(multiply(inverse(double_divide(Y, X)), Z), double_divide(Z, X))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 multiply(inverse(double_divide(Z, inverse(double_divide(Y, X)))), double_divide(Z, X))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 inverse(double_divide(double_divide(Z, X), inverse(double_divide(Z, inverse(double_divide(Y, X))))))
% 0.21/0.43 = { by axiom 2 (single_axiom) }
% 0.21/0.43 Y
% 0.21/0.43
% 0.21/0.43 Lemma 4: multiply(X, double_divide(double_divide(Y, Z), multiply(Z, X))) = Y.
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(X, double_divide(double_divide(Y, Z), multiply(Z, X)))
% 0.21/0.43 = { by lemma 3 R->L }
% 0.21/0.43 multiply(multiply(multiply(multiply(Z, X), Y), double_divide(Y, Z)), double_divide(double_divide(Y, Z), multiply(Z, X)))
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 Y
% 0.21/0.43
% 0.21/0.43 Lemma 5: multiply(multiply(X, Y), double_divide(Y, Z)) = double_divide(double_divide(X, W), multiply(W, Z)).
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(multiply(X, Y), double_divide(Y, Z))
% 0.21/0.43 = { by lemma 4 R->L }
% 0.21/0.43 multiply(multiply(multiply(Z, double_divide(double_divide(X, W), multiply(W, Z))), Y), double_divide(Y, Z))
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 double_divide(double_divide(X, W), multiply(W, Z))
% 0.21/0.43
% 0.21/0.43 Lemma 6: multiply(multiply(X, Y), double_divide(Y, inverse(Z))) = double_divide(double_divide(multiply(X, Z), W), W).
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(multiply(X, Y), double_divide(Y, inverse(Z)))
% 0.21/0.43 = { by lemma 3 R->L }
% 0.21/0.43 multiply(multiply(multiply(multiply(multiply(W, X), double_divide(multiply(X, Z), W)), double_divide(double_divide(multiply(X, Z), W), W)), Y), double_divide(Y, inverse(Z)))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 multiply(multiply(multiply(inverse(double_divide(double_divide(multiply(X, Z), W), multiply(W, X))), double_divide(double_divide(multiply(X, Z), W), W)), Y), double_divide(Y, inverse(Z)))
% 0.21/0.43 = { by lemma 5 R->L }
% 0.21/0.43 multiply(multiply(multiply(inverse(multiply(multiply(multiply(X, Z), V), double_divide(V, X))), double_divide(double_divide(multiply(X, Z), W), W)), Y), double_divide(Y, inverse(Z)))
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 multiply(multiply(multiply(inverse(Z), double_divide(double_divide(multiply(X, Z), W), W)), Y), double_divide(Y, inverse(Z)))
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 double_divide(double_divide(multiply(X, Z), W), W)
% 0.21/0.43
% 0.21/0.43 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(inverse(a1), a1)
% 0.21/0.43 = { by lemma 4 R->L }
% 0.21/0.43 multiply(X, double_divide(double_divide(multiply(inverse(a1), a1), Y), multiply(Y, X)))
% 0.21/0.43 = { by lemma 4 R->L }
% 0.21/0.43 multiply(X, double_divide(multiply(Z, double_divide(double_divide(double_divide(multiply(inverse(a1), a1), Y), Y), multiply(Y, Z))), multiply(Y, X)))
% 0.21/0.43 = { by lemma 6 R->L }
% 0.21/0.43 multiply(X, double_divide(multiply(Z, double_divide(multiply(multiply(inverse(a1), W), double_divide(W, inverse(a1))), multiply(Y, Z))), multiply(Y, X)))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 multiply(X, double_divide(multiply(Z, double_divide(inverse(double_divide(double_divide(W, inverse(a1)), multiply(inverse(a1), W))), multiply(Y, Z))), multiply(Y, X)))
% 0.21/0.43 = { by lemma 3 R->L }
% 0.21/0.43 multiply(X, double_divide(multiply(Z, double_divide(inverse(multiply(multiply(multiply(W, double_divide(double_divide(W, inverse(a1)), multiply(inverse(a1), W))), V), double_divide(V, W))), multiply(Y, Z))), multiply(Y, X)))
% 0.21/0.43 = { by lemma 4 }
% 0.21/0.43 multiply(X, double_divide(multiply(Z, double_divide(inverse(multiply(multiply(W, V), double_divide(V, W))), multiply(Y, Z))), multiply(Y, X)))
% 0.21/0.43 = { by lemma 5 }
% 0.21/0.43 multiply(X, double_divide(multiply(Z, double_divide(inverse(double_divide(double_divide(W, inverse(b1)), multiply(inverse(b1), W))), multiply(Y, Z))), multiply(Y, X)))
% 0.21/0.43 = { by axiom 1 (multiply) R->L }
% 0.21/0.43 multiply(X, double_divide(multiply(Z, double_divide(multiply(multiply(inverse(b1), W), double_divide(W, inverse(b1))), multiply(Y, Z))), multiply(Y, X)))
% 0.21/0.43 = { by lemma 6 }
% 0.21/0.43 multiply(X, double_divide(multiply(Z, double_divide(double_divide(double_divide(multiply(inverse(b1), b1), Y), Y), multiply(Y, Z))), multiply(Y, X)))
% 0.21/0.43 = { by lemma 4 }
% 0.21/0.43 multiply(X, double_divide(double_divide(multiply(inverse(b1), b1), Y), multiply(Y, X)))
% 0.21/0.43 = { by lemma 4 }
% 0.21/0.43 multiply(inverse(b1), b1)
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43
% 0.21/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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