TSTP Solution File: GRP597-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP597-1 : 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 : n007.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 01:19:03 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP597-1 : TPTP v8.1.2. Released v2.6.0.
% 0.04/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n007.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 : Mon Aug 28 19:29:13 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --no-flatten-goal
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.19/0.39 Axiom 2 (single_axiom): double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y))))) = Z.
% 0.19/0.39
% 0.19/0.39 Lemma 3: double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X)) = Z.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X))
% 0.19/0.39 = { by axiom 1 (multiply) }
% 0.19/0.39 double_divide(double_divide(X, Y), multiply(inverse(double_divide(inverse(Z), Y)), X))
% 0.19/0.39 = { by axiom 1 (multiply) }
% 0.19/0.39 double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y)))))
% 0.19/0.39 = { by axiom 2 (single_axiom) }
% 0.19/0.39 Z
% 0.19/0.39
% 0.19/0.39 Lemma 4: multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X)) = inverse(Y).
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X))
% 0.19/0.39 = { by axiom 1 (multiply) }
% 0.19/0.39 inverse(double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.19/0.39 = { by lemma 3 }
% 0.19/0.39 inverse(Y)
% 0.19/0.39
% 0.19/0.39 Lemma 5: multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y) = inverse(W).
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y)
% 0.19/0.39 = { by lemma 3 R->L }
% 0.19/0.39 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.19/0.39 = { by lemma 4 }
% 0.19/0.39 inverse(W)
% 0.19/0.39
% 0.19/0.39 Lemma 6: multiply(multiply(inverse(X), inverse(Y)), X) = inverse(Y).
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(multiply(inverse(X), inverse(Y)), X)
% 0.19/0.39 = { by lemma 3 R->L }
% 0.19/0.39 multiply(multiply(inverse(X), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), X)
% 0.19/0.39 = { by lemma 5 R->L }
% 0.19/0.39 multiply(multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), X)
% 0.19/0.39 = { by lemma 5 }
% 0.19/0.39 inverse(Y)
% 0.19/0.39
% 0.19/0.39 Lemma 7: double_divide(double_divide(X, inverse(X)), inverse(Y)) = Y.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(double_divide(X, inverse(X)), inverse(Y))
% 0.19/0.39 = { by lemma 6 R->L }
% 0.19/0.39 double_divide(double_divide(X, inverse(X)), multiply(multiply(inverse(X), inverse(Y)), X))
% 0.19/0.39 = { by lemma 3 }
% 0.19/0.39 Y
% 0.19/0.39
% 0.19/0.39 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(inverse(a1), a1)
% 0.19/0.39 = { by axiom 1 (multiply) }
% 0.19/0.39 inverse(double_divide(a1, inverse(a1)))
% 0.19/0.40 = { by lemma 7 R->L }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(b1, inverse(b1)), inverse(a1)), inverse(a1)))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(inverse(double_divide(b1, inverse(b1))))), X)), multiply(multiply(multiply(multiply(Y, inverse(inverse(double_divide(b1, inverse(b1))))), X), inverse(double_divide(Z, inverse(Z)))), double_divide(X, Y))), multiply(multiply(multiply(multiply(multiply(multiply(Y, inverse(inverse(double_divide(b1, inverse(b1))))), X), inverse(double_divide(Z, inverse(Z)))), double_divide(X, Y)), inverse(double_divide(b1, inverse(b1)))), double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(inverse(double_divide(b1, inverse(b1))))), X)))), inverse(a1)), inverse(a1)))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(double_divide(Z, inverse(Z)), multiply(multiply(multiply(multiply(multiply(multiply(Y, inverse(inverse(double_divide(b1, inverse(b1))))), X), inverse(double_divide(Z, inverse(Z)))), double_divide(X, Y)), inverse(double_divide(b1, inverse(b1)))), double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(inverse(double_divide(b1, inverse(b1))))), X)))), inverse(a1)), inverse(a1)))
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(double_divide(Z, inverse(Z)), multiply(inverse(double_divide(Z, inverse(Z))), double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(inverse(double_divide(b1, inverse(b1))))), X)))), inverse(a1)), inverse(a1)))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(double_divide(Z, inverse(Z)), multiply(inverse(double_divide(Z, inverse(Z))), inverse(double_divide(b1, inverse(b1))))), inverse(a1)), inverse(a1)))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(double_divide(Z, inverse(Z)), inverse(double_divide(inverse(double_divide(b1, inverse(b1))), inverse(double_divide(Z, inverse(Z)))))), inverse(a1)), inverse(a1)))
% 0.19/0.40 = { by lemma 7 }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(inverse(double_divide(b1, inverse(b1))), inverse(double_divide(Z, inverse(Z)))), inverse(a1)), inverse(a1)))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(inverse(double_divide(b1, inverse(b1))), multiply(inverse(Z), Z)), inverse(a1)), inverse(a1)))
% 0.19/0.40 = { by lemma 6 R->L }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(inverse(double_divide(b1, inverse(b1))), multiply(inverse(Z), Z)), multiply(multiply(inverse(double_divide(Z, inverse(Z))), inverse(a1)), double_divide(Z, inverse(Z)))), inverse(a1)))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(inverse(double_divide(b1, inverse(b1))), multiply(inverse(Z), Z)), multiply(inverse(double_divide(inverse(a1), inverse(double_divide(Z, inverse(Z))))), double_divide(Z, inverse(Z)))), inverse(a1)))
% 0.19/0.40 = { by lemma 6 R->L }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(inverse(double_divide(b1, inverse(b1))), multiply(inverse(Z), Z)), multiply(multiply(multiply(inverse(Z), inverse(double_divide(inverse(a1), inverse(double_divide(Z, inverse(Z)))))), Z), double_divide(Z, inverse(Z)))), inverse(a1)))
% 0.19/0.40 = { by lemma 4 }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(inverse(double_divide(b1, inverse(b1))), multiply(inverse(Z), Z)), inverse(double_divide(inverse(a1), inverse(double_divide(Z, inverse(Z)))))), inverse(a1)))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(inverse(double_divide(b1, inverse(b1))), multiply(inverse(Z), Z)), multiply(inverse(double_divide(Z, inverse(Z))), inverse(a1))), inverse(a1)))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(inverse(double_divide(b1, inverse(b1))), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(a1))), inverse(a1)))
% 0.19/0.40 = { by lemma 4 R->L }
% 0.19/0.40 inverse(double_divide(double_divide(double_divide(inverse(double_divide(b1, inverse(b1))), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(a1))), multiply(multiply(multiply(multiply(inverse(Z), Z), inverse(a1)), inverse(double_divide(b1, inverse(b1)))), double_divide(inverse(double_divide(b1, inverse(b1))), multiply(inverse(Z), Z)))))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 inverse(double_divide(b1, inverse(b1)))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 multiply(inverse(b1), b1)
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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