TSTP Solution File: GRP610-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP610-1 : 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 : n023.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 01:19:06 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% 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
% 0.00/0.12 % Problem : GRP610-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n023.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 20:41:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.19/0.40 Axiom 2 (single_axiom): inverse(double_divide(inverse(double_divide(inverse(double_divide(X, Y)), Z)), double_divide(X, Z))) = Y.
% 0.19/0.40
% 0.19/0.40 Lemma 3: multiply(double_divide(X, Y), multiply(Y, multiply(Z, X))) = Z.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 multiply(double_divide(X, Y), multiply(Y, inverse(double_divide(X, Z))))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 multiply(double_divide(X, Y), inverse(double_divide(inverse(double_divide(X, Z)), Y)))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(inverse(double_divide(inverse(double_divide(X, Z)), Y)), double_divide(X, Y)))
% 0.19/0.40 = { by axiom 2 (single_axiom) }
% 0.19/0.40 Z
% 0.19/0.40
% 0.19/0.40 Lemma 4: multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y)) = double_divide(Z, X).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, multiply(double_divide(Z, X), multiply(X, multiply(Y, Z)))))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 double_divide(Z, X)
% 0.19/0.40
% 0.19/0.40 Lemma 5: double_divide(X, multiply(double_divide(multiply(Y, X), Z), Y)) = Z.
% 0.19/0.40 Proof:
% 0.19/0.40 double_divide(X, multiply(double_divide(multiply(Y, X), Z), Y))
% 0.19/0.40 = { by lemma 4 R->L }
% 0.19/0.40 multiply(double_divide(multiply(multiply(double_divide(multiply(Y, X), Z), Y), multiply(Y, X)), double_divide(multiply(Y, X), Z)), multiply(double_divide(multiply(Y, X), Z), Y))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(double_divide(multiply(multiply(double_divide(multiply(Y, X), Z), Y), multiply(Y, X)), double_divide(multiply(Y, X), Z)), multiply(double_divide(multiply(Y, X), Z), multiply(Z, multiply(multiply(double_divide(multiply(Y, X), Z), Y), multiply(Y, X)))))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 Z
% 0.19/0.40
% 0.19/0.40 Lemma 6: multiply(multiply(double_divide(multiply(X, Y), Z), X), Y) = inverse(Z).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(multiply(double_divide(multiply(X, Y), Z), X), Y)
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(Y, multiply(double_divide(multiply(X, Y), Z), X)))
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 inverse(Z)
% 0.19/0.40
% 0.19/0.40 Lemma 7: multiply(double_divide(X, double_divide(X, multiply(Y, Z))), inverse(Y)) = Z.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(double_divide(X, double_divide(X, multiply(Y, Z))), inverse(Y))
% 0.19/0.40 = { by lemma 6 R->L }
% 0.19/0.40 multiply(double_divide(X, double_divide(X, multiply(Y, Z))), multiply(multiply(double_divide(multiply(multiply(Y, Z), multiply(Z, X)), Y), multiply(Y, Z)), multiply(Z, X)))
% 0.19/0.40 = { by lemma 4 }
% 0.19/0.40 multiply(double_divide(X, double_divide(X, multiply(Y, Z))), multiply(double_divide(X, multiply(Y, Z)), multiply(Z, X)))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 Z
% 0.19/0.40
% 0.19/0.40 Lemma 8: multiply(double_divide(X, Y), X) = inverse(Y).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(double_divide(X, Y), X)
% 0.19/0.40 = { by lemma 7 R->L }
% 0.19/0.40 multiply(double_divide(X, multiply(double_divide(X, double_divide(X, multiply(double_divide(multiply(Y, X), Y), Y))), inverse(double_divide(multiply(Y, X), Y)))), X)
% 0.19/0.40 = { by lemma 7 R->L }
% 0.19/0.40 multiply(double_divide(X, multiply(double_divide(X, multiply(double_divide(multiply(inverse(double_divide(multiply(Y, X), Y)), X), double_divide(multiply(inverse(double_divide(multiply(Y, X), Y)), X), multiply(double_divide(multiply(Y, X), Y), double_divide(X, multiply(double_divide(multiply(Y, X), Y), Y))))), inverse(double_divide(multiply(Y, X), Y)))), inverse(double_divide(multiply(Y, X), Y)))), X)
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 multiply(double_divide(X, multiply(double_divide(multiply(inverse(double_divide(multiply(Y, X), Y)), X), multiply(double_divide(multiply(Y, X), Y), double_divide(X, multiply(double_divide(multiply(Y, X), Y), Y)))), inverse(double_divide(multiply(Y, X), Y)))), X)
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 multiply(multiply(double_divide(multiply(Y, X), Y), double_divide(X, multiply(double_divide(multiply(Y, X), Y), Y))), X)
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 multiply(multiply(double_divide(multiply(Y, X), Y), Y), X)
% 0.19/0.40 = { by lemma 6 }
% 0.19/0.40 inverse(Y)
% 0.19/0.40
% 0.19/0.40 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(multiply(inverse(b2), b2), a2)
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(a2, multiply(inverse(b2), b2)))
% 0.19/0.40 = { by lemma 8 R->L }
% 0.19/0.40 multiply(double_divide(multiply(b2, a2), double_divide(a2, multiply(inverse(b2), b2))), multiply(b2, a2))
% 0.19/0.40 = { by lemma 4 R->L }
% 0.19/0.40 multiply(double_divide(multiply(b2, a2), multiply(double_divide(multiply(multiply(inverse(b2), b2), multiply(b2, a2)), inverse(b2)), multiply(inverse(b2), b2))), multiply(b2, a2))
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 multiply(inverse(b2), multiply(b2, a2))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 multiply(inverse(b2), inverse(double_divide(a2, b2)))
% 0.19/0.40 = { by lemma 8 R->L }
% 0.19/0.40 multiply(multiply(double_divide(a2, b2), a2), inverse(double_divide(a2, b2)))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(inverse(double_divide(a2, b2)), multiply(double_divide(a2, b2), a2)))
% 0.19/0.40 = { by lemma 8 R->L }
% 0.19/0.40 multiply(double_divide(inverse(double_divide(a2, b2)), double_divide(inverse(double_divide(a2, b2)), multiply(double_divide(a2, b2), a2))), inverse(double_divide(a2, b2)))
% 0.19/0.40 = { by lemma 7 }
% 0.19/0.40 a2
% 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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