TSTP Solution File: GRP482-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP482-1 : 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 : n004.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 01:18:36 EDT 2023
% Result : Unsatisfiable 0.21s 0.39s
% 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
% 0.12/0.12 % Problem : GRP482-1 : 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
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 19:58:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.39
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.21/0.40 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.21/0.40 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.21/0.40 Axiom 4 (single_axiom): double_divide(double_divide(double_divide(X, double_divide(Y, identity)), double_divide(double_divide(Z, double_divide(W, double_divide(W, identity))), double_divide(X, identity))), Y) = Z.
% 0.21/0.40
% 0.21/0.40 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.21/0.40 Proof:
% 0.21/0.40 inverse(double_divide(X, Y))
% 0.21/0.40 = { by axiom 1 (inverse) }
% 0.21/0.40 double_divide(double_divide(X, Y), identity)
% 0.21/0.40 = { by axiom 3 (multiply) R->L }
% 0.21/0.40 multiply(Y, X)
% 0.21/0.40
% 0.21/0.40 Lemma 6: double_divide(double_divide(double_divide(X, inverse(Y)), double_divide(inverse(Z), inverse(X))), Y) = Z.
% 0.21/0.40 Proof:
% 0.21/0.40 double_divide(double_divide(double_divide(X, inverse(Y)), double_divide(inverse(Z), inverse(X))), Y)
% 0.21/0.40 = { by axiom 1 (inverse) }
% 0.21/0.40 double_divide(double_divide(double_divide(X, inverse(Y)), double_divide(inverse(Z), double_divide(X, identity))), Y)
% 0.21/0.40 = { by axiom 1 (inverse) }
% 0.21/0.40 double_divide(double_divide(double_divide(X, inverse(Y)), double_divide(double_divide(Z, identity), double_divide(X, identity))), Y)
% 0.21/0.40 = { by axiom 2 (identity) }
% 0.21/0.40 double_divide(double_divide(double_divide(X, inverse(Y)), double_divide(double_divide(Z, double_divide(W, inverse(W))), double_divide(X, identity))), Y)
% 0.21/0.40 = { by axiom 1 (inverse) }
% 0.21/0.40 double_divide(double_divide(double_divide(X, inverse(Y)), double_divide(double_divide(Z, double_divide(W, double_divide(W, identity))), double_divide(X, identity))), Y)
% 0.21/0.40 = { by axiom 1 (inverse) }
% 0.21/0.40 double_divide(double_divide(double_divide(X, double_divide(Y, identity)), double_divide(double_divide(Z, double_divide(W, double_divide(W, identity))), double_divide(X, identity))), Y)
% 0.21/0.40 = { by axiom 4 (single_axiom) }
% 0.21/0.40 Z
% 0.21/0.40
% 0.21/0.40 Lemma 7: double_divide(multiply(inverse(X), inverse(Y)), X) = Y.
% 0.21/0.40 Proof:
% 0.21/0.40 double_divide(multiply(inverse(X), inverse(Y)), X)
% 0.21/0.40 = { by lemma 5 R->L }
% 0.21/0.40 double_divide(inverse(double_divide(inverse(Y), inverse(X))), X)
% 0.21/0.40 = { by axiom 1 (inverse) }
% 0.21/0.40 double_divide(double_divide(double_divide(inverse(Y), inverse(X)), identity), X)
% 0.21/0.40 = { by axiom 2 (identity) }
% 0.21/0.40 double_divide(double_divide(double_divide(inverse(Y), inverse(X)), double_divide(inverse(Y), inverse(inverse(Y)))), X)
% 0.21/0.40 = { by lemma 6 }
% 0.21/0.40 Y
% 0.21/0.40
% 0.21/0.40 Lemma 8: double_divide(inverse(identity), inverse(X)) = X.
% 0.21/0.40 Proof:
% 0.21/0.40 double_divide(inverse(identity), inverse(X))
% 0.21/0.40 = { by axiom 2 (identity) }
% 0.21/0.40 double_divide(inverse(double_divide(inverse(X), inverse(inverse(X)))), inverse(X))
% 0.21/0.40 = { by lemma 5 }
% 0.21/0.40 double_divide(multiply(inverse(inverse(X)), inverse(X)), inverse(X))
% 0.21/0.40 = { by lemma 7 }
% 0.21/0.40 X
% 0.21/0.40
% 0.21/0.40 Lemma 9: inverse(identity) = identity.
% 0.21/0.40 Proof:
% 0.21/0.40 inverse(identity)
% 0.21/0.40 = { by lemma 8 R->L }
% 0.21/0.40 double_divide(inverse(identity), inverse(inverse(identity)))
% 0.21/0.40 = { by axiom 2 (identity) R->L }
% 0.21/0.40 identity
% 0.21/0.40
% 0.21/0.40 Lemma 10: inverse(multiply(inverse(identity), inverse(X))) = X.
% 0.21/0.40 Proof:
% 0.21/0.40 inverse(multiply(inverse(identity), inverse(X)))
% 0.21/0.40 = { by axiom 1 (inverse) }
% 0.21/0.40 double_divide(multiply(inverse(identity), inverse(X)), identity)
% 0.21/0.40 = { by lemma 7 }
% 0.21/0.40 X
% 0.21/0.40
% 0.21/0.40 Goal 1 (prove_these_axioms_2): multiply(identity, a2) = a2.
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(identity, a2)
% 0.21/0.40 = { by lemma 10 R->L }
% 0.21/0.40 inverse(multiply(inverse(identity), inverse(multiply(identity, a2))))
% 0.21/0.40 = { by lemma 8 R->L }
% 0.21/0.40 inverse(double_divide(inverse(identity), inverse(multiply(inverse(identity), inverse(multiply(identity, a2))))))
% 0.21/0.40 = { by lemma 5 }
% 0.21/0.40 multiply(inverse(multiply(inverse(identity), inverse(multiply(identity, a2)))), inverse(identity))
% 0.21/0.40 = { by lemma 9 }
% 0.21/0.40 multiply(inverse(multiply(inverse(identity), inverse(multiply(identity, a2)))), identity)
% 0.21/0.40 = { by lemma 10 }
% 0.21/0.40 multiply(multiply(identity, a2), identity)
% 0.21/0.40 = { by lemma 5 R->L }
% 0.21/0.40 inverse(double_divide(identity, multiply(identity, a2)))
% 0.21/0.40 = { by axiom 1 (inverse) }
% 0.21/0.40 double_divide(double_divide(identity, multiply(identity, a2)), identity)
% 0.21/0.40 = { by lemma 5 R->L }
% 0.21/0.40 double_divide(double_divide(identity, inverse(double_divide(a2, identity))), identity)
% 0.21/0.40 = { by axiom 1 (inverse) R->L }
% 0.21/0.40 double_divide(double_divide(identity, inverse(inverse(a2))), identity)
% 0.21/0.40 = { by axiom 1 (inverse) }
% 0.21/0.40 double_divide(double_divide(identity, double_divide(inverse(a2), identity)), identity)
% 0.21/0.40 = { by lemma 9 R->L }
% 0.21/0.40 double_divide(double_divide(identity, double_divide(inverse(a2), inverse(identity))), identity)
% 0.21/0.40 = { by lemma 8 R->L }
% 0.21/0.40 double_divide(double_divide(double_divide(inverse(identity), inverse(identity)), double_divide(inverse(a2), inverse(identity))), identity)
% 0.21/0.40 = { by lemma 9 }
% 0.21/0.40 double_divide(double_divide(double_divide(identity, inverse(identity)), double_divide(inverse(a2), inverse(identity))), identity)
% 0.21/0.40 = { by lemma 6 }
% 0.21/0.40 a2
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40
% 0.21/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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