TSTP Solution File: GRP570-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP570-1 : 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 : n005.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 01:18:57 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
% 0.07/0.12 % Problem : GRP570-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 23:10:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --flatten
% 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 (inverse): inverse(X) = double_divide(X, identity).
% 0.19/0.39 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.19/0.39 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.19/0.39 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(Z, identity))), double_divide(identity, identity)) = Y.
% 0.19/0.39
% 0.19/0.39 Lemma 5: double_divide(X, double_divide(X, identity)) = identity.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(X, double_divide(X, identity))
% 0.19/0.39 = { by axiom 1 (inverse) R->L }
% 0.19/0.39 double_divide(X, inverse(X))
% 0.19/0.39 = { by axiom 2 (identity) R->L }
% 0.19/0.39 identity
% 0.19/0.39
% 0.19/0.39 Lemma 6: double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), inverse(Z))), double_divide(identity, identity)) = Y.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), inverse(Z))), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 1 (inverse) }
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(Z, identity))), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 4 (single_axiom) }
% 0.19/0.39 Y
% 0.19/0.39
% 0.19/0.39 Lemma 7: double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), double_divide(identity, identity))), double_divide(identity, identity)) = Y.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 1 (inverse) R->L }
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 1 (inverse) }
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), inverse(identity))), double_divide(identity, identity))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 Y
% 0.19/0.39
% 0.19/0.39 Lemma 8: double_divide(inverse(X), double_divide(identity, identity)) = X.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(inverse(X), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 1 (inverse) }
% 0.19/0.39 double_divide(double_divide(X, identity), double_divide(identity, identity))
% 0.19/0.39 = { by lemma 5 R->L }
% 0.19/0.39 double_divide(double_divide(X, double_divide(identity, double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 2 (identity) }
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(X, inverse(X)), double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.39 = { by lemma 7 }
% 0.19/0.39 X
% 0.19/0.39
% 0.19/0.39 Lemma 9: double_divide(double_divide(X, double_divide(inverse(Y), inverse(double_divide(X, identity)))), double_divide(identity, identity)) = Y.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(double_divide(X, double_divide(inverse(Y), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 1 (inverse) }
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(Y, identity), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.39 = { by lemma 5 R->L }
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, double_divide(X, identity))), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 Y
% 0.19/0.39
% 0.19/0.39 Goal 1 (prove_these_axioms_2): multiply(identity, a2) = a2.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(identity, a2)
% 0.19/0.39 = { by lemma 9 R->L }
% 0.19/0.39 double_divide(double_divide(X, double_divide(inverse(multiply(identity, a2)), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 1 (inverse) }
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(multiply(identity, a2), identity), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.39 = { by lemma 8 R->L }
% 0.19/0.39 double_divide(double_divide(X, double_divide(double_divide(multiply(identity, a2), double_divide(inverse(identity), double_divide(identity, identity))), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 1 (inverse) }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(identity, identity), double_divide(identity, identity))), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by lemma 5 R->L }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(identity, double_divide(identity, double_divide(identity, identity))), double_divide(identity, identity))), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by lemma 9 R->L }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(identity, double_divide(double_divide(double_divide(identity, double_divide(inverse(identity), inverse(double_divide(identity, identity)))), double_divide(identity, identity)), double_divide(identity, identity))), double_divide(identity, identity))), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by axiom 1 (inverse) }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(identity, double_divide(double_divide(double_divide(identity, double_divide(double_divide(identity, identity), inverse(double_divide(identity, identity)))), double_divide(identity, identity)), double_divide(identity, identity))), double_divide(identity, identity))), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by axiom 2 (identity) R->L }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(identity, double_divide(double_divide(double_divide(identity, identity), double_divide(identity, identity)), double_divide(identity, identity))), double_divide(identity, identity))), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by axiom 1 (inverse) R->L }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(identity, double_divide(double_divide(double_divide(identity, identity), inverse(identity)), double_divide(identity, identity))), double_divide(identity, identity))), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by lemma 7 }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(multiply(identity, a2), double_divide(identity, identity)), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by axiom 3 (multiply) }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(double_divide(double_divide(a2, identity), identity), double_divide(identity, identity)), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by axiom 1 (inverse) R->L }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(inverse(double_divide(a2, identity)), double_divide(identity, identity)), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by axiom 1 (inverse) R->L }
% 0.19/0.40 double_divide(double_divide(X, double_divide(double_divide(inverse(inverse(a2)), double_divide(identity, identity)), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by lemma 8 }
% 0.19/0.40 double_divide(double_divide(X, double_divide(inverse(a2), inverse(double_divide(X, identity)))), double_divide(identity, identity))
% 0.19/0.40 = { by lemma 9 }
% 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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