TSTP Solution File: GRP580-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP580-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n029.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 01:18:59 EDT 2023
% Result : Unsatisfiable 0.14s 0.34s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : GRP580-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.03/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n029.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 23:05:56 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.14/0.34 Command-line arguments: --flatten
% 0.14/0.34
% 0.14/0.34 % SZS status Unsatisfiable
% 0.14/0.34
% 0.14/0.36 % SZS output start Proof
% 0.14/0.36 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.14/0.36 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.14/0.36 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.14/0.36 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), double_divide(Y, identity))), double_divide(identity, identity)) = Z.
% 0.14/0.36
% 0.14/0.36 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.14/0.36 Proof:
% 0.14/0.36 inverse(double_divide(X, Y))
% 0.14/0.36 = { by axiom 1 (inverse) }
% 0.14/0.36 double_divide(double_divide(X, Y), identity)
% 0.14/0.36 = { by axiom 3 (multiply) R->L }
% 0.14/0.36 multiply(Y, X)
% 0.14/0.36
% 0.14/0.36 Lemma 6: double_divide(X, double_divide(X, identity)) = identity.
% 0.14/0.36 Proof:
% 0.14/0.36 double_divide(X, double_divide(X, identity))
% 0.14/0.36 = { by axiom 1 (inverse) R->L }
% 0.14/0.36 double_divide(X, inverse(X))
% 0.14/0.36 = { by axiom 2 (identity) R->L }
% 0.14/0.36 identity
% 0.14/0.36
% 0.14/0.36 Lemma 7: multiply(double_divide(X, identity), X) = double_divide(identity, identity).
% 0.14/0.36 Proof:
% 0.14/0.36 multiply(double_divide(X, identity), X)
% 0.14/0.36 = { by lemma 5 R->L }
% 0.14/0.36 inverse(double_divide(X, double_divide(X, identity)))
% 0.14/0.36 = { by lemma 6 }
% 0.14/0.36 inverse(identity)
% 0.14/0.36 = { by axiom 1 (inverse) }
% 0.14/0.36 double_divide(identity, identity)
% 0.14/0.36
% 0.14/0.36 Lemma 8: double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), double_divide(identity, identity)) = Z.
% 0.14/0.36 Proof:
% 0.14/0.36 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), double_divide(identity, identity))
% 0.14/0.36 = { by axiom 1 (inverse) }
% 0.14/0.36 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), double_divide(Y, identity))), double_divide(identity, identity))
% 0.14/0.36 = { by axiom 4 (single_axiom) }
% 0.14/0.36 Z
% 0.14/0.36
% 0.14/0.36 Lemma 9: double_divide(double_divide(X, double_divide(identity, inverse(Y))), double_divide(identity, identity)) = multiply(X, Y).
% 0.14/0.36 Proof:
% 0.14/0.36 double_divide(double_divide(X, double_divide(identity, inverse(Y))), double_divide(identity, identity))
% 0.14/0.36 = { by axiom 2 (identity) }
% 0.14/0.36 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), inverse(double_divide(Y, X))), inverse(Y))), double_divide(identity, identity))
% 0.14/0.36 = { by lemma 8 }
% 0.14/0.36 inverse(double_divide(Y, X))
% 0.14/0.36 = { by lemma 5 }
% 0.14/0.36 multiply(X, Y)
% 0.14/0.36
% 0.14/0.36 Lemma 10: double_divide(inverse(X), double_divide(identity, identity)) = multiply(X, identity).
% 0.14/0.36 Proof:
% 0.14/0.36 double_divide(inverse(X), double_divide(identity, identity))
% 0.14/0.36 = { by axiom 1 (inverse) }
% 0.14/0.36 double_divide(double_divide(X, identity), double_divide(identity, identity))
% 0.14/0.36 = { by lemma 6 R->L }
% 0.14/0.36 double_divide(double_divide(X, double_divide(identity, double_divide(identity, identity))), double_divide(identity, identity))
% 0.14/0.36 = { by axiom 1 (inverse) R->L }
% 0.14/0.36 double_divide(double_divide(X, double_divide(identity, inverse(identity))), double_divide(identity, identity))
% 0.14/0.36 = { by lemma 9 }
% 0.14/0.36 multiply(X, identity)
% 0.14/0.36
% 0.14/0.36 Lemma 11: multiply(identity, X) = inverse(inverse(X)).
% 0.14/0.36 Proof:
% 0.14/0.36 multiply(identity, X)
% 0.14/0.36 = { by lemma 5 R->L }
% 0.14/0.36 inverse(double_divide(X, identity))
% 0.14/0.36 = { by axiom 1 (inverse) R->L }
% 0.14/0.36 inverse(inverse(X))
% 0.14/0.36
% 0.14/0.36 Lemma 12: double_divide(double_divide(double_divide(X, identity), double_divide(double_divide(identity, Y), double_divide(X, identity))), double_divide(identity, identity)) = Y.
% 0.14/0.37 Proof:
% 0.14/0.37 double_divide(double_divide(double_divide(X, identity), double_divide(double_divide(identity, Y), double_divide(X, identity))), double_divide(identity, identity))
% 0.14/0.37 = { by axiom 1 (inverse) R->L }
% 0.14/0.37 double_divide(double_divide(double_divide(X, identity), double_divide(double_divide(identity, Y), inverse(X))), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 6 R->L }
% 0.14/0.37 double_divide(double_divide(double_divide(X, identity), double_divide(double_divide(double_divide(X, double_divide(X, identity)), Y), inverse(X))), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 8 }
% 0.14/0.37 Y
% 0.14/0.37
% 0.14/0.37 Lemma 13: double_divide(double_divide(double_divide(identity, identity), Y), double_divide(identity, identity)) = double_divide(double_divide(inverse(X), Y), inverse(X)).
% 0.14/0.37 Proof:
% 0.14/0.37 double_divide(double_divide(double_divide(identity, identity), Y), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 8 R->L }
% 0.14/0.37 double_divide(double_divide(double_divide(identity, identity), double_divide(double_divide(identity, double_divide(double_divide(double_divide(X, identity), Y), inverse(X))), double_divide(identity, identity))), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 12 }
% 0.14/0.37 double_divide(double_divide(double_divide(X, identity), Y), inverse(X))
% 0.14/0.37 = { by axiom 1 (inverse) R->L }
% 0.14/0.37 double_divide(double_divide(inverse(X), Y), inverse(X))
% 0.14/0.37
% 0.14/0.37 Lemma 14: double_divide(identity, identity) = identity.
% 0.14/0.37 Proof:
% 0.14/0.37 double_divide(identity, identity)
% 0.14/0.37 = { by lemma 7 R->L }
% 0.14/0.37 multiply(double_divide(identity, identity), identity)
% 0.14/0.37 = { by lemma 10 R->L }
% 0.14/0.37 double_divide(inverse(double_divide(identity, identity)), double_divide(identity, identity))
% 0.14/0.37 = { by axiom 1 (inverse) R->L }
% 0.14/0.37 double_divide(inverse(inverse(identity)), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 11 R->L }
% 0.14/0.37 double_divide(multiply(identity, identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 10 R->L }
% 0.14/0.37 double_divide(double_divide(inverse(identity), double_divide(identity, identity)), double_divide(identity, identity))
% 0.14/0.37 = { by axiom 1 (inverse) }
% 0.14/0.37 double_divide(double_divide(double_divide(identity, identity), double_divide(identity, identity)), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 13 }
% 0.14/0.37 double_divide(double_divide(inverse(double_divide(identity, identity)), double_divide(identity, identity)), inverse(double_divide(identity, identity)))
% 0.14/0.37 = { by lemma 10 }
% 0.14/0.37 double_divide(multiply(double_divide(identity, identity), identity), inverse(double_divide(identity, identity)))
% 0.14/0.37 = { by lemma 7 }
% 0.14/0.37 double_divide(double_divide(identity, identity), inverse(double_divide(identity, identity)))
% 0.14/0.37 = { by axiom 2 (identity) R->L }
% 0.14/0.37 identity
% 0.14/0.37
% 0.14/0.37 Lemma 15: double_divide(X, double_divide(identity, identity)) = inverse(X).
% 0.14/0.37 Proof:
% 0.14/0.37 double_divide(X, double_divide(identity, identity))
% 0.14/0.37 = { by lemma 14 }
% 0.14/0.37 double_divide(X, identity)
% 0.14/0.37 = { by axiom 1 (inverse) R->L }
% 0.14/0.37 inverse(X)
% 0.14/0.37
% 0.14/0.37 Lemma 16: multiply(X, double_divide(identity, identity)) = inverse(inverse(X)).
% 0.14/0.37 Proof:
% 0.14/0.37 multiply(X, double_divide(identity, identity))
% 0.14/0.37 = { by lemma 14 }
% 0.14/0.37 multiply(X, identity)
% 0.14/0.37 = { by lemma 10 R->L }
% 0.14/0.37 double_divide(inverse(X), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 15 }
% 0.14/0.37 inverse(inverse(X))
% 0.14/0.37
% 0.14/0.37 Lemma 17: multiply(double_divide(identity, identity), X) = inverse(inverse(X)).
% 0.14/0.37 Proof:
% 0.14/0.37 multiply(double_divide(identity, identity), X)
% 0.14/0.37 = { by lemma 14 }
% 0.14/0.37 multiply(identity, X)
% 0.14/0.37 = { by lemma 11 }
% 0.14/0.37 inverse(inverse(X))
% 0.14/0.37
% 0.14/0.37 Lemma 18: inverse(inverse(inverse(inverse(X)))) = X.
% 0.14/0.37 Proof:
% 0.14/0.37 inverse(inverse(inverse(inverse(X))))
% 0.14/0.37 = { by lemma 16 R->L }
% 0.14/0.37 inverse(inverse(multiply(X, double_divide(identity, identity))))
% 0.14/0.37 = { by lemma 14 }
% 0.14/0.37 inverse(inverse(multiply(X, identity)))
% 0.14/0.37 = { by lemma 5 R->L }
% 0.14/0.37 inverse(inverse(inverse(double_divide(identity, X))))
% 0.14/0.37 = { by lemma 17 R->L }
% 0.14/0.37 inverse(multiply(double_divide(identity, identity), double_divide(identity, X)))
% 0.14/0.37 = { by lemma 5 R->L }
% 0.14/0.37 inverse(inverse(double_divide(double_divide(identity, X), double_divide(identity, identity))))
% 0.14/0.37 = { by lemma 16 R->L }
% 0.14/0.37 multiply(double_divide(double_divide(identity, X), double_divide(identity, identity)), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 5 R->L }
% 0.14/0.37 inverse(double_divide(double_divide(identity, identity), double_divide(double_divide(identity, X), double_divide(identity, identity))))
% 0.14/0.37 = { by lemma 15 R->L }
% 0.14/0.37 double_divide(double_divide(double_divide(identity, identity), double_divide(double_divide(identity, X), double_divide(identity, identity))), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 12 }
% 0.14/0.37 X
% 0.14/0.37
% 0.14/0.37 Lemma 19: inverse(inverse(inverse(X))) = inverse(X).
% 0.14/0.37 Proof:
% 0.14/0.37 inverse(inverse(inverse(X)))
% 0.14/0.37 = { by lemma 16 R->L }
% 0.14/0.37 multiply(inverse(X), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 14 }
% 0.14/0.37 multiply(inverse(X), identity)
% 0.14/0.37 = { by axiom 2 (identity) }
% 0.14/0.37 multiply(inverse(X), double_divide(inverse(X), inverse(inverse(X))))
% 0.14/0.37 = { by lemma 5 R->L }
% 0.14/0.37 inverse(double_divide(double_divide(inverse(X), inverse(inverse(X))), inverse(X)))
% 0.14/0.37 = { by lemma 13 R->L }
% 0.14/0.37 inverse(double_divide(double_divide(double_divide(identity, identity), inverse(inverse(X))), double_divide(identity, identity)))
% 0.14/0.37 = { by lemma 5 }
% 0.14/0.37 multiply(double_divide(identity, identity), double_divide(double_divide(identity, identity), inverse(inverse(X))))
% 0.14/0.37 = { by lemma 17 }
% 0.14/0.37 inverse(inverse(double_divide(double_divide(identity, identity), inverse(inverse(X)))))
% 0.14/0.37 = { by lemma 5 }
% 0.14/0.37 inverse(multiply(inverse(inverse(X)), double_divide(identity, identity)))
% 0.14/0.37 = { by lemma 16 }
% 0.14/0.37 inverse(inverse(inverse(inverse(inverse(X)))))
% 0.14/0.37 = { by lemma 18 }
% 0.14/0.37 inverse(X)
% 0.14/0.37
% 0.14/0.37 Lemma 20: inverse(inverse(X)) = X.
% 0.14/0.37 Proof:
% 0.14/0.37 inverse(inverse(X))
% 0.14/0.37 = { by lemma 16 R->L }
% 0.14/0.37 multiply(X, double_divide(identity, identity))
% 0.14/0.37 = { by lemma 14 }
% 0.14/0.37 multiply(X, identity)
% 0.14/0.37 = { by lemma 10 R->L }
% 0.14/0.37 double_divide(inverse(X), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 19 R->L }
% 0.14/0.37 double_divide(inverse(inverse(inverse(X))), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 10 }
% 0.14/0.37 multiply(inverse(inverse(X)), identity)
% 0.14/0.37 = { by lemma 14 R->L }
% 0.14/0.37 multiply(inverse(inverse(X)), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 16 }
% 0.14/0.37 inverse(inverse(inverse(inverse(X))))
% 0.14/0.37 = { by lemma 18 }
% 0.14/0.37 X
% 0.14/0.37
% 0.14/0.37 Lemma 21: inverse(multiply(X, Y)) = double_divide(Y, X).
% 0.14/0.37 Proof:
% 0.14/0.37 inverse(multiply(X, Y))
% 0.14/0.37 = { by lemma 5 R->L }
% 0.14/0.37 inverse(inverse(double_divide(Y, X)))
% 0.14/0.37 = { by lemma 20 }
% 0.14/0.37 double_divide(Y, X)
% 0.14/0.37
% 0.14/0.37 Lemma 22: double_divide(double_divide(X, Y), X) = Y.
% 0.14/0.37 Proof:
% 0.14/0.37 double_divide(double_divide(X, Y), X)
% 0.14/0.37 = { by lemma 20 R->L }
% 0.14/0.37 double_divide(double_divide(X, Y), inverse(inverse(X)))
% 0.14/0.37 = { by lemma 20 R->L }
% 0.14/0.37 double_divide(double_divide(inverse(inverse(X)), Y), inverse(inverse(X)))
% 0.14/0.37 = { by lemma 13 R->L }
% 0.14/0.37 double_divide(double_divide(double_divide(identity, identity), Y), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 15 }
% 0.14/0.37 inverse(double_divide(double_divide(identity, identity), Y))
% 0.14/0.37 = { by lemma 5 }
% 0.14/0.37 multiply(Y, double_divide(identity, identity))
% 0.14/0.37 = { by lemma 16 }
% 0.14/0.37 inverse(inverse(Y))
% 0.14/0.37 = { by lemma 20 }
% 0.14/0.37 Y
% 0.14/0.37
% 0.14/0.37 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.14/0.37 Proof:
% 0.14/0.37 multiply(a, b)
% 0.14/0.37 = { by lemma 20 R->L }
% 0.14/0.37 inverse(inverse(multiply(a, b)))
% 0.14/0.37 = { by lemma 16 R->L }
% 0.14/0.37 multiply(multiply(a, b), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 14 }
% 0.14/0.37 multiply(multiply(a, b), identity)
% 0.14/0.37 = { by lemma 10 R->L }
% 0.14/0.37 double_divide(inverse(multiply(a, b)), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 15 R->L }
% 0.14/0.37 double_divide(double_divide(multiply(a, b), double_divide(identity, identity)), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 5 R->L }
% 0.14/0.37 double_divide(double_divide(inverse(double_divide(b, a)), double_divide(identity, identity)), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 10 }
% 0.14/0.37 double_divide(multiply(double_divide(b, a), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 22 R->L }
% 0.14/0.37 double_divide(multiply(double_divide(double_divide(b, double_divide(b, a)), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 20 R->L }
% 0.14/0.37 double_divide(multiply(double_divide(double_divide(b, double_divide(inverse(inverse(b)), a)), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 19 R->L }
% 0.14/0.37 double_divide(multiply(double_divide(double_divide(b, double_divide(inverse(inverse(inverse(inverse(b)))), a)), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 16 R->L }
% 0.14/0.37 double_divide(multiply(double_divide(double_divide(b, double_divide(inverse(multiply(inverse(b), double_divide(identity, identity))), a)), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 21 }
% 0.14/0.37 double_divide(multiply(double_divide(double_divide(b, double_divide(double_divide(double_divide(identity, identity), inverse(b)), a)), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 14 }
% 0.14/0.37 double_divide(multiply(double_divide(double_divide(b, double_divide(double_divide(identity, inverse(b)), a)), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 21 R->L }
% 0.14/0.37 double_divide(multiply(double_divide(inverse(multiply(double_divide(double_divide(identity, inverse(b)), a), b)), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 9 R->L }
% 0.14/0.37 double_divide(multiply(double_divide(inverse(double_divide(double_divide(double_divide(double_divide(identity, inverse(b)), a), double_divide(identity, inverse(b))), double_divide(identity, identity))), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 5 }
% 0.14/0.37 double_divide(multiply(double_divide(multiply(double_divide(identity, identity), double_divide(double_divide(double_divide(identity, inverse(b)), a), double_divide(identity, inverse(b)))), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 22 }
% 0.14/0.37 double_divide(multiply(double_divide(multiply(double_divide(identity, identity), a), b), identity), double_divide(identity, identity))
% 0.14/0.37 = { by lemma 17 }
% 0.14/0.38 double_divide(multiply(double_divide(inverse(inverse(a)), b), identity), double_divide(identity, identity))
% 0.14/0.38 = { by lemma 20 }
% 0.14/0.38 double_divide(multiply(double_divide(a, b), identity), double_divide(identity, identity))
% 0.14/0.38 = { by lemma 21 R->L }
% 0.14/0.38 double_divide(multiply(inverse(multiply(b, a)), identity), double_divide(identity, identity))
% 0.14/0.38 = { by lemma 14 R->L }
% 0.14/0.38 double_divide(multiply(inverse(multiply(b, a)), double_divide(identity, identity)), double_divide(identity, identity))
% 0.14/0.38 = { by lemma 16 }
% 0.14/0.38 double_divide(inverse(inverse(inverse(multiply(b, a)))), double_divide(identity, identity))
% 0.14/0.38 = { by lemma 19 }
% 0.14/0.38 double_divide(inverse(multiply(b, a)), double_divide(identity, identity))
% 0.14/0.38 = { by lemma 10 }
% 0.14/0.38 multiply(multiply(b, a), identity)
% 0.14/0.38 = { by lemma 14 R->L }
% 0.14/0.38 multiply(multiply(b, a), double_divide(identity, identity))
% 0.14/0.38 = { by lemma 16 }
% 0.14/0.38 inverse(inverse(multiply(b, a)))
% 0.14/0.38 = { by lemma 20 }
% 0.14/0.38 multiply(b, a)
% 0.14/0.38 % SZS output end Proof
% 0.14/0.38
% 0.14/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------