TSTP Solution File: GRP566-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP566-1 : 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 : n008.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 01:18:56 EDT 2023
% Result : Unsatisfiable 0.15s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP566-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 00:03:47 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.41 Command-line arguments: --ground-connectedness --complete-subsets
% 0.15/0.41
% 0.15/0.41 % SZS status Unsatisfiable
% 0.15/0.41
% 0.15/0.42 % SZS output start Proof
% 0.22/0.42 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.22/0.42 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.22/0.42 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.22/0.42 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), double_divide(identity, identity)) = Y.
% 0.22/0.42
% 0.22/0.42 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.22/0.42 Proof:
% 0.22/0.42 inverse(double_divide(X, Y))
% 0.22/0.42 = { by axiom 1 (inverse) }
% 0.22/0.42 double_divide(double_divide(X, Y), identity)
% 0.22/0.42 = { by axiom 3 (multiply) R->L }
% 0.22/0.42 multiply(Y, X)
% 0.22/0.42
% 0.22/0.42 Lemma 6: multiply(identity, X) = inverse(inverse(X)).
% 0.22/0.42 Proof:
% 0.22/0.42 multiply(identity, X)
% 0.22/0.42 = { by lemma 5 R->L }
% 0.22/0.42 inverse(double_divide(X, identity))
% 0.22/0.42 = { by axiom 1 (inverse) R->L }
% 0.22/0.42 inverse(inverse(X))
% 0.22/0.42
% 0.22/0.42 Lemma 7: double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), inverse(identity)) = Y.
% 0.22/0.42 Proof:
% 0.22/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), inverse(identity))
% 0.22/0.42 = { by axiom 1 (inverse) }
% 0.22/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), double_divide(identity, identity))
% 0.22/0.42 = { by axiom 4 (single_axiom) }
% 0.22/0.42 Y
% 0.22/0.42
% 0.22/0.42 Lemma 8: double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity)) = Y.
% 0.22/0.42 Proof:
% 0.22/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity))
% 0.22/0.42 = { by axiom 1 (inverse) }
% 0.22/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), double_divide(identity, identity))), inverse(identity))
% 0.22/0.42 = { by axiom 1 (inverse) }
% 0.22/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), double_divide(identity, identity))), inverse(identity))
% 0.22/0.42 = { by lemma 7 }
% 0.22/0.42 Y
% 0.22/0.42
% 0.22/0.42 Goal 1 (prove_these_axioms_2): multiply(identity, a2) = a2.
% 0.22/0.42 Proof:
% 0.22/0.42 multiply(identity, a2)
% 0.22/0.42 = { by lemma 6 }
% 0.22/0.42 inverse(inverse(a2))
% 0.22/0.42 = { by lemma 8 R->L }
% 0.22/0.42 double_divide(double_divide(a2, double_divide(double_divide(inverse(inverse(a2)), inverse(a2)), inverse(identity))), inverse(identity))
% 0.22/0.42 = { by lemma 7 R->L }
% 0.22/0.42 double_divide(double_divide(a2, double_divide(double_divide(inverse(inverse(a2)), double_divide(double_divide(identity, double_divide(double_divide(inverse(a2), double_divide(identity, inverse(identity))), double_divide(identity, inverse(identity)))), inverse(identity))), inverse(identity))), inverse(identity))
% 0.22/0.42 = { by axiom 2 (identity) R->L }
% 0.22/0.42 double_divide(double_divide(a2, double_divide(double_divide(inverse(inverse(a2)), double_divide(double_divide(identity, double_divide(double_divide(inverse(a2), double_divide(identity, inverse(identity))), identity)), inverse(identity))), inverse(identity))), inverse(identity))
% 0.22/0.42 = { by axiom 1 (inverse) R->L }
% 0.22/0.42 double_divide(double_divide(a2, double_divide(double_divide(inverse(inverse(a2)), double_divide(double_divide(identity, inverse(double_divide(inverse(a2), double_divide(identity, inverse(identity))))), inverse(identity))), inverse(identity))), inverse(identity))
% 0.22/0.42 = { by lemma 5 }
% 0.22/0.42 double_divide(double_divide(a2, double_divide(double_divide(inverse(inverse(a2)), double_divide(double_divide(identity, multiply(double_divide(identity, inverse(identity)), inverse(a2))), inverse(identity))), inverse(identity))), inverse(identity))
% 0.22/0.42 = { by axiom 2 (identity) R->L }
% 0.22/0.42 double_divide(double_divide(a2, double_divide(double_divide(inverse(inverse(a2)), double_divide(double_divide(identity, multiply(identity, inverse(a2))), inverse(identity))), inverse(identity))), inverse(identity))
% 0.22/0.42 = { by lemma 6 }
% 0.22/0.42 double_divide(double_divide(a2, double_divide(double_divide(inverse(inverse(a2)), double_divide(double_divide(identity, inverse(inverse(inverse(a2)))), inverse(identity))), inverse(identity))), inverse(identity))
% 0.22/0.42 = { by lemma 8 }
% 0.22/0.42 double_divide(double_divide(a2, identity), inverse(identity))
% 0.22/0.42 = { by axiom 2 (identity) }
% 0.22/0.42 double_divide(double_divide(a2, double_divide(identity, inverse(identity))), inverse(identity))
% 0.22/0.42 = { by axiom 2 (identity) }
% 0.22/0.42 double_divide(double_divide(a2, double_divide(double_divide(a2, inverse(a2)), inverse(identity))), inverse(identity))
% 0.22/0.42 = { by lemma 8 }
% 0.22/0.42 a2
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42
% 0.22/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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