%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:35:24 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:53:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.57 % Refutation found
% 0.12/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.57 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.57 fof(f1,axiom,(
% 0.12/0.57 (![X]: (multiply(identity,X) = X ))),
% 0.12/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.57 fof(f2,axiom,(
% 0.12/0.57 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.12/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.57 fof(f3,axiom,(
% 0.12/0.57 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.12/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.57 fof(f4,axiom,(
% 0.12/0.57 (![X,Y]: (commutator(X,Y) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))) ))),
% 0.12/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.57 fof(f5,hypothesis,(
% 0.12/0.57 (![X]: (multiply(X,multiply(X,X)) = identity ))),
% 0.12/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.57 fof(f6,negated_conjecture,(
% 0.12/0.57 commutator(commutator(a,b),b) != identity ),
% 0.12/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.57 fof(f7,plain,(
% 0.12/0.57 ![X0]: (multiply(identity,X0)=X0)),
% 0.12/0.57 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.57 fof(f8,plain,(
% 0.12/0.57 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.12/0.57 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.57 fof(f9,plain,(
% 0.12/0.57 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.12/0.57 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.57 fof(f10,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(X0,X1)=multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))))),
% 0.12/0.57 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.57 fof(f11,plain,(
% 0.12/0.57 ![X0]: (multiply(X0,multiply(X0,X0))=identity)),
% 0.12/0.57 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.57 fof(f12,plain,(
% 0.12/0.57 ~commutator(commutator(a,b),b)=identity),
% 0.12/0.57 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.57 fof(f19,plain,(
% 0.12/0.57 ![X0,X1]: (identity=multiply(X0,multiply(X1,multiply(multiply(X0,X1),multiply(X0,X1)))))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f11,f9])).
% 0.12/0.57 fof(f21,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f8,f9])).
% 0.12/0.57 fof(f26,plain,(
% 0.12/0.57 ![X0,X1]: (identity=multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f9,f19])).
% 0.12/0.57 fof(f29,plain,(
% 0.12/0.57 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f7,f21])).
% 0.12/0.57 fof(f35,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f29,f29])).
% 0.12/0.57 fof(f36,plain,(
% 0.12/0.57 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f8,f29])).
% 0.12/0.57 fof(f38,plain,(
% 0.12/0.57 ![X0]: (multiply(X0,X0)=multiply(inverse(X0),identity))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f11,f29])).
% 0.12/0.57 fof(f40,plain,(
% 0.12/0.57 ![X0]: (X0=multiply(X0,identity))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f35,f36])).
% 0.12/0.57 fof(f41,plain,(
% 0.12/0.57 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 0.12/0.57 inference(backward_demodulation,[status(thm)],[f42,f11])).
% 0.12/0.57 fof(f42,plain,(
% 0.12/0.57 ![X0]: (multiply(X0,X0)=inverse(X0))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f40,f38])).
% 0.12/0.57 fof(f44,plain,(
% 0.12/0.57 ![X0,X1,X2]: (commutator(multiply(X0,X1),X2)=multiply(X0,multiply(X1,multiply(X2,multiply(inverse(multiply(X0,X1)),inverse(X2))))))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f9,f10])).
% 0.12/0.57 fof(f47,plain,(
% 0.12/0.57 ![X0,X1,X2]: (commutator(X0,multiply(X1,X2))=multiply(X0,multiply(X1,multiply(X2,multiply(inverse(X0),inverse(multiply(X1,X2)))))))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f9,f10])).
% 0.12/0.57 fof(f88,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(X0,multiply(X1,multiply(X0,X1)))=inverse(multiply(X0,X1)))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f9,f42])).
% 0.12/0.57 fof(f95,plain,(
% 0.12/0.57 ![X0]: (X0=multiply(inverse(X0),inverse(X0)))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f42,f29])).
% 0.12/0.57 fof(f96,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(inverse(X0),X1)=multiply(X0,multiply(X0,X1)))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f42,f9])).
% 0.12/0.57 fof(f97,plain,(
% 0.12/0.57 ![X0,X1]: (identity=multiply(X0,multiply(X1,inverse(multiply(X0,X1)))))),
% 0.12/0.57 inference(backward_demodulation,[status(thm)],[f88,f26])).
% 0.12/0.57 fof(f101,plain,(
% 0.12/0.57 ![X0]: (X0=inverse(inverse(X0)))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f42,f95])).
% 0.12/0.57 fof(f110,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(inverse(X0),X1)=multiply(inverse(X0),multiply(X1,multiply(X0,inverse(X1)))))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f101,f10])).
% 0.12/0.57 fof(f111,plain,(
% 0.12/0.57 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),X0)))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f101,f29])).
% 0.12/0.57 fof(f234,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=multiply(inverse(X1),identity))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f97,f29])).
% 0.12/0.57 fof(f269,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=inverse(X1))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f40,f234])).
% 0.12/0.57 fof(f282,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(multiply(X0,X1),X1)=multiply(X0,multiply(inverse(X1),multiply(inverse(multiply(X0,X1)),inverse(X1)))))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f96,f44])).
% 0.12/0.57 fof(f411,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(inverse(multiply(X0,X1)),inverse(inverse(X0)))=inverse(X1))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f269,f269])).
% 0.12/0.57 fof(f421,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(X0,multiply(X1,inverse(X0)))=multiply(X0,multiply(multiply(X1,inverse(X0)),inverse(X1))))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f269,f10])).
% 0.12/0.57 fof(f422,plain,(
% 0.12/0.57 ![X0,X1]: (inverse(multiply(X0,inverse(X1)))=multiply(X1,inverse(X0)))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f269,f111])).
% 0.12/0.57 fof(f426,plain,(
% 0.12/0.57 ![X0,X1]: (inverse(multiply(X0,X1))=multiply(inverse(X1),inverse(X0)))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f269,f29])).
% 0.12/0.57 fof(f436,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(inverse(multiply(X0,X1)),X0)=inverse(X1))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f101,f411])).
% 0.12/0.57 fof(f453,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(X0,multiply(X1,inverse(X0)))=multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f9,f421])).
% 0.12/0.57 fof(f455,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(X0,multiply(X1,inverse(X0)))=commutator(X0,X1))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f10,f453])).
% 0.12/0.57 fof(f459,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(X0,X1)=multiply(X0,multiply(X1,inverse(multiply(X1,X0)))))),
% 0.12/0.57 inference(backward_demodulation,[status(thm)],[f426,f10])).
% 0.12/0.57 fof(f465,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(multiply(X0,X1),X1)=multiply(X0,multiply(inverse(X1),inverse(multiply(X1,multiply(X0,X1))))))),
% 0.12/0.57 inference(backward_demodulation,[status(thm)],[f426,f282])).
% 0.12/0.57 fof(f468,plain,(
% 0.12/0.57 ![X0,X1,X2]: (commutator(X0,multiply(X1,X2))=multiply(X0,multiply(X1,multiply(X2,inverse(multiply(multiply(X1,X2),X0))))))),
% 0.12/0.57 inference(backward_demodulation,[status(thm)],[f426,f47])).
% 0.12/0.57 fof(f474,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(multiply(X0,X1),X1)=multiply(X0,inverse(multiply(multiply(X1,multiply(X0,X1)),X1))))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f426,f465])).
% 0.12/0.57 fof(f475,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(multiply(X0,X1),X1)=multiply(X0,inverse(multiply(X1,multiply(multiply(X0,X1),X1)))))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f9,f474])).
% 0.12/0.57 fof(f476,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(multiply(X0,X1),X1)=multiply(X0,inverse(multiply(X1,multiply(X0,multiply(X1,X1))))))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f9,f475])).
% 0.12/0.57 fof(f477,plain,(
% 0.12/0.57 ![X0,X1]: (commutator(multiply(X0,X1),X1)=multiply(X0,inverse(multiply(X1,multiply(X0,inverse(X1))))))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f42,f476])).
% 0.12/0.57 fof(f482,plain,(
% 0.12/0.57 ![X0,X1,X2]: (commutator(X0,multiply(X1,X2))=multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X1,multiply(X2,X0)))))))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f9,f468])).
% 0.12/0.57 fof(f492,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(inverse(X0),X1)=inverse(multiply(inverse(X1),X0)))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f111,f436])).
% 0.12/0.57 fof(f498,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(inverse(inverse(multiply(X0,X1))),X0)=multiply(inverse(multiply(X0,X1)),inverse(X1)))),
% 0.12/0.57 inference(paramodulation,[status(thm)],[f436,f96])).
% 0.12/0.57 fof(f515,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(multiply(X0,X1),X0)=multiply(inverse(multiply(X0,X1)),inverse(X1)))),
% 0.12/0.57 inference(forward_demodulation,[status(thm)],[f101,f498])).
% 0.12/0.57 fof(f516,plain,(
% 0.12/0.57 ![X0,X1]: (multiply(X0,multiply(X1,X0))=multiply(inverse(multiply(X0,X1)),inverse(X1)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f9,f515])).
% 0.12/0.58 fof(f517,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(X0,multiply(X1,X0))=inverse(multiply(X1,multiply(X0,X1))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f426,f516])).
% 0.12/0.58 fof(f529,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),inverse(X0))=commutator(multiply(X0,X1),X1))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f269,f455])).
% 0.12/0.58 fof(f543,plain,(
% 0.12/0.58 ![X0,X1,X2]: (inverse(multiply(X0,multiply(X1,inverse(X2))))=multiply(X2,inverse(multiply(X0,X1))))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f9,f422])).
% 0.12/0.58 fof(f563,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),X1)=multiply(X0,multiply(X1,inverse(multiply(X1,X0)))))),
% 0.12/0.58 inference(backward_demodulation,[status(thm)],[f543,f477])).
% 0.12/0.58 fof(f592,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),inverse(X0))=commutator(X0,X1))),
% 0.12/0.58 inference(backward_demodulation,[status(thm)],[f593,f529])).
% 0.12/0.58 fof(f593,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),X1)=commutator(X0,X1))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f459,f563])).
% 0.12/0.58 fof(f597,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,multiply(X1,X0))=commutator(inverse(X1),multiply(X1,X0)))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f29,f593])).
% 0.12/0.58 fof(f615,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,inverse(inverse(X1)))=commutator(inverse(X1),multiply(X1,X0)))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f29,f592])).
% 0.12/0.58 fof(f630,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,multiply(X1,X0))=commutator(X0,X1))),
% 0.12/0.58 inference(backward_demodulation,[status(thm)],[f631,f597])).
% 0.12/0.58 fof(f631,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,X1)=commutator(inverse(X1),multiply(X1,X0)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f101,f615])).
% 0.12/0.58 fof(f652,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,inverse(multiply(X0,X1)))=multiply(X0,multiply(inverse(multiply(X0,X1)),inverse(inverse(X1)))))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f436,f459])).
% 0.12/0.58 fof(f661,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),X0)=multiply(multiply(X0,X1),multiply(X0,inverse(multiply(inverse(X0),X1)))))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f96,f459])).
% 0.12/0.58 fof(f669,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(commutator(X0,X1),inverse(X0))=commutator(X0,multiply(X1,inverse(multiply(X1,X0)))))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f459,f592])).
% 0.12/0.58 fof(f675,plain,(
% 0.12/0.58 ![X0,X1,X2]: (multiply(commutator(X0,X1),X2)=multiply(X0,multiply(multiply(X1,inverse(multiply(X1,X0))),X2)))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f459,f9])).
% 0.12/0.58 fof(f692,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,inverse(multiply(X0,X1)))=multiply(X0,inverse(multiply(inverse(X1),multiply(X0,X1)))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f426,f652])).
% 0.12/0.58 fof(f693,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,inverse(multiply(X0,X1)))=multiply(X0,multiply(inverse(multiply(X0,X1)),X1)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f492,f692])).
% 0.12/0.58 fof(f709,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),X0)=multiply(X0,multiply(X1,multiply(X0,inverse(multiply(inverse(X0),X1))))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f9,f661])).
% 0.12/0.58 fof(f710,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),X0)=multiply(X0,multiply(X1,multiply(X0,multiply(inverse(X1),X0)))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f492,f709])).
% 0.12/0.58 fof(f730,plain,(
% 0.12/0.58 ![X0,X1,X2]: (multiply(commutator(X0,X1),X2)=multiply(X0,multiply(X1,multiply(inverse(multiply(X1,X0)),X2))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f9,f675])).
% 0.12/0.58 fof(f733,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,inverse(X1))=commutator(X0,inverse(multiply(X0,X1))))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f436,f630])).
% 0.12/0.58 fof(f745,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,inverse(X1))=multiply(X0,multiply(inverse(multiply(X0,X1)),X1)))),
% 0.12/0.58 inference(backward_demodulation,[status(thm)],[f733,f693])).
% 0.12/0.58 fof(f799,plain,(
% 0.12/0.58 ![X0,X1,X2]: (inverse(multiply(multiply(X0,inverse(X1)),X2))=multiply(inverse(X2),multiply(X1,inverse(X0))))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f422,f426])).
% 0.12/0.58 fof(f820,plain,(
% 0.12/0.58 ![X0,X1,X2]: (multiply(inverse(multiply(X0,X1)),X2)=multiply(inverse(X1),multiply(inverse(X0),X2)))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f426,f9])).
% 0.12/0.58 fof(f829,plain,(
% 0.12/0.58 ![X0,X1,X2]: (inverse(multiply(X0,multiply(inverse(X1),X2)))=multiply(inverse(X2),multiply(X1,inverse(X0))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f9,f799])).
% 0.12/0.58 fof(f875,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(inverse(multiply(X0,inverse(multiply(X0,inverse(X1))))),X1)=inverse(commutator(inverse(X1),X0)))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f459,f492])).
% 0.12/0.58 fof(f914,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(multiply(multiply(X0,inverse(X1)),inverse(X0)),X1)=inverse(commutator(inverse(X1),X0)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f422,f875])).
% 0.12/0.58 fof(f915,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(multiply(X0,inverse(X1)),multiply(inverse(X0),X1))=inverse(commutator(inverse(X1),X0)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f9,f914])).
% 0.12/0.58 fof(f916,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(X0,multiply(inverse(X1),multiply(inverse(X0),X1)))=inverse(commutator(inverse(X1),X0)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f9,f915])).
% 0.12/0.58 fof(f917,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(X0,multiply(inverse(multiply(X0,X1)),X1))=inverse(commutator(inverse(X1),X0)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f820,f916])).
% 0.12/0.58 fof(f918,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,inverse(X1))=inverse(commutator(inverse(X1),X0)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f745,f917])).
% 0.12/0.58 fof(f951,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),inverse(X0))=inverse(commutator(X1,X0)))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f631,f918])).
% 0.12/0.58 fof(f980,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(X0,X1)=inverse(commutator(X1,X0)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f592,f951])).
% 0.12/0.58 fof(f1005,plain,(
% 0.12/0.58 ![X0,X1,X2]: (multiply(inverse(X0),commutator(X1,X2))=inverse(multiply(commutator(X2,X1),X0)))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f980,f492])).
% 0.12/0.58 fof(f1012,plain,(
% 0.12/0.58 ![X0,X1,X2]: (X0=multiply(commutator(X1,X2),multiply(commutator(X2,X1),X0)))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f980,f111])).
% 0.12/0.58 fof(f1015,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(commutator(X0,X1),commutator(X1,X0))=identity)),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f980,f41])).
% 0.12/0.58 fof(f2434,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(multiply(X0,X1),multiply(inverse(X0),X1))=inverse(multiply(X0,multiply(multiply(X0,X1),X0))))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f96,f517])).
% 0.12/0.58 fof(f2577,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(X0,multiply(X1,multiply(inverse(X0),X1)))=inverse(multiply(X0,multiply(multiply(X0,X1),X0))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f9,f2434])).
% 0.12/0.58 fof(f2578,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(X0,multiply(X1,multiply(inverse(X0),X1)))=inverse(multiply(X0,multiply(X0,multiply(X1,X0)))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f9,f2577])).
% 0.12/0.58 fof(f2579,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(X0,multiply(X1,multiply(inverse(X0),X1)))=inverse(multiply(inverse(X0),multiply(X1,X0))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f96,f2578])).
% 0.12/0.58 fof(f2580,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),X0)=multiply(X0,multiply(inverse(multiply(X0,X1)),X1)))),
% 0.12/0.58 inference(backward_demodulation,[status(thm)],[f2581,f710])).
% 0.12/0.58 fof(f2581,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(X0,multiply(X1,multiply(inverse(X0),X1)))=multiply(inverse(multiply(X1,X0)),X0))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f492,f2579])).
% 0.12/0.58 fof(f2784,plain,(
% 0.12/0.58 ![X0,X1]: (commutator(multiply(X0,X1),X0)=commutator(X0,inverse(X1)))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f745,f2580])).
% 0.12/0.58 fof(f2791,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(commutator(X0,X1),inverse(multiply(X1,multiply(inverse(multiply(X1,X0)),X0))))=commutator(X0,multiply(X1,inverse(multiply(X1,X0)))))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f482,f730])).
% 0.12/0.58 fof(f2889,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(commutator(X0,X1),multiply(inverse(X0),multiply(multiply(X1,X0),inverse(X1))))=commutator(X0,multiply(X1,inverse(multiply(X1,X0)))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f829,f2791])).
% 0.12/0.58 fof(f2890,plain,(
% 0.12/0.58 ![X0,X1]: (multiply(commutator(X0,X1),multiply(inverse(X0),multiply(X1,multiply(X0,inverse(X1)))))=commutator(X0,multiply(X1,inverse(multiply(X1,X0)))))),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f9,f2889])).
% 0.12/0.58 fof(f2891,plain,(
% 1.50/0.59 ![X0,X1]: (multiply(commutator(X0,X1),commutator(inverse(X0),X1))=commutator(X0,multiply(X1,inverse(multiply(X1,X0)))))),
% 1.50/0.59 inference(forward_demodulation,[status(thm)],[f110,f2890])).
% 1.50/0.59 fof(f2892,plain,(
% 1.50/0.59 ![X0,X1]: (multiply(commutator(X0,X1),commutator(inverse(X0),X1))=commutator(commutator(X0,X1),inverse(X0)))),
% 1.50/0.59 inference(forward_demodulation,[status(thm)],[f669,f2891])).
% 1.50/0.59 fof(f3144,plain,(
% 1.50/0.59 ![X0,X1,X2]: (commutator(X0,commutator(X1,X2))=commutator(commutator(X1,X2),inverse(multiply(commutator(X2,X1),X0))))),
% 1.50/0.59 inference(paramodulation,[status(thm)],[f1012,f2784])).
% 1.50/0.59 fof(f3152,plain,(
% 1.50/0.59 ![X0,X1]: (commutator(inverse(X0),X1)=commutator(X1,inverse(inverse(multiply(X0,X1)))))),
% 1.50/0.59 inference(paramodulation,[status(thm)],[f269,f2784])).
% 1.50/0.59 fof(f3178,plain,(
% 1.50/0.59 ![X0,X1,X2]: (commutator(X0,commutator(X1,X2))=commutator(commutator(X1,X2),multiply(inverse(X0),commutator(X1,X2))))),
% 1.50/0.59 inference(forward_demodulation,[status(thm)],[f1005,f3144])).
% 1.50/0.59 fof(f3183,plain,(
% 1.50/0.59 ![X0,X1]: (multiply(commutator(X0,X1),commutator(inverse(X0),X1))=commutator(X0,commutator(X0,X1)))),
% 1.50/0.59 inference(backward_demodulation,[status(thm)],[f3186,f2892])).
% 1.50/0.59 fof(f3186,plain,(
% 1.50/0.59 ![X0,X1,X2]: (commutator(X0,commutator(X1,X2))=commutator(commutator(X1,X2),inverse(X0)))),
% 1.50/0.59 inference(forward_demodulation,[status(thm)],[f630,f3178])).
% 1.50/0.59 fof(f3196,plain,(
% 1.50/0.59 ![X0,X1]: (commutator(inverse(X0),X1)=commutator(X1,multiply(X0,X1)))),
% 1.50/0.59 inference(forward_demodulation,[status(thm)],[f101,f3152])).
% 1.50/0.59 fof(f3255,plain,(
% 1.50/0.59 ![X0,X1]: (commutator(inverse(X0),X1)=commutator(X1,X0))),
% 1.50/0.59 inference(forward_demodulation,[status(thm)],[f630,f3196])).
% 1.50/0.59 fof(f3322,plain,(
% 1.50/0.59 ![X0,X1]: (multiply(commutator(X0,X1),commutator(X1,X0))=commutator(X0,commutator(X0,X1)))),
% 1.50/0.59 inference(forward_demodulation,[status(thm)],[f3255,f3183])).
% 1.50/0.59 fof(f3325,plain,(
% 1.50/0.59 ![X0,X1]: (identity=commutator(X0,commutator(X0,X1)))),
% 1.50/0.59 inference(forward_demodulation,[status(thm)],[f1015,f3322])).
% 1.50/0.59 fof(f3449,plain,(
% 1.50/0.59 ![X0,X1]: (identity=commutator(commutator(inverse(X0),X1),X0))),
% 1.50/0.59 inference(paramodulation,[status(thm)],[f3325,f3255])).
% 1.50/0.59 fof(f3474,plain,(
% 1.50/0.59 ~identity=identity),
% 1.50/0.59 inference(backward_demodulation,[status(thm)],[f3479,f12])).
% 1.50/0.59 fof(f3479,plain,(
% 1.50/0.59 ![X0,X1]: (identity=commutator(commutator(X0,X1),X1))),
% 1.50/0.59 inference(forward_demodulation,[status(thm)],[f3255,f3449])).
% 1.50/0.59 fof(f3503,plain,(
% 1.50/0.59 $false),
% 1.50/0.59 inference(trivial_equality_resolution,[status(thm)],[f3474])).
% 1.50/0.59 % SZS output end CNFRefutation for theBenchmark.p
% 10.54/1.81 % Elapsed time: 1.232554 seconds
% 10.54/1.81 % CPU time: 0.840357 seconds
% 10.54/1.81 % Total memory used: 23.800 MB
% 10.54/1.81 % Net memory used: 22.990 MB
%------------------------------------------------------------------------------