%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP510-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 12:36:44 PM UTC 2026
% Result : Unsatisfiable 0.15s 10.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP510-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.39 % Computer : n008.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sun Sep 20 20:16:22 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.40 % Drodi V4.1.1
% 0.15/10.42 % Refutation found
% 0.15/10.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/10.42 % SZS output start CNFRefutation for theBenchmark
% 0.15/10.42 fof(f1,axiom,(
% 0.15/10.42 (![A,B,C]: (multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ))),
% 0.15/10.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/10.42 fof(f2,negated_conjecture,(
% 0.15/10.42 multiply(multiply(inverse(b2),b2),a2) != a2 ),
% 0.15/10.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/10.42 fof(f3,plain,(
% 0.15/10.42 ![X0,X1,X2]: (multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2)))=X1)),
% 0.15/10.42 inference(cnf_transformation,[status(thm)],[f1])).
% 0.15/10.42 fof(f4,plain,(
% 0.15/10.42 ~multiply(multiply(inverse(b2),b2),a2)=a2),
% 0.15/10.42 inference(cnf_transformation,[status(thm)],[f2])).
% 0.15/10.42 fof(f5,definition,(
% 0.15/10.42 sF2_fnc=inverse(b2)),
% 0.15/10.42 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 0.15/10.42 fof(f6,definition,(
% 0.15/10.42 sF1_fnc=multiply(sF2_fnc,b2)),
% 0.15/10.42 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.15/10.42 fof(f7,definition,(
% 0.15/10.42 sF0_fnc=multiply(sF1_fnc,a2)),
% 0.15/10.42 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.15/10.42 fof(f8,plain,(
% 0.15/10.42 ~sF0_fnc=a2),
% 0.15/10.42 inference(definition_folding,[],[f4,f7,f6,f5])).
% 0.15/10.42 fof(f9,plain,(
% 0.15/10.42 ![X0,X1,X2]: (multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2)))))=X2)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f3,f3])).
% 0.15/10.42 fof(f10,plain,(
% 0.15/10.42 ![X0,X1,X2,X3]: (multiply(multiply(X0,X1),inverse(multiply(multiply(multiply(X2,X0),X3),X1)))=inverse(multiply(X2,X3)))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f3,f3])).
% 0.15/10.42 fof(f12,plain,(
% 0.15/10.42 ![X0]: (multiply(multiply(sF1_fnc,X0),inverse(multiply(sF2_fnc,X0)))=b2)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f6,f3])).
% 0.15/10.42 fof(f13,plain,(
% 0.15/10.42 ![X0,X1,X2,X3]: (multiply(multiply(multiply(multiply(multiply(X0,X1),X2),X3),inverse(multiply(X0,X2))),inverse(X1))=X3)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f3,f3])).
% 0.15/10.42 fof(f15,plain,(
% 0.15/10.42 ![X0]: (multiply(multiply(multiply(sF2_fnc,X0),b2),inverse(sF1_fnc))=X0)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f6,f3])).
% 0.15/10.42 fof(f29,plain,(
% 0.15/10.42 ![X0,X1,X2,X3]: (multiply(X0,inverse(multiply(multiply(X1,X0),inverse(X2))))=inverse(multiply(multiply(X3,X1),inverse(multiply(X3,X2)))))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f9,f9])).
% 0.15/10.42 fof(f34,plain,(
% 0.15/10.42 ![X0,X1,X2,X3]: (multiply(multiply(X0,X1),inverse(multiply(X2,X1)))=inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X0)))))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f9,f3])).
% 0.15/10.42 fof(f91,plain,(
% 0.15/10.42 ![X0]: (multiply(multiply(X0,inverse(sF1_fnc)),inverse(X0))=inverse(multiply(sF2_fnc,b2)))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f15,f10])).
% 0.15/10.42 fof(f122,plain,(
% 0.15/10.42 ![X0]: (multiply(multiply(X0,inverse(sF1_fnc)),inverse(X0))=inverse(sF1_fnc))),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f6,f91])).
% 0.15/10.42 fof(f147,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(inverse(multiply(sF2_fnc,X0)),inverse(multiply(b2,inverse(multiply(multiply(sF1_fnc,X0),X1)))))=X1)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f12,f9])).
% 0.15/10.42 fof(f173,plain,(
% 0.15/10.42 multiply(multiply(b2,inverse(sF1_fnc)),sF2_fnc)=inverse(sF1_fnc)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f5,f122])).
% 0.15/10.42 fof(f176,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(multiply(inverse(sF1_fnc),X0),inverse(multiply(inverse(sF1_fnc),X0)))=inverse(multiply(X1,inverse(X1))))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f122,f10])).
% 0.15/10.42 fof(f194,plain,(
% 0.15/10.42 ![X0]: (multiply(multiply(inverse(sF1_fnc),X0),inverse(multiply(inverse(sF1_fnc),X0)))=inverse(multiply(b2,sF2_fnc)))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f173,f10])).
% 0.15/10.42 fof(f199,plain,(
% 0.15/10.42 ![X0]: (multiply(sF2_fnc,inverse(multiply(inverse(sF1_fnc),inverse(multiply(multiply(b2,inverse(sF1_fnc)),X0)))))=X0)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f173,f9])).
% 0.15/10.42 fof(f202,plain,(
% 0.15/10.42 ![X0]: (inverse(multiply(b2,sF2_fnc))=inverse(multiply(X0,inverse(X0))))),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f194,f176])).
% 0.15/10.42 fof(f230,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(multiply(inverse(sF1_fnc),inverse(multiply(X0,inverse(sF1_fnc)))),inverse(X1))=inverse(multiply(X0,X1)))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f122,f13])).
% 0.15/10.42 fof(f232,plain,(
% 0.15/10.42 ![X0,X1,X2,X3,X4]: (multiply(multiply(X0,inverse(multiply(X1,X2))),inverse(X3))=inverse(multiply(multiply(X4,multiply(multiply(X1,X3),X2)),inverse(multiply(X4,X0)))))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f9,f13])).
% 0.15/10.42 fof(f281,plain,(
% 0.15/10.42 ![X0,X1,X2,X3,X4]: (multiply(multiply(inverse(multiply(X0,X1)),X2),inverse(multiply(X3,X2)))=inverse(multiply(multiply(multiply(multiply(X0,X4),X1),X3),inverse(X4))))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f13,f10])).
% 0.15/10.42 fof(f284,plain,(
% 0.15/10.42 ![X0,X1,X2,X3,X4,X5]: (multiply(multiply(inverse(X0),X1),inverse(multiply(multiply(X2,X3),X1)))=inverse(multiply(multiply(multiply(multiply(multiply(X4,X0),X5),X2),inverse(multiply(X4,X5))),X3)))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f13,f10])).
% 0.15/10.42 fof(f326,plain,(
% 0.15/10.42 ![X0,X1,X2]: (multiply(multiply(X0,inverse(multiply(multiply(X1,X0),X2))),inverse(multiply(b2,sF2_fnc)))=inverse(multiply(X1,X2)))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f202,f10])).
% 0.15/10.42 fof(f327,plain,(
% 0.15/10.42 ![X0]: (multiply(X0,inverse(multiply(b2,sF2_fnc)))=X0)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f202,f9])).
% 0.15/10.42 fof(f330,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(b2,sF2_fnc)))))=inverse(X1))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f202,f9])).
% 0.15/10.42 fof(f331,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(multiply(multiply(X0,X1),inverse(X0)),inverse(multiply(b2,sF2_fnc)))=X1)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f202,f3])).
% 0.15/10.42 fof(f344,plain,(
% 0.15/10.42 ![X0,X1,X2]: (multiply(X0,inverse(multiply(multiply(X1,X0),X2)))=inverse(multiply(X1,X2)))),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f327,f326])).
% 0.15/10.42 fof(f349,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(inverse(X0),inverse(X1))=inverse(multiply(X0,X1)))),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f351,f230])).
% 0.15/10.42 fof(f351,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=inverse(X1))),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f327,f330])).
% 0.15/10.42 fof(f359,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(multiply(X0,X1),inverse(X0))=X1)),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f327,f331])).
% 0.15/10.42 fof(f368,plain,(
% 0.15/10.42 ![X0,X1]: (inverse(multiply(X0,inverse(multiply(X0,X1))))=X1)),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f344,f9])).
% 0.15/10.42 fof(f370,plain,(
% 0.15/10.42 ![X0]: (multiply(sF2_fnc,inverse(inverse(multiply(b2,X0))))=X0)),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f344,f199])).
% 0.15/10.42 fof(f384,plain,(
% 0.15/10.42 ![X0,X1,X2]: (inverse(multiply(X0,inverse(X1)))=inverse(multiply(multiply(X2,X0),inverse(multiply(X2,X1)))))),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f344,f29])).
% 0.15/10.42 fof(f395,plain,(
% 0.15/10.42 ![X0,X1]: (inverse(multiply(multiply(sF2_fnc,X0),multiply(b2,inverse(multiply(multiply(sF1_fnc,X0),X1)))))=X1)),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f349,f147])).
% 0.15/10.42 fof(f417,plain,(
% 0.15/10.42 ![X0,X1,X2,X3]: (multiply(multiply(X0,inverse(multiply(X1,X2))),inverse(X3))=inverse(multiply(multiply(multiply(X1,X3),X2),inverse(X0))))),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f384,f232])).
% 0.15/10.42 fof(f425,plain,(
% 0.15/10.42 ![X0,X1,X2]: (multiply(multiply(X0,X1),inverse(multiply(X2,X1)))=inverse(multiply(X2,inverse(X0))))),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f384,f34])).
% 0.15/10.42 fof(f437,plain,(
% 0.15/10.42 ![X0,X1,X2,X3,X4]: (multiply(multiply(inverse(multiply(X0,X1)),X2),inverse(multiply(X3,X2)))=multiply(multiply(X4,inverse(multiply(multiply(X0,X4),X3))),inverse(X1)))),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f417,f281])).
% 0.15/10.42 fof(f458,plain,(
% 0.15/10.42 ![X0,X1,X2,X3,X4]: (inverse(multiply(multiply(X0,X1),inverse(inverse(X2))))=inverse(multiply(multiply(multiply(multiply(multiply(X3,X2),X4),X0),inverse(multiply(X3,X4))),X1)))),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f425,f284])).
% 0.15/10.42 fof(f466,plain,(
% 0.15/10.42 ![X0,X1,X2,X3]: (inverse(multiply(X0,inverse(inverse(multiply(X1,X2)))))=multiply(multiply(X3,inverse(multiply(multiply(X1,X3),X0))),inverse(X2)))),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f425,f437])).
% 0.15/10.42 fof(f467,plain,(
% 0.15/10.42 ![X0,X1,X2]: (inverse(multiply(X0,inverse(inverse(multiply(X1,X2)))))=multiply(inverse(multiply(X1,X0)),inverse(X2)))),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f344,f466])).
% 0.15/10.42 fof(f469,plain,(
% 0.15/10.42 ![X0,X1,X2]: (inverse(multiply(X0,inverse(inverse(multiply(X1,X2)))))=inverse(multiply(multiply(X1,X0),X2)))),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f349,f467])).
% 0.15/10.42 fof(f512,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(multiply(multiply(X0,inverse(X0)),X1),inverse(multiply(b2,sF2_fnc)))=X1)),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f202,f359])).
% 0.15/10.42 fof(f527,plain,(
% 0.15/10.42 ![X0,X1]: (multiply(multiply(X0,inverse(X0)),X1)=X1)),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f327,f512])).
% 0.15/10.42 fof(f540,plain,(
% 0.15/10.42 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(multiply(multiply(X0,X1),X2),X3),inverse(multiply(X0,X2))),inverse(X3)))=inverse(X1))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f13,f368])).
% 0.15/10.42 fof(f549,plain,(
% 0.15/10.42 ![X0,X1]: (inverse(multiply(multiply(X0,inverse(X0)),inverse(inverse(X1))))=inverse(X1))),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f458,f540])).
% 0.15/10.42 fof(f550,plain,(
% 0.15/10.42 ![X0]: (inverse(inverse(inverse(X0)))=inverse(X0))),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f527,f549])).
% 0.15/10.42 fof(f558,plain,(
% 0.15/10.42 ![X0,X1]: (inverse(inverse(X0))=inverse(multiply(X1,inverse(multiply(X1,X0)))))),
% 0.15/10.42 inference(paramodulation,[status(thm)],[f368,f550])).
% 0.15/10.42 fof(f583,plain,(
% 0.15/10.42 ![X0]: (multiply(sF2_fnc,multiply(b2,X0))=X0)),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f594,f370])).
% 0.15/10.42 fof(f586,plain,(
% 0.15/10.42 ![X0,X1,X2]: (inverse(multiply(X0,multiply(X1,X2)))=inverse(multiply(multiply(X1,X0),X2)))),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f594,f469])).
% 0.15/10.42 fof(f594,plain,(
% 0.15/10.42 ![X0]: (inverse(inverse(X0))=X0)),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f368,f558])).
% 0.15/10.42 fof(f614,plain,(
% 0.15/10.42 ![X0,X1]: (inverse(multiply(X0,multiply(sF2_fnc,multiply(b2,inverse(multiply(multiply(sF1_fnc,X0),X1))))))=X1)),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f586,f395])).
% 0.15/10.42 fof(f663,plain,(
% 0.15/10.42 ![X0,X1]: (inverse(multiply(X0,inverse(multiply(multiply(sF1_fnc,X0),X1))))=X1)),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f583,f614])).
% 0.15/10.42 fof(f664,plain,(
% 0.15/10.42 ![X0]: (inverse(inverse(multiply(sF1_fnc,X0)))=X0)),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f344,f663])).
% 0.15/10.42 fof(f666,plain,(
% 0.15/10.42 sF0_fnc=a2),
% 0.15/10.42 inference(backward_demodulation,[status(thm)],[f694,f7])).
% 0.15/10.42 fof(f694,plain,(
% 0.15/10.42 ![X0]: (multiply(sF1_fnc,X0)=X0)),
% 0.15/10.42 inference(forward_demodulation,[status(thm)],[f594,f664])).
% 0.15/10.42 fof(f720,plain,(
% 0.15/10.42 $false),
% 0.15/10.42 inference(forward_subsumption_resolution,[status(thm)],[f666,f8])).
% 0.15/10.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/10.44 % Elapsed time: 0.042186 seconds
% 0.15/10.44 % CPU time: 0.195147 seconds
% 0.15/10.44 % Total memory used: 8.548 MB
% 0.15/10.44 % Net memory used: 7.858 MB
%------------------------------------------------------------------------------