%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP434-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:36:37 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP434-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 20:12:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.40 fof(f1,axiom,(
% 0.12/0.40 (![A,B,C,D]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C ))),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f2,negated_conjecture,(
% 0.12/0.40 multiply(multiply(inverse(b2),b2),a2) != a2 ),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f3,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3))))=X2)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.40 fof(f4,plain,(
% 0.12/0.40 ~multiply(multiply(inverse(b2),b2),a2)=a2),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.40 fof(f5,definition,(
% 0.12/0.40 sF2_fnc=inverse(b2)),
% 0.12/0.40 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 0.12/0.40 fof(f6,definition,(
% 0.12/0.40 sF1_fnc=multiply(sF2_fnc,b2)),
% 0.12/0.40 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.12/0.40 fof(f7,definition,(
% 0.12/0.40 sF0_fnc=multiply(sF1_fnc,a2)),
% 0.12/0.40 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.12/0.40 fof(f8,plain,(
% 0.12/0.40 ~sF0_fnc=a2),
% 0.12/0.40 inference(definition_folding,[],[f4,f7,f6,f5])).
% 0.12/0.40 fof(f9,plain,(
% 0.12/0.40 ![X0,X1,X2,X3,X4]: (inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3))))=multiply(X4,inverse(X4)))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f3,f3])).
% 0.12/0.40 fof(f11,plain,(
% 0.12/0.40 ![X0,X1]: (inverse(multiply(multiply(multiply(inverse(multiply(sF1_fnc,X0)),sF2_fnc),b2),multiply(X1,inverse(X1))))=X0)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f6,f3])).
% 0.12/0.40 fof(f13,plain,(
% 0.12/0.40 ![X0,X1,X2]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(b2,sF2_fnc)))=X2)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f5,f3])).
% 0.12/0.40 fof(f19,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(multiply(inverse(sF0_fnc),sF2_fnc),b2),multiply(X0,inverse(X0))))=a2)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f7,f11])).
% 0.12/0.40 fof(f31,plain,(
% 0.12/0.40 inverse(multiply(multiply(multiply(inverse(sF0_fnc),sF2_fnc),b2),multiply(b2,sF2_fnc)))=a2),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f5,f19])).
% 0.12/0.40 fof(f32,plain,(
% 0.12/0.40 ![X0,X1]: (inverse(multiply(multiply(multiply(a2,multiply(inverse(sF0_fnc),sF2_fnc)),b2),multiply(X0,inverse(X0))))=multiply(X1,inverse(X1)))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f19,f3])).
% 0.12/0.40 fof(f36,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(multiply(a2,multiply(inverse(sF0_fnc),sF2_fnc)),b2),multiply(X0,inverse(X0))))=multiply(b2,sF2_fnc))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f31,f3])).
% 0.12/0.40 fof(f41,plain,(
% 0.12/0.40 ![X0]: (multiply(b2,sF2_fnc)=multiply(X0,inverse(X0)))),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f36,f32])).
% 0.12/0.40 fof(f65,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3))))=multiply(b2,sF2_fnc))),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f41,f9])).
% 0.12/0.40 fof(f68,plain,(
% 0.12/0.40 ![X0,X1,X2]: (inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(b2,sF2_fnc)))=multiply(b2,sF2_fnc))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f41,f65])).
% 0.12/0.40 fof(f92,plain,(
% 0.12/0.40 ![X0,X1]: (inverse(multiply(multiply(multiply(inverse(multiply(b2,sF2_fnc)),X0),X1),multiply(b2,sF2_fnc)))=inverse(multiply(X0,X1)))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f41,f13])).
% 0.12/0.40 fof(f95,plain,(
% 0.12/0.40 ![X0,X1]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(b2,sF2_fnc),X0)),X1),inverse(X1)),multiply(b2,sF2_fnc)))=X0)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f41,f13])).
% 0.12/0.40 fof(f107,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(multiply(b2,sF2_fnc),X0),multiply(b2,sF2_fnc)))=inverse(multiply(inverse(inverse(multiply(b2,sF2_fnc))),X0)))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f41,f92])).
% 0.12/0.40 fof(f110,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(multiply(b2,sF2_fnc),inverse(inverse(inverse(multiply(multiply(b2,sF2_fnc),X0))))),multiply(b2,sF2_fnc)))=X0)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f41,f95])).
% 0.12/0.40 fof(f121,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(inverse(inverse(multiply(b2,sF2_fnc))),inverse(inverse(inverse(multiply(multiply(b2,sF2_fnc),X0))))))=X0)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f107,f110])).
% 0.12/0.40 fof(f133,plain,(
% 0.12/0.40 ![X0,X1]: (inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),inverse(multiply(b2,sF2_fnc)))),X0),X1))=multiply(b2,sF2_fnc))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f92,f68])).
% 0.12/0.40 fof(f168,plain,(
% 0.12/0.40 inverse(multiply(multiply(inverse(multiply(b2,sF2_fnc)),b2),sF2_fnc))=multiply(b2,sF2_fnc)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f41,f133])).
% 0.12/0.40 fof(f173,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(inverse(multiply(multiply(b2,sF2_fnc),inverse(multiply(b2,sF2_fnc)))),X0),inverse(X0)))=multiply(b2,sF2_fnc))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f41,f133])).
% 0.12/0.40 fof(f180,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(inverse(multiply(b2,sF2_fnc)),X0),inverse(X0)))=multiply(b2,sF2_fnc))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f41,f173])).
% 0.12/0.40 fof(f183,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(b2,sF2_fnc),X0)),multiply(multiply(inverse(multiply(b2,sF2_fnc)),b2),sF2_fnc)),multiply(b2,sF2_fnc)),multiply(b2,sF2_fnc)))=X0)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f168,f95])).
% 0.12/0.40 fof(f215,plain,(
% 0.12/0.40 inverse(multiply(multiply(multiply(b2,sF2_fnc),inverse(multiply(b2,sF2_fnc))),multiply(b2,sF2_fnc)))=multiply(b2,sF2_fnc)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f180,f133])).
% 0.12/0.40 fof(f217,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(multiply(multiply(b2,sF2_fnc),inverse(multiply(b2,sF2_fnc))),X0),multiply(b2,sF2_fnc)))=inverse(X0))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f180,f13])).
% 0.12/0.40 fof(f220,plain,(
% 0.12/0.40 inverse(multiply(inverse(inverse(multiply(b2,sF2_fnc))),inverse(multiply(b2,sF2_fnc))))=multiply(b2,sF2_fnc)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f107,f215])).
% 0.12/0.40 fof(f222,plain,(
% 0.12/0.40 ![X0]: (inverse(X0)=inverse(multiply(inverse(inverse(multiply(b2,sF2_fnc))),X0)))),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f223,f107])).
% 0.12/0.40 fof(f223,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(multiply(b2,sF2_fnc),X0),multiply(b2,sF2_fnc)))=inverse(X0))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f41,f217])).
% 0.12/0.40 fof(f225,plain,(
% 0.12/0.40 ![X0]: (inverse(inverse(inverse(inverse(multiply(multiply(b2,sF2_fnc),X0)))))=X0)),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f222,f121])).
% 0.12/0.40 fof(f226,plain,(
% 0.12/0.40 inverse(inverse(multiply(b2,sF2_fnc)))=multiply(b2,sF2_fnc)),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f222,f220])).
% 0.12/0.40 fof(f228,plain,(
% 0.12/0.40 ![X0]: (inverse(X0)=inverse(multiply(multiply(b2,sF2_fnc),X0)))),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f226,f222])).
% 0.12/0.40 fof(f238,plain,(
% 0.12/0.40 ![X0]: (inverse(inverse(inverse(inverse(X0))))=X0)),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f228,f225])).
% 0.12/0.40 fof(f241,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(multiply(inverse(X0),multiply(multiply(inverse(multiply(b2,sF2_fnc)),b2),sF2_fnc)),multiply(b2,sF2_fnc)),multiply(b2,sF2_fnc)))=X0)),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f228,f183])).
% 0.12/0.40 fof(f269,plain,(
% 0.12/0.40 inverse(inverse(inverse(multiply(b2,sF2_fnc))))=multiply(multiply(inverse(multiply(b2,sF2_fnc)),b2),sF2_fnc)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f168,f238])).
% 0.12/0.40 fof(f274,plain,(
% 0.12/0.40 ![X0,X1]: (inverse(inverse(inverse(inverse(multiply(X0,X1)))))=multiply(multiply(multiply(inverse(multiply(b2,sF2_fnc)),X0),X1),multiply(b2,sF2_fnc)))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f92,f238])).
% 0.12/0.40 fof(f281,plain,(
% 0.12/0.40 inverse(inverse(inverse(sF2_fnc)))=b2),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f5,f238])).
% 0.12/0.40 fof(f285,plain,(
% 0.12/0.40 ![X0]: (inverse(multiply(multiply(multiply(inverse(X0),inverse(multiply(b2,sF2_fnc))),multiply(b2,sF2_fnc)),multiply(b2,sF2_fnc)))=X0)),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f288,f241])).
% 0.12/0.40 fof(f288,plain,(
% 0.12/0.40 inverse(multiply(b2,sF2_fnc))=multiply(multiply(inverse(multiply(b2,sF2_fnc)),b2),sF2_fnc)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f226,f269])).
% 0.12/0.40 fof(f314,plain,(
% 0.12/0.40 ![X0,X1]: (multiply(X0,X1)=multiply(multiply(multiply(inverse(multiply(b2,sF2_fnc)),X0),X1),multiply(b2,sF2_fnc)))),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f238,f274])).
% 0.12/0.42 fof(f347,plain,(
% 0.12/0.42 multiply(b2,sF2_fnc)=multiply(inverse(inverse(sF2_fnc)),b2)),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f281,f41])).
% 0.12/0.42 fof(f348,plain,(
% 0.12/0.42 inverse(inverse(multiply(b2,sF2_fnc)))=inverse(multiply(b2,sF2_fnc))),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f41,f228])).
% 0.12/0.42 fof(f349,plain,(
% 0.12/0.42 ![X0]: (inverse(inverse(inverse(inverse(X0))))=multiply(multiply(b2,sF2_fnc),X0))),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f228,f238])).
% 0.12/0.42 fof(f353,plain,(
% 0.12/0.42 ![X0]: (inverse(multiply(multiply(multiply(inverse(X0),multiply(b2,sF2_fnc)),multiply(b2,sF2_fnc)),multiply(b2,sF2_fnc)))=X0)),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f380,f285])).
% 0.12/0.42 fof(f357,plain,(
% 0.12/0.42 ![X0,X1]: (multiply(X0,X1)=multiply(multiply(multiply(multiply(b2,sF2_fnc),X0),X1),multiply(b2,sF2_fnc)))),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f380,f314])).
% 0.12/0.42 fof(f380,plain,(
% 0.12/0.42 multiply(b2,sF2_fnc)=inverse(multiply(b2,sF2_fnc))),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f226,f348])).
% 0.12/0.42 fof(f395,plain,(
% 0.12/0.42 ![X0]: (inverse(multiply(X0,multiply(b2,sF2_fnc)))=inverse(X0))),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f396,f223])).
% 0.12/0.42 fof(f396,plain,(
% 0.12/0.42 ![X0]: (X0=multiply(multiply(b2,sF2_fnc),X0))),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f238,f349])).
% 0.12/0.42 fof(f401,plain,(
% 0.12/0.42 ![X0]: (inverse(multiply(multiply(inverse(X0),multiply(b2,sF2_fnc)),multiply(b2,sF2_fnc)))=X0)),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f417,f353])).
% 0.12/0.42 fof(f417,plain,(
% 0.12/0.42 ![X0,X1]: (multiply(X0,X1)=multiply(multiply(X0,X1),multiply(b2,sF2_fnc)))),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f396,f357])).
% 0.12/0.42 fof(f485,plain,(
% 0.12/0.42 ![X0]: (inverse(multiply(inverse(X0),multiply(b2,sF2_fnc)))=X0)),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f395,f401])).
% 0.12/0.42 fof(f488,plain,(
% 0.12/0.42 multiply(b2,sF2_fnc)=multiply(sF2_fnc,b2)),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f491,f347])).
% 0.12/0.42 fof(f491,plain,(
% 0.12/0.42 ![X0]: (inverse(inverse(X0))=X0)),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f395,f485])).
% 0.12/0.42 fof(f522,plain,(
% 0.12/0.42 ![X0]: (X0=multiply(sF1_fnc,X0))),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f524,f396])).
% 0.12/0.42 fof(f524,plain,(
% 0.12/0.42 multiply(b2,sF2_fnc)=sF1_fnc),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f6,f488])).
% 0.12/0.42 fof(f543,plain,(
% 0.12/0.42 sF0_fnc=a2),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f522,f7])).
% 0.12/0.42 fof(f549,plain,(
% 0.12/0.42 $false),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f543,f8])).
% 0.12/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.44 % Elapsed time: 0.061270 seconds
% 0.12/0.44 % CPU time: 0.104112 seconds
% 0.12/0.44 % Total memory used: 4.437 MB
% 0.12/0.44 % Net memory used: 4.223 MB
%------------------------------------------------------------------------------