%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP602-1 : 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 : 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 12:36:53 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP602-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 20:17:54 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.41 fof(f1,axiom,(
% 0.12/0.41 (![A,B,C]: (inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B ))),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f2,axiom,(
% 0.12/0.41 (![A,B]: (multiply(A,B) = inverse(double_divide(B,A)) ))),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f3,negated_conjecture,(
% 0.12/0.41 multiply(multiply(inverse(b2),b2),a2) != a2 ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f4,plain,(
% 0.12/0.41 ![X0,X1,X2]: (inverse(double_divide(inverse(double_divide(X0,inverse(double_divide(X1,double_divide(X0,X2))))),X2))=X1)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.41 fof(f5,plain,(
% 0.12/0.41 ![X0,X1]: (multiply(X0,X1)=inverse(double_divide(X1,X0)))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.41 fof(f6,plain,(
% 0.12/0.41 ~multiply(multiply(inverse(b2),b2),a2)=a2),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.41 fof(f7,definition,(
% 0.12/0.41 sF2_fnc=inverse(b2)),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 0.12/0.41 fof(f8,definition,(
% 0.12/0.41 sF1_fnc=multiply(sF2_fnc,b2)),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.12/0.41 fof(f9,definition,(
% 0.12/0.41 sF0_fnc=multiply(sF1_fnc,a2)),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.12/0.41 fof(f10,plain,(
% 0.12/0.41 ~sF0_fnc=a2),
% 0.12/0.41 inference(definition_folding,[],[f6,f9,f8,f7])).
% 0.12/0.41 fof(f11,plain,(
% 0.12/0.41 ![X0,X1,X2]: (multiply(X0,inverse(double_divide(X1,inverse(double_divide(X2,double_divide(X1,X0))))))=X2)),
% 0.12/0.41 inference(backward_demodulation,[status(thm)],[f5,f4])).
% 0.12/0.41 fof(f12,plain,(
% 0.12/0.41 ![X0,X1,X2]: (multiply(X0,multiply(inverse(double_divide(X1,double_divide(X2,X0))),X2))=X1)),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f5,f11])).
% 0.12/0.41 fof(f13,plain,(
% 0.12/0.41 ![X0,X1,X2]: (multiply(X0,multiply(multiply(double_divide(X1,X0),X2),X1))=X2)),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f5,f12])).
% 0.12/0.41 fof(f14,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (multiply(X0,multiply(X1,X2))=multiply(multiply(double_divide(X3,double_divide(X2,X0)),X1),X3))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f13,f13])).
% 0.12/0.41 fof(f16,plain,(
% 0.12/0.41 ![X0,X1,X2]: (multiply(double_divide(X0,X1),multiply(X1,multiply(X2,X0)))=X2)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f14,f13])).
% 0.12/0.41 fof(f18,plain,(
% 0.12/0.41 ![X0,X1,X2]: (multiply(double_divide(multiply(X0,X1),double_divide(X1,X2)),X0)=X2)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f16,f16])).
% 0.12/0.41 fof(f19,plain,(
% 0.12/0.41 ![X0,X1,X2,X3,X4]: (multiply(double_divide(X0,multiply(double_divide(multiply(X1,X0),double_divide(X2,X3)),X4)),multiply(X3,multiply(X4,X2)))=X1)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f14,f16])).
% 0.12/0.41 fof(f21,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),multiply(X3,X1))=double_divide(X2,X0))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f16,f16])).
% 0.12/0.41 fof(f23,plain,(
% 0.12/0.41 ![X0]: (multiply(double_divide(a2,X0),multiply(X0,sF0_fnc))=sF1_fnc)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f9,f16])).
% 0.12/0.41 fof(f24,plain,(
% 0.12/0.41 ![X0]: (multiply(double_divide(b2,X0),multiply(X0,sF1_fnc))=sF2_fnc)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f8,f16])).
% 0.12/0.41 fof(f31,plain,(
% 0.12/0.41 ![X0]: (multiply(double_divide(sF0_fnc,double_divide(a2,X0)),sF1_fnc)=X0)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f23,f16])).
% 0.12/0.41 fof(f32,plain,(
% 0.12/0.41 ![X0,X1]: (multiply(double_divide(multiply(X0,sF0_fnc),X1),multiply(X1,sF1_fnc))=double_divide(a2,X0))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f23,f16])).
% 0.12/0.41 fof(f37,plain,(
% 0.12/0.41 ![X0]: (multiply(double_divide(b2,double_divide(sF0_fnc,double_divide(a2,X0))),X0)=sF2_fnc)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f31,f24])).
% 0.12/0.41 fof(f41,plain,(
% 0.12/0.41 ![X0]: (multiply(double_divide(sF1_fnc,double_divide(b2,X0)),sF2_fnc)=X0)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f24,f16])).
% 0.12/0.41 fof(f42,plain,(
% 0.12/0.41 ![X0,X1]: (multiply(double_divide(multiply(X0,sF1_fnc),X1),multiply(X1,sF2_fnc))=double_divide(b2,X0))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f24,f16])).
% 0.12/0.41 fof(f46,plain,(
% 0.12/0.41 ![X0,X1]: (multiply(double_divide(sF2_fnc,X0),multiply(X0,X1))=double_divide(sF1_fnc,double_divide(b2,X1)))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f41,f16])).
% 0.12/0.41 fof(f185,plain,(
% 0.12/0.41 ![X0,X1,X2]: (X0=double_divide(X1,multiply(double_divide(multiply(X2,X1),X0),X2)))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f18,f21])).
% 0.12/0.41 fof(f264,plain,(
% 0.12/0.41 ![X0]: (X0=double_divide(sF1_fnc,double_divide(b2,multiply(X0,sF2_fnc))))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f42,f185])).
% 0.12/0.41 fof(f265,plain,(
% 0.12/0.41 ![X0]: (X0=double_divide(sF0_fnc,double_divide(a2,multiply(X0,sF1_fnc))))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f32,f185])).
% 0.12/0.41 fof(f268,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),X0)=double_divide(X2,multiply(X3,X1)))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f185,f185])).
% 0.12/0.41 fof(f347,plain,(
% 0.12/0.41 ![X0,X1]: (multiply(multiply(X0,sF1_fnc),multiply(X1,a2))=multiply(multiply(X0,X1),sF0_fnc))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f265,f14])).
% 0.12/0.41 fof(f353,plain,(
% 0.12/0.41 ![X0]: (multiply(double_divide(a2,multiply(X0,sF1_fnc)),sF0_fnc)=inverse(X0))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f265,f5])).
% 0.12/0.41 fof(f368,plain,(
% 0.12/0.41 multiply(double_divide(a2,sF2_fnc),sF0_fnc)=inverse(double_divide(b2,double_divide(sF0_fnc,double_divide(a2,sF1_fnc))))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f37,f353])).
% 0.12/0.41 fof(f371,plain,(
% 0.12/0.41 ![X0]: (multiply(multiply(X0,sF1_fnc),multiply(inverse(X0),a2))=sF0_fnc)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f353,f13])).
% 0.12/0.41 fof(f383,plain,(
% 0.12/0.41 multiply(double_divide(a2,sF2_fnc),sF0_fnc)=multiply(double_divide(sF0_fnc,double_divide(a2,sF1_fnc)),b2)),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f5,f368])).
% 0.12/0.41 fof(f384,plain,(
% 0.12/0.41 ![X0]: (multiply(multiply(X0,inverse(X0)),sF0_fnc)=sF0_fnc)),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f347,f371])).
% 0.12/0.41 fof(f389,plain,(
% 0.12/0.41 multiply(multiply(b2,sF2_fnc),sF0_fnc)=sF0_fnc),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f7,f384])).
% 0.12/0.41 fof(f398,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (multiply(double_divide(sF0_fnc,multiply(double_divide(sF0_fnc,double_divide(X0,X1)),X2)),multiply(X1,multiply(X2,X0)))=multiply(X3,inverse(X3)))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f384,f19])).
% 0.12/0.41 fof(f409,plain,(
% 0.12/0.41 ![X0,X1,X2]: (multiply(double_divide(sF0_fnc,multiply(double_divide(sF0_fnc,double_divide(X0,X1)),X2)),multiply(X1,multiply(X2,X0)))=multiply(b2,sF2_fnc))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f389,f19])).
% 0.12/0.41 fof(f413,plain,(
% 0.12/0.41 ![X0]: (multiply(b2,sF2_fnc)=multiply(X0,inverse(X0)))),
% 0.12/0.41 inference(backward_demodulation,[status(thm)],[f409,f398])).
% 0.12/0.41 fof(f426,plain,(
% 0.12/0.41 ![X0,X1,X2]: (multiply(X0,multiply(inverse(double_divide(X1,double_divide(X2,X0))),X2))=multiply(multiply(b2,sF2_fnc),X1))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f413,f14])).
% 0.12/0.41 fof(f439,plain,(
% 0.12/0.41 ![X0,X1,X2]: (multiply(X0,multiply(multiply(double_divide(X1,X0),X2),X1))=multiply(multiply(b2,sF2_fnc),X2))),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f5,f426])).
% 0.12/0.41 fof(f441,plain,(
% 0.12/0.41 ![X0]: (X0=multiply(multiply(b2,sF2_fnc),X0))),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f13,f439])).
% 0.12/0.41 fof(f446,plain,(
% 0.12/0.41 multiply(b2,sF2_fnc)=double_divide(sF1_fnc,double_divide(b2,sF2_fnc))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f441,f264])).
% 0.12/0.41 fof(f449,plain,(
% 0.12/0.41 multiply(b2,sF2_fnc)=double_divide(sF0_fnc,double_divide(a2,sF1_fnc))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f441,f265])).
% 0.12/0.41 fof(f464,plain,(
% 0.12/0.41 ![X0,X1]: (multiply(double_divide(X0,double_divide(X0,X1)),multiply(b2,sF2_fnc))=X1)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f441,f18])).
% 0.12/0.41 fof(f468,plain,(
% 0.12/0.41 multiply(double_divide(a2,sF2_fnc),sF0_fnc)=multiply(multiply(b2,sF2_fnc),b2)),
% 0.12/0.41 inference(backward_demodulation,[status(thm)],[f449,f383])).
% 0.12/0.41 fof(f479,plain,(
% 0.12/0.41 multiply(double_divide(a2,sF2_fnc),sF0_fnc)=b2),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f441,f468])).
% 0.12/0.41 fof(f481,plain,(
% 0.12/0.41 ![X0]: (multiply(double_divide(b2,X0),multiply(X0,sF1_fnc))=double_divide(a2,double_divide(a2,sF2_fnc)))),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f479,f32])).
% 0.12/0.41 fof(f490,plain,(
% 0.12/0.41 sF2_fnc=double_divide(a2,double_divide(a2,sF2_fnc))),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f24,f481])).
% 0.12/0.41 fof(f1169,plain,(
% 0.12/0.42 multiply(sF2_fnc,multiply(b2,sF2_fnc))=sF2_fnc),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f490,f464])).
% 0.12/0.42 fof(f1175,plain,(
% 0.12/0.42 ![X0,X1,X2]: (multiply(double_divide(X0,X1),multiply(b2,sF2_fnc))=multiply(double_divide(multiply(X2,X0),X1),X2))),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f185,f464])).
% 0.12/0.42 fof(f1196,plain,(
% 0.12/0.42 ![X0,X1,X2]: (multiply(double_divide(multiply(X0,X1),X2),multiply(b2,sF2_fnc))=double_divide(X1,multiply(X2,X0)))),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f1175,f268])).
% 0.12/0.42 fof(f1281,plain,(
% 0.12/0.42 ![X0,X1]: (multiply(double_divide(multiply(X0,sF2_fnc),X1),multiply(X1,sF2_fnc))=double_divide(multiply(b2,sF2_fnc),X0))),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f1169,f21])).
% 0.12/0.42 fof(f1282,plain,(
% 0.12/0.42 ![X0]: (multiply(double_divide(multiply(b2,sF2_fnc),X0),multiply(X0,sF2_fnc))=sF2_fnc)),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f1169,f16])).
% 0.12/0.42 fof(f1285,plain,(
% 0.12/0.42 double_divide(multiply(b2,sF2_fnc),b2)=sF2_fnc),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f1281,f1282])).
% 0.12/0.42 fof(f1286,plain,(
% 0.12/0.42 multiply(double_divide(multiply(b2,sF2_fnc),sF2_fnc),multiply(b2,sF2_fnc))=b2),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f1285,f464])).
% 0.12/0.42 fof(f1292,plain,(
% 0.12/0.42 double_divide(sF2_fnc,multiply(sF2_fnc,b2))=b2),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f1196,f1286])).
% 0.12/0.42 fof(f1293,plain,(
% 0.12/0.42 double_divide(sF2_fnc,sF1_fnc)=b2),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f8,f1292])).
% 0.12/0.42 fof(f1297,plain,(
% 0.12/0.42 multiply(double_divide(sF2_fnc,b2),multiply(b2,sF2_fnc))=sF1_fnc),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f1293,f464])).
% 0.12/0.42 fof(f1303,plain,(
% 0.12/0.42 multiply(b2,sF2_fnc)=sF1_fnc),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f1304,f446])).
% 0.12/0.42 fof(f1304,plain,(
% 0.12/0.42 double_divide(sF1_fnc,double_divide(b2,sF2_fnc))=sF1_fnc),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f46,f1297])).
% 0.12/0.42 fof(f1313,plain,(
% 0.12/0.42 ![X0]: (X0=multiply(sF1_fnc,X0))),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f1303,f441])).
% 0.12/0.42 fof(f1412,plain,(
% 0.12/0.42 sF0_fnc=a2),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f1313,f9])).
% 0.12/0.42 fof(f1623,plain,(
% 0.12/0.42 $false),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f1412,f10])).
% 0.12/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.43 % Elapsed time: 0.076382 seconds
% 0.12/0.43 % CPU time: 0.424235 seconds
% 0.12/0.43 % Total memory used: 16.381 MB
% 0.12/0.43 % Net memory used: 16.298 MB
%------------------------------------------------------------------------------