%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP421-1 : 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 : n026.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 12:36:36 PM UTC 2026
% Result : Unsatisfiable 6.53s 1.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP421-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.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 20:15:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 6.53/1.36 % Refutation found
% 6.53/1.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.53/1.36 % SZS output start CNFRefutation for theBenchmark
% 6.53/1.36 fof(f1,axiom,(
% 6.53/1.36 (![A,B,C]: (inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C))) = B ))),
% 6.53/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.53/1.36 fof(f2,negated_conjecture,(
% 6.53/1.36 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
% 6.53/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.53/1.36 fof(f3,plain,(
% 6.53/1.36 ![X0,X1,X2]: (inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X0,X2)))=X1)),
% 6.53/1.36 inference(cnf_transformation,[status(thm)],[f1])).
% 6.53/1.36 fof(f4,plain,(
% 6.53/1.36 ~multiply(inverse(a1),a1)=multiply(inverse(b1),b1)),
% 6.53/1.36 inference(cnf_transformation,[status(thm)],[f2])).
% 6.53/1.36 fof(f5,definition,(
% 6.53/1.36 sF1_fnc=inverse(a1)),
% 6.53/1.36 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 6.53/1.36 fof(f6,definition,(
% 6.53/1.36 sF0_fnc=multiply(sF1_fnc,a1)),
% 6.53/1.36 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 6.53/1.36 fof(f7,definition,(
% 6.53/1.36 sF3_fnc=inverse(b1)),
% 6.53/1.36 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 6.53/1.36 fof(f8,definition,(
% 6.53/1.36 sF2_fnc=multiply(sF3_fnc,b1)),
% 6.53/1.36 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 6.53/1.36 fof(f9,plain,(
% 6.53/1.36 ~sF0_fnc=sF2_fnc),
% 6.53/1.36 inference(definition_folding,[],[f4,f8,f7,f6,f5])).
% 6.53/1.36 fof(f10,plain,(
% 6.53/1.36 ![X0,X1,X2]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))=multiply(inverse(X2),inverse(multiply(inverse(X1),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2)))))))))),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f3,f3])).
% 6.53/1.36 fof(f20,plain,(
% 6.53/1.36 ![X0]: (inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(inverse(a1),inverse(multiply(inverse(a1),a1))))))),sF0_fnc))=X0)),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f6,f3])).
% 6.53/1.36 fof(f31,plain,(
% 6.53/1.36 ![X0]: (inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(multiply(inverse(a1),a1))))))),sF0_fnc))=X0)),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f5,f20])).
% 6.53/1.36 fof(f32,plain,(
% 6.53/1.36 ![X0]: (inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(multiply(sF1_fnc,a1))))))),sF0_fnc))=X0)),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f5,f31])).
% 6.53/1.36 fof(f33,plain,(
% 6.53/1.36 ![X0]: (inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc))=X0)),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f6,f32])).
% 6.53/1.36 fof(f38,plain,(
% 6.53/1.36 ![X0]: (inverse(multiply(inverse(multiply(sF1_fnc,X0)),sF0_fnc))=multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(inverse(inverse(sF0_fnc)),inverse(multiply(inverse(inverse(sF0_fnc)),inverse(sF0_fnc))))))))),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f3,f33])).
% 6.53/1.36 fof(f39,plain,(
% 6.53/1.36 ![X0]: (inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(X0,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc))=multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc))),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f33,f33])).
% 6.53/1.36 fof(f41,plain,(
% 6.53/1.36 inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(sF3_fnc,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc))=b1),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f7,f33])).
% 6.53/1.36 fof(f42,plain,(
% 6.53/1.36 inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc))=a1),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f5,f33])).
% 6.53/1.36 fof(f46,plain,(
% 6.53/1.36 ![X0]: (multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(X0)),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)=X0)),
% 6.53/1.36 inference(backward_demodulation,[status(thm)],[f39,f33])).
% 6.53/1.36 fof(f51,plain,(
% 6.53/1.36 multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF3_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)=b1),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f39,f41])).
% 6.53/1.36 fof(f52,plain,(
% 6.53/1.36 multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)=a1),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f39,f42])).
% 6.53/1.36 fof(f66,plain,(
% 6.53/1.36 ![X0,X1,X2,X3]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))=inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,X2))))),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f10,f10])).
% 6.53/1.36 fof(f69,plain,(
% 6.53/1.36 ![X0,X1]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,a1)))=multiply(sF1_fnc,inverse(multiply(inverse(X1),multiply(inverse(inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1)))))))))),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f5,f10])).
% 6.53/1.36 fof(f96,plain,(
% 6.53/1.36 ![X0,X1]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,a1)))=multiply(sF1_fnc,inverse(multiply(inverse(X1),multiply(inverse(inverse(multiply(sF1_fnc,a1))),inverse(multiply(inverse(inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1)))))))))),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f5,f69])).
% 6.53/1.36 fof(f97,plain,(
% 6.53/1.36 ![X0,X1]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,a1)))=multiply(sF1_fnc,inverse(multiply(inverse(X1),multiply(inverse(inverse(sF0_fnc)),inverse(multiply(inverse(inverse(multiply(inverse(a1),a1))),inverse(multiply(inverse(a1),a1)))))))))),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f6,f96])).
% 6.53/1.36 fof(f98,plain,(
% 6.53/1.36 ![X0,X1]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,a1)))=multiply(sF1_fnc,inverse(multiply(inverse(X1),multiply(inverse(inverse(sF0_fnc)),inverse(multiply(inverse(inverse(multiply(sF1_fnc,a1))),inverse(multiply(inverse(a1),a1)))))))))),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f5,f97])).
% 6.53/1.36 fof(f99,plain,(
% 6.53/1.36 ![X0,X1]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,a1)))=multiply(sF1_fnc,inverse(multiply(inverse(X1),multiply(inverse(inverse(sF0_fnc)),inverse(multiply(inverse(inverse(sF0_fnc)),inverse(multiply(inverse(a1),a1)))))))))),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f6,f98])).
% 6.53/1.36 fof(f100,plain,(
% 6.53/1.36 ![X0,X1]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,a1)))=multiply(sF1_fnc,inverse(multiply(inverse(X1),multiply(inverse(inverse(sF0_fnc)),inverse(multiply(inverse(inverse(sF0_fnc)),inverse(multiply(sF1_fnc,a1)))))))))),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f5,f99])).
% 6.53/1.36 fof(f101,plain,(
% 6.53/1.36 ![X0,X1]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,a1)))=multiply(sF1_fnc,inverse(multiply(inverse(X1),multiply(inverse(inverse(sF0_fnc)),inverse(multiply(inverse(inverse(sF0_fnc)),inverse(sF0_fnc))))))))),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f6,f100])).
% 6.53/1.36 fof(f103,plain,(
% 6.53/1.36 ![X0,X1]: (inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,a1)))=inverse(multiply(inverse(multiply(sF1_fnc,X1)),sF0_fnc)))),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f38,f101])).
% 6.53/1.36 fof(f208,plain,(
% 6.53/1.36 ![X0,X1]: (multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(inverse(multiply(sF1_fnc,X0)),sF0_fnc))),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)=multiply(inverse(multiply(X1,X0)),multiply(X1,a1)))),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f103,f46])).
% 6.53/1.36 fof(f257,plain,(
% 6.53/1.36 ![X0,X1]: (multiply(inverse(multiply(sF1_fnc,X0)),sF0_fnc)=multiply(inverse(multiply(X1,X0)),multiply(X1,a1)))),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f46,f208])).
% 6.53/1.36 fof(f293,plain,(
% 6.53/1.36 multiply(inverse(multiply(sF1_fnc,b1)),sF0_fnc)=multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1))),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f8,f257])).
% 6.53/1.36 fof(f455,plain,(
% 6.53/1.36 ![X0,X1,X2,X3]: (multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)=multiply(inverse(multiply(X3,X1)),multiply(X3,X2)))),
% 6.53/1.36 inference(paramodulation,[status(thm)],[f66,f46])).
% 6.53/1.36 fof(f482,plain,(
% 6.53/1.36 ![X0,X1,X2,X3]: (multiply(inverse(multiply(X0,X1)),multiply(X0,X2))=multiply(inverse(multiply(X3,X1)),multiply(X3,X2)))),
% 6.53/1.36 inference(forward_demodulation,[status(thm)],[f46,f455])).
% 6.53/1.38 fof(f492,plain,(
% 6.53/1.38 ![X0,X1]: (multiply(inverse(multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1))),multiply(inverse(multiply(sF1_fnc,b1)),X0))=multiply(inverse(multiply(X1,sF0_fnc)),multiply(X1,X0)))),
% 6.53/1.38 inference(paramodulation,[status(thm)],[f293,f482])).
% 6.53/1.38 fof(f1294,plain,(
% 6.53/1.38 multiply(inverse(multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1))),multiply(inverse(multiply(sF1_fnc,b1)),sF0_fnc))=multiply(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)),a1)),
% 6.53/1.38 inference(paramodulation,[status(thm)],[f52,f492])).
% 6.53/1.38 fof(f1295,plain,(
% 6.53/1.38 multiply(inverse(multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1))),multiply(inverse(multiply(sF1_fnc,b1)),sF0_fnc))=multiply(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF3_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)),b1)),
% 6.53/1.38 inference(paramodulation,[status(thm)],[f51,f492])).
% 6.53/1.38 fof(f1393,plain,(
% 6.53/1.38 multiply(inverse(multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1))),multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1)))=multiply(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)),a1)),
% 6.53/1.38 inference(forward_demodulation,[status(thm)],[f293,f1294])).
% 6.53/1.38 fof(f1394,plain,(
% 6.53/1.38 multiply(inverse(multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1))),multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1)))=multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(sF1_fnc)),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc),a1)),
% 6.53/1.38 inference(forward_demodulation,[status(thm)],[f39,f1393])).
% 6.53/1.38 fof(f1395,plain,(
% 6.53/1.38 multiply(inverse(multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1))),multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1)))=multiply(sF1_fnc,a1)),
% 6.53/1.38 inference(forward_demodulation,[status(thm)],[f46,f1394])).
% 6.53/1.38 fof(f1397,plain,(
% 6.53/1.38 multiply(inverse(multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1))),multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1)))=sF0_fnc),
% 6.53/1.38 inference(forward_demodulation,[status(thm)],[f6,f1395])).
% 6.53/1.38 fof(f1398,plain,(
% 6.53/1.38 multiply(inverse(multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1))),multiply(inverse(sF2_fnc),multiply(sF3_fnc,a1)))=multiply(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF3_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)),b1)),
% 6.53/1.38 inference(forward_demodulation,[status(thm)],[f293,f1295])).
% 6.53/1.38 fof(f1399,plain,(
% 6.53/1.38 sF0_fnc=multiply(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF3_fnc),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc)),b1)),
% 6.53/1.38 inference(forward_demodulation,[status(thm)],[f1397,f1398])).
% 6.53/1.38 fof(f1400,plain,(
% 6.53/1.38 sF0_fnc=multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(sF3_fnc)),multiply(sF1_fnc,inverse(sF0_fnc)))))),sF0_fnc),b1)),
% 6.53/1.38 inference(forward_demodulation,[status(thm)],[f39,f1399])).
% 6.53/1.38 fof(f1401,plain,(
% 6.53/1.38 sF2_fnc=sF0_fnc),
% 6.53/1.38 inference(backward_demodulation,[status(thm)],[f1402,f8])).
% 6.53/1.38 fof(f1402,plain,(
% 6.53/1.38 sF0_fnc=multiply(sF3_fnc,b1)),
% 6.53/1.38 inference(forward_demodulation,[status(thm)],[f46,f1400])).
% 6.53/1.38 fof(f1625,plain,(
% 6.53/1.38 $false),
% 6.53/1.38 inference(forward_subsumption_resolution,[status(thm)],[f1401,f9])).
% 6.53/1.38 % SZS output end CNFRefutation for theBenchmark.p
% 1.86/1.40 % Elapsed time: 1.032395 seconds
% 1.86/1.40 % CPU time: 7.972610 seconds
% 1.86/1.40 % Total memory used: 214.159 MB
% 1.86/1.40 % Net memory used: 212.926 MB
%------------------------------------------------------------------------------