%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP433-1 : 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 : n009.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 0.11s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:12:42 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.39 fof(f1,axiom,(
% 0.11/0.39 (![A,B,C,D]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C ))),
% 0.11/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f2,negated_conjecture,(
% 0.11/0.39 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
% 0.11/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f3,plain,(
% 0.11/0.39 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3))))=X2)),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.11/0.39 fof(f4,plain,(
% 0.11/0.39 ~multiply(inverse(a1),a1)=multiply(inverse(b1),b1)),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.11/0.39 fof(f5,definition,(
% 0.11/0.39 sF1_fnc=inverse(a1)),
% 0.11/0.39 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.11/0.39 fof(f6,definition,(
% 0.11/0.39 sF0_fnc=multiply(sF1_fnc,a1)),
% 0.11/0.39 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.11/0.39 fof(f7,definition,(
% 0.11/0.39 sF3_fnc=inverse(b1)),
% 0.11/0.39 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 0.11/0.39 fof(f8,definition,(
% 0.11/0.39 sF2_fnc=multiply(sF3_fnc,b1)),
% 0.11/0.39 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 0.11/0.39 fof(f9,plain,(
% 0.11/0.39 ~sF0_fnc=sF2_fnc),
% 0.11/0.39 inference(definition_folding,[],[f4,f8,f7,f6,f5])).
% 0.11/0.39 fof(f10,plain,(
% 0.11/0.39 ![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)))),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f3,f3])).
% 0.11/0.39 fof(f11,plain,(
% 0.11/0.39 ![X0,X1]: (inverse(multiply(multiply(multiply(inverse(multiply(sF2_fnc,X0)),sF3_fnc),b1),multiply(X1,inverse(X1))))=X0)),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f8,f3])).
% 0.11/0.39 fof(f15,plain,(
% 0.11/0.39 ![X0,X1,X2]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(a1,sF1_fnc)))=X2)),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f5,f3])).
% 0.11/0.39 fof(f18,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(multiply(multiply(inverse(multiply(sF2_fnc,X0)),sF3_fnc),b1),multiply(b1,sF3_fnc)))=X0)),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f7,f11])).
% 0.11/0.39 fof(f20,plain,(
% 0.11/0.39 ![X0,X1,X2]: (inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(sF2_fnc,X0)),sF3_fnc)),b1),multiply(X1,inverse(X1))))=multiply(X2,inverse(X2)))),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f11,f3])).
% 0.11/0.39 fof(f22,plain,(
% 0.11/0.39 ![X0,X1]: (inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(sF2_fnc,X0)),sF3_fnc)),b1),multiply(X1,inverse(X1))))=multiply(b1,sF3_fnc))),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f18,f3])).
% 0.11/0.39 fof(f25,plain,(
% 0.11/0.39 ![X0]: (multiply(b1,sF3_fnc)=multiply(X0,inverse(X0)))),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f22,f20])).
% 0.11/0.39 fof(f34,plain,(
% 0.11/0.39 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3))))=multiply(b1,sF3_fnc))),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f25,f10])).
% 0.11/0.39 fof(f35,plain,(
% 0.11/0.39 ![X0,X1,X2]: (inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(b1,sF3_fnc)))=multiply(b1,sF3_fnc))),
% 0.11/0.39 inference(forward_demodulation,[status(thm)],[f25,f34])).
% 0.11/0.39 fof(f38,plain,(
% 0.11/0.39 multiply(b1,sF3_fnc)=multiply(a1,sF1_fnc)),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f5,f25])).
% 0.11/0.39 fof(f42,plain,(
% 0.11/0.39 ![X0]: (multiply(a1,sF1_fnc)=multiply(X0,inverse(X0)))),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f38,f25])).
% 0.11/0.39 fof(f45,plain,(
% 0.11/0.39 ![X0,X1,X2]: (inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(b1,sF3_fnc)))=multiply(a1,sF1_fnc))),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f38,f35])).
% 0.11/0.39 fof(f56,plain,(
% 0.11/0.39 ![X0,X1,X2]: (inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(a1,sF1_fnc)))=multiply(a1,sF1_fnc))),
% 0.11/0.39 inference(forward_demodulation,[status(thm)],[f38,f45])).
% 0.11/0.39 fof(f67,plain,(
% 0.11/0.39 ![X0,X1]: (inverse(multiply(multiply(multiply(inverse(multiply(a1,sF1_fnc)),X0),X1),multiply(a1,sF1_fnc)))=inverse(multiply(X0,X1)))),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f42,f15])).
% 0.11/0.39 fof(f71,plain,(
% 0.11/0.39 ![X0,X1]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(a1,sF1_fnc),X0)),X1),inverse(X1)),multiply(a1,sF1_fnc)))=X0)),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f42,f15])).
% 0.11/0.39 fof(f82,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(multiply(multiply(a1,sF1_fnc),X0),multiply(a1,sF1_fnc)))=inverse(multiply(inverse(inverse(multiply(a1,sF1_fnc))),X0)))),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f42,f67])).
% 0.11/0.39 fof(f85,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(multiply(multiply(a1,sF1_fnc),inverse(inverse(inverse(multiply(multiply(a1,sF1_fnc),X0))))),multiply(a1,sF1_fnc)))=X0)),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f42,f71])).
% 0.11/0.39 fof(f97,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(inverse(inverse(multiply(a1,sF1_fnc))),inverse(inverse(inverse(multiply(multiply(a1,sF1_fnc),X0))))))=X0)),
% 0.11/0.39 inference(forward_demodulation,[status(thm)],[f82,f85])).
% 0.11/0.39 fof(f106,plain,(
% 0.11/0.39 ![X0,X1]: (inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),inverse(multiply(a1,sF1_fnc)))),X0),X1))=multiply(a1,sF1_fnc))),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f67,f56])).
% 0.11/0.39 fof(f140,plain,(
% 0.11/0.39 inverse(multiply(multiply(inverse(multiply(multiply(a1,sF1_fnc),inverse(multiply(a1,sF1_fnc)))),b1),sF3_fnc))=multiply(a1,sF1_fnc)),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f38,f106])).
% 0.11/0.39 fof(f143,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(multiply(inverse(multiply(multiply(a1,sF1_fnc),inverse(multiply(a1,sF1_fnc)))),X0),inverse(X0)))=multiply(a1,sF1_fnc))),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f42,f106])).
% 0.11/0.39 fof(f149,plain,(
% 0.11/0.39 inverse(multiply(multiply(inverse(multiply(a1,sF1_fnc)),b1),sF3_fnc))=multiply(a1,sF1_fnc)),
% 0.11/0.39 inference(forward_demodulation,[status(thm)],[f42,f140])).
% 0.11/0.39 fof(f150,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(multiply(inverse(multiply(a1,sF1_fnc)),X0),inverse(X0)))=multiply(a1,sF1_fnc))),
% 0.11/0.39 inference(forward_demodulation,[status(thm)],[f42,f143])).
% 0.11/0.39 fof(f162,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(a1,sF1_fnc),X0)),multiply(multiply(inverse(multiply(a1,sF1_fnc)),b1),sF3_fnc)),multiply(a1,sF1_fnc)),multiply(a1,sF1_fnc)))=X0)),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f149,f71])).
% 0.11/0.39 fof(f204,plain,(
% 0.11/0.39 inverse(multiply(multiply(multiply(a1,sF1_fnc),inverse(multiply(a1,sF1_fnc))),multiply(a1,sF1_fnc)))=multiply(a1,sF1_fnc)),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f150,f106])).
% 0.11/0.39 fof(f206,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(multiply(multiply(multiply(a1,sF1_fnc),inverse(multiply(a1,sF1_fnc))),X0),multiply(a1,sF1_fnc)))=inverse(X0))),
% 0.11/0.39 inference(paramodulation,[status(thm)],[f150,f15])).
% 0.11/0.39 fof(f209,plain,(
% 0.11/0.39 inverse(multiply(inverse(inverse(multiply(a1,sF1_fnc))),inverse(multiply(a1,sF1_fnc))))=multiply(a1,sF1_fnc)),
% 0.11/0.39 inference(forward_demodulation,[status(thm)],[f82,f204])).
% 0.11/0.39 fof(f211,plain,(
% 0.11/0.39 ![X0]: (inverse(X0)=inverse(multiply(inverse(inverse(multiply(a1,sF1_fnc))),X0)))),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f212,f82])).
% 0.11/0.39 fof(f212,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(multiply(multiply(a1,sF1_fnc),X0),multiply(a1,sF1_fnc)))=inverse(X0))),
% 0.11/0.39 inference(forward_demodulation,[status(thm)],[f42,f206])).
% 0.11/0.39 fof(f215,plain,(
% 0.11/0.39 ![X0]: (inverse(inverse(inverse(inverse(multiply(multiply(a1,sF1_fnc),X0)))))=X0)),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f211,f97])).
% 0.11/0.39 fof(f216,plain,(
% 0.11/0.39 inverse(inverse(multiply(a1,sF1_fnc)))=multiply(a1,sF1_fnc)),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f211,f209])).
% 0.11/0.39 fof(f219,plain,(
% 0.11/0.39 ![X0]: (inverse(X0)=inverse(multiply(multiply(a1,sF1_fnc),X0)))),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f216,f211])).
% 0.11/0.39 fof(f233,plain,(
% 0.11/0.39 ![X0]: (inverse(inverse(inverse(inverse(X0))))=X0)),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f219,f215])).
% 0.11/0.39 fof(f237,plain,(
% 0.11/0.39 ![X0]: (inverse(multiply(multiply(multiply(inverse(X0),multiply(multiply(inverse(multiply(a1,sF1_fnc)),b1),sF3_fnc)),multiply(a1,sF1_fnc)),multiply(a1,sF1_fnc)))=X0)),
% 0.11/0.39 inference(backward_demodulation,[status(thm)],[f219,f162])).
% 0.11/0.39 fof(f270,plain,(
% 0.11/0.39 inverse(inverse(inverse(multiply(a1,sF1_fnc))))=multiply(multiply(inverse(multiply(a1,sF1_fnc)),b1),sF3_fnc)),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f149,f233])).
% 0.14/0.39 fof(f275,plain,(
% 0.14/0.39 ![X0,X1]: (inverse(inverse(inverse(inverse(multiply(X0,X1)))))=multiply(multiply(multiply(inverse(multiply(a1,sF1_fnc)),X0),X1),multiply(a1,sF1_fnc)))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f67,f233])).
% 0.14/0.39 fof(f281,plain,(
% 0.14/0.39 inverse(inverse(inverse(sF3_fnc)))=b1),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f7,f233])).
% 0.14/0.39 fof(f282,plain,(
% 0.14/0.39 inverse(inverse(inverse(sF1_fnc)))=a1),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f5,f233])).
% 0.14/0.39 fof(f286,plain,(
% 0.14/0.39 ![X0]: (inverse(multiply(multiply(multiply(inverse(X0),inverse(multiply(a1,sF1_fnc))),multiply(a1,sF1_fnc)),multiply(a1,sF1_fnc)))=X0)),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f289,f237])).
% 0.14/0.39 fof(f289,plain,(
% 0.14/0.39 inverse(multiply(a1,sF1_fnc))=multiply(multiply(inverse(multiply(a1,sF1_fnc)),b1),sF3_fnc)),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f216,f270])).
% 0.14/0.39 fof(f315,plain,(
% 0.14/0.39 ![X0,X1]: (multiply(X0,X1)=multiply(multiply(multiply(inverse(multiply(a1,sF1_fnc)),X0),X1),multiply(a1,sF1_fnc)))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f233,f275])).
% 0.14/0.39 fof(f343,plain,(
% 0.14/0.39 multiply(a1,sF1_fnc)=multiply(inverse(inverse(sF3_fnc)),b1)),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f281,f42])).
% 0.14/0.39 fof(f347,plain,(
% 0.14/0.39 multiply(a1,sF1_fnc)=multiply(inverse(inverse(sF1_fnc)),a1)),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f282,f42])).
% 0.14/0.39 fof(f348,plain,(
% 0.14/0.39 inverse(inverse(multiply(a1,sF1_fnc)))=inverse(multiply(a1,sF1_fnc))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f42,f219])).
% 0.14/0.39 fof(f349,plain,(
% 0.14/0.39 ![X0]: (inverse(inverse(inverse(inverse(X0))))=multiply(multiply(a1,sF1_fnc),X0))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f219,f233])).
% 0.14/0.39 fof(f353,plain,(
% 0.14/0.39 ![X0]: (inverse(multiply(multiply(multiply(inverse(X0),multiply(a1,sF1_fnc)),multiply(a1,sF1_fnc)),multiply(a1,sF1_fnc)))=X0)),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f381,f286])).
% 0.14/0.39 fof(f357,plain,(
% 0.14/0.39 ![X0,X1]: (multiply(X0,X1)=multiply(multiply(multiply(multiply(a1,sF1_fnc),X0),X1),multiply(a1,sF1_fnc)))),
% 0.14/0.40 inference(backward_demodulation,[status(thm)],[f381,f315])).
% 0.14/0.40 fof(f381,plain,(
% 0.14/0.40 multiply(a1,sF1_fnc)=inverse(multiply(a1,sF1_fnc))),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f216,f348])).
% 0.14/0.40 fof(f398,plain,(
% 0.14/0.40 ![X0]: (inverse(multiply(X0,multiply(a1,sF1_fnc)))=inverse(X0))),
% 0.14/0.40 inference(backward_demodulation,[status(thm)],[f399,f212])).
% 0.14/0.40 fof(f399,plain,(
% 0.14/0.40 ![X0]: (X0=multiply(multiply(a1,sF1_fnc),X0))),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f233,f349])).
% 0.14/0.40 fof(f404,plain,(
% 0.14/0.40 ![X0]: (inverse(multiply(multiply(inverse(X0),multiply(a1,sF1_fnc)),multiply(a1,sF1_fnc)))=X0)),
% 0.14/0.40 inference(backward_demodulation,[status(thm)],[f424,f353])).
% 0.14/0.40 fof(f424,plain,(
% 0.14/0.40 ![X0,X1]: (multiply(X0,X1)=multiply(multiply(X0,X1),multiply(a1,sF1_fnc)))),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f399,f357])).
% 0.14/0.40 fof(f492,plain,(
% 0.14/0.40 ![X0]: (inverse(multiply(inverse(X0),multiply(a1,sF1_fnc)))=X0)),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f398,f404])).
% 0.14/0.40 fof(f496,plain,(
% 0.14/0.40 multiply(a1,sF1_fnc)=multiply(sF1_fnc,a1)),
% 0.14/0.40 inference(backward_demodulation,[status(thm)],[f500,f347])).
% 0.14/0.40 fof(f497,plain,(
% 0.14/0.40 multiply(a1,sF1_fnc)=multiply(sF3_fnc,b1)),
% 0.14/0.40 inference(backward_demodulation,[status(thm)],[f500,f343])).
% 0.14/0.40 fof(f500,plain,(
% 0.14/0.40 ![X0]: (inverse(inverse(X0))=X0)),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f398,f492])).
% 0.14/0.40 fof(f535,plain,(
% 0.14/0.40 multiply(a1,sF1_fnc)=sF0_fnc),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f6,f496])).
% 0.14/0.40 fof(f536,plain,(
% 0.14/0.40 sF2_fnc=sF0_fnc),
% 0.14/0.40 inference(backward_demodulation,[status(thm)],[f537,f8])).
% 0.14/0.40 fof(f537,plain,(
% 0.14/0.40 sF0_fnc=multiply(sF3_fnc,b1)),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f535,f497])).
% 0.14/0.40 fof(f558,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f536,f9])).
% 0.14/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.46 % Elapsed time: 0.090921 seconds
% 0.14/0.46 % CPU time: 0.143285 seconds
% 0.14/0.46 % Total memory used: 7.965 MB
% 0.14/0.46 % Net memory used: 7.708 MB
%------------------------------------------------------------------------------