%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP059-1 : TPTP v9.3.1. Released v1.0.0.
% 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 12:35:34 PM UTC 2026
% Result : Unsatisfiable 34.68s 4.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP059-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 19:58:52 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 34.68/4.98 % Refutation found
% 34.68/4.98 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 34.68/4.98 % SZS output start CNFRefutation for theBenchmark
% 34.68/4.98 fof(f1,axiom,(
% 34.68/4.98 (![X,Y,Z,U]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(X,Y),Z)),X),Y),multiply(U,inverse(U)))) = Z ))),
% 34.68/4.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/4.98 fof(f2,negated_conjecture,(
% 34.68/4.98 ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)| multiply(multiply(inverse(b2),b2),a2) != a2| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
% 34.68/4.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/4.98 fof(f3,plain,(
% 34.68/4.98 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3))))=X2)),
% 34.68/4.98 inference(cnf_transformation,[status(thm)],[f1])).
% 34.68/4.98 fof(f4,plain,(
% 34.68/4.98 ~multiply(inverse(a1),a1)=multiply(inverse(b1),b1)|~multiply(multiply(inverse(b2),b2),a2)=a2|~multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3))),
% 34.68/4.98 inference(cnf_transformation,[status(thm)],[f2])).
% 34.68/4.98 fof(f5,definition,(
% 34.68/4.98 sQ0_spl <=> (multiply(inverse(a1),a1)=multiply(inverse(b1),b1))),
% 34.68/4.98 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 34.68/4.98 fof(f7,plain,(
% 34.68/4.98 ~multiply(inverse(a1),a1)=multiply(inverse(b1),b1)|sQ0_spl),
% 34.68/4.98 inference(component_clause,[status(thm)],[f5])).
% 34.68/4.98 fof(f8,definition,(
% 34.68/4.98 sQ1_spl <=> (multiply(multiply(inverse(b2),b2),a2)=a2)),
% 34.68/4.98 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 34.68/4.98 fof(f10,plain,(
% 34.68/4.98 ~multiply(multiply(inverse(b2),b2),a2)=a2|sQ1_spl),
% 34.68/4.98 inference(component_clause,[status(thm)],[f8])).
% 34.68/4.98 fof(f11,definition,(
% 34.68/4.98 sQ2_spl <=> (multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3)))),
% 34.68/4.98 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 34.68/4.98 fof(f13,plain,(
% 34.68/4.98 ~multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3))|sQ2_spl),
% 34.68/4.98 inference(component_clause,[status(thm)],[f11])).
% 34.68/4.98 fof(f14,plain,(
% 34.68/4.98 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 34.68/4.98 inference(split_clause,[status(thm)],[f4,f5,f8,f11])).
% 34.68/4.98 fof(f15,plain,(
% 34.68/4.98 ![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)))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f3,f3])).
% 34.68/4.98 fof(f17,plain,(
% 34.68/4.98 ![X0,X1]: (multiply(X0,inverse(X0))=multiply(X1,inverse(X1)))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f15,f15])).
% 34.68/4.98 fof(f44,plain,(
% 34.68/4.98 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(X3,inverse(X3))))=inverse(multiply(X1,X2)))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f17,f3])).
% 34.68/4.98 fof(f49,plain,(
% 34.68/4.98 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(X3,inverse(X3))))=X1)),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f17,f3])).
% 34.68/4.98 fof(f123,plain,(
% 34.68/4.98 ![X0,X1]: (inverse(multiply(X0,inverse(X0)))=inverse(multiply(X1,inverse(X1))))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f44,f49])).
% 34.68/4.98 fof(f204,plain,(
% 34.68/4.98 ![X0,X1,X2]: (multiply(X0,inverse(X0))=multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f123,f17])).
% 34.68/4.98 fof(f246,plain,(
% 34.68/4.98 ![X0,X1,X2,X3]: (multiply(X0,inverse(X0))=multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),inverse(multiply(X3,inverse(X3)))))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f204,f204])).
% 34.68/4.98 fof(f299,plain,(
% 34.68/4.98 ![X0,X1,X2,X3,X4]: (inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),multiply(inverse(multiply(X1,inverse(X1))),X2)),inverse(X2)),multiply(X3,inverse(X3))))=multiply(X4,inverse(X4)))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f204,f15])).
% 34.68/4.98 fof(f319,plain,(
% 34.68/4.98 ![X0,X1,X2]: (inverse(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),inverse(X1)))=multiply(X2,inverse(X2)))),
% 34.68/4.98 inference(forward_demodulation,[status(thm)],[f44,f299])).
% 34.68/4.98 fof(f639,plain,(
% 34.68/4.98 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))),X2),multiply(X3,inverse(X3))))=inverse(X2))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f319,f3])).
% 34.68/4.98 fof(f5201,plain,(
% 34.68/4.98 ![X0,X1,X2]: (inverse(multiply(multiply(multiply(X0,inverse(X0)),X1),multiply(X2,inverse(X2))))=inverse(X1))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f246,f639])).
% 34.68/4.98 fof(f5465,plain,(
% 34.68/4.98 ![X0,X1]: (X0=inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X0))))))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f49,f5201])).
% 34.68/4.98 fof(f5690,plain,(
% 34.68/4.98 ![X0,X1,X2]: (multiply(X0,inverse(X0))=inverse(inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2))))))))))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f639,f5465])).
% 34.68/4.98 fof(f5847,plain,(
% 34.68/4.98 ![X0,X1]: (multiply(X0,inverse(X0))=inverse(inverse(multiply(X1,inverse(X1)))))),
% 34.68/4.98 inference(forward_demodulation,[status(thm)],[f5465,f5690])).
% 34.68/4.98 fof(f6098,plain,(
% 34.68/4.98 ![X0,X1,X2,X3]: (inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),multiply(X1,inverse(X1))),X2),multiply(X3,inverse(X3))))=inverse(X2))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f5847,f5201])).
% 34.68/4.98 fof(f6177,plain,(
% 34.68/4.98 ![X0,X1]: (inverse(multiply(multiply(X0,inverse(X0)),X1))=inverse(X1))),
% 34.68/4.98 inference(forward_demodulation,[status(thm)],[f44,f6098])).
% 34.68/4.98 fof(f6181,plain,(
% 34.68/4.98 ![X0]: (X0=inverse(inverse(inverse(inverse(X0)))))),
% 34.68/4.98 inference(backward_demodulation,[status(thm)],[f6177,f5465])).
% 34.68/4.98 fof(f7237,plain,(
% 34.68/4.98 ![X0,X1]: (multiply(multiply(X0,inverse(X0)),X1)=inverse(inverse(inverse(inverse(X1)))))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f6177,f6181])).
% 34.68/4.98 fof(f7318,plain,(
% 34.68/4.98 ![X0,X1]: (multiply(multiply(X0,inverse(X0)),X1)=X1)),
% 34.68/4.98 inference(forward_demodulation,[status(thm)],[f6181,f7237])).
% 34.68/4.98 fof(f7329,plain,(
% 34.68/4.98 ![X0,X1]: (inverse(multiply(X0,multiply(X1,inverse(X1))))=inverse(X0))),
% 34.68/4.98 inference(backward_demodulation,[status(thm)],[f7318,f5201])).
% 34.68/4.98 fof(f8236,plain,(
% 34.68/4.98 ![X0,X1,X2]: (inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1))=X2)),
% 34.68/4.98 inference(backward_demodulation,[status(thm)],[f7329,f3])).
% 34.68/4.98 fof(f8285,plain,(
% 34.68/4.98 ![X0,X1]: (multiply(X0,multiply(X1,inverse(X1)))=inverse(inverse(inverse(inverse(X0)))))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f7329,f6181])).
% 34.68/4.98 fof(f8315,plain,(
% 34.68/4.98 ![X0,X1]: (multiply(X0,multiply(X1,inverse(X1)))=X0)),
% 34.68/4.98 inference(forward_demodulation,[status(thm)],[f6181,f8285])).
% 34.68/4.98 fof(f8391,plain,(
% 34.68/4.98 ![X0,X1,X2]: (inverse(multiply(inverse(multiply(multiply(X0,multiply(X1,inverse(X1))),X2)),X0))=X2)),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f8315,f8236])).
% 34.68/4.98 fof(f8396,plain,(
% 34.68/4.98 ![X0,X1,X2]: (inverse(multiply(multiply(X0,inverse(multiply(multiply(X1,X2),X0))),X1))=X2)),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f8236,f8236])).
% 34.68/4.98 fof(f8400,plain,(
% 34.68/4.98 ![X0,X1]: (inverse(multiply(multiply(inverse(X0),X1),inverse(X1)))=X0)),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f7318,f8236])).
% 34.68/4.98 fof(f8428,plain,(
% 34.68/4.98 ![X0,X1]: (inverse(multiply(inverse(multiply(X0,X1)),X0))=X1)),
% 34.68/4.98 inference(forward_demodulation,[status(thm)],[f8315,f8391])).
% 34.68/4.98 fof(f8555,plain,(
% 34.68/4.98 ![X0,X1]: (inverse(inverse(multiply(multiply(X0,inverse(X0)),X1)))=X1)),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f8315,f8428])).
% 34.68/4.98 fof(f8557,plain,(
% 34.68/4.98 ![X0,X1]: (inverse(multiply(X0,inverse(multiply(X1,X0))))=X1)),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f8428,f8428])).
% 34.68/4.98 fof(f8586,plain,(
% 34.68/4.98 ![X0]: (inverse(inverse(X0))=X0)),
% 34.68/4.98 inference(forward_demodulation,[status(thm)],[f7318,f8555])).
% 34.68/4.98 fof(f8594,plain,(
% 34.68/4.98 ![X0,X1]: (inverse(X0)=multiply(inverse(multiply(X1,X0)),X1))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f8428,f8586])).
% 34.68/4.98 fof(f8602,plain,(
% 34.68/4.98 ![X0,X1]: (multiply(X0,multiply(inverse(X1),X1))=X0)),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f8586,f8315])).
% 34.68/4.98 fof(f8606,plain,(
% 34.68/4.98 ![X0,X1]: (multiply(multiply(inverse(X0),X0),X1)=X1)),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f8586,f7318])).
% 34.68/4.98 fof(f8648,plain,(
% 34.68/4.98 ![X0,X1]: (multiply(inverse(X0),X0)=multiply(inverse(X1),X1))),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f8602,f8606])).
% 34.68/4.98 fof(f8853,plain,(
% 34.68/4.98 ![X0,X1,X2]: (inverse(multiply(multiply(X0,X1),inverse(multiply(multiply(X2,X0),X1))))=X2)),
% 34.68/4.98 inference(paramodulation,[status(thm)],[f8236,f8396])).
% 34.68/4.98 fof(f9088,plain,(
% 34.68/4.98 ![X0,X1]: (inverse(X0)=multiply(X1,inverse(multiply(X0,X1))))),
% 34.68/5.00 inference(paramodulation,[status(thm)],[f8557,f8586])).
% 34.68/5.00 fof(f15880,plain,(
% 34.68/5.00 ![X0,X1]: (inverse(inverse(X0))=multiply(X1,multiply(inverse(X1),X0)))),
% 34.68/5.00 inference(paramodulation,[status(thm)],[f8400,f8594])).
% 34.68/5.00 fof(f15996,plain,(
% 34.68/5.00 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),X0)))),
% 34.68/5.00 inference(forward_demodulation,[status(thm)],[f8586,f15880])).
% 34.68/5.00 fof(f16005,plain,(
% 34.68/5.00 ![X0,X1]: (X0=multiply(multiply(X0,X1),inverse(X1)))),
% 34.68/5.00 inference(paramodulation,[status(thm)],[f8594,f15996])).
% 34.68/5.00 fof(f16014,plain,(
% 34.68/5.00 ![X0,X1]: (inverse(multiply(X0,inverse(X1)))=multiply(X1,inverse(X0)))),
% 34.68/5.00 inference(paramodulation,[status(thm)],[f9088,f15996])).
% 34.68/5.00 fof(f16021,plain,(
% 34.68/5.00 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 34.68/5.00 inference(paramodulation,[status(thm)],[f8586,f15996])).
% 34.68/5.00 fof(f16185,plain,(
% 34.68/5.00 ![X0,X1]: (X0=multiply(multiply(X0,inverse(X1)),X1))),
% 34.68/5.00 inference(paramodulation,[status(thm)],[f8586,f16005])).
% 34.68/5.00 fof(f33092,plain,(
% 34.68/5.00 ![X0,X1,X2]: (multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X1,X2)))=X0)),
% 34.68/5.00 inference(forward_demodulation,[status(thm)],[f16014,f8853])).
% 34.68/5.00 fof(f33299,plain,(
% 34.68/5.00 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 34.68/5.00 inference(paramodulation,[status(thm)],[f33092,f16185])).
% 34.68/5.00 fof(f33685,plain,(
% 34.68/5.00 ~multiply(a3,multiply(b3,c3))=multiply(a3,multiply(b3,c3))|sQ2_spl),
% 34.68/5.00 inference(backward_demodulation,[status(thm)],[f33299,f13])).
% 34.68/5.00 fof(f33919,plain,(
% 34.68/5.00 $false|sQ2_spl),
% 34.68/5.00 inference(trivial_equality_resolution,[status(thm)],[f33685])).
% 34.68/5.00 fof(f33920,plain,(
% 34.68/5.00 sQ2_spl),
% 34.68/5.00 inference(contradiction_clause,[status(thm)],[f33919])).
% 34.68/5.00 fof(f33973,plain,(
% 34.68/5.00 $false|sQ0_spl),
% 34.68/5.00 inference(forward_subsumption_resolution,[status(thm)],[f7,f8648])).
% 34.68/5.00 fof(f33974,plain,(
% 34.68/5.00 sQ0_spl),
% 34.68/5.00 inference(contradiction_clause,[status(thm)],[f33973])).
% 34.68/5.00 fof(f33975,plain,(
% 34.68/5.00 ~multiply(inverse(b2),multiply(b2,a2))=a2|sQ1_spl),
% 34.68/5.00 inference(forward_demodulation,[status(thm)],[f33299,f10])).
% 34.68/5.00 fof(f33976,plain,(
% 34.68/5.00 ~a2=a2|sQ1_spl),
% 34.68/5.00 inference(forward_demodulation,[status(thm)],[f16021,f33975])).
% 34.68/5.00 fof(f33977,plain,(
% 34.68/5.00 $false|sQ1_spl),
% 34.68/5.00 inference(trivial_equality_resolution,[status(thm)],[f33976])).
% 34.68/5.00 fof(f33978,plain,(
% 34.68/5.00 sQ1_spl),
% 34.68/5.00 inference(contradiction_clause,[status(thm)],[f33977])).
% 34.68/5.00 fof(f33979,plain,(
% 34.68/5.00 $false),
% 34.68/5.00 inference(sat_refutation,[status(thm)],[f14,f33920,f33974,f33978])).
% 34.68/5.00 % SZS output end CNFRefutation for theBenchmark.p
% 34.68/5.04 % Elapsed time: 4.580086 seconds
% 34.68/5.04 % CPU time: 35.587404 seconds
% 34.68/5.04 % Total memory used: 188.109 MB
% 34.68/5.04 % Net memory used: 186.463 MB
%------------------------------------------------------------------------------