%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO035-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:06:48 PM UTC 2026
% Result : Unsatisfiable 15.72s 2.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO035-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 13:50:47 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 15.72/2.44 % Refutation found
% 15.72/2.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 15.72/2.44 % SZS output start CNFRefutation for theBenchmark
% 15.72/2.44 fof(f1,axiom,(
% 15.72/2.44 (![X,Y,Z,U,V,W,V6]: (multiply(multiply(X,inverse(X),Y),inverse(multiply(multiply(Z,U,V),W,multiply(Z,U,V6))),multiply(U,multiply(V6,W,V),Z)) = Y ))),
% 15.72/2.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.72/2.44 fof(f2,negated_conjecture,(
% 15.72/2.44 ( multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c))| multiply(b,a,a) != a| multiply(a,b,inverse(b)) != a| multiply(a,a,b) != a| multiply(inverse(b),b,a) != a ) ),
% 15.72/2.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.72/2.44 fof(f3,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4,X5,X6]: (multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2))=X1)),
% 15.72/2.44 inference(cnf_transformation,[status(thm)],[f1])).
% 15.72/2.44 fof(f4,plain,(
% 15.72/2.44 ~multiply(multiply(d,e,a),b,multiply(d,e,c))=multiply(d,e,multiply(a,b,c))|~multiply(b,a,a)=a|~multiply(a,b,inverse(b))=a|~multiply(a,a,b)=a|~multiply(inverse(b),b,a)=a),
% 15.72/2.44 inference(cnf_transformation,[status(thm)],[f2])).
% 15.72/2.44 fof(f5,definition,(
% 15.72/2.44 sQ0_spl <=> (multiply(multiply(d,e,a),b,multiply(d,e,c))=multiply(d,e,multiply(a,b,c)))),
% 15.72/2.44 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 15.72/2.44 fof(f7,plain,(
% 15.72/2.44 ~multiply(multiply(d,e,a),b,multiply(d,e,c))=multiply(d,e,multiply(a,b,c))|sQ0_spl),
% 15.72/2.44 inference(component_clause,[status(thm)],[f5])).
% 15.72/2.44 fof(f8,definition,(
% 15.72/2.44 sQ1_spl <=> (multiply(b,a,a)=a)),
% 15.72/2.44 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 15.72/2.44 fof(f10,plain,(
% 15.72/2.44 ~multiply(b,a,a)=a|sQ1_spl),
% 15.72/2.44 inference(component_clause,[status(thm)],[f8])).
% 15.72/2.44 fof(f11,definition,(
% 15.72/2.44 sQ2_spl <=> (multiply(a,b,inverse(b))=a)),
% 15.72/2.44 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 15.72/2.44 fof(f13,plain,(
% 15.72/2.44 ~multiply(a,b,inverse(b))=a|sQ2_spl),
% 15.72/2.44 inference(component_clause,[status(thm)],[f11])).
% 15.72/2.44 fof(f14,definition,(
% 15.72/2.44 sQ3_spl <=> (multiply(a,a,b)=a)),
% 15.72/2.44 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 15.72/2.44 fof(f16,plain,(
% 15.72/2.44 ~multiply(a,a,b)=a|sQ3_spl),
% 15.72/2.44 inference(component_clause,[status(thm)],[f14])).
% 15.72/2.44 fof(f17,definition,(
% 15.72/2.44 sQ4_spl <=> (multiply(inverse(b),b,a)=a)),
% 15.72/2.44 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 15.72/2.44 fof(f19,plain,(
% 15.72/2.44 ~multiply(inverse(b),b,a)=a|sQ4_spl),
% 15.72/2.44 inference(component_clause,[status(thm)],[f17])).
% 15.72/2.44 fof(f20,plain,(
% 15.72/2.44 ~sQ0_spl|~sQ1_spl|~sQ2_spl|~sQ3_spl|~sQ4_spl),
% 15.72/2.44 inference(split_clause,[status(thm)],[f4,f5,f8,f11,f14,f17])).
% 15.72/2.44 fof(f21,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (multiply(multiply(X0,X1,X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3))=multiply(X1,multiply(X2,inverse(multiply(X0,X1,X8)),X8),X0))),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f3,f3])).
% 15.72/2.44 fof(f24,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10]: (multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,multiply(X4,multiply(X5,X6,X7),X8)),inverse(multiply(multiply(X8,X4,X7),X6,multiply(X8,X4,X5))),multiply(X2,X3,multiply(X9,inverse(X9),X10)))),multiply(X3,X10,X2))=X1)),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f3,f3])).
% 15.72/2.44 fof(f25,plain,(
% 15.72/2.44 ![X0,X1,X2]: (X0=multiply(inverse(X1),multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),X1))),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f3,f21])).
% 15.72/2.44 fof(f48,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10]: (multiply(multiply(X0,multiply(multiply(X1,X2,X3),inverse(multiply(multiply(X1,X2,X4),X0,X5)),X5),multiply(X1,X2,X4)),inverse(multiply(multiply(X6,X7,X8),X9,multiply(X6,X7,X10))),multiply(X7,multiply(X10,X9,X8),X6))=multiply(X2,multiply(X3,X0,X4),X1))),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f21,f3])).
% 15.72/2.44 fof(f62,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4]: (multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,inverse(X2),X3),inverse(multiply(X2,inverse(X2),X3)),multiply(X2,inverse(X2),X4))),X4)=X1)),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f25,f3])).
% 15.72/2.44 fof(f1006,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4,X5,X6]: (multiply(multiply(X0,inverse(X0),X1),inverse(multiply(inverse(X2),multiply(multiply(X3,inverse(X3),multiply(X4,inverse(X4),X5)),inverse(multiply(X2,inverse(X2),X6)),X6),X2)),multiply(inverse(X3),X5,X3))=X1)),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f62,f24])).
% 15.72/2.44 fof(f1159,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4]: (multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2))=X1)),
% 15.72/2.44 inference(forward_demodulation,[status(thm)],[f25,f1006])).
% 15.72/2.44 fof(f1187,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4,X5]: (multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2))=multiply(inverse(X5),X1,X5))),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f1159,f1159])).
% 15.72/2.44 fof(f1279,plain,(
% 15.72/2.44 ![X0,X1]: (X0=multiply(inverse(X1),X0,X1))),
% 15.72/2.44 inference(forward_demodulation,[status(thm)],[f1159,f1187])).
% 15.72/2.44 fof(f1322,plain,(
% 15.72/2.44 ![X0,X1,X2]: (X0=multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2))),
% 15.72/2.44 inference(backward_demodulation,[status(thm)],[f1279,f25])).
% 15.72/2.44 fof(f1433,plain,(
% 15.72/2.44 ![X0,X1]: (inverse(X0)=inverse(multiply(X1,inverse(X1),X0)))),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f1279,f1322])).
% 15.72/2.44 fof(f1556,plain,(
% 15.72/2.44 ![X0,X1,X2,X3]: (multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),X3)),X3)=X1)),
% 15.72/2.44 inference(backward_demodulation,[status(thm)],[f1433,f62])).
% 15.72/2.44 fof(f1559,plain,(
% 15.72/2.44 ![X0,X1]: (X0=multiply(X0,inverse(X1),X1))),
% 15.72/2.44 inference(backward_demodulation,[status(thm)],[f1433,f1322])).
% 15.72/2.44 fof(f1589,plain,(
% 15.72/2.44 ![X0,X1,X2]: (multiply(multiply(X0,inverse(X0),X1),inverse(X2),X2)=X1)),
% 15.72/2.44 inference(forward_demodulation,[status(thm)],[f1433,f1556])).
% 15.72/2.44 fof(f3557,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4,X5]: (multiply(X0,inverse(multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))),multiply(X2,multiply(X5,X4,X3),X1))=X0)),
% 15.72/2.44 inference(backward_demodulation,[status(thm)],[f3558,f3])).
% 15.72/2.44 fof(f3558,plain,(
% 15.72/2.44 ![X0,X1]: (multiply(X0,inverse(X0),X1)=X1)),
% 15.72/2.44 inference(forward_demodulation,[status(thm)],[f1559,f1589])).
% 15.72/2.44 fof(f3560,plain,(
% 15.72/2.44 ![X0]: (inverse(inverse(X0))=X0)),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f1279,f3558])).
% 15.72/2.44 fof(f3725,plain,(
% 15.72/2.44 ![X0,X1,X2,X3]: (multiply(X0,X1,X2)=multiply(X1,multiply(X2,inverse(multiply(X0,X1,X3)),X3),X0))),
% 15.72/2.44 inference(backward_demodulation,[status(thm)],[f3557,f21])).
% 15.72/2.44 fof(f3740,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4]: (multiply(X0,inverse(multiply(X1,X2,multiply(X3,inverse(X3),X4))),multiply(inverse(X3),multiply(X4,X2,X1),X3))=X0)),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f3558,f3557])).
% 15.72/2.44 fof(f3784,plain,(
% 15.72/2.44 ![X0,X1,X2,X3,X4]: (multiply(X0,inverse(multiply(X1,X2,X3)),multiply(inverse(X4),multiply(X3,X2,X1),X4))=X0)),
% 15.72/2.44 inference(forward_demodulation,[status(thm)],[f3558,f3740])).
% 15.72/2.44 fof(f3785,plain,(
% 15.72/2.44 ![X0,X1,X2,X3]: (multiply(X0,inverse(multiply(X1,X2,X3)),multiply(X3,X2,X1))=X0)),
% 15.72/2.44 inference(forward_demodulation,[status(thm)],[f1279,f3784])).
% 15.72/2.44 fof(f3935,plain,(
% 15.72/2.44 ![X0,X1]: (multiply(inverse(X0),X0,X1)=X1)),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f3560,f3558])).
% 15.72/2.44 fof(f3936,plain,(
% 15.72/2.44 ![X0,X1]: (X0=multiply(X0,X1,inverse(X1)))),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f3560,f1559])).
% 15.72/2.44 fof(f3937,plain,(
% 15.72/2.44 ![X0,X1]: (X0=multiply(X1,X0,inverse(X1)))),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f3560,f1279])).
% 15.72/2.44 fof(f3938,plain,(
% 15.72/2.44 ~a=a|sQ4_spl),
% 15.72/2.44 inference(backward_demodulation,[status(thm)],[f3935,f19])).
% 15.72/2.44 fof(f3973,plain,(
% 15.72/2.44 $false|sQ4_spl),
% 15.72/2.44 inference(trivial_equality_resolution,[status(thm)],[f3938])).
% 15.72/2.44 fof(f3974,plain,(
% 15.72/2.44 sQ4_spl),
% 15.72/2.44 inference(contradiction_clause,[status(thm)],[f3973])).
% 15.72/2.44 fof(f4684,plain,(
% 15.72/2.44 ![X0,X1,X2]: (multiply(X0,X1,inverse(inverse(multiply(X0,X1,X2))))=multiply(X1,X2,X0))),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f3935,f3725])).
% 15.72/2.44 fof(f4742,plain,(
% 15.72/2.44 ![X0,X1,X2]: (multiply(X0,X1,multiply(X0,X1,X2))=multiply(X1,X2,X0))),
% 15.72/2.44 inference(forward_demodulation,[status(thm)],[f3560,f4684])).
% 15.72/2.44 fof(f4787,plain,(
% 15.72/2.44 ![X0,X1]: (multiply(X0,X1,X1)=multiply(X1,inverse(X0),X0))),
% 15.72/2.44 inference(paramodulation,[status(thm)],[f3937,f4742])).
% 15.72/2.44 fof(f4828,plain,(
% 15.72/2.44 ![X0,X1]: (multiply(X0,X1,X1)=X1)),
% 15.72/2.44 inference(forward_demodulation,[status(thm)],[f1559,f4787])).
% 15.72/2.45 fof(f4868,plain,(
% 15.72/2.45 ![X0,X1]: (multiply(X0,X1,X1)=multiply(X1,X1,X0))),
% 15.72/2.45 inference(paramodulation,[status(thm)],[f4828,f4742])).
% 15.72/2.45 fof(f4869,plain,(
% 15.72/2.45 ![X0,X1,X2]: (multiply(X0,X1,X2)=multiply(X1,multiply(X2,inverse(X1),X1),X0))),
% 15.72/2.45 inference(paramodulation,[status(thm)],[f4828,f3725])).
% 15.72/2.45 fof(f4892,plain,(
% 15.72/2.45 ![X0,X1]: (X0=multiply(X0,X0,X1))),
% 15.72/2.45 inference(forward_demodulation,[status(thm)],[f4828,f4868])).
% 15.72/2.45 fof(f4893,plain,(
% 15.72/2.45 ![X0,X1,X2]: (multiply(X0,X1,X2)=multiply(X1,X2,X0))),
% 15.72/2.45 inference(forward_demodulation,[status(thm)],[f1559,f4869])).
% 15.72/2.45 fof(f5189,plain,(
% 15.72/2.45 ~a=a|sQ3_spl),
% 15.72/2.45 inference(backward_demodulation,[status(thm)],[f4892,f16])).
% 15.72/2.45 fof(f5258,plain,(
% 15.72/2.45 $false|sQ3_spl),
% 15.72/2.45 inference(trivial_equality_resolution,[status(thm)],[f5189])).
% 15.72/2.45 fof(f5259,plain,(
% 15.72/2.45 sQ3_spl),
% 15.72/2.45 inference(contradiction_clause,[status(thm)],[f5258])).
% 15.72/2.45 fof(f5348,plain,(
% 15.72/2.45 ~a=a|sQ2_spl),
% 15.72/2.45 inference(forward_demodulation,[status(thm)],[f3936,f13])).
% 15.72/2.45 fof(f5349,plain,(
% 15.72/2.45 $false|sQ2_spl),
% 15.72/2.45 inference(trivial_equality_resolution,[status(thm)],[f5348])).
% 15.72/2.45 fof(f5350,plain,(
% 15.72/2.45 sQ2_spl),
% 15.72/2.45 inference(contradiction_clause,[status(thm)],[f5349])).
% 15.72/2.45 fof(f10976,plain,(
% 15.72/2.45 ![X0,X1,X2]: (multiply(X0,X1,X2)=inverse(inverse(multiply(X2,X1,X0))))),
% 15.72/2.45 inference(paramodulation,[status(thm)],[f3935,f3785])).
% 15.72/2.45 fof(f11166,plain,(
% 15.72/2.45 ![X0,X1,X2]: (multiply(X0,X1,X2)=multiply(X2,X1,X0))),
% 15.72/2.45 inference(forward_demodulation,[status(thm)],[f3560,f10976])).
% 15.72/2.45 fof(f13461,plain,(
% 15.72/2.45 ![X0,X1,X2,X3,X4,X5]: (multiply(X0,multiply(multiply(X1,X2,X3),inverse(multiply(multiply(X1,X2,X4),X0,X5)),X5),multiply(X1,X2,X4))=multiply(X2,multiply(X3,X0,X4),X1))),
% 15.72/2.45 inference(forward_demodulation,[status(thm)],[f3557,f48])).
% 15.72/2.45 fof(f13462,plain,(
% 15.72/2.45 ~multiply(e,multiply(c,b,a),d)=multiply(d,e,multiply(a,b,c))|sQ0_spl),
% 15.72/2.45 inference(backward_demodulation,[status(thm)],[f13470,f7])).
% 15.72/2.45 fof(f13470,plain,(
% 15.72/2.45 ![X0,X1,X2,X3,X4]: (multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4))=multiply(X1,multiply(X4,X3,X2),X0))),
% 15.72/2.45 inference(forward_demodulation,[status(thm)],[f3725,f13461])).
% 15.72/2.45 fof(f13763,plain,(
% 15.72/2.45 ~multiply(e,multiply(a,b,c),d)=multiply(d,e,multiply(a,b,c))|sQ0_spl),
% 15.72/2.45 inference(paramodulation,[status(thm)],[f11166,f13462])).
% 15.72/2.45 fof(f13767,plain,(
% 15.72/2.45 $false|sQ0_spl),
% 15.72/2.45 inference(forward_subsumption_resolution,[status(thm)],[f13763,f4893])).
% 15.72/2.45 fof(f13768,plain,(
% 15.72/2.45 sQ0_spl),
% 15.72/2.45 inference(contradiction_clause,[status(thm)],[f13767])).
% 15.72/2.45 fof(f13769,plain,(
% 15.72/2.45 ~a=a|sQ1_spl),
% 15.72/2.45 inference(forward_demodulation,[status(thm)],[f4828,f10])).
% 15.72/2.45 fof(f13770,plain,(
% 15.72/2.45 $false|sQ1_spl),
% 15.72/2.45 inference(trivial_equality_resolution,[status(thm)],[f13769])).
% 15.72/2.45 fof(f13771,plain,(
% 15.72/2.45 sQ1_spl),
% 15.72/2.45 inference(contradiction_clause,[status(thm)],[f13770])).
% 15.72/2.45 fof(f13772,plain,(
% 15.72/2.45 $false),
% 15.72/2.45 inference(sat_refutation,[status(thm)],[f20,f3974,f5259,f5350,f13768,f13771])).
% 15.72/2.45 % SZS output end CNFRefutation for theBenchmark.p
% 15.72/2.49 % Elapsed time: 2.119325 seconds
% 15.72/2.49 % CPU time: 16.397386 seconds
% 15.72/2.49 % Total memory used: 284.895 MB
% 15.72/2.49 % Net memory used: 283.400 MB
%------------------------------------------------------------------------------