%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:35:37 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.60s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.56 % Computer : n020.cluster.edu
% 0.11/0.56 % Model : x86_64 x86_64
% 0.11/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.56 % Memory : 8046.5625MB
% 0.11/0.56 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Sun Sep 20 19:57:48 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.58 % Drodi V4.1.1
% 0.11/0.60 % Refutation found
% 0.11/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.60 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.60 fof(f1,axiom,(
% 0.11/0.60 (![X,Y,Z]: (divide(divide(identity,divide(divide(divide(X,Y),Z),X)),Z) = Y ))),
% 0.11/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.60 fof(f2,axiom,(
% 0.11/0.60 (![X,Y]: (multiply(X,Y) = divide(X,divide(identity,Y)) ))),
% 0.11/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.60 fof(f3,axiom,(
% 0.11/0.60 (![X]: (inverse(X) = divide(identity,X) ))),
% 0.11/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.60 fof(f4,axiom,(
% 0.11/0.60 (![X]: (identity = divide(X,X) ))),
% 0.11/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.60 fof(f5,negated_conjecture,(
% 0.11/0.60 ( 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))| multiply(a4,b4) != multiply(b4,a4) ) ),
% 0.11/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.60 fof(f6,plain,(
% 0.11/0.60 ![X0,X1,X2]: (divide(divide(identity,divide(divide(divide(X0,X1),X2),X0)),X2)=X1)),
% 0.11/0.60 inference(cnf_transformation,[status(thm)],[f1])).
% 0.11/0.60 fof(f7,plain,(
% 0.11/0.60 ![X0,X1]: (multiply(X0,X1)=divide(X0,divide(identity,X1)))),
% 0.11/0.60 inference(cnf_transformation,[status(thm)],[f2])).
% 0.11/0.60 fof(f8,plain,(
% 0.11/0.60 ![X0]: (inverse(X0)=divide(identity,X0))),
% 0.11/0.60 inference(cnf_transformation,[status(thm)],[f3])).
% 0.11/0.60 fof(f9,plain,(
% 0.11/0.60 ![X0]: (identity=divide(X0,X0))),
% 0.11/0.60 inference(cnf_transformation,[status(thm)],[f4])).
% 0.11/0.60 fof(f10,plain,(
% 0.11/0.60 ~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))|~multiply(a4,b4)=multiply(b4,a4)),
% 0.11/0.60 inference(cnf_transformation,[status(thm)],[f5])).
% 0.11/0.60 fof(f11,definition,(
% 0.11/0.60 sQ0_spl <=> (multiply(inverse(a1),a1)=multiply(inverse(b1),b1))),
% 0.11/0.60 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.11/0.60 fof(f13,plain,(
% 0.11/0.60 ~multiply(inverse(a1),a1)=multiply(inverse(b1),b1)|sQ0_spl),
% 0.11/0.60 inference(component_clause,[status(thm)],[f11])).
% 0.11/0.60 fof(f14,definition,(
% 0.11/0.60 sQ1_spl <=> (multiply(multiply(inverse(b2),b2),a2)=a2)),
% 0.11/0.60 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.11/0.60 fof(f16,plain,(
% 0.11/0.60 ~multiply(multiply(inverse(b2),b2),a2)=a2|sQ1_spl),
% 0.11/0.60 inference(component_clause,[status(thm)],[f14])).
% 0.11/0.60 fof(f17,definition,(
% 0.11/0.60 sQ2_spl <=> (multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3)))),
% 0.11/0.60 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.11/0.60 fof(f19,plain,(
% 0.11/0.60 ~multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3))|sQ2_spl),
% 0.11/0.60 inference(component_clause,[status(thm)],[f17])).
% 0.11/0.60 fof(f20,definition,(
% 0.11/0.60 sQ3_spl <=> (multiply(a4,b4)=multiply(b4,a4))),
% 0.11/0.60 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.11/0.60 fof(f22,plain,(
% 0.11/0.60 ~multiply(a4,b4)=multiply(b4,a4)|sQ3_spl),
% 0.11/0.60 inference(component_clause,[status(thm)],[f20])).
% 0.11/0.60 fof(f23,plain,(
% 0.11/0.60 ~sQ0_spl|~sQ1_spl|~sQ2_spl|~sQ3_spl),
% 0.11/0.60 inference(split_clause,[status(thm)],[f10,f11,f14,f17,f20])).
% 0.11/0.60 fof(f24,plain,(
% 0.11/0.60 ![X0,X1,X2]: (divide(inverse(divide(divide(divide(X0,X1),X2),X0)),X2)=X1)),
% 0.11/0.60 inference(backward_demodulation,[status(thm)],[f8,f6])).
% 0.11/0.60 fof(f25,plain,(
% 0.11/0.60 ![X0,X1]: (multiply(X0,X1)=divide(X0,inverse(X1)))),
% 0.11/0.60 inference(backward_demodulation,[status(thm)],[f8,f7])).
% 0.11/0.60 fof(f26,plain,(
% 0.11/0.60 inverse(identity)=identity),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f9,f8])).
% 0.11/0.60 fof(f50,plain,(
% 0.11/0.60 ![X0,X1,X2]: (multiply(inverse(divide(divide(divide(X0,X1),inverse(X2)),X0)),X2)=X1)),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f25,f24])).
% 0.11/0.60 fof(f51,plain,(
% 0.11/0.60 ![X0,X1,X2]: (divide(inverse(multiply(divide(divide(inverse(X0),X1),X2),X0)),X2)=X1)),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f25,f24])).
% 0.11/0.60 fof(f53,plain,(
% 0.11/0.60 ![X0,X1]: (divide(inverse(divide(identity,X0)),divide(X0,X1))=X1)),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f9,f24])).
% 0.11/0.60 fof(f59,plain,(
% 0.11/0.60 ![X0,X1,X2]: (multiply(inverse(divide(multiply(divide(X0,X1),X2),X0)),X2)=X1)),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f25,f50])).
% 0.11/0.60 fof(f61,plain,(
% 0.11/0.60 ![X0,X1]: (divide(inverse(inverse(X0)),divide(X0,X1))=X1)),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f8,f53])).
% 0.11/0.60 fof(f65,plain,(
% 0.11/0.60 ![X0]: (divide(inverse(identity),divide(identity,X0))=X0)),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f26,f61])).
% 0.11/0.60 fof(f68,plain,(
% 0.11/0.60 ![X0]: (divide(inverse(inverse(identity)),inverse(X0))=X0)),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f8,f61])).
% 0.11/0.60 fof(f69,plain,(
% 0.11/0.60 ![X0,X1]: (divide(inverse(inverse(X0)),multiply(X0,X1))=inverse(X1))),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f25,f61])).
% 0.11/0.60 fof(f70,plain,(
% 0.11/0.60 ![X0]: (divide(inverse(inverse(X0)),identity)=X0)),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f9,f61])).
% 0.11/0.60 fof(f72,plain,(
% 0.11/0.60 ![X0]: (divide(identity,divide(identity,X0))=X0)),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f26,f65])).
% 0.11/0.60 fof(f73,plain,(
% 0.11/0.60 ![X0]: (inverse(divide(identity,X0))=X0)),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f8,f72])).
% 0.11/0.60 fof(f74,plain,(
% 0.11/0.60 ![X0,X1]: (divide(X0,divide(X0,X1))=X1)),
% 0.11/0.60 inference(backward_demodulation,[status(thm)],[f76,f61])).
% 0.11/0.60 fof(f76,plain,(
% 0.11/0.60 ![X0]: (inverse(inverse(X0))=X0)),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f8,f73])).
% 0.11/0.60 fof(f79,plain,(
% 0.11/0.60 ![X0]: (multiply(inverse(inverse(identity)),X0)=X0)),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f25,f68])).
% 0.11/0.60 fof(f80,plain,(
% 0.11/0.60 ![X0]: (multiply(identity,X0)=X0)),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f76,f79])).
% 0.11/0.60 fof(f81,plain,(
% 0.11/0.60 ![X0,X1]: (divide(X0,multiply(X0,X1))=inverse(X1))),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f76,f69])).
% 0.11/0.60 fof(f84,plain,(
% 0.11/0.60 ![X0]: (divide(X0,identity)=X0)),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f76,f70])).
% 0.11/0.60 fof(f89,plain,(
% 0.11/0.60 ![X0,X1]: (multiply(X0,inverse(X1))=divide(X0,X1))),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f76,f25])).
% 0.11/0.60 fof(f97,plain,(
% 0.11/0.60 ![X0,X1]: (multiply(inverse(divide(multiply(identity,X0),X1)),X0)=X1)),
% 0.11/0.60 inference(paramodulation,[status(thm)],[f9,f59])).
% 0.11/0.60 fof(f99,plain,(
% 0.11/0.60 ![X0,X1]: (multiply(inverse(divide(X0,X1)),X0)=X1)),
% 0.11/0.60 inference(forward_demodulation,[status(thm)],[f80,f97])).
% 0.11/0.60 fof(f124,plain,(
% 0.11/0.60 ![X0,X1,X2]: (multiply(inverse(divide(multiply(X0,X1),X2)),X1)=divide(X2,X0))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f74,f59])).
% 0.11/0.61 fof(f138,plain,(
% 0.11/0.61 ![X0,X1]: (inverse(multiply(divide(divide(inverse(X0),X1),identity),X0))=X1)),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f84,f51])).
% 0.11/0.61 fof(f157,plain,(
% 0.11/0.61 ![X0,X1]: (inverse(multiply(divide(inverse(X0),X1),X0))=X1)),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f84,f138])).
% 0.11/0.61 fof(f193,plain,(
% 0.11/0.61 ![X0,X1]: (multiply(inverse(inverse(X0)),X1)=multiply(X1,X0))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f81,f99])).
% 0.11/0.61 fof(f194,plain,(
% 0.11/0.61 ![X0,X1]: (multiply(inverse(X0),X1)=divide(X1,X0))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f74,f99])).
% 0.11/0.61 fof(f203,plain,(
% 0.11/0.61 $false|sQ3_spl),
% 0.11/0.61 inference(backward_subsumption_resolution,[status(thm)],[f22,f204])).
% 0.11/0.61 fof(f204,plain,(
% 0.11/0.61 ![X0,X1]: (multiply(X0,X1)=multiply(X1,X0))),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f76,f193])).
% 0.11/0.61 fof(f207,plain,(
% 0.11/0.61 ![X0,X1,X2]: (divide(X0,divide(multiply(X1,X0),X2))=divide(X2,X1))),
% 0.11/0.61 inference(backward_demodulation,[status(thm)],[f194,f124])).
% 0.11/0.61 fof(f216,plain,(
% 0.11/0.61 sQ3_spl),
% 0.11/0.61 inference(contradiction_clause,[status(thm)],[f203])).
% 0.11/0.61 fof(f231,plain,(
% 0.11/0.61 ![X0,X1]: (divide(X0,multiply(X1,X0))=inverse(X1))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f204,f81])).
% 0.11/0.61 fof(f236,plain,(
% 0.11/0.61 ![X0,X1]: (divide(inverse(X0),X1)=divide(inverse(X1),X0))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f89,f194])).
% 0.11/0.61 fof(f240,plain,(
% 0.11/0.61 ![X0,X1]: (multiply(X0,X1)=divide(X1,inverse(X0)))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f76,f194])).
% 0.11/0.61 fof(f281,plain,(
% 0.11/0.61 ![X0,X1]: (inverse(multiply(inverse(X0),X1))=multiply(X0,inverse(X1)))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f231,f157])).
% 0.11/0.61 fof(f283,plain,(
% 0.11/0.61 ![X0,X1]: (inverse(multiply(X0,X1))=divide(inverse(X1),X0))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f74,f157])).
% 0.11/0.61 fof(f299,plain,(
% 0.11/0.61 ![X0,X1]: (inverse(divide(X0,X1))=multiply(X1,inverse(X0)))),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f194,f281])).
% 0.11/0.61 fof(f306,plain,(
% 0.11/0.61 ![X0,X1]: (inverse(divide(X0,X1))=divide(X1,X0))),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f89,f299])).
% 0.11/0.61 fof(f315,plain,(
% 0.11/0.61 ![X0,X1]: (divide(inverse(X0),X1)=inverse(multiply(X0,X1)))),
% 0.11/0.61 inference(backward_demodulation,[status(thm)],[f283,f236])).
% 0.11/0.61 fof(f444,plain,(
% 0.11/0.61 ![X0,X1,X2]: (divide(X0,divide(X1,X2))=divide(multiply(X2,X0),X1))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f207,f74])).
% 0.11/0.61 fof(f528,plain,(
% 0.11/0.61 ![X0,X1,X2]: (multiply(X0,divide(X1,X2))=divide(X0,divide(X2,X1)))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f306,f89])).
% 0.11/0.61 fof(f650,plain,(
% 0.11/0.61 ![X0,X1]: (inverse(multiply(X0,X1))=inverse(multiply(X1,X0)))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f283,f315])).
% 0.11/0.61 fof(f837,plain,(
% 0.11/0.61 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=divide(X2,inverse(multiply(X1,X0))))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f650,f240])).
% 0.11/0.61 fof(f855,plain,(
% 0.11/0.61 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(multiply(X1,X0),X2))),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f240,f837])).
% 0.11/0.61 fof(f871,plain,(
% 0.11/0.61 ![X0,X1,X2]: (divide(X0,divide(inverse(X1),X2))=multiply(X1,multiply(X2,X0)))),
% 0.11/0.61 inference(paramodulation,[status(thm)],[f240,f444])).
% 0.11/0.61 fof(f902,plain,(
% 0.11/0.61 ![X0,X1,X2]: (divide(X0,inverse(multiply(X1,X2)))=multiply(X1,multiply(X2,X0)))),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f315,f871])).
% 0.11/0.61 fof(f903,plain,(
% 0.11/0.61 ~multiply(a3,multiply(b3,c3))=multiply(a3,multiply(b3,c3))|sQ2_spl),
% 0.11/0.61 inference(backward_demodulation,[status(thm)],[f910,f19])).
% 0.11/0.61 fof(f904,plain,(
% 0.11/0.61 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X1,multiply(X0,X2)))),
% 0.11/0.61 inference(backward_demodulation,[status(thm)],[f910,f855])).
% 0.11/0.61 fof(f910,plain,(
% 0.11/0.61 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f240,f902])).
% 0.11/0.61 fof(f946,plain,(
% 0.11/0.61 $false|sQ2_spl),
% 0.11/0.61 inference(trivial_equality_resolution,[status(thm)],[f903])).
% 0.11/0.61 fof(f947,plain,(
% 0.11/0.61 sQ2_spl),
% 0.11/0.61 inference(contradiction_clause,[status(thm)],[f946])).
% 0.11/0.61 fof(f949,plain,(
% 0.11/0.61 ~divide(a1,a1)=multiply(inverse(b1),b1)|sQ0_spl),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f194,f13])).
% 0.11/0.61 fof(f950,plain,(
% 0.11/0.61 ~identity=multiply(inverse(b1),b1)|sQ0_spl),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f9,f949])).
% 0.11/0.61 fof(f951,plain,(
% 0.11/0.61 ~identity=divide(b1,b1)|sQ0_spl),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f194,f950])).
% 0.11/0.61 fof(f952,plain,(
% 0.11/0.61 ~identity=identity|sQ0_spl),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f9,f951])).
% 0.11/0.61 fof(f953,plain,(
% 0.11/0.61 $false|sQ0_spl),
% 0.11/0.61 inference(trivial_equality_resolution,[status(thm)],[f952])).
% 0.11/0.61 fof(f954,plain,(
% 0.11/0.61 sQ0_spl),
% 0.11/0.61 inference(contradiction_clause,[status(thm)],[f953])).
% 0.11/0.61 fof(f956,plain,(
% 0.11/0.61 ~multiply(b2,multiply(inverse(b2),a2))=a2|sQ1_spl),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f904,f16])).
% 0.11/0.61 fof(f957,plain,(
% 0.11/0.61 ~multiply(b2,divide(a2,b2))=a2|sQ1_spl),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f194,f956])).
% 0.11/0.61 fof(f958,plain,(
% 0.11/0.61 ~divide(b2,divide(b2,a2))=a2|sQ1_spl),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f528,f957])).
% 0.11/0.61 fof(f959,plain,(
% 0.11/0.61 ~a2=a2|sQ1_spl),
% 0.11/0.61 inference(forward_demodulation,[status(thm)],[f74,f958])).
% 0.11/0.61 fof(f960,plain,(
% 0.11/0.61 $false|sQ1_spl),
% 0.11/0.61 inference(trivial_equality_resolution,[status(thm)],[f959])).
% 0.11/0.61 fof(f961,plain,(
% 0.11/0.61 sQ1_spl),
% 0.11/0.61 inference(contradiction_clause,[status(thm)],[f960])).
% 0.11/0.61 fof(f962,plain,(
% 0.11/0.61 $false),
% 0.11/0.61 inference(sat_refutation,[status(thm)],[f23,f216,f947,f954,f961])).
% 0.11/0.61 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.64 % Elapsed time: 0.056896 seconds
% 0.14/0.64 % CPU time: 0.252035 seconds
% 0.14/0.64 % Total memory used: 31.116 MB
% 0.14/0.64 % Net memory used: 30.744 MB
%------------------------------------------------------------------------------