%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP104-1 : 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 : n001.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 12:35:38 PM UTC 2026
% Result : Unsatisfiable 0.87s 0.64s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP104-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38 % Computer : n001.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun Sep 20 20:02:58 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.40 % Drodi V4.1.1
% 0.87/0.64 % Refutation found
% 0.87/0.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.87/0.64 % SZS output start CNFRefutation for theBenchmark
% 0.87/0.64 fof(f1,axiom,(
% 0.87/0.64 (![X,Y,Z]: (double_divide(X,inverse(double_divide(inverse(double_divide(double_divide(X,Y),inverse(Z))),Y))) = Z ))),
% 0.87/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.87/0.64 fof(f2,axiom,(
% 0.87/0.64 (![X,Y]: (multiply(X,Y) = inverse(double_divide(Y,X)) ))),
% 0.87/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.87/0.64 fof(f3,negated_conjecture,(
% 0.87/0.64 ( 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) ) ),
% 0.87/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.87/0.64 fof(f4,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),inverse(X2))),X1)))=X2)),
% 0.87/0.64 inference(cnf_transformation,[status(thm)],[f1])).
% 0.87/0.64 fof(f5,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(X0,X1)=inverse(double_divide(X1,X0)))),
% 0.87/0.64 inference(cnf_transformation,[status(thm)],[f2])).
% 0.87/0.64 fof(f6,plain,(
% 0.87/0.64 ~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)),
% 0.87/0.64 inference(cnf_transformation,[status(thm)],[f3])).
% 0.87/0.64 fof(f7,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(X0,inverse(double_divide(multiply(inverse(X1),double_divide(X0,X2)),X2)))=X1)),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f5,f4])).
% 0.87/0.64 fof(f8,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(X0,multiply(X1,multiply(inverse(X2),double_divide(X0,X1))))=X2)),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f5,f7])).
% 0.87/0.64 fof(f9,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (double_divide(X0,multiply(X1,multiply(multiply(X2,X3),double_divide(X0,X1))))=double_divide(X3,X2))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f5,f8])).
% 0.87/0.64 fof(f10,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (double_divide(X0,multiply(multiply(X1,multiply(inverse(X2),double_divide(X0,X1))),multiply(inverse(X3),X2)))=X3)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f8,f8])).
% 0.87/0.64 fof(f11,plain,(
% 0.87/0.64 ![X0,X1,X2]: (multiply(multiply(X0,multiply(inverse(X1),double_divide(X2,X0))),X2)=inverse(X1))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f8,f5])).
% 0.87/0.64 fof(f12,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(multiply(X0,multiply(multiply(X1,X2),double_divide(X3,X0))),X3)=inverse(double_divide(X2,X1)))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f5,f11])).
% 0.87/0.64 fof(f13,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(multiply(multiply(X0,multiply(inverse(X1),double_divide(X2,X0))),multiply(inverse(X3),X1)),X2)=inverse(X3))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f8,f11])).
% 0.87/0.64 fof(f14,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(multiply(X0,multiply(multiply(X1,X2),double_divide(X3,X0))),X3)=multiply(X1,X2))),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f5,f12])).
% 0.87/0.64 fof(f15,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (double_divide(X0,multiply(X1,inverse(X2)))=double_divide(multiply(inverse(X2),double_divide(double_divide(X0,X1),X3)),X3))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f11,f9])).
% 0.87/0.64 fof(f24,plain,(
% 0.87/0.64 ![X0,X1,X2,X3,X4]: (multiply(multiply(X0,multiply(X1,X2)),X3)=multiply(X4,multiply(multiply(X1,X2),double_divide(double_divide(X3,X0),X4))))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f14,f14])).
% 0.87/0.64 fof(f35,plain,(
% 0.87/0.64 ![X0,X1]: (double_divide(multiply(inverse(X0),X1),inverse(X1))=X0)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f11,f10])).
% 0.87/0.64 fof(f46,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(multiply(multiply(X0,X1),X2),inverse(X2))=double_divide(X1,X0))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f5,f35])).
% 0.87/0.64 fof(f47,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(multiply(inverse(X0),double_divide(X1,X2)),multiply(X2,X1))=X0)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f5,f35])).
% 0.87/0.64 fof(f53,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(inverse(X0),multiply(inverse(X1),X0))=inverse(X1))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f35,f5])).
% 0.87/0.64 fof(f56,plain,(
% 0.87/0.64 ![X0,X1,X2]: (multiply(inverse(X0),multiply(multiply(X1,X2),X0))=inverse(double_divide(X2,X1)))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f5,f53])).
% 0.87/0.64 fof(f57,plain,(
% 0.87/0.64 ![X0,X1]: (double_divide(inverse(X0),inverse(multiply(inverse(X0),X1)))=X1)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f53,f35])).
% 0.87/0.64 fof(f61,plain,(
% 0.87/0.64 ![X0,X1,X2]: (multiply(inverse(X0),multiply(multiply(X1,X2),X0))=multiply(X1,X2))),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f5,f56])).
% 0.87/0.64 fof(f95,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(inverse(X0),inverse(X1))=double_divide(multiply(inverse(X0),double_divide(X1,X2)),X2))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f11,f46])).
% 0.87/0.64 fof(f109,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(X0,multiply(X1,inverse(X2)))=double_divide(inverse(X2),inverse(double_divide(X0,X1))))),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f95,f15])).
% 0.87/0.64 fof(f116,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(X0,multiply(X1,inverse(X2)))=double_divide(inverse(X2),multiply(X1,X0)))),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f5,f109])).
% 0.87/0.64 fof(f252,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(inverse(X0),inverse(X1))=multiply(multiply(X2,multiply(inverse(X3),double_divide(X0,X2))),multiply(inverse(X1),X3)))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f13,f61])).
% 0.87/0.64 fof(f253,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(inverse(X0),multiply(X1,X2))=multiply(X3,multiply(multiply(X1,X2),double_divide(X0,X3))))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f14,f61])).
% 0.87/0.64 fof(f262,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(inverse(X0),inverse(multiply(X1,X2)))=multiply(multiply(X1,X2),X0))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f61,f57])).
% 0.87/0.64 fof(f272,plain,(
% 0.87/0.64 ![X0,X1]: (double_divide(X0,multiply(inverse(X0),inverse(X1)))=X1)),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f252,f10])).
% 0.87/0.64 fof(f281,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(X0,multiply(inverse(X0),multiply(X1,X2)))=double_divide(X2,X1))),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f253,f9])).
% 0.87/0.64 fof(f282,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(multiply(X0,multiply(X1,X2)),X3)=multiply(inverse(double_divide(X3,X0)),multiply(X1,X2)))),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f253,f24])).
% 0.87/0.64 fof(f318,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(multiply(inverse(X0),X1),X0)=X1)),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f262,f57])).
% 0.87/0.64 fof(f325,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(multiply(X0,multiply(X1,X2)),X3)=multiply(multiply(X0,X3),multiply(X1,X2)))),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f5,f282])).
% 0.87/0.64 fof(f341,plain,(
% 0.87/0.64 ![X0,X1,X2]: (multiply(inverse(X0),multiply(X1,X0))=multiply(multiply(inverse(X2),X1),X2))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f318,f61])).
% 0.87/0.64 fof(f346,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(inverse(X0),multiply(X1,X0))=X1)),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f318,f341])).
% 0.87/0.64 fof(f348,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(inverse(multiply(X0,X1)),X0)=inverse(X1))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f346,f346])).
% 0.87/0.64 fof(f351,plain,(
% 0.87/0.64 ![X0,X1]: (double_divide(X0,inverse(multiply(X0,X1)))=X1)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f346,f35])).
% 0.87/0.64 fof(f358,plain,(
% 0.87/0.64 ![X0,X1]: (double_divide(inverse(X0),inverse(X1))=multiply(X1,X0))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f346,f351])).
% 0.87/0.64 fof(f367,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(double_divide(X0,X1),multiply(multiply(X1,X0),inverse(X2)))=X2)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f5,f272])).
% 0.87/0.64 fof(f376,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(inverse(X0),multiply(X1,X2))=multiply(double_divide(X2,X1),X0))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f348,f47])).
% 0.87/0.64 fof(f405,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(X0,multiply(X1,inverse(X2)))=multiply(double_divide(X0,X1),X2))),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f376,f116])).
% 0.87/0.64 fof(f420,plain,(
% 0.87/0.64 ![X0,X1,X2]: (multiply(double_divide(double_divide(X0,X1),multiply(X1,X0)),X2)=X2)),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f405,f367])).
% 0.87/0.64 fof(f425,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(multiply(X0,X1),inverse(X2))=multiply(X2,double_divide(X1,X0)))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f5,f358])).
% 0.87/0.64 fof(f431,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(X0,double_divide(X0,inverse(X1)))=X1)),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f425,f35])).
% 0.87/0.64 fof(f445,plain,(
% 0.87/0.64 ![X0,X1]: (double_divide(X0,multiply(inverse(X0),inverse(X1)))=X1)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f431,f47])).
% 0.87/0.64 fof(f451,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(double_divide(X0,inverse(X0)),X1)=X1)),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f405,f445])).
% 0.87/0.64 fof(f454,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(multiply(inverse(X0),X0),X1)=X1)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f358,f451])).
% 0.87/0.64 fof(f459,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(inverse(X0),X0)=double_divide(X1,inverse(X1)))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f451,f346])).
% 0.87/0.64 fof(f461,plain,(
% 0.87/0.64 ~multiply(inverse(a1),a1)=multiply(inverse(b1),b1)|~a2=a2|~multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3))|~multiply(a4,b4)=multiply(b4,a4)),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f454,f6])).
% 0.87/0.64 fof(f462,plain,(
% 0.87/0.64 ~multiply(inverse(a1),a1)=multiply(inverse(b1),b1)|~multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3))|~multiply(a4,b4)=multiply(b4,a4)),
% 0.87/0.64 inference(trivial_equality_resolution,[status(thm)],[f461])).
% 0.87/0.64 fof(f464,plain,(
% 0.87/0.64 ![X0,X1]: (X0=double_divide(multiply(inverse(X1),X1),inverse(X0)))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f431,f454])).
% 0.87/0.64 fof(f470,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(inverse(X0),X0)=multiply(inverse(X1),X1))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f454,f346])).
% 0.87/0.64 fof(f473,plain,(
% 0.87/0.64 ![X0,X1]: (X0=multiply(X0,double_divide(X1,inverse(X1))))),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f425,f464])).
% 0.87/0.64 fof(f476,plain,(
% 0.87/0.64 ~multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3))|~multiply(a4,b4)=multiply(b4,a4)),
% 0.87/0.64 inference(backward_subsumption_resolution,[status(thm)],[f462,f470])).
% 0.87/0.64 fof(f556,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(multiply(inverse(X0),double_divide(X1,inverse(X1))),double_divide(X2,inverse(X2)))=X0)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f459,f47])).
% 0.87/0.64 fof(f569,plain,(
% 0.87/0.64 ![X0,X1]: (double_divide(inverse(X0),double_divide(X1,inverse(X1)))=X0)),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f473,f556])).
% 0.87/0.64 fof(f695,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(multiply(X0,X1),double_divide(X2,inverse(X2)))=double_divide(X1,X0))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f459,f281])).
% 0.87/0.64 fof(f764,plain,(
% 0.87/0.64 ![X0,X1,X2]: (double_divide(multiply(inverse(X0),X1),multiply(double_divide(X2,inverse(X2)),inverse(X1)))=X0)),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f569,f47])).
% 0.87/0.64 fof(f768,plain,(
% 0.87/0.64 ![X0,X1,X2]: (multiply(double_divide(multiply(inverse(X0),X1),double_divide(X2,inverse(X2))),X1)=X0)),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f405,f764])).
% 0.87/0.64 fof(f769,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(double_divide(X0,inverse(X1)),X0)=X1)),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f695,f768])).
% 0.87/0.64 fof(f776,plain,(
% 0.87/0.64 ![X0,X1]: (multiply(X0,X1)=multiply(X1,X0))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f351,f769])).
% 0.87/0.64 fof(f792,plain,(
% 0.87/0.64 ~multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3))),
% 0.87/0.64 inference(backward_subsumption_resolution,[status(thm)],[f476,f776])).
% 0.87/0.64 fof(f2135,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(X0,multiply(X1,multiply(X2,X3)))=multiply(multiply(X1,X0),multiply(X2,X3)))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f776,f325])).
% 0.87/0.64 fof(f2179,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(multiply(X0,multiply(X1,X2)),X3)=multiply(multiply(X3,X0),multiply(X1,X2)))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f776,f325])).
% 0.87/0.64 fof(f2183,plain,(
% 0.87/0.64 ![X0,X1,X2,X3,X4]: (multiply(multiply(X0,multiply(double_divide(double_divide(X1,X2),multiply(X2,X1)),X3)),X4)=multiply(multiply(X0,X4),X3))),
% 0.87/0.64 inference(paramodulation,[status(thm)],[f420,f325])).
% 0.87/0.64 fof(f2309,plain,(
% 0.87/0.64 ![X0,X1,X2,X3]: (multiply(multiply(X0,multiply(X1,X2)),X3)=multiply(X0,multiply(X3,multiply(X1,X2))))),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f2135,f2179])).
% 0.87/0.64 fof(f2319,plain,(
% 0.87/0.64 ![X0,X1,X2,X3,X4]: (multiply(X0,multiply(X1,multiply(double_divide(double_divide(X2,X3),multiply(X3,X2)),X4)))=multiply(multiply(X0,X1),X4))),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f2309,f2183])).
% 0.87/0.64 fof(f2320,plain,(
% 0.87/0.64 ~multiply(a3,multiply(b3,c3))=multiply(a3,multiply(b3,c3))),
% 0.87/0.64 inference(backward_demodulation,[status(thm)],[f2357,f792])).
% 0.87/0.64 fof(f2357,plain,(
% 0.87/0.64 ![X0,X1,X2]: (multiply(X0,multiply(X1,X2))=multiply(multiply(X0,X1),X2))),
% 0.87/0.64 inference(forward_demodulation,[status(thm)],[f420,f2319])).
% 0.87/0.65 fof(f2490,plain,(
% 0.87/0.65 $false),
% 0.87/0.65 inference(trivial_equality_resolution,[status(thm)],[f2320])).
% 0.87/0.65 % SZS output end CNFRefutation for theBenchmark.p
% 0.87/0.66 % Elapsed time: 0.267218 seconds
% 0.87/0.66 % CPU time: 1.954144 seconds
% 0.87/0.66 % Total memory used: 100.420 MB
% 0.87/0.66 % Net memory used: 98.901 MB
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