%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP039-6 : 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 : n016.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 12:35:32 PM UTC 2026
% Result : Unsatisfiable 14.26s 2.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:00:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 14.26/2.38 % Refutation found
% 14.26/2.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 14.26/2.38 % SZS output start CNFRefutation for theBenchmark
% 14.26/2.38 fof(f1,axiom,(
% 14.26/2.38 (![A,B]: (( ~ equalish(A,B)| ~ subgroup_member(A)| subgroup_member(B) ) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f5,axiom,(
% 14.26/2.38 (![X]: (( ~ subgroup_member(X)| subgroup_member(inverse(X)) ) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f6,axiom,(
% 14.26/2.38 (![A,B,C]: (( ~ subgroup_member(A)| ~ subgroup_member(B)| ~ product(A,B,C)| subgroup_member(C) ) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f7,axiom,(
% 14.26/2.38 (![X]: (product(identity,X,X) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f8,axiom,(
% 14.26/2.38 (![X]: (product(X,identity,X) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f9,axiom,(
% 14.26/2.38 (![X]: (product(inverse(X),X,identity) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f11,axiom,(
% 14.26/2.38 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W)| product(X,V,W) ) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f12,axiom,(
% 14.26/2.38 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(X,V,W)| product(U,Z,W) ) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f15,axiom,(
% 14.26/2.38 (![A,B,C,D]: (( ~ product(A,B,C)| ~ product(A,D,C)| equalish(D,B) ) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f17,axiom,(
% 14.26/2.38 (![A,B]: (( subgroup_member(element_in_O2(A,B))| subgroup_member(B)| subgroup_member(A) ) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f18,axiom,(
% 14.26/2.38 (![A,B]: (( product(A,element_in_O2(A,B),B)| subgroup_member(B)| subgroup_member(A) ) ))),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f19,negated_conjecture,(
% 14.26/2.38 subgroup_member(b) ),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f20,negated_conjecture,(
% 14.26/2.38 product(b,inverse(a),c) ),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f21,negated_conjecture,(
% 14.26/2.38 product(a,c,d) ),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f22,negated_conjecture,(
% 14.26/2.38 ~ subgroup_member(d) ),
% 14.26/2.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.26/2.38 fof(f23,plain,(
% 14.26/2.38 ![B]: ((![A]: (~equalish(A,B)|~subgroup_member(A)))|subgroup_member(B))),
% 14.26/2.38 inference(miniscoping,[status(thm)],[f1])).
% 14.26/2.38 fof(f24,plain,(
% 14.26/2.38 ![X0,X1]: (~equalish(X0,X1)|~subgroup_member(X0)|subgroup_member(X1))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f23])).
% 14.26/2.38 fof(f31,plain,(
% 14.26/2.38 ![X0]: (~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f5])).
% 14.26/2.38 fof(f32,plain,(
% 14.26/2.38 ![C]: ((![A,B]: ((~subgroup_member(A)|~subgroup_member(B))|~product(A,B,C)))|subgroup_member(C))),
% 14.26/2.38 inference(miniscoping,[status(thm)],[f6])).
% 14.26/2.38 fof(f33,plain,(
% 14.26/2.38 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~product(X0,X1,X2)|subgroup_member(X2))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f32])).
% 14.26/2.38 fof(f34,plain,(
% 14.26/2.38 ![X0]: (product(identity,X0,X0))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f7])).
% 14.26/2.38 fof(f35,plain,(
% 14.26/2.38 ![X0]: (product(X0,identity,X0))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f8])).
% 14.26/2.38 fof(f36,plain,(
% 14.26/2.38 ![X0]: (product(inverse(X0),X0,identity))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f9])).
% 14.26/2.38 fof(f38,plain,(
% 14.26/2.38 ![X,V,W]: ((![U,Z]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))),
% 14.26/2.38 inference(miniscoping,[status(thm)],[f11])).
% 14.26/2.38 fof(f39,plain,(
% 14.26/2.38 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f38])).
% 14.26/2.38 fof(f40,plain,(
% 14.26/2.38 ![U,Z,W]: ((![X,V]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(X,V,W)))|product(U,Z,W))),
% 14.26/2.38 inference(miniscoping,[status(thm)],[f12])).
% 14.26/2.38 fof(f41,plain,(
% 14.26/2.38 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X0,X4,X5)|product(X2,X3,X5))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f40])).
% 14.26/2.38 fof(f45,plain,(
% 14.26/2.38 ![B,D]: ((![A,C]: (~product(A,B,C)|~product(A,D,C)))|equalish(D,B))),
% 14.26/2.38 inference(miniscoping,[status(thm)],[f15])).
% 14.26/2.38 fof(f46,plain,(
% 14.26/2.38 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X3,X1))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f45])).
% 14.26/2.38 fof(f49,plain,(
% 14.26/2.38 ![A]: ((![B]: (subgroup_member(element_in_O2(A,B))|subgroup_member(B)))|subgroup_member(A))),
% 14.26/2.38 inference(miniscoping,[status(thm)],[f17])).
% 14.26/2.38 fof(f50,plain,(
% 14.26/2.38 ![X0,X1]: (subgroup_member(element_in_O2(X0,X1))|subgroup_member(X1)|subgroup_member(X0))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f49])).
% 14.26/2.38 fof(f51,plain,(
% 14.26/2.38 ![A]: ((![B]: (product(A,element_in_O2(A,B),B)|subgroup_member(B)))|subgroup_member(A))),
% 14.26/2.38 inference(miniscoping,[status(thm)],[f18])).
% 14.26/2.38 fof(f52,plain,(
% 14.26/2.38 ![X0,X1]: (product(X0,element_in_O2(X0,X1),X1)|subgroup_member(X1)|subgroup_member(X0))),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f51])).
% 14.26/2.38 fof(f53,plain,(
% 14.26/2.38 subgroup_member(b)),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f19])).
% 14.26/2.38 fof(f54,plain,(
% 14.26/2.38 product(b,inverse(a),c)),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f20])).
% 14.26/2.38 fof(f55,plain,(
% 14.26/2.38 product(a,c,d)),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f21])).
% 14.26/2.38 fof(f56,plain,(
% 14.26/2.38 ~subgroup_member(d)),
% 14.26/2.38 inference(cnf_transformation,[status(thm)],[f22])).
% 14.26/2.38 fof(f57,plain,(
% 14.26/2.38 ~subgroup_member(a)|~subgroup_member(c)|subgroup_member(d)),
% 14.26/2.38 inference(resolution,[status(thm)],[f33,f55])).
% 14.26/2.38 fof(f58,plain,(
% 14.26/2.38 ~subgroup_member(b)|~subgroup_member(inverse(a))|subgroup_member(c)),
% 14.26/2.38 inference(resolution,[status(thm)],[f33,f54])).
% 14.26/2.38 fof(f59,plain,(
% 14.26/2.38 ~subgroup_member(a)|~subgroup_member(c)),
% 14.26/2.38 inference(forward_subsumption_resolution,[status(thm)],[f57,f56])).
% 14.26/2.38 fof(f60,plain,(
% 14.26/2.38 ~subgroup_member(inverse(a))|subgroup_member(c)),
% 14.26/2.38 inference(forward_subsumption_resolution,[status(thm)],[f58,f53])).
% 14.26/2.38 fof(f61,plain,(
% 14.26/2.38 subgroup_member(inverse(b))),
% 14.26/2.38 inference(resolution,[status(thm)],[f31,f53])).
% 14.26/2.38 fof(f96,plain,(
% 14.26/2.38 ![X0,X1,X2,X3]: (~product(X0,X1,identity)|~product(X1,X2,X3)|product(X0,X3,X2))),
% 14.26/2.38 inference(resolution,[status(thm)],[f39,f34])).
% 14.26/2.38 fof(f116,plain,(
% 14.26/2.38 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X1,X3,identity)|product(X2,X3,X0))),
% 14.26/2.38 inference(resolution,[status(thm)],[f41,f35])).
% 14.26/2.38 fof(f151,plain,(
% 14.26/2.38 ![X0,X1,X2]: (~product(X0,X1,X2)|equalish(element_in_O2(X0,X2),X1)|subgroup_member(X2)|subgroup_member(X0))),
% 14.26/2.38 inference(resolution,[status(thm)],[f46,f52])).
% 14.26/2.38 fof(f384,plain,(
% 14.26/2.38 ![X0,X1,X2]: (~product(X0,X1,X2)|product(inverse(X0),X2,X1))),
% 14.26/2.38 inference(resolution,[status(thm)],[f96,f36])).
% 14.26/2.38 fof(f403,plain,(
% 14.26/2.38 product(inverse(b),c,inverse(a))),
% 14.26/2.38 inference(resolution,[status(thm)],[f384,f54])).
% 14.26/2.38 fof(f813,plain,(
% 14.26/2.38 ![X0,X1,X2]: (~product(X0,inverse(X1),X2)|product(X2,X1,X0))),
% 14.26/2.38 inference(resolution,[status(thm)],[f116,f36])).
% 14.26/2.38 fof(f826,plain,(
% 14.26/2.38 product(c,a,b)),
% 14.26/2.38 inference(resolution,[status(thm)],[f813,f54])).
% 14.26/2.38 fof(f832,plain,(
% 14.26/2.38 product(inverse(c),b,a)),
% 14.26/2.38 inference(resolution,[status(thm)],[f826,f384])).
% 14.26/2.38 fof(f1021,plain,(
% 14.26/2.38 ~subgroup_member(inverse(c))|~subgroup_member(b)|subgroup_member(a)),
% 14.26/2.38 inference(resolution,[status(thm)],[f832,f33])).
% 14.26/2.38 fof(f1022,plain,(
% 14.26/2.38 ~subgroup_member(inverse(c))|subgroup_member(a)),
% 14.26/2.38 inference(forward_subsumption_resolution,[status(thm)],[f1021,f53])).
% 14.26/2.38 fof(f1346,plain,(
% 14.26/2.38 equalish(element_in_O2(a,d),c)|subgroup_member(d)|subgroup_member(a)),
% 14.26/2.38 inference(resolution,[status(thm)],[f151,f55])).
% 14.26/2.38 fof(f1361,plain,(
% 14.26/2.38 equalish(element_in_O2(a,d),c)|subgroup_member(a)),
% 14.26/2.38 inference(forward_subsumption_resolution,[status(thm)],[f1346,f56])).
% 14.26/2.38 fof(f1654,plain,(
% 14.26/2.38 ~subgroup_member(inverse(b))|~subgroup_member(c)|subgroup_member(inverse(a))),
% 14.26/2.38 inference(resolution,[status(thm)],[f403,f33])).
% 14.26/2.38 fof(f1655,plain,(
% 14.26/2.38 ~subgroup_member(c)|subgroup_member(inverse(a))),
% 14.26/2.38 inference(forward_subsumption_resolution,[status(thm)],[f1654,f61])).
% 14.26/2.38 fof(f3908,plain,(
% 14.26/2.38 subgroup_member(a)|~subgroup_member(element_in_O2(a,d))|subgroup_member(c)),
% 14.26/2.38 inference(resolution,[status(thm)],[f1361,f24])).
% 14.26/2.38 fof(f6604,plain,(
% 14.26/2.38 subgroup_member(a)|subgroup_member(c)|subgroup_member(d)|subgroup_member(a)),
% 14.26/2.38 inference(resolution,[status(thm)],[f3908,f50])).
% 14.26/2.38 fof(f6605,plain,(
% 14.26/2.38 subgroup_member(a)|subgroup_member(c)|subgroup_member(d)),
% 14.26/2.39 inference(duplicate_literals_removal,[status(thm)],[f6604])).
% 14.26/2.39 fof(f6606,plain,(
% 14.26/2.39 subgroup_member(a)|subgroup_member(c)),
% 14.26/2.39 inference(forward_subsumption_resolution,[status(thm)],[f6605,f56])).
% 14.26/2.39 fof(f6608,plain,(
% 14.26/2.39 subgroup_member(a)|subgroup_member(inverse(a))),
% 14.26/2.39 inference(resolution,[status(thm)],[f6606,f1655])).
% 14.26/2.39 fof(f6612,plain,(
% 14.26/2.39 subgroup_member(inverse(a))),
% 14.26/2.39 inference(forward_subsumption_resolution,[status(thm)],[f6608,f31])).
% 14.26/2.39 fof(f6614,plain,(
% 14.26/2.39 subgroup_member(c)),
% 14.26/2.39 inference(backward_subsumption_resolution,[status(thm)],[f60,f6612])).
% 14.26/2.39 fof(f6619,plain,(
% 14.26/2.39 ~subgroup_member(a)),
% 14.26/2.39 inference(backward_subsumption_resolution,[status(thm)],[f59,f6614])).
% 14.26/2.39 fof(f6621,plain,(
% 14.26/2.39 subgroup_member(inverse(c))),
% 14.26/2.39 inference(resolution,[status(thm)],[f6614,f31])).
% 14.26/2.39 fof(f6638,plain,(
% 14.26/2.39 ~subgroup_member(inverse(c))),
% 14.26/2.39 inference(backward_subsumption_resolution,[status(thm)],[f1022,f6619])).
% 14.26/2.39 fof(f6655,plain,(
% 14.26/2.39 $false),
% 14.26/2.39 inference(forward_subsumption_resolution,[status(thm)],[f6638,f6621])).
% 14.26/2.39 % SZS output end CNFRefutation for theBenchmark.p
% 14.26/2.40 % Elapsed time: 2.031005 seconds
% 14.26/2.40 % CPU time: 15.824461 seconds
% 14.26/2.40 % Total memory used: 77.208 MB
% 14.26/2.40 % Net memory used: 59.997 MB
%------------------------------------------------------------------------------