%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% 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 12:35:32 PM UTC 2026
% Result : Unsatisfiable 1.31s 0.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:01:12 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 1.31/0.61 % Refutation found
% 1.31/0.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.31/0.61 % SZS output start CNFRefutation for theBenchmark
% 1.31/0.61 fof(f1,axiom,(
% 1.31/0.61 (![X]: (product(identity,X,X) ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f2,axiom,(
% 1.31/0.61 (![X]: (product(X,identity,X) ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f3,axiom,(
% 1.31/0.61 (![X]: (product(inverse(X),X,identity) ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f5,axiom,(
% 1.31/0.61 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f6,axiom,(
% 1.31/0.61 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f7,axiom,(
% 1.31/0.61 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W)| product(X,V,W) ) ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f9,axiom,(
% 1.31/0.61 (![A,B,C]: (( ~ subgroup_member(A)| ~ subgroup_member(B)| ~ product(A,inverse(B),C)| subgroup_member(C) ) ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f10,axiom,(
% 1.31/0.61 (![A,B]: (( subgroup_member(element_in_O2(A,B))| subgroup_member(B)| subgroup_member(A) ) ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f11,axiom,(
% 1.31/0.61 (![A,B]: (( product(A,element_in_O2(A,B),B)| subgroup_member(B)| subgroup_member(A) ) ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f12,hypothesis,(
% 1.31/0.61 ~ subgroup_member(a) ),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f13,hypothesis,(
% 1.31/0.61 subgroup_member(b) ),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f14,hypothesis,(
% 1.31/0.61 ~ subgroup_member(d) ),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f15,hypothesis,(
% 1.31/0.61 product(b,inverse(a),c) ),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f16,hypothesis,(
% 1.31/0.61 product(a,c,d) ),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f17,negated_conjecture,(
% 1.31/0.61 (![A]: (inverse(inverse(A)) = A ))),
% 1.31/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.31/0.61 fof(f18,plain,(
% 1.31/0.61 ![X0]: (product(identity,X0,X0))),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f1])).
% 1.31/0.61 fof(f19,plain,(
% 1.31/0.61 ![X0]: (product(X0,identity,X0))),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f2])).
% 1.31/0.61 fof(f20,plain,(
% 1.31/0.61 ![X0]: (product(inverse(X0),X0,identity))),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f3])).
% 1.31/0.61 fof(f22,plain,(
% 1.31/0.61 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f5])).
% 1.31/0.61 fof(f23,plain,(
% 1.31/0.61 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 1.31/0.61 inference(miniscoping,[status(thm)],[f6])).
% 1.31/0.61 fof(f24,plain,(
% 1.31/0.61 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/0.61 fof(f25,plain,(
% 1.31/0.61 ![X,V,W]: ((![U,Z]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))),
% 1.31/0.61 inference(miniscoping,[status(thm)],[f7])).
% 1.31/0.61 fof(f26,plain,(
% 1.31/0.61 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f25])).
% 1.31/0.61 fof(f29,plain,(
% 1.31/0.61 ![C]: ((![A,B]: ((~subgroup_member(A)|~subgroup_member(B))|~product(A,inverse(B),C)))|subgroup_member(C))),
% 1.31/0.61 inference(miniscoping,[status(thm)],[f9])).
% 1.31/0.61 fof(f30,plain,(
% 1.31/0.61 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~product(X0,inverse(X1),X2)|subgroup_member(X2))),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f29])).
% 1.31/0.61 fof(f31,plain,(
% 1.31/0.61 ![A]: ((![B]: (subgroup_member(element_in_O2(A,B))|subgroup_member(B)))|subgroup_member(A))),
% 1.31/0.61 inference(miniscoping,[status(thm)],[f10])).
% 1.31/0.61 fof(f32,plain,(
% 1.31/0.61 ![X0,X1]: (subgroup_member(element_in_O2(X0,X1))|subgroup_member(X1)|subgroup_member(X0))),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f31])).
% 1.31/0.61 fof(f33,plain,(
% 1.31/0.61 ![A]: ((![B]: (product(A,element_in_O2(A,B),B)|subgroup_member(B)))|subgroup_member(A))),
% 1.31/0.61 inference(miniscoping,[status(thm)],[f11])).
% 1.31/0.61 fof(f34,plain,(
% 1.31/0.61 ![X0,X1]: (product(X0,element_in_O2(X0,X1),X1)|subgroup_member(X1)|subgroup_member(X0))),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f33])).
% 1.31/0.61 fof(f35,plain,(
% 1.31/0.61 ~subgroup_member(a)),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f12])).
% 1.31/0.61 fof(f36,plain,(
% 1.31/0.61 subgroup_member(b)),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f13])).
% 1.31/0.61 fof(f37,plain,(
% 1.31/0.61 ~subgroup_member(d)),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f14])).
% 1.31/0.61 fof(f38,plain,(
% 1.31/0.61 product(b,inverse(a),c)),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f15])).
% 1.31/0.61 fof(f39,plain,(
% 1.31/0.61 product(a,c,d)),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f16])).
% 1.31/0.61 fof(f40,plain,(
% 1.31/0.61 ![X0]: (inverse(inverse(X0))=X0)),
% 1.31/0.61 inference(cnf_transformation,[status(thm)],[f17])).
% 1.31/0.61 fof(f42,plain,(
% 1.31/0.61 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(inverse(X1))|~product(X0,X1,X2)|subgroup_member(X2))),
% 1.31/0.61 inference(paramodulation,[status(thm)],[f40,f30])).
% 1.31/0.61 fof(f43,plain,(
% 1.31/0.61 ![X0]: (~subgroup_member(identity)|~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 1.31/0.61 inference(resolution,[status(thm)],[f18,f30])).
% 1.31/0.61 fof(f47,plain,(
% 1.31/0.61 ![X0]: (~subgroup_member(inverse(inverse(X0)))|~subgroup_member(X0)|subgroup_member(identity))),
% 1.31/0.61 inference(resolution,[status(thm)],[f20,f30])).
% 1.31/0.61 fof(f49,plain,(
% 1.31/0.61 ![X0]: (product(X0,inverse(X0),identity))),
% 1.31/0.61 inference(paramodulation,[status(thm)],[f40,f20])).
% 1.31/0.61 fof(f50,plain,(
% 1.31/0.61 ![X0]: (~subgroup_member(X0)|~subgroup_member(X0)|subgroup_member(identity))),
% 1.31/0.61 inference(forward_demodulation,[status(thm)],[f40,f47])).
% 1.31/0.61 fof(f51,plain,(
% 1.31/0.61 ![X0]: (~subgroup_member(X0)|subgroup_member(identity))),
% 1.31/0.61 inference(duplicate_literals_removal,[status(thm)],[f50])).
% 1.31/0.61 fof(f54,plain,(
% 1.31/0.61 ![X0]: (~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 1.31/0.61 inference(backward_subsumption_resolution,[status(thm)],[f43,f51])).
% 1.31/0.61 fof(f64,plain,(
% 1.31/0.61 subgroup_member(inverse(b))),
% 1.31/0.61 inference(resolution,[status(thm)],[f54,f36])).
% 1.31/0.61 fof(f78,plain,(
% 1.31/0.61 ![X0]: (~product(a,c,X0)|d=X0)),
% 1.31/0.61 inference(resolution,[status(thm)],[f24,f39])).
% 1.31/0.61 fof(f82,plain,(
% 1.31/0.61 ![X0,X1]: (~product(X0,identity,X1)|X0=X1)),
% 1.31/0.61 inference(resolution,[status(thm)],[f24,f19])).
% 1.31/0.61 fof(f83,plain,(
% 1.31/0.61 ![X0,X1,X2]: (~product(X0,X1,X2)|multiply(X0,X1)=X2)),
% 1.31/0.61 inference(resolution,[status(thm)],[f24,f22])).
% 1.31/0.61 fof(f104,plain,(
% 1.31/0.61 d=multiply(a,c)),
% 1.31/0.61 inference(resolution,[status(thm)],[f78,f22])).
% 1.31/0.61 fof(f134,plain,(
% 1.31/0.61 ![X0,X1,X2]: (~product(inverse(a),X0,X1)|~product(c,X0,X2)|product(b,X1,X2))),
% 1.31/0.61 inference(resolution,[status(thm)],[f26,f38])).
% 1.31/0.61 fof(f138,plain,(
% 1.31/0.61 ![X0,X1,X2,X3]: (~product(inverse(X0),X1,X2)|~product(identity,X1,X3)|product(X0,X2,X3))),
% 1.31/0.61 inference(resolution,[status(thm)],[f26,f49])).
% 1.31/0.61 fof(f183,plain,(
% 1.31/0.61 ![X0,X1,X2]: (~product(identity,X0,X1)|product(X2,multiply(inverse(X2),X0),X1))),
% 1.31/0.61 inference(resolution,[status(thm)],[f138,f22])).
% 1.31/0.61 fof(f295,plain,(
% 1.31/0.61 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|multiply(X1,element_in_O2(X1,X0))=X0)),
% 1.31/0.61 inference(resolution,[status(thm)],[f34,f83])).
% 1.31/0.61 fof(f331,plain,(
% 1.31/0.61 ![X0]: (subgroup_member(X0)|multiply(X0,element_in_O2(X0,d))=d)),
% 1.31/0.61 inference(resolution,[status(thm)],[f295,f37])).
% 1.31/0.61 fof(f373,plain,(
% 1.31/0.61 multiply(a,element_in_O2(a,d))=d),
% 1.31/0.61 inference(resolution,[status(thm)],[f331,f35])).
% 1.31/0.61 fof(f399,plain,(
% 1.31/0.61 ![X0]: (~product(c,inverse(inverse(a)),X0)|product(b,identity,X0))),
% 1.31/0.61 inference(resolution,[status(thm)],[f134,f49])).
% 1.31/0.61 fof(f402,plain,(
% 1.31/0.61 ![X0]: (~product(c,a,X0)|product(b,identity,X0))),
% 1.31/0.61 inference(forward_demodulation,[status(thm)],[f40,f399])).
% 1.31/0.61 fof(f453,plain,(
% 1.31/0.61 product(b,identity,multiply(c,a))),
% 1.31/0.61 inference(resolution,[status(thm)],[f402,f22])).
% 1.31/0.61 fof(f456,plain,(
% 1.31/0.61 b=multiply(c,a)),
% 1.31/0.61 inference(resolution,[status(thm)],[f453,f82])).
% 1.31/0.61 fof(f520,plain,(
% 1.31/0.61 ![X0,X1]: (product(X0,multiply(inverse(X0),X1),X1))),
% 1.31/0.61 inference(resolution,[status(thm)],[f183,f18])).
% 1.31/0.61 fof(f555,plain,(
% 1.31/0.61 ![X0,X1]: (product(inverse(X0),multiply(X0,X1),X1))),
% 1.31/0.61 inference(paramodulation,[status(thm)],[f40,f520])).
% 1.31/0.61 fof(f592,plain,(
% 1.31/0.61 product(inverse(c),b,a)),
% 1.31/0.61 inference(paramodulation,[status(thm)],[f456,f555])).
% 1.31/0.61 fof(f597,plain,(
% 1.31/0.61 product(inverse(a),d,element_in_O2(a,d))),
% 1.31/0.61 inference(paramodulation,[status(thm)],[f373,f555])).
% 1.31/0.61 fof(f599,plain,(
% 1.31/0.61 product(inverse(a),d,c)),
% 1.31/0.61 inference(paramodulation,[status(thm)],[f104,f555])).
% 1.31/0.61 fof(f659,plain,(
% 1.31/0.61 ~subgroup_member(inverse(c))|~subgroup_member(inverse(b))|subgroup_member(a)),
% 1.31/0.61 inference(resolution,[status(thm)],[f592,f42])).
% 1.31/0.61 fof(f661,plain,(
% 1.31/0.61 ~subgroup_member(inverse(c))|subgroup_member(a)),
% 1.31/0.61 inference(forward_subsumption_resolution,[status(thm)],[f659,f64])).
% 1.31/0.61 fof(f669,plain,(
% 1.31/0.61 ![X0]: (~product(inverse(a),d,X0)|c=X0)),
% 1.31/0.61 inference(resolution,[status(thm)],[f599,f24])).
% 1.31/0.61 fof(f686,plain,(
% 1.31/0.61 ~subgroup_member(inverse(c))),
% 1.31/0.61 inference(forward_subsumption_resolution,[status(thm)],[f661,f35])).
% 1.31/0.61 fof(f1047,plain,(
% 1.31/0.61 c=element_in_O2(a,d)),
% 1.31/0.61 inference(resolution,[status(thm)],[f597,f669])).
% 1.31/0.61 fof(f1072,plain,(
% 1.31/0.61 subgroup_member(c)|subgroup_member(d)|subgroup_member(a)),
% 1.31/0.61 inference(paramodulation,[status(thm)],[f1047,f32])).
% 1.31/0.61 fof(f1074,plain,(
% 1.31/0.61 subgroup_member(c)|subgroup_member(a)),
% 1.31/0.61 inference(forward_subsumption_resolution,[status(thm)],[f1072,f37])).
% 1.31/0.61 fof(f1075,plain,(
% 1.31/0.61 subgroup_member(c)),
% 1.31/0.61 inference(forward_subsumption_resolution,[status(thm)],[f1074,f35])).
% 1.31/0.61 fof(f1081,plain,(
% 1.31/0.61 subgroup_member(inverse(c))),
% 1.31/0.61 inference(resolution,[status(thm)],[f1075,f54])).
% 1.31/0.61 fof(f1082,plain,(
% 1.31/0.61 $false),
% 1.31/0.61 inference(forward_subsumption_resolution,[status(thm)],[f1081,f686])).
% 1.31/0.61 % SZS output end CNFRefutation for theBenchmark.p
% 1.31/0.62 % Elapsed time: 0.239833 seconds
% 1.31/0.62 % CPU time: 1.587355 seconds
% 1.31/0.62 % Total memory used: 116.634 MB
% 1.31/0.62 % Net memory used: 112.797 MB
%------------------------------------------------------------------------------