%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP035-3 : 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 : n014.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 12:35:31 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n014.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 19:55:11 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.13/5.40 % Refutation found
% 0.13/5.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.40 % SZS output start CNFRefutation for theBenchmark
% 0.13/5.40 fof(f1,axiom,(
% 0.13/5.40 (![X]: (product(identity,X,X) ))),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f2,axiom,(
% 0.13/5.40 (![X]: (product(X,identity,X) ))),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f3,axiom,(
% 0.13/5.40 (![X]: (product(inverse(X),X,identity) ))),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f4,axiom,(
% 0.13/5.40 (![X]: (product(X,inverse(X),identity) ))),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f5,axiom,(
% 0.13/5.40 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f6,axiom,(
% 0.13/5.40 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f7,axiom,(
% 0.13/5.40 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W)| product(X,V,W) ) ))),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f9,axiom,(
% 0.13/5.40 (![A,B,C]: (( ~ subgroup_member(A)| ~ subgroup_member(B)| ~ product(A,inverse(B),C)| subgroup_member(C) ) ))),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f10,hypothesis,(
% 0.13/5.40 subgroup_member(a) ),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f11,hypothesis,(
% 0.13/5.40 subgroup_member(b) ),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f12,hypothesis,(
% 0.13/5.40 product(a,b,c) ),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f13,negated_conjecture,(
% 0.13/5.40 ~ subgroup_member(c) ),
% 0.13/5.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.40 fof(f14,plain,(
% 0.13/5.40 ![X0]: (product(identity,X0,X0))),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/5.40 fof(f15,plain,(
% 0.13/5.40 ![X0]: (product(X0,identity,X0))),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/5.40 fof(f16,plain,(
% 0.13/5.40 ![X0]: (product(inverse(X0),X0,identity))),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/5.40 fof(f17,plain,(
% 0.13/5.40 ![X0]: (product(X0,inverse(X0),identity))),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/5.40 fof(f18,plain,(
% 0.13/5.40 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/5.40 fof(f19,plain,(
% 0.13/5.40 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.13/5.40 inference(miniscoping,[status(thm)],[f6])).
% 0.13/5.40 fof(f20,plain,(
% 0.13/5.40 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/5.40 fof(f21,plain,(
% 0.13/5.40 ![X,V,W]: ((![U,Z]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))),
% 0.13/5.40 inference(miniscoping,[status(thm)],[f7])).
% 0.13/5.40 fof(f22,plain,(
% 0.13/5.40 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f21])).
% 0.13/5.40 fof(f25,plain,(
% 0.13/5.40 ![C]: ((![A,B]: ((~subgroup_member(A)|~subgroup_member(B))|~product(A,inverse(B),C)))|subgroup_member(C))),
% 0.13/5.40 inference(miniscoping,[status(thm)],[f9])).
% 0.13/5.40 fof(f26,plain,(
% 0.13/5.40 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~product(X0,inverse(X1),X2)|subgroup_member(X2))),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f25])).
% 0.13/5.40 fof(f27,plain,(
% 0.13/5.40 subgroup_member(a)),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f10])).
% 0.13/5.40 fof(f28,plain,(
% 0.13/5.40 subgroup_member(b)),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/5.40 fof(f29,plain,(
% 0.13/5.40 product(a,b,c)),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f12])).
% 0.13/5.40 fof(f30,plain,(
% 0.13/5.40 ~subgroup_member(c)),
% 0.13/5.40 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/5.40 fof(f35,plain,(
% 0.13/5.40 ![X0,X1]: (~product(X0,identity,X1)|X0=X1)),
% 0.13/5.40 inference(resolution,[status(thm)],[f20,f15])).
% 0.13/5.40 fof(f51,plain,(
% 0.13/5.40 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(identity,X1,X3)|product(inverse(X0),X2,X3))),
% 0.13/5.40 inference(resolution,[status(thm)],[f22,f16])).
% 0.13/5.40 fof(f53,plain,(
% 0.13/5.40 ![X0,X1,X2]: (~product(b,X0,X1)|~product(c,X0,X2)|product(a,X1,X2))),
% 0.13/5.40 inference(resolution,[status(thm)],[f22,f29])).
% 0.13/5.40 fof(f64,plain,(
% 0.13/5.40 ![X0]: (~subgroup_member(identity)|~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 0.13/5.40 inference(resolution,[status(thm)],[f26,f14])).
% 0.13/5.40 fof(f65,plain,(
% 0.13/5.40 ![X0]: (~subgroup_member(X0)|~subgroup_member(X0)|subgroup_member(identity))),
% 0.13/5.40 inference(resolution,[status(thm)],[f26,f17])).
% 0.13/5.40 fof(f68,plain,(
% 0.13/5.40 ![X0]: (~subgroup_member(X0)|subgroup_member(identity))),
% 0.13/5.40 inference(duplicate_literals_removal,[status(thm)],[f65])).
% 0.13/5.40 fof(f74,plain,(
% 0.13/5.40 ![X0,X1]: (~product(c,X0,X1)|product(a,multiply(b,X0),X1))),
% 0.13/5.40 inference(resolution,[status(thm)],[f53,f18])).
% 0.13/5.40 fof(f88,plain,(
% 0.13/5.40 product(a,multiply(b,inverse(c)),identity)),
% 0.13/5.40 inference(resolution,[status(thm)],[f74,f17])).
% 0.13/5.40 fof(f92,plain,(
% 0.13/5.40 subgroup_member(identity)),
% 0.13/5.40 inference(resolution,[status(thm)],[f68,f28])).
% 0.13/5.40 fof(f112,plain,(
% 0.13/5.40 ![X0,X1]: (~product(identity,X0,X1)|product(inverse(inverse(X0)),identity,X1))),
% 0.13/5.40 inference(resolution,[status(thm)],[f51,f16])).
% 0.13/5.40 fof(f117,plain,(
% 0.13/5.40 ![X0,X1,X2]: (~product(identity,X0,X1)|product(inverse(X2),multiply(X2,X0),X1))),
% 0.13/5.40 inference(resolution,[status(thm)],[f51,f18])).
% 0.13/5.40 fof(f142,plain,(
% 0.13/5.40 ![X0]: (~product(identity,multiply(b,inverse(c)),X0)|product(inverse(a),identity,X0))),
% 0.13/5.40 inference(resolution,[status(thm)],[f88,f51])).
% 0.13/5.40 fof(f183,plain,(
% 0.13/5.40 ![X0]: (~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 0.13/5.40 inference(forward_subsumption_resolution,[status(thm)],[f64,f92])).
% 0.13/5.40 fof(f185,plain,(
% 0.13/5.40 subgroup_member(inverse(b))),
% 0.13/5.40 inference(resolution,[status(thm)],[f183,f28])).
% 0.13/5.40 fof(f400,plain,(
% 0.13/5.40 product(inverse(a),identity,multiply(b,inverse(c)))),
% 0.13/5.40 inference(resolution,[status(thm)],[f142,f14])).
% 0.13/5.40 fof(f455,plain,(
% 0.13/5.40 ![X0]: (product(inverse(inverse(X0)),identity,X0))),
% 0.13/5.40 inference(resolution,[status(thm)],[f112,f14])).
% 0.13/5.40 fof(f486,plain,(
% 0.13/5.40 inverse(a)=multiply(b,inverse(c))),
% 0.13/5.40 inference(resolution,[status(thm)],[f400,f35])).
% 0.13/5.40 fof(f538,plain,(
% 0.13/5.40 ![X0]: (inverse(inverse(X0))=X0)),
% 0.13/5.40 inference(resolution,[status(thm)],[f455,f35])).
% 0.13/5.40 fof(f580,plain,(
% 0.13/5.40 ![X0,X1]: (product(inverse(X0),multiply(X0,X1),X1))),
% 0.13/5.40 inference(resolution,[status(thm)],[f117,f14])).
% 0.13/5.40 fof(f687,plain,(
% 0.13/5.40 product(inverse(b),inverse(a),inverse(c))),
% 0.13/5.40 inference(paramodulation,[status(thm)],[f486,f580])).
% 0.13/5.40 fof(f972,plain,(
% 0.13/5.40 ~subgroup_member(inverse(b))|~subgroup_member(a)|subgroup_member(inverse(c))),
% 0.13/5.40 inference(resolution,[status(thm)],[f687,f26])).
% 0.13/5.40 fof(f984,plain,(
% 0.13/5.40 ~subgroup_member(a)|subgroup_member(inverse(c))),
% 0.13/5.40 inference(forward_subsumption_resolution,[status(thm)],[f972,f185])).
% 0.13/5.40 fof(f987,plain,(
% 0.13/5.40 subgroup_member(inverse(c))),
% 0.13/5.40 inference(forward_subsumption_resolution,[status(thm)],[f984,f27])).
% 0.13/5.40 fof(f991,plain,(
% 0.13/5.40 subgroup_member(inverse(inverse(c)))),
% 0.13/5.40 inference(resolution,[status(thm)],[f987,f183])).
% 0.13/5.40 fof(f994,plain,(
% 0.13/5.40 subgroup_member(c)),
% 0.13/5.40 inference(forward_demodulation,[status(thm)],[f538,f991])).
% 0.13/5.40 fof(f995,plain,(
% 0.13/5.40 $false),
% 0.13/5.40 inference(forward_subsumption_resolution,[status(thm)],[f994,f30])).
% 0.13/5.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/5.42 % Elapsed time: 0.050852 seconds
% 0.13/5.42 % CPU time: 0.220564 seconds
% 0.13/5.42 % Total memory used: 33.739 MB
% 0.13/5.42 % Net memory used: 33.111 MB
%------------------------------------------------------------------------------