%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP037-3 : 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 : n005.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 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:55:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f2,axiom,(
% 0.09/0.39 (![X]: (product(X,identity,X) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f4,axiom,(
% 0.09/0.39 (![X]: (product(X,inverse(X),identity) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f6,axiom,(
% 0.09/0.39 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f9,axiom,(
% 0.09/0.39 (![A,B,C]: (( ~ subgroup_member(A)| ~ subgroup_member(B)| ~ product(A,inverse(B),C)| subgroup_member(C) ) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f10,hypothesis,(
% 0.09/0.39 (![A]: (( ~ subgroup_member(A)| product(another_identity,A,A) ) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f12,hypothesis,(
% 0.09/0.39 (![A]: (( ~ subgroup_member(A)| product(A,another_inverse(A),another_identity) ) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f15,hypothesis,(
% 0.09/0.39 (![A,B,C,D]: (( ~ product(A,B,C)| ~ product(A,D,C)| D = B ) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f17,hypothesis,(
% 0.09/0.39 subgroup_member(a) ),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f18,hypothesis,(
% 0.09/0.39 subgroup_member(another_identity) ),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f19,negated_conjecture,(
% 0.09/0.39 inverse(a) != another_inverse(a) ),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f21,plain,(
% 0.09/0.39 ![X0]: (product(X0,identity,X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/0.39 fof(f23,plain,(
% 0.09/0.39 ![X0]: (product(X0,inverse(X0),identity))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.09/0.39 fof(f25,plain,(
% 0.09/0.39 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f6])).
% 0.09/0.39 fof(f26,plain,(
% 0.09/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f25])).
% 0.09/0.39 fof(f31,plain,(
% 0.09/0.39 ![C]: ((![A,B]: ((~subgroup_member(A)|~subgroup_member(B))|~product(A,inverse(B),C)))|subgroup_member(C))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f9])).
% 0.09/0.39 fof(f32,plain,(
% 0.09/0.39 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~product(X0,inverse(X1),X2)|subgroup_member(X2))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.39 fof(f33,plain,(
% 0.09/0.39 ![X0]: (~subgroup_member(X0)|product(another_identity,X0,X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.09/0.39 fof(f35,plain,(
% 0.09/0.39 ![X0]: (~subgroup_member(X0)|product(X0,another_inverse(X0),another_identity))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/0.39 fof(f38,plain,(
% 0.09/0.39 ![B,D]: ((![A,C]: (~product(A,B,C)|~product(A,D,C)))|D=B)),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f15])).
% 0.09/0.39 fof(f39,plain,(
% 0.09/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|X3=X1)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f38])).
% 0.09/0.39 fof(f42,plain,(
% 0.09/0.39 subgroup_member(a)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f17])).
% 0.09/0.39 fof(f43,plain,(
% 0.09/0.39 subgroup_member(another_identity)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.09/0.39 fof(f44,plain,(
% 0.09/0.39 ~inverse(a)=another_inverse(a)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.09/0.39 fof(f49,plain,(
% 0.09/0.39 ![X0]: (~subgroup_member(X0)|~subgroup_member(X0)|subgroup_member(identity))),
% 0.09/0.39 inference(resolution,[status(thm)],[f32,f23])).
% 0.09/0.39 fof(f50,plain,(
% 0.09/0.39 ![X0]: (~subgroup_member(X0)|subgroup_member(identity))),
% 0.09/0.39 inference(duplicate_literals_removal,[status(thm)],[f49])).
% 0.09/0.39 fof(f53,plain,(
% 0.09/0.39 product(a,another_inverse(a),another_identity)),
% 0.09/0.39 inference(resolution,[status(thm)],[f35,f42])).
% 0.09/0.39 fof(f59,plain,(
% 0.09/0.39 subgroup_member(identity)),
% 0.09/0.39 inference(resolution,[status(thm)],[f50,f43])).
% 0.09/0.39 fof(f69,plain,(
% 0.09/0.39 ![X0,X1]: (~product(X0,identity,X1)|X0=X1)),
% 0.09/0.39 inference(resolution,[status(thm)],[f26,f21])).
% 0.09/0.39 fof(f116,plain,(
% 0.09/0.39 product(another_identity,identity,identity)),
% 0.09/0.39 inference(resolution,[status(thm)],[f33,f59])).
% 0.09/0.39 fof(f134,plain,(
% 0.09/0.39 another_identity=identity),
% 0.09/0.39 inference(resolution,[status(thm)],[f116,f69])).
% 0.09/0.39 fof(f141,plain,(
% 0.09/0.39 product(a,another_inverse(a),identity)),
% 0.09/0.39 inference(backward_demodulation,[status(thm)],[f134,f53])).
% 0.09/0.39 fof(f195,plain,(
% 0.09/0.39 ![X0,X1]: (~product(X0,X1,identity)|X1=inverse(X0))),
% 0.09/0.39 inference(resolution,[status(thm)],[f39,f23])).
% 0.09/0.39 fof(f341,plain,(
% 0.09/0.39 another_inverse(a)=inverse(a)),
% 0.09/0.39 inference(resolution,[status(thm)],[f195,f141])).
% 0.09/0.39 fof(f347,plain,(
% 0.09/0.39 $false),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f341,f44])).
% 0.09/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.41 % Elapsed time: 0.046916 seconds
% 0.09/0.41 % CPU time: 0.151309 seconds
% 0.09/0.41 % Total memory used: 43.830 MB
% 0.09/0.41 % Net memory used: 43.400 MB
%------------------------------------------------------------------------------