%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP036-3 : 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 : n004.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 0.18s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n004.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 19:55:05 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.48 % Refutation found
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.48 fof(f1,axiom,(
% 0.18/0.48 (![X]: (product(identity,X,X) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f4,axiom,(
% 0.18/0.48 (![X]: (product(X,inverse(X),identity) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f6,axiom,(
% 0.18/0.48 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f9,axiom,(
% 0.18/0.48 (![A,B,C]: (( ~ subgroup_member(A)| ~ subgroup_member(B)| ~ product(A,inverse(B),C)| subgroup_member(C) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f11,hypothesis,(
% 0.18/0.48 (![A]: (( ~ subgroup_member(A)| product(A,another_identity,A) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f15,hypothesis,(
% 0.18/0.48 subgroup_member(another_identity) ),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f16,negated_conjecture,(
% 0.18/0.48 identity != another_identity ),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f17,plain,(
% 0.18/0.48 ![X0]: (product(identity,X0,X0))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f1])).
% 0.18/0.48 fof(f20,plain,(
% 0.18/0.48 ![X0]: (product(X0,inverse(X0),identity))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f4])).
% 0.18/0.48 fof(f22,plain,(
% 0.18/0.48 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f6])).
% 0.18/0.48 fof(f23,plain,(
% 0.18/0.48 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f22])).
% 0.18/0.48 fof(f28,plain,(
% 0.18/0.48 ![C]: ((![A,B]: ((~subgroup_member(A)|~subgroup_member(B))|~product(A,inverse(B),C)))|subgroup_member(C))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f9])).
% 0.18/0.48 fof(f29,plain,(
% 0.18/0.48 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~product(X0,inverse(X1),X2)|subgroup_member(X2))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f28])).
% 0.18/0.48 fof(f31,plain,(
% 0.18/0.48 ![X0]: (~subgroup_member(X0)|product(X0,another_identity,X0))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f11])).
% 0.18/0.48 fof(f35,plain,(
% 0.18/0.48 subgroup_member(another_identity)),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f15])).
% 0.18/0.48 fof(f36,plain,(
% 0.18/0.48 ~identity=another_identity),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f16])).
% 0.18/0.48 fof(f55,plain,(
% 0.18/0.48 ![X0,X1]: (~product(identity,X0,X1)|X0=X1)),
% 0.18/0.48 inference(resolution,[status(thm)],[f23,f17])).
% 0.18/0.48 fof(f127,plain,(
% 0.18/0.48 ![X0]: (~subgroup_member(X0)|~subgroup_member(X0)|subgroup_member(identity))),
% 0.18/0.48 inference(resolution,[status(thm)],[f29,f20])).
% 0.18/0.48 fof(f130,plain,(
% 0.18/0.48 ![X0]: (~subgroup_member(X0)|subgroup_member(identity))),
% 0.18/0.48 inference(duplicate_literals_removal,[status(thm)],[f127])).
% 0.18/0.48 fof(f185,plain,(
% 0.18/0.48 subgroup_member(identity)),
% 0.18/0.48 inference(resolution,[status(thm)],[f130,f35])).
% 0.18/0.48 fof(f189,plain,(
% 0.18/0.48 product(identity,another_identity,identity)),
% 0.18/0.48 inference(resolution,[status(thm)],[f185,f31])).
% 0.18/0.48 fof(f208,plain,(
% 0.18/0.48 another_identity=identity),
% 0.18/0.48 inference(resolution,[status(thm)],[f189,f55])).
% 0.18/0.48 fof(f216,plain,(
% 0.18/0.48 $false),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f208,f36])).
% 0.18/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.23/0.51 % Elapsed time: 0.060004 seconds
% 0.23/0.51 % CPU time: 0.198756 seconds
% 0.23/0.51 % Total memory used: 45.130 MB
% 0.23/0.51 % Net memory used: 44.655 MB
%------------------------------------------------------------------------------