%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP040-4 : 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 : n015.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 0.14s 0.71s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP040-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.44 % Computer : n015.cluster.edu
% 0.14/0.44 % Model : x86_64 x86_64
% 0.14/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.44 % Memory : 8046.5625MB
% 0.14/0.44 % OS : Linux 6.8.0-71-generic
% 0.14/0.44 % CPULimit : 300
% 0.14/0.44 % WCLimit : 300
% 0.14/0.45 % DateTime : Sun Sep 20 19:58:50 UTC 2026
% 0.14/0.45 % CPUTime :
% 0.14/0.48 % Drodi V4.1.1
% 0.14/0.71 % Refutation found
% 0.14/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.71 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.71 fof(f1,axiom,(
% 0.14/0.71 (![X]: (product(identity,X,X) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f2,axiom,(
% 0.14/0.71 (![X]: (product(X,identity,X) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f3,axiom,(
% 0.14/0.71 (![X]: (product(inverse(X),X,identity) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f5,axiom,(
% 0.14/0.71 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f6,axiom,(
% 0.14/0.71 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f7,axiom,(
% 0.14/0.71 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W)| product(X,V,W) ) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f9,axiom,(
% 0.14/0.71 (![A,B,C]: (( ~ subgroup_member(A)| ~ subgroup_member(B)| ~ product(A,inverse(B),C)| subgroup_member(C) ) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f11,axiom,(
% 0.14/0.71 (![A]: (( ~ subgroup_member(A)| subgroup_member(inverse(A)) ) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f12,axiom,(
% 0.14/0.71 (![A,B,C,D]: (( ~ product(A,B,C)| ~ product(A,D,C)| D = B ) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f14,axiom,(
% 0.14/0.71 (![A,B]: (( subgroup_member(element_in_O2(A,B))| subgroup_member(B)| subgroup_member(A) ) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f15,axiom,(
% 0.14/0.71 (![A,B]: (( product(A,element_in_O2(A,B),B)| subgroup_member(B)| subgroup_member(A) ) ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f16,hypothesis,(
% 0.14/0.71 ~ subgroup_member(a) ),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f17,hypothesis,(
% 0.14/0.71 subgroup_member(b) ),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f18,hypothesis,(
% 0.14/0.71 ~ subgroup_member(d) ),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f19,hypothesis,(
% 0.14/0.71 product(b,inverse(a),c) ),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f20,hypothesis,(
% 0.14/0.71 product(a,c,d) ),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f21,negated_conjecture,(
% 0.14/0.71 (![A]: (inverse(inverse(A)) = A ))),
% 0.14/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.71 fof(f22,plain,(
% 0.14/0.71 ![X0]: (product(identity,X0,X0))),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.71 fof(f23,plain,(
% 0.14/0.71 ![X0]: (product(X0,identity,X0))),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.71 fof(f24,plain,(
% 0.14/0.71 ![X0]: (product(inverse(X0),X0,identity))),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.71 fof(f26,plain,(
% 0.14/0.71 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/0.71 fof(f27,plain,(
% 0.14/0.71 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.14/0.71 inference(miniscoping,[status(thm)],[f6])).
% 0.14/0.71 fof(f28,plain,(
% 0.14/0.71 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f27])).
% 0.14/0.71 fof(f29,plain,(
% 0.14/0.71 ![X,V,W]: ((![U,Z]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))),
% 0.14/0.71 inference(miniscoping,[status(thm)],[f7])).
% 0.14/0.71 fof(f30,plain,(
% 0.14/0.71 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f29])).
% 0.14/0.71 fof(f33,plain,(
% 0.14/0.71 ![C]: ((![A,B]: ((~subgroup_member(A)|~subgroup_member(B))|~product(A,inverse(B),C)))|subgroup_member(C))),
% 0.14/0.71 inference(miniscoping,[status(thm)],[f9])).
% 0.14/0.71 fof(f34,plain,(
% 0.14/0.71 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~product(X0,inverse(X1),X2)|subgroup_member(X2))),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f33])).
% 0.14/0.71 fof(f36,plain,(
% 0.14/0.71 ![X0]: (~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f11])).
% 0.14/0.71 fof(f37,plain,(
% 0.14/0.71 ![B,D]: ((![A,C]: (~product(A,B,C)|~product(A,D,C)))|D=B)),
% 0.14/0.71 inference(miniscoping,[status(thm)],[f12])).
% 0.14/0.71 fof(f38,plain,(
% 0.14/0.71 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|X3=X1)),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f37])).
% 0.14/0.71 fof(f41,plain,(
% 0.14/0.71 ![A]: ((![B]: (subgroup_member(element_in_O2(A,B))|subgroup_member(B)))|subgroup_member(A))),
% 0.14/0.71 inference(miniscoping,[status(thm)],[f14])).
% 0.14/0.71 fof(f42,plain,(
% 0.14/0.71 ![X0,X1]: (subgroup_member(element_in_O2(X0,X1))|subgroup_member(X1)|subgroup_member(X0))),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f41])).
% 0.14/0.71 fof(f43,plain,(
% 0.14/0.71 ![A]: ((![B]: (product(A,element_in_O2(A,B),B)|subgroup_member(B)))|subgroup_member(A))),
% 0.14/0.71 inference(miniscoping,[status(thm)],[f15])).
% 0.14/0.71 fof(f44,plain,(
% 0.14/0.71 ![X0,X1]: (product(X0,element_in_O2(X0,X1),X1)|subgroup_member(X1)|subgroup_member(X0))),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/0.71 fof(f45,plain,(
% 0.14/0.71 ~subgroup_member(a)),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f16])).
% 0.14/0.71 fof(f46,plain,(
% 0.14/0.71 subgroup_member(b)),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/0.71 fof(f47,plain,(
% 0.14/0.71 ~subgroup_member(d)),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f18])).
% 0.14/0.71 fof(f48,plain,(
% 0.14/0.71 product(b,inverse(a),c)),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/0.71 fof(f49,plain,(
% 0.14/0.71 product(a,c,d)),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f20])).
% 0.14/0.71 fof(f50,plain,(
% 0.14/0.71 ![X0]: (inverse(inverse(X0))=X0)),
% 0.14/0.71 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/0.71 fof(f52,plain,(
% 0.14/0.71 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(inverse(X1))|~product(X0,X1,X2)|subgroup_member(X2))),
% 0.14/0.71 inference(paramodulation,[status(thm)],[f50,f34])).
% 0.14/0.71 fof(f61,plain,(
% 0.14/0.71 subgroup_member(inverse(b))),
% 0.14/0.71 inference(resolution,[status(thm)],[f46,f36])).
% 0.14/0.71 fof(f68,plain,(
% 0.14/0.71 ![X0]: (product(X0,inverse(X0),identity))),
% 0.14/0.71 inference(paramodulation,[status(thm)],[f50,f24])).
% 0.14/0.71 fof(f79,plain,(
% 0.14/0.71 ![X0,X1]: (~subgroup_member(X0)|~subgroup_member(inverse(X1))|subgroup_member(multiply(X0,X1)))),
% 0.14/0.71 inference(resolution,[status(thm)],[f26,f52])).
% 0.14/0.71 fof(f157,plain,(
% 0.14/0.71 ![X0,X1]: (~product(X0,identity,X1)|X0=X1)),
% 0.14/0.71 inference(resolution,[status(thm)],[f28,f23])).
% 0.14/0.71 fof(f185,plain,(
% 0.14/0.71 ![X0,X1,X2]: (~product(inverse(a),X0,X1)|~product(c,X0,X2)|product(b,X1,X2))),
% 0.14/0.71 inference(resolution,[status(thm)],[f30,f48])).
% 0.14/0.71 fof(f189,plain,(
% 0.14/0.71 ![X0,X1,X2,X3]: (~product(inverse(X0),X1,X2)|~product(identity,X1,X3)|product(X0,X2,X3))),
% 0.14/0.71 inference(resolution,[status(thm)],[f30,f68])).
% 0.14/0.71 fof(f200,plain,(
% 0.14/0.71 ![X0]: (~product(a,X0,d)|X0=c)),
% 0.14/0.71 inference(resolution,[status(thm)],[f38,f49])).
% 0.14/0.71 fof(f205,plain,(
% 0.14/0.71 ![X0,X1,X2]: (~product(X0,X1,multiply(X0,X2))|X1=X2)),
% 0.14/0.71 inference(resolution,[status(thm)],[f38,f26])).
% 0.14/0.71 fof(f240,plain,(
% 0.14/0.71 ![X0,X1,X2]: (~product(identity,X0,X1)|product(X2,multiply(inverse(X2),X0),X1))),
% 0.14/0.71 inference(resolution,[status(thm)],[f189,f26])).
% 0.14/0.71 fof(f349,plain,(
% 0.14/0.71 subgroup_member(d)|subgroup_member(a)|element_in_O2(a,d)=c),
% 0.14/0.71 inference(resolution,[status(thm)],[f44,f200])).
% 0.14/0.71 fof(f363,plain,(
% 0.14/0.71 subgroup_member(a)|element_in_O2(a,d)=c),
% 0.14/0.71 inference(forward_subsumption_resolution,[status(thm)],[f349,f47])).
% 0.14/0.71 fof(f367,plain,(
% 0.14/0.71 ![X0]: (~product(c,inverse(inverse(a)),X0)|product(b,identity,X0))),
% 0.14/0.71 inference(resolution,[status(thm)],[f185,f68])).
% 0.14/0.71 fof(f370,plain,(
% 0.14/0.71 ![X0]: (~product(c,a,X0)|product(b,identity,X0))),
% 0.14/0.71 inference(forward_demodulation,[status(thm)],[f50,f367])).
% 0.14/0.71 fof(f396,plain,(
% 0.14/0.71 product(b,identity,multiply(c,a))),
% 0.14/0.71 inference(resolution,[status(thm)],[f370,f26])).
% 0.14/0.71 fof(f399,plain,(
% 0.14/0.71 b=multiply(c,a)),
% 0.14/0.71 inference(resolution,[status(thm)],[f396,f157])).
% 0.14/0.71 fof(f419,plain,(
% 0.14/0.71 ![X0]: (~product(c,X0,b)|X0=a)),
% 0.14/0.71 inference(paramodulation,[status(thm)],[f399,f205])).
% 0.14/0.71 fof(f504,plain,(
% 0.14/0.71 element_in_O2(a,d)=c),
% 0.14/0.71 inference(forward_subsumption_resolution,[status(thm)],[f363,f45])).
% 0.14/0.71 fof(f507,plain,(
% 0.14/0.71 subgroup_member(c)|subgroup_member(d)|subgroup_member(a)),
% 0.14/0.71 inference(paramodulation,[status(thm)],[f504,f42])).
% 0.14/0.71 fof(f509,plain,(
% 0.14/0.71 subgroup_member(c)|subgroup_member(a)),
% 0.14/0.71 inference(forward_subsumption_resolution,[status(thm)],[f507,f47])).
% 0.14/0.71 fof(f510,plain,(
% 0.14/0.71 subgroup_member(c)),
% 0.14/0.71 inference(forward_subsumption_resolution,[status(thm)],[f509,f45])).
% 0.14/0.71 fof(f516,plain,(
% 0.14/0.71 subgroup_member(inverse(c))),
% 0.14/0.71 inference(resolution,[status(thm)],[f510,f36])).
% 0.14/0.71 fof(f522,plain,(
% 0.14/0.71 ![X0]: (~subgroup_member(inverse(X0))|subgroup_member(multiply(inverse(c),X0)))),
% 0.14/0.71 inference(resolution,[status(thm)],[f516,f79])).
% 0.14/0.71 fof(f1018,plain,(
% 0.14/0.71 subgroup_member(multiply(inverse(c),b))),
% 0.14/0.71 inference(resolution,[status(thm)],[f522,f61])).
% 0.14/0.71 fof(f1305,plain,(
% 0.14/0.71 ![X0,X1]: (product(X0,multiply(inverse(X0),X1),X1))),
% 0.14/0.71 inference(resolution,[status(thm)],[f240,f22])).
% 0.14/0.71 fof(f1315,plain,(
% 0.14/0.71 multiply(inverse(c),b)=a),
% 0.14/0.71 inference(resolution,[status(thm)],[f1305,f419])).
% 0.14/0.71 fof(f1367,plain,(
% 0.14/0.71 subgroup_member(a)),
% 0.14/0.71 inference(backward_demodulation,[status(thm)],[f1315,f1018])).
% 0.14/0.71 fof(f1373,plain,(
% 0.14/0.71 $false),
% 0.14/0.71 inference(forward_subsumption_resolution,[status(thm)],[f1367,f45])).
% 0.14/0.71 % SZS output end CNFRefutation for theBenchmark.p
% 1.26/0.76 % Elapsed time: 0.290141 seconds
% 1.26/0.76 % CPU time: 1.631881 seconds
% 1.26/0.76 % Total memory used: 112.781 MB
% 1.26/0.76 % Net memory used: 110.121 MB
%------------------------------------------------------------------------------