%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP012-1 : 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 : n002.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 12:35:26 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:56:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.39 fof(f1,axiom,(
% 0.12/0.39 (![X]: (product(identity,X,X) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f2,axiom,(
% 0.12/0.39 (![X]: (product(X,identity,X) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f3,axiom,(
% 0.12/0.39 (![X]: (product(inverse(X),X,identity) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f4,axiom,(
% 0.12/0.39 (![X]: (product(X,inverse(X),identity) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f5,axiom,(
% 0.12/0.39 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f6,axiom,(
% 0.12/0.39 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f7,axiom,(
% 0.12/0.39 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W)| product(X,V,W) ) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f8,axiom,(
% 0.12/0.39 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(X,V,W)| product(U,Z,W) ) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f9,hypothesis,(
% 0.12/0.39 product(a,b,c) ),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f10,hypothesis,(
% 0.12/0.39 product(inverse(b),inverse(a),d) ),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f11,negated_conjecture,(
% 0.12/0.39 ~ product(c,d,identity) ),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f12,plain,(
% 0.12/0.39 ![X0]: (product(identity,X0,X0))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.39 fof(f13,plain,(
% 0.12/0.39 ![X0]: (product(X0,identity,X0))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.39 fof(f14,plain,(
% 0.12/0.39 ![X0]: (product(inverse(X0),X0,identity))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.39 fof(f15,plain,(
% 0.12/0.39 ![X0]: (product(X0,inverse(X0),identity))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.39 fof(f16,plain,(
% 0.12/0.39 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.39 fof(f17,plain,(
% 0.12/0.39 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f6])).
% 0.12/0.39 fof(f18,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.39 fof(f19,plain,(
% 0.12/0.39 ![X,V,W]: ((![U,Z]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f7])).
% 0.12/0.39 fof(f20,plain,(
% 0.12/0.39 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.12/0.39 fof(f21,plain,(
% 0.12/0.39 ![U,Z,W]: ((![X,V]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(X,V,W)))|product(U,Z,W))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f8])).
% 0.12/0.39 fof(f22,plain,(
% 0.12/0.39 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X0,X4,X5)|product(X2,X3,X5))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f21])).
% 0.12/0.39 fof(f23,plain,(
% 0.12/0.39 product(a,b,c)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.12/0.39 fof(f24,plain,(
% 0.12/0.39 product(inverse(b),inverse(a),d)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.12/0.39 fof(f25,plain,(
% 0.12/0.39 ~product(c,d,identity)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.12/0.39 fof(f27,plain,(
% 0.12/0.39 ![X0,X1]: (~product(identity,X0,X1)|X0=X1)),
% 0.12/0.39 inference(resolution,[status(thm)],[f18,f12])).
% 0.12/0.39 fof(f33,plain,(
% 0.12/0.39 ![X0,X1,X2]: (~product(b,X0,X1)|~product(c,X0,X2)|product(a,X1,X2))),
% 0.12/0.39 inference(resolution,[status(thm)],[f20,f23])).
% 0.12/0.39 fof(f40,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(inverse(X0),X2,X3)|product(identity,X1,X3))),
% 0.12/0.39 inference(resolution,[status(thm)],[f14,f22])).
% 0.12/0.39 fof(f41,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(identity,X1,X3)|product(inverse(X0),X2,X3))),
% 0.12/0.39 inference(resolution,[status(thm)],[f14,f20])).
% 0.12/0.39 fof(f47,plain,(
% 0.12/0.39 ![X0,X1]: (~product(X0,inverse(X0),X1)|identity=X1)),
% 0.12/0.39 inference(resolution,[status(thm)],[f15,f18])).
% 0.12/0.39 fof(f53,plain,(
% 0.12/0.39 ![X0,X1,X2]: (~product(X0,X1,X2)|multiply(X0,X1)=X2)),
% 0.12/0.41 inference(resolution,[status(thm)],[f16,f18])).
% 0.12/0.41 fof(f65,plain,(
% 0.12/0.41 ![X0,X1]: (~product(c,X0,X1)|product(a,multiply(b,X0),X1))),
% 0.12/0.41 inference(resolution,[status(thm)],[f33,f16])).
% 0.12/0.41 fof(f84,plain,(
% 0.12/0.41 ![X0]: (identity=multiply(X0,inverse(X0)))),
% 0.12/0.41 inference(resolution,[status(thm)],[f47,f16])).
% 0.12/0.41 fof(f137,plain,(
% 0.12/0.41 ![X0,X1]: (~product(inverse(inverse(X0)),identity,X1)|product(identity,X0,X1))),
% 0.12/0.41 inference(resolution,[status(thm)],[f40,f14])).
% 0.12/0.41 fof(f155,plain,(
% 0.12/0.41 ![X0]: (~product(identity,inverse(a),X0)|product(inverse(inverse(b)),d,X0))),
% 0.12/0.41 inference(resolution,[status(thm)],[f41,f24])).
% 0.12/0.41 fof(f271,plain,(
% 0.12/0.41 ![X0]: (product(a,multiply(b,X0),multiply(c,X0)))),
% 0.12/0.41 inference(resolution,[status(thm)],[f65,f16])).
% 0.12/0.41 fof(f321,plain,(
% 0.12/0.41 ![X0]: (multiply(a,multiply(b,X0))=multiply(c,X0))),
% 0.12/0.41 inference(resolution,[status(thm)],[f271,f53])).
% 0.12/0.41 fof(f358,plain,(
% 0.12/0.41 ![X0]: (product(identity,X0,inverse(inverse(X0))))),
% 0.12/0.41 inference(resolution,[status(thm)],[f137,f13])).
% 0.12/0.41 fof(f370,plain,(
% 0.12/0.41 ![X0]: (X0=inverse(inverse(X0)))),
% 0.12/0.41 inference(resolution,[status(thm)],[f358,f27])).
% 0.12/0.41 fof(f444,plain,(
% 0.12/0.41 ![X0]: (~product(identity,inverse(a),X0)|product(b,d,X0))),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f370,f155])).
% 0.12/0.41 fof(f445,plain,(
% 0.12/0.41 product(b,d,inverse(a))),
% 0.12/0.41 inference(resolution,[status(thm)],[f444,f12])).
% 0.12/0.41 fof(f461,plain,(
% 0.12/0.41 multiply(b,d)=inverse(a)),
% 0.12/0.41 inference(resolution,[status(thm)],[f445,f53])).
% 0.12/0.41 fof(f494,plain,(
% 0.12/0.41 multiply(a,inverse(a))=multiply(c,d)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f461,f321])).
% 0.12/0.41 fof(f500,plain,(
% 0.12/0.41 identity=multiply(c,d)),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f84,f494])).
% 0.12/0.41 fof(f505,plain,(
% 0.12/0.41 product(c,d,identity)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f500,f16])).
% 0.12/0.41 fof(f507,plain,(
% 0.12/0.41 $false),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f505,f25])).
% 0.12/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.41 % Elapsed time: 0.054683 seconds
% 0.12/0.41 % CPU time: 0.220381 seconds
% 0.12/0.41 % Total memory used: 45.460 MB
% 0.12/0.41 % Net memory used: 44.912 MB
%------------------------------------------------------------------------------