%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP012-2 : 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 : n003.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 0.14s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.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 19:55:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.40 fof(f1,axiom,(
% 0.14/0.40 (![X]: (product(identity,X,X) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f2,axiom,(
% 0.14/0.40 (![X]: (product(X,identity,X) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f3,axiom,(
% 0.14/0.40 (![X]: (product(inverse(X),X,identity) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f4,axiom,(
% 0.14/0.40 (![X]: (product(X,inverse(X),identity) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f5,axiom,(
% 0.14/0.40 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f6,axiom,(
% 0.14/0.40 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f7,axiom,(
% 0.14/0.40 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W)| product(X,V,W) ) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f9,hypothesis,(
% 0.14/0.40 product(a,b,c) ),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f10,hypothesis,(
% 0.14/0.40 product(inverse(b),inverse(a),d) ),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f11,negated_conjecture,(
% 0.14/0.40 inverse(c) != d ),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f12,plain,(
% 0.14/0.40 ![X0]: (product(identity,X0,X0))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.40 fof(f13,plain,(
% 0.14/0.40 ![X0]: (product(X0,identity,X0))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.40 fof(f14,plain,(
% 0.14/0.40 ![X0]: (product(inverse(X0),X0,identity))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.40 fof(f15,plain,(
% 0.14/0.40 ![X0]: (product(X0,inverse(X0),identity))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.40 fof(f16,plain,(
% 0.14/0.40 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/0.40 fof(f17,plain,(
% 0.14/0.40 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f6])).
% 0.14/0.40 fof(f18,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/0.40 fof(f19,plain,(
% 0.14/0.40 ![X,V,W]: ((![U,Z]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f7])).
% 0.14/0.40 fof(f20,plain,(
% 0.14/0.40 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/0.40 fof(f23,plain,(
% 0.14/0.40 product(a,b,c)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f9])).
% 0.14/0.40 fof(f24,plain,(
% 0.14/0.40 product(inverse(b),inverse(a),d)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/0.40 fof(f25,plain,(
% 0.14/0.40 ~inverse(c)=d),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f11])).
% 0.14/0.40 fof(f30,plain,(
% 0.14/0.40 ![X0,X1]: (~product(X0,inverse(X0),X1)|identity=X1)),
% 0.14/0.40 inference(resolution,[status(thm)],[f18,f15])).
% 0.14/0.40 fof(f31,plain,(
% 0.14/0.40 ![X0,X1]: (~product(X0,identity,X1)|X0=X1)),
% 0.14/0.40 inference(resolution,[status(thm)],[f18,f13])).
% 0.14/0.40 fof(f32,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~product(X0,X1,X2)|multiply(X0,X1)=X2)),
% 0.14/0.40 inference(resolution,[status(thm)],[f18,f16])).
% 0.14/0.40 fof(f43,plain,(
% 0.14/0.40 ![X0]: (X0=multiply(X0,identity))),
% 0.14/0.40 inference(resolution,[status(thm)],[f31,f16])).
% 0.14/0.40 fof(f53,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(identity,X1,X3)|product(inverse(X0),X2,X3))),
% 0.14/0.40 inference(resolution,[status(thm)],[f20,f14])).
% 0.14/0.40 fof(f54,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~product(b,X0,X1)|~product(c,X0,X2)|product(a,X1,X2))),
% 0.14/0.40 inference(resolution,[status(thm)],[f20,f23])).
% 0.14/0.40 fof(f55,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~product(inverse(X0),X1,X2)|~product(identity,X1,X3)|product(X0,X2,X3))),
% 0.14/0.40 inference(resolution,[status(thm)],[f20,f15])).
% 0.14/0.40 fof(f84,plain,(
% 0.14/0.40 ![X0,X1]: (~product(c,X0,X1)|product(a,multiply(b,X0),X1))),
% 0.14/0.40 inference(resolution,[status(thm)],[f54,f16])).
% 0.14/0.40 fof(f95,plain,(
% 0.14/0.40 ![X0]: (identity=multiply(X0,inverse(X0)))),
% 0.14/0.40 inference(resolution,[status(thm)],[f30,f16])).
% 0.14/0.40 fof(f130,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~product(identity,X0,X1)|product(inverse(X2),multiply(X2,X0),X1))),
% 0.14/0.40 inference(resolution,[status(thm)],[f53,f16])).
% 0.14/0.41 fof(f131,plain,(
% 0.14/0.41 ![X0]: (~product(identity,inverse(a),X0)|product(b,d,X0))),
% 0.14/0.41 inference(resolution,[status(thm)],[f55,f24])).
% 0.14/0.41 fof(f214,plain,(
% 0.14/0.41 ![X0]: (product(a,multiply(b,X0),multiply(c,X0)))),
% 0.14/0.41 inference(resolution,[status(thm)],[f84,f16])).
% 0.14/0.41 fof(f235,plain,(
% 0.14/0.41 ![X0]: (multiply(a,multiply(b,X0))=multiply(c,X0))),
% 0.14/0.41 inference(resolution,[status(thm)],[f214,f32])).
% 0.14/0.41 fof(f440,plain,(
% 0.14/0.41 product(b,d,inverse(a))),
% 0.14/0.41 inference(resolution,[status(thm)],[f131,f12])).
% 0.14/0.41 fof(f452,plain,(
% 0.14/0.41 multiply(b,d)=inverse(a)),
% 0.14/0.41 inference(resolution,[status(thm)],[f440,f32])).
% 0.14/0.41 fof(f456,plain,(
% 0.14/0.41 multiply(a,inverse(a))=multiply(c,d)),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f452,f235])).
% 0.14/0.41 fof(f461,plain,(
% 0.14/0.41 identity=multiply(c,d)),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f95,f456])).
% 0.14/0.41 fof(f533,plain,(
% 0.14/0.41 ![X0,X1]: (product(inverse(X0),multiply(X0,X1),X1))),
% 0.14/0.41 inference(resolution,[status(thm)],[f130,f12])).
% 0.14/0.41 fof(f578,plain,(
% 0.14/0.41 ![X0,X1]: (multiply(inverse(X0),multiply(X0,X1))=X1)),
% 0.14/0.41 inference(resolution,[status(thm)],[f533,f32])).
% 0.14/0.41 fof(f606,plain,(
% 0.14/0.41 multiply(inverse(c),identity)=d),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f461,f578])).
% 0.14/0.41 fof(f624,plain,(
% 0.14/0.41 inverse(c)=d),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f43,f606])).
% 0.14/0.41 fof(f625,plain,(
% 0.14/0.41 $false),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f624,f25])).
% 0.14/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.42 % Elapsed time: 0.060234 seconds
% 0.14/0.42 % CPU time: 0.259855 seconds
% 0.14/0.42 % Total memory used: 40.602 MB
% 0.14/0.42 % Net memory used: 40.032 MB
%------------------------------------------------------------------------------