%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO006-1 : 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 : n026.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 12:06:42 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.70s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n026.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 13:50:06 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.70 % Refutation found
% 0.17/0.70 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.70 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.70 fof(f2,axiom,(
% 0.17/0.70 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 0.17/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.70 fof(f4,axiom,(
% 0.17/0.70 (![X,Y,Z]: (( ~ product(X,Y,Z)| product(Y,X,Z) ) ))),
% 0.17/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.70 fof(f5,axiom,(
% 0.17/0.70 (![X]: (sum(additive_identity,X,X) ))),
% 0.17/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.70 fof(f6,axiom,(
% 0.17/0.70 (![X]: (sum(X,additive_identity,X) ))),
% 0.17/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.70 fof(f9,axiom,(
% 0.17/0.70 (![X,Y,V1,Z,V2,V3,V4]: (( ~ product(X,Y,V1)| ~ product(X,Z,V2)| ~ sum(Y,Z,V3)| ~ product(X,V3,V4)| sum(V1,V2,V4) ) ))),
% 0.17/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.70 fof(f20,axiom,(
% 0.17/0.70 (![X]: (product(X,inverse(X),additive_identity) ))),
% 0.17/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.70 fof(f21,axiom,(
% 0.17/0.70 (![X,Y,U,V]: (( ~ sum(X,Y,U)| ~ sum(X,Y,V)| U = V ) ))),
% 0.17/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.70 fof(f22,axiom,(
% 0.17/0.70 (![X,Y,U,V]: (( ~ product(X,Y,U)| ~ product(X,Y,V)| U = V ) ))),
% 0.17/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.70 fof(f23,negated_conjecture,(
% 0.17/0.70 ~ product(x,additive_identity,additive_identity) ),
% 0.17/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.70 fof(f25,plain,(
% 0.17/0.70 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 0.17/0.70 inference(cnf_transformation,[status(thm)],[f2])).
% 0.17/0.70 fof(f27,plain,(
% 0.17/0.70 ![X0,X1,X2]: (~product(X0,X1,X2)|product(X1,X0,X2))),
% 0.17/0.70 inference(cnf_transformation,[status(thm)],[f4])).
% 0.17/0.70 fof(f28,plain,(
% 0.17/0.70 ![X0]: (sum(additive_identity,X0,X0))),
% 0.17/0.70 inference(cnf_transformation,[status(thm)],[f5])).
% 0.17/0.70 fof(f29,plain,(
% 0.17/0.70 ![X0]: (sum(X0,additive_identity,X0))),
% 0.17/0.70 inference(cnf_transformation,[status(thm)],[f6])).
% 0.17/0.70 fof(f32,plain,(
% 0.17/0.70 ![V1,V2,V4]: ((![X,V3]: ((![Y,Z]: ((~product(X,Y,V1)|~product(X,Z,V2))|~sum(Y,Z,V3)))|~product(X,V3,V4)))|sum(V1,V2,V4))),
% 0.17/0.70 inference(miniscoping,[status(thm)],[f9])).
% 0.17/0.70 fof(f33,plain,(
% 0.17/0.70 ![X0,X1,X2,X3,X4,X5,X6]: (~product(X0,X1,X2)|~product(X0,X3,X4)|~sum(X1,X3,X5)|~product(X0,X5,X6)|sum(X2,X4,X6))),
% 0.17/0.70 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.70 fof(f51,plain,(
% 0.17/0.70 ![X0]: (product(X0,inverse(X0),additive_identity))),
% 0.17/0.70 inference(cnf_transformation,[status(thm)],[f20])).
% 0.17/0.70 fof(f52,plain,(
% 0.17/0.70 ![U,V]: ((![X,Y]: (~sum(X,Y,U)|~sum(X,Y,V)))|U=V)),
% 0.17/0.70 inference(miniscoping,[status(thm)],[f21])).
% 0.17/0.70 fof(f53,plain,(
% 0.17/0.70 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|X2=X3)),
% 0.17/0.70 inference(cnf_transformation,[status(thm)],[f52])).
% 0.17/0.70 fof(f54,plain,(
% 0.17/0.70 ![U,V]: ((![X,Y]: (~product(X,Y,U)|~product(X,Y,V)))|U=V)),
% 0.17/0.70 inference(miniscoping,[status(thm)],[f22])).
% 0.17/0.70 fof(f55,plain,(
% 0.17/0.70 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.17/0.70 inference(cnf_transformation,[status(thm)],[f54])).
% 0.17/0.70 fof(f56,plain,(
% 0.17/0.70 ~product(x,additive_identity,additive_identity)),
% 0.17/0.70 inference(cnf_transformation,[status(thm)],[f23])).
% 0.17/0.70 fof(f60,plain,(
% 0.17/0.70 ![X0,X1]: (~sum(additive_identity,X0,X1)|X1=X0)),
% 0.17/0.70 inference(resolution,[status(thm)],[f53,f28])).
% 0.17/0.70 fof(f74,plain,(
% 0.17/0.70 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,additive_identity)|~product(X0,X2,X3)|~sum(X1,X2,X4)|~product(X0,X4,X5)|X5=X3)),
% 0.17/0.70 inference(resolution,[status(thm)],[f33,f60])).
% 0.17/0.70 fof(f164,plain,(
% 0.17/0.70 ![X0,X1,X2]: (~product(X0,X1,X2)|X2=multiply(X0,X1))),
% 0.17/0.70 inference(resolution,[status(thm)],[f55,f25])).
% 0.17/0.70 fof(f244,plain,(
% 0.17/0.70 ![X0,X1,X2]: (X0=multiply(X1,X2)|~product(X2,X1,X0))),
% 0.17/0.70 inference(resolution,[status(thm)],[f164,f27])).
% 0.17/0.70 fof(f249,plain,(
% 0.17/0.70 ![X0,X1]: (multiply(X0,X1)=multiply(X1,X0))),
% 0.17/0.70 inference(resolution,[status(thm)],[f244,f25])).
% 0.17/0.70 fof(f267,plain,(
% 0.17/0.70 ![X0,X1]: (product(X0,X1,multiply(X1,X0)))),
% 0.17/0.70 inference(paramodulation,[status(thm)],[f249,f25])).
% 0.17/0.70 fof(f317,plain,(
% 0.17/0.70 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~sum(inverse(X0),X1,X3)|~product(X0,X3,X4)|X4=X2)),
% 0.17/0.70 inference(resolution,[status(thm)],[f74,f51])).
% 0.17/0.70 fof(f326,plain,(
% 0.17/0.70 ![X0,X1,X2]: (~product(X0,additive_identity,X1)|~product(X0,inverse(X0),X2)|X2=X1)),
% 0.17/0.70 inference(resolution,[status(thm)],[f317,f29])).
% 0.17/0.70 fof(f441,plain,(
% 0.17/0.71 ![X0,X1]: (~product(X0,inverse(X0),X1)|X1=multiply(additive_identity,X0))),
% 0.17/0.71 inference(resolution,[status(thm)],[f326,f267])).
% 0.17/0.71 fof(f455,plain,(
% 0.17/0.71 ![X0]: (additive_identity=multiply(additive_identity,X0))),
% 0.17/0.71 inference(resolution,[status(thm)],[f441,f51])).
% 0.17/0.71 fof(f479,plain,(
% 0.17/0.71 ![X0]: (product(X0,additive_identity,additive_identity))),
% 0.17/0.71 inference(paramodulation,[status(thm)],[f455,f267])).
% 0.17/0.71 fof(f509,plain,(
% 0.17/0.71 $false),
% 0.17/0.71 inference(backward_subsumption_resolution,[status(thm)],[f56,f479])).
% 0.17/0.71 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.74 % Elapsed time: 0.282038 seconds
% 0.17/0.74 % CPU time: 1.755758 seconds
% 0.17/0.74 % Total memory used: 51.784 MB
% 0.17/0.74 % Net memory used: 50.262 MB
%------------------------------------------------------------------------------