%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO012-1 : 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 : 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 12:06:44 PM UTC 2026
% Result : Unsatisfiable 24.30s 3.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:49:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 24.30/3.52 % Refutation found
% 24.30/3.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 24.30/3.52 % SZS output start CNFRefutation for theBenchmark
% 24.30/3.52 fof(f2,axiom,(
% 24.30/3.52 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f4,axiom,(
% 24.30/3.52 (![X,Y,Z]: (( ~ product(X,Y,Z)| product(Y,X,Z) ) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f5,axiom,(
% 24.30/3.52 (![X]: (sum(additive_identity,X,X) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f8,axiom,(
% 24.30/3.52 (![X]: (product(X,multiplicative_identity,X) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f9,axiom,(
% 24.30/3.52 (![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) ) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f10,axiom,(
% 24.30/3.52 (![X,Y,V1,Z,V2,V3,V4]: (( ~ product(X,Y,V1)| ~ product(X,Z,V2)| ~ sum(Y,Z,V3)| ~ sum(V1,V2,V4)| product(X,V3,V4) ) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f14,axiom,(
% 24.30/3.52 (![X,Y,V1,Z,V2,V3,V4]: (( ~ sum(X,Y,V1)| ~ sum(X,Z,V2)| ~ product(Y,Z,V3)| ~ product(V1,V2,V4)| sum(X,V3,V4) ) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f17,axiom,(
% 24.30/3.52 (![X]: (sum(inverse(X),X,multiplicative_identity) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f18,axiom,(
% 24.30/3.52 (![X]: (sum(X,inverse(X),multiplicative_identity) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f19,axiom,(
% 24.30/3.52 (![X]: (product(inverse(X),X,additive_identity) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f20,axiom,(
% 24.30/3.52 (![X]: (product(X,inverse(X),additive_identity) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f21,axiom,(
% 24.30/3.52 (![X,Y,U,V]: (( ~ sum(X,Y,U)| ~ sum(X,Y,V)| U = V ) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f22,axiom,(
% 24.30/3.52 (![X,Y,U,V]: (( ~ product(X,Y,U)| ~ product(X,Y,V)| U = V ) ))),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f23,negated_conjecture,(
% 24.30/3.52 inverse(inverse(x)) != x ),
% 24.30/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 24.30/3.52 fof(f25,plain,(
% 24.30/3.52 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 24.30/3.52 inference(cnf_transformation,[status(thm)],[f2])).
% 24.30/3.52 fof(f27,plain,(
% 24.30/3.52 ![X0,X1,X2]: (~product(X0,X1,X2)|product(X1,X0,X2))),
% 24.30/3.52 inference(cnf_transformation,[status(thm)],[f4])).
% 24.30/3.52 fof(f28,plain,(
% 24.30/3.52 ![X0]: (sum(additive_identity,X0,X0))),
% 24.30/3.52 inference(cnf_transformation,[status(thm)],[f5])).
% 24.30/3.52 fof(f31,plain,(
% 24.30/3.52 ![X0]: (product(X0,multiplicative_identity,X0))),
% 24.30/3.52 inference(cnf_transformation,[status(thm)],[f8])).
% 24.30/3.52 fof(f32,plain,(
% 24.30/3.52 ![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))),
% 24.30/3.52 inference(miniscoping,[status(thm)],[f9])).
% 24.30/3.52 fof(f33,plain,(
% 24.30/3.52 ![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))),
% 24.30/3.52 inference(cnf_transformation,[status(thm)],[f32])).
% 24.30/3.52 fof(f34,plain,(
% 24.30/3.52 ![X,V3,V4]: ((![V1,V2]: ((![Y,Z]: ((~product(X,Y,V1)|~product(X,Z,V2))|~sum(Y,Z,V3)))|~sum(V1,V2,V4)))|product(X,V3,V4))),
% 24.30/3.52 inference(miniscoping,[status(thm)],[f10])).
% 24.30/3.52 fof(f35,plain,(
% 24.30/3.52 ![X0,X1,X2,X3,X4,X5,X6]: (~product(X0,X1,X2)|~product(X0,X3,X4)|~sum(X1,X3,X5)|~sum(X2,X4,X6)|product(X0,X5,X6))),
% 24.30/3.52 inference(cnf_transformation,[status(thm)],[f34])).
% 24.30/3.52 fof(f42,plain,(
% 24.30/3.52 ![X,V3,V4]: ((![V1,V2]: ((![Y,Z]: ((~sum(X,Y,V1)|~sum(X,Z,V2))|~product(Y,Z,V3)))|~product(V1,V2,V4)))|sum(X,V3,V4))),
% 24.30/3.52 inference(miniscoping,[status(thm)],[f14])).
% 24.30/3.52 fof(f43,plain,(
% 24.30/3.52 ![X0,X1,X2,X3,X4,X5,X6]: (~sum(X0,X1,X2)|~sum(X0,X3,X4)|~product(X1,X3,X5)|~product(X2,X4,X6)|sum(X0,X5,X6))),
% 24.30/3.52 inference(cnf_transformation,[status(thm)],[f42])).
% 24.30/3.52 fof(f48,plain,(
% 24.30/3.52 ![X0]: (sum(inverse(X0),X0,multiplicative_identity))),
% 24.30/3.52 inference(cnf_transformation,[status(thm)],[f17])).
% 24.30/3.52 fof(f49,plain,(
% 24.30/3.52 ![X0]: (sum(X0,inverse(X0),multiplicative_identity))),
% 24.30/3.52 inference(cnf_transformation,[status(thm)],[f18])).
% 24.30/3.52 fof(f50,plain,(
% 24.30/3.52 ![X0]: (product(inverse(X0),X0,additive_identity))),
% 24.30/3.53 inference(cnf_transformation,[status(thm)],[f19])).
% 24.30/3.53 fof(f51,plain,(
% 24.30/3.53 ![X0]: (product(X0,inverse(X0),additive_identity))),
% 24.30/3.53 inference(cnf_transformation,[status(thm)],[f20])).
% 24.30/3.53 fof(f52,plain,(
% 24.30/3.53 ![U,V]: ((![X,Y]: (~sum(X,Y,U)|~sum(X,Y,V)))|U=V)),
% 24.30/3.53 inference(miniscoping,[status(thm)],[f21])).
% 24.30/3.53 fof(f53,plain,(
% 24.30/3.53 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|X2=X3)),
% 24.30/3.53 inference(cnf_transformation,[status(thm)],[f52])).
% 24.30/3.53 fof(f54,plain,(
% 24.30/3.53 ![U,V]: ((![X,Y]: (~product(X,Y,U)|~product(X,Y,V)))|U=V)),
% 24.30/3.53 inference(miniscoping,[status(thm)],[f22])).
% 24.30/3.53 fof(f55,plain,(
% 24.30/3.53 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 24.30/3.53 inference(cnf_transformation,[status(thm)],[f54])).
% 24.30/3.53 fof(f56,plain,(
% 24.30/3.53 ~inverse(inverse(x))=x),
% 24.30/3.53 inference(cnf_transformation,[status(thm)],[f23])).
% 24.30/3.53 fof(f62,plain,(
% 24.30/3.53 ![X0,X1]: (product(X0,X1,multiply(X1,X0)))),
% 24.30/3.53 inference(resolution,[status(thm)],[f27,f25])).
% 24.30/3.53 fof(f71,plain,(
% 24.30/3.53 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~sum(inverse(X0),X1,X3)|~product(X0,X3,X4)|sum(additive_identity,X2,X4))),
% 24.30/3.54 inference(resolution,[status(thm)],[f33,f51])).
% 24.30/3.54 fof(f75,plain,(
% 24.30/3.54 ![X0,X1,X2,X3,X4]: (~product(inverse(X0),X1,X2)|~sum(X0,X1,X3)|~sum(additive_identity,X2,X4)|product(inverse(X0),X3,X4))),
% 24.30/3.54 inference(resolution,[status(thm)],[f35,f50])).
% 24.30/3.54 fof(f117,plain,(
% 24.30/3.54 ![X0,X1,X2,X3,X4]: (~sum(additive_identity,X0,X1)|~product(X2,X0,X3)|~product(X2,X1,X4)|sum(additive_identity,X3,X4))),
% 24.30/3.54 inference(resolution,[status(thm)],[f43,f28])).
% 24.30/3.54 fof(f166,plain,(
% 24.30/3.54 ![X0,X1]: (~product(X0,multiplicative_identity,X1)|X0=X1)),
% 24.30/3.54 inference(resolution,[status(thm)],[f55,f31])).
% 24.30/3.54 fof(f220,plain,(
% 24.30/3.54 ![X0,X1,X2,X3]: (~sum(inverse(X0),X1,X2)|~product(X0,X2,X3)|sum(additive_identity,multiply(X1,X0),X3))),
% 24.30/3.54 inference(resolution,[status(thm)],[f71,f62])).
% 24.30/3.54 fof(f289,plain,(
% 24.30/3.54 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(additive_identity,multiply(X1,inverse(X0)),X3)|product(inverse(X0),X2,X3))),
% 24.30/3.54 inference(resolution,[status(thm)],[f75,f62])).
% 24.30/3.54 fof(f893,plain,(
% 24.30/3.54 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|sum(additive_identity,X2,X3))),
% 24.30/3.54 inference(resolution,[status(thm)],[f117,f28])).
% 24.30/3.54 fof(f1095,plain,(
% 24.30/3.54 ![X0,X1,X2]: (~product(X0,X1,X2)|sum(additive_identity,multiply(X1,X0),X2))),
% 24.30/3.54 inference(resolution,[status(thm)],[f893,f62])).
% 24.30/3.54 fof(f1122,plain,(
% 24.30/3.54 ![X0,X1]: (sum(additive_identity,multiply(X0,X1),multiply(X1,X0)))),
% 24.30/3.54 inference(resolution,[status(thm)],[f1095,f25])).
% 24.30/3.54 fof(f1179,plain,(
% 24.30/3.54 ![X0,X1,X2]: (~sum(additive_identity,multiply(X0,X1),X2)|multiply(X1,X0)=X2)),
% 24.30/3.54 inference(resolution,[status(thm)],[f1122,f53])).
% 24.30/3.54 fof(f1851,plain,(
% 24.30/3.54 ![X0,X1]: (~product(X0,multiplicative_identity,X1)|sum(additive_identity,multiply(inverse(inverse(X0)),X0),X1))),
% 24.30/3.54 inference(resolution,[status(thm)],[f220,f49])).
% 24.30/3.54 fof(f2419,plain,(
% 24.30/3.54 ![X0,X1]: (~sum(additive_identity,multiply(X0,inverse(inverse(X0))),X1)|product(inverse(inverse(X0)),multiplicative_identity,X1))),
% 24.30/3.54 inference(resolution,[status(thm)],[f289,f48])).
% 24.30/3.54 fof(f11916,plain,(
% 24.30/3.54 ![X0]: (sum(additive_identity,multiply(inverse(inverse(X0)),X0),X0))),
% 24.30/3.54 inference(resolution,[status(thm)],[f1851,f31])).
% 24.30/3.54 fof(f13686,plain,(
% 24.30/3.54 ![X0]: (multiply(X0,inverse(inverse(X0)))=X0)),
% 24.30/3.54 inference(resolution,[status(thm)],[f11916,f1179])).
% 24.30/3.54 fof(f14509,plain,(
% 24.30/3.54 ![X0,X1]: (~sum(additive_identity,X0,X1)|product(inverse(inverse(X0)),multiplicative_identity,X1))),
% 24.30/3.54 inference(forward_demodulation,[status(thm)],[f13686,f2419])).
% 24.30/3.54 fof(f14512,plain,(
% 24.30/3.54 ![X0]: (product(inverse(inverse(X0)),multiplicative_identity,X0))),
% 24.30/3.54 inference(resolution,[status(thm)],[f14509,f28])).
% 24.30/3.54 fof(f14552,plain,(
% 24.30/3.54 ![X0]: (inverse(inverse(X0))=X0)),
% 24.30/3.54 inference(resolution,[status(thm)],[f14512,f166])).
% 24.30/3.54 fof(f14666,plain,(
% 24.30/3.54 ~x=x),
% 24.30/3.54 inference(backward_demodulation,[status(thm)],[f14552,f56])).
% 24.30/3.54 fof(f14813,plain,(
% 24.30/3.54 $false),
% 24.30/3.54 inference(trivial_equality_resolution,[status(thm)],[f14666])).
% 24.30/3.54 % SZS output end CNFRefutation for theBenchmark.p
% 24.30/3.55 % Elapsed time: 3.164308 seconds
% 24.30/3.55 % CPU time: 24.654080 seconds
% 24.30/3.55 % Total memory used: 93.269 MB
% 24.30/3.55 % Net memory used: 83.038 MB
%------------------------------------------------------------------------------