%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG001-4 : 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 : n019.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 02:05:05 PM UTC 2026
% Result : Unsatisfiable 13.68s 2.28s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 04:09:50 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 13.68/2.28 % Refutation found
% 13.68/2.28 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.68/2.28 % SZS output start CNFRefutation for theBenchmark
% 13.68/2.28 fof(f1,axiom,(
% 13.68/2.28 (![X]: (sum(additive_identity,X,X) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f2,axiom,(
% 13.68/2.28 (![X]: (sum(X,additive_identity,X) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f3,axiom,(
% 13.68/2.28 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f4,axiom,(
% 13.68/2.28 (![X,Y]: (sum(X,Y,add(X,Y)) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f5,axiom,(
% 13.68/2.28 (![X]: (sum(additive_inverse(X),X,additive_identity) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f7,axiom,(
% 13.68/2.28 (![X,Y,U,Z,V,W]: (( ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(U,Z,W)| sum(X,V,W) ) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f9,axiom,(
% 13.68/2.28 (![X,Y,Z]: (( ~ sum(X,Y,Z)| sum(Y,X,Z) ) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f12,axiom,(
% 13.68/2.28 (![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) ) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f13,axiom,(
% 13.68/2.28 (![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) ) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f14,axiom,(
% 13.68/2.28 (![Y,X,V1,Z,V2,V3,V4]: (( ~ product(Y,X,V1)| ~ product(Z,X,V2)| ~ sum(Y,Z,V3)| ~ product(V3,X,V4)| sum(V1,V2,V4) ) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f16,axiom,(
% 13.68/2.28 (![X,Y,U,V]: (( ~ sum(X,Y,U)| ~ sum(X,Y,V)| U = V ) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f19,axiom,(
% 13.68/2.28 (![X,Y,Z,W]: (( ~ sum(X,Y,Z)| ~ sum(W,Y,Z)| X = W ) ))),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f20,negated_conjecture,(
% 13.68/2.28 ~ product(a,additive_identity,additive_identity) ),
% 13.68/2.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.68/2.28 fof(f21,plain,(
% 13.68/2.28 ![X0]: (sum(additive_identity,X0,X0))),
% 13.68/2.28 inference(cnf_transformation,[status(thm)],[f1])).
% 13.68/2.28 fof(f22,plain,(
% 13.68/2.28 ![X0]: (sum(X0,additive_identity,X0))),
% 13.68/2.28 inference(cnf_transformation,[status(thm)],[f2])).
% 13.68/2.28 fof(f23,plain,(
% 13.68/2.28 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 13.68/2.28 inference(cnf_transformation,[status(thm)],[f3])).
% 13.68/2.28 fof(f24,plain,(
% 13.68/2.28 ![X0,X1]: (sum(X0,X1,add(X0,X1)))),
% 13.68/2.28 inference(cnf_transformation,[status(thm)],[f4])).
% 13.68/2.28 fof(f25,plain,(
% 13.68/2.28 ![X0]: (sum(additive_inverse(X0),X0,additive_identity))),
% 13.68/2.28 inference(cnf_transformation,[status(thm)],[f5])).
% 13.68/2.28 fof(f27,plain,(
% 13.68/2.28 ![X,V,W]: ((![U,Z]: ((![Y]: (~sum(X,Y,U)|~sum(Y,Z,V)))|~sum(U,Z,W)))|sum(X,V,W))),
% 13.68/2.28 inference(miniscoping,[status(thm)],[f7])).
% 13.68/2.28 fof(f28,plain,(
% 13.68/2.28 ![X0,X1,X2,X3,X4,X5]: (~sum(X0,X1,X2)|~sum(X1,X3,X4)|~sum(X2,X3,X5)|sum(X0,X4,X5))),
% 13.68/2.28 inference(cnf_transformation,[status(thm)],[f27])).
% 13.68/2.28 fof(f31,plain,(
% 13.68/2.28 ![X0,X1,X2]: (~sum(X0,X1,X2)|sum(X1,X0,X2))),
% 13.68/2.28 inference(cnf_transformation,[status(thm)],[f9])).
% 13.68/2.28 fof(f36,plain,(
% 13.68/2.28 ![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))),
% 13.68/2.28 inference(miniscoping,[status(thm)],[f12])).
% 13.68/2.28 fof(f37,plain,(
% 13.68/2.28 ![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))),
% 13.68/2.28 inference(cnf_transformation,[status(thm)],[f36])).
% 13.68/2.28 fof(f38,plain,(
% 13.68/2.28 ![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))),
% 13.68/2.28 inference(miniscoping,[status(thm)],[f13])).
% 13.68/2.28 fof(f39,plain,(
% 13.68/2.28 ![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))),
% 13.68/2.28 inference(cnf_transformation,[status(thm)],[f38])).
% 13.68/2.28 fof(f40,plain,(
% 13.68/2.28 ![V1,V2,V4]: ((![X,V3]: ((![Y,Z]: ((~product(Y,X,V1)|~product(Z,X,V2))|~sum(Y,Z,V3)))|~product(V3,X,V4)))|sum(V1,V2,V4))),
% 13.68/2.28 inference(miniscoping,[status(thm)],[f14])).
% 13.68/2.28 fof(f41,plain,(
% 13.68/2.28 ![X0,X1,X2,X3,X4,X5,X6]: (~product(X0,X1,X2)|~product(X3,X1,X4)|~sum(X0,X3,X5)|~product(X5,X1,X6)|sum(X2,X4,X6))),
% 13.68/2.29 inference(cnf_transformation,[status(thm)],[f40])).
% 13.68/2.29 fof(f44,plain,(
% 13.68/2.29 ![U,V]: ((![X,Y]: (~sum(X,Y,U)|~sum(X,Y,V)))|U=V)),
% 13.68/2.29 inference(miniscoping,[status(thm)],[f16])).
% 13.68/2.29 fof(f45,plain,(
% 13.68/2.29 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|X2=X3)),
% 13.68/2.29 inference(cnf_transformation,[status(thm)],[f44])).
% 13.68/2.29 fof(f50,plain,(
% 13.68/2.29 ![X,W]: ((![Y,Z]: (~sum(X,Y,Z)|~sum(W,Y,Z)))|X=W)),
% 13.68/2.29 inference(miniscoping,[status(thm)],[f19])).
% 13.68/2.29 fof(f51,plain,(
% 13.68/2.29 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X3,X1,X2)|X0=X3)),
% 13.68/2.29 inference(cnf_transformation,[status(thm)],[f50])).
% 13.68/2.29 fof(f52,plain,(
% 13.68/2.29 ~product(a,additive_identity,additive_identity)),
% 13.68/2.29 inference(cnf_transformation,[status(thm)],[f20])).
% 13.68/2.29 fof(f53,plain,(
% 13.68/2.29 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~sum(X3,X0,X4)|~product(X4,X1,X5)|sum(multiply(X3,X1),X2,X5))),
% 13.68/2.29 inference(resolution,[status(thm)],[f23,f41])).
% 13.68/2.29 fof(f54,plain,(
% 13.68/2.29 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~sum(X3,X1,X4)|~sum(multiply(X0,X3),X2,X5)|product(X0,X4,X5))),
% 13.68/2.29 inference(resolution,[status(thm)],[f23,f39])).
% 13.68/2.29 fof(f55,plain,(
% 13.68/2.29 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~sum(X3,X1,X4)|~product(X0,X4,X5)|sum(multiply(X0,X3),X2,X5))),
% 13.68/2.29 inference(resolution,[status(thm)],[f23,f37])).
% 13.68/2.29 fof(f63,plain,(
% 13.68/2.29 ![X0,X1]: (sum(X0,X1,add(X1,X0)))),
% 13.68/2.29 inference(resolution,[status(thm)],[f31,f24])).
% 13.68/2.29 fof(f66,plain,(
% 13.68/2.29 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|sum(additive_identity,X2,X3))),
% 13.68/2.29 inference(resolution,[status(thm)],[f28,f21])).
% 13.68/2.29 fof(f79,plain,(
% 13.68/2.29 ![X0,X1]: (~sum(additive_inverse(X0),X0,X1)|sum(additive_identity,additive_identity,X1))),
% 13.68/2.29 inference(resolution,[status(thm)],[f66,f25])).
% 13.68/2.29 fof(f85,plain,(
% 13.68/2.29 ![X0,X1,X2,X3,X4]: (~sum(X0,X1,X2)|~product(X2,X3,X4)|sum(multiply(X0,X3),multiply(X1,X3),X4))),
% 13.68/2.29 inference(resolution,[status(thm)],[f53,f23])).
% 13.68/2.29 fof(f87,plain,(
% 13.68/2.29 sum(additive_identity,additive_identity,additive_inverse(additive_identity))),
% 13.68/2.29 inference(resolution,[status(thm)],[f79,f22])).
% 13.68/2.29 fof(f102,plain,(
% 13.68/2.29 ![X0,X1,X2,X3,X4]: (~sum(X0,X1,X2)|~sum(multiply(X3,X0),multiply(X3,X1),X4)|product(X3,X2,X4))),
% 13.68/2.29 inference(resolution,[status(thm)],[f54,f23])).
% 13.68/2.29 fof(f103,plain,(
% 13.68/2.29 ![X0,X1,X2,X3,X4]: (~sum(X0,X1,X2)|~product(X3,X2,X4)|sum(multiply(X3,X0),multiply(X3,X1),X4))),
% 13.68/2.29 inference(resolution,[status(thm)],[f55,f23])).
% 13.68/2.29 fof(f108,plain,(
% 13.68/2.29 ![X0,X1]: (~sum(additive_identity,X0,X1)|X0=X1)),
% 13.68/2.29 inference(resolution,[status(thm)],[f45,f21])).
% 13.68/2.29 fof(f115,plain,(
% 13.68/2.29 additive_identity=additive_inverse(additive_identity)),
% 13.68/2.29 inference(resolution,[status(thm)],[f108,f87])).
% 13.68/2.29 fof(f148,plain,(
% 13.68/2.29 ![X0,X1]: (~sum(X0,X1,X1)|additive_identity=X0)),
% 13.68/2.29 inference(resolution,[status(thm)],[f51,f21])).
% 13.68/2.29 fof(f366,plain,(
% 13.68/2.29 ![X0,X1,X2,X3]: (~product(add(X0,X1),X2,X3)|sum(multiply(X1,X2),multiply(X0,X2),X3))),
% 13.68/2.29 inference(resolution,[status(thm)],[f85,f63])).
% 13.68/2.29 fof(f449,plain,(
% 13.68/2.29 ![X0,X1,X2]: (~sum(multiply(X0,additive_identity),multiply(X0,X1),X2)|product(X0,X1,X2))),
% 13.68/2.29 inference(resolution,[status(thm)],[f102,f21])).
% 13.68/2.29 fof(f459,plain,(
% 13.68/2.29 ![X0,X1,X2]: (~product(X0,additive_identity,X1)|sum(multiply(X0,additive_inverse(X2)),multiply(X0,X2),X1))),
% 13.68/2.29 inference(resolution,[status(thm)],[f103,f25])).
% 13.68/2.29 fof(f1280,plain,(
% 13.68/2.29 ![X0,X1,X2]: (sum(multiply(X0,X1),multiply(X2,X1),multiply(add(X2,X0),X1)))),
% 13.68/2.29 inference(resolution,[status(thm)],[f366,f23])).
% 13.68/2.29 fof(f1808,plain,(
% 13.68/2.29 ![X0,X1]: (sum(multiply(X0,additive_inverse(X1)),multiply(X0,X1),multiply(X0,additive_identity)))),
% 13.68/2.29 inference(resolution,[status(thm)],[f459,f23])).
% 13.68/2.29 fof(f7726,plain,(
% 13.68/2.29 ![X0]: (product(X0,additive_identity,multiply(add(X0,X0),additive_identity)))),
% 13.68/2.29 inference(resolution,[status(thm)],[f1280,f449])).
% 13.68/2.29 fof(f8744,plain,(
% 13.68/2.29 ![X0]: (additive_identity=multiply(X0,additive_inverse(additive_identity)))),
% 13.68/2.29 inference(resolution,[status(thm)],[f1808,f148])).
% 13.68/2.29 fof(f8769,plain,(
% 13.68/2.29 ![X0]: (additive_identity=multiply(X0,additive_identity))),
% 13.68/2.29 inference(forward_demodulation,[status(thm)],[f115,f8744])).
% 13.68/2.29 fof(f8776,plain,(
% 13.68/2.29 ![X0]: (product(X0,additive_identity,additive_identity))),
% 13.68/2.29 inference(backward_demodulation,[status(thm)],[f8769,f7726])).
% 13.68/2.29 fof(f8895,plain,(
% 13.68/2.29 $false),
% 13.68/2.29 inference(backward_subsumption_resolution,[status(thm)],[f52,f8776])).
% 13.68/2.30 % SZS output end CNFRefutation for theBenchmark.p
% 1.95/2.32 % Elapsed time: 1.844547 seconds
% 1.95/2.32 % CPU time: 14.154147 seconds
% 1.95/2.32 % Total memory used: 64.670 MB
% 1.95/2.32 % Net memory used: 60.946 MB
%------------------------------------------------------------------------------