%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG004-1 : 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 : n012.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 0.08s 0.63s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Mon Sep 21 04:09:39 UTC 2026
% 0.02/0.31 % CPUTime :
% 0.02/0.31 % Drodi V4.1.1
% 0.08/0.63 % Refutation found
% 0.08/0.63 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.63 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.63 fof(f1,axiom,(
% 0.08/0.63 (![X]: (sum(additive_identity,X,X) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f2,axiom,(
% 0.08/0.63 (![X]: (sum(X,additive_identity,X) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f3,axiom,(
% 0.08/0.63 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f4,axiom,(
% 0.08/0.63 (![X,Y]: (sum(X,Y,add(X,Y)) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f5,axiom,(
% 0.08/0.63 (![X]: (sum(additive_inverse(X),X,additive_identity) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f6,axiom,(
% 0.08/0.63 (![X]: (sum(X,additive_inverse(X),additive_identity) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f7,axiom,(
% 0.08/0.63 (![X,Y,U,Z,V,W]: (( ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(U,Z,W)| sum(X,V,W) ) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f9,axiom,(
% 0.08/0.63 (![X,Y,Z]: (( ~ sum(X,Y,Z)| sum(Y,X,Z) ) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f12,axiom,(
% 0.08/0.63 (![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) ) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f14,axiom,(
% 0.08/0.63 (![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) ) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f16,axiom,(
% 0.08/0.63 (![X,Y,U,V]: (( ~ sum(X,Y,U)| ~ sum(X,Y,V)| U = V ) ))),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f18,hypothesis,(
% 0.08/0.63 product(a,b,c) ),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f19,hypothesis,(
% 0.08/0.63 product(additive_inverse(a),additive_inverse(b),d) ),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f20,negated_conjecture,(
% 0.08/0.63 c != d ),
% 0.08/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.63 fof(f21,plain,(
% 0.08/0.63 ![X0]: (sum(additive_identity,X0,X0))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.63 fof(f22,plain,(
% 0.08/0.63 ![X0]: (sum(X0,additive_identity,X0))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f2])).
% 0.08/0.63 fof(f23,plain,(
% 0.08/0.63 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f3])).
% 0.08/0.63 fof(f24,plain,(
% 0.08/0.63 ![X0,X1]: (sum(X0,X1,add(X0,X1)))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f4])).
% 0.08/0.63 fof(f25,plain,(
% 0.08/0.63 ![X0]: (sum(additive_inverse(X0),X0,additive_identity))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f5])).
% 0.08/0.63 fof(f26,plain,(
% 0.08/0.63 ![X0]: (sum(X0,additive_inverse(X0),additive_identity))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.63 fof(f27,plain,(
% 0.08/0.63 ![X,V,W]: ((![U,Z]: ((![Y]: (~sum(X,Y,U)|~sum(Y,Z,V)))|~sum(U,Z,W)))|sum(X,V,W))),
% 0.08/0.63 inference(miniscoping,[status(thm)],[f7])).
% 0.08/0.63 fof(f28,plain,(
% 0.08/0.63 ![X0,X1,X2,X3,X4,X5]: (~sum(X0,X1,X2)|~sum(X1,X3,X4)|~sum(X2,X3,X5)|sum(X0,X4,X5))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f27])).
% 0.08/0.63 fof(f31,plain,(
% 0.08/0.63 ![X0,X1,X2]: (~sum(X0,X1,X2)|sum(X1,X0,X2))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f9])).
% 0.08/0.63 fof(f36,plain,(
% 0.08/0.63 ![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))),
% 0.08/0.63 inference(miniscoping,[status(thm)],[f12])).
% 0.08/0.63 fof(f37,plain,(
% 0.08/0.63 ![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))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f36])).
% 0.08/0.63 fof(f40,plain,(
% 0.08/0.63 ![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))),
% 0.08/0.63 inference(miniscoping,[status(thm)],[f14])).
% 0.08/0.63 fof(f41,plain,(
% 0.08/0.63 ![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))),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f40])).
% 0.08/0.63 fof(f44,plain,(
% 0.08/0.63 ![U,V]: ((![X,Y]: (~sum(X,Y,U)|~sum(X,Y,V)))|U=V)),
% 0.08/0.63 inference(miniscoping,[status(thm)],[f16])).
% 0.08/0.63 fof(f45,plain,(
% 0.08/0.63 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|X2=X3)),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f44])).
% 0.08/0.63 fof(f48,plain,(
% 0.08/0.63 product(a,b,c)),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f18])).
% 0.08/0.63 fof(f49,plain,(
% 0.08/0.63 product(additive_inverse(a),additive_inverse(b),d)),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f19])).
% 0.08/0.63 fof(f50,plain,(
% 0.08/0.63 ~c=d),
% 0.08/0.63 inference(cnf_transformation,[status(thm)],[f20])).
% 0.08/0.63 fof(f55,plain,(
% 0.08/0.63 ![X0,X1]: (sum(X0,X1,add(X1,X0)))),
% 0.08/0.63 inference(resolution,[status(thm)],[f31,f24])).
% 0.08/0.63 fof(f57,plain,(
% 0.08/0.63 ![X0,X1]: (~sum(additive_inverse(X0),X0,X1)|additive_identity=X1)),
% 0.08/0.63 inference(resolution,[status(thm)],[f45,f25])).
% 0.08/0.63 fof(f58,plain,(
% 0.08/0.63 ![X0,X1]: (~sum(additive_identity,X0,X1)|X0=X1)),
% 0.08/0.63 inference(resolution,[status(thm)],[f45,f21])).
% 0.08/0.63 fof(f60,plain,(
% 0.08/0.63 ![X0,X1]: (~sum(X0,additive_identity,X1)|X0=X1)),
% 0.08/0.63 inference(resolution,[status(thm)],[f45,f22])).
% 0.08/0.63 fof(f61,plain,(
% 0.08/0.63 ![X0,X1,X2]: (~sum(X0,X1,X2)|add(X1,X0)=X2)),
% 0.08/0.63 inference(resolution,[status(thm)],[f45,f55])).
% 0.08/0.63 fof(f62,plain,(
% 0.08/0.63 ![X0,X1,X2]: (~sum(X0,X1,X2)|add(X0,X1)=X2)),
% 0.08/0.63 inference(resolution,[status(thm)],[f45,f24])).
% 0.08/0.63 fof(f67,plain,(
% 0.08/0.63 ![X0]: (X0=add(additive_identity,X0))),
% 0.08/0.63 inference(resolution,[status(thm)],[f58,f24])).
% 0.08/0.63 fof(f72,plain,(
% 0.08/0.63 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(additive_identity,X1,X3)|sum(additive_inverse(X0),X2,X3))),
% 0.08/0.63 inference(resolution,[status(thm)],[f28,f25])).
% 0.08/0.63 fof(f107,plain,(
% 0.08/0.63 ![X0]: (additive_identity=add(X0,additive_inverse(X0)))),
% 0.08/0.63 inference(resolution,[status(thm)],[f57,f55])).
% 0.08/0.63 fof(f131,plain,(
% 0.08/0.63 ![X0,X1,X2,X3]: (~product(additive_inverse(a),X0,X1)|~sum(additive_inverse(b),X0,X2)|~product(additive_inverse(a),X2,X3)|sum(d,X1,X3))),
% 0.08/0.63 inference(resolution,[status(thm)],[f37,f49])).
% 0.08/0.63 fof(f162,plain,(
% 0.08/0.63 ![X0,X1,X2]: (~sum(additive_inverse(b),X0,X1)|~product(additive_inverse(a),X1,X2)|sum(d,multiply(additive_inverse(a),X0),X2))),
% 0.08/0.63 inference(resolution,[status(thm)],[f131,f23])).
% 0.08/0.63 fof(f172,plain,(
% 0.08/0.63 ![X0,X1]: (add(X0,X1)=add(X1,X0))),
% 0.08/0.63 inference(resolution,[status(thm)],[f61,f24])).
% 0.08/0.63 fof(f216,plain,(
% 0.08/0.63 ![X0,X1,X2,X3]: (~product(X0,b,X1)|~sum(a,X0,X2)|~product(X2,b,X3)|sum(c,X1,X3))),
% 0.08/0.63 inference(resolution,[status(thm)],[f41,f48])).
% 0.08/0.63 fof(f226,plain,(
% 0.08/0.63 ![X0,X1]: (~sum(additive_identity,X0,X1)|sum(additive_inverse(additive_inverse(X0)),additive_identity,X1))),
% 0.08/0.63 inference(resolution,[status(thm)],[f72,f25])).
% 0.08/0.63 fof(f230,plain,(
% 0.08/0.63 ![X0,X1,X2]: (~sum(additive_identity,X0,X1)|sum(additive_inverse(X2),add(X0,X2),X1))),
% 0.08/0.63 inference(resolution,[status(thm)],[f72,f55])).
% 0.08/0.63 fof(f318,plain,(
% 0.08/0.63 ![X0,X1,X2]: (~sum(a,X0,X1)|~product(X1,b,X2)|sum(c,multiply(X0,b),X2))),
% 0.08/0.63 inference(resolution,[status(thm)],[f216,f23])).
% 0.08/0.63 fof(f502,plain,(
% 0.08/0.63 ![X0]: (~product(additive_inverse(a),additive_identity,X0)|sum(d,multiply(additive_inverse(a),b),X0))),
% 0.08/0.63 inference(resolution,[status(thm)],[f162,f25])).
% 0.08/0.63 fof(f504,plain,(
% 0.08/0.63 ![X0]: (~product(additive_inverse(a),additive_inverse(b),X0)|sum(d,multiply(additive_inverse(a),additive_identity),X0))),
% 0.08/0.63 inference(resolution,[status(thm)],[f162,f22])).
% 0.08/0.63 fof(f658,plain,(
% 0.08/0.63 ![X0]: (sum(additive_inverse(additive_inverse(X0)),additive_identity,X0))),
% 0.08/0.63 inference(resolution,[status(thm)],[f226,f21])).
% 0.08/0.63 fof(f672,plain,(
% 0.08/0.63 ![X0]: (additive_inverse(additive_inverse(X0))=X0)),
% 0.08/0.63 inference(resolution,[status(thm)],[f658,f60])).
% 0.08/0.63 fof(f858,plain,(
% 0.08/0.63 ![X0]: (~product(additive_identity,b,X0)|sum(c,multiply(additive_inverse(a),b),X0))),
% 0.08/0.63 inference(resolution,[status(thm)],[f318,f26])).
% 0.08/0.63 fof(f859,plain,(
% 0.08/0.63 ![X0]: (~product(a,b,X0)|sum(c,multiply(additive_identity,b),X0))),
% 0.08/0.63 inference(resolution,[status(thm)],[f318,f22])).
% 0.08/0.63 fof(f866,plain,(
% 0.08/0.63 ![X0,X1]: (sum(additive_inverse(X0),add(X1,X0),X1))),
% 0.08/0.63 inference(resolution,[status(thm)],[f230,f21])).
% 0.08/0.63 fof(f892,plain,(
% 0.08/0.63 ![X0,X1]: (add(add(X0,X1),additive_inverse(X1))=X0)),
% 0.08/0.63 inference(resolution,[status(thm)],[f866,f61])).
% 0.08/0.63 fof(f1017,plain,(
% 0.08/0.63 ![X0,X1]: (add(add(X0,X1),additive_inverse(X0))=X1)),
% 0.08/0.63 inference(paramodulation,[status(thm)],[f172,f892])).
% 0.08/0.63 fof(f1019,plain,(
% 0.08/0.63 ![X0,X1]: (add(add(X0,additive_inverse(X1)),X1)=X0)),
% 0.08/0.63 inference(paramodulation,[status(thm)],[f672,f892])).
% 0.08/0.63 fof(f2018,plain,(
% 0.08/0.63 sum(d,multiply(additive_inverse(a),additive_identity),d)),
% 0.08/0.63 inference(resolution,[status(thm)],[f504,f49])).
% 0.08/0.63 fof(f2091,plain,(
% 0.08/0.63 add(d,multiply(additive_inverse(a),additive_identity))=d),
% 0.08/0.63 inference(resolution,[status(thm)],[f2018,f62])).
% 0.08/0.63 fof(f2113,plain,(
% 0.08/0.63 add(d,additive_inverse(d))=multiply(additive_inverse(a),additive_identity)),
% 0.08/0.63 inference(paramodulation,[status(thm)],[f2091,f1017])).
% 0.08/0.63 fof(f2135,plain,(
% 0.08/0.63 additive_identity=multiply(additive_inverse(a),additive_identity)),
% 0.08/0.63 inference(forward_demodulation,[status(thm)],[f107,f2113])).
% 0.08/0.63 fof(f2143,plain,(
% 0.08/0.63 product(additive_inverse(a),additive_identity,additive_identity)),
% 0.08/0.63 inference(paramodulation,[status(thm)],[f2135,f23])).
% 0.08/0.63 fof(f2144,plain,(
% 0.08/0.63 sum(d,multiply(additive_inverse(a),b),additive_identity)),
% 0.08/0.63 inference(resolution,[status(thm)],[f2143,f502])).
% 0.08/0.63 fof(f2345,plain,(
% 0.08/0.63 add(d,multiply(additive_inverse(a),b))=additive_identity),
% 0.08/0.63 inference(resolution,[status(thm)],[f2144,f62])).
% 0.08/0.63 fof(f2481,plain,(
% 0.08/0.63 add(additive_identity,additive_inverse(d))=multiply(additive_inverse(a),b)),
% 0.08/0.63 inference(paramodulation,[status(thm)],[f2345,f1017])).
% 0.08/0.63 fof(f2503,plain,(
% 0.08/0.63 additive_inverse(d)=multiply(additive_inverse(a),b)),
% 0.08/0.63 inference(forward_demodulation,[status(thm)],[f67,f2481])).
% 0.08/0.63 fof(f3287,plain,(
% 0.08/0.63 ![X0]: (~product(additive_identity,b,X0)|sum(c,additive_inverse(d),X0))),
% 0.08/0.63 inference(forward_demodulation,[status(thm)],[f2503,f858])).
% 0.08/0.63 fof(f3294,plain,(
% 0.08/0.63 sum(c,multiply(additive_identity,b),c)),
% 0.08/0.63 inference(resolution,[status(thm)],[f859,f48])).
% 0.08/0.63 fof(f3812,plain,(
% 0.08/0.63 add(c,multiply(additive_identity,b))=c),
% 0.08/0.63 inference(resolution,[status(thm)],[f3294,f62])).
% 0.08/0.63 fof(f3837,plain,(
% 0.08/0.63 add(c,additive_inverse(c))=multiply(additive_identity,b)),
% 0.08/0.63 inference(paramodulation,[status(thm)],[f3812,f1017])).
% 0.08/0.63 fof(f3861,plain,(
% 0.08/0.63 additive_identity=multiply(additive_identity,b)),
% 0.08/0.63 inference(forward_demodulation,[status(thm)],[f107,f3837])).
% 0.08/0.63 fof(f3868,plain,(
% 0.08/0.63 product(additive_identity,b,additive_identity)),
% 0.08/0.63 inference(paramodulation,[status(thm)],[f3861,f23])).
% 0.08/0.63 fof(f3869,plain,(
% 0.08/0.63 sum(c,additive_inverse(d),additive_identity)),
% 0.08/0.63 inference(resolution,[status(thm)],[f3868,f3287])).
% 0.08/0.63 fof(f3908,plain,(
% 0.08/0.63 add(c,additive_inverse(d))=additive_identity),
% 0.08/0.63 inference(resolution,[status(thm)],[f3869,f62])).
% 0.08/0.63 fof(f3921,plain,(
% 0.08/0.63 add(additive_identity,d)=c),
% 0.08/0.63 inference(paramodulation,[status(thm)],[f3908,f1019])).
% 0.08/0.63 fof(f3968,plain,(
% 0.08/0.63 d=c),
% 0.08/0.63 inference(forward_demodulation,[status(thm)],[f67,f3921])).
% 0.08/0.63 fof(f3969,plain,(
% 0.08/0.63 $false),
% 0.08/0.63 inference(forward_subsumption_resolution,[status(thm)],[f3968,f50])).
% 0.08/0.63 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.66 % Elapsed time: 0.335680 seconds
% 0.13/0.66 % CPU time: 2.447860 seconds
% 0.13/0.66 % Total memory used: 57.790 MB
% 0.13/0.66 % Net memory used: 55.386 MB
%------------------------------------------------------------------------------