%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG001-1 : 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 : n009.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 02:05:04 PM UTC 2026
% Result : Unsatisfiable 7.06s 1.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n009.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 21 04:09:28 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 7.06/1.41 % Refutation found
% 7.06/1.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.06/1.41 % SZS output start CNFRefutation for theBenchmark
% 7.06/1.41 fof(f1,axiom,(
% 7.06/1.41 (![X]: (sum(additive_identity,X,X) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f3,axiom,(
% 7.06/1.41 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f4,axiom,(
% 7.06/1.41 (![X,Y]: (sum(X,Y,add(X,Y)) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f5,axiom,(
% 7.06/1.41 (![X]: (sum(additive_inverse(X),X,additive_identity) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f7,axiom,(
% 7.06/1.41 (![X,Y,U,Z,V,W]: (( ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(U,Z,W)| sum(X,V,W) ) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f9,axiom,(
% 7.06/1.41 (![X,Y,Z]: (( ~ sum(X,Y,Z)| sum(Y,X,Z) ) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f13,axiom,(
% 7.06/1.41 (![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) ) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f14,axiom,(
% 7.06/1.41 (![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) ) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f16,axiom,(
% 7.06/1.41 (![X,Y,U,V]: (( ~ sum(X,Y,U)| ~ sum(X,Y,V)| U = V ) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f17,axiom,(
% 7.06/1.41 (![X,Y,U,V]: (( ~ product(X,Y,U)| ~ product(X,Y,V)| U = V ) ))),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f18,negated_conjecture,(
% 7.06/1.41 ~ product(a,additive_identity,additive_identity) ),
% 7.06/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.06/1.41 fof(f19,plain,(
% 7.06/1.41 ![X0]: (sum(additive_identity,X0,X0))),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f1])).
% 7.06/1.41 fof(f21,plain,(
% 7.06/1.41 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f3])).
% 7.06/1.41 fof(f22,plain,(
% 7.06/1.41 ![X0,X1]: (sum(X0,X1,add(X0,X1)))),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f4])).
% 7.06/1.41 fof(f23,plain,(
% 7.06/1.41 ![X0]: (sum(additive_inverse(X0),X0,additive_identity))),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f5])).
% 7.06/1.41 fof(f25,plain,(
% 7.06/1.41 ![X,V,W]: ((![U,Z]: ((![Y]: (~sum(X,Y,U)|~sum(Y,Z,V)))|~sum(U,Z,W)))|sum(X,V,W))),
% 7.06/1.41 inference(miniscoping,[status(thm)],[f7])).
% 7.06/1.41 fof(f26,plain,(
% 7.06/1.41 ![X0,X1,X2,X3,X4,X5]: (~sum(X0,X1,X2)|~sum(X1,X3,X4)|~sum(X2,X3,X5)|sum(X0,X4,X5))),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f25])).
% 7.06/1.41 fof(f29,plain,(
% 7.06/1.41 ![X0,X1,X2]: (~sum(X0,X1,X2)|sum(X1,X0,X2))),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f9])).
% 7.06/1.41 fof(f36,plain,(
% 7.06/1.41 ![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))),
% 7.06/1.41 inference(miniscoping,[status(thm)],[f13])).
% 7.06/1.41 fof(f37,plain,(
% 7.06/1.41 ![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))),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f36])).
% 7.06/1.41 fof(f38,plain,(
% 7.06/1.41 ![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))),
% 7.06/1.41 inference(miniscoping,[status(thm)],[f14])).
% 7.06/1.41 fof(f39,plain,(
% 7.06/1.41 ![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))),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f38])).
% 7.06/1.41 fof(f42,plain,(
% 7.06/1.41 ![U,V]: ((![X,Y]: (~sum(X,Y,U)|~sum(X,Y,V)))|U=V)),
% 7.06/1.41 inference(miniscoping,[status(thm)],[f16])).
% 7.06/1.41 fof(f43,plain,(
% 7.06/1.41 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|X2=X3)),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f42])).
% 7.06/1.41 fof(f44,plain,(
% 7.06/1.41 ![U,V]: ((![X,Y]: (~product(X,Y,U)|~product(X,Y,V)))|U=V)),
% 7.06/1.41 inference(miniscoping,[status(thm)],[f17])).
% 7.06/1.41 fof(f45,plain,(
% 7.06/1.41 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f44])).
% 7.06/1.41 fof(f46,plain,(
% 7.06/1.41 ~product(a,additive_identity,additive_identity)),
% 7.06/1.41 inference(cnf_transformation,[status(thm)],[f18])).
% 7.06/1.41 fof(f47,plain,(
% 7.06/1.41 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~sum(X3,X0,X4)|~product(X4,X1,X5)|sum(multiply(X3,X1),X2,X5))),
% 7.06/1.41 inference(resolution,[status(thm)],[f21,f39])).
% 7.06/1.41 fof(f48,plain,(
% 7.06/1.41 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~sum(X3,X1,X4)|~sum(multiply(X0,X3),X2,X5)|product(X0,X4,X5))),
% 7.06/1.41 inference(resolution,[status(thm)],[f21,f37])).
% 7.06/1.41 fof(f52,plain,(
% 7.06/1.41 ![X0,X1,X2]: (~product(X0,X1,X2)|multiply(X0,X1)=X2)),
% 7.06/1.41 inference(resolution,[status(thm)],[f21,f45])).
% 7.06/1.41 fof(f57,plain,(
% 7.06/1.41 ![X0,X1]: (sum(X0,X1,add(X1,X0)))),
% 7.06/1.41 inference(resolution,[status(thm)],[f29,f22])).
% 7.06/1.41 fof(f59,plain,(
% 7.06/1.41 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(additive_identity,X1,X3)|sum(additive_inverse(X0),X2,X3))),
% 7.06/1.41 inference(resolution,[status(thm)],[f26,f23])).
% 7.06/1.41 fof(f60,plain,(
% 7.06/1.41 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|sum(additive_identity,X2,X3))),
% 7.06/1.41 inference(resolution,[status(thm)],[f26,f19])).
% 7.06/1.41 fof(f73,plain,(
% 7.06/1.41 ![X0,X1]: (~sum(additive_inverse(X0),X0,X1)|sum(additive_identity,additive_identity,X1))),
% 7.06/1.41 inference(resolution,[status(thm)],[f60,f23])).
% 7.06/1.41 fof(f79,plain,(
% 7.06/1.41 ![X0,X1,X2,X3,X4]: (~sum(X0,X1,X2)|~product(X2,X3,X4)|sum(multiply(X0,X3),multiply(X1,X3),X4))),
% 7.06/1.41 inference(resolution,[status(thm)],[f47,f21])).
% 7.06/1.41 fof(f83,plain,(
% 7.06/1.41 ![X0]: (sum(additive_identity,additive_identity,add(additive_inverse(X0),X0)))),
% 7.06/1.41 inference(resolution,[status(thm)],[f73,f22])).
% 7.06/1.41 fof(f96,plain,(
% 7.06/1.41 ![X0,X1,X2,X3,X4]: (~sum(X0,X1,X2)|~sum(multiply(X3,X0),multiply(X3,X1),X4)|product(X3,X2,X4))),
% 7.06/1.41 inference(resolution,[status(thm)],[f48,f21])).
% 7.06/1.41 fof(f102,plain,(
% 7.06/1.41 ![X0,X1]: (~sum(additive_identity,X0,X1)|X0=X1)),
% 7.06/1.41 inference(resolution,[status(thm)],[f43,f19])).
% 7.06/1.41 fof(f105,plain,(
% 7.06/1.41 ![X0,X1,X2]: (~sum(X0,X1,X2)|add(X1,X0)=X2)),
% 7.06/1.41 inference(resolution,[status(thm)],[f43,f57])).
% 7.06/1.41 fof(f106,plain,(
% 7.06/1.41 ![X0,X1,X2]: (~sum(X0,X1,X2)|add(X0,X1)=X2)),
% 7.06/1.41 inference(resolution,[status(thm)],[f43,f22])).
% 7.06/1.41 fof(f107,plain,(
% 7.06/1.41 ![X0]: (additive_identity=add(additive_inverse(X0),X0))),
% 7.06/1.41 inference(resolution,[status(thm)],[f102,f83])).
% 7.06/1.41 fof(f114,plain,(
% 7.06/1.41 ![X0]: (X0=add(additive_identity,X0))),
% 7.06/1.41 inference(resolution,[status(thm)],[f102,f22])).
% 7.06/1.41 fof(f139,plain,(
% 7.06/1.41 ![X0,X1,X2]: (~sum(additive_identity,X0,X1)|sum(additive_inverse(X2),add(X0,X2),X1))),
% 7.06/1.41 inference(resolution,[status(thm)],[f59,f57])).
% 7.06/1.41 fof(f195,plain,(
% 7.06/1.41 ![X0,X1]: (add(X0,X1)=add(X1,X0))),
% 7.06/1.41 inference(resolution,[status(thm)],[f105,f22])).
% 7.06/1.41 fof(f358,plain,(
% 7.06/1.41 ![X0,X1,X2,X3]: (~product(add(X0,X1),X2,X3)|sum(multiply(X1,X2),multiply(X0,X2),X3))),
% 7.06/1.41 inference(resolution,[status(thm)],[f79,f57])).
% 7.06/1.41 fof(f363,plain,(
% 7.06/1.41 ![X0,X1,X2]: (~sum(multiply(X0,additive_identity),multiply(X0,X1),X2)|product(X0,X1,X2))),
% 7.06/1.41 inference(resolution,[status(thm)],[f96,f19])).
% 7.06/1.41 fof(f367,plain,(
% 7.06/1.41 ![X0,X1,X2,X3]: (~sum(multiply(X0,X1),multiply(X0,X2),X3)|product(X0,add(X1,X2),X3))),
% 7.06/1.41 inference(resolution,[status(thm)],[f96,f22])).
% 7.06/1.41 fof(f575,plain,(
% 7.06/1.41 ![X0,X1]: (sum(additive_inverse(X0),add(X1,X0),X1))),
% 7.06/1.41 inference(resolution,[status(thm)],[f139,f19])).
% 7.06/1.41 fof(f657,plain,(
% 7.06/1.41 ![X0,X1]: (add(additive_inverse(X0),add(X1,X0))=X1)),
% 7.06/1.41 inference(resolution,[status(thm)],[f575,f106])).
% 7.06/1.41 fof(f707,plain,(
% 7.06/1.41 ![X0,X1]: (add(additive_inverse(add(X0,X1)),X0)=additive_inverse(X1))),
% 7.06/1.41 inference(paramodulation,[status(thm)],[f657,f657])).
% 7.06/1.41 fof(f712,plain,(
% 7.06/1.41 ![X0,X1]: (add(additive_inverse(X0),add(X0,X1))=X1)),
% 7.06/1.41 inference(paramodulation,[status(thm)],[f195,f657])).
% 7.06/1.41 fof(f906,plain,(
% 7.06/1.41 ![X0,X1,X2]: (sum(multiply(X0,X1),multiply(X2,X1),multiply(add(X2,X0),X1)))),
% 7.06/1.41 inference(resolution,[status(thm)],[f358,f21])).
% 7.06/1.41 fof(f1112,plain,(
% 7.06/1.41 ![X0,X1]: (product(X0,X1,add(multiply(X0,X1),multiply(X0,additive_identity))))),
% 7.06/1.41 inference(resolution,[status(thm)],[f363,f57])).
% 7.06/1.41 fof(f1771,plain,(
% 7.06/1.41 ![X0,X1]: (add(additive_inverse(X0),additive_inverse(X1))=additive_inverse(add(X1,X0)))),
% 7.06/1.41 inference(paramodulation,[status(thm)],[f712,f707])).
% 7.06/1.41 fof(f1772,plain,(
% 7.06/1.41 ![X0,X1]: (add(additive_inverse(X0),additive_inverse(X1))=additive_inverse(add(X0,X1)))),
% 7.06/1.41 inference(paramodulation,[status(thm)],[f657,f707])).
% 7.06/1.41 fof(f5216,plain,(
% 7.06/1.41 ![X0,X1]: (additive_inverse(add(X0,X1))=additive_inverse(add(X1,X0)))),
% 7.06/1.41 inference(paramodulation,[status(thm)],[f1771,f1772])).
% 7.06/1.41 fof(f5508,plain,(
% 7.06/1.41 ![X0,X1]: (additive_identity=add(additive_inverse(add(X0,X1)),add(X1,X0)))),
% 7.06/1.43 inference(paramodulation,[status(thm)],[f5216,f107])).
% 7.06/1.43 fof(f10472,plain,(
% 7.06/1.43 ![X0,X1]: (product(X0,add(X1,X1),multiply(add(X0,X0),X1)))),
% 7.06/1.43 inference(resolution,[status(thm)],[f906,f367])).
% 7.06/1.43 fof(f11223,plain,(
% 7.06/1.43 ![X0,X1]: (multiply(X0,X1)=add(multiply(X0,X1),multiply(X0,additive_identity)))),
% 7.06/1.43 inference(resolution,[status(thm)],[f1112,f52])).
% 7.06/1.43 fof(f34000,plain,(
% 7.06/1.43 ![X0,X1]: (additive_identity=add(additive_inverse(multiply(X0,X1)),add(multiply(X0,additive_identity),multiply(X0,X1))))),
% 7.06/1.43 inference(paramodulation,[status(thm)],[f11223,f5508])).
% 7.06/1.43 fof(f34159,plain,(
% 7.06/1.43 ![X0]: (additive_identity=multiply(X0,additive_identity))),
% 7.06/1.43 inference(forward_demodulation,[status(thm)],[f657,f34000])).
% 7.06/1.43 fof(f34262,plain,(
% 7.06/1.43 ![X0]: (product(X0,add(additive_identity,additive_identity),additive_identity))),
% 7.06/1.43 inference(paramodulation,[status(thm)],[f34159,f10472])).
% 7.06/1.43 fof(f34350,plain,(
% 7.06/1.43 ![X0]: (product(X0,additive_identity,additive_identity))),
% 7.06/1.43 inference(forward_demodulation,[status(thm)],[f114,f34262])).
% 7.06/1.43 fof(f34579,plain,(
% 7.06/1.43 $false),
% 7.06/1.43 inference(backward_subsumption_resolution,[status(thm)],[f46,f34350])).
% 7.06/1.43 % SZS output end CNFRefutation for theBenchmark.p
% 7.06/1.46 % Elapsed time: 1.048310 seconds
% 7.06/1.46 % CPU time: 8.032841 seconds
% 7.06/1.46 % Total memory used: 71.092 MB
% 7.06/1.46 % Net memory used: 67.027 MB
%------------------------------------------------------------------------------