%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUN087+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 01:57:28 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN087+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 03:28:01 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f1,axiom,(
% 0.09/0.39 (? [Y24] :(! [X19] :( ( ~ r1(X19)& X19 != Y24 )| ( r1(X19)& X19 = Y24 ) ) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f9,axiom,(
% 0.09/0.39 (! [X5] :(? [Y8] :( (? [Y17] :( r1(Y17)& r4(X5,Y17,Y8) ))& (? [Y18] :( r1(Y18)& Y8 = Y18 ) )) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f12,conjecture,(
% 0.09/0.39 (? [Y1] :( (? [Y2] :( r1(Y2)& r4(Y2,Y2,Y1) ))& (? [Y3] :( r1(Y3)& Y1 = Y3 ) )) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f13,negated_conjecture,(
% 0.09/0.39 ~((? [Y1] :( (? [Y2] :( r1(Y2)& r4(Y2,Y2,Y1) ))& (? [Y3] :( r1(Y3)& Y1 = Y3 ) )) ))),
% 0.09/0.39 inference(negated_conjecture,[status(cth)],[f12])).
% 0.09/0.39 fof(f14,definition,(
% 0.09/0.39 ![Y24,X19]: (sP0_prd(X19,Y24)<=>(~r1(X19)&~X19=Y24))),
% 0.09/0.39 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/0.39 fof(f15,plain,(
% 0.09/0.39 ?[Y24]: ![X19]: (sP0_prd(X19,Y24)|(r1(X19)&X19=Y24))),
% 0.09/0.39 inference(formula_renaming,[status(thm)],[f1,f14])).
% 0.09/0.39 fof(f16,plain,(
% 0.09/0.39 ![X19]: (sP0_prd(X19,sK0_skl)|(r1(X19)&X19=sK0_skl))),
% 0.09/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f15])).
% 0.09/0.39 fof(f17,plain,(
% 0.09/0.39 ![X0]: (sP0_prd(X0,sK0_skl)|r1(X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f16])).
% 0.09/0.39 fof(f18,plain,(
% 0.09/0.39 ![X0]: (sP0_prd(X0,sK0_skl)|X0=sK0_skl)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f16])).
% 0.09/0.39 fof(f51,plain,(
% 0.09/0.39 ![X5]: ((r1(sK15_skl(X5))&r4(X5,sK15_skl(X5),sK14_skl(X5)))&(r1(sK16_skl(X5))&sK14_skl(X5)=sK16_skl(X5)))),
% 0.09/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(Y8,sK14_skl(X5)),skolemize(Y17,sK15_skl(X5)),skolemize(Y18,sK16_skl(X5))],[f9])).
% 0.09/0.39 fof(f52,plain,(
% 0.09/0.39 ![X0]: (r1(sK15_skl(X0)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f51])).
% 0.09/0.39 fof(f53,plain,(
% 0.09/0.39 ![X0]: (r4(X0,sK15_skl(X0),sK14_skl(X0)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f51])).
% 0.09/0.39 fof(f54,plain,(
% 0.09/0.39 ![X0]: (r1(sK16_skl(X0)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f51])).
% 0.09/0.39 fof(f55,plain,(
% 0.09/0.39 ![X0]: (sK14_skl(X0)=sK16_skl(X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f51])).
% 0.09/0.39 fof(f64,plain,(
% 0.09/0.39 (![Y1]: ((![Y2]: (~r1(Y2)|~r4(Y2,Y2,Y1)))|(![Y3]: (~r1(Y3)|~Y1=Y3))))),
% 0.09/0.39 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.09/0.39 fof(f65,plain,(
% 0.09/0.39 ![X0,X1,X2]: (~r1(X0)|~r4(X0,X0,X1)|~r1(X2)|~X1=X2)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f64])).
% 0.09/0.39 fof(f66,plain,(
% 0.09/0.39 ![Y24,X19]: ((~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24))&(sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 0.09/0.39 inference(NNF_transformation,[status(thm)],[f14])).
% 0.09/0.39 fof(f67,plain,(
% 0.09/0.39 (![Y24,X19]: (~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24)))&(![Y24,X19]: (sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f66])).
% 0.09/0.39 fof(f68,plain,(
% 0.09/0.39 ![X0,X1]: (~sP0_prd(X0,X1)|~r1(X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f67])).
% 0.09/0.39 fof(f69,plain,(
% 0.09/0.39 ![X0,X1]: (~sP0_prd(X0,X1)|~X0=X1)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f67])).
% 0.09/0.39 fof(f95,plain,(
% 0.09/0.39 ![X0]: (r1(sK14_skl(X0)))),
% 0.09/0.39 inference(backward_demodulation,[status(thm)],[f55,f54])).
% 0.09/0.39 fof(f97,plain,(
% 0.09/0.39 ![X0,X1]: (~r1(X0)|~r4(X0,X0,X1)|~r1(X1))),
% 0.09/0.39 inference(destructive_equality_resolution,[status(thm)],[f65])).
% 0.09/0.39 fof(f98,plain,(
% 0.09/0.39 ![X0]: (~sP0_prd(X0,X0))),
% 0.09/0.39 inference(destructive_equality_resolution,[status(thm)],[f69])).
% 0.09/0.39 fof(f103,plain,(
% 0.09/0.39 r1(sK0_skl)),
% 0.09/0.39 inference(resolution,[status(thm)],[f98,f17])).
% 0.09/0.39 fof(f104,plain,(
% 0.09/0.39 ![X0]: (~r1(X0)|~r4(X0,X0,sK0_skl))),
% 0.09/0.39 inference(resolution,[status(thm)],[f103,f97])).
% 0.09/0.39 fof(f118,plain,(
% 0.09/0.39 ![X0]: (~r1(X0)|X0=sK0_skl)),
% 0.09/0.39 inference(resolution,[status(thm)],[f68,f18])).
% 0.09/0.39 fof(f120,plain,(
% 0.09/0.39 ![X0]: (sK14_skl(X0)=sK0_skl)),
% 0.09/0.39 inference(resolution,[status(thm)],[f118,f95])).
% 0.09/0.39 fof(f121,plain,(
% 0.09/0.39 ![X0]: (sK15_skl(X0)=sK0_skl)),
% 0.09/0.39 inference(resolution,[status(thm)],[f118,f52])).
% 0.09/0.39 fof(f127,plain,(
% 0.09/0.39 ![X0]: (r4(X0,sK15_skl(X0),sK0_skl))),
% 0.09/0.39 inference(backward_demodulation,[status(thm)],[f120,f53])).
% 0.09/0.39 fof(f133,plain,(
% 0.09/0.39 ![X0]: (r4(X0,sK0_skl,sK0_skl))),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f121,f127])).
% 0.13/0.39 fof(f138,plain,(
% 0.13/0.39 ~r1(sK0_skl)),
% 0.13/0.39 inference(resolution,[status(thm)],[f133,f104])).
% 0.13/0.39 fof(f139,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f138,f103])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.057188 seconds
% 0.13/0.42 % CPU time: 0.156059 seconds
% 0.13/0.42 % Total memory used: 102.357 MB
% 0.13/0.42 % Net memory used: 102.248 MB
%------------------------------------------------------------------------------