%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUN081+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 01:57:27 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN081+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n002.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 03:27:46 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Drodi V4.1.1
% 0.15/0.45 % Refutation found
% 0.15/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.45 fof(f1,axiom,(
% 0.15/0.45 (? [Y24] :(! [X19] :( ( ~ r1(X19)& X19 != Y24 )| ( r1(X19)& X19 = Y24 ) ) ))),
% 0.15/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.45 fof(f2,axiom,(
% 0.15/0.45 (! [X11] :(? [Y21] :(! [X12] :( ( ~ r2(X11,X12)& X12 != Y21 )| ( r2(X11,X12)& X12 = Y21 ) ) )))),
% 0.15/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.45 fof(f8,axiom,(
% 0.15/0.45 (! [X4] :(? [Y9] :( (? [Y16] :( r1(Y16)& r3(X4,Y16,Y9) ))& Y9 = X4 ) ))),
% 0.15/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.45 fof(f12,conjecture,(
% 0.15/0.45 (? [Y1,Y2,Y3] :( r3(Y1,Y2,Y3)& (? [Y4] :( Y3 = Y4& (? [Y5] :( r2(Y5,Y4)& (? [Y6] :( r2(Y6,Y5)& (? [Y7] :( r1(Y7)& r2(Y7,Y6) ) )) )) )) )) )),
% 0.15/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.45 fof(f13,negated_conjecture,(
% 0.15/0.45 ~((? [Y1,Y2,Y3] :( r3(Y1,Y2,Y3)& (? [Y4] :( Y3 = Y4& (? [Y5] :( r2(Y5,Y4)& (? [Y6] :( r2(Y6,Y5)& (? [Y7] :( r1(Y7)& r2(Y7,Y6) ) )) )) )) )) ))),
% 0.15/0.45 inference(negated_conjecture,[status(cth)],[f12])).
% 0.15/0.45 fof(f14,definition,(
% 0.15/0.45 ![Y24,X19]: (sP0_prd(X19,Y24)<=>(~r1(X19)&~X19=Y24))),
% 0.15/0.45 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.15/0.45 fof(f15,plain,(
% 0.15/0.45 ?[Y24]: ![X19]: (sP0_prd(X19,Y24)|(r1(X19)&X19=Y24))),
% 0.15/0.45 inference(formula_renaming,[status(thm)],[f1,f14])).
% 0.15/0.45 fof(f16,plain,(
% 0.15/0.45 ![X19]: (sP0_prd(X19,sK0_skl)|(r1(X19)&X19=sK0_skl))),
% 0.15/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f15])).
% 0.15/0.45 fof(f17,plain,(
% 0.15/0.45 ![X0]: (sP0_prd(X0,sK0_skl)|r1(X0))),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/0.45 fof(f18,plain,(
% 0.15/0.45 ![X0]: (sP0_prd(X0,sK0_skl)|X0=sK0_skl)),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/0.45 fof(f19,definition,(
% 0.15/0.45 ![X11,Y21,X12]: (sP1_prd(X12,Y21,X11)<=>(~r2(X11,X12)&~X12=Y21))),
% 0.15/0.45 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.15/0.45 fof(f20,plain,(
% 0.15/0.45 ![X11]: ?[Y21]: ![X12]: (sP1_prd(X12,Y21,X11)|(r2(X11,X12)&X12=Y21))),
% 0.15/0.45 inference(formula_renaming,[status(thm)],[f2,f19])).
% 0.15/0.45 fof(f21,plain,(
% 0.15/0.45 ![X11]: ![X12]: (sP1_prd(X12,sK1_skl(X11),X11)|(r2(X11,X12)&X12=sK1_skl(X11)))),
% 0.15/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y21,sK1_skl(X11))],[f20])).
% 0.15/0.45 fof(f22,plain,(
% 0.15/0.45 ![X0,X1]: (sP1_prd(X0,sK1_skl(X1),X1)|r2(X1,X0))),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f21])).
% 0.15/0.45 fof(f47,plain,(
% 0.15/0.45 ![X4]: ((r1(sK13_skl(X4))&r3(X4,sK13_skl(X4),sK12_skl(X4)))&sK12_skl(X4)=X4)),
% 0.15/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f8])).
% 0.15/0.45 fof(f48,plain,(
% 0.15/0.45 ![X0]: (r1(sK13_skl(X0)))),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f47])).
% 0.15/0.45 fof(f49,plain,(
% 0.15/0.45 ![X0]: (r3(X0,sK13_skl(X0),sK12_skl(X0)))),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f47])).
% 0.15/0.45 fof(f50,plain,(
% 0.15/0.45 ![X0]: (sK12_skl(X0)=X0)),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f47])).
% 0.15/0.45 fof(f64,plain,(
% 0.15/0.45 (![Y1,Y2,Y3]: (~r3(Y1,Y2,Y3)|(![Y4]: (~Y3=Y4|(![Y5]: (~r2(Y5,Y4)|(![Y6]: (~r2(Y6,Y5)|(![Y7]: (~r1(Y7)|~r2(Y7,Y6)))))))))))),
% 0.15/0.45 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.15/0.45 fof(f65,plain,(
% 0.15/0.45 ![Y3]: ((![Y1,Y2]: ~r3(Y1,Y2,Y3))|(![Y4]: (~Y3=Y4|(![Y5]: (~r2(Y5,Y4)|(![Y6]: (~r2(Y6,Y5)|(![Y7]: (~r1(Y7)|~r2(Y7,Y6))))))))))),
% 0.15/0.45 inference(miniscoping,[status(thm)],[f64])).
% 0.15/0.45 fof(f66,plain,(
% 0.15/0.45 ![X0,X1,X2,X3,X4,X5,X6]: (~r3(X0,X1,X2)|~X2=X3|~r2(X4,X3)|~r2(X5,X4)|~r1(X6)|~r2(X6,X5))),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f65])).
% 0.15/0.45 fof(f67,plain,(
% 0.15/0.45 ![Y24,X19]: ((~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24))&(sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 0.15/0.45 inference(NNF_transformation,[status(thm)],[f14])).
% 0.15/0.45 fof(f68,plain,(
% 0.15/0.45 (![Y24,X19]: (~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24)))&(![Y24,X19]: (sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 0.15/0.45 inference(miniscoping,[status(thm)],[f67])).
% 0.15/0.45 fof(f69,plain,(
% 0.15/0.45 ![X0,X1]: (~sP0_prd(X0,X1)|~r1(X0))),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f68])).
% 0.15/0.45 fof(f70,plain,(
% 0.15/0.45 ![X0,X1]: (~sP0_prd(X0,X1)|~X0=X1)),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f68])).
% 0.15/0.45 fof(f72,plain,(
% 0.15/0.45 ![X11,Y21,X12]: ((~sP1_prd(X12,Y21,X11)|(~r2(X11,X12)&~X12=Y21))&(sP1_prd(X12,Y21,X11)|(r2(X11,X12)|X12=Y21)))),
% 0.15/0.45 inference(NNF_transformation,[status(thm)],[f19])).
% 0.15/0.45 fof(f73,plain,(
% 0.15/0.45 (![X11,Y21,X12]: (~sP1_prd(X12,Y21,X11)|(~r2(X11,X12)&~X12=Y21)))&(![X11,Y21,X12]: (sP1_prd(X12,Y21,X11)|(r2(X11,X12)|X12=Y21)))),
% 0.15/0.45 inference(miniscoping,[status(thm)],[f72])).
% 0.15/0.45 fof(f75,plain,(
% 0.15/0.45 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|~X0=X1)),
% 0.15/0.45 inference(cnf_transformation,[status(thm)],[f73])).
% 0.15/0.45 fof(f94,plain,(
% 0.15/0.45 ![X0,X1,X2,X3,X4,X5]: (~r3(X0,X1,X2)|~r2(X3,X2)|~r2(X4,X3)|~r1(X5)|~r2(X5,X4))),
% 0.15/0.45 inference(destructive_equality_resolution,[status(thm)],[f66])).
% 0.15/0.45 fof(f95,plain,(
% 0.15/0.45 ![X0]: (~sP0_prd(X0,X0))),
% 0.15/0.45 inference(destructive_equality_resolution,[status(thm)],[f70])).
% 0.15/0.45 fof(f96,plain,(
% 0.15/0.45 ![X0,X1]: (~sP1_prd(X0,X0,X1))),
% 0.15/0.45 inference(destructive_equality_resolution,[status(thm)],[f75])).
% 0.15/0.45 fof(f100,plain,(
% 0.15/0.45 r1(sK0_skl)),
% 0.15/0.45 inference(resolution,[status(thm)],[f17,f95])).
% 0.15/0.45 fof(f113,plain,(
% 0.15/0.45 ![X0]: (X0=sK0_skl|~r1(X0))),
% 0.15/0.45 inference(resolution,[status(thm)],[f18,f69])).
% 0.15/0.45 fof(f117,plain,(
% 0.15/0.45 ![X0]: (sK13_skl(X0)=sK0_skl)),
% 0.15/0.45 inference(resolution,[status(thm)],[f113,f48])).
% 0.15/0.45 fof(f124,plain,(
% 0.15/0.45 ![X0]: (r2(X0,sK1_skl(X0)))),
% 0.15/0.45 inference(resolution,[status(thm)],[f22,f96])).
% 0.15/0.45 fof(f139,plain,(
% 0.15/0.45 ![X0]: (r3(X0,sK0_skl,sK12_skl(X0)))),
% 0.15/0.45 inference(forward_demodulation,[status(thm)],[f117,f49])).
% 0.15/0.45 fof(f140,plain,(
% 0.15/0.45 ![X0]: (r3(X0,sK0_skl,X0))),
% 0.15/0.45 inference(forward_demodulation,[status(thm)],[f50,f139])).
% 0.15/0.45 fof(f141,plain,(
% 0.15/0.45 ![X0,X1,X2,X3]: (~r2(X0,X1)|~r2(X2,X0)|~r1(X3)|~r2(X3,X2))),
% 0.15/0.45 inference(resolution,[status(thm)],[f140,f94])).
% 0.15/0.45 fof(f142,plain,(
% 0.15/0.45 ![X0,X1,X2]: (~r2(sK1_skl(X0),X1)|~r1(X2)|~r2(X2,X0))),
% 0.15/0.45 inference(resolution,[status(thm)],[f141,f124])).
% 0.15/0.45 fof(f148,plain,(
% 0.15/0.45 ![X0,X1]: (~r1(X0)|~r2(X0,X1))),
% 0.15/0.45 inference(resolution,[status(thm)],[f142,f124])).
% 0.15/0.45 fof(f151,plain,(
% 0.15/0.45 ![X0]: (~r1(X0))),
% 0.15/0.45 inference(resolution,[status(thm)],[f148,f124])).
% 0.15/0.45 fof(f157,plain,(
% 0.15/0.45 $false),
% 0.15/0.45 inference(backward_subsumption_resolution,[status(thm)],[f100,f151])).
% 0.15/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.50 % Elapsed time: 0.058167 seconds
% 0.15/0.50 % CPU time: 0.160817 seconds
% 0.15/0.50 % Total memory used: 80.052 MB
% 0.15/0.50 % Net memory used: 79.961 MB
%------------------------------------------------------------------------------