%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUN076+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 : n001.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 01:57:26 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN076+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
% 0.18/0.44 % Computer : n001.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 03:30:14 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.49 % Refutation found
% 0.18/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.49 fof(f1,axiom,(
% 0.18/0.49 (? [Y24] :(! [X19] :( ( ~ r1(X19)& X19 != Y24 )| ( r1(X19)& X19 = Y24 ) ) ))),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f2,axiom,(
% 0.18/0.49 (! [X11] :(? [Y21] :(! [X12] :( ( ~ r2(X11,X12)& X12 != Y21 )| ( r2(X11,X12)& X12 = Y21 ) ) )))),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f8,axiom,(
% 0.18/0.49 (! [X4] :(? [Y9] :( (? [Y16] :( r1(Y16)& r3(X4,Y16,Y9) ))& Y9 = X4 ) ))),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f9,axiom,(
% 0.18/0.49 (! [X5] :(? [Y8] :( (? [Y17] :( r1(Y17)& r4(X5,Y17,Y8) ))& (? [Y18] :( r1(Y18)& Y8 = Y18 ) )) ))),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f12,conjecture,(
% 0.18/0.49 (? [Y1,Y2,Y3] :( (? [Y4] :( Y4 = Y1& (? [Y6] :( r4(Y6,Y2,Y4)& (? [Y7] :( r2(Y7,Y6)& (? [Y8] :( r1(Y8)& r2(Y8,Y7) ) )) )) )))& (? [Y5] :( r3(Y2,Y3,Y5)& Y5 = Y1 ) )) )),
% 0.18/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f13,negated_conjecture,(
% 0.18/0.49 ~((? [Y1,Y2,Y3] :( (? [Y4] :( Y4 = Y1& (? [Y6] :( r4(Y6,Y2,Y4)& (? [Y7] :( r2(Y7,Y6)& (? [Y8] :( r1(Y8)& r2(Y8,Y7) ) )) )) )))& (? [Y5] :( r3(Y2,Y3,Y5)& Y5 = Y1 ) )) ))),
% 0.18/0.49 inference(negated_conjecture,[status(cth)],[f12])).
% 0.18/0.49 fof(f14,definition,(
% 0.18/0.49 ![Y24,X19]: (sP0_prd(X19,Y24)<=>(~r1(X19)&~X19=Y24))),
% 0.18/0.49 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.18/0.49 fof(f15,plain,(
% 0.18/0.49 ?[Y24]: ![X19]: (sP0_prd(X19,Y24)|(r1(X19)&X19=Y24))),
% 0.18/0.49 inference(formula_renaming,[status(thm)],[f1,f14])).
% 0.18/0.49 fof(f16,plain,(
% 0.18/0.49 ![X19]: (sP0_prd(X19,sK0_skl)|(r1(X19)&X19=sK0_skl))),
% 0.18/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f15])).
% 0.18/0.49 fof(f17,plain,(
% 0.18/0.49 ![X0]: (sP0_prd(X0,sK0_skl)|r1(X0))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f16])).
% 0.18/0.49 fof(f18,plain,(
% 0.18/0.49 ![X0]: (sP0_prd(X0,sK0_skl)|X0=sK0_skl)),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f16])).
% 0.18/0.49 fof(f19,definition,(
% 0.18/0.49 ![X11,Y21,X12]: (sP1_prd(X12,Y21,X11)<=>(~r2(X11,X12)&~X12=Y21))),
% 0.18/0.49 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.18/0.49 fof(f20,plain,(
% 0.18/0.49 ![X11]: ?[Y21]: ![X12]: (sP1_prd(X12,Y21,X11)|(r2(X11,X12)&X12=Y21))),
% 0.18/0.49 inference(formula_renaming,[status(thm)],[f2,f19])).
% 0.18/0.49 fof(f21,plain,(
% 0.18/0.49 ![X11]: ![X12]: (sP1_prd(X12,sK1_skl(X11),X11)|(r2(X11,X12)&X12=sK1_skl(X11)))),
% 0.18/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y21,sK1_skl(X11))],[f20])).
% 0.18/0.49 fof(f22,plain,(
% 0.18/0.49 ![X0,X1]: (sP1_prd(X0,sK1_skl(X1),X1)|r2(X1,X0))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f21])).
% 0.18/0.49 fof(f47,plain,(
% 0.18/0.49 ![X4]: ((r1(sK13_skl(X4))&r3(X4,sK13_skl(X4),sK12_skl(X4)))&sK12_skl(X4)=X4)),
% 0.18/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f8])).
% 0.18/0.49 fof(f48,plain,(
% 0.18/0.49 ![X0]: (r1(sK13_skl(X0)))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f47])).
% 0.18/0.49 fof(f49,plain,(
% 0.18/0.49 ![X0]: (r3(X0,sK13_skl(X0),sK12_skl(X0)))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f47])).
% 0.18/0.49 fof(f50,plain,(
% 0.18/0.49 ![X0]: (sK12_skl(X0)=X0)),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f47])).
% 0.18/0.49 fof(f51,plain,(
% 0.18/0.49 ![X5]: ((r1(sK15_skl(X5))&r4(X5,sK15_skl(X5),sK14_skl(X5)))&(r1(sK16_skl(X5))&sK14_skl(X5)=sK16_skl(X5)))),
% 0.18/0.49 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])).
% 0.18/0.49 fof(f52,plain,(
% 0.18/0.49 ![X0]: (r1(sK15_skl(X0)))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f51])).
% 0.18/0.49 fof(f53,plain,(
% 0.18/0.49 ![X0]: (r4(X0,sK15_skl(X0),sK14_skl(X0)))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f51])).
% 0.18/0.49 fof(f54,plain,(
% 0.18/0.49 ![X0]: (r1(sK16_skl(X0)))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f51])).
% 0.18/0.49 fof(f55,plain,(
% 0.18/0.49 ![X0]: (sK14_skl(X0)=sK16_skl(X0))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f51])).
% 0.18/0.49 fof(f64,plain,(
% 0.18/0.49 (![Y1,Y2,Y3]: ((![Y4]: (~Y4=Y1|(![Y6]: (~r4(Y6,Y2,Y4)|(![Y7]: (~r2(Y7,Y6)|(![Y8]: (~r1(Y8)|~r2(Y8,Y7)))))))))|(![Y5]: (~r3(Y2,Y3,Y5)|~Y5=Y1))))),
% 0.18/0.49 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.18/0.49 fof(f65,plain,(
% 0.18/0.49 ![Y1,Y2]: ((![Y4]: (~Y4=Y1|(![Y6]: (~r4(Y6,Y2,Y4)|(![Y7]: (~r2(Y7,Y6)|(![Y8]: (~r1(Y8)|~r2(Y8,Y7)))))))))|(![Y5]: ((![Y3]: ~r3(Y2,Y3,Y5))|~Y5=Y1)))),
% 0.18/0.49 inference(miniscoping,[status(thm)],[f64])).
% 0.18/0.49 fof(f66,plain,(
% 0.18/0.49 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~X0=X1|~r4(X2,X3,X0)|~r2(X4,X2)|~r1(X5)|~r2(X5,X4)|~r3(X3,X6,X7)|~X7=X1)),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f65])).
% 0.18/0.49 fof(f67,plain,(
% 0.18/0.49 ![Y24,X19]: ((~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24))&(sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 0.18/0.49 inference(NNF_transformation,[status(thm)],[f14])).
% 0.18/0.49 fof(f68,plain,(
% 0.18/0.49 (![Y24,X19]: (~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24)))&(![Y24,X19]: (sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 0.18/0.49 inference(miniscoping,[status(thm)],[f67])).
% 0.18/0.49 fof(f69,plain,(
% 0.18/0.49 ![X0,X1]: (~sP0_prd(X0,X1)|~r1(X0))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f68])).
% 0.18/0.49 fof(f70,plain,(
% 0.18/0.49 ![X0,X1]: (~sP0_prd(X0,X1)|~X0=X1)),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f68])).
% 0.18/0.49 fof(f72,plain,(
% 0.18/0.49 ![X11,Y21,X12]: ((~sP1_prd(X12,Y21,X11)|(~r2(X11,X12)&~X12=Y21))&(sP1_prd(X12,Y21,X11)|(r2(X11,X12)|X12=Y21)))),
% 0.18/0.49 inference(NNF_transformation,[status(thm)],[f19])).
% 0.18/0.49 fof(f73,plain,(
% 0.18/0.49 (![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)))),
% 0.18/0.49 inference(miniscoping,[status(thm)],[f72])).
% 0.18/0.49 fof(f75,plain,(
% 0.18/0.49 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|~X0=X1)),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f73])).
% 0.18/0.49 fof(f94,plain,(
% 0.18/0.49 ![X0,X1,X2,X3,X4,X5]: (~r4(X0,X1,X2)|~r2(X3,X0)|~r1(X4)|~r2(X4,X3)|~r3(X1,X5,X2))),
% 0.18/0.49 inference(destructive_equality_resolution,[status(thm)],[f66])).
% 0.18/0.49 fof(f95,plain,(
% 0.18/0.49 ![X0]: (~sP0_prd(X0,X0))),
% 0.18/0.49 inference(destructive_equality_resolution,[status(thm)],[f70])).
% 0.18/0.49 fof(f96,plain,(
% 0.18/0.49 ![X0,X1]: (~sP1_prd(X0,X0,X1))),
% 0.18/0.49 inference(destructive_equality_resolution,[status(thm)],[f75])).
% 0.18/0.49 fof(f100,plain,(
% 0.18/0.49 r1(sK0_skl)),
% 0.18/0.49 inference(resolution,[status(thm)],[f17,f95])).
% 0.18/0.49 fof(f113,plain,(
% 0.18/0.49 ![X0]: (X0=sK0_skl|~r1(X0))),
% 0.18/0.49 inference(resolution,[status(thm)],[f18,f69])).
% 0.18/0.49 fof(f115,plain,(
% 0.18/0.49 ![X0]: (sK16_skl(X0)=sK0_skl)),
% 0.18/0.49 inference(resolution,[status(thm)],[f113,f54])).
% 0.18/0.49 fof(f116,plain,(
% 0.18/0.49 ![X0]: (sK15_skl(X0)=sK0_skl)),
% 0.18/0.49 inference(resolution,[status(thm)],[f113,f52])).
% 0.18/0.49 fof(f117,plain,(
% 0.18/0.49 ![X0]: (sK13_skl(X0)=sK0_skl)),
% 0.18/0.49 inference(resolution,[status(thm)],[f113,f48])).
% 0.18/0.49 fof(f119,plain,(
% 0.18/0.49 ![X0]: (sK14_skl(X0)=sK0_skl)),
% 0.18/0.49 inference(backward_demodulation,[status(thm)],[f115,f55])).
% 0.18/0.49 fof(f124,plain,(
% 0.18/0.49 ![X0]: (r2(X0,sK1_skl(X0)))),
% 0.18/0.49 inference(resolution,[status(thm)],[f22,f96])).
% 0.18/0.49 fof(f139,plain,(
% 0.18/0.49 ![X0]: (r3(X0,sK0_skl,sK12_skl(X0)))),
% 0.18/0.49 inference(forward_demodulation,[status(thm)],[f117,f49])).
% 0.18/0.49 fof(f140,plain,(
% 0.18/0.49 ![X0]: (r3(X0,sK0_skl,X0))),
% 0.18/0.49 inference(forward_demodulation,[status(thm)],[f50,f139])).
% 0.18/0.49 fof(f141,plain,(
% 0.18/0.49 ![X0,X1,X2,X3]: (~r4(X0,X1,X1)|~r2(X2,X0)|~r1(X3)|~r2(X3,X2))),
% 0.18/0.49 inference(resolution,[status(thm)],[f140,f94])).
% 0.18/0.49 fof(f142,plain,(
% 0.18/0.49 ![X0]: (r4(X0,sK0_skl,sK14_skl(X0)))),
% 0.18/0.49 inference(forward_demodulation,[status(thm)],[f116,f53])).
% 0.18/0.49 fof(f143,plain,(
% 0.18/0.49 ![X0]: (r4(X0,sK0_skl,sK0_skl))),
% 0.18/0.49 inference(forward_demodulation,[status(thm)],[f119,f142])).
% 0.18/0.49 fof(f144,plain,(
% 0.18/0.49 ![X0,X1,X2]: (~r2(X0,X1)|~r1(X2)|~r2(X2,X0))),
% 0.18/0.49 inference(resolution,[status(thm)],[f143,f141])).
% 0.18/0.49 fof(f145,plain,(
% 0.18/0.49 ![X0,X1]: (~r2(sK1_skl(X0),X1)|~r1(X0))),
% 0.18/0.49 inference(resolution,[status(thm)],[f144,f124])).
% 0.18/0.49 fof(f148,plain,(
% 0.18/0.49 ![X0]: (~r1(X0))),
% 0.18/0.49 inference(resolution,[status(thm)],[f145,f124])).
% 0.18/0.49 fof(f157,plain,(
% 0.18/0.49 $false),
% 0.18/0.49 inference(backward_subsumption_resolution,[status(thm)],[f100,f148])).
% 0.18/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.54 % Elapsed time: 0.075577 seconds
% 0.18/0.54 % CPU time: 0.116345 seconds
% 0.18/0.54 % Total memory used: 28.927 MB
% 0.18/0.54 % Net memory used: 28.899 MB
%------------------------------------------------------------------------------