%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUN072+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 01:57:26 PM UTC 2026
% Result : Theorem 5.80s 1.35s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN072+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
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 03:26:48 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 5.80/1.35 % Refutation found
% 5.80/1.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.80/1.35 % SZS output start CNFRefutation for theBenchmark
% 5.80/1.35 fof(f1,axiom,(
% 5.80/1.35 (? [Y24] :(! [X19] :( ( ~ r1(X19)& X19 != Y24 )| ( r1(X19)& X19 = Y24 ) ) ))),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f2,axiom,(
% 5.80/1.35 (! [X11] :(? [Y21] :(! [X12] :( ( ~ r2(X11,X12)& X12 != Y21 )| ( r2(X11,X12)& X12 = Y21 ) ) )))),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f3,axiom,(
% 5.80/1.35 (! [X13,X14] :(? [Y22] :(! [X15] :( ( ~ r3(X13,X14,X15)& X15 != Y22 )| ( r3(X13,X14,X15)& X15 = Y22 ) ) )))),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f4,axiom,(
% 5.80/1.35 (! [X16,X17] :(? [Y23] :(! [X18] :( ( ~ r4(X16,X17,X18)& X18 != Y23 )| ( r4(X16,X17,X18)& X18 = Y23 ) ) )))),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f5,axiom,(
% 5.80/1.35 (! [X1,X8] :(? [Y4] :( (? [Y5] :( (? [Y15] :( r2(X8,Y15)& r3(X1,Y15,Y5) ))& Y5 = Y4 ))& (? [Y7] :( r2(Y7,Y4)& r3(X1,X8,Y7) ) )) ))),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f6,axiom,(
% 5.80/1.35 (! [X2,X9] :(? [Y2] :( (? [Y3] :( (? [Y14] :( r2(X9,Y14)& r4(X2,Y14,Y3) ))& Y3 = Y2 ))& (? [Y6] :( r3(Y6,X2,Y2)& r4(X2,X9,Y6) ) )) ))),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f7,axiom,(
% 5.80/1.35 (! [X3,X10] :( (! [Y12] :( (! [Y13] :( ~ r2(X3,Y13)| Y13 != Y12 ))| ~ r2(X10,Y12) ))| X3 = X10 ) )),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f8,axiom,(
% 5.80/1.35 (! [X4] :(? [Y9] :( (? [Y16] :( r1(Y16)& r3(X4,Y16,Y9) ))& Y9 = X4 ) ))),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f9,axiom,(
% 5.80/1.35 (! [X5] :(? [Y8] :( (? [Y17] :( r1(Y17)& r4(X5,Y17,Y8) ))& (? [Y18] :( r1(Y18)& Y8 = Y18 ) )) ))),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f12,conjecture,(
% 5.80/1.35 (? [Y1] :( (? [Y2] :( (? [Y4] :( r2(Y4,Y2)& (? [Y7] :( r1(Y7)& r2(Y7,Y4) ) )))& (? [Y5] :( r4(Y5,Y2,Y1)& (? [Y8] :( r1(Y8)& r2(Y8,Y5) ) )) )))& (? [Y3] :( Y1 = Y3& (? [Y6] :( r2(Y6,Y3)& (? [Y9] :( r1(Y9)& r2(Y9,Y6) ) )) )) )) )),
% 5.80/1.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.80/1.35 fof(f13,negated_conjecture,(
% 5.80/1.35 ~((? [Y1] :( (? [Y2] :( (? [Y4] :( r2(Y4,Y2)& (? [Y7] :( r1(Y7)& r2(Y7,Y4) ) )))& (? [Y5] :( r4(Y5,Y2,Y1)& (? [Y8] :( r1(Y8)& r2(Y8,Y5) ) )) )))& (? [Y3] :( Y1 = Y3& (? [Y6] :( r2(Y6,Y3)& (? [Y9] :( r1(Y9)& r2(Y9,Y6) ) )) )) )) ))),
% 5.80/1.35 inference(negated_conjecture,[status(cth)],[f12])).
% 5.80/1.35 fof(f14,definition,(
% 5.80/1.35 ![Y24,X19]: (sP0_prd(X19,Y24)<=>(~r1(X19)&~X19=Y24))),
% 5.80/1.35 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 5.80/1.35 fof(f15,plain,(
% 5.80/1.35 ?[Y24]: ![X19]: (sP0_prd(X19,Y24)|(r1(X19)&X19=Y24))),
% 5.80/1.35 inference(formula_renaming,[status(thm)],[f1,f14])).
% 5.80/1.35 fof(f16,plain,(
% 5.80/1.35 ![X19]: (sP0_prd(X19,sK0_skl)|(r1(X19)&X19=sK0_skl))),
% 5.80/1.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f15])).
% 5.80/1.35 fof(f17,plain,(
% 5.80/1.35 ![X0]: (sP0_prd(X0,sK0_skl)|r1(X0))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f16])).
% 5.80/1.35 fof(f18,plain,(
% 5.80/1.35 ![X0]: (sP0_prd(X0,sK0_skl)|X0=sK0_skl)),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f16])).
% 5.80/1.35 fof(f19,definition,(
% 5.80/1.35 ![X11,Y21,X12]: (sP1_prd(X12,Y21,X11)<=>(~r2(X11,X12)&~X12=Y21))),
% 5.80/1.35 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 5.80/1.35 fof(f20,plain,(
% 5.80/1.35 ![X11]: ?[Y21]: ![X12]: (sP1_prd(X12,Y21,X11)|(r2(X11,X12)&X12=Y21))),
% 5.80/1.35 inference(formula_renaming,[status(thm)],[f2,f19])).
% 5.80/1.35 fof(f21,plain,(
% 5.80/1.35 ![X11]: ![X12]: (sP1_prd(X12,sK1_skl(X11),X11)|(r2(X11,X12)&X12=sK1_skl(X11)))),
% 5.80/1.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y21,sK1_skl(X11))],[f20])).
% 5.80/1.35 fof(f22,plain,(
% 5.80/1.35 ![X0,X1]: (sP1_prd(X0,sK1_skl(X1),X1)|r2(X1,X0))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f21])).
% 5.80/1.35 fof(f23,plain,(
% 5.80/1.35 ![X0,X1]: (sP1_prd(X0,sK1_skl(X1),X1)|X0=sK1_skl(X1))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f21])).
% 5.80/1.35 fof(f24,definition,(
% 5.80/1.35 ![X13,X14,Y22,X15]: (sP2_prd(X15,Y22,X14,X13)<=>(~r3(X13,X14,X15)&~X15=Y22))),
% 5.80/1.35 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 5.80/1.35 fof(f25,plain,(
% 5.80/1.35 ![X13,X14]: ?[Y22]: ![X15]: (sP2_prd(X15,Y22,X14,X13)|(r3(X13,X14,X15)&X15=Y22))),
% 5.80/1.35 inference(formula_renaming,[status(thm)],[f3,f24])).
% 5.80/1.35 fof(f26,plain,(
% 5.80/1.35 ![X13,X14]: ![X15]: (sP2_prd(X15,sK2_skl(X14,X13),X14,X13)|(r3(X13,X14,X15)&X15=sK2_skl(X14,X13)))),
% 5.80/1.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y22,sK2_skl(X14,X13))],[f25])).
% 5.80/1.35 fof(f28,plain,(
% 5.80/1.35 ![X0,X1,X2]: (sP2_prd(X0,sK2_skl(X1,X2),X1,X2)|X0=sK2_skl(X1,X2))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f26])).
% 5.80/1.35 fof(f29,definition,(
% 5.80/1.35 ![X16,X17,Y23,X18]: (sP3_prd(X18,Y23,X17,X16)<=>(~r4(X16,X17,X18)&~X18=Y23))),
% 5.80/1.35 introduced(definition,[new_symbols(definition,[sP3_prd])],[])).
% 5.80/1.35 fof(f30,plain,(
% 5.80/1.35 ![X16,X17]: ?[Y23]: ![X18]: (sP3_prd(X18,Y23,X17,X16)|(r4(X16,X17,X18)&X18=Y23))),
% 5.80/1.35 inference(formula_renaming,[status(thm)],[f4,f29])).
% 5.80/1.35 fof(f31,plain,(
% 5.80/1.35 ![X16,X17]: ![X18]: (sP3_prd(X18,sK3_skl(X17,X16),X17,X16)|(r4(X16,X17,X18)&X18=sK3_skl(X17,X16)))),
% 5.80/1.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y23,sK3_skl(X17,X16))],[f30])).
% 5.80/1.35 fof(f33,plain,(
% 5.80/1.35 ![X0,X1,X2]: (sP3_prd(X0,sK3_skl(X1,X2),X1,X2)|X0=sK3_skl(X1,X2))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f31])).
% 5.80/1.35 fof(f34,plain,(
% 5.80/1.35 ![X1,X8]: (((r2(X8,sK6_skl(X8,X1))&r3(X1,sK6_skl(X8,X1),sK5_skl(X8,X1)))&sK5_skl(X8,X1)=sK4_skl(X8,X1))&(r2(sK7_skl(X8,X1),sK4_skl(X8,X1))&r3(X1,X8,sK7_skl(X8,X1))))),
% 5.80/1.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(Y4,sK4_skl(X8,X1)),skolemize(Y5,sK5_skl(X8,X1)),skolemize(Y15,sK6_skl(X8,X1)),skolemize(Y7,sK7_skl(X8,X1))],[f5])).
% 5.80/1.35 fof(f35,plain,(
% 5.80/1.35 ![X0,X1]: (r2(X0,sK6_skl(X0,X1)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f34])).
% 5.80/1.35 fof(f36,plain,(
% 5.80/1.35 ![X0,X1]: (r3(X0,sK6_skl(X1,X0),sK5_skl(X1,X0)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f34])).
% 5.80/1.35 fof(f37,plain,(
% 5.80/1.35 ![X0,X1]: (sK5_skl(X0,X1)=sK4_skl(X0,X1))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f34])).
% 5.80/1.35 fof(f38,plain,(
% 5.80/1.35 ![X0,X1]: (r2(sK7_skl(X0,X1),sK4_skl(X0,X1)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f34])).
% 5.80/1.35 fof(f39,plain,(
% 5.80/1.35 ![X0,X1]: (r3(X0,X1,sK7_skl(X1,X0)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f34])).
% 5.80/1.35 fof(f40,plain,(
% 5.80/1.35 ![X2,X9]: (((r2(X9,sK10_skl(X9,X2))&r4(X2,sK10_skl(X9,X2),sK9_skl(X9,X2)))&sK9_skl(X9,X2)=sK8_skl(X9,X2))&(r3(sK11_skl(X9,X2),X2,sK8_skl(X9,X2))&r4(X2,X9,sK11_skl(X9,X2))))),
% 5.80/1.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl]),skolemize(Y2,sK8_skl(X9,X2)),skolemize(Y3,sK9_skl(X9,X2)),skolemize(Y14,sK10_skl(X9,X2)),skolemize(Y6,sK11_skl(X9,X2))],[f6])).
% 5.80/1.35 fof(f41,plain,(
% 5.80/1.35 ![X0,X1]: (r2(X0,sK10_skl(X0,X1)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f40])).
% 5.80/1.35 fof(f42,plain,(
% 5.80/1.35 ![X0,X1]: (r4(X0,sK10_skl(X1,X0),sK9_skl(X1,X0)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f40])).
% 5.80/1.35 fof(f43,plain,(
% 5.80/1.35 ![X0,X1]: (sK9_skl(X0,X1)=sK8_skl(X0,X1))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f40])).
% 5.80/1.35 fof(f44,plain,(
% 5.80/1.35 ![X0,X1]: (r3(sK11_skl(X0,X1),X1,sK8_skl(X0,X1)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f40])).
% 5.80/1.35 fof(f45,plain,(
% 5.80/1.35 ![X0,X1]: (r4(X0,X1,sK11_skl(X1,X0)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f40])).
% 5.80/1.35 fof(f46,plain,(
% 5.80/1.35 ![X0,X1,X2,X3]: (~r2(X0,X1)|~X1=X2|~r2(X3,X2)|X0=X3)),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 5.80/1.35 fof(f47,plain,(
% 5.80/1.35 ![X4]: ((r1(sK13_skl(X4))&r3(X4,sK13_skl(X4),sK12_skl(X4)))&sK12_skl(X4)=X4)),
% 5.80/1.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f8])).
% 5.80/1.35 fof(f48,plain,(
% 5.80/1.35 ![X0]: (r1(sK13_skl(X0)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f47])).
% 5.80/1.35 fof(f49,plain,(
% 5.80/1.35 ![X0]: (r3(X0,sK13_skl(X0),sK12_skl(X0)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f47])).
% 5.80/1.35 fof(f50,plain,(
% 5.80/1.35 ![X0]: (sK12_skl(X0)=X0)),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f47])).
% 5.80/1.35 fof(f51,plain,(
% 5.80/1.35 ![X5]: ((r1(sK15_skl(X5))&r4(X5,sK15_skl(X5),sK14_skl(X5)))&(r1(sK16_skl(X5))&sK14_skl(X5)=sK16_skl(X5)))),
% 5.80/1.35 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])).
% 5.80/1.35 fof(f52,plain,(
% 5.80/1.35 ![X0]: (r1(sK15_skl(X0)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f51])).
% 5.80/1.35 fof(f53,plain,(
% 5.80/1.35 ![X0]: (r4(X0,sK15_skl(X0),sK14_skl(X0)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f51])).
% 5.80/1.35 fof(f54,plain,(
% 5.80/1.35 ![X0]: (r1(sK16_skl(X0)))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f51])).
% 5.80/1.35 fof(f55,plain,(
% 5.80/1.35 ![X0]: (sK14_skl(X0)=sK16_skl(X0))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f51])).
% 5.80/1.35 fof(f64,plain,(
% 5.80/1.35 (![Y1]: ((![Y2]: ((![Y4]: (~r2(Y4,Y2)|(![Y7]: (~r1(Y7)|~r2(Y7,Y4)))))|(![Y5]: (~r4(Y5,Y2,Y1)|(![Y8]: (~r1(Y8)|~r2(Y8,Y5)))))))|(![Y3]: (~Y1=Y3|(![Y6]: (~r2(Y6,Y3)|(![Y9]: (~r1(Y9)|~r2(Y9,Y6)))))))))),
% 5.80/1.35 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 5.80/1.35 fof(f65,plain,(
% 5.80/1.35 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (~r2(X0,X1)|~r1(X2)|~r2(X2,X0)|~r4(X3,X1,X4)|~r1(X5)|~r2(X5,X3)|~X4=X6|~r2(X7,X6)|~r1(X8)|~r2(X8,X7))),
% 5.80/1.35 inference(cnf_transformation,[status(thm)],[f64])).
% 5.80/1.35 fof(f66,plain,(
% 5.80/1.35 ![Y24,X19]: ((~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24))&(sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 5.80/1.35 inference(NNF_transformation,[status(thm)],[f14])).
% 5.80/1.36 fof(f67,plain,(
% 5.80/1.36 (![Y24,X19]: (~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24)))&(![Y24,X19]: (sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 5.80/1.36 inference(miniscoping,[status(thm)],[f66])).
% 5.80/1.36 fof(f68,plain,(
% 5.80/1.36 ![X0,X1]: (~sP0_prd(X0,X1)|~r1(X0))),
% 5.80/1.36 inference(cnf_transformation,[status(thm)],[f67])).
% 5.80/1.36 fof(f69,plain,(
% 5.80/1.36 ![X0,X1]: (~sP0_prd(X0,X1)|~X0=X1)),
% 5.80/1.36 inference(cnf_transformation,[status(thm)],[f67])).
% 5.80/1.36 fof(f71,plain,(
% 5.80/1.36 ![X11,Y21,X12]: ((~sP1_prd(X12,Y21,X11)|(~r2(X11,X12)&~X12=Y21))&(sP1_prd(X12,Y21,X11)|(r2(X11,X12)|X12=Y21)))),
% 5.80/1.36 inference(NNF_transformation,[status(thm)],[f19])).
% 5.80/1.36 fof(f72,plain,(
% 5.80/1.36 (![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)))),
% 5.80/1.36 inference(miniscoping,[status(thm)],[f71])).
% 5.80/1.36 fof(f73,plain,(
% 5.80/1.36 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|~r2(X2,X0))),
% 5.80/1.36 inference(cnf_transformation,[status(thm)],[f72])).
% 5.80/1.36 fof(f74,plain,(
% 5.80/1.36 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|~X0=X1)),
% 5.80/1.36 inference(cnf_transformation,[status(thm)],[f72])).
% 5.80/1.36 fof(f76,plain,(
% 5.80/1.36 ![X13,X14,Y22,X15]: ((~sP2_prd(X15,Y22,X14,X13)|(~r3(X13,X14,X15)&~X15=Y22))&(sP2_prd(X15,Y22,X14,X13)|(r3(X13,X14,X15)|X15=Y22)))),
% 5.80/1.36 inference(NNF_transformation,[status(thm)],[f24])).
% 5.80/1.36 fof(f77,plain,(
% 5.80/1.36 (![X13,X14,Y22,X15]: (~sP2_prd(X15,Y22,X14,X13)|(~r3(X13,X14,X15)&~X15=Y22)))&(![X13,X14,Y22,X15]: (sP2_prd(X15,Y22,X14,X13)|(r3(X13,X14,X15)|X15=Y22)))),
% 5.80/1.36 inference(miniscoping,[status(thm)],[f76])).
% 5.80/1.36 fof(f78,plain,(
% 5.80/1.36 ![X0,X1,X2,X3]: (~sP2_prd(X0,X1,X2,X3)|~r3(X3,X2,X0))),
% 5.80/1.36 inference(cnf_transformation,[status(thm)],[f77])).
% 5.80/1.36 fof(f81,plain,(
% 5.80/1.36 ![X16,X17,Y23,X18]: ((~sP3_prd(X18,Y23,X17,X16)|(~r4(X16,X17,X18)&~X18=Y23))&(sP3_prd(X18,Y23,X17,X16)|(r4(X16,X17,X18)|X18=Y23)))),
% 5.80/1.36 inference(NNF_transformation,[status(thm)],[f29])).
% 5.80/1.36 fof(f82,plain,(
% 5.80/1.36 (![X16,X17,Y23,X18]: (~sP3_prd(X18,Y23,X17,X16)|(~r4(X16,X17,X18)&~X18=Y23)))&(![X16,X17,Y23,X18]: (sP3_prd(X18,Y23,X17,X16)|(r4(X16,X17,X18)|X18=Y23)))),
% 5.80/1.36 inference(miniscoping,[status(thm)],[f81])).
% 5.80/1.36 fof(f83,plain,(
% 5.80/1.36 ![X0,X1,X2,X3]: (~sP3_prd(X0,X1,X2,X3)|~r4(X3,X2,X0))),
% 5.80/1.36 inference(cnf_transformation,[status(thm)],[f82])).
% 5.80/1.36 fof(f91,plain,(
% 5.80/1.36 ![X0,X1,X2]: (~r2(X0,X1)|~r2(X2,X1)|X0=X2)),
% 5.80/1.36 inference(destructive_equality_resolution,[status(thm)],[f46])).
% 5.80/1.36 fof(f93,plain,(
% 5.80/1.36 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~r2(X0,X1)|~r1(X2)|~r2(X2,X0)|~r4(X3,X1,X4)|~r1(X5)|~r2(X5,X3)|~r2(X6,X4)|~r1(X7)|~r2(X7,X6))),
% 5.80/1.36 inference(destructive_equality_resolution,[status(thm)],[f65])).
% 5.80/1.36 fof(f94,plain,(
% 5.80/1.36 ![X0]: (~sP0_prd(X0,X0))),
% 5.80/1.36 inference(destructive_equality_resolution,[status(thm)],[f69])).
% 5.80/1.36 fof(f95,plain,(
% 5.80/1.36 ![X0,X1]: (~sP1_prd(X0,X0,X1))),
% 5.80/1.36 inference(destructive_equality_resolution,[status(thm)],[f74])).
% 5.80/1.36 fof(f99,plain,(
% 5.80/1.36 r1(sK0_skl)),
% 5.80/1.36 inference(resolution,[status(thm)],[f94,f17])).
% 5.80/1.36 fof(f101,plain,(
% 5.80/1.36 ![X0,X1,X2,X3,X4,X5]: (~r2(X0,X1)|~r1(X2)|~r2(X2,X0)|~r4(X3,X1,X4)|~r2(sK0_skl,X3)|~r2(X5,X4)|~r2(sK0_skl,X5))),
% 5.80/1.36 inference(resolution,[status(thm)],[f99,f93])).
% 5.80/1.36 fof(f120,plain,(
% 5.80/1.36 ![X0]: (r1(sK14_skl(X0)))),
% 5.80/1.36 inference(backward_demodulation,[status(thm)],[f55,f54])).
% 5.80/1.36 fof(f127,plain,(
% 5.80/1.36 ![X0]: (r2(X0,sK1_skl(X0)))),
% 5.80/1.36 inference(resolution,[status(thm)],[f22,f95])).
% 5.80/1.36 fof(f140,plain,(
% 5.80/1.36 ![X0,X1,X2,X3,X4]: (~r2(X0,X1)|~r1(X2)|~r2(X2,X0)|~r4(X3,X1,X4)|~r2(sK0_skl,X3)|~r2(sK1_skl(sK0_skl),X4))),
% 5.80/1.36 inference(resolution,[status(thm)],[f127,f101])).
% 5.80/1.36 fof(f141,plain,(
% 5.80/1.36 ![X0,X1]: (~r2(X0,sK1_skl(X1))|X0=X1)),
% 5.80/1.36 inference(resolution,[status(thm)],[f127,f91])).
% 5.80/1.36 fof(f162,plain,(
% 5.80/1.36 ![X0]: (~r1(X0)|X0=sK0_skl)),
% 5.80/1.36 inference(resolution,[status(thm)],[f68,f18])).
% 5.80/1.36 fof(f164,plain,(
% 5.80/1.36 ![X0]: (sK14_skl(X0)=sK0_skl)),
% 5.80/1.36 inference(resolution,[status(thm)],[f162,f120])).
% 5.80/1.36 fof(f165,plain,(
% 5.80/1.36 ![X0]: (sK15_skl(X0)=sK0_skl)),
% 5.80/1.36 inference(resolution,[status(thm)],[f162,f52])).
% 5.80/1.36 fof(f166,plain,(
% 5.80/1.36 ![X0]: (sK13_skl(X0)=sK0_skl)),
% 5.80/1.36 inference(resolution,[status(thm)],[f162,f48])).
% 5.80/1.36 fof(f205,plain,(
% 5.80/1.36 ![X0,X1,X2,X3]: (~r2(X0,X1)|~r1(X2)|~r2(X2,X0)|~r2(sK0_skl,X3)|~r2(sK1_skl(sK0_skl),sK11_skl(X1,X3)))),
% 5.80/1.36 inference(resolution,[status(thm)],[f45,f140])).
% 5.80/1.36 fof(f210,plain,(
% 5.80/1.36 ![X0,X1]: (r3(X0,sK6_skl(X1,X0),sK4_skl(X1,X0)))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f37,f36])).
% 5.80/1.36 fof(f219,plain,(
% 5.80/1.36 ![X0]: (r3(X0,sK0_skl,sK12_skl(X0)))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f166,f49])).
% 5.80/1.36 fof(f220,plain,(
% 5.80/1.36 ![X0]: (r3(X0,sK0_skl,X0))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f50,f219])).
% 5.80/1.36 fof(f221,plain,(
% 5.80/1.36 ![X0]: (r4(X0,sK0_skl,sK14_skl(X0)))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f165,f53])).
% 5.80/1.36 fof(f222,plain,(
% 5.80/1.36 ![X0]: (r4(X0,sK0_skl,sK0_skl))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f164,f221])).
% 5.80/1.36 fof(f250,plain,(
% 5.80/1.36 ![X0,X1]: (~r2(X0,X1)|X1=sK1_skl(X0))),
% 5.80/1.36 inference(resolution,[status(thm)],[f73,f23])).
% 5.80/1.36 fof(f252,plain,(
% 5.80/1.36 ![X0,X1]: (sK4_skl(X0,X1)=sK1_skl(sK7_skl(X0,X1)))),
% 5.80/1.36 inference(resolution,[status(thm)],[f250,f38])).
% 5.80/1.36 fof(f253,plain,(
% 5.80/1.36 ![X0,X1]: (sK10_skl(X0,X1)=sK1_skl(X0))),
% 5.80/1.36 inference(resolution,[status(thm)],[f250,f41])).
% 5.80/1.36 fof(f254,plain,(
% 5.80/1.36 ![X0,X1]: (sK6_skl(X0,X1)=sK1_skl(X0))),
% 5.80/1.36 inference(resolution,[status(thm)],[f250,f35])).
% 5.80/1.36 fof(f258,plain,(
% 5.80/1.36 ![X0,X1]: (r3(X0,sK1_skl(X1),sK4_skl(X1,X0)))),
% 5.80/1.36 inference(backward_demodulation,[status(thm)],[f254,f210])).
% 5.80/1.36 fof(f263,plain,(
% 5.80/1.36 ![X0,X1]: (r4(X0,sK1_skl(X1),sK9_skl(X1,X0)))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f253,f42])).
% 5.80/1.36 fof(f264,plain,(
% 5.80/1.36 ![X0,X1]: (r4(X0,sK1_skl(X1),sK8_skl(X1,X0)))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f43,f263])).
% 5.80/1.36 fof(f363,plain,(
% 5.80/1.36 ![X0,X1,X2]: (~r3(X0,X1,X2)|X2=sK2_skl(X1,X0))),
% 5.80/1.36 inference(resolution,[status(thm)],[f78,f28])).
% 5.80/1.36 fof(f415,plain,(
% 5.80/1.36 ![X0,X1]: (sK8_skl(X0,X1)=sK2_skl(X1,sK11_skl(X0,X1)))),
% 5.80/1.36 inference(resolution,[status(thm)],[f363,f44])).
% 5.80/1.36 fof(f416,plain,(
% 5.80/1.36 ![X0,X1]: (sK4_skl(X0,X1)=sK2_skl(sK1_skl(X0),X1))),
% 5.80/1.36 inference(resolution,[status(thm)],[f363,f258])).
% 5.80/1.36 fof(f417,plain,(
% 5.80/1.36 ![X0]: (X0=sK2_skl(sK0_skl,X0))),
% 5.80/1.36 inference(resolution,[status(thm)],[f363,f220])).
% 5.80/1.36 fof(f419,plain,(
% 5.80/1.36 ![X0,X1]: (sK7_skl(X0,X1)=sK2_skl(X0,X1))),
% 5.80/1.36 inference(resolution,[status(thm)],[f363,f39])).
% 5.80/1.36 fof(f424,plain,(
% 5.80/1.36 ![X0]: (X0=sK7_skl(sK0_skl,X0))),
% 5.80/1.36 inference(backward_demodulation,[status(thm)],[f419,f417])).
% 5.80/1.36 fof(f425,plain,(
% 5.80/1.36 ![X0,X1,X2]: (~r3(X0,X1,X2)|X2=sK7_skl(X1,X0))),
% 5.80/1.36 inference(backward_demodulation,[status(thm)],[f419,f363])).
% 5.80/1.36 fof(f430,plain,(
% 5.80/1.36 ![X0]: (sK4_skl(sK0_skl,X0)=sK1_skl(X0))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f424,f252])).
% 5.80/1.36 fof(f444,plain,(
% 5.80/1.36 ![X0,X1,X2]: (~r4(X0,X1,X2)|X2=sK3_skl(X1,X0))),
% 5.80/1.36 inference(resolution,[status(thm)],[f83,f33])).
% 5.80/1.36 fof(f517,plain,(
% 5.80/1.36 ![X0,X1]: (sK4_skl(X0,X1)=sK7_skl(sK1_skl(X0),X1))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f419,f416])).
% 5.80/1.36 fof(f521,plain,(
% 5.80/1.36 ![X0,X1]: (sK4_skl(sK1_skl(X0),X1)=sK1_skl(sK4_skl(X0,X1)))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f517,f252])).
% 5.80/1.36 fof(f543,plain,(
% 5.80/1.36 ![X0,X1]: (sK8_skl(X0,X1)=sK3_skl(sK1_skl(X0),X1))),
% 5.80/1.36 inference(resolution,[status(thm)],[f444,f264])).
% 5.80/1.36 fof(f544,plain,(
% 5.80/1.36 ![X0]: (sK0_skl=sK3_skl(sK0_skl,X0))),
% 5.80/1.36 inference(resolution,[status(thm)],[f444,f222])).
% 5.80/1.36 fof(f546,plain,(
% 5.80/1.36 ![X0,X1]: (sK11_skl(X0,X1)=sK3_skl(X0,X1))),
% 5.80/1.36 inference(resolution,[status(thm)],[f444,f45])).
% 5.80/1.36 fof(f553,plain,(
% 5.80/1.36 ![X0]: (sK0_skl=sK11_skl(sK0_skl,X0))),
% 5.80/1.36 inference(backward_demodulation,[status(thm)],[f546,f544])).
% 5.80/1.36 fof(f563,plain,(
% 5.80/1.36 ![X0]: (r3(sK0_skl,X0,sK8_skl(sK0_skl,X0)))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f553,f44])).
% 5.80/1.36 fof(f652,plain,(
% 5.80/1.36 ![X0,X1]: (sK8_skl(X0,X1)=sK11_skl(sK1_skl(X0),X1))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f546,f543])).
% 5.80/1.36 fof(f668,plain,(
% 5.80/1.36 ![X0]: (sK8_skl(sK0_skl,X0)=sK7_skl(X0,sK0_skl))),
% 5.80/1.36 inference(resolution,[status(thm)],[f563,f425])).
% 5.80/1.36 fof(f728,plain,(
% 5.80/1.36 ![X0,X1]: (sK8_skl(X0,X1)=sK7_skl(X1,sK11_skl(X0,X1)))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f419,f415])).
% 5.80/1.36 fof(f731,plain,(
% 5.80/1.36 ![X0,X1]: (sK8_skl(sK1_skl(X0),X1)=sK7_skl(X1,sK8_skl(X0,X1)))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f652,f728])).
% 5.80/1.36 fof(f756,plain,(
% 5.80/1.36 ![X0]: (sK4_skl(sK1_skl(sK0_skl),X0)=sK1_skl(sK1_skl(X0)))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f430,f521])).
% 5.80/1.36 fof(f763,plain,(
% 5.80/1.36 ![X0,X1,X2]: (~r2(X0,sK4_skl(sK1_skl(X1),X2))|X0=sK4_skl(X1,X2))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f521,f141])).
% 5.80/1.36 fof(f1283,plain,(
% 5.80/1.36 ![X0,X1]: (r2(sK8_skl(sK1_skl(X0),X1),sK4_skl(X1,sK8_skl(X0,X1))))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f731,f38])).
% 5.80/1.36 fof(f2827,plain,(
% 5.80/1.36 ![X0,X1]: (sK8_skl(sK1_skl(X0),sK1_skl(X1))=sK4_skl(X1,sK8_skl(X0,sK1_skl(X1))))),
% 5.80/1.36 inference(resolution,[status(thm)],[f1283,f763])).
% 5.80/1.36 fof(f2897,plain,(
% 5.80/1.36 ![X0,X1,X2]: (~r2(X0,X1)|~r1(X2)|~r2(X2,X0)|~r2(sK1_skl(sK0_skl),sK11_skl(X1,sK1_skl(sK0_skl))))),
% 5.80/1.36 inference(resolution,[status(thm)],[f205,f127])).
% 5.80/1.36 fof(f2905,plain,(
% 5.80/1.36 ![X0,X1,X2]: (~r2(X0,sK1_skl(X1))|~r1(X2)|~r2(X2,X0)|~r2(sK1_skl(sK0_skl),sK8_skl(X1,sK1_skl(sK0_skl))))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f652,f2897])).
% 5.80/1.36 fof(f4368,plain,(
% 5.80/1.36 ![X0]: (sK8_skl(sK1_skl(sK0_skl),sK1_skl(X0))=sK4_skl(X0,sK7_skl(sK1_skl(X0),sK0_skl)))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f668,f2827])).
% 5.80/1.36 fof(f4428,plain,(
% 5.80/1.36 ![X0]: (sK8_skl(sK1_skl(sK0_skl),sK1_skl(X0))=sK4_skl(X0,sK4_skl(X0,sK0_skl)))),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f517,f4368])).
% 5.80/1.36 fof(f5019,plain,(
% 5.80/1.36 ![X0,X1]: (~r2(X0,sK1_skl(sK1_skl(sK0_skl)))|~r1(X1)|~r2(X1,X0)|~r2(sK1_skl(sK0_skl),sK4_skl(sK0_skl,sK4_skl(sK0_skl,sK0_skl))))),
% 5.80/1.36 inference(paramodulation,[status(thm)],[f4428,f2905])).
% 5.80/1.36 fof(f5101,definition,(
% 5.80/1.36 ![X0,X1]: (sQ156_spl <=> (~r2(X0,sK1_skl(sK1_skl(sK0_skl)))|~r1(X1)|~r2(X1,X0)))),
% 5.80/1.36 introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition])).
% 5.80/1.36 fof(f5102,plain,(
% 5.80/1.36 ![X0,X1]: (~r2(X0,sK1_skl(sK1_skl(sK0_skl)))|~r1(X1)|~r2(X1,X0)|~sQ156_spl)),
% 5.80/1.36 inference(component_clause,[status(thm)],[f5101])).
% 5.80/1.36 fof(f5104,definition,(
% 5.80/1.36 sQ157_spl <=> (r2(sK1_skl(sK0_skl),sK4_skl(sK0_skl,sK4_skl(sK0_skl,sK0_skl))))),
% 5.80/1.36 introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition])).
% 5.80/1.36 fof(f5106,plain,(
% 5.80/1.36 ~r2(sK1_skl(sK0_skl),sK4_skl(sK0_skl,sK4_skl(sK0_skl,sK0_skl)))|sQ157_spl),
% 5.80/1.36 inference(component_clause,[status(thm)],[f5104])).
% 5.80/1.36 fof(f5107,plain,(
% 5.80/1.36 sQ156_spl|~sQ157_spl),
% 5.80/1.36 inference(split_clause,[status(thm)],[f5019,f5101,f5104])).
% 5.80/1.36 fof(f5158,plain,(
% 5.80/1.36 ![X0]: (~r1(X0)|~r2(X0,sK1_skl(sK0_skl))|~sQ156_spl)),
% 5.80/1.36 inference(resolution,[status(thm)],[f5102,f127])).
% 5.80/1.36 fof(f5167,plain,(
% 5.80/1.36 ~r1(sK0_skl)|~sQ156_spl),
% 5.80/1.36 inference(resolution,[status(thm)],[f5158,f127])).
% 5.80/1.36 fof(f5173,plain,(
% 5.80/1.36 $false|~sQ156_spl),
% 5.80/1.36 inference(forward_subsumption_resolution,[status(thm)],[f5167,f99])).
% 5.80/1.36 fof(f5174,plain,(
% 5.80/1.36 ~sQ156_spl),
% 5.80/1.36 inference(contradiction_clause,[status(thm)],[f5173])).
% 5.80/1.36 fof(f5175,plain,(
% 5.80/1.36 ~r2(sK1_skl(sK0_skl),sK1_skl(sK4_skl(sK0_skl,sK0_skl)))|sQ157_spl),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f430,f5106])).
% 5.80/1.36 fof(f5176,plain,(
% 5.80/1.36 ~r2(sK1_skl(sK0_skl),sK4_skl(sK1_skl(sK0_skl),sK0_skl))|sQ157_spl),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f521,f5175])).
% 5.80/1.36 fof(f5177,plain,(
% 5.80/1.36 ~r2(sK1_skl(sK0_skl),sK1_skl(sK1_skl(sK0_skl)))|sQ157_spl),
% 5.80/1.36 inference(forward_demodulation,[status(thm)],[f756,f5176])).
% 5.80/1.36 fof(f5178,plain,(
% 5.80/1.36 $false|sQ157_spl),
% 5.80/1.36 inference(forward_subsumption_resolution,[status(thm)],[f5177,f127])).
% 5.80/1.36 fof(f5179,plain,(
% 5.80/1.36 sQ157_spl),
% 5.80/1.36 inference(contradiction_clause,[status(thm)],[f5178])).
% 5.80/1.37 fof(f5180,plain,(
% 5.80/1.37 $false),
% 5.80/1.37 inference(sat_refutation,[status(thm)],[f5107,f5174,f5179])).
% 5.80/1.37 % SZS output end CNFRefutation for theBenchmark.p
% 5.80/1.38 % Elapsed time: 0.914042 seconds
% 5.80/1.38 % CPU time: 6.928359 seconds
% 5.80/1.38 % Total memory used: 155.567 MB
% 5.80/1.38 % Net memory used: 144.602 MB
%------------------------------------------------------------------------------