%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUN071+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 : n014.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 0.12s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN071+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 03:24:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.39 fof(f1,axiom,(
% 0.12/0.39 (? [Y24] :(! [X19] :( ( ~ r1(X19)& X19 != Y24 )| ( r1(X19)& X19 = Y24 ) ) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f2,axiom,(
% 0.12/0.39 (! [X11] :(? [Y21] :(! [X12] :( ( ~ r2(X11,X12)& X12 != Y21 )| ( r2(X11,X12)& X12 = Y21 ) ) )))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f3,axiom,(
% 0.12/0.39 (! [X13,X14] :(? [Y22] :(! [X15] :( ( ~ r3(X13,X14,X15)& X15 != Y22 )| ( r3(X13,X14,X15)& X15 = Y22 ) ) )))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f4,axiom,(
% 0.12/0.39 (! [X16,X17] :(? [Y23] :(! [X18] :( ( ~ r4(X16,X17,X18)& X18 != Y23 )| ( r4(X16,X17,X18)& X18 = Y23 ) ) )))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f5,axiom,(
% 0.12/0.39 (! [X1,X8] :(? [Y4] :( (? [Y5] :( (? [Y15] :( r2(X8,Y15)& r3(X1,Y15,Y5) ))& Y5 = Y4 ))& (? [Y7] :( r2(Y7,Y4)& r3(X1,X8,Y7) ) )) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f6,axiom,(
% 0.12/0.39 (! [X2,X9] :(? [Y2] :( (? [Y3] :( (? [Y14] :( r2(X9,Y14)& r4(X2,Y14,Y3) ))& Y3 = Y2 ))& (? [Y6] :( r3(Y6,X2,Y2)& r4(X2,X9,Y6) ) )) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f8,axiom,(
% 0.12/0.39 (! [X4] :(? [Y9] :( (? [Y16] :( r1(Y16)& r3(X4,Y16,Y9) ))& Y9 = X4 ) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f9,axiom,(
% 0.12/0.39 (! [X5] :(? [Y8] :( (? [Y17] :( r1(Y17)& r4(X5,Y17,Y8) ))& (? [Y18] :( r1(Y18)& Y8 = Y18 ) )) ))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f11,axiom,(
% 0.12/0.39 (! [X7,Y10] :( (! [Y20] :( ~ r1(Y20)| Y20 != Y10 ))| ~ r2(X7,Y10) ) )),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f12,conjecture,(
% 0.12/0.39 (? [Y1] :( (? [Y2] :( r4(Y2,Y2,Y1)& (? [Y4] :( r1(Y4)& r2(Y4,Y2) ) )))& (? [Y3] :( Y1 = Y3& (? [Y5] :( r1(Y5)& r2(Y5,Y3) ) )) )) )),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f13,negated_conjecture,(
% 0.12/0.39 ~((? [Y1] :( (? [Y2] :( r4(Y2,Y2,Y1)& (? [Y4] :( r1(Y4)& r2(Y4,Y2) ) )))& (? [Y3] :( Y1 = Y3& (? [Y5] :( r1(Y5)& r2(Y5,Y3) ) )) )) ))),
% 0.12/0.39 inference(negated_conjecture,[status(cth)],[f12])).
% 0.12/0.39 fof(f14,definition,(
% 0.12/0.39 ![Y24,X19]: (sP0_prd(X19,Y24)<=>(~r1(X19)&~X19=Y24))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.12/0.39 fof(f15,plain,(
% 0.12/0.39 ?[Y24]: ![X19]: (sP0_prd(X19,Y24)|(r1(X19)&X19=Y24))),
% 0.12/0.39 inference(formula_renaming,[status(thm)],[f1,f14])).
% 0.12/0.39 fof(f16,plain,(
% 0.12/0.39 ![X19]: (sP0_prd(X19,sK0_skl)|(r1(X19)&X19=sK0_skl))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f15])).
% 0.12/0.39 fof(f17,plain,(
% 0.12/0.39 ![X0]: (sP0_prd(X0,sK0_skl)|r1(X0))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f16])).
% 0.12/0.39 fof(f18,plain,(
% 0.12/0.39 ![X0]: (sP0_prd(X0,sK0_skl)|X0=sK0_skl)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f16])).
% 0.12/0.39 fof(f19,definition,(
% 0.12/0.39 ![X11,Y21,X12]: (sP1_prd(X12,Y21,X11)<=>(~r2(X11,X12)&~X12=Y21))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.12/0.39 fof(f20,plain,(
% 0.12/0.39 ![X11]: ?[Y21]: ![X12]: (sP1_prd(X12,Y21,X11)|(r2(X11,X12)&X12=Y21))),
% 0.12/0.39 inference(formula_renaming,[status(thm)],[f2,f19])).
% 0.12/0.39 fof(f21,plain,(
% 0.12/0.39 ![X11]: ![X12]: (sP1_prd(X12,sK1_skl(X11),X11)|(r2(X11,X12)&X12=sK1_skl(X11)))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y21,sK1_skl(X11))],[f20])).
% 0.12/0.39 fof(f22,plain,(
% 0.12/0.39 ![X0,X1]: (sP1_prd(X0,sK1_skl(X1),X1)|r2(X1,X0))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f21])).
% 0.12/0.39 fof(f23,plain,(
% 0.12/0.39 ![X0,X1]: (sP1_prd(X0,sK1_skl(X1),X1)|X0=sK1_skl(X1))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f21])).
% 0.12/0.39 fof(f24,definition,(
% 0.12/0.39 ![X13,X14,Y22,X15]: (sP2_prd(X15,Y22,X14,X13)<=>(~r3(X13,X14,X15)&~X15=Y22))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 0.12/0.39 fof(f25,plain,(
% 0.12/0.39 ![X13,X14]: ?[Y22]: ![X15]: (sP2_prd(X15,Y22,X14,X13)|(r3(X13,X14,X15)&X15=Y22))),
% 0.12/0.39 inference(formula_renaming,[status(thm)],[f3,f24])).
% 0.12/0.39 fof(f26,plain,(
% 0.12/0.39 ![X13,X14]: ![X15]: (sP2_prd(X15,sK2_skl(X14,X13),X14,X13)|(r3(X13,X14,X15)&X15=sK2_skl(X14,X13)))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y22,sK2_skl(X14,X13))],[f25])).
% 0.12/0.40 fof(f28,plain,(
% 0.12/0.40 ![X0,X1,X2]: (sP2_prd(X0,sK2_skl(X1,X2),X1,X2)|X0=sK2_skl(X1,X2))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f26])).
% 0.12/0.40 fof(f29,definition,(
% 0.12/0.40 ![X16,X17,Y23,X18]: (sP3_prd(X18,Y23,X17,X16)<=>(~r4(X16,X17,X18)&~X18=Y23))),
% 0.12/0.40 introduced(definition,[new_symbols(definition,[sP3_prd])],[])).
% 0.12/0.40 fof(f30,plain,(
% 0.12/0.40 ![X16,X17]: ?[Y23]: ![X18]: (sP3_prd(X18,Y23,X17,X16)|(r4(X16,X17,X18)&X18=Y23))),
% 0.12/0.40 inference(formula_renaming,[status(thm)],[f4,f29])).
% 0.12/0.40 fof(f31,plain,(
% 0.12/0.40 ![X16,X17]: ![X18]: (sP3_prd(X18,sK3_skl(X17,X16),X17,X16)|(r4(X16,X17,X18)&X18=sK3_skl(X17,X16)))),
% 0.12/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y23,sK3_skl(X17,X16))],[f30])).
% 0.12/0.40 fof(f33,plain,(
% 0.12/0.40 ![X0,X1,X2]: (sP3_prd(X0,sK3_skl(X1,X2),X1,X2)|X0=sK3_skl(X1,X2))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f31])).
% 0.12/0.40 fof(f34,plain,(
% 0.12/0.40 ![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))))),
% 0.12/0.40 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])).
% 0.12/0.40 fof(f35,plain,(
% 0.12/0.40 ![X0,X1]: (r2(X0,sK6_skl(X0,X1)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f34])).
% 0.12/0.40 fof(f36,plain,(
% 0.12/0.40 ![X0,X1]: (r3(X0,sK6_skl(X1,X0),sK5_skl(X1,X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f34])).
% 0.12/0.40 fof(f37,plain,(
% 0.12/0.40 ![X0,X1]: (sK5_skl(X0,X1)=sK4_skl(X0,X1))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f34])).
% 0.12/0.40 fof(f38,plain,(
% 0.12/0.40 ![X0,X1]: (r2(sK7_skl(X0,X1),sK4_skl(X0,X1)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f34])).
% 0.12/0.40 fof(f39,plain,(
% 0.12/0.40 ![X0,X1]: (r3(X0,X1,sK7_skl(X1,X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f34])).
% 0.12/0.40 fof(f40,plain,(
% 0.12/0.40 ![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))))),
% 0.12/0.40 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])).
% 0.12/0.40 fof(f41,plain,(
% 0.12/0.40 ![X0,X1]: (r2(X0,sK10_skl(X0,X1)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.12/0.40 fof(f42,plain,(
% 0.12/0.40 ![X0,X1]: (r4(X0,sK10_skl(X1,X0),sK9_skl(X1,X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.12/0.40 fof(f43,plain,(
% 0.12/0.40 ![X0,X1]: (sK9_skl(X0,X1)=sK8_skl(X0,X1))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.12/0.40 fof(f44,plain,(
% 0.12/0.40 ![X0,X1]: (r3(sK11_skl(X0,X1),X1,sK8_skl(X0,X1)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.12/0.40 fof(f45,plain,(
% 0.12/0.40 ![X0,X1]: (r4(X0,X1,sK11_skl(X1,X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.12/0.40 fof(f47,plain,(
% 0.12/0.40 ![X4]: ((r1(sK13_skl(X4))&r3(X4,sK13_skl(X4),sK12_skl(X4)))&sK12_skl(X4)=X4)),
% 0.12/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f8])).
% 0.12/0.40 fof(f48,plain,(
% 0.12/0.40 ![X0]: (r1(sK13_skl(X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f47])).
% 0.12/0.40 fof(f49,plain,(
% 0.12/0.40 ![X0]: (r3(X0,sK13_skl(X0),sK12_skl(X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f47])).
% 0.12/0.40 fof(f50,plain,(
% 0.12/0.40 ![X0]: (sK12_skl(X0)=X0)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f47])).
% 0.12/0.40 fof(f51,plain,(
% 0.12/0.40 ![X5]: ((r1(sK15_skl(X5))&r4(X5,sK15_skl(X5),sK14_skl(X5)))&(r1(sK16_skl(X5))&sK14_skl(X5)=sK16_skl(X5)))),
% 0.12/0.40 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])).
% 0.12/0.40 fof(f52,plain,(
% 0.12/0.40 ![X0]: (r1(sK15_skl(X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f51])).
% 0.12/0.40 fof(f53,plain,(
% 0.12/0.40 ![X0]: (r4(X0,sK15_skl(X0),sK14_skl(X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f51])).
% 0.12/0.40 fof(f54,plain,(
% 0.12/0.40 ![X0]: (r1(sK16_skl(X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f51])).
% 0.12/0.40 fof(f55,plain,(
% 0.12/0.40 ![X0]: (sK14_skl(X0)=sK16_skl(X0))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f51])).
% 0.12/0.40 fof(f62,plain,(
% 0.12/0.40 ![Y10]: ((![Y20]: (~r1(Y20)|~Y20=Y10))|(![X7]: ~r2(X7,Y10)))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f11])).
% 0.12/0.40 fof(f63,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~r1(X0)|~X0=X1|~r2(X2,X1))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f62])).
% 0.12/0.40 fof(f64,plain,(
% 0.12/0.40 (![Y1]: ((![Y2]: (~r4(Y2,Y2,Y1)|(![Y4]: (~r1(Y4)|~r2(Y4,Y2)))))|(![Y3]: (~Y1=Y3|(![Y5]: (~r1(Y5)|~r2(Y5,Y3)))))))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.12/0.40 fof(f65,plain,(
% 0.12/0.40 ![X0,X1,X2,X3,X4]: (~r4(X0,X0,X1)|~r1(X2)|~r2(X2,X0)|~X1=X3|~r1(X4)|~r2(X4,X3))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f64])).
% 0.12/0.40 fof(f66,plain,(
% 0.12/0.40 ![Y24,X19]: ((~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24))&(sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f14])).
% 0.12/0.40 fof(f67,plain,(
% 0.12/0.40 (![Y24,X19]: (~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24)))&(![Y24,X19]: (sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f66])).
% 0.12/0.40 fof(f68,plain,(
% 0.12/0.40 ![X0,X1]: (~sP0_prd(X0,X1)|~r1(X0))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f67])).
% 0.12/0.40 fof(f69,plain,(
% 0.12/0.40 ![X0,X1]: (~sP0_prd(X0,X1)|~X0=X1)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f67])).
% 0.12/0.40 fof(f71,plain,(
% 0.12/0.40 ![X11,Y21,X12]: ((~sP1_prd(X12,Y21,X11)|(~r2(X11,X12)&~X12=Y21))&(sP1_prd(X12,Y21,X11)|(r2(X11,X12)|X12=Y21)))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f19])).
% 0.12/0.40 fof(f72,plain,(
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f71])).
% 0.12/0.40 fof(f73,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|~r2(X2,X0))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f72])).
% 0.12/0.40 fof(f74,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|~X0=X1)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f72])).
% 0.12/0.40 fof(f76,plain,(
% 0.12/0.40 ![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)))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f24])).
% 0.12/0.40 fof(f77,plain,(
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f76])).
% 0.12/0.40 fof(f78,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~sP2_prd(X0,X1,X2,X3)|~r3(X3,X2,X0))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f77])).
% 0.12/0.40 fof(f81,plain,(
% 0.12/0.40 ![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)))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f29])).
% 0.12/0.40 fof(f82,plain,(
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f81])).
% 0.12/0.40 fof(f83,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~sP3_prd(X0,X1,X2,X3)|~r4(X3,X2,X0))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f82])).
% 0.12/0.40 fof(f92,plain,(
% 0.12/0.40 ![X0,X1]: (~r1(X0)|~r2(X1,X0))),
% 0.12/0.40 inference(destructive_equality_resolution,[status(thm)],[f63])).
% 0.12/0.40 fof(f93,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~r4(X0,X0,X1)|~r1(X2)|~r2(X2,X0)|~r1(X3)|~r2(X3,X1))),
% 0.12/0.40 inference(destructive_equality_resolution,[status(thm)],[f65])).
% 0.12/0.40 fof(f94,plain,(
% 0.12/0.40 ![X0]: (~sP0_prd(X0,X0))),
% 0.12/0.40 inference(destructive_equality_resolution,[status(thm)],[f69])).
% 0.12/0.40 fof(f95,plain,(
% 0.12/0.40 ![X0,X1]: (~sP1_prd(X0,X0,X1))),
% 0.12/0.40 inference(destructive_equality_resolution,[status(thm)],[f74])).
% 0.12/0.40 fof(f99,plain,(
% 0.12/0.40 r1(sK0_skl)),
% 0.12/0.40 inference(resolution,[status(thm)],[f17,f94])).
% 0.12/0.40 fof(f112,plain,(
% 0.12/0.40 ![X0]: (X0=sK0_skl|~r1(X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f18,f68])).
% 0.12/0.40 fof(f114,plain,(
% 0.12/0.40 ![X0]: (sK16_skl(X0)=sK0_skl)),
% 0.12/0.40 inference(resolution,[status(thm)],[f112,f54])).
% 0.12/0.40 fof(f115,plain,(
% 0.12/0.40 ![X0]: (sK15_skl(X0)=sK0_skl)),
% 0.12/0.40 inference(resolution,[status(thm)],[f112,f52])).
% 0.12/0.40 fof(f116,plain,(
% 0.12/0.40 ![X0]: (sK13_skl(X0)=sK0_skl)),
% 0.12/0.40 inference(resolution,[status(thm)],[f112,f48])).
% 0.12/0.40 fof(f118,plain,(
% 0.12/0.40 ![X0]: (sK14_skl(X0)=sK0_skl)),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f114,f55])).
% 0.12/0.40 fof(f122,plain,(
% 0.12/0.40 ![X0]: (r2(X0,sK1_skl(X0)))),
% 0.12/0.40 inference(resolution,[status(thm)],[f22,f95])).
% 0.12/0.40 fof(f136,plain,(
% 0.12/0.40 ![X0]: (r3(X0,sK0_skl,sK12_skl(X0)))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f116,f49])).
% 0.12/0.40 fof(f137,plain,(
% 0.12/0.40 ![X0]: (r3(X0,sK0_skl,X0))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f50,f136])).
% 0.12/0.40 fof(f138,plain,(
% 0.12/0.40 ![X0]: (r4(X0,sK0_skl,sK14_skl(X0)))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f115,f53])).
% 0.12/0.40 fof(f139,plain,(
% 0.12/0.40 ![X0]: (r4(X0,sK0_skl,sK0_skl))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f118,f138])).
% 0.12/0.40 fof(f147,plain,(
% 0.12/0.40 ![X0,X1]: (~r2(X0,X1)|X1=sK1_skl(X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f73,f23])).
% 0.12/0.40 fof(f150,plain,(
% 0.12/0.40 ![X0,X1]: (sK10_skl(X0,X1)=sK1_skl(X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f147,f41])).
% 0.12/0.40 fof(f151,plain,(
% 0.12/0.40 ![X0,X1]: (sK6_skl(X0,X1)=sK1_skl(X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f147,f35])).
% 0.12/0.40 fof(f161,plain,(
% 0.12/0.40 ![X0,X1]: (r2(sK7_skl(X0,X1),sK5_skl(X0,X1)))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f37,f38])).
% 0.12/0.40 fof(f162,plain,(
% 0.12/0.40 ![X0,X1]: (sK5_skl(X0,X1)=sK1_skl(sK7_skl(X0,X1)))),
% 0.12/0.40 inference(resolution,[status(thm)],[f161,f147])).
% 0.12/0.40 fof(f205,plain,(
% 0.12/0.40 ![X0,X1]: (r3(X0,sK1_skl(X1),sK5_skl(X1,X0)))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f151,f36])).
% 0.12/0.40 fof(f206,plain,(
% 0.12/0.40 ![X0,X1]: (r4(X0,sK1_skl(X1),sK9_skl(X1,X0)))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f150,f42])).
% 0.12/0.40 fof(f207,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~r1(X0)|~r2(X0,sK1_skl(X1))|~r1(X2)|~r2(X2,sK9_skl(X1,sK1_skl(X1))))),
% 0.12/0.40 inference(resolution,[status(thm)],[f206,f93])).
% 0.12/0.40 fof(f209,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~r1(X0)|~r2(X0,sK1_skl(sK7_skl(X1,X2)))|~r1(X3)|~r2(X3,sK9_skl(sK7_skl(X1,X2),sK5_skl(X1,X2))))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f162,f207])).
% 0.12/0.40 fof(f217,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~r1(X0)|~r2(X0,sK5_skl(X1,X2))|~r1(X3)|~r2(X3,sK9_skl(sK7_skl(X1,X2),sK5_skl(X1,X2))))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f162,f209])).
% 0.12/0.40 fof(f219,plain,(
% 0.12/0.40 ![X0,X1]: (r3(sK11_skl(X0,X1),X1,sK9_skl(X0,X1)))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f43,f44])).
% 0.12/0.40 fof(f222,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~r3(X0,X1,X2)|X2=sK2_skl(X1,X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f78,f28])).
% 0.12/0.40 fof(f225,plain,(
% 0.12/0.40 ![X0,X1]: (sK5_skl(X0,X1)=sK2_skl(sK1_skl(X0),X1))),
% 0.12/0.40 inference(resolution,[status(thm)],[f222,f205])).
% 0.12/0.40 fof(f226,plain,(
% 0.12/0.40 ![X0]: (X0=sK2_skl(sK0_skl,X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f222,f137])).
% 0.12/0.40 fof(f228,plain,(
% 0.12/0.40 ![X0,X1]: (sK7_skl(X0,X1)=sK2_skl(X0,X1))),
% 0.12/0.40 inference(resolution,[status(thm)],[f222,f39])).
% 0.12/0.40 fof(f229,plain,(
% 0.12/0.40 ![X0,X1]: (sP2_prd(X0,X1,sK0_skl,X1)|X0=sK2_skl(sK0_skl,X1))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f226,f28])).
% 0.12/0.40 fof(f232,plain,(
% 0.12/0.40 ![X0,X1]: (sP2_prd(X0,X1,sK0_skl,X1)|X0=X1)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f226,f229])).
% 0.12/0.40 fof(f233,plain,(
% 0.12/0.40 ![X0]: (X0=sK7_skl(sK0_skl,X0))),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f228,f226])).
% 0.12/0.40 fof(f234,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~r3(X0,X1,X2)|X2=sK7_skl(X1,X0))),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f228,f222])).
% 0.12/0.40 fof(f240,plain,(
% 0.12/0.40 ![X0]: (sK5_skl(sK0_skl,X0)=sK1_skl(X0))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f233,f162])).
% 0.12/0.40 fof(f284,plain,(
% 0.12/0.40 ![X0,X1]: (X0=X1|~r3(X1,sK0_skl,X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f232,f78])).
% 0.12/0.40 fof(f286,plain,(
% 0.12/0.40 ![X0]: (sK9_skl(X0,sK0_skl)=sK11_skl(X0,sK0_skl))),
% 0.12/0.40 inference(resolution,[status(thm)],[f284,f219])).
% 0.12/0.40 fof(f301,plain,(
% 0.12/0.40 ![X0,X1]: (sK5_skl(X0,X1)=sK7_skl(sK1_skl(X0),X1))),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f228,f225])).
% 0.12/0.40 fof(f313,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~r4(X0,X1,X2)|X2=sK3_skl(X1,X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f83,f33])).
% 0.12/0.40 fof(f387,plain,(
% 0.12/0.40 ![X0]: (sK0_skl=sK3_skl(sK0_skl,X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f313,f139])).
% 0.12/0.40 fof(f389,plain,(
% 0.12/0.40 ![X0,X1]: (sK11_skl(X0,X1)=sK3_skl(X0,X1))),
% 0.12/0.40 inference(resolution,[status(thm)],[f313,f45])).
% 0.12/0.40 fof(f396,plain,(
% 0.12/0.40 ![X0]: (sK0_skl=sK11_skl(sK0_skl,X0))),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f389,f387])).
% 0.12/0.40 fof(f403,plain,(
% 0.12/0.40 ![X0]: (r3(sK0_skl,X0,sK9_skl(sK0_skl,X0)))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f396,f219])).
% 0.12/0.40 fof(f416,plain,(
% 0.12/0.40 ![X0]: (sK9_skl(sK0_skl,X0)=sK7_skl(X0,sK0_skl))),
% 0.12/0.40 inference(resolution,[status(thm)],[f403,f234])).
% 0.12/0.40 fof(f420,plain,(
% 0.12/0.40 ![X0]: (sK9_skl(sK0_skl,sK1_skl(X0))=sK5_skl(X0,sK0_skl))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f301,f416])).
% 0.12/0.40 fof(f430,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~r1(X0)|~r2(X0,sK5_skl(X1,sK0_skl))|~r1(X2)|~r2(X2,sK9_skl(sK9_skl(sK0_skl,X1),sK5_skl(X1,sK0_skl))))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f416,f217])).
% 0.12/0.40 fof(f504,plain,(
% 0.12/0.40 ![X0,X1]: (~r1(X0)|~r2(X0,sK5_skl(sK0_skl,sK0_skl))|~r1(X1)|~r2(X1,sK9_skl(sK11_skl(sK0_skl,sK0_skl),sK5_skl(sK0_skl,sK0_skl))))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f286,f430])).
% 0.12/0.40 fof(f506,definition,(
% 0.12/0.40 ![X0]: (sQ6_spl <=> (~r1(X0)|~r2(X0,sK5_skl(sK0_skl,sK0_skl))))),
% 0.12/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/0.40 fof(f507,plain,(
% 0.12/0.40 ![X0]: (~r1(X0)|~r2(X0,sK5_skl(sK0_skl,sK0_skl))|~sQ6_spl)),
% 0.12/0.40 inference(component_clause,[status(thm)],[f506])).
% 0.12/0.40 fof(f509,definition,(
% 0.12/0.40 ![X1]: (sQ7_spl <=> (~r1(X1)|~r2(X1,sK9_skl(sK11_skl(sK0_skl,sK0_skl),sK5_skl(sK0_skl,sK0_skl)))))),
% 0.12/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.40 fof(f510,plain,(
% 0.12/0.40 ![X0]: (~r1(X0)|~r2(X0,sK9_skl(sK11_skl(sK0_skl,sK0_skl),sK5_skl(sK0_skl,sK0_skl)))|~sQ7_spl)),
% 0.12/0.40 inference(component_clause,[status(thm)],[f509])).
% 0.12/0.40 fof(f512,plain,(
% 0.12/0.40 sQ6_spl|sQ7_spl),
% 0.12/0.40 inference(split_clause,[status(thm)],[f504,f506,f509])).
% 0.12/0.40 fof(f517,plain,(
% 0.12/0.40 ![X0]: (~r1(X0)|~r2(X0,sK1_skl(sK0_skl))|~sQ6_spl)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f240,f507])).
% 0.12/0.40 fof(f518,plain,(
% 0.12/0.40 ~r1(sK0_skl)|~sQ6_spl),
% 0.12/0.40 inference(resolution,[status(thm)],[f517,f122])).
% 0.12/0.40 fof(f519,plain,(
% 0.12/0.40 $false|~sQ6_spl),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f518,f99])).
% 0.12/0.40 fof(f520,plain,(
% 0.12/0.40 ~sQ6_spl),
% 0.12/0.40 inference(contradiction_clause,[status(thm)],[f519])).
% 0.12/0.40 fof(f521,plain,(
% 0.12/0.40 ![X0]: (~r1(X0)|~r2(X0,sK9_skl(sK0_skl,sK5_skl(sK0_skl,sK0_skl)))|~sQ7_spl)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f396,f510])).
% 0.12/0.40 fof(f522,plain,(
% 0.12/0.40 ![X0]: (~r1(X0)|~r2(X0,sK9_skl(sK0_skl,sK1_skl(sK0_skl)))|~sQ7_spl)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f240,f521])).
% 0.12/0.40 fof(f736,definition,(
% 0.12/0.40 sQ21_spl <=> (r2(sK19_skl(sK0_skl),sK0_skl))),
% 0.12/0.40 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.12/0.40 fof(f737,plain,(
% 0.12/0.40 r2(sK19_skl(sK0_skl),sK0_skl)|~sQ21_spl),
% 0.12/0.40 inference(component_clause,[status(thm)],[f736])).
% 0.12/0.40 fof(f745,plain,(
% 0.12/0.40 ~r1(sK0_skl)|~sQ21_spl),
% 0.12/0.40 inference(resolution,[status(thm)],[f737,f92])).
% 0.12/0.40 fof(f746,plain,(
% 0.12/0.40 $false|~sQ21_spl),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f745,f99])).
% 0.12/0.40 fof(f747,plain,(
% 0.12/0.40 ~sQ21_spl),
% 0.12/0.40 inference(contradiction_clause,[status(thm)],[f746])).
% 0.12/0.40 fof(f1120,plain,(
% 0.12/0.40 ![X0]: (~r1(X0)|~r2(X0,sK5_skl(sK0_skl,sK0_skl))|~sQ7_spl)),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f420,f522])).
% 0.12/0.40 fof(f1135,plain,(
% 0.12/0.40 sQ6_spl|~sQ7_spl),
% 0.12/0.40 inference(split_clause,[status(thm)],[f1120,f506,f509])).
% 0.12/0.40 fof(f1149,plain,(
% 0.12/0.40 $false),
% 0.12/0.40 inference(sat_refutation,[status(thm)],[f512,f520,f747,f1135])).
% 0.12/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.42 % Elapsed time: 0.061011 seconds
% 0.12/0.42 % CPU time: 0.236510 seconds
% 0.12/0.42 % Total memory used: 104.951 MB
% 0.12/0.42 % Net memory used: 104.544 MB
%------------------------------------------------------------------------------