%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUN077+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 : n013.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 88.16s 11.87s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN077+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
% 0.09/0.54 % Computer : n013.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Mon Sep 21 03:24:06 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.14/0.55 % Drodi V4.1.1
% 88.16/11.87 % Refutation found
% 88.16/11.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 88.16/11.87 % SZS output start CNFRefutation for theBenchmark
% 88.16/11.87 fof(f1,axiom,(
% 88.16/11.87 (? [Y24] :(! [X19] :( ( ~ r1(X19)& X19 != Y24 )| ( r1(X19)& X19 = Y24 ) ) ))),
% 88.16/11.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 88.16/11.87 fof(f2,axiom,(
% 88.16/11.87 (! [X11] :(? [Y21] :(! [X12] :( ( ~ r2(X11,X12)& X12 != Y21 )| ( r2(X11,X12)& X12 = Y21 ) ) )))),
% 88.16/11.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 88.16/11.87 fof(f3,axiom,(
% 88.16/11.87 (! [X13,X14] :(? [Y22] :(! [X15] :( ( ~ r3(X13,X14,X15)& X15 != Y22 )| ( r3(X13,X14,X15)& X15 = Y22 ) ) )))),
% 88.16/11.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 88.16/11.87 fof(f4,axiom,(
% 88.16/11.87 (! [X16,X17] :(? [Y23] :(! [X18] :( ( ~ r4(X16,X17,X18)& X18 != Y23 )| ( r4(X16,X17,X18)& X18 = Y23 ) ) )))),
% 88.16/11.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 88.16/11.87 fof(f5,axiom,(
% 88.16/11.87 (! [X1,X8] :(? [Y4] :( (? [Y5] :( (? [Y15] :( r2(X8,Y15)& r3(X1,Y15,Y5) ))& Y5 = Y4 ))& (? [Y7] :( r2(Y7,Y4)& r3(X1,X8,Y7) ) )) ))),
% 88.16/11.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 88.16/11.87 fof(f6,axiom,(
% 88.16/11.87 (! [X2,X9] :(? [Y2] :( (? [Y3] :( (? [Y14] :( r2(X9,Y14)& r4(X2,Y14,Y3) ))& Y3 = Y2 ))& (? [Y6] :( r3(Y6,X2,Y2)& r4(X2,X9,Y6) ) )) ))),
% 88.16/11.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 88.16/11.87 fof(f8,axiom,(
% 88.16/11.87 (! [X4] :(? [Y9] :( (? [Y16] :( r1(Y16)& r3(X4,Y16,Y9) ))& Y9 = X4 ) ))),
% 88.16/11.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 88.16/11.87 fof(f9,axiom,(
% 88.16/11.87 (! [X5] :(? [Y8] :( (? [Y17] :( r1(Y17)& r4(X5,Y17,Y8) ))& (? [Y18] :( r1(Y18)& Y8 = Y18 ) )) ))),
% 88.16/11.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 88.16/11.87 fof(f12,conjecture,(
% 88.16/11.87 (? [Y1] :( (? [Y2] :( Y1 = Y2& (? [Y3] :( r2(Y3,Y2)& (? [Y4] :( r2(Y4,Y3)& (? [Y5] :( r2(Y5,Y4)& (? [Y7] :( r2(Y7,Y5)& (? [Y10] :( r2(Y10,Y7)& (? [Y13] :( r1(Y13)& r2(Y13,Y10) ) )) )) )) )) )) )))& (? [Y6] :( (? [Y8] :( r2(Y8,Y6)& (? [Y11] :( r2(Y11,Y8)& (? [Y14] :( r1(Y14)& r2(Y14,Y11) ) )) )))& (? [Y9] :( r4(Y9,Y6,Y1)& (? [Y12] :( r2(Y12,Y9)& (? [Y15] :( r1(Y15)& r2(Y15,Y12) ) )) )) )) )) )),
% 88.16/11.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 88.16/11.87 fof(f13,negated_conjecture,(
% 88.16/11.87 ~((? [Y1] :( (? [Y2] :( Y1 = Y2& (? [Y3] :( r2(Y3,Y2)& (? [Y4] :( r2(Y4,Y3)& (? [Y5] :( r2(Y5,Y4)& (? [Y7] :( r2(Y7,Y5)& (? [Y10] :( r2(Y10,Y7)& (? [Y13] :( r1(Y13)& r2(Y13,Y10) ) )) )) )) )) )) )))& (? [Y6] :( (? [Y8] :( r2(Y8,Y6)& (? [Y11] :( r2(Y11,Y8)& (? [Y14] :( r1(Y14)& r2(Y14,Y11) ) )) )))& (? [Y9] :( r4(Y9,Y6,Y1)& (? [Y12] :( r2(Y12,Y9)& (? [Y15] :( r1(Y15)& r2(Y15,Y12) ) )) )) )) )) ))),
% 88.16/11.87 inference(negated_conjecture,[status(cth)],[f12])).
% 88.16/11.87 fof(f14,definition,(
% 88.16/11.87 ![Y24,X19]: (sP0_prd(X19,Y24)<=>(~r1(X19)&~X19=Y24))),
% 88.16/11.87 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 88.16/11.87 fof(f15,plain,(
% 88.16/11.87 ?[Y24]: ![X19]: (sP0_prd(X19,Y24)|(r1(X19)&X19=Y24))),
% 88.16/11.87 inference(formula_renaming,[status(thm)],[f1,f14])).
% 88.16/11.87 fof(f16,plain,(
% 88.16/11.87 ![X19]: (sP0_prd(X19,sK0_skl)|(r1(X19)&X19=sK0_skl))),
% 88.16/11.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f15])).
% 88.16/11.87 fof(f17,plain,(
% 88.16/11.87 ![X0]: (sP0_prd(X0,sK0_skl)|r1(X0))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f16])).
% 88.16/11.87 fof(f18,plain,(
% 88.16/11.87 ![X0]: (sP0_prd(X0,sK0_skl)|X0=sK0_skl)),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f16])).
% 88.16/11.87 fof(f19,definition,(
% 88.16/11.87 ![X11,Y21,X12]: (sP1_prd(X12,Y21,X11)<=>(~r2(X11,X12)&~X12=Y21))),
% 88.16/11.87 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 88.16/11.87 fof(f20,plain,(
% 88.16/11.87 ![X11]: ?[Y21]: ![X12]: (sP1_prd(X12,Y21,X11)|(r2(X11,X12)&X12=Y21))),
% 88.16/11.87 inference(formula_renaming,[status(thm)],[f2,f19])).
% 88.16/11.87 fof(f21,plain,(
% 88.16/11.87 ![X11]: ![X12]: (sP1_prd(X12,sK1_skl(X11),X11)|(r2(X11,X12)&X12=sK1_skl(X11)))),
% 88.16/11.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y21,sK1_skl(X11))],[f20])).
% 88.16/11.87 fof(f22,plain,(
% 88.16/11.87 ![X0,X1]: (sP1_prd(X0,sK1_skl(X1),X1)|r2(X1,X0))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f21])).
% 88.16/11.87 fof(f23,plain,(
% 88.16/11.87 ![X0,X1]: (sP1_prd(X0,sK1_skl(X1),X1)|X0=sK1_skl(X1))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f21])).
% 88.16/11.87 fof(f24,definition,(
% 88.16/11.87 ![X13,X14,Y22,X15]: (sP2_prd(X15,Y22,X14,X13)<=>(~r3(X13,X14,X15)&~X15=Y22))),
% 88.16/11.87 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 88.16/11.87 fof(f25,plain,(
% 88.16/11.87 ![X13,X14]: ?[Y22]: ![X15]: (sP2_prd(X15,Y22,X14,X13)|(r3(X13,X14,X15)&X15=Y22))),
% 88.16/11.87 inference(formula_renaming,[status(thm)],[f3,f24])).
% 88.16/11.87 fof(f26,plain,(
% 88.16/11.87 ![X13,X14]: ![X15]: (sP2_prd(X15,sK2_skl(X14,X13),X14,X13)|(r3(X13,X14,X15)&X15=sK2_skl(X14,X13)))),
% 88.16/11.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y22,sK2_skl(X14,X13))],[f25])).
% 88.16/11.87 fof(f28,plain,(
% 88.16/11.87 ![X0,X1,X2]: (sP2_prd(X0,sK2_skl(X1,X2),X1,X2)|X0=sK2_skl(X1,X2))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f26])).
% 88.16/11.87 fof(f29,definition,(
% 88.16/11.87 ![X16,X17,Y23,X18]: (sP3_prd(X18,Y23,X17,X16)<=>(~r4(X16,X17,X18)&~X18=Y23))),
% 88.16/11.87 introduced(definition,[new_symbols(definition,[sP3_prd])],[])).
% 88.16/11.87 fof(f30,plain,(
% 88.16/11.87 ![X16,X17]: ?[Y23]: ![X18]: (sP3_prd(X18,Y23,X17,X16)|(r4(X16,X17,X18)&X18=Y23))),
% 88.16/11.87 inference(formula_renaming,[status(thm)],[f4,f29])).
% 88.16/11.87 fof(f31,plain,(
% 88.16/11.87 ![X16,X17]: ![X18]: (sP3_prd(X18,sK3_skl(X17,X16),X17,X16)|(r4(X16,X17,X18)&X18=sK3_skl(X17,X16)))),
% 88.16/11.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y23,sK3_skl(X17,X16))],[f30])).
% 88.16/11.87 fof(f32,plain,(
% 88.16/11.87 ![X0,X1,X2]: (sP3_prd(X0,sK3_skl(X1,X2),X1,X2)|r4(X2,X1,X0))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f31])).
% 88.16/11.87 fof(f33,plain,(
% 88.16/11.87 ![X0,X1,X2]: (sP3_prd(X0,sK3_skl(X1,X2),X1,X2)|X0=sK3_skl(X1,X2))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f31])).
% 88.16/11.87 fof(f34,plain,(
% 88.16/11.87 ![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))))),
% 88.16/11.87 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])).
% 88.16/11.87 fof(f35,plain,(
% 88.16/11.87 ![X0,X1]: (r2(X0,sK6_skl(X0,X1)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f34])).
% 88.16/11.87 fof(f36,plain,(
% 88.16/11.87 ![X0,X1]: (r3(X0,sK6_skl(X1,X0),sK5_skl(X1,X0)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f34])).
% 88.16/11.87 fof(f37,plain,(
% 88.16/11.87 ![X0,X1]: (sK5_skl(X0,X1)=sK4_skl(X0,X1))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f34])).
% 88.16/11.87 fof(f38,plain,(
% 88.16/11.87 ![X0,X1]: (r2(sK7_skl(X0,X1),sK4_skl(X0,X1)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f34])).
% 88.16/11.87 fof(f39,plain,(
% 88.16/11.87 ![X0,X1]: (r3(X0,X1,sK7_skl(X1,X0)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f34])).
% 88.16/11.87 fof(f40,plain,(
% 88.16/11.87 ![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))))),
% 88.16/11.87 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])).
% 88.16/11.87 fof(f41,plain,(
% 88.16/11.87 ![X0,X1]: (r2(X0,sK10_skl(X0,X1)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f40])).
% 88.16/11.87 fof(f42,plain,(
% 88.16/11.87 ![X0,X1]: (r4(X0,sK10_skl(X1,X0),sK9_skl(X1,X0)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f40])).
% 88.16/11.87 fof(f43,plain,(
% 88.16/11.87 ![X0,X1]: (sK9_skl(X0,X1)=sK8_skl(X0,X1))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f40])).
% 88.16/11.87 fof(f44,plain,(
% 88.16/11.87 ![X0,X1]: (r3(sK11_skl(X0,X1),X1,sK8_skl(X0,X1)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f40])).
% 88.16/11.87 fof(f45,plain,(
% 88.16/11.87 ![X0,X1]: (r4(X0,X1,sK11_skl(X1,X0)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f40])).
% 88.16/11.87 fof(f47,plain,(
% 88.16/11.87 ![X4]: ((r1(sK13_skl(X4))&r3(X4,sK13_skl(X4),sK12_skl(X4)))&sK12_skl(X4)=X4)),
% 88.16/11.87 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f8])).
% 88.16/11.87 fof(f48,plain,(
% 88.16/11.87 ![X0]: (r1(sK13_skl(X0)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f47])).
% 88.16/11.87 fof(f49,plain,(
% 88.16/11.87 ![X0]: (r3(X0,sK13_skl(X0),sK12_skl(X0)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f47])).
% 88.16/11.87 fof(f50,plain,(
% 88.16/11.87 ![X0]: (sK12_skl(X0)=X0)),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f47])).
% 88.16/11.87 fof(f51,plain,(
% 88.16/11.87 ![X5]: ((r1(sK15_skl(X5))&r4(X5,sK15_skl(X5),sK14_skl(X5)))&(r1(sK16_skl(X5))&sK14_skl(X5)=sK16_skl(X5)))),
% 88.16/11.87 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])).
% 88.16/11.87 fof(f52,plain,(
% 88.16/11.87 ![X0]: (r1(sK15_skl(X0)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f51])).
% 88.16/11.87 fof(f53,plain,(
% 88.16/11.87 ![X0]: (r4(X0,sK15_skl(X0),sK14_skl(X0)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f51])).
% 88.16/11.87 fof(f54,plain,(
% 88.16/11.87 ![X0]: (r1(sK16_skl(X0)))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f51])).
% 88.16/11.87 fof(f55,plain,(
% 88.16/11.87 ![X0]: (sK14_skl(X0)=sK16_skl(X0))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f51])).
% 88.16/11.87 fof(f64,plain,(
% 88.16/11.87 (![Y1]: ((![Y2]: (~Y1=Y2|(![Y3]: (~r2(Y3,Y2)|(![Y4]: (~r2(Y4,Y3)|(![Y5]: (~r2(Y5,Y4)|(![Y7]: (~r2(Y7,Y5)|(![Y10]: (~r2(Y10,Y7)|(![Y13]: (~r1(Y13)|~r2(Y13,Y10)))))))))))))))|(![Y6]: ((![Y8]: (~r2(Y8,Y6)|(![Y11]: (~r2(Y11,Y8)|(![Y14]: (~r1(Y14)|~r2(Y14,Y11)))))))|(![Y9]: (~r4(Y9,Y6,Y1)|(![Y12]: (~r2(Y12,Y9)|(![Y15]: (~r1(Y15)|~r2(Y15,Y12)))))))))))),
% 88.16/11.87 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 88.16/11.87 fof(f65,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14]: (~X0=X1|~r2(X2,X1)|~r2(X3,X2)|~r2(X4,X3)|~r2(X5,X4)|~r2(X6,X5)|~r1(X7)|~r2(X7,X6)|~r2(X8,X9)|~r2(X10,X8)|~r1(X11)|~r2(X11,X10)|~r4(X12,X9,X0)|~r2(X13,X12)|~r1(X14)|~r2(X14,X13))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f64])).
% 88.16/11.87 fof(f66,plain,(
% 88.16/11.87 ![Y24,X19]: ((~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24))&(sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 88.16/11.87 inference(NNF_transformation,[status(thm)],[f14])).
% 88.16/11.87 fof(f67,plain,(
% 88.16/11.87 (![Y24,X19]: (~sP0_prd(X19,Y24)|(~r1(X19)&~X19=Y24)))&(![Y24,X19]: (sP0_prd(X19,Y24)|(r1(X19)|X19=Y24)))),
% 88.16/11.87 inference(miniscoping,[status(thm)],[f66])).
% 88.16/11.87 fof(f68,plain,(
% 88.16/11.87 ![X0,X1]: (~sP0_prd(X0,X1)|~r1(X0))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f67])).
% 88.16/11.87 fof(f69,plain,(
% 88.16/11.87 ![X0,X1]: (~sP0_prd(X0,X1)|~X0=X1)),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f67])).
% 88.16/11.87 fof(f71,plain,(
% 88.16/11.87 ![X11,Y21,X12]: ((~sP1_prd(X12,Y21,X11)|(~r2(X11,X12)&~X12=Y21))&(sP1_prd(X12,Y21,X11)|(r2(X11,X12)|X12=Y21)))),
% 88.16/11.87 inference(NNF_transformation,[status(thm)],[f19])).
% 88.16/11.87 fof(f72,plain,(
% 88.16/11.87 (![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)))),
% 88.16/11.87 inference(miniscoping,[status(thm)],[f71])).
% 88.16/11.87 fof(f73,plain,(
% 88.16/11.87 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|~r2(X2,X0))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f72])).
% 88.16/11.87 fof(f74,plain,(
% 88.16/11.87 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|~X0=X1)),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f72])).
% 88.16/11.87 fof(f76,plain,(
% 88.16/11.87 ![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)))),
% 88.16/11.87 inference(NNF_transformation,[status(thm)],[f24])).
% 88.16/11.87 fof(f77,plain,(
% 88.16/11.87 (![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)))),
% 88.16/11.87 inference(miniscoping,[status(thm)],[f76])).
% 88.16/11.87 fof(f78,plain,(
% 88.16/11.87 ![X0,X1,X2,X3]: (~sP2_prd(X0,X1,X2,X3)|~r3(X3,X2,X0))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f77])).
% 88.16/11.87 fof(f81,plain,(
% 88.16/11.87 ![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)))),
% 88.16/11.87 inference(NNF_transformation,[status(thm)],[f29])).
% 88.16/11.87 fof(f82,plain,(
% 88.16/11.87 (![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)))),
% 88.16/11.87 inference(miniscoping,[status(thm)],[f81])).
% 88.16/11.87 fof(f83,plain,(
% 88.16/11.87 ![X0,X1,X2,X3]: (~sP3_prd(X0,X1,X2,X3)|~r4(X3,X2,X0))),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f82])).
% 88.16/11.87 fof(f84,plain,(
% 88.16/11.87 ![X0,X1,X2,X3]: (~sP3_prd(X0,X1,X2,X3)|~X0=X1)),
% 88.16/11.87 inference(cnf_transformation,[status(thm)],[f82])).
% 88.16/11.87 fof(f91,plain,(
% 88.16/11.87 ![X0,X1]: (r3(X0,sK6_skl(X1,X0),sK4_skl(X1,X0)))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f37,f36])).
% 88.16/11.87 fof(f92,plain,(
% 88.16/11.87 ![X0,X1]: (r4(X0,sK10_skl(X1,X0),sK8_skl(X1,X0)))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f43,f42])).
% 88.16/11.87 fof(f94,plain,(
% 88.16/11.87 ![X0]: (r3(X0,sK13_skl(X0),X0))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f50,f49])).
% 88.16/11.87 fof(f95,plain,(
% 88.16/11.87 ![X0]: (r1(sK14_skl(X0)))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f55,f54])).
% 88.16/11.87 fof(f97,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13]: (~r2(X0,X1)|~r2(X2,X0)|~r2(X3,X2)|~r2(X4,X3)|~r2(X5,X4)|~r1(X6)|~r2(X6,X5)|~r2(X7,X8)|~r2(X9,X7)|~r1(X10)|~r2(X10,X9)|~r4(X11,X8,X1)|~r2(X12,X11)|~r1(X13)|~r2(X13,X12))),
% 88.16/11.87 inference(destructive_equality_resolution,[status(thm)],[f65])).
% 88.16/11.87 fof(f98,plain,(
% 88.16/11.87 ![X0]: (~sP0_prd(X0,X0))),
% 88.16/11.87 inference(destructive_equality_resolution,[status(thm)],[f69])).
% 88.16/11.87 fof(f99,plain,(
% 88.16/11.87 ![X0,X1]: (~sP1_prd(X0,X0,X1))),
% 88.16/11.87 inference(destructive_equality_resolution,[status(thm)],[f74])).
% 88.16/11.87 fof(f101,plain,(
% 88.16/11.87 ![X0,X1,X2]: (~sP3_prd(X0,X0,X1,X2))),
% 88.16/11.87 inference(destructive_equality_resolution,[status(thm)],[f84])).
% 88.16/11.87 fof(f103,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12]: (~r2(X0,X1)|~r2(X2,X0)|~r2(X3,X2)|~r2(X4,X3)|~r2(X5,X4)|~r1(X6)|~r2(X6,X5)|~r2(X7,X8)|~r2(X9,X7)|~r1(X10)|~r2(X10,X9)|~r4(X11,X8,X1)|~r2(X12,X11)|~r2(X10,X12))),
% 88.16/11.87 inference(factoring,[status(thm)],[f97])).
% 88.16/11.87 fof(f122,plain,(
% 88.16/11.87 r1(sK0_skl)),
% 88.16/11.87 inference(resolution,[status(thm)],[f17,f98])).
% 88.16/11.87 fof(f124,plain,(
% 88.16/11.87 ![X0]: (r2(X0,sK1_skl(X0)))),
% 88.16/11.87 inference(resolution,[status(thm)],[f22,f99])).
% 88.16/11.87 fof(f126,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11]: (~r2(X0,X1)|~r2(X2,X0)|~r2(X3,X2)|~r2(X4,X3)|~r2(X5,X4)|~r1(X6)|~r2(X6,X5)|~r2(X7,X8)|~r2(X9,X7)|~r2(sK0_skl,X9)|~r4(X10,X8,X1)|~r2(X11,X10)|~r2(sK0_skl,X11))),
% 88.16/11.87 inference(resolution,[status(thm)],[f122,f103])).
% 88.16/11.87 fof(f163,plain,(
% 88.16/11.87 ![X0]: (~r1(X0)|X0=sK0_skl)),
% 88.16/11.87 inference(resolution,[status(thm)],[f68,f18])).
% 88.16/11.87 fof(f166,plain,(
% 88.16/11.87 ![X0]: (sK14_skl(X0)=sK0_skl)),
% 88.16/11.87 inference(resolution,[status(thm)],[f163,f95])).
% 88.16/11.87 fof(f167,plain,(
% 88.16/11.87 ![X0]: (sK15_skl(X0)=sK0_skl)),
% 88.16/11.87 inference(resolution,[status(thm)],[f163,f52])).
% 88.16/11.87 fof(f168,plain,(
% 88.16/11.87 ![X0]: (sK13_skl(X0)=sK0_skl)),
% 88.16/11.87 inference(resolution,[status(thm)],[f163,f48])).
% 88.16/11.87 fof(f181,plain,(
% 88.16/11.87 ![X0]: (r4(X0,sK15_skl(X0),sK0_skl))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f166,f53])).
% 88.16/11.87 fof(f210,plain,(
% 88.16/11.87 ![X0]: (r3(X0,sK0_skl,X0))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f168,f94])).
% 88.16/11.87 fof(f212,plain,(
% 88.16/11.87 ![X0]: (r4(X0,sK0_skl,sK0_skl))),
% 88.16/11.87 inference(forward_demodulation,[status(thm)],[f167,f181])).
% 88.16/11.87 fof(f221,plain,(
% 88.16/11.87 ![X0,X1]: (r4(X0,X1,sK3_skl(X1,X0)))),
% 88.16/11.87 inference(resolution,[status(thm)],[f32,f101])).
% 88.16/11.87 fof(f265,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10]: (~r2(X0,sK3_skl(X1,X2))|~r2(X3,X0)|~r2(X4,X3)|~r2(X5,X4)|~r2(X6,X5)|~r1(X7)|~r2(X7,X6)|~r2(X8,X1)|~r2(X9,X8)|~r2(sK0_skl,X9)|~r2(X10,X2)|~r2(sK0_skl,X10))),
% 88.16/11.87 inference(resolution,[status(thm)],[f221,f126])).
% 88.16/11.87 fof(f266,plain,(
% 88.16/11.87 ![X0,X1]: (~r2(X0,X1)|X1=sK1_skl(X0))),
% 88.16/11.87 inference(resolution,[status(thm)],[f73,f23])).
% 88.16/11.87 fof(f268,plain,(
% 88.16/11.87 ![X0,X1]: (sK4_skl(X0,X1)=sK1_skl(sK7_skl(X0,X1)))),
% 88.16/11.87 inference(resolution,[status(thm)],[f266,f38])).
% 88.16/11.87 fof(f269,plain,(
% 88.16/11.87 ![X0,X1]: (sK10_skl(X0,X1)=sK1_skl(X0))),
% 88.16/11.87 inference(resolution,[status(thm)],[f266,f41])).
% 88.16/11.87 fof(f270,plain,(
% 88.16/11.87 ![X0,X1]: (sK6_skl(X0,X1)=sK1_skl(X0))),
% 88.16/11.87 inference(resolution,[status(thm)],[f266,f35])).
% 88.16/11.87 fof(f283,plain,(
% 88.16/11.87 ![X0,X1]: (r4(X0,sK1_skl(X1),sK8_skl(X1,X0)))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f269,f92])).
% 88.16/11.87 fof(f295,plain,(
% 88.16/11.87 ![X0,X1]: (r3(X0,sK1_skl(X1),sK4_skl(X1,X0)))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f270,f91])).
% 88.16/11.87 fof(f309,plain,(
% 88.16/11.87 ![X0,X1,X2]: (~r4(X0,X1,X2)|X2=sK3_skl(X1,X0))),
% 88.16/11.87 inference(resolution,[status(thm)],[f83,f33])).
% 88.16/11.87 fof(f311,plain,(
% 88.16/11.87 ![X0,X1]: (sK8_skl(X0,X1)=sK3_skl(sK1_skl(X0),X1))),
% 88.16/11.87 inference(resolution,[status(thm)],[f309,f283])).
% 88.16/11.87 fof(f312,plain,(
% 88.16/11.87 ![X0]: (sK0_skl=sK3_skl(sK0_skl,X0))),
% 88.16/11.87 inference(resolution,[status(thm)],[f309,f212])).
% 88.16/11.87 fof(f314,plain,(
% 88.16/11.87 ![X0,X1]: (sK11_skl(X0,X1)=sK3_skl(X0,X1))),
% 88.16/11.87 inference(resolution,[status(thm)],[f309,f45])).
% 88.16/11.87 fof(f322,plain,(
% 88.16/11.87 ![X0,X1]: (r3(sK3_skl(X0,X1),X1,sK8_skl(X0,X1)))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f314,f44])).
% 88.16/11.87 fof(f335,plain,(
% 88.16/11.87 ![X0,X1,X2]: (~r3(X0,X1,X2)|X2=sK2_skl(X1,X0))),
% 88.16/11.87 inference(resolution,[status(thm)],[f78,f28])).
% 88.16/11.87 fof(f342,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (~r2(X0,sK3_skl(X1,X2))|~r2(X3,X0)|~r2(X4,X3)|~r2(X5,X4)|~r2(X6,X5)|~r1(X7)|~r2(X7,X6)|~r2(X8,X1)|~r2(sK1_skl(sK0_skl),X8)|~r2(sK1_skl(sK0_skl),X2))),
% 88.16/11.87 inference(resolution,[status(thm)],[f265,f124])).
% 88.16/11.87 fof(f350,plain,(
% 88.16/11.87 ![X0,X1]: (sK8_skl(X0,X1)=sK2_skl(X1,sK3_skl(X0,X1)))),
% 88.16/11.87 inference(resolution,[status(thm)],[f335,f322])).
% 88.16/11.87 fof(f351,plain,(
% 88.16/11.87 ![X0]: (X0=sK2_skl(sK0_skl,X0))),
% 88.16/11.87 inference(resolution,[status(thm)],[f335,f210])).
% 88.16/11.87 fof(f353,plain,(
% 88.16/11.87 ![X0,X1]: (sK7_skl(X0,X1)=sK2_skl(X0,X1))),
% 88.16/11.87 inference(resolution,[status(thm)],[f335,f39])).
% 88.16/11.87 fof(f356,plain,(
% 88.16/11.87 ![X0,X1]: (r2(sK2_skl(X0,X1),sK4_skl(X0,X1)))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f353,f38])).
% 88.16/11.87 fof(f357,plain,(
% 88.16/11.87 ![X0,X1]: (sK4_skl(X0,X1)=sK1_skl(sK2_skl(X0,X1)))),
% 88.16/11.87 inference(backward_demodulation,[status(thm)],[f353,f268])).
% 88.16/11.87 fof(f378,plain,(
% 88.16/11.87 ![X0,X1]: (sK4_skl(X0,X1)=sK2_skl(sK1_skl(X0),X1))),
% 88.16/11.87 inference(resolution,[status(thm)],[f295,f335])).
% 88.16/11.87 fof(f381,plain,(
% 88.16/11.87 ![X0]: (r2(X0,sK4_skl(sK0_skl,X0)))),
% 88.16/11.87 inference(paramodulation,[status(thm)],[f351,f356])).
% 88.16/11.87 fof(f413,plain,(
% 88.16/11.87 ![X0]: (sK4_skl(sK0_skl,X0)=sK1_skl(X0))),
% 88.16/11.87 inference(resolution,[status(thm)],[f381,f266])).
% 88.16/11.87 fof(f477,plain,(
% 88.16/11.87 ![X0]: (sK8_skl(sK0_skl,X0)=sK2_skl(X0,sK0_skl))),
% 88.16/11.87 inference(paramodulation,[status(thm)],[f312,f350])).
% 88.16/11.87 fof(f600,plain,(
% 88.16/11.87 ![X0,X1]: (sK4_skl(X0,sK3_skl(X1,sK1_skl(X0)))=sK8_skl(X1,sK1_skl(X0)))),
% 88.16/11.87 inference(paramodulation,[status(thm)],[f350,f378])).
% 88.16/11.87 fof(f603,plain,(
% 88.16/11.87 ![X0,X1]: (sK4_skl(sK1_skl(X0),X1)=sK1_skl(sK4_skl(X0,X1)))),
% 88.16/11.87 inference(paramodulation,[status(thm)],[f378,f357])).
% 88.16/11.87 fof(f617,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4,X5,X6]: (~r2(X0,sK3_skl(X1,sK1_skl(sK1_skl(sK0_skl))))|~r2(X2,X0)|~r2(X3,X2)|~r2(X4,X3)|~r2(X5,X4)|~r1(X6)|~r2(X6,X5)|~r2(sK1_skl(sK1_skl(sK0_skl)),X1))),
% 88.16/11.87 inference(resolution,[status(thm)],[f342,f124])).
% 88.16/11.87 fof(f625,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4,X5]: (~r2(X0,sK3_skl(sK1_skl(sK1_skl(sK1_skl(sK0_skl))),sK1_skl(sK1_skl(sK0_skl))))|~r2(X1,X0)|~r2(X2,X1)|~r2(X3,X2)|~r2(X4,X3)|~r1(X5)|~r2(X5,X4))),
% 88.16/11.87 inference(resolution,[status(thm)],[f617,f124])).
% 88.16/11.87 fof(f626,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4,X5]: (~r2(X0,sK8_skl(sK1_skl(sK1_skl(sK0_skl)),sK1_skl(sK1_skl(sK0_skl))))|~r2(X1,X0)|~r2(X2,X1)|~r2(X3,X2)|~r2(X4,X3)|~r1(X5)|~r2(X5,X4))),
% 88.16/11.87 inference(forward_demodulation,[status(thm)],[f311,f625])).
% 88.16/11.87 fof(f1542,plain,(
% 88.16/11.87 ![X0,X1]: (r2(sK2_skl(X0,sK3_skl(X1,sK1_skl(X0))),sK8_skl(X1,sK1_skl(X0))))),
% 88.16/11.87 inference(paramodulation,[status(thm)],[f600,f356])).
% 88.16/11.87 fof(f10369,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4]: (~r2(X0,sK2_skl(sK1_skl(sK0_skl),sK3_skl(sK1_skl(sK1_skl(sK0_skl)),sK1_skl(sK1_skl(sK0_skl)))))|~r2(X1,X0)|~r2(X2,X1)|~r2(X3,X2)|~r1(X4)|~r2(X4,X3))),
% 88.16/11.87 inference(resolution,[status(thm)],[f1542,f626])).
% 88.16/11.87 fof(f10418,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4]: (~r2(X0,sK4_skl(sK0_skl,sK3_skl(sK1_skl(sK1_skl(sK0_skl)),sK1_skl(sK1_skl(sK0_skl)))))|~r2(X1,X0)|~r2(X2,X1)|~r2(X3,X2)|~r1(X4)|~r2(X4,X3))),
% 88.16/11.87 inference(forward_demodulation,[status(thm)],[f378,f10369])).
% 88.16/11.87 fof(f10419,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4]: (~r2(X0,sK1_skl(sK3_skl(sK1_skl(sK1_skl(sK0_skl)),sK1_skl(sK1_skl(sK0_skl)))))|~r2(X1,X0)|~r2(X2,X1)|~r2(X3,X2)|~r1(X4)|~r2(X4,X3))),
% 88.16/11.87 inference(forward_demodulation,[status(thm)],[f413,f10418])).
% 88.16/11.87 fof(f10420,plain,(
% 88.16/11.87 ![X0,X1,X2,X3,X4]: (~r2(X0,sK1_skl(sK8_skl(sK1_skl(sK0_skl),sK1_skl(sK1_skl(sK0_skl)))))|~r2(X1,X0)|~r2(X2,X1)|~r2(X3,X2)|~r1(X4)|~r2(X4,X3))),
% 88.16/11.87 inference(forward_demodulation,[status(thm)],[f311,f10419])).
% 88.16/11.87 fof(f10502,plain,(
% 88.16/11.87 ![X0,X1,X2,X3]: (~r2(X0,sK8_skl(sK1_skl(sK0_skl),sK1_skl(sK1_skl(sK0_skl))))|~r2(X1,X0)|~r2(X2,X1)|~r1(X3)|~r2(X3,X2))),
% 88.16/11.87 inference(resolution,[status(thm)],[f10420,f124])).
% 88.16/11.87 fof(f10514,plain,(
% 88.16/11.87 ![X0,X1,X2]: (~r2(X0,sK2_skl(sK1_skl(sK0_skl),sK3_skl(sK1_skl(sK0_skl),sK1_skl(sK1_skl(sK0_skl)))))|~r2(X1,X0)|~r1(X2)|~r2(X2,X1))),
% 88.16/11.87 inference(resolution,[status(thm)],[f10502,f1542])).
% 88.16/11.87 fof(f10517,plain,(
% 88.16/11.87 ![X0,X1,X2]: (~r2(X0,sK4_skl(sK0_skl,sK3_skl(sK1_skl(sK0_skl),sK1_skl(sK1_skl(sK0_skl)))))|~r2(X1,X0)|~r1(X2)|~r2(X2,X1))),
% 88.16/11.87 inference(forward_demodulation,[status(thm)],[f378,f10514])).
% 88.16/11.87 fof(f10518,plain,(
% 88.16/11.87 ![X0,X1,X2]: (~r2(X0,sK1_skl(sK3_skl(sK1_skl(sK0_skl),sK1_skl(sK1_skl(sK0_skl)))))|~r2(X1,X0)|~r1(X2)|~r2(X2,X1))),
% 88.16/11.92 inference(forward_demodulation,[status(thm)],[f413,f10517])).
% 88.16/11.92 fof(f10519,plain,(
% 88.16/11.92 ![X0,X1,X2]: (~r2(X0,sK1_skl(sK8_skl(sK0_skl,sK1_skl(sK1_skl(sK0_skl)))))|~r2(X1,X0)|~r1(X2)|~r2(X2,X1))),
% 88.16/11.92 inference(forward_demodulation,[status(thm)],[f311,f10518])).
% 88.16/11.92 fof(f10520,plain,(
% 88.16/11.92 ![X0,X1,X2]: (~r2(X0,sK1_skl(sK2_skl(sK1_skl(sK1_skl(sK0_skl)),sK0_skl)))|~r2(X1,X0)|~r1(X2)|~r2(X2,X1))),
% 88.16/11.92 inference(forward_demodulation,[status(thm)],[f477,f10519])).
% 88.16/11.92 fof(f10521,plain,(
% 88.16/11.92 ![X0,X1,X2]: (~r2(X0,sK4_skl(sK1_skl(sK1_skl(sK0_skl)),sK0_skl))|~r2(X1,X0)|~r1(X2)|~r2(X2,X1))),
% 88.16/11.92 inference(forward_demodulation,[status(thm)],[f357,f10520])).
% 88.16/11.92 fof(f10522,plain,(
% 88.16/11.92 ![X0,X1,X2]: (~r2(X0,sK1_skl(sK4_skl(sK1_skl(sK0_skl),sK0_skl)))|~r2(X1,X0)|~r1(X2)|~r2(X2,X1))),
% 88.16/11.92 inference(forward_demodulation,[status(thm)],[f603,f10521])).
% 88.16/11.92 fof(f10523,plain,(
% 88.16/11.92 ![X0,X1,X2]: (~r2(X0,sK1_skl(sK1_skl(sK4_skl(sK0_skl,sK0_skl))))|~r2(X1,X0)|~r1(X2)|~r2(X2,X1))),
% 88.16/11.92 inference(forward_demodulation,[status(thm)],[f603,f10522])).
% 88.16/11.92 fof(f10524,plain,(
% 88.16/11.92 ![X0,X1,X2]: (~r2(X0,sK1_skl(sK1_skl(sK1_skl(sK0_skl))))|~r2(X1,X0)|~r1(X2)|~r2(X2,X1))),
% 88.16/11.92 inference(forward_demodulation,[status(thm)],[f413,f10523])).
% 88.16/11.92 fof(f10527,plain,(
% 88.16/11.92 ![X0,X1]: (~r2(X0,sK1_skl(sK1_skl(sK0_skl)))|~r1(X1)|~r2(X1,X0))),
% 88.16/11.92 inference(resolution,[status(thm)],[f10524,f124])).
% 88.16/11.92 fof(f10530,plain,(
% 88.16/11.92 ![X0]: (~r1(X0)|~r2(X0,sK1_skl(sK0_skl)))),
% 88.16/11.92 inference(resolution,[status(thm)],[f10527,f124])).
% 88.16/11.92 fof(f10533,plain,(
% 88.16/11.92 ~r1(sK0_skl)),
% 88.16/11.92 inference(resolution,[status(thm)],[f10530,f124])).
% 88.16/11.92 fof(f10534,plain,(
% 88.16/11.92 $false),
% 88.16/11.92 inference(forward_subsumption_resolution,[status(thm)],[f10533,f122])).
% 88.16/11.92 % SZS output end CNFRefutation for theBenchmark.p
% 3.03/11.95 % Elapsed time: 11.394251 seconds
% 3.03/11.95 % CPU time: 89.831636 seconds
% 3.03/11.95 % Total memory used: 377.401 MB
% 3.03/11.95 % Net memory used: 339.552 MB
%------------------------------------------------------------------------------