%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN077+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 01:57:13 PM UTC 2026
% Result : Theorem 283.20s 36.43s
% Output : CNFRefutation 283.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 25
% Syntax : Number of formulae : 197 ( 59 unt; 13 def)
% Number of atoms : 616 ( 126 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 726 ( 307 ~; 304 |; 102 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 9 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-2 aty)
% Number of variables : 496 ( 436 !; 60 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 = Y23
& r4(X16,X17,X18) )
| ( X18 != Y23
& ~ r4(X16,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X6] :
( ? [Y1,Y11] :
( X6 = Y11
& r2(Y1,Y11) )
| ? [Y19] :
( X6 = Y19
& r1(Y19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1] :
( ? [Y6] :
( ? [Y9] :
( ? [Y12] :
( ? [Y15] :
( r2(Y15,Y12)
& r1(Y15) )
& r2(Y12,Y9) )
& r4(Y9,Y6,Y1) )
& ? [Y8] :
( ? [Y11] :
( ? [Y14] :
( r2(Y14,Y11)
& r1(Y14) )
& r2(Y11,Y8) )
& r2(Y8,Y6) ) )
& ? [Y2] :
( ? [Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y7] :
( ? [Y10] :
( ? [Y13] :
( r2(Y13,Y10)
& r1(Y13) )
& r2(Y10,Y7) )
& r2(Y7,Y5) )
& r2(Y5,Y4) )
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ? [Y6] :
( ? [Y9] :
( ? [Y12] :
( ? [Y15] :
( r2(Y15,Y12)
& r1(Y15) )
& r2(Y12,Y9) )
& r4(Y9,Y6,Y1) )
& ? [Y8] :
( ? [Y11] :
( ? [Y14] :
( r2(Y14,Y11)
& r1(Y14) )
& r2(Y11,Y8) )
& r2(Y8,Y6) ) )
& ? [Y2] :
( ? [Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y7] :
( ? [Y10] :
( ? [Y13] :
( r2(Y13,Y10)
& r1(Y13) )
& r2(Y10,Y7) )
& r2(Y7,Y5) )
& r2(Y5,Y4) )
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,definition,
! [Y24,X19] :
( sP0_prd(X19,Y24)
<=> ( X19 != Y24
& ~ r1(X19) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f15,plain,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| sP0_prd(X19,Y24) ),
inference(formula_renaming,[status(thm)],[f1,f14]) ).
fof(f16,plain,
! [X19] :
( ( X19 = sK0_skl
& r1(X19) )
| sP0_prd(X19,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f15]) ).
fof(f17,plain,
! [X0] :
( r1(X0)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0] :
( X0 = sK0_skl
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,definition,
! [X11,Y21,X12] :
( sP1_prd(X12,Y21,X11)
<=> ( X12 != Y21
& ~ r2(X11,X12) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f20,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| sP1_prd(X12,Y21,X11) ),
inference(formula_renaming,[status(thm)],[f2,f19]) ).
fof(f21,plain,
! [X11,X12] :
( ( X12 = sK1_skl(X11)
& r2(X11,X12) )
| sP1_prd(X12,sK1_skl(X11),X11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y21,sK1_skl(X11))],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( r2(X1,X0)
| sP1_prd(X0,sK1_skl(X1),X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = sK1_skl(X1)
| sP1_prd(X0,sK1_skl(X1),X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f24,definition,
! [X13,X14,Y22,X15] :
( sP2_prd(X15,Y22,X14,X13)
<=> ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f25,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| sP2_prd(X15,Y22,X14,X13) ),
inference(formula_renaming,[status(thm)],[f3,f24]) ).
fof(f26,plain,
! [X13,X14,X15] :
( ( X15 = sK2_skl(X14,X13)
& r3(X13,X14,X15) )
| sP2_prd(X15,sK2_skl(X14,X13),X14,X13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y22,sK2_skl(X14,X13))],[f25]) ).
fof(f28,plain,
! [X0,X1,X2] :
( X0 = sK2_skl(X1,X2)
| sP2_prd(X0,sK2_skl(X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,definition,
! [X16,X17,Y23,X18] :
( sP3_prd(X18,Y23,X17,X16)
<=> ( X18 != Y23
& ~ r4(X16,X17,X18) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f30,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 = Y23
& r4(X16,X17,X18) )
| sP3_prd(X18,Y23,X17,X16) ),
inference(formula_renaming,[status(thm)],[f4,f29]) ).
fof(f31,plain,
! [X16,X17,X18] :
( ( X18 = sK3_skl(X17,X16)
& r4(X16,X17,X18) )
| sP3_prd(X18,sK3_skl(X17,X16),X17,X16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y23,sK3_skl(X17,X16))],[f30]) ).
fof(f33,plain,
! [X0,X1,X2] :
( X0 = sK3_skl(X1,X2)
| sP3_prd(X0,sK3_skl(X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X1,X8] :
( r3(X1,X8,sK7_skl(X8,X1))
& r2(sK7_skl(X8,X1),sK4_skl(X8,X1))
& sK5_skl(X8,X1) = sK4_skl(X8,X1)
& r3(X1,sK6_skl(X8,X1),sK5_skl(X8,X1))
& r2(X8,sK6_skl(X8,X1)) ),
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]) ).
fof(f35,plain,
! [X0,X1] : r2(X0,sK6_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] : r3(X0,sK6_skl(X1,X0),sK5_skl(X1,X0)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1] : sK5_skl(X0,X1) = sK4_skl(X0,X1),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [X0,X1] : r2(sK7_skl(X0,X1),sK4_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,plain,
! [X0,X1] : r3(X0,X1,sK7_skl(X1,X0)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f40,plain,
! [X2,X9] :
( r4(X2,X9,sK11_skl(X9,X2))
& r3(sK11_skl(X9,X2),X2,sK8_skl(X9,X2))
& sK9_skl(X9,X2) = sK8_skl(X9,X2)
& r4(X2,sK10_skl(X9,X2),sK9_skl(X9,X2))
& r2(X9,sK10_skl(X9,X2)) ),
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]) ).
fof(f41,plain,
! [X0,X1] : r2(X0,sK10_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] : r4(X0,sK10_skl(X1,X0),sK9_skl(X1,X0)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] : sK9_skl(X0,X1) = sK8_skl(X0,X1),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
! [X0,X1] : r3(sK11_skl(X0,X1),X1,sK8_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0,X1] : r4(X0,X1,sK11_skl(X1,X0)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| ~ r2(X3,X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f47,plain,
! [X4] :
( sK12_skl(X4) = X4
& r3(X4,sK13_skl(X4),sK12_skl(X4))
& r1(sK13_skl(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f8]) ).
fof(f48,plain,
! [X0] : r1(sK13_skl(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0] : r3(X0,sK13_skl(X0),sK12_skl(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0] : sK12_skl(X0) = X0,
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
! [X5] :
( sK14_skl(X5) = sK16_skl(X5)
& r1(sK16_skl(X5))
& r4(X5,sK15_skl(X5),sK14_skl(X5))
& r1(sK15_skl(X5)) ),
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]) ).
fof(f52,plain,
! [X0] : r1(sK15_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0] : r4(X0,sK15_skl(X0),sK14_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0] : r1(sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [X0] : sK14_skl(X0) = sK16_skl(X0),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f56,definition,
! [X6,Y19] :
( sP4_prd(Y19,X6)
<=> ( X6 = Y19
& r1(Y19) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f57,plain,
! [X6] :
( ? [Y1,Y11] :
( X6 = Y11
& r2(Y1,Y11) )
| ? [Y19] : sP4_prd(Y19,X6) ),
inference(formula_renaming,[status(thm)],[f10,f56]) ).
fof(f58,plain,
! [X6] :
( ? [Y11] :
( X6 = Y11
& ? [Y1] : r2(Y1,Y11) )
| ? [Y19] : sP4_prd(Y19,X6) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [X6] :
( ( X6 = sK18_skl(X6)
& r2(sK19_skl(X6),sK18_skl(X6)) )
| sP4_prd(sK17_skl(X6),X6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(Y19,sK17_skl(X6)),skolemize(Y11,sK18_skl(X6)),skolemize(Y1,sK19_skl(X6))],[f58]) ).
fof(f60,plain,
! [X0] :
( r2(sK19_skl(X0),sK18_skl(X0))
| sP4_prd(sK17_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] :
( X0 = sK18_skl(X0)
| sP4_prd(sK17_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [Y10] :
( ! [X7] : ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ r2(X2,X1)
| X0 != X1
| ~ r1(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [Y1] :
( ! [Y6] :
( ! [Y9] :
( ! [Y12] :
( ! [Y15] :
( ~ r2(Y15,Y12)
| ~ r1(Y15) )
| ~ r2(Y12,Y9) )
| ~ r4(Y9,Y6,Y1) )
| ! [Y8] :
( ! [Y11] :
( ! [Y14] :
( ~ r2(Y14,Y11)
| ~ r1(Y14) )
| ~ r2(Y11,Y8) )
| ~ r2(Y8,Y6) ) )
| ! [Y2] :
( ! [Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y7] :
( ! [Y10] :
( ! [Y13] :
( ~ r2(Y13,Y10)
| ~ r1(Y13) )
| ~ r2(Y10,Y7) )
| ~ r2(Y7,Y5) )
| ~ r2(Y5,Y4) )
| ~ r2(Y4,Y3) )
| ~ r2(Y3,Y2) )
| Y1 != Y2 ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14] :
( ~ r2(X14,X13)
| ~ r1(X14)
| ~ r2(X13,X12)
| ~ r4(X12,X9,X0)
| ~ r2(X11,X10)
| ~ r1(X11)
| ~ r2(X10,X8)
| ~ r2(X8,X9)
| ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [Y24,X19] :
( ( X19 = Y24
| r1(X19)
| sP0_prd(X19,Y24) )
& ( ( X19 != Y24
& ~ r1(X19) )
| ~ sP0_prd(X19,Y24) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f67,plain,
( ! [Y24,X19] :
( X19 = Y24
| r1(X19)
| sP0_prd(X19,Y24) )
& ! [Y24,X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ~ sP0_prd(X19,Y24) ) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( X0 != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
! [X11,Y21,X12] :
( ( X12 = Y21
| r2(X11,X12)
| sP1_prd(X12,Y21,X11) )
& ( ( X12 != Y21
& ~ r2(X11,X12) )
| ~ sP1_prd(X12,Y21,X11) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f72,plain,
( ! [X11,Y21,X12] :
( X12 = Y21
| r2(X11,X12)
| sP1_prd(X12,Y21,X11) )
& ! [X11,Y21,X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ~ sP1_prd(X12,Y21,X11) ) ),
inference(miniscoping,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ r2(X2,X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,plain,
! [X13,X14,Y22,X15] :
( ( X15 = Y22
| r3(X13,X14,X15)
| sP2_prd(X15,Y22,X14,X13) )
& ( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ~ sP2_prd(X15,Y22,X14,X13) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f77,plain,
( ! [X13,X14,Y22,X15] :
( X15 = Y22
| r3(X13,X14,X15)
| sP2_prd(X15,Y22,X14,X13) )
& ! [X13,X14,Y22,X15] :
( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ~ sP2_prd(X15,Y22,X14,X13) ) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ~ r3(X3,X2,X0)
| ~ sP2_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f81,plain,
! [X16,X17,Y23,X18] :
( ( X18 = Y23
| r4(X16,X17,X18)
| sP3_prd(X18,Y23,X17,X16) )
& ( ( X18 != Y23
& ~ r4(X16,X17,X18) )
| ~ sP3_prd(X18,Y23,X17,X16) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f82,plain,
( ! [X16,X17,Y23,X18] :
( X18 = Y23
| r4(X16,X17,X18)
| sP3_prd(X18,Y23,X17,X16) )
& ! [X16,X17,Y23,X18] :
( ( X18 != Y23
& ~ r4(X16,X17,X18) )
| ~ sP3_prd(X18,Y23,X17,X16) ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ~ r4(X3,X2,X0)
| ~ sP3_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f86,plain,
! [X6,Y19] :
( ( X6 != Y19
| ~ r1(Y19)
| sP4_prd(Y19,X6) )
& ( ( X6 = Y19
& r1(Y19) )
| ~ sP4_prd(Y19,X6) ) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f87,plain,
( ! [X6,Y19] :
( X6 != Y19
| ~ r1(Y19)
| sP4_prd(Y19,X6) )
& ! [X6,Y19] :
( ( X6 = Y19
& r1(Y19) )
| ~ sP4_prd(Y19,X6) ) ),
inference(miniscoping,[status(thm)],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( r1(X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( X1 = X0
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f91,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ r2(X2,X1)
| ~ r2(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f92,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13] :
( ~ r2(X13,X12)
| ~ r1(X13)
| ~ r2(X12,X11)
| ~ r4(X11,X8,X1)
| ~ r2(X10,X9)
| ~ r1(X10)
| ~ r2(X9,X7)
| ~ r2(X7,X8)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f65]) ).
fof(f94,plain,
! [X0] : ~ sP0_prd(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f95,plain,
! [X0,X1] : ~ sP1_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f74]) ).
fof(f99,plain,
r1(sK0_skl),
inference(resolution,[status(thm)],[f17,f94]) ).
fof(f108,plain,
! [X0] :
( ~ r1(X0)
| X0 = sK0_skl ),
inference(resolution,[status(thm)],[f18,f68]) ).
fof(f110,plain,
! [X0] : r2(X0,sK1_skl(X0)),
inference(resolution,[status(thm)],[f22,f95]) ).
fof(f114,plain,
! [X0] : ~ r1(sK1_skl(X0)),
inference(resolution,[status(thm)],[f110,f92]) ).
fof(f118,plain,
! [X0,X1] :
( X1 = sK1_skl(X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f73,f23]) ).
fof(f121,plain,
! [X0,X1] : sK10_skl(X0,X1) = sK1_skl(X0),
inference(resolution,[status(thm)],[f118,f41]) ).
fof(f122,plain,
! [X0,X1] : sK6_skl(X0,X1) = sK1_skl(X0),
inference(resolution,[status(thm)],[f118,f35]) ).
fof(f129,plain,
! [X0,X1] : r4(X0,sK1_skl(X1),sK9_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f121,f42]) ).
fof(f130,plain,
! [X0,X1] : r4(X0,sK1_skl(X1),sK8_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f43,f129]) ).
fof(f131,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ~ r2(X12,X11)
| ~ r1(X12)
| ~ r2(X11,X2)
| ~ r2(X10,X9)
| ~ r1(X10)
| ~ r2(X9,X8)
| ~ r2(X8,sK1_skl(X1))
| ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X0)
| ~ r2(X0,sK8_skl(X1,X2)) ),
inference(resolution,[status(thm)],[f130,f93]) ).
fof(f132,plain,
! [X0] : sK13_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f48,f108]) ).
fof(f134,plain,
! [X0] : sK15_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f52,f108]) ).
fof(f136,plain,
! [X0] : r4(X0,sK0_skl,sK14_skl(X0)),
inference(backward_demodulation,[status(thm)],[f134,f53]) ).
fof(f147,plain,
! [X0] : r1(sK14_skl(X0)),
inference(forward_demodulation,[status(thm)],[f55,f54]) ).
fof(f148,plain,
! [X0] : sK14_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f147,f108]) ).
fof(f151,plain,
! [X0] : r4(X0,sK0_skl,sK0_skl),
inference(backward_demodulation,[status(thm)],[f148,f136]) ).
fof(f170,plain,
! [X0,X1,X2] :
( ~ r4(X2,X1,X0)
| X0 = sK3_skl(X1,X2) ),
inference(resolution,[status(thm)],[f33,f83]) ).
fof(f178,plain,
! [X0] : sK0_skl = sK3_skl(sK0_skl,X0),
inference(resolution,[status(thm)],[f170,f151]) ).
fof(f179,plain,
! [X0,X1] : sK8_skl(X0,X1) = sK3_skl(sK1_skl(X0),X1),
inference(resolution,[status(thm)],[f170,f130]) ).
fof(f180,plain,
! [X0,X1] : sK11_skl(X0,X1) = sK3_skl(X0,X1),
inference(resolution,[status(thm)],[f170,f45]) ).
fof(f196,plain,
! [X0,X1] : r3(X0,sK1_skl(X1),sK5_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f122,f36]) ).
fof(f197,plain,
! [X0,X1] : r3(X0,sK1_skl(X1),sK4_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f37,f196]) ).
fof(f198,plain,
! [X0,X1] : ~ r1(sK4_skl(X0,X1)),
inference(resolution,[status(thm)],[f38,f92]) ).
fof(f201,plain,
! [X0,X1] : r3(sK3_skl(X0,X1),X1,sK8_skl(X0,X1)),
inference(forward_demodulation,[status(thm)],[f180,f44]) ).
fof(f202,plain,
! [X0] : r3(sK0_skl,X0,sK8_skl(sK0_skl,X0)),
inference(paramodulation,[status(thm)],[f178,f201]) ).
fof(f204,plain,
! [X0] : r3(X0,sK0_skl,sK12_skl(X0)),
inference(forward_demodulation,[status(thm)],[f132,f49]) ).
fof(f205,plain,
! [X0] : r3(X0,sK0_skl,X0),
inference(forward_demodulation,[status(thm)],[f50,f204]) ).
fof(f208,plain,
! [X0] :
( X0 = sK17_skl(X0)
| X0 = sK18_skl(X0) ),
inference(resolution,[status(thm)],[f61,f89]) ).
fof(f209,plain,
! [X0] :
( r1(sK17_skl(X0))
| X0 = sK18_skl(X0) ),
inference(resolution,[status(thm)],[f61,f88]) ).
fof(f212,plain,
! [X0,X1] :
( X1 = sK19_skl(X0)
| ~ r2(X1,sK18_skl(X0))
| sP4_prd(sK17_skl(X0),X0) ),
inference(resolution,[status(thm)],[f60,f91]) ).
fof(f216,plain,
! [X0,X1] :
( X0 = sK17_skl(X0)
| X1 = sK19_skl(X0)
| ~ r2(X1,X0)
| sP4_prd(sK17_skl(X0),X0) ),
inference(paramodulation,[status(thm)],[f208,f212]) ).
fof(f220,plain,
! [X0,X1] :
( X1 = sK17_skl(X1)
| X0 = sK19_skl(X1)
| ~ r2(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f89]) ).
fof(f224,plain,
! [X0,X1] :
( sK4_skl(X0,X1) = sK17_skl(sK4_skl(X0,X1))
| sK7_skl(X0,X1) = sK19_skl(sK4_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f220,f38]) ).
fof(f277,definition,
( sQ7_spl
<=> r1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( sQ7_spl
| ~ r1(sK0_skl) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f295,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f99]) ).
fof(f296,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f305,plain,
! [X0,X1] :
( r1(sK17_skl(X0))
| X1 = sK19_skl(X0)
| ~ r2(X1,X0)
| sP4_prd(sK17_skl(X0),X0) ),
inference(paramodulation,[status(thm)],[f209,f212]) ).
fof(f309,plain,
! [X0,X1] :
( r1(sK17_skl(X1))
| X0 = sK19_skl(X1)
| ~ r2(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f88]) ).
fof(f360,plain,
! [X0,X1,X2] :
( X2 = sK2_skl(X1,X0)
| ~ r3(X0,X1,X2) ),
inference(resolution,[status(thm)],[f78,f28]) ).
fof(f362,plain,
! [X0] : sK8_skl(sK0_skl,X0) = sK2_skl(X0,sK0_skl),
inference(resolution,[status(thm)],[f360,f202]) ).
fof(f363,plain,
! [X0,X1] : sK8_skl(X0,X1) = sK2_skl(X1,sK3_skl(X0,X1)),
inference(resolution,[status(thm)],[f360,f201]) ).
fof(f364,plain,
! [X0] : X0 = sK2_skl(sK0_skl,X0),
inference(resolution,[status(thm)],[f360,f205]) ).
fof(f365,plain,
! [X0,X1] : sK4_skl(X0,X1) = sK2_skl(sK1_skl(X0),X1),
inference(resolution,[status(thm)],[f360,f197]) ).
fof(f367,plain,
! [X0,X1] : sK7_skl(X0,X1) = sK2_skl(X0,X1),
inference(resolution,[status(thm)],[f360,f39]) ).
fof(f369,plain,
! [X0,X1] :
( sK4_skl(X0,X1) = sK17_skl(sK4_skl(X0,X1))
| sK2_skl(X0,X1) = sK19_skl(sK4_skl(X0,X1)) ),
inference(backward_demodulation,[status(thm)],[f367,f224]) ).
fof(f371,plain,
! [X0,X1] : r2(sK2_skl(X0,X1),sK4_skl(X0,X1)),
inference(backward_demodulation,[status(thm)],[f367,f38]) ).
fof(f393,plain,
! [X0] : r2(X0,sK4_skl(sK0_skl,X0)),
inference(paramodulation,[status(thm)],[f364,f371]) ).
fof(f402,plain,
! [X0,X1] :
( r1(sK17_skl(sK4_skl(X0,X1)))
| sK2_skl(X0,X1) = sK19_skl(sK4_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f309,f371]) ).
fof(f439,plain,
! [X0,X1] :
( r1(sK17_skl(sK4_skl(X0,X1)))
| r2(sK2_skl(X0,X1),sK18_skl(sK4_skl(X0,X1)))
| sP4_prd(sK17_skl(sK4_skl(X0,X1)),sK4_skl(X0,X1)) ),
inference(paramodulation,[status(thm)],[f402,f60]) ).
fof(f440,plain,
! [X0,X1] :
( r1(sK17_skl(sK4_skl(X0,X1)))
| r2(sK2_skl(X0,X1),sK18_skl(sK4_skl(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f439,f88]) ).
fof(f447,plain,
! [X0] :
( r1(sK17_skl(sK4_skl(sK0_skl,X0)))
| r2(X0,sK18_skl(sK4_skl(sK0_skl,X0))) ),
inference(paramodulation,[status(thm)],[f364,f440]) ).
fof(f451,plain,
! [X0] :
( X0 = sK19_skl(sK4_skl(sK0_skl,X0))
| sP4_prd(sK17_skl(sK4_skl(sK0_skl,X0)),sK4_skl(sK0_skl,X0))
| r1(sK17_skl(sK4_skl(sK0_skl,X0))) ),
inference(resolution,[status(thm)],[f447,f212]) ).
fof(f457,plain,
! [X0] :
( r1(sK17_skl(sK4_skl(sK0_skl,X0)))
| r1(sK17_skl(sK4_skl(sK0_skl,X0)))
| r2(X0,sK4_skl(sK0_skl,X0)) ),
inference(paramodulation,[status(thm)],[f209,f447]) ).
fof(f459,plain,
! [X0] :
( X0 = sK19_skl(sK4_skl(sK0_skl,X0))
| r1(sK17_skl(sK4_skl(sK0_skl,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f88]) ).
fof(f460,plain,
! [X0] :
( r1(sK17_skl(sK4_skl(sK0_skl,X0)))
| r2(X0,sK4_skl(sK0_skl,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f457]) ).
fof(f471,plain,
! [X0] :
( sK4_skl(sK0_skl,X0) = sK1_skl(X0)
| r1(sK17_skl(sK4_skl(sK0_skl,X0))) ),
inference(resolution,[status(thm)],[f460,f118]) ).
fof(f475,plain,
! [X0] :
( r1(sK17_skl(sK4_skl(sK0_skl,X0)))
| X0 = sK19_skl(sK1_skl(X0))
| r1(sK17_skl(sK4_skl(sK0_skl,X0))) ),
inference(paramodulation,[status(thm)],[f471,f459]) ).
fof(f486,plain,
! [X0] :
( X0 = sK19_skl(sK1_skl(X0))
| r1(sK17_skl(sK4_skl(sK0_skl,X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f475]) ).
fof(f497,plain,
! [X0] :
( sK2_skl(sK0_skl,X0) = sK19_skl(sK4_skl(sK0_skl,X0))
| X0 = sK19_skl(sK1_skl(X0))
| r1(sK4_skl(sK0_skl,X0)) ),
inference(paramodulation,[status(thm)],[f369,f486]) ).
fof(f499,plain,
! [X0] :
( X0 = sK19_skl(sK4_skl(sK0_skl,X0))
| X0 = sK19_skl(sK1_skl(X0))
| r1(sK4_skl(sK0_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f364,f497]) ).
fof(f500,plain,
! [X0] :
( X0 = sK19_skl(sK4_skl(sK0_skl,X0))
| X0 = sK19_skl(sK1_skl(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f198]) ).
fof(f537,plain,
! [X0] : sK4_skl(sK0_skl,X0) = sK1_skl(X0),
inference(resolution,[status(thm)],[f393,f118]) ).
fof(f917,plain,
! [X0] :
( X0 = sK19_skl(sK1_skl(X0))
| X0 = sK19_skl(sK1_skl(X0)) ),
inference(backward_demodulation,[status(thm)],[f537,f500]) ).
fof(f931,plain,
! [X0] : X0 = sK19_skl(sK1_skl(X0)),
inference(duplicate_literals_removal,[status(thm)],[f917]) ).
fof(f1058,plain,
! [X0,X1] : sK4_skl(X0,sK3_skl(X1,sK1_skl(X0))) = sK8_skl(X1,sK1_skl(X0)),
inference(paramodulation,[status(thm)],[f363,f365]) ).
fof(f2030,definition,
! [X5,X6] :
( sQ112_spl
<=> ( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,sK1_skl(sK1_skl(sK0_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f2031,plain,
! [X0,X1] :
( ~ sQ112_spl
| ~ r2(X1,X0)
| ~ r1(X1)
| ~ r2(X0,sK1_skl(sK1_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f2030]) ).
fof(f2036,plain,
! [X0] :
( ~ sQ112_spl
| ~ r2(X0,sK1_skl(sK0_skl))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f2031,f110]) ).
fof(f2052,definition,
( sQ116_spl
<=> r1(sK19_skl(sK1_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f2054,plain,
( sQ116_spl
| ~ r1(sK19_skl(sK1_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f2052]) ).
fof(f2058,plain,
( sQ116_spl
| ~ r1(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f931,f2054]) ).
fof(f2059,plain,
( sQ116_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2058,f99]) ).
fof(f2060,plain,
sQ116_spl,
inference(contradiction_clause,[status(thm)],[f2059]) ).
fof(f3880,definition,
( sQ182_spl
<=> sP4_prd(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f3881,plain,
( ~ sQ182_spl
| sP4_prd(sK1_skl(sK0_skl),sK1_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f3880]) ).
fof(f4004,definition,
! [X3] :
( sQ190_spl
<=> ( ~ r2(X3,sK1_skl(sK0_skl))
| ~ r1(X3) ) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f4005,plain,
! [X0] :
( ~ sQ190_spl
| ~ r2(X0,sK1_skl(sK0_skl))
| ~ r1(X0) ),
inference(component_clause,[status(thm)],[f4004]) ).
fof(f4028,plain,
( ~ sQ190_spl
| ~ r1(sK0_skl) ),
inference(resolution,[status(thm)],[f4005,f110]) ).
fof(f4031,plain,
( ~ sQ190_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4028,f277,f4004]) ).
fof(f4104,plain,
( ~ sQ182_spl
| r1(sK1_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f3881,f88]) ).
fof(f4105,plain,
( ~ sQ182_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4104,f114]) ).
fof(f4106,plain,
~ sQ182_spl,
inference(contradiction_clause,[status(thm)],[f4105]) ).
fof(f4402,plain,
! [X0,X1] : r2(sK2_skl(X0,sK3_skl(X1,sK1_skl(X0))),sK8_skl(X1,sK1_skl(X0))),
inference(paramodulation,[status(thm)],[f1058,f371]) ).
fof(f4618,plain,
! [X0,X1] : r2(sK4_skl(X0,sK3_skl(X1,sK1_skl(sK1_skl(X0)))),sK8_skl(X1,sK1_skl(sK1_skl(X0)))),
inference(paramodulation,[status(thm)],[f365,f4402]) ).
fof(f4678,plain,
! [X0] : r2(sK1_skl(sK3_skl(X0,sK1_skl(sK1_skl(sK0_skl)))),sK8_skl(X0,sK1_skl(sK1_skl(sK0_skl)))),
inference(paramodulation,[status(thm)],[f537,f4618]) ).
fof(f4699,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ~ r2(X10,X9)
| ~ r1(X10)
| ~ r2(X9,sK1_skl(sK1_skl(sK0_skl)))
| ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r2(X6,sK1_skl(X1))
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,sK1_skl(sK3_skl(X1,sK1_skl(sK1_skl(sK0_skl))))) ),
inference(resolution,[status(thm)],[f4678,f131]) ).
fof(f4713,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ201_spl
<=> ( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r2(X6,sK1_skl(X1))
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,sK1_skl(sK3_skl(X1,sK1_skl(sK1_skl(sK0_skl))))) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f4714,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ201_spl
| ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r2(X6,sK1_skl(X1))
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,sK1_skl(sK3_skl(X1,sK1_skl(sK1_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f4713]) ).
fof(f4716,plain,
( sQ112_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f4699,f4713,f2030]) ).
fof(f4723,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ201_spl
| ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,sK1_skl(X1))
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,sK3_skl(X1,sK1_skl(sK1_skl(sK0_skl)))) ),
inference(resolution,[status(thm)],[f4714,f110]) ).
fof(f4737,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ201_spl
| ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,sK1_skl(sK1_skl(X1)))
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,sK8_skl(X1,sK1_skl(sK1_skl(sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f179,f4723]) ).
fof(f4740,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ201_spl
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r2(X4,sK1_skl(sK1_skl(X1)))
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ r2(X0,sK1_skl(sK3_skl(X1,sK1_skl(sK1_skl(sK0_skl))))) ),
inference(resolution,[status(thm)],[f4737,f4678]) ).
fof(f4769,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ201_spl
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,sK1_skl(sK1_skl(X1)))
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,sK3_skl(X1,sK1_skl(sK1_skl(sK0_skl)))) ),
inference(resolution,[status(thm)],[f4740,f110]) ).
fof(f4799,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ201_spl
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,sK1_skl(sK1_skl(sK1_skl(X1))))
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,sK8_skl(X1,sK1_skl(sK1_skl(sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f179,f4769]) ).
fof(f4809,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ201_spl
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,sK1_skl(sK1_skl(sK1_skl(sK0_skl))))
| ~ r2(X1,X0)
| ~ r1(X1)
| ~ r2(X0,sK2_skl(sK1_skl(sK1_skl(sK0_skl)),sK0_skl)) ),
inference(paramodulation,[status(thm)],[f362,f4799]) ).
fof(f4814,definition,
! [X0,X1] :
( sQ205_spl
<=> ( ~ r2(X1,X0)
| ~ r1(X1)
| ~ r2(X0,sK2_skl(sK1_skl(sK1_skl(sK0_skl)),sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f4815,plain,
! [X0,X1] :
( ~ sQ205_spl
| ~ r2(X1,X0)
| ~ r1(X1)
| ~ r2(X0,sK2_skl(sK1_skl(sK1_skl(sK0_skl)),sK0_skl)) ),
inference(component_clause,[status(thm)],[f4814]) ).
fof(f4817,definition,
! [X2,X3,X4] :
( sQ206_spl
<=> ( ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,sK1_skl(sK1_skl(sK1_skl(sK0_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f4818,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| ~ r2(X2,X1)
| ~ r1(X2)
| ~ r2(X1,X0)
| ~ r2(X0,sK1_skl(sK1_skl(sK1_skl(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f4817]) ).
fof(f4820,plain,
( ~ sQ201_spl
| sQ206_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f4809,f4814,f4817,f4713]) ).
fof(f4821,plain,
! [X0,X1] :
( ~ sQ205_spl
| ~ r2(X1,X0)
| ~ r1(X1)
| ~ r2(X0,sK4_skl(sK1_skl(sK0_skl),sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f365,f4815]) ).
fof(f4822,plain,
! [X0] :
( ~ sQ205_spl
| ~ r2(X0,sK2_skl(sK1_skl(sK0_skl),sK0_skl))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f4821,f371]) ).
fof(f4825,plain,
! [X0] :
( ~ sQ205_spl
| ~ r2(X0,sK4_skl(sK0_skl,sK0_skl))
| ~ r1(X0) ),
inference(forward_demodulation,[status(thm)],[f365,f4822]) ).
fof(f4826,plain,
! [X0] :
( ~ sQ205_spl
| ~ r2(X0,sK1_skl(sK0_skl))
| ~ r1(X0) ),
inference(forward_demodulation,[status(thm)],[f537,f4825]) ).
fof(f4837,plain,
( ~ sQ205_spl
| ~ r1(sK0_skl) ),
inference(resolution,[status(thm)],[f4826,f110]) ).
fof(f4840,plain,
( ~ sQ205_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4837,f277,f4814]) ).
fof(f4846,plain,
( ~ sQ112_spl
| sQ190_spl ),
inference(split_clause,[status(thm)],[f2036,f4004,f2030]) ).
fof(f4905,plain,
! [X0,X1] :
( ~ sQ206_spl
| ~ r2(X1,X0)
| ~ r1(X1)
| ~ r2(X0,sK1_skl(sK1_skl(sK0_skl))) ),
inference(resolution,[status(thm)],[f4818,f110]) ).
fof(f4917,plain,
( ~ sQ206_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f4905,f2030,f4817]) ).
fof(f4918,plain,
$false,
inference(sat_refutation,[status(thm)],[f296,f2060,f4031,f4106,f4716,f4820,f4840,f4846,f4917]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN077+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.66 % Computer : n017.cluster.edu
% 0.20/0.66 % Model : x86_64 x86_64
% 0.20/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.66 % Memory : 8046.5625MB
% 0.20/0.66 % OS : Linux 6.8.0-71-generic
% 0.20/0.66 % CPULimit : 300
% 0.20/0.66 % WCLimit : 300
% 0.20/0.66 % DateTime : Mon Sep 21 03:19:42 UTC 2026
% 0.20/0.66 % CPUTime :
% 0.20/0.68 % Drodi V4.1.1
% 283.20/36.43 % Refutation found
% 283.20/36.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 283.20/36.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 283.20/36.51 % Elapsed time: 35.824930 seconds
% 283.20/36.51 % CPU time: 283.716734 seconds
% 283.20/36.51 % Total memory used: 551.282 MB
% 283.20/36.51 % Net memory used: 487.827 MB
%------------------------------------------------------------------------------