%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN072+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 : n019.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 01:57:12 PM UTC 2026
% Result : Theorem 1.52s 0.63s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 116 ( 54 unt; 4 def)
% Number of atoms : 320 ( 78 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 344 ( 140 ~; 120 |; 80 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 302 ( 263 !; 39 ?)
% 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(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(f12,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( ? [Y9] :
( r2(Y9,Y6)
& r1(Y9) )
& r2(Y6,Y3) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r4(Y5,Y2,Y1) )
& ? [Y4] :
( ? [Y7] :
( r2(Y7,Y4)
& r1(Y7) )
& r2(Y4,Y2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( ? [Y9] :
( r2(Y9,Y6)
& r1(Y9) )
& r2(Y6,Y3) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( ? [Y8] :
( r2(Y8,Y5)
& r1(Y8) )
& r4(Y5,Y2,Y1) )
& ? [Y4] :
( ? [Y7] :
( r2(Y7,Y4)
& r1(Y7) )
& r2(Y4,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(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(f64,plain,
! [Y1] :
( ! [Y3] :
( ! [Y6] :
( ! [Y9] :
( ~ r2(Y9,Y6)
| ~ r1(Y9) )
| ~ r2(Y6,Y3) )
| Y1 != Y3 )
| ! [Y2] :
( ! [Y5] :
( ! [Y8] :
( ~ r2(Y8,Y5)
| ~ r1(Y8) )
| ~ r4(Y5,Y2,Y1) )
| ! [Y4] :
( ! [Y7] :
( ~ r2(Y7,Y4)
| ~ r1(Y7) )
| ~ r2(Y4,Y2) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| X4 != X6
| ~ r2(X5,X3)
| ~ r1(X5)
| ~ r4(X3,X1,X4)
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(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(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X4)
| ~ r2(X5,X3)
| ~ r1(X5)
| ~ r4(X3,X1,X4)
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ 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(f107,plain,
! [X0] :
( ~ r1(X0)
| X0 = sK0_skl ),
inference(resolution,[status(thm)],[f18,f68]) ).
fof(f109,plain,
! [X0] : r2(X0,sK1_skl(X0)),
inference(resolution,[status(thm)],[f22,f95]) ).
fof(f110,plain,
! [X0] : sK16_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f107,f54]) ).
fof(f111,plain,
! [X0] : sK15_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f107,f52]) ).
fof(f113,plain,
! [X0] : sK13_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f107,f48]) ).
fof(f123,plain,
! [X0] : r4(X0,sK0_skl,sK14_skl(X0)),
inference(forward_demodulation,[status(thm)],[f111,f53]) ).
fof(f130,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| X0 = sK1_skl(X1) ),
inference(resolution,[status(thm)],[f23,f73]) ).
fof(f135,plain,
! [X0,X1] : sK10_skl(X0,X1) = sK1_skl(X0),
inference(resolution,[status(thm)],[f130,f41]) ).
fof(f136,plain,
! [X0,X1] : sK6_skl(X0,X1) = sK1_skl(X0),
inference(resolution,[status(thm)],[f130,f35]) ).
fof(f143,plain,
! [X0,X1] : r4(X0,sK1_skl(X1),sK9_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f135,f42]) ).
fof(f144,plain,
! [X0,X1] : r4(X0,sK1_skl(X1),sK8_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f43,f143]) ).
fof(f145,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,sK8_skl(X1,X4))
| ~ r2(X3,X4)
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,sK1_skl(X1)) ),
inference(resolution,[status(thm)],[f144,f93]) ).
fof(f146,plain,
! [X0,X1,X2] :
( X2 = sK3_skl(X1,X0)
| ~ r4(X0,X1,X2) ),
inference(resolution,[status(thm)],[f83,f33]) ).
fof(f148,plain,
! [X0,X1] : sK8_skl(X0,X1) = sK3_skl(sK1_skl(X0),X1),
inference(resolution,[status(thm)],[f146,f144]) ).
fof(f150,plain,
! [X0,X1] : sK11_skl(X0,X1) = sK3_skl(X0,X1),
inference(resolution,[status(thm)],[f146,f45]) ).
fof(f156,plain,
! [X0] : r4(X0,sK0_skl,sK0_skl),
inference(backward_demodulation,[status(thm)],[f157,f123]) ).
fof(f157,plain,
! [X0] : sK14_skl(X0) = sK0_skl,
inference(forward_demodulation,[status(thm)],[f110,f55]) ).
fof(f158,plain,
! [X0] : sK0_skl = sK3_skl(sK0_skl,X0),
inference(resolution,[status(thm)],[f156,f146]) ).
fof(f164,plain,
! [X0,X1] : r3(X0,sK1_skl(X1),sK5_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f136,f36]) ).
fof(f165,plain,
! [X0,X1] : r3(X0,sK1_skl(X1),sK4_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f37,f164]) ).
fof(f172,plain,
! [X0] : r3(X0,sK0_skl,sK12_skl(X0)),
inference(forward_demodulation,[status(thm)],[f113,f49]) ).
fof(f173,plain,
! [X0] : r3(X0,sK0_skl,X0),
inference(forward_demodulation,[status(thm)],[f50,f172]) ).
fof(f193,plain,
! [X0,X1] : r3(sK3_skl(X0,X1),X1,sK8_skl(X0,X1)),
inference(forward_demodulation,[status(thm)],[f150,f44]) ).
fof(f195,plain,
! [X0] : r3(sK0_skl,X0,sK8_skl(sK0_skl,X0)),
inference(paramodulation,[status(thm)],[f158,f193]) ).
fof(f198,plain,
! [X0,X1,X2] :
( X2 = sK2_skl(X1,X0)
| ~ r3(X0,X1,X2) ),
inference(resolution,[status(thm)],[f78,f28]) ).
fof(f200,plain,
! [X0] : sK8_skl(sK0_skl,X0) = sK2_skl(X0,sK0_skl),
inference(resolution,[status(thm)],[f198,f195]) ).
fof(f201,plain,
! [X0,X1] : sK8_skl(X0,X1) = sK2_skl(X1,sK3_skl(X0,X1)),
inference(resolution,[status(thm)],[f198,f193]) ).
fof(f202,plain,
! [X0] : X0 = sK2_skl(sK0_skl,X0),
inference(resolution,[status(thm)],[f198,f173]) ).
fof(f203,plain,
! [X0,X1] : sK4_skl(X0,X1) = sK2_skl(sK1_skl(X0),X1),
inference(resolution,[status(thm)],[f198,f165]) ).
fof(f205,plain,
! [X0,X1] : sK7_skl(X0,X1) = sK2_skl(X0,X1),
inference(resolution,[status(thm)],[f198,f39]) ).
fof(f213,plain,
! [X0,X1] : r2(sK2_skl(X0,X1),sK4_skl(X0,X1)),
inference(backward_demodulation,[status(thm)],[f205,f38]) ).
fof(f217,plain,
! [X0] : r2(X0,sK4_skl(sK0_skl,X0)),
inference(paramodulation,[status(thm)],[f202,f213]) ).
fof(f290,plain,
! [X0] : sK4_skl(sK0_skl,X0) = sK1_skl(X0),
inference(resolution,[status(thm)],[f217,f130]) ).
fof(f348,plain,
! [X0,X1] : sK4_skl(X0,sK3_skl(X1,sK1_skl(X0))) = sK8_skl(X1,sK1_skl(X0)),
inference(paramodulation,[status(thm)],[f201,f203]) ).
fof(f499,plain,
! [X0,X1] : r2(sK2_skl(X0,sK3_skl(X1,sK1_skl(X0))),sK8_skl(X1,sK1_skl(X0))),
inference(paramodulation,[status(thm)],[f348,f213]) ).
fof(f563,plain,
! [X0] : r2(sK3_skl(X0,sK1_skl(sK0_skl)),sK8_skl(X0,sK1_skl(sK0_skl))),
inference(paramodulation,[status(thm)],[f202,f499]) ).
fof(f581,plain,
! [X0] : r2(sK8_skl(X0,sK1_skl(sK0_skl)),sK8_skl(sK1_skl(X0),sK1_skl(sK0_skl))),
inference(paramodulation,[status(thm)],[f148,f563]) ).
fof(f665,plain,
! [X0,X1,X2,X3,X4] :
( ~ r2(X4,sK8_skl(X1,sK1_skl(sK0_skl)))
| ~ r1(X4)
| ~ r2(X3,sK1_skl(sK0_skl))
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,sK1_skl(sK1_skl(X1))) ),
inference(resolution,[status(thm)],[f581,f145]) ).
fof(f793,plain,
! [X0,X1,X2,X3] :
( ~ r2(X3,sK2_skl(sK1_skl(sK0_skl),sK0_skl))
| ~ r1(X3)
| ~ r2(X2,sK1_skl(sK0_skl))
| ~ r1(X2)
| ~ r2(X1,X0)
| ~ r1(X1)
| ~ r2(X0,sK1_skl(sK1_skl(sK0_skl))) ),
inference(paramodulation,[status(thm)],[f200,f665]) ).
fof(f795,plain,
! [X0,X1,X2,X3] :
( ~ r2(X3,sK4_skl(sK0_skl,sK0_skl))
| ~ r1(X3)
| ~ r2(X2,sK1_skl(sK0_skl))
| ~ r1(X2)
| ~ r2(X1,X0)
| ~ r1(X1)
| ~ r2(X0,sK1_skl(sK1_skl(sK0_skl))) ),
inference(forward_demodulation,[status(thm)],[f203,f793]) ).
fof(f796,plain,
! [X0,X1,X2,X3] :
( ~ r2(X3,sK1_skl(sK0_skl))
| ~ r1(X3)
| ~ r2(X2,sK1_skl(sK0_skl))
| ~ r1(X2)
| ~ r2(X1,X0)
| ~ r1(X1)
| ~ r2(X0,sK1_skl(sK1_skl(sK0_skl))) ),
inference(forward_demodulation,[status(thm)],[f290,f795]) ).
fof(f798,plain,
! [X0,X1,X2] :
( ~ r2(X2,sK1_skl(sK0_skl))
| ~ r1(X2)
| ~ r2(X1,sK1_skl(sK0_skl))
| ~ r1(X1)
| ~ r2(X0,sK1_skl(sK0_skl))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f796,f109]) ).
fof(f802,plain,
! [X0] :
( ~ r1(sK0_skl)
| ~ r1(sK0_skl)
| ~ r2(X0,sK1_skl(sK0_skl))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f798,f109]) ).
fof(f812,plain,
! [X0] :
( ~ r1(sK0_skl)
| ~ r2(X0,sK1_skl(sK0_skl))
| ~ r1(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f802]) ).
fof(f813,plain,
! [X0] :
( ~ r2(X0,sK1_skl(sK0_skl))
| ~ r1(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f812,f99]) ).
fof(f819,plain,
~ r1(sK0_skl),
inference(resolution,[status(thm)],[f813,f109]) ).
fof(f822,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f819,f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN072+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.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 03:24:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 1.52/0.63 % Refutation found
% 1.52/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.52/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.52/0.64 % Elapsed time: 0.279966 seconds
% 1.52/0.64 % CPU time: 2.023927 seconds
% 1.52/0.64 % Total memory used: 130.773 MB
% 1.52/0.64 % Net memory used: 125.145 MB
%------------------------------------------------------------------------------