%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN075+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:57:13 PM UTC 2026
% Result : Theorem 24.87s 3.91s
% Output : CNFRefutation 24.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 91 ( 31 unt; 3 def)
% Number of atoms : 492 ( 55 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 746 ( 345 ~; 315 |; 83 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 10 avg)
% Maximal term depth : 10 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 461 ( 405 !; 56 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1] :
( ? [Y5] :
( ? [Y7] :
( ? [Y9] :
( ? [Y11] :
( ? [Y13] :
( ? [Y15] :
( ? [Y18] :
( ? [Y21] :
( r2(Y21,Y18)
& r1(Y21) )
& r2(Y18,Y15) )
& r2(Y15,Y13) )
& r2(Y13,Y11) )
& r2(Y11,Y9) )
& r2(Y9,Y7) )
& r2(Y7,Y5) )
& ? [Y16] :
( ? [Y19] :
( ? [Y22] :
( r2(Y22,Y19)
& r1(Y22) )
& r2(Y19,Y16) )
& r3(Y5,Y16,Y1) ) )
& ? [Y2] :
( ? [Y3] :
( ? [Y4] :
( ? [Y6] :
( ? [Y8] :
( ? [Y10] :
( ? [Y12] :
( ? [Y14] :
( ? [Y17] :
( ? [Y20] :
( r2(Y20,Y17)
& r1(Y20) )
& r2(Y17,Y14) )
& r2(Y14,Y12) )
& r2(Y12,Y10) )
& r2(Y10,Y8) )
& r2(Y8,Y6) )
& r2(Y6,Y4) )
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ? [Y5] :
( ? [Y7] :
( ? [Y9] :
( ? [Y11] :
( ? [Y13] :
( ? [Y15] :
( ? [Y18] :
( ? [Y21] :
( r2(Y21,Y18)
& r1(Y21) )
& r2(Y18,Y15) )
& r2(Y15,Y13) )
& r2(Y13,Y11) )
& r2(Y11,Y9) )
& r2(Y9,Y7) )
& r2(Y7,Y5) )
& ? [Y16] :
( ? [Y19] :
( ? [Y22] :
( r2(Y22,Y19)
& r1(Y22) )
& r2(Y19,Y16) )
& r3(Y5,Y16,Y1) ) )
& ? [Y2] :
( ? [Y3] :
( ? [Y4] :
( ? [Y6] :
( ? [Y8] :
( ? [Y10] :
( ? [Y12] :
( ? [Y14] :
( ? [Y17] :
( ? [Y20] :
( r2(Y20,Y17)
& r1(Y20) )
& r2(Y17,Y14) )
& r2(Y14,Y12) )
& r2(Y12,Y10) )
& r2(Y10,Y8) )
& r2(Y8,Y6) )
& r2(Y6,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(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(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(f64,plain,
! [Y1] :
( ! [Y5] :
( ! [Y7] :
( ! [Y9] :
( ! [Y11] :
( ! [Y13] :
( ! [Y15] :
( ! [Y18] :
( ! [Y21] :
( ~ r2(Y21,Y18)
| ~ r1(Y21) )
| ~ r2(Y18,Y15) )
| ~ r2(Y15,Y13) )
| ~ r2(Y13,Y11) )
| ~ r2(Y11,Y9) )
| ~ r2(Y9,Y7) )
| ~ r2(Y7,Y5) )
| ! [Y16] :
( ! [Y19] :
( ! [Y22] :
( ~ r2(Y22,Y19)
| ~ r1(Y22) )
| ~ r2(Y19,Y16) )
| ~ r3(Y5,Y16,Y1) ) )
| ! [Y2] :
( ! [Y3] :
( ! [Y4] :
( ! [Y6] :
( ! [Y8] :
( ! [Y10] :
( ! [Y12] :
( ! [Y14] :
( ! [Y17] :
( ! [Y20] :
( ~ r2(Y20,Y17)
| ~ r1(Y20) )
| ~ r2(Y17,Y14) )
| ~ r2(Y14,Y12) )
| ~ r2(Y12,Y10) )
| ~ r2(Y10,Y8) )
| ~ r2(Y8,Y6) )
| ~ r2(Y6,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,X15,X16,X17,X18,X19,X20,X21] :
( ~ r2(X21,X20)
| ~ r1(X21)
| ~ r2(X20,X19)
| ~ r2(X19,X18)
| ~ r2(X18,X17)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X11)
| ~ r2(X14,X13)
| ~ r1(X14)
| ~ r2(X13,X12)
| ~ r3(X11,X12,X0)
| ~ r2(X10,X9)
| ~ r1(X10)
| ~ r2(X9,X8)
| ~ r2(X8,X7)
| ~ r2(X7,X6)
| ~ 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(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X20] :
( ~ r2(X20,X19)
| ~ r1(X20)
| ~ r2(X19,X18)
| ~ r2(X18,X17)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X10)
| ~ r2(X13,X12)
| ~ r1(X13)
| ~ r2(X12,X11)
| ~ r3(X10,X11,X1)
| ~ r2(X9,X8)
| ~ r1(X9)
| ~ r2(X8,X7)
| ~ r2(X7,X6)
| ~ r2(X6,X5)
| ~ 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(f102,plain,
! [X0] : r2(X0,sK1_skl(X0)),
inference(resolution,[status(thm)],[f22,f95]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19] :
( ~ r2(X19,X18)
| ~ r1(X19)
| ~ r2(X18,X17)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X9)
| ~ r2(X12,X11)
| ~ r1(X12)
| ~ r2(X11,X10)
| ~ r3(X9,X10,sK1_skl(X1))
| ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f102,f93]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17,X18] :
( ~ r2(X18,X17)
| ~ r1(X18)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X8)
| ~ r2(X11,X10)
| ~ r1(X11)
| ~ r2(X10,X9)
| ~ r3(X8,X9,sK1_skl(sK1_skl(X1)))
| ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f108,f102]) ).
fof(f111,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17] :
( ~ r2(X17,X16)
| ~ r1(X17)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X7)
| ~ r2(X10,X9)
| ~ r1(X10)
| ~ r2(X9,X8)
| ~ r3(X7,X8,sK1_skl(sK1_skl(sK1_skl(X1))))
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f110,f102]) ).
fof(f112,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ~ r2(X16,X15)
| ~ r1(X16)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,X6)
| ~ r2(X9,X8)
| ~ r1(X9)
| ~ r2(X8,X7)
| ~ r3(X6,X7,sK1_skl(sK1_skl(sK1_skl(sK1_skl(X1)))))
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f111,f102]) ).
fof(f125,plain,
! [X0] :
( X0 = sK0_skl
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f68,f18]) ).
fof(f130,plain,
! [X0] : sK13_skl(X0) = sK0_skl,
inference(resolution,[status(thm)],[f125,f48]) ).
fof(f135,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( ~ r2(X15,X14)
| ~ r1(X15)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,X9)
| ~ r2(X9,X5)
| ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r3(X5,X6,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X1))))))
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f112,f102]) ).
fof(f138,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14] :
( ~ r2(X14,X13)
| ~ r1(X14)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,X9)
| ~ r2(X9,X8)
| ~ r2(X8,X4)
| ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r3(X4,X5,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X1)))))))
| ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f135,f102]) ).
fof(f146,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13] :
( ~ r2(X13,X12)
| ~ r1(X13)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,X9)
| ~ r2(X9,X8)
| ~ r2(X8,X7)
| ~ r2(X7,X3)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r3(X3,X4,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X1))))))))
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f138,f102]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ~ r2(X12,X11)
| ~ r1(X12)
| ~ r2(X11,X10)
| ~ r2(X10,X9)
| ~ r2(X9,X8)
| ~ r2(X8,X7)
| ~ r2(X7,X6)
| ~ r2(X6,X2)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r3(X2,X3,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X1)))))))))
| ~ r2(X0,X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f146,f102]) ).
fof(f161,plain,
! [X0,X1] : r3(X0,sK6_skl(X1,X0),sK4_skl(X1,X0)),
inference(backward_demodulation,[status(thm)],[f37,f36]) ).
fof(f178,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ r2(X11,X10)
| ~ r1(X11)
| ~ r2(X10,X9)
| ~ r2(X9,X8)
| ~ r2(X8,X7)
| ~ r2(X7,X6)
| ~ r2(X6,X5)
| ~ r2(X5,X1)
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r3(X1,X2,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X0))))))))))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f149,f102]) ).
fof(f190,plain,
! [X0] : r3(X0,sK0_skl,sK12_skl(X0)),
inference(forward_demodulation,[status(thm)],[f130,f49]) ).
fof(f191,plain,
! [X0] : r3(X0,sK0_skl,X0),
inference(forward_demodulation,[status(thm)],[f50,f190]) ).
fof(f217,plain,
! [X0,X1] :
( X1 = sK1_skl(X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f73,f23]) ).
fof(f219,plain,
! [X0,X1] : sK4_skl(X0,X1) = sK1_skl(sK7_skl(X0,X1)),
inference(resolution,[status(thm)],[f217,f38]) ).
fof(f221,plain,
! [X0,X1] : sK6_skl(X0,X1) = sK1_skl(X0),
inference(resolution,[status(thm)],[f217,f35]) ).
fof(f263,plain,
! [X0,X1,X2] :
( X2 = sK2_skl(X1,X0)
| ~ r3(X0,X1,X2) ),
inference(resolution,[status(thm)],[f78,f28]) ).
fof(f327,plain,
! [X0] : X0 = sK2_skl(sK0_skl,X0),
inference(resolution,[status(thm)],[f263,f191]) ).
fof(f329,plain,
! [X0,X1] : sK7_skl(X0,X1) = sK2_skl(X0,X1),
inference(resolution,[status(thm)],[f263,f39]) ).
fof(f335,plain,
! [X0,X1] : sK4_skl(X0,X1) = sK1_skl(sK2_skl(X0,X1)),
inference(backward_demodulation,[status(thm)],[f329,f219]) ).
fof(f341,plain,
! [X0,X1] : r2(sK2_skl(X0,X1),sK4_skl(X0,X1)),
inference(backward_demodulation,[status(thm)],[f329,f38]) ).
fof(f347,plain,
! [X0,X1] : r3(X0,sK1_skl(X1),sK4_skl(X1,X0)),
inference(forward_demodulation,[status(thm)],[f221,f161]) ).
fof(f348,plain,
! [X0,X1] : sK4_skl(X0,X1) = sK2_skl(sK1_skl(X0),X1),
inference(resolution,[status(thm)],[f347,f263]) ).
fof(f362,plain,
! [X0] : r2(X0,sK4_skl(sK0_skl,X0)),
inference(paramodulation,[status(thm)],[f327,f341]) ).
fof(f397,plain,
! [X0] : sK4_skl(sK0_skl,X0) = sK1_skl(X0),
inference(resolution,[status(thm)],[f362,f217]) ).
fof(f511,plain,
! [X0,X1] : sK4_skl(sK1_skl(X0),X1) = sK1_skl(sK4_skl(X0,X1)),
inference(paramodulation,[status(thm)],[f348,f335]) ).
fof(f700,plain,
! [X0] : sK4_skl(sK1_skl(sK0_skl),X0) = sK1_skl(sK1_skl(X0)),
inference(paramodulation,[status(thm)],[f397,f511]) ).
fof(f915,plain,
! [X0] : r3(X0,sK1_skl(sK1_skl(sK0_skl)),sK1_skl(sK1_skl(X0))),
inference(paramodulation,[status(thm)],[f700,f347]) ).
fof(f2874,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ r2(X9,X8)
| ~ r1(X9)
| ~ r2(X8,X7)
| ~ r2(X7,X6)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X0))))))))
| ~ r2(X2,X1)
| ~ r1(X2)
| ~ r2(X1,sK1_skl(sK1_skl(sK0_skl)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f915,f178]) ).
fof(f2962,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X0))))))))
| ~ r2(X1,sK1_skl(sK0_skl))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f2874,f102]) ).
fof(f2965,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| ~ r2(X1,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X0))))))))
| ~ r1(sK0_skl)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f2962,f102]) ).
fof(f2966,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| ~ r2(X1,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X0))))))))
| ~ r1(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2965,f99]) ).
fof(f3284,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| ~ r2(X1,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X0)))))))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f2966,f102]) ).
fof(f3305,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| ~ r2(X1,sK1_skl(sK1_skl(sK1_skl(sK1_skl(sK1_skl(X0))))))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f3284,f102]) ).
fof(f3524,plain,
! [X0,X1,X2,X3,X4] :
( ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| ~ r2(X1,sK1_skl(sK1_skl(sK1_skl(sK1_skl(X0)))))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f3305,f102]) ).
fof(f3541,plain,
! [X0,X1,X2,X3] :
( ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X1)
| ~ r2(X1,sK1_skl(sK1_skl(sK1_skl(X0))))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f3524,f102]) ).
fof(f3893,plain,
! [X0,X1,X2] :
( ~ r2(X2,X1)
| ~ r1(X2)
| ~ r2(X1,sK1_skl(sK1_skl(X0)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f3541,f102]) ).
fof(f3906,plain,
! [X0,X1] :
( ~ r2(X1,sK1_skl(X0))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f3893,f102]) ).
fof(f3917,plain,
! [X0] :
( ~ r1(X0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f3906,f102]) ).
fof(f3924,plain,
! [X0] : ~ r1(X0),
inference(duplicate_literals_removal,[status(thm)],[f3917]) ).
fof(f3931,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f99,f3924]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN075+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n019.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 03:24:50 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 24.87/3.91 % Refutation found
% 24.87/3.91 % SZS status Theorem for theBenchmark: Theorem is valid
% 24.87/3.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.41/3.94 % Elapsed time: 3.490247 seconds
% 7.41/3.94 % CPU time: 27.232092 seconds
% 7.41/3.94 % Total memory used: 136.656 MB
% 7.41/3.94 % Net memory used: 128.987 MB
%------------------------------------------------------------------------------