%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN068+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:57:11 PM UTC 2026
% Result : Theorem 14.18s 2.33s
% Output : CNFRefutation 14.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 109 ( 13 unt; 5 def)
% Number of atoms : 332 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 379 ( 156 ~; 154 |; 64 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 266 ( 246 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,Y21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X20] : id(X20,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X23,X24,X25] :
( ~ id(X24,X25)
| id(X23,X25)
| ~ id(X23,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X28,X29,X30,X31] :
( ( r2(X30,X31)
& r2(X28,X29) )
| ( ~ r2(X30,X31)
& ~ r2(X28,X29) )
| ~ id(X29,X31)
| ~ id(X28,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X3,X10] :
( id(X3,X10)
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( ~ r2(X3,Y13)
| ~ id(Y13,Y12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
? [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| ~ id(Y1,Y4) )
& ! [Y2] :
( ~ id(Y1,Y2)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ? [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| ~ id(Y1,Y4) )
& ! [Y2] :
( ~ id(Y1,Y2)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,definition,
! [Y24,X19] :
( sP0_prd(X19,Y24)
<=> ( r1(X19)
& id(X19,Y24) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f22,plain,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| sP0_prd(X19,Y24) ),
inference(formula_renaming,[status(thm)],[f1,f21]) ).
fof(f23,plain,
! [X19] :
( ( ~ id(X19,sK0_skl)
& ~ r1(X19) )
| sP0_prd(X19,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f22]) ).
fof(f24,plain,
! [X0] :
( ~ r1(X0)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0] :
( ~ id(X0,sK0_skl)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,definition,
! [X11,Y21,X12] :
( sP1_prd(X12,Y21,X11)
<=> ( r2(X11,X12)
& id(X12,Y21) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f27,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| sP1_prd(X12,Y21,X11) ),
inference(formula_renaming,[status(thm)],[f2,f26]) ).
fof(f28,plain,
! [X11,X12] :
( ( ~ id(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))],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sP1_prd(X0,sK1_skl(X1),X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ~ id(X0,sK1_skl(X1))
| sP1_prd(X0,sK1_skl(X1),X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f41,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f42,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
! [X24,X25] :
( ~ id(X24,X25)
| ! [X23] :
( id(X23,X25)
| ~ id(X23,X24) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,definition,
! [X26,X27] :
( sP4_prd(X27,X26)
<=> ( ~ r1(X27)
& ~ r1(X26) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f46,plain,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| sP4_prd(X27,X26)
| ~ id(X26,X27) ),
inference(formula_renaming,[status(thm)],[f8,f45]) ).
fof(f47,plain,
! [X0,X1] :
( r1(X0)
| sP4_prd(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,definition,
! [X28,X29,X30,X31] :
( sP5_prd(X31,X30,X29,X28)
<=> ( ~ r2(X30,X31)
& ~ r2(X28,X29) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f50,plain,
! [X28,X29,X30,X31] :
( ( r2(X30,X31)
& r2(X28,X29) )
| sP5_prd(X31,X30,X29,X28)
| ~ id(X29,X31)
| ~ id(X28,X30) ),
inference(formula_renaming,[status(thm)],[f9,f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( r2(X0,X2)
| sP5_prd(X3,X1,X2,X0)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f61,plain,
! [X1,X8] :
( r3(X1,X8,sK7_skl(X8,X1))
& r2(sK7_skl(X8,X1),sK4_skl(X8,X1))
& r3(X1,sK6_skl(X8,X1),sK5_skl(X8,X1))
& r2(X8,sK6_skl(X8,X1))
& id(sK5_skl(X8,X1),sK4_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))],[f12]) ).
fof(f63,plain,
! [X0,X1] : r2(X0,sK6_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( id(X2,X3)
| ~ r2(X3,X1)
| ~ r2(X2,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f74,plain,
! [X4] :
( r3(X4,sK13_skl(X4),sK12_skl(X4))
& r1(sK13_skl(X4))
& id(sK12_skl(X4),X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f15]) ).
fof(f75,plain,
! [X0] : id(sK12_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f89,plain,
! [Y10] :
( ! [X7] : ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ r2(X2,X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [Y1] :
( ? [Y4] :
( r1(Y4)
& id(Y1,Y4) )
| ? [Y2] :
( id(Y1,Y2)
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f92,definition,
! [Y1,Y2] :
( sP9_prd(Y2,Y1)
<=> ( id(Y1,Y2)
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f93,plain,
! [Y1] :
( ? [Y4] :
( r1(Y4)
& id(Y1,Y4) )
| ? [Y2] : sP9_prd(Y2,Y1) ),
inference(formula_renaming,[status(thm)],[f91,f92]) ).
fof(f94,plain,
! [Y1] :
( ( r1(sK21_skl(Y1))
& id(Y1,sK21_skl(Y1)) )
| sP9_prd(sK20_skl(Y1),Y1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl]),skolemize(Y2,sK20_skl(Y1)),skolemize(Y4,sK21_skl(Y1))],[f93]) ).
fof(f95,plain,
! [X0] :
( id(X0,sK21_skl(X0))
| sP9_prd(sK20_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0] :
( r1(sK21_skl(X0))
| sP9_prd(sK20_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [Y24,X19] :
( ( ~ r1(X19)
| ~ id(X19,Y24)
| sP0_prd(X19,Y24) )
& ( ( r1(X19)
& id(X19,Y24) )
| ~ sP0_prd(X19,Y24) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f98,plain,
( ! [Y24,X19] :
( ~ r1(X19)
| ~ id(X19,Y24)
| sP0_prd(X19,Y24) )
& ! [Y24,X19] :
( ( r1(X19)
& id(X19,Y24) )
| ~ sP0_prd(X19,Y24) ) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( id(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f102,plain,
! [X11,Y21,X12] :
( ( ~ r2(X11,X12)
| ~ id(X12,Y21)
| sP1_prd(X12,Y21,X11) )
& ( ( r2(X11,X12)
& id(X12,Y21) )
| ~ sP1_prd(X12,Y21,X11) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f103,plain,
( ! [X11,Y21,X12] :
( ~ r2(X11,X12)
| ~ id(X12,Y21)
| sP1_prd(X12,Y21,X11) )
& ! [X11,Y21,X12] :
( ( r2(X11,X12)
& id(X12,Y21) )
| ~ sP1_prd(X12,Y21,X11) ) ),
inference(miniscoping,[status(thm)],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( id(X0,X1)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
! [X0,X1,X2] :
( r2(X2,X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f117,plain,
! [X26,X27] :
( ( r1(X27)
| r1(X26)
| sP4_prd(X27,X26) )
& ( ( ~ r1(X27)
& ~ r1(X26) )
| ~ sP4_prd(X27,X26) ) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f118,plain,
( ! [X26,X27] :
( r1(X27)
| r1(X26)
| sP4_prd(X27,X26) )
& ! [X26,X27] :
( ( ~ r1(X27)
& ~ r1(X26) )
| ~ sP4_prd(X27,X26) ) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f120,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f122,plain,
! [X28,X29,X30,X31] :
( ( r2(X30,X31)
| r2(X28,X29)
| sP5_prd(X31,X30,X29,X28) )
& ( ( ~ r2(X30,X31)
& ~ r2(X28,X29) )
| ~ sP5_prd(X31,X30,X29,X28) ) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f123,plain,
( ! [X28,X29,X30,X31] :
( r2(X30,X31)
| r2(X28,X29)
| sP5_prd(X31,X30,X29,X28) )
& ! [X28,X29,X30,X31] :
( ( ~ r2(X30,X31)
& ~ r2(X28,X29) )
| ~ sP5_prd(X31,X30,X29,X28) ) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ~ r2(X1,X0)
| ~ sP5_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f142,plain,
! [Y1,Y2] :
( ( ~ id(Y1,Y2)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) )
| sP9_prd(Y2,Y1) )
& ( ( id(Y1,Y2)
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) )
| ~ sP9_prd(Y2,Y1) ) ),
inference(NNF_transformation,[status(thm)],[f92]) ).
fof(f143,plain,
( ! [Y1,Y2] :
( ~ id(Y1,Y2)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) )
| sP9_prd(Y2,Y1) )
& ! [Y1,Y2] :
( ( id(Y1,Y2)
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) )
| ~ sP9_prd(Y2,Y1) ) ),
inference(miniscoping,[status(thm)],[f142]) ).
fof(f144,plain,
( ! [Y1,Y2] :
( ~ id(Y1,Y2)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) )
| sP9_prd(Y2,Y1) )
& ! [Y1,Y2] :
( ( id(Y1,Y2)
& r2(sK22_skl(Y2,Y1),Y2)
& r1(sK22_skl(Y2,Y1)) )
| ~ sP9_prd(Y2,Y1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl]),skolemize(Y3,sK22_skl(Y2,Y1))],[f143]) ).
fof(f145,plain,
! [X0,X1] :
( r1(sK22_skl(X0,X1))
| ~ sP9_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( r2(sK22_skl(X0,X1),X0)
| ~ sP9_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f147,plain,
! [X0,X1] :
( id(X1,X0)
| ~ sP9_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f189,plain,
! [X0] :
( id(X0,sK0_skl)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f24,f99]) ).
fof(f195,plain,
sP0_prd(sK0_skl,sK0_skl),
inference(resolution,[status(thm)],[f25,f41]) ).
fof(f198,plain,
! [X0,X1] :
( id(X1,sK1_skl(X0))
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[f29,f104]) ).
fof(f216,plain,
r1(sK0_skl),
inference(resolution,[status(thm)],[f195,f100]) ).
fof(f217,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| ~ id(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f216,f90]) ).
fof(f279,plain,
! [X0] :
( sP9_prd(sK20_skl(X0),X0)
| r1(X0)
| sP4_prd(sK21_skl(X0),X0) ),
inference(resolution,[status(thm)],[f47,f95]) ).
fof(f302,plain,
! [X0,X1] :
( r2(X1,X0)
| ~ id(X0,sK1_skl(X1)) ),
inference(resolution,[status(thm)],[f30,f105]) ).
fof(f316,plain,
! [X0] :
( ~ r1(sK21_skl(X0))
| sP9_prd(sK20_skl(X0),X0)
| r1(X0) ),
inference(resolution,[status(thm)],[f279,f120]) ).
fof(f318,plain,
! [X0] :
( sP9_prd(sK20_skl(X0),X0)
| r1(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f96]) ).
fof(f329,plain,
! [X0] :
( r1(sK22_skl(sK20_skl(X0),X0))
| r1(X0) ),
inference(resolution,[status(thm)],[f318,f145]) ).
fof(f390,plain,
! [X0,X1,X2] :
( ~ id(X2,sK1_skl(X0))
| ~ id(X1,X2)
| r2(X0,X1) ),
inference(resolution,[status(thm)],[f302,f44]) ).
fof(f391,plain,
! [X0,X1] :
( ~ id(sK1_skl(X0),X1)
| r2(X0,X1) ),
inference(resolution,[status(thm)],[f302,f42]) ).
fof(f392,plain,
! [X0] : r2(X0,sK1_skl(X0)),
inference(resolution,[status(thm)],[f302,f41]) ).
fof(f402,plain,
! [X0] : ~ id(sK0_skl,sK1_skl(X0)),
inference(resolution,[status(thm)],[f392,f217]) ).
fof(f406,plain,
! [X0,X1,X2] :
( ~ r2(sK1_skl(X2),X1)
| ~ r2(sK0_skl,X0)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f402,f73]) ).
fof(f427,plain,
! [X0,X1] :
( ~ r2(X1,sK1_skl(X0))
| r2(X0,sK1_skl(X1)) ),
inference(resolution,[status(thm)],[f391,f198]) ).
fof(f485,plain,
! [X0,X1,X2,X3] :
( ~ r2(X1,X3)
| r2(X0,X2)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f51,f125]) ).
fof(f848,plain,
! [X0,X1,X2] :
( ~ r2(X0,X2)
| ~ id(X1,X2)
| r2(X0,X1) ),
inference(resolution,[status(thm)],[f390,f198]) ).
fof(f874,plain,
! [X0,X1,X2] :
( ~ sP9_prd(X0,X1)
| ~ id(X2,X0)
| r2(sK22_skl(X0,X1),X2) ),
inference(resolution,[status(thm)],[f848,f146]) ).
fof(f879,plain,
! [X0,X1,X2] :
( ~ id(X1,sK6_skl(X0,X2))
| r2(X0,X1) ),
inference(resolution,[status(thm)],[f848,f63]) ).
fof(f899,plain,
! [X0,X1] : r2(X0,sK12_skl(sK6_skl(X0,X1))),
inference(resolution,[status(thm)],[f879,f75]) ).
fof(f961,plain,
! [X0,X1] :
( r1(X0)
| ~ id(X1,sK20_skl(X0))
| r2(sK22_skl(sK20_skl(X0),X0),X1) ),
inference(resolution,[status(thm)],[f874,f318]) ).
fof(f967,plain,
! [X0] :
( r1(X0)
| r2(sK22_skl(sK20_skl(X0),X0),sK20_skl(X0)) ),
inference(resolution,[status(thm)],[f961,f41]) ).
fof(f1476,plain,
! [X0,X1,X2] :
( r2(X0,X2)
| ~ id(X2,sK1_skl(X1))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f485,f392]) ).
fof(f1484,plain,
! [X0,X1] :
( r2(X0,sK1_skl(X1))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f1476,f41]) ).
fof(f1555,plain,
! [X0,X1] :
( r2(X1,sK1_skl(X0))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f1484,f427]) ).
fof(f1578,plain,
! [X0,X1,X2] :
( ~ id(X2,sK1_skl(X0))
| r2(X1,X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f1555,f848]) ).
fof(f1724,plain,
! [X0,X1,X2] :
( ~ r2(X0,X2)
| r2(X1,X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f1578,f198]) ).
fof(f1769,plain,
! [X0,X1] :
( ~ r2(sK12_skl(X0),X1)
| r2(X0,X1) ),
inference(resolution,[status(thm)],[f1724,f75]) ).
fof(f1772,plain,
! [X0,X1] :
( ~ r1(X1)
| ~ r2(X1,X0)
| r2(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f1724,f189]) ).
fof(f1780,plain,
! [X0,X1] : r2(X0,sK12_skl(sK6_skl(sK12_skl(X0),X1))),
inference(resolution,[status(thm)],[f1769,f899]) ).
fof(f2000,plain,
! [X0,X1] : r2(X0,sK12_skl(sK6_skl(sK12_skl(sK12_skl(X0)),X1))),
inference(resolution,[status(thm)],[f1780,f1769]) ).
fof(f2315,plain,
! [X0,X1] :
( r1(X1)
| ~ r2(sK22_skl(sK20_skl(X1),X1),X0)
| r2(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f1772,f329]) ).
fof(f4776,plain,
! [X0] :
( r1(X0)
| r1(X0)
| r2(sK0_skl,sK20_skl(X0)) ),
inference(resolution,[status(thm)],[f2315,f967]) ).
fof(f4823,plain,
! [X0] :
( r1(X0)
| r2(sK0_skl,sK20_skl(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f4776]) ).
fof(f4834,plain,
! [X0,X1] :
( ~ id(X1,sK20_skl(X0))
| r2(sK0_skl,X1)
| r1(X0) ),
inference(resolution,[status(thm)],[f4823,f848]) ).
fof(f5269,plain,
! [X0,X1] :
( ~ sP9_prd(sK20_skl(X0),X1)
| r2(sK0_skl,X1)
| r1(X0) ),
inference(resolution,[status(thm)],[f4834,f147]) ).
fof(f5302,plain,
! [X0] :
( r1(X0)
| r2(sK0_skl,X0)
| r1(X0) ),
inference(resolution,[status(thm)],[f5269,f318]) ).
fof(f5304,plain,
! [X0] :
( r2(sK0_skl,X0)
| r1(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f5302]) ).
fof(f5309,plain,
! [X0,X1,X2] :
( ~ r2(sK1_skl(X2),X1)
| ~ id(X0,X1)
| r1(X0) ),
inference(resolution,[status(thm)],[f5304,f406]) ).
fof(f5330,plain,
! [X0,X1,X2] :
( ~ r2(sK1_skl(X2),X1)
| ~ id(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f5309,f90]) ).
fof(f5395,plain,
! [X0,X1] : ~ r2(sK1_skl(X0),X1),
inference(resolution,[status(thm)],[f5330,f75]) ).
fof(f5405,plain,
$false,
inference(resolution,[status(thm)],[f5395,f2000]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN068+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 03:23:58 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 14.18/2.33 % Refutation found
% 14.18/2.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.18/2.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.18/2.38 % Elapsed time: 1.981021 seconds
% 14.18/2.38 % CPU time: 15.514657 seconds
% 14.18/2.38 % Total memory used: 136.960 MB
% 14.18/2.38 % Net memory used: 108.622 MB
%------------------------------------------------------------------------------