%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 01:57:09 PM UTC 2026
% Result : Theorem 38.91s 5.33s
% Output : CNFRefutation 38.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 115 ( 26 unt; 8 def)
% Number of atoms : 321 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 370 ( 164 ~; 137 |; 61 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 4 prp; 0-6 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 307 ( 282 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ id(X15,Y22)
& ~ r3(X13,X14,X15) )
| ( r3(X13,X14,X15)
& id(X15,Y22) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( ~ id(X18,Y23)
& ~ r4(X16,X17,X18) )
| ( r4(X16,X17,X18)
& id(X18,Y23) ) ),
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(f11,axiom,
! [X38,X39,X40,X41,X42,X43] :
( ( r4(X41,X42,X43)
& r4(X38,X39,X40) )
| ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) )
| ~ id(X40,X43)
| ~ id(X39,X42)
| ~ id(X38,X41) ),
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(f16,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
? [Y1,Y3,Y2,Y4] :
( ? [Y6] :
( ? [Y7] :
( r3(Y7,Y6,Y4)
& r4(Y1,Y1,Y7) )
& r4(Y3,Y3,Y6) )
& ? [Y5] :
( r4(Y2,Y2,Y5)
& id(Y4,Y5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ? [Y1,Y3,Y2,Y4] :
( ? [Y6] :
( ? [Y7] :
( r3(Y7,Y6,Y4)
& r4(Y1,Y1,Y7) )
& r4(Y3,Y3,Y6) )
& ? [Y5] :
( r4(Y2,Y2,Y5)
& id(Y4,Y5) ) ),
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(f31,definition,
! [X13,X14,Y22,X15] :
( sP2_prd(X15,Y22,X14,X13)
<=> ( r3(X13,X14,X15)
& id(X15,Y22) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f32,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ id(X15,Y22)
& ~ r3(X13,X14,X15) )
| sP2_prd(X15,Y22,X14,X13) ),
inference(formula_renaming,[status(thm)],[f3,f31]) ).
fof(f33,plain,
! [X13,X14,X15] :
( ( ~ id(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))],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ r3(X2,X1,X0)
| sP2_prd(X0,sK2_skl(X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ id(X0,sK2_skl(X1,X2))
| sP2_prd(X0,sK2_skl(X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f36,definition,
! [X16,X17,Y23,X18] :
( sP3_prd(X18,Y23,X17,X16)
<=> ( r4(X16,X17,X18)
& id(X18,Y23) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f37,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( ~ id(X18,Y23)
& ~ r4(X16,X17,X18) )
| sP3_prd(X18,Y23,X17,X16) ),
inference(formula_renaming,[status(thm)],[f4,f36]) ).
fof(f38,plain,
! [X16,X17,X18] :
( ( ~ id(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))],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ r4(X2,X1,X0)
| sP3_prd(X0,sK3_skl(X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ id(X0,sK3_skl(X1,X2))
| sP3_prd(X0,sK3_skl(X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
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(f48,plain,
! [X0,X1] :
( r1(X1)
| sP4_prd(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f57,definition,
! [X38,X39,X40,X41,X42,X43] :
( sP7_prd(X43,X42,X41,X40,X39,X38)
<=> ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f58,plain,
! [X38,X39,X40,X41,X42,X43] :
( ( r4(X41,X42,X43)
& r4(X38,X39,X40) )
| sP7_prd(X43,X42,X41,X40,X39,X38)
| ~ id(X40,X43)
| ~ id(X39,X42)
| ~ id(X38,X41) ),
inference(formula_renaming,[status(thm)],[f11,f57]) ).
fof(f60,plain,
! [X0,X1,X2,X3,X4,X5] :
( r4(X1,X3,X5)
| sP7_prd(X5,X3,X1,X4,X2,X0)
| ~ id(X4,X5)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
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(f76,plain,
! [X0] : r1(sK13_skl(X0)),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f77,plain,
! [X0] : r3(X0,sK13_skl(X0),sK12_skl(X0)),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f78,plain,
! [X5] :
( r1(sK16_skl(X5))
& id(sK14_skl(X5),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))],[f16]) ).
fof(f79,plain,
! [X0] : r1(sK15_skl(X0)),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0] : r4(X0,sK15_skl(X0),sK14_skl(X0)),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
! [X0] : id(sK14_skl(X0),sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
! [X0] : r1(sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f91,plain,
! [Y1,Y3,Y2,Y4] :
( ! [Y6] :
( ! [Y7] :
( ~ r3(Y7,Y6,Y4)
| ~ r4(Y1,Y1,Y7) )
| ~ r4(Y3,Y3,Y6) )
| ! [Y5] :
( ~ r4(Y2,Y2,Y5)
| ~ id(Y4,Y5) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f92,plain,
! [Y4] :
( ! [Y6] :
( ! [Y7] :
( ~ r3(Y7,Y6,Y4)
| ! [Y1] : ~ r4(Y1,Y1,Y7) )
| ! [Y3] : ~ r4(Y3,Y3,Y6) )
| ! [Y5] :
( ! [Y2] : ~ r4(Y2,Y2,Y5)
| ~ id(Y4,Y5) ) ),
inference(miniscoping,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ r3(X6,X4,X0)
| ~ r4(X5,X5,X6)
| ~ r4(X3,X3,X4)
| ~ r4(X2,X2,X1)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,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(f95,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)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( id(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f104,plain,
! [X13,X14,Y22,X15] :
( ( ~ r3(X13,X14,X15)
| ~ id(X15,Y22)
| sP2_prd(X15,Y22,X14,X13) )
& ( ( r3(X13,X14,X15)
& id(X15,Y22) )
| ~ sP2_prd(X15,Y22,X14,X13) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f105,plain,
( ! [X13,X14,Y22,X15] :
( ~ r3(X13,X14,X15)
| ~ id(X15,Y22)
| sP2_prd(X15,Y22,X14,X13) )
& ! [X13,X14,Y22,X15] :
( ( r3(X13,X14,X15)
& id(X15,Y22) )
| ~ sP2_prd(X15,Y22,X14,X13) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( id(X0,X1)
| ~ sP2_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( r3(X3,X2,X0)
| ~ sP2_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f109,plain,
! [X16,X17,Y23,X18] :
( ( ~ r4(X16,X17,X18)
| ~ id(X18,Y23)
| sP3_prd(X18,Y23,X17,X16) )
& ( ( r4(X16,X17,X18)
& id(X18,Y23) )
| ~ sP3_prd(X18,Y23,X17,X16) ) ),
inference(NNF_transformation,[status(thm)],[f36]) ).
fof(f110,plain,
( ! [X16,X17,Y23,X18] :
( ~ r4(X16,X17,X18)
| ~ id(X18,Y23)
| sP3_prd(X18,Y23,X17,X16) )
& ! [X16,X17,Y23,X18] :
( ( r4(X16,X17,X18)
& id(X18,Y23) )
| ~ sP3_prd(X18,Y23,X17,X16) ) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( id(X0,X1)
| ~ sP3_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( r4(X3,X2,X0)
| ~ sP3_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,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(f115,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)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( ~ r1(X1)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f129,plain,
! [X38,X39,X40,X41,X42,X43] :
( ( r4(X41,X42,X43)
| r4(X38,X39,X40)
| sP7_prd(X43,X42,X41,X40,X39,X38) )
& ( ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) )
| ~ sP7_prd(X43,X42,X41,X40,X39,X38) ) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f130,plain,
( ! [X38,X39,X40,X41,X42,X43] :
( r4(X41,X42,X43)
| r4(X38,X39,X40)
| sP7_prd(X43,X42,X41,X40,X39,X38) )
& ! [X38,X39,X40,X41,X42,X43] :
( ( ~ r4(X41,X42,X43)
& ~ r4(X38,X39,X40) )
| ~ sP7_prd(X43,X42,X41,X40,X39,X38) ) ),
inference(miniscoping,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r4(X5,X4,X3)
| ~ sP7_prd(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f142,plain,
! [X0,X1] :
( ~ id(X1,sK0_skl)
| ~ id(X0,X1)
| sP0_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f25,f44]) ).
fof(f146,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r3(X5,X3,sK12_skl(X1))
| ~ r4(X4,X4,X5)
| ~ r4(X2,X2,X3)
| ~ r4(X0,X0,X1) ),
inference(resolution,[status(thm)],[f75,f93]) ).
fof(f148,plain,
! [X0] :
( ~ id(X0,sK12_skl(sK0_skl))
| sP0_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f142,f75]) ).
fof(f163,plain,
! [X0] :
( ~ id(sK12_skl(sK0_skl),X0)
| sP0_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f148,f42]) ).
fof(f176,plain,
! [X0] : sP2_prd(sK12_skl(X0),sK2_skl(sK13_skl(X0),X0),sK13_skl(X0),X0),
inference(resolution,[status(thm)],[f77,f34]) ).
fof(f184,plain,
! [X0,X1] :
( ~ id(X0,X1)
| r1(X0)
| sP4_prd(X0,X1) ),
inference(resolution,[status(thm)],[f48,f42]) ).
fof(f250,plain,
! [X0] : sP0_prd(sK13_skl(X0),sK0_skl),
inference(resolution,[status(thm)],[f76,f24]) ).
fof(f251,plain,
! [X0] : sP0_prd(sK15_skl(X0),sK0_skl),
inference(resolution,[status(thm)],[f79,f24]) ).
fof(f270,plain,
! [X0] :
( r1(sK14_skl(X0))
| sP4_prd(sK14_skl(X0),sK16_skl(X0)) ),
inference(resolution,[status(thm)],[f81,f184]) ).
fof(f365,plain,
! [X0,X1,X2] :
( ~ id(X2,sK2_skl(X1,X0))
| r3(X0,X1,X2) ),
inference(resolution,[status(thm)],[f107,f35]) ).
fof(f384,plain,
! [X0,X1,X2] :
( ~ id(X2,sK3_skl(X1,X0))
| r4(X0,X1,X2) ),
inference(resolution,[status(thm)],[f112,f40]) ).
fof(f388,plain,
! [X0,X1] : ~ sP4_prd(X0,sK16_skl(X1)),
inference(resolution,[status(thm)],[f116,f82]) ).
fof(f562,plain,
! [X0,X1,X2,X3,X4,X5] :
( r4(X3,X4,X5)
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3)
| ~ r4(X0,X1,X2) ),
inference(resolution,[status(thm)],[f131,f60]) ).
fof(f641,plain,
! [X0,X1,X2] :
( ~ id(sK2_skl(X1,X0),X2)
| r3(X0,X1,X2) ),
inference(resolution,[status(thm)],[f365,f42]) ).
fof(f644,plain,
! [X0,X1,X2,X3] :
( ~ id(X3,sK3_skl(X1,X0))
| ~ id(X2,X3)
| r4(X0,X1,X2) ),
inference(resolution,[status(thm)],[f384,f44]) ).
fof(f723,plain,
! [X0,X1,X2] :
( id(X2,sK3_skl(X1,X0))
| ~ r4(X0,X1,X2) ),
inference(resolution,[status(thm)],[f39,f111]) ).
fof(f727,plain,
! [X0] : id(sK12_skl(X0),sK2_skl(sK13_skl(X0),X0)),
inference(resolution,[status(thm)],[f176,f106]) ).
fof(f731,plain,
! [X0,X1,X2,X3] :
( ~ id(X3,X2)
| ~ id(sK2_skl(X1,X0),X3)
| r3(X0,X1,X2) ),
inference(resolution,[status(thm)],[f641,f44]) ).
fof(f871,plain,
! [X0] : id(sK13_skl(X0),sK0_skl),
inference(resolution,[status(thm)],[f250,f96]) ).
fof(f873,plain,
! [X0] : id(sK15_skl(X0),sK0_skl),
inference(resolution,[status(thm)],[f251,f96]) ).
fof(f1032,plain,
! [X0] : r1(sK14_skl(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f270,f388]) ).
fof(f1337,plain,
! [X0] :
( id(X0,sK0_skl)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f24,f96]) ).
fof(f1461,plain,
! [X0] : id(sK14_skl(X0),sK0_skl),
inference(resolution,[status(thm)],[f1032,f1337]) ).
fof(f1580,plain,
! [X0,X1,X2,X3] :
( r4(X1,X2,X3)
| ~ id(sK14_skl(X0),X3)
| ~ id(sK15_skl(X0),X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f562,f80]) ).
fof(f2851,plain,
sP0_prd(sK2_skl(sK13_skl(sK0_skl),sK0_skl),sK0_skl),
inference(resolution,[status(thm)],[f163,f727]) ).
fof(f2869,plain,
id(sK2_skl(sK13_skl(sK0_skl),sK0_skl),sK0_skl),
inference(resolution,[status(thm)],[f2851,f96]) ).
fof(f3129,plain,
! [X0,X1,X2] :
( r4(X1,sK0_skl,X2)
| ~ id(sK14_skl(X0),X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f1580,f873]) ).
fof(f3564,plain,
! [X0] :
( ~ id(sK0_skl,X0)
| r3(sK0_skl,sK13_skl(sK0_skl),X0) ),
inference(resolution,[status(thm)],[f731,f2869]) ).
fof(f4404,plain,
! [X0,X1,X2,X3] :
( ~ r4(X3,X3,sK0_skl)
| ~ r4(X2,X2,sK13_skl(sK0_skl))
| ~ r4(X1,X1,X0)
| ~ id(sK0_skl,sK12_skl(X0)) ),
inference(resolution,[status(thm)],[f3564,f146]) ).
fof(f4408,definition,
! [X0,X1] :
( sQ105_spl
<=> ( ~ r4(X1,X1,X0)
| ~ id(sK0_skl,sK12_skl(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f4409,plain,
! [X0,X1] :
( ~ sQ105_spl
| ~ r4(X1,X1,X0)
| ~ id(sK0_skl,sK12_skl(X0)) ),
inference(component_clause,[status(thm)],[f4408]) ).
fof(f4411,definition,
! [X2] :
( sQ106_spl
<=> ~ r4(X2,X2,sK13_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f4412,plain,
! [X0] :
( ~ sQ106_spl
| ~ r4(X0,X0,sK13_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f4411]) ).
fof(f4414,definition,
! [X3] :
( sQ107_spl
<=> ~ r4(X3,X3,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f4415,plain,
! [X0] :
( ~ sQ107_spl
| ~ r4(X0,X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f4414]) ).
fof(f4417,plain,
( sQ107_spl
| sQ106_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f4404,f4408,f4411,f4414]) ).
fof(f7730,plain,
! [X0,X1] :
( r4(X1,sK0_skl,sK0_skl)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f3129,f1461]) ).
fof(f7770,plain,
r4(sK0_skl,sK0_skl,sK0_skl),
inference(resolution,[status(thm)],[f7730,f2869]) ).
fof(f7798,plain,
! [X0] : r4(X0,sK0_skl,sK0_skl),
inference(resolution,[status(thm)],[f7730,f75]) ).
fof(f7807,plain,
( ~ sQ107_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7770,f4415]) ).
fof(f7808,plain,
~ sQ107_spl,
inference(contradiction_clause,[status(thm)],[f7807]) ).
fof(f7890,plain,
! [X0] : id(sK0_skl,sK3_skl(sK0_skl,X0)),
inference(resolution,[status(thm)],[f7798,f723]) ).
fof(f8155,plain,
! [X0,X1] :
( ~ sQ105_spl
| ~ id(sK12_skl(X1),sK0_skl)
| ~ r4(X0,X0,X1) ),
inference(resolution,[status(thm)],[f4409,f42]) ).
fof(f8211,plain,
! [X0,X1] :
( ~ id(X1,sK0_skl)
| r4(X0,sK0_skl,X1) ),
inference(resolution,[status(thm)],[f7890,f644]) ).
fof(f8576,plain,
! [X0,X1] : r4(X0,sK0_skl,sK13_skl(X1)),
inference(resolution,[status(thm)],[f8211,f871]) ).
fof(f8697,plain,
( ~ sQ105_spl
| ~ id(sK12_skl(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f8155,f7798]) ).
fof(f8701,plain,
( ~ sQ105_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8697,f75]) ).
fof(f8702,plain,
~ sQ105_spl,
inference(contradiction_clause,[status(thm)],[f8701]) ).
fof(f9106,plain,
( ~ sQ106_spl
| $false ),
inference(resolution,[status(thm)],[f4412,f8576]) ).
fof(f9107,plain,
~ sQ106_spl,
inference(contradiction_clause,[status(thm)],[f9106]) ).
fof(f9108,plain,
$false,
inference(sat_refutation,[status(thm)],[f4417,f7808,f8702,f9107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 03:21:35 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 38.91/5.33 % Refutation found
% 38.91/5.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 38.91/5.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 38.91/5.38 % Elapsed time: 5.004842 seconds
% 38.91/5.38 % CPU time: 39.406479 seconds
% 38.91/5.38 % Total memory used: 235.499 MB
% 38.91/5.38 % Net memory used: 182.187 MB
%------------------------------------------------------------------------------