%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 : Tue Sep 29 11:59:26 AM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 98 ( 19 unt; 9 def)
% Number of atoms : 524 ( 0 equ)
% Maximal formula atoms : 29 ( 5 avg)
% Number of connectives : 873 ( 447 ~; 366 |; 51 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-1 aty)
% Number of variables : 234 ( 0 sgn 211 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) )
& ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| ~ p1(X3) ) )
& p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ~ ( ~ ! [X6] :
( ~ r1(X5,X6)
| ~ ! [X7] :
( ~ r1(X6,X7)
| p1(X7) ) )
& ~ ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) ) )
| ~ ! [X9] :
( ~ r1(X0,X9)
| ~ ( ~ ! [X10] :
( ~ r1(X9,X10)
| ~ ! [X11] :
( ~ r1(X10,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
& ~ ! [X13] :
( ~ r1(X9,X13)
| ~ ! [X14] :
( ~ r1(X13,X14)
| p1(X14) ) ) ) )
| ~ ! [X15] :
( ~ r1(X0,X15)
| ~ ! [X16] :
( ~ r1(X15,X16)
| $false ) )
| ! [X17] :
( ~ r1(X0,X17)
| ! [X18] :
( ~ r1(X17,X18)
| ! [X19] :
( ~ r1(X18,X19)
| p1(X19) ) )
| ~ ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| ~ p1(X3) ) )
& p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ~ ( ~ ! [X6] :
( ~ r1(X5,X6)
| ~ ! [X7] :
( ~ r1(X6,X7)
| p1(X7) ) )
& ~ ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) ) )
| ~ ! [X9] :
( ~ r1(X0,X9)
| ~ ( ~ ! [X10] :
( ~ r1(X9,X10)
| ~ ! [X11] :
( ~ r1(X10,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
& ~ ! [X13] :
( ~ r1(X9,X13)
| ~ ! [X14] :
( ~ r1(X13,X14)
| p1(X14) ) ) ) )
| ~ ! [X15] :
( ~ r1(X0,X15)
| ~ ! [X16] : ~ r1(X15,X16) )
| ! [X17] :
( ~ r1(X0,X17)
| ! [X18] :
( ~ r1(X17,X18)
| ! [X19] :
( ~ r1(X18,X19)
| p1(X19) ) )
| ~ ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(true_and_false_elimination,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| ~ p1(X3) ) )
& p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ~ ( ~ ! [X6] :
( ~ r1(X5,X6)
| ~ ! [X7] :
( ~ r1(X6,X7)
| p1(X7) ) )
& ~ ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) ) )
| ~ ! [X9] :
( ~ r1(X0,X9)
| ~ ( ~ ! [X10] :
( ~ r1(X9,X10)
| ~ ! [X11] :
( ~ r1(X10,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
& ~ ! [X13] :
( ~ r1(X9,X13)
| ~ ! [X14] :
( ~ r1(X13,X14)
| p1(X14) ) ) ) )
| ~ ! [X15] :
( ~ r1(X0,X15)
| ~ ! [X16] : ~ r1(X15,X16) )
| ! [X17] :
( ~ r1(X0,X17)
| ! [X18] :
( ~ r1(X17,X18)
| ! [X19] :
( ~ r1(X18,X19)
| p1(X19) ) )
| ~ ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ? [X3] :
( r1(X2,X3)
& p1(X3) ) )
| ~ p1(X1) )
& ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ! [X6] :
( ~ r1(X5,X6)
| ? [X7] :
( r1(X6,X7)
& ~ p1(X7) ) )
| ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) )
& ! [X9] :
( ~ r1(X0,X9)
| ! [X10] :
( ~ r1(X9,X10)
| ? [X11] :
( r1(X10,X11)
& ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
| ! [X13] :
( ~ r1(X9,X13)
| ? [X14] :
( r1(X13,X14)
& ~ p1(X14) ) ) )
& ! [X15] :
( ~ r1(X0,X15)
| ? [X16] : r1(X15,X16) )
& ? [X17] :
( r1(X0,X17)
& ? [X18] :
( r1(X17,X18)
& ? [X19] :
( r1(X18,X19)
& ~ p1(X19) ) )
& ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ? [X3] :
( r1(X2,X3)
& p1(X3) ) )
| ~ p1(X1) )
& ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ! [X6] :
( ~ r1(X5,X6)
| ? [X7] :
( r1(X6,X7)
& ~ p1(X7) ) )
| ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) )
& ! [X9] :
( ~ r1(X0,X9)
| ! [X10] :
( ~ r1(X9,X10)
| ? [X11] :
( r1(X10,X11)
& ! [X12] :
( ~ r1(X11,X12)
| p1(X12) ) ) )
| ! [X13] :
( ~ r1(X9,X13)
| ? [X14] :
( r1(X13,X14)
& ~ p1(X14) ) ) )
& ! [X15] :
( ~ r1(X0,X15)
| ? [X16] : r1(X15,X16) )
& ? [X17] :
( r1(X0,X17)
& ? [X18] :
( r1(X17,X18)
& ? [X19] :
( r1(X18,X19)
& ~ p1(X19) ) )
& ! [X20] :
( ~ r1(X17,X20)
| p1(X20) ) ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
( ! [X1] :
( ~ r1(sK0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ( r1(X2,sK1(X2))
& p1(sK1(X2)) ) )
| ~ p1(X1) )
& ! [X4] :
( ~ r1(sK0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ! [X6] :
( ~ r1(X5,X6)
| ( r1(X6,sK2(X6))
& ~ p1(sK2(X6)) ) )
| ! [X8] :
( ~ r1(X5,X8)
| p1(X8) ) ) )
& ! [X9] :
( ~ r1(sK0,X9)
| ! [X10] :
( ~ r1(X9,X10)
| ( r1(X10,sK3(X10))
& ! [X12] :
( ~ r1(sK3(X10),X12)
| p1(X12) ) ) )
| ! [X13] :
( ~ r1(X9,X13)
| ( r1(X13,sK4(X13))
& ~ p1(sK4(X13)) ) ) )
& ! [X15] :
( ~ r1(sK0,X15)
| r1(X15,sK5(X15)) )
& r1(sK0,sK6)
& r1(sK6,sK7)
& r1(sK7,sK8)
& ~ p1(sK8)
& ! [X20] :
( ~ r1(sK6,X20)
| p1(X20) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X3,sK1(X2)),skolemize(X7,sK2(X6)),skolemize(X11,sK3(X10)),skolemize(X14,sK4(X13)),skolemize(X16,sK5(X15)),skolemize(X17,sK6),skolemize(X18,sK7),skolemize(X19,sK8)],[f8]) ).
fof(f10,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X20] :
( ~ r1(sK6,X20)
| p1(X20) ),
inference(cnf_transformation,[],[f9]) ).
fof(f12,plain,
~ p1(sK8),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
r1(sK7,sK8),
inference(cnf_transformation,[],[f9]) ).
fof(f14,plain,
r1(sK6,sK7),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
r1(sK0,sK6),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X10,X9,X12,X13] :
( ~ r1(sK3(X10),X12)
| ~ r1(X9,X10)
| ~ r1(sK0,X9)
| p1(X12)
| ~ r1(X9,X13)
| ~ p1(sK4(X13)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
! [X10,X9,X12,X13] :
( ~ r1(sK3(X10),X12)
| ~ r1(X9,X10)
| ~ r1(sK0,X9)
| p1(X12)
| ~ r1(X9,X13)
| r1(X13,sK4(X13)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X10,X9,X13] :
( ~ p1(sK4(X13))
| ~ r1(X9,X10)
| r1(X10,sK3(X10))
| ~ r1(X9,X13)
| ~ r1(sK0,X9) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
! [X10,X9,X13] :
( ~ r1(sK0,X9)
| ~ r1(X9,X10)
| r1(X10,sK3(X10))
| ~ r1(X9,X13)
| r1(X13,sK4(X13)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X8,X6,X4,X5] :
( ~ p1(sK2(X6))
| ~ r1(X4,X5)
| ~ r1(X5,X6)
| ~ r1(sK0,X4)
| ~ r1(X5,X8)
| p1(X8) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X8,X6,X4,X5] :
( ~ r1(sK0,X4)
| ~ r1(X4,X5)
| ~ r1(X5,X6)
| r1(X6,sK2(X6))
| ~ r1(X5,X8)
| p1(X8) ),
inference(cnf_transformation,[],[f9]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ r1(sK6,X0)
| ~ r1(X0,X1)
| r1(X1,sK2(X1))
| ~ r1(X0,X2)
| p1(X2) ),
inference(resolution,[],[f22,f15]) ).
fof(f131,definition,
( spl9_15
<=> ! [X0] :
( ~ r1(sK7,X0)
| p1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_15])],[avatar_definition]) ).
fof(f132,plain,
( ! [X0] :
( ~ r1(sK7,X0)
| p1(X0) )
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f149,plain,
( p1(sK8)
| ~ spl9_15 ),
inference(resolution,[],[f132,f13]) ).
fof(f155,plain,
( $false
| ~ spl9_15 ),
inference(forward_subsumption_resolution,[],[f149,f12]) ).
fof(f156,plain,
~ spl9_15,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f312,plain,
! [X0,X1] :
( ~ r1(sK7,X0)
| r1(X0,sK2(X0))
| ~ r1(sK7,X1)
| p1(X1) ),
inference(resolution,[],[f97,f14]) ).
fof(f316,definition,
( spl9_38
<=> ! [X0] :
( ~ r1(sK7,X0)
| r1(X0,sK2(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl9_38])],[avatar_definition]) ).
fof(f317,plain,
( ! [X0] :
( r1(X0,sK2(X0))
| ~ r1(sK7,X0) )
| ~ spl9_38 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f318,plain,
( spl9_15
| spl9_38 ),
inference(avatar_split_clause,[],[f312,f316,f131]) ).
fof(f328,plain,
( ! [X2,X0,X1] :
( ~ r1(sK7,sK3(X0))
| ~ r1(X1,X0)
| ~ r1(sK0,X1)
| p1(sK2(sK3(X0)))
| ~ r1(X1,X2)
| r1(X2,sK4(X2)) )
| ~ spl9_38 ),
inference(resolution,[],[f317,f18]) ).
fof(f388,plain,
! [X0,X1] :
( ~ r1(sK6,X0)
| r1(X0,sK3(X0))
| ~ r1(sK6,X1)
| r1(X1,sK4(X1)) ),
inference(resolution,[],[f20,f15]) ).
fof(f392,definition,
( spl9_52
<=> ! [X1] :
( ~ r1(sK6,X1)
| r1(X1,sK4(X1)) ) ),
introduced(definition,[new_symbols(definition,[spl9_52])],[avatar_definition]) ).
fof(f393,plain,
( ! [X1] :
( r1(X1,sK4(X1))
| ~ r1(sK6,X1) )
| ~ spl9_52 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f395,definition,
( spl9_53
<=> ! [X0] :
( ~ r1(sK6,X0)
| r1(X0,sK3(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl9_53])],[avatar_definition]) ).
fof(f396,plain,
( ! [X0] :
( r1(X0,sK3(X0))
| ~ r1(sK6,X0) )
| ~ spl9_53 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f397,plain,
( spl9_52
| spl9_53 ),
inference(avatar_split_clause,[],[f388,f395,f392]) ).
fof(f409,plain,
( ~ r1(sK6,sK6)
| p1(sK4(sK6))
| ~ spl9_52 ),
inference(resolution,[],[f393,f11]) ).
fof(f418,definition,
( spl9_54
<=> p1(sK4(sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_54])],[avatar_definition]) ).
fof(f420,plain,
( p1(sK4(sK6))
| ~ spl9_54 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f422,definition,
( spl9_55
<=> r1(sK6,sK6) ),
introduced(definition,[new_symbols(definition,[spl9_55])],[avatar_definition]) ).
fof(f424,plain,
( ~ r1(sK6,sK6)
| spl9_55 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f425,plain,
( spl9_54
| ~ spl9_55
| ~ spl9_52 ),
inference(avatar_split_clause,[],[f409,f392,f422,f418]) ).
fof(f426,plain,
( ! [X0,X1] :
( ~ r1(sK0,X0)
| r1(X1,sK3(X1))
| ~ r1(X0,sK6)
| ~ r1(X0,X1) )
| ~ spl9_54 ),
inference(resolution,[],[f420,f19]) ).
fof(f460,plain,
( ! [X0] :
( r1(X0,sK3(X0))
| ~ r1(sK6,sK6)
| ~ r1(sK6,X0) )
| ~ spl9_54 ),
inference(resolution,[],[f426,f15]) ).
fof(f464,plain,
( ~ spl9_55
| spl9_53
| ~ spl9_54 ),
inference(avatar_split_clause,[],[f460,f418,f395,f422]) ).
fof(f514,plain,
( ! [X2,X0,X1] :
( ~ r1(sK7,sK3(X1))
| ~ r1(sK0,X0)
| p1(sK2(sK3(X1)))
| ~ r1(X0,X2)
| ~ p1(sK4(X2))
| ~ r1(X0,X1) )
| ~ spl9_38 ),
inference(resolution,[],[f17,f317]) ).
fof(f601,plain,
( $false
| spl9_55 ),
inference(resolution,[],[f10,f424]) ).
fof(f602,plain,
spl9_55,
inference(avatar_contradiction_clause,[],[f601]) ).
fof(f640,plain,
( ! [X0,X1] :
( ~ r1(sK6,sK7)
| ~ r1(X0,sK7)
| ~ r1(sK0,X0)
| p1(sK2(sK3(sK7)))
| ~ r1(X0,X1)
| r1(X1,sK4(X1)) )
| ~ spl9_38
| ~ spl9_53 ),
inference(resolution,[],[f396,f328]) ).
fof(f884,definition,
( spl9_89
<=> ! [X0] :
( ~ r1(X0,sK7)
| ~ r1(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_89])],[avatar_definition]) ).
fof(f885,plain,
( ! [X0] :
( ~ r1(sK0,X0)
| ~ r1(X0,sK7) )
| ~ spl9_89 ),
inference(avatar_component_clause,[],[f884]) ).
fof(f891,plain,
( ~ r1(sK6,sK7)
| ~ spl9_89 ),
inference(resolution,[],[f885,f15]) ).
fof(f901,plain,
( $false
| ~ spl9_89 ),
inference(forward_subsumption_resolution,[],[f891,f14]) ).
fof(f902,plain,
~ spl9_89,
inference(avatar_contradiction_clause,[],[f901]) ).
fof(f903,plain,
( ! [X0,X1] :
( ~ r1(X0,sK7)
| ~ r1(sK0,X0)
| p1(sK2(sK3(sK7)))
| ~ r1(X0,X1)
| r1(X1,sK4(X1)) )
| ~ spl9_38
| ~ spl9_53 ),
inference(forward_subsumption_resolution,[],[f640,f14]) ).
fof(f1870,definition,
( spl9_180
<=> p1(sK2(sK3(sK7))) ),
introduced(definition,[new_symbols(definition,[spl9_180])],[avatar_definition]) ).
fof(f1871,plain,
( ~ p1(sK2(sK3(sK7)))
| spl9_180 ),
inference(avatar_component_clause,[],[f1870]) ).
fof(f1872,plain,
( p1(sK2(sK3(sK7)))
| ~ spl9_180 ),
inference(avatar_component_clause,[],[f1870]) ).
fof(f1874,definition,
( spl9_181
<=> ! [X0,X1] :
( ~ r1(X0,sK7)
| r1(X1,sK4(X1))
| ~ r1(X0,X1)
| ~ r1(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_181])],[avatar_definition]) ).
fof(f1875,plain,
( ! [X0,X1] :
( ~ r1(sK0,X0)
| r1(X1,sK4(X1))
| ~ r1(X0,X1)
| ~ r1(X0,sK7) )
| ~ spl9_181 ),
inference(avatar_component_clause,[],[f1874]) ).
fof(f1876,plain,
( spl9_180
| spl9_181
| ~ spl9_38
| ~ spl9_53 ),
inference(avatar_split_clause,[],[f903,f395,f316,f1874,f1870]) ).
fof(f1877,plain,
( ! [X2,X0,X1] :
( ~ r1(X1,sK3(sK7))
| ~ r1(X0,X1)
| ~ r1(sK0,X0)
| ~ r1(X1,X2)
| p1(X2) )
| ~ spl9_180 ),
inference(resolution,[],[f1872,f21]) ).
fof(f1883,plain,
( ! [X0,X1] :
( ~ r1(X0,sK7)
| ~ r1(sK0,X0)
| ~ r1(sK7,X1)
| p1(X1)
| ~ r1(sK6,sK7) )
| ~ spl9_53
| ~ spl9_180 ),
inference(resolution,[],[f1877,f396]) ).
fof(f1885,plain,
( ! [X0,X1] :
( ~ r1(X0,sK7)
| ~ r1(sK0,X0)
| ~ r1(sK7,X1)
| p1(X1) )
| ~ spl9_53
| ~ spl9_180 ),
inference(forward_subsumption_resolution,[],[f1883,f14]) ).
fof(f1899,plain,
( spl9_15
| spl9_89
| ~ spl9_53
| ~ spl9_180 ),
inference(avatar_split_clause,[],[f1885,f1870,f395,f884,f131]) ).
fof(f1907,plain,
( ! [X0] :
( r1(X0,sK4(X0))
| ~ r1(sK6,X0)
| ~ r1(sK6,sK7) )
| ~ spl9_181 ),
inference(resolution,[],[f1875,f15]) ).
fof(f1917,plain,
( ! [X0] :
( r1(X0,sK4(X0))
| ~ r1(sK6,X0) )
| ~ spl9_181 ),
inference(forward_subsumption_resolution,[],[f1907,f14]) ).
fof(f1918,plain,
( spl9_52
| ~ spl9_181 ),
inference(avatar_split_clause,[],[f1917,f1874,f392]) ).
fof(f2340,plain,
( ! [X0,X1] :
( ~ r1(sK0,X0)
| p1(sK2(sK3(sK7)))
| ~ r1(X0,X1)
| ~ p1(sK4(X1))
| ~ r1(X0,sK7)
| ~ r1(sK6,sK7) )
| ~ spl9_38
| ~ spl9_53 ),
inference(resolution,[],[f514,f396]) ).
fof(f2341,plain,
( ! [X0,X1] :
( ~ r1(sK0,X0)
| ~ r1(X0,X1)
| ~ p1(sK4(X1))
| ~ r1(X0,sK7)
| ~ r1(sK6,sK7) )
| ~ spl9_38
| ~ spl9_53
| spl9_180 ),
inference(forward_subsumption_resolution,[],[f2340,f1871]) ).
fof(f2343,plain,
( ! [X0,X1] :
( ~ p1(sK4(X1))
| ~ r1(X0,X1)
| ~ r1(sK0,X0)
| ~ r1(X0,sK7) )
| ~ spl9_38
| ~ spl9_53
| spl9_180 ),
inference(forward_subsumption_resolution,[],[f2341,f14]) ).
fof(f2398,plain,
( ! [X0] :
( ~ r1(sK0,X0)
| ~ r1(X0,sK6)
| ~ r1(X0,sK7) )
| ~ spl9_38
| ~ spl9_53
| ~ spl9_54
| spl9_180 ),
inference(resolution,[],[f2343,f420]) ).
fof(f2399,plain,
( ~ r1(sK6,sK6)
| ~ r1(sK6,sK7)
| ~ spl9_38
| ~ spl9_53
| ~ spl9_54
| spl9_180 ),
inference(resolution,[],[f2398,f15]) ).
fof(f2410,plain,
( ~ r1(sK6,sK7)
| ~ spl9_38
| ~ spl9_53
| ~ spl9_54
| spl9_180 ),
inference(forward_subsumption_resolution,[],[f2399,f10]) ).
fof(f2411,plain,
( $false
| ~ spl9_38
| ~ spl9_53
| ~ spl9_54
| spl9_180 ),
inference(forward_subsumption_resolution,[],[f2410,f14]) ).
fof(f2412,plain,
( ~ spl9_38
| ~ spl9_53
| ~ spl9_54
| spl9_180 ),
inference(avatar_contradiction_clause,[],[f2411]) ).
cnf(s114,plain,
~ spl9_15,
inference(sat_conversion,[],[f156]) ).
cnf(s222,plain,
( spl9_15
| spl9_38 ),
inference(sat_conversion,[],[f318]) ).
cnf(s277,plain,
( spl9_52
| spl9_53 ),
inference(sat_conversion,[],[f397]) ).
cnf(s301,plain,
( ~ spl9_52
| spl9_54
| ~ spl9_55 ),
inference(sat_conversion,[],[f425]) ).
cnf(s327,plain,
( spl9_53
| ~ spl9_54
| ~ spl9_55 ),
inference(sat_conversion,[],[f464]) ).
cnf(s423,plain,
spl9_55,
inference(sat_conversion,[],[f602]) ).
cnf(s575,plain,
~ spl9_89,
inference(sat_conversion,[],[f902]) ).
cnf(s1089,plain,
( ~ spl9_38
| ~ spl9_53
| spl9_180
| spl9_181 ),
inference(sat_conversion,[],[f1876]) ).
cnf(s1124,plain,
( spl9_15
| ~ spl9_53
| spl9_89
| ~ spl9_180 ),
inference(sat_conversion,[],[f1899]) ).
cnf(s1135,plain,
( spl9_52
| ~ spl9_181 ),
inference(sat_conversion,[],[f1918]) ).
cnf(s1435,plain,
( ~ spl9_38
| ~ spl9_53
| ~ spl9_54
| spl9_180 ),
inference(sat_conversion,[],[f2412]) ).
cnf(s1439,plain,
( spl9_53
| ~ spl9_54 ),
inference(rat,[],[s327,s423]) ).
cnf(s1441,plain,
( ~ spl9_52
| spl9_54 ),
inference(rat,[],[s301,s423]) ).
cnf(s1444,plain,
spl9_38,
inference(rat,[],[s222,s114]) ).
cnf(s1446,plain,
spl9_52,
inference(rat,[],[s1089,s1124,s277,s1135,s1444,s575,s114]) ).
cnf(s1448,plain,
spl9_54,
inference(rat,[],[s1441,s1446]) ).
cnf(s1450,plain,
spl9_53,
inference(rat,[],[s1439,s1448]) ).
cnf(s1451,plain,
spl9_180,
inference(rat,[],[s1435,s1450,s1444,s1448]) ).
cnf(s1453,plain,
$false,
inference(rat,[],[s1124,s114,s575,s1451,s1450]) ).
fof(f2413,plain,
$false,
inference(avatar_sat_refutation,[],[s1453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.35 % Computer : n003.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 : Sun Sep 27 16:19:41 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.45 % (755882)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (755889)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=926844395:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.45 % (755888)% WARNING: option uhcvi not known.
% 0.13/0.45 % (755887)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2273647813_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.45 % (755888)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=401253865:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.45 % (755890)dis+10_1_sil=32000:sp=arity:random_seed=4066755352:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.45 % (755891)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1458214052:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.45 % (755892)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=176429709:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.45 % (755893)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=991221295:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.45 % TRYING [1]
% 0.13/0.45 % TRYING [2]
% 0.13/0.45 % TRYING [3]
% 0.13/0.45 % TRYING [4]
% 0.13/0.45 % TRYING [5]
% 0.13/0.45 % (755889) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-755882-755889"...
% 0.13/0.45 % (755889)...printing done.
% 0.13/0.45 % TRYING [6]
% 0.13/0.45 % (755889)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.45 % (755889)------------------------------
% 0.13/0.45 % (755889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.45 % (755889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.45 % (755889)CaDiCaL version: 2.1.3
% 0.13/0.45 % (755889)Termination reason: Refutation
% 0.13/0.45 % (755889)Time elapsed: 0.024 s
% 0.13/0.45 % (755889)Peak memory usage: 13 MB
% 0.13/0.45 % (755889)Instructions burned: 59 (million)
% 0.13/0.45 % (755882)Success in time 0.051 s
% 0.13/0.45 % Vampire exiting
%------------------------------------------------------------------------------