%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU688^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 : Wed Sep 30 08:30:47 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 88 ( 31 unt; 0 typ; 11 def)
% Number of atoms : 733 ( 187 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 860 ( 127 ~; 111 |; 45 &; 522 @)
% ( 16 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 28 con; 0-4 aty)
% Number of variables : 140 ( 0 sgn 109 !; 31 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
breln: $i > $i > $i > $o ).
thf(func_def_11,type,
func: $i > $i > $i > $o ).
thf(func_def_12,type,
funcSet: $i > $i > $i ).
thf(func_def_13,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_14,type,
infuncsetfunc: $o ).
thf(func_def_15,type,
funcGraphProp2: $o ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f5,axiom,
( infuncsetfunc
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f6,axiom,
( funcGraphProp2
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(f7,conjecture,
( infuncsetfunc
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(f8,negated_conjecture,
~ ( infuncsetfunc
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
=> ( func @ X1 @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f10,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
=> ( $true
= ( func @ X1 @ X2 @ X0 ) ) )
<=> ( infuncsetfunc = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f12,plain,
( funcGraphProp2
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f13,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( func @ X1 @ X2 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f18,plain,
~ ( infuncsetfunc
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f19,plain,
~ ( ( infuncsetfunc = $true )
=> ( ( funcGraphProp2 = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( funcGraphProp2 = $true )
& ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f23,plain,
( ( funcGraphProp2 = $true )
& ( infuncsetfunc = $true )
& ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X3 )
!= X4 )
& ( ( in @ X4 @ X1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) ) ) ) ),
inference(flattening,[],[f22]) ).
thf(f24,plain,
( ( infuncsetfunc = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X1 @ X2 @ X0 ) )
| ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f25,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( $true
!= ( in @ X4 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f26,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) ) )
<=> ( funcGraphProp2 = $true ) ),
inference(flattening,[],[f25]) ).
thf(f27,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X2 @ X0 ) )
& ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X1 @ X2 @ X0 ) )
| ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
!= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(nnf_transformation,[],[f24]) ).
thf(f28,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X2 @ X0 ) )
& ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( func @ X4 @ X5 @ X3 )
= $true )
| ( ( in @ X3 @ ( funcSet @ X4 @ X5 ) )
!= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(rectify,[],[f27]) ).
thf(f29,plain,
( ( ( infuncsetfunc = $true )
| ( ( ( func @ sK1 @ sK2 @ sK0 )
!= $true )
& ( $true
= ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( func @ X4 @ X5 @ X3 )
= $true )
| ( ( in @ X3 @ ( funcSet @ X4 @ X5 ) )
!= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f28]) ).
thf(f30,plain,
( ( funcGraphProp2 = $true )
& ( infuncsetfunc = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ? [X4: $i] :
( ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= X4 )
& ( ( in @ X4 @ X0 )
= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f31,plain,
( ( funcGraphProp2 = $true )
& ( infuncsetfunc = $true )
& ( ( in @ sK4 @ ( funcSet @ sK5 @ sK3 ) )
= $true )
& ( ( in @ sK6 @ sK5 )
= $true )
& ( sK7
!= ( ap @ sK5 @ sK3 @ sK4 @ sK6 ) )
& ( $true
= ( in @ sK7 @ sK3 ) )
& ( $true
= ( in @ ( kpair @ sK6 @ sK7 ) @ sK4 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6),skolemize(X4,sK7)],[f30]) ).
thf(f32,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) ) )
| ( funcGraphProp2 != $true ) )
& ( ( funcGraphProp2 = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
& ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= X4 ) ) )
& ( $true
= ( func @ X1 @ X2 @ X0 ) ) ) ) ),
inference(nnf_transformation,[],[f26]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) )
| ( ( func @ X0 @ X1 @ X2 )
!= $true ) )
| ( funcGraphProp2 != $true ) )
& ( ( funcGraphProp2 = $true )
| ? [X5: $i,X6: $i,X7: $i] :
( ? [X8: $i] :
( ( $true
= ( in @ X8 @ X5 ) )
& ? [X9: $i] :
( ( ( in @ X9 @ X6 )
= $true )
& ( ( in @ ( kpair @ X8 @ X9 ) @ X7 )
= $true )
& ( ( ap @ X5 @ X6 @ X7 @ X8 )
!= X9 ) ) )
& ( ( func @ X5 @ X6 @ X7 )
= $true ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) )
| ( ( func @ X0 @ X1 @ X2 )
!= $true ) )
| ( funcGraphProp2 != $true ) )
& ( ( funcGraphProp2 = $true )
| ( ( ( in @ sK11 @ sK8 )
= $true )
& ( $true
= ( in @ sK12 @ sK9 ) )
& ( ( in @ ( kpair @ sK11 @ sK12 ) @ sK10 )
= $true )
& ( ( ap @ sK8 @ sK9 @ sK10 @ sK11 )
!= sK12 )
& ( $true
= ( func @ sK8 @ sK9 @ sK10 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12]),skolemize(X5,sK8),skolemize(X6,sK9),skolemize(X7,sK10),skolemize(X8,sK11),skolemize(X9,sK12)],[f33]) ).
thf(f36,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( infuncsetfunc != $true )
| ( ( func @ X4 @ X5 @ X3 )
= $true )
| ( ( in @ X3 @ ( funcSet @ X4 @ X5 ) )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f40,plain,
( $true
= ( in @ ( kpair @ sK6 @ sK7 ) @ sK4 ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f41,plain,
( $true
= ( in @ sK7 @ sK3 ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f42,plain,
( sK7
!= ( ap @ sK5 @ sK3 @ sK4 @ sK6 ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f43,plain,
( ( in @ sK6 @ sK5 )
= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f44,plain,
( ( in @ sK4 @ ( funcSet @ sK5 @ sK3 ) )
= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f45,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[],[f31]) ).
thf(f46,plain,
funcGraphProp2 = $true,
inference(cnf_transformation,[],[f31]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 )
| ( ( func @ X0 @ X1 @ X2 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true )
| ( funcGraphProp2 != $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f58,definition,
( spl13_1
<=> ( funcGraphProp2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
thf(f62,definition,
( spl13_2
<=> ! [X4: $i,X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( func @ X0 @ X1 @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
thf(f63,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 )
| ( ( func @ X0 @ X1 @ X2 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true ) )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f64,plain,
( ~ spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f54,f62,f58]) ).
thf(f81,definition,
( spl13_6
<=> ( ( in @ sK4 @ ( funcSet @ sK5 @ sK3 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
thf(f83,plain,
( ( ( in @ sK4 @ ( funcSet @ sK5 @ sK3 ) )
= $true )
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f81]) ).
thf(f84,plain,
spl13_6,
inference(avatar_split_clause,[],[f44,f81]) ).
thf(f91,definition,
( spl13_8
<=> ( $true
= ( in @ ( kpair @ sK6 @ sK7 ) @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
thf(f93,plain,
( ( $true
= ( in @ ( kpair @ sK6 @ sK7 ) @ sK4 ) )
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f94,plain,
spl13_8,
inference(avatar_split_clause,[],[f40,f91]) ).
thf(f100,plain,
spl13_1,
inference(avatar_split_clause,[],[f46,f58]) ).
thf(f107,definition,
( spl13_11
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( func @ X4 @ X5 @ X3 )
= $true )
| ( ( in @ X3 @ ( funcSet @ X4 @ X5 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
thf(f108,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( funcSet @ X4 @ X5 ) )
!= $true )
| ( ( func @ X4 @ X5 @ X3 )
= $true ) )
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f107]) ).
thf(f110,definition,
( spl13_12
<=> ( infuncsetfunc = $true ) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
thf(f113,plain,
( spl13_11
| ~ spl13_12 ),
inference(avatar_split_clause,[],[f36,f110,f107]) ).
thf(f135,definition,
( spl13_17
<=> ( $true
= ( in @ sK7 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_17])],[avatar_definition]) ).
thf(f137,plain,
( ( $true
= ( in @ sK7 @ sK3 ) )
| ~ spl13_17 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f138,plain,
spl13_17,
inference(avatar_split_clause,[],[f41,f135]) ).
thf(f140,definition,
( spl13_18
<=> ( ( in @ sK6 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
thf(f142,plain,
( ( ( in @ sK6 @ sK5 )
= $true )
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f140]) ).
thf(f143,plain,
spl13_18,
inference(avatar_split_clause,[],[f43,f140]) ).
thf(f144,plain,
spl13_12,
inference(avatar_split_clause,[],[f45,f110]) ).
thf(f151,definition,
( spl13_20
<=> ( sK7
= ( ap @ sK5 @ sK3 @ sK4 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_20])],[avatar_definition]) ).
thf(f153,plain,
( ( sK7
!= ( ap @ sK5 @ sK3 @ sK4 @ sK6 ) )
| spl13_20 ),
inference(avatar_component_clause,[],[f151]) ).
thf(f154,plain,
~ spl13_20,
inference(avatar_split_clause,[],[f42,f151]) ).
thf(f157,plain,
( ( $true
= ( func @ sK5 @ sK3 @ sK4 ) )
| ( $true != $true )
| ~ spl13_6
| ~ spl13_11 ),
inference(superposition,[],[f108,f83]) ).
thf(f158,plain,
( ( $true
= ( func @ sK5 @ sK3 @ sK4 ) )
| ~ spl13_6
| ~ spl13_11 ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f160,definition,
( spl13_21
<=> ( $true
= ( func @ sK5 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_21])],[avatar_definition]) ).
thf(f163,plain,
( spl13_21
| ~ spl13_6
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f158,f107,f81,f160]) ).
thf(f165,plain,
( ! [X0: $i] :
( ( $true
!= ( func @ sK5 @ sK3 @ sK4 ) )
| ( sK7 != X0 )
| ( $true
!= ( in @ ( kpair @ sK6 @ X0 ) @ sK4 ) )
| ( ( in @ sK6 @ sK5 )
!= $true )
| ( ( in @ X0 @ sK3 )
!= $true ) )
| ~ spl13_2
| spl13_20 ),
inference(superposition,[],[f153,f63]) ).
thf(f167,plain,
( ! [X0: $i] :
( ( sK7 != X0 )
| ( $true
!= ( func @ sK5 @ sK3 @ sK4 ) )
| ( ( in @ X0 @ sK3 )
!= $true )
| ( $true
!= ( in @ ( kpair @ sK6 @ X0 ) @ sK4 ) ) )
| ~ spl13_2
| ~ spl13_18
| spl13_20 ),
inference(forward_subsumption_resolution,[],[f165,f142]) ).
thf(f169,definition,
( spl13_22
<=> ! [X0: $i] :
( ( sK7 != X0 )
| ( $true
!= ( in @ ( kpair @ sK6 @ X0 ) @ sK4 ) )
| ( ( in @ X0 @ sK3 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl13_22])],[avatar_definition]) ).
thf(f170,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( kpair @ sK6 @ X0 ) @ sK4 ) )
| ( sK7 != X0 )
| ( ( in @ X0 @ sK3 )
!= $true ) )
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f171,plain,
( spl13_22
| ~ spl13_21
| ~ spl13_2
| ~ spl13_18
| spl13_20 ),
inference(avatar_split_clause,[],[f167,f151,f140,f62,f160,f169]) ).
thf(f174,plain,
( ( sK7 != sK7 )
| ( $true
!= ( in @ sK7 @ sK3 ) )
| ( $true != $true )
| ~ spl13_8
| ~ spl13_22 ),
inference(superposition,[],[f170,f93]) ).
thf(f175,plain,
( ( $true
!= ( in @ sK7 @ sK3 ) )
| ~ spl13_8
| ~ spl13_22 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f176,plain,
( $false
| ~ spl13_8
| ~ spl13_17
| ~ spl13_22 ),
inference(forward_subsumption_resolution,[],[f175,f137]) ).
thf(f177,plain,
( ~ spl13_8
| ~ spl13_17
| ~ spl13_22 ),
inference(avatar_contradiction_clause,[],[f176]) ).
cnf(s1,plain,
( ~ spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f64]) ).
cnf(s5,plain,
spl13_6,
inference(sat_conversion,[],[f84]) ).
cnf(s7,plain,
spl13_8,
inference(sat_conversion,[],[f94]) ).
cnf(s9,plain,
spl13_1,
inference(sat_conversion,[],[f100]) ).
cnf(s11,plain,
( spl13_11
| ~ spl13_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s16,plain,
spl13_17,
inference(sat_conversion,[],[f138]) ).
cnf(s17,plain,
spl13_18,
inference(sat_conversion,[],[f143]) ).
cnf(s18,plain,
spl13_12,
inference(sat_conversion,[],[f144]) ).
cnf(s20,plain,
~ spl13_20,
inference(sat_conversion,[],[f154]) ).
cnf(s21,plain,
( ~ spl13_6
| ~ spl13_11
| spl13_21 ),
inference(sat_conversion,[],[f163]) ).
cnf(s22,plain,
( ~ spl13_2
| ~ spl13_18
| spl13_20
| ~ spl13_21
| spl13_22 ),
inference(sat_conversion,[],[f171]) ).
cnf(s23,plain,
( ~ spl13_8
| ~ spl13_17
| ~ spl13_22 ),
inference(sat_conversion,[],[f177]) ).
cnf(s24,plain,
spl13_11,
inference(rat,[],[s11,s18]) ).
cnf(s25,plain,
~ spl13_22,
inference(rat,[],[s23,s16,s7]) ).
cnf(s26,plain,
spl13_21,
inference(rat,[],[s21,s24,s5]) ).
cnf(s27,plain,
~ spl13_2,
inference(rat,[],[s22,s25,s17,s20,s26]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s1,s27,s9]) ).
thf(f178,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU688^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n003.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:10:59 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.31 % (2562064)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (2562074)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4129687136:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (2562075)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (2562075)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.31 % (2562072)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4223456352:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.31 % (2562069)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2971658340:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (2562070)lrs+10_16_si=on:nwc=1.5:random_seed=4212369366:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (2562071)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4294563800:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (2562073)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1420529814:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (2562075)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2845388373:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (2562071)Instruction limit reached!
% 0.21/0.31 % (2562071)------------------------------
% 0.21/0.31 % (2562071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2562071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2562071)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2562071)Termination reason: Instruction limit
% 0.21/0.31 % (2562071)Termination phase: Property scanning
% 0.21/0.31 % (2562071)Time elapsed: 0.002 s
% 0.21/0.31 % (2562071)Peak memory usage: 10 MB
% 0.21/0.31 % (2562071)Instructions burned: 3 (million)
% 0.21/0.31 % (2562073) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2562064-2562073"...
% 0.21/0.31 % (2562072) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2562064-2562072"...
% 0.21/0.31 % (2562069)Refutation not found, incomplete strategy
% 0.21/0.31 % (2562069)------------------------------
% 0.21/0.31 % (2562069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2562069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2562069)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2562069)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (2562069)Time elapsed: 0.006 s
% 0.21/0.31 % (2562069)Peak memory usage: 12 MB
% 0.21/0.31 % (2562069)Instructions burned: 10 (million)
% 0.21/0.31 % (2562069)------------------------------
% 0.21/0.31 % (2562069)------------------------------
% 0.21/0.31 % (2562073)...printing done.
% 0.21/0.31 % (2562072)...printing done.
% 0.21/0.31 % (2562072)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (2562072)------------------------------
% 0.21/0.31 % (2562072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2562072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2562072)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2562072)Termination reason: Refutation
% 0.21/0.31 % (2562072)Time elapsed: 0.008 s
% 0.21/0.31 % (2562072)Peak memory usage: 13 MB
% 0.21/0.31 % (2562072)Instructions burned: 12 (million)
% 0.21/0.31 % (2562064)Success in time 0.051 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------