%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU685^2 : 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 08:30:46 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 25 unt; 0 typ; 8 def)
% Number of atoms : 553 ( 126 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 667 ( 86 ~; 74 |; 31 &; 439 @)
% ( 12 <=>; 25 =>; 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 : 47 ( 44 usr; 23 con; 0-4 aty)
% Number of variables : 112 ( 0 sgn 86 !; 26 ?; 112 :)
% 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,
funcGraphProp1: $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
db3:
!>[X0: $tType] : X0 ).
thf(f5,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) )
= infuncsetfunc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f6,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) )
= funcGraphProp1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(f7,conjecture,
( infuncsetfunc
=> ( funcGraphProp1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(f8,negated_conjecture,
~ ( infuncsetfunc
=> ( funcGraphProp1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) )
= infuncsetfunc ),
inference(rectify,[],[f5]) ).
thf(f10,plain,
( ( infuncsetfunc = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ( ( func @ X0 @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f14,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) ) )
= funcGraphProp1 ),
inference(rectify,[],[f6]) ).
thf(f15,plain,
( ( funcGraphProp1 = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f18,plain,
~ ( infuncsetfunc
=> ( funcGraphProp1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f19,plain,
~ ( ( infuncsetfunc = $true )
=> ( ( funcGraphProp1 = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( func @ X2 @ X1 @ X0 ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) ) ) )
<=> ( funcGraphProp1 = $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f23,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true ) )
<=> ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f24,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 )
!= $true ) )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( funcGraphProp1 = $true )
& ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f25,plain,
( ( funcGraphProp1 = $true )
& ( infuncsetfunc = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ ( ap @ X0 @ X1 @ X2 @ X3 ) ) @ X2 )
!= $true ) )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) ) ),
inference(flattening,[],[f24]) ).
thf(f26,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( func @ X2 @ X1 @ X0 ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) ) ) )
| ( funcGraphProp1 != $true ) )
& ( ( funcGraphProp1 = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X2 @ X1 @ X0 @ X3 ) ) @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X2 @ X0 ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 ) ) ) )
| ( funcGraphProp1 != $true ) )
& ( ( funcGraphProp1 = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ( $true
= ( func @ X5 @ X6 @ X4 ) )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X6 @ X4 @ X7 ) ) @ X4 ) ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X2 @ X0 ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 ) ) ) )
| ( funcGraphProp1 != $true ) )
& ( ( funcGraphProp1 = $true )
| ( ( $true
= ( func @ sK1 @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ ( ap @ sK1 @ sK2 @ sK0 @ sK3 ) ) @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X4,sK0),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3)],[f27]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true ) )
| ( infuncsetfunc != $true ) )
& ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
!= $true )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[],[f23]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true ) )
| ( infuncsetfunc != $true ) )
& ( ( infuncsetfunc = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( func @ X3 @ X4 @ X5 ) )
& ( ( in @ X5 @ ( funcSet @ X3 @ X4 ) )
= $true ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
| ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true ) )
| ( infuncsetfunc != $true ) )
& ( ( infuncsetfunc = $true )
| ( ( $true
!= ( func @ sK4 @ sK5 @ sK6 ) )
& ( $true
= ( in @ sK6 @ ( funcSet @ sK4 @ sK5 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6)],[f30]) ).
thf(f32,plain,
( ( funcGraphProp1 = $true )
& ( infuncsetfunc = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 ) ) )
& ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f33,plain,
( ( funcGraphProp1 = $true )
& ( infuncsetfunc = $true )
& ( $true
= ( in @ sK10 @ sK7 ) )
& ( $true
!= ( in @ ( kpair @ sK10 @ ( ap @ sK7 @ sK9 @ sK8 @ sK10 ) ) @ sK8 ) )
& ( ( in @ sK8 @ ( funcSet @ sK7 @ sK9 ) )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f32]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 ) )
| ( funcGraphProp1 != $true )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f43,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true )
| ( infuncsetfunc != $true )
| ( ( func @ X0 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f45,plain,
( ( in @ sK8 @ ( funcSet @ sK7 @ sK9 ) )
= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f46,plain,
( $true
!= ( in @ ( kpair @ sK10 @ ( ap @ sK7 @ sK9 @ sK8 @ sK10 ) ) @ sK8 ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f47,plain,
( $true
= ( in @ sK10 @ sK7 ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f48,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f49,plain,
funcGraphProp1 = $true,
inference(cnf_transformation,[],[f33]) ).
thf(f57,definition,
( spl11_2
<=> ( funcGraphProp1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f67,definition,
( spl11_4
<=> ( infuncsetfunc = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f70,plain,
spl11_4,
inference(avatar_split_clause,[],[f48,f67]) ).
thf(f91,plain,
spl11_2,
inference(avatar_split_clause,[],[f49,f57]) ).
thf(f93,definition,
( spl11_9
<=> ( $true
= ( in @ ( kpair @ sK10 @ ( ap @ sK7 @ sK9 @ sK8 @ sK10 ) ) @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
thf(f95,plain,
( ( $true
!= ( in @ ( kpair @ sK10 @ ( ap @ sK7 @ sK9 @ sK8 @ sK10 ) ) @ sK8 ) )
| spl11_9 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f96,plain,
~ spl11_9,
inference(avatar_split_clause,[],[f46,f93]) ).
thf(f113,definition,
( spl11_13
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true )
| ( ( func @ X0 @ X1 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
thf(f114,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true )
| ( ( func @ X0 @ X1 @ X2 )
= $true ) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f115,plain,
( spl11_13
| ~ spl11_4 ),
inference(avatar_split_clause,[],[f43,f67,f113]) ).
thf(f117,definition,
( spl11_14
<=> ( $true
= ( in @ sK10 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f119,plain,
( ( $true
= ( in @ sK10 @ sK7 ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f120,plain,
spl11_14,
inference(avatar_split_clause,[],[f47,f117]) ).
thf(f122,definition,
( spl11_15
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f123,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X2 @ X0 @ X3 ) ) @ X0 ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) ) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f124,plain,
( ~ spl11_2
| spl11_15 ),
inference(avatar_split_clause,[],[f40,f122,f57]) ).
thf(f126,definition,
( spl11_16
<=> ( ( in @ sK8 @ ( funcSet @ sK7 @ sK9 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
thf(f128,plain,
( ( ( in @ sK8 @ ( funcSet @ sK7 @ sK9 ) )
= $true )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f129,plain,
spl11_16,
inference(avatar_split_clause,[],[f45,f126]) ).
thf(f132,plain,
( ( $true
= ( func @ sK7 @ sK9 @ sK8 ) )
| ( $true != $true )
| ~ spl11_13
| ~ spl11_16 ),
inference(superposition,[],[f114,f128]) ).
thf(f133,plain,
( ( $true
= ( func @ sK7 @ sK9 @ sK8 ) )
| ~ spl11_13
| ~ spl11_16 ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f135,definition,
( spl11_17
<=> ( $true
= ( func @ sK7 @ sK9 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_17])],[avatar_definition]) ).
thf(f137,plain,
( ( $true
= ( func @ sK7 @ sK9 @ sK8 ) )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f138,plain,
( spl11_17
| ~ spl11_13
| ~ spl11_16 ),
inference(avatar_split_clause,[],[f133,f126,f113,f135]) ).
thf(f143,plain,
( ( $true
!= ( func @ sK7 @ sK9 @ sK8 ) )
| ( $true != $true )
| ( $true
!= ( in @ sK10 @ sK7 ) )
| spl11_9
| ~ spl11_15 ),
inference(superposition,[],[f95,f123]) ).
thf(f144,plain,
( ( $true
!= ( in @ sK10 @ sK7 ) )
| ( $true
!= ( func @ sK7 @ sK9 @ sK8 ) )
| spl11_9
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f145,plain,
( ( $true
!= ( func @ sK7 @ sK9 @ sK8 ) )
| spl11_9
| ~ spl11_14
| ~ spl11_15 ),
inference(forward_subsumption_resolution,[],[f144,f119]) ).
thf(f146,plain,
( $false
| spl11_9
| ~ spl11_14
| ~ spl11_15
| ~ spl11_17 ),
inference(forward_subsumption_resolution,[],[f145,f137]) ).
thf(f147,plain,
( spl11_9
| ~ spl11_14
| ~ spl11_15
| ~ spl11_17 ),
inference(avatar_contradiction_clause,[],[f146]) ).
cnf(s3,plain,
spl11_4,
inference(sat_conversion,[],[f70]) ).
cnf(s8,plain,
spl11_2,
inference(sat_conversion,[],[f91]) ).
cnf(s9,plain,
~ spl11_9,
inference(sat_conversion,[],[f96]) ).
cnf(s13,plain,
( ~ spl11_4
| spl11_13 ),
inference(sat_conversion,[],[f115]) ).
cnf(s14,plain,
spl11_14,
inference(sat_conversion,[],[f120]) ).
cnf(s15,plain,
( ~ spl11_2
| spl11_15 ),
inference(sat_conversion,[],[f124]) ).
cnf(s16,plain,
spl11_16,
inference(sat_conversion,[],[f129]) ).
cnf(s17,plain,
( ~ spl11_13
| ~ spl11_16
| spl11_17 ),
inference(sat_conversion,[],[f138]) ).
cnf(s18,plain,
( spl11_9
| ~ spl11_14
| ~ spl11_15
| ~ spl11_17 ),
inference(sat_conversion,[],[f147]) ).
cnf(s19,plain,
spl11_15,
inference(rat,[],[s15,s8]) ).
cnf(s20,plain,
~ spl11_17,
inference(rat,[],[s18,s9,s14,s19]) ).
cnf(s21,plain,
~ spl11_13,
inference(rat,[],[s17,s16,s20]) ).
cnf(s22,plain,
~ spl11_4,
inference(rat,[],[s13,s21]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s3,s22]) ).
thf(f148,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU685^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:10:28 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.27 % (2561210)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2561218)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=2073719690: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)
% 0.20/0.27 % (2561218) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2561210-2561218"...
% 0.20/0.27 % (2561218)...printing done.
% 0.20/0.27 % (2561218)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (2561218)------------------------------
% 0.20/0.27 % (2561218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2561218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2561218)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2561218)Termination reason: Refutation
% 0.20/0.27 % (2561218)Time elapsed: 0.004 s
% 0.20/0.27 % (2561218)Peak memory usage: 13 MB
% 0.20/0.27 % (2561218)Instructions burned: 10 (million)
% 0.20/0.27 % (2561210)Success in time 0.032 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------