%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV448^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:39:31 AM UTC 2026
% Result : Theorem 0.21s 0.35s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 122 ( 21 unt; 0 typ; 9 def)
% Number of atoms : 606 ( 133 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 596 ( 88 ~; 142 |; 11 &; 332 @)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 26 usr; 13 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 99 ( 0 sgn 90 !; 3 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
vAND: $o > $o > $o ).
thf(func_def_9,type,
sK1: sK0 > $o ).
thf(func_def_10,type,
sK2: sK0 > $o ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK6:
!>[X0: $tType] : ( X0 > ( X0 > sK0 > sK0 ) > sK0 ) ).
thf(func_def_19,type,
sK7: sK0 ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_') ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_ANTISYM_EQ_') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( X1 = X2 ) ) ),
inference(rectify,[],[f5]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 = X2 )
= ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 = X2 )
!= ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ( sK1 = sK2 )
!= ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
& ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
thf(f13,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f15,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( sK1 = sK2 )
!= ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
& ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f19,plain,
( ( ( sK1 = sK2 )
= $true )
| ( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
& ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f20,plain,
( ( ( sK1 = sK2 )
= $false )
| ( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
& ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f21,plain,
( ( sK1 != sK2 )
| ( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
& ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( sK1 != sK2 )
| ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
= $false )
| ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( sK1 = sK2 )
| ( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
& ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) )
= $true ) ),
inference(equality_proxy_clausification,[],[f19]) ).
thf(f24,plain,
( ( sK1 = sK2 )
| ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( sK1 = sK2 )
| ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f26,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f27,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false )
| ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f28,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( $false
= ( ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) )
@ ( sK3 @ X0 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f26]) ).
thf(f32,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 )
=> ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $false
= ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X2 ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f32]) ).
thf(f49,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( ( X1 @ X2 )
= $false ) ),
inference(iff_proxy_clausification,[],[f13]) ).
thf(f50,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f13]) ).
thf(f52,definition,
( spl5_1
<=> ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f54,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $false )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f56,definition,
( spl5_2
<=> ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f57,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
!= $false )
| spl5_2 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f58,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
= $false )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f60,definition,
( spl5_3
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f61,plain,
( ( sK1 = sK2 )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f62,plain,
( ( sK1 != sK2 )
| spl5_3 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f63,plain,
( spl5_1
| spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f22,f60,f56,f52]) ).
thf(f65,definition,
( spl5_4
<=> ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f67,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f68,plain,
( spl5_4
| spl5_3 ),
inference(avatar_split_clause,[],[f25,f60,f65]) ).
thf(f70,definition,
( spl5_5
<=> ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f72,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
= $true )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,plain,
( spl5_5
| spl5_3 ),
inference(avatar_split_clause,[],[f24,f60,f70]) ).
thf(f84,plain,
( ( $false
= ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK1 ) )
| ~ spl5_2
| ~ spl5_3 ),
inference(forward_demodulation,[],[f58,f61]) ).
thf(f110,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true = $false )
| ( $true
= ( X2 @ X1 ) )
| ( $false
= ( 'const/sets/SUBSET' @ X0 @ X3 @ X2 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(constrained_superposition,[],[f50,f30]) ).
thf(f112,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( X2 @ X1 ) )
| ( $false
= ( 'const/sets/SUBSET' @ X0 @ X3 @ X2 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f425,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = $false )
| ( $true
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X1 ) )
| ( $true
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X1 ) ) ),
inference(constrained_superposition,[],[f33,f34]) ).
thf(f429,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = $false )
| ( $true
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f425]) ).
thf(f430,plain,
! [X0: $tType,X1: X0 > $o] :
( $true
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X1 ) ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f825,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_3 ),
inference(constrained_superposition,[],[f430,f84]) ).
thf(f869,plain,
( $false
| ~ spl5_2
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f825]) ).
thf(f870,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f869]) ).
thf(f871,plain,
( ( $false
= ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK1 ) )
| ~ spl5_1
| ~ spl5_3 ),
inference(forward_demodulation,[],[f54,f61]) ).
thf(f874,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_3 ),
inference(constrained_superposition,[],[f871,f430]) ).
thf(f884,plain,
( $false
| ~ spl5_1
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f874]) ).
thf(f885,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f884]) ).
thf(f887,plain,
( ( ( sK1 @ sK7 )
!= ( sK2 @ sK7 ) )
| spl5_3 ),
inference(negative_extensionality,[],[f62]) ).
thf(f888,plain,
( ( $true
= ( sK1 @ sK7 ) )
| ( $true
= ( sK2 @ sK7 ) )
| spl5_3 ),
inference(xor_proxy_clausification,[],[f887]) ).
thf(f889,plain,
( ( $false
= ( sK1 @ sK7 ) )
| ( $false
= ( sK2 @ sK7 ) )
| spl5_3 ),
inference(xor_proxy_clausification,[],[f887]) ).
thf(f891,definition,
( spl5_9
<=> ( $false
= ( sK2 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f892,plain,
( ( $false
!= ( sK2 @ sK7 ) )
| spl5_9 ),
inference(avatar_component_clause,[],[f891]) ).
thf(f893,plain,
( ( $false
= ( sK2 @ sK7 ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f891]) ).
thf(f895,definition,
( spl5_10
<=> ( $false
= ( sK1 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
thf(f897,plain,
( ( $false
= ( sK1 @ sK7 ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f895]) ).
thf(f898,plain,
( spl5_9
| spl5_10
| spl5_3 ),
inference(avatar_split_clause,[],[f889,f60,f895,f891]) ).
thf(f900,definition,
( spl5_11
<=> ( $true
= ( sK2 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
thf(f902,plain,
( ( $true
= ( sK2 @ sK7 ) )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f900]) ).
thf(f904,definition,
( spl5_12
<=> ( $true
= ( sK1 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
thf(f906,plain,
( ( $true
= ( sK1 @ sK7 ) )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f904]) ).
thf(f907,plain,
( spl5_11
| spl5_12
| spl5_3 ),
inference(avatar_split_clause,[],[f888,f60,f904,f900]) ).
thf(f912,plain,
( ! [X0: sK0] :
( ( $false != $false )
| ( $true
= ( sK1 @ X0 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) ) )
| spl5_2 ),
inference(constrained_superposition,[],[f57,f112]) ).
thf(f920,plain,
( ! [X0: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) )
| ( $true
= ( sK1 @ X0 ) ) )
| spl5_2 ),
inference(trivial_inequality_removal,[],[f912]) ).
thf(f931,plain,
( ! [X0: sK0] :
( ( $true = $false )
| ( $true
= ( sK2 @ X0 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) ) )
| ~ spl5_4 ),
inference(constrained_superposition,[],[f112,f67]) ).
thf(f937,plain,
( ! [X0: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f931]) ).
thf(f1039,plain,
( ! [X0: sK0] :
( ( $true = $false )
| ( $false
= ( sK2 @ X0 ) )
| ( $true
= ( sK1 @ X0 ) ) )
| spl5_2 ),
inference(constrained_superposition,[],[f49,f920]) ).
thf(f1053,plain,
( ! [X0: sK0] :
( ( $false
= ( sK2 @ X0 ) )
| ( $true
= ( sK1 @ X0 ) ) )
| spl5_2 ),
inference(trivial_inequality_removal,[],[f1039]) ).
thf(f1118,plain,
( ! [X0: sK0] :
( ( $true = $false )
| ( $false
= ( sK1 @ X0 ) )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl5_4 ),
inference(constrained_superposition,[],[f49,f937]) ).
thf(f1134,plain,
( ! [X0: sK0] :
( ( $true
= ( sK2 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f1118]) ).
thf(f1205,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK7 ) )
| ~ spl5_4
| ~ spl5_9 ),
inference(constrained_superposition,[],[f893,f1134]) ).
thf(f1208,plain,
( ( $false
= ( sK1 @ sK7 ) )
| ~ spl5_4
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f1205]) ).
thf(f1213,plain,
( spl5_10
| ~ spl5_4
| ~ spl5_9 ),
inference(avatar_split_clause,[],[f1208,f891,f65,f895]) ).
thf(f1219,plain,
( ( $true = $false )
| ~ spl5_10
| ~ spl5_12 ),
inference(constrained_superposition,[],[f906,f897]) ).
thf(f1223,plain,
( $false
| ~ spl5_10
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f1219]) ).
thf(f1224,plain,
( ~ spl5_10
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f1223]) ).
thf(f1232,plain,
( ( $true = $false )
| ~ spl5_9
| ~ spl5_11 ),
inference(forward_demodulation,[],[f902,f893]) ).
thf(f1233,plain,
( $false
| ~ spl5_9
| ~ spl5_11 ),
inference(trivial_inequality_removal,[],[f1232]) ).
thf(f1234,plain,
( ~ spl5_9
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f1233]) ).
thf(f1238,plain,
( ( $false != $false )
| ( $true
= ( sK1 @ sK7 ) )
| spl5_2
| spl5_9 ),
inference(constrained_superposition,[],[f892,f1053]) ).
thf(f1244,plain,
( ( $true
= ( sK1 @ sK7 ) )
| spl5_2
| spl5_9 ),
inference(trivial_inequality_removal,[],[f1238]) ).
thf(f1245,plain,
( ( $true = $false )
| spl5_2
| spl5_9
| ~ spl5_10 ),
inference(forward_demodulation,[],[f1244,f897]) ).
thf(f1246,plain,
( $false
| spl5_2
| spl5_9
| ~ spl5_10 ),
inference(trivial_inequality_removal,[],[f1245]) ).
thf(f1247,plain,
( spl5_2
| spl5_9
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f1246]) ).
thf(f1249,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_5 ),
inference(constrained_superposition,[],[f58,f72]) ).
thf(f1259,plain,
( $false
| ~ spl5_2
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f1249]) ).
thf(f1260,plain,
( ~ spl5_2
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f1259]) ).
cnf(s1,plain,
( spl5_1
| spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
( spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f68]) ).
cnf(s3,plain,
( spl5_3
| spl5_5 ),
inference(sat_conversion,[],[f73]) ).
cnf(s9,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f870]) ).
cnf(s11,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f885]) ).
cnf(s12,plain,
( spl5_3
| spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f898]) ).
cnf(s13,plain,
( spl5_3
| spl5_11
| spl5_12 ),
inference(sat_conversion,[],[f907]) ).
cnf(s14,plain,
( ~ spl5_4
| ~ spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f1213]) ).
cnf(s16,plain,
( ~ spl5_10
| ~ spl5_12 ),
inference(sat_conversion,[],[f1224]) ).
cnf(s18,plain,
( ~ spl5_9
| ~ spl5_11 ),
inference(sat_conversion,[],[f1234]) ).
cnf(s19,plain,
( spl5_2
| spl5_9
| ~ spl5_10 ),
inference(sat_conversion,[],[f1247]) ).
cnf(s21,plain,
( ~ spl5_2
| ~ spl5_5 ),
inference(sat_conversion,[],[f1260]) ).
cnf(s22,plain,
( spl5_9
| spl5_3
| spl5_2 ),
inference(rat,[],[s12,s19]) ).
cnf(s23,plain,
( spl5_2
| spl5_1 ),
inference(rat,[],[s16,s13,s14,s18,s22,s2,s1]) ).
cnf(s24,plain,
~ spl5_2,
inference(rat,[],[s3,s9,s21]) ).
cnf(s25,plain,
spl5_1,
inference(rat,[],[s23,s24]) ).
cnf(s26,plain,
~ spl5_3,
inference(rat,[],[s11,s25]) ).
cnf(s28,plain,
spl5_4,
inference(rat,[],[s2,s26]) ).
cnf(s29,plain,
spl5_9,
inference(rat,[],[s22,s24,s26]) ).
cnf(s30,plain,
~ spl5_11,
inference(rat,[],[s18,s29]) ).
cnf(s31,plain,
spl5_10,
inference(rat,[],[s14,s28,s29]) ).
cnf(s32,plain,
spl5_12,
inference(rat,[],[s13,s26,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s16,s32,s31]) ).
thf(f1262,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV448^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n011.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 15:48:30 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.35 % (249520)Will run a generic schedule for satisfiability detection.
% 0.21/0.35 % (249530)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1905463831:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.35 % (249526)% WARNING: option uhcvi not known.
% 0.21/0.35 % (249528)dis+10_1_sil=32000:sp=arity:random_seed=952412858:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.35 % (249527)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2492391113:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.35 % (249526)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1940519906:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.35 % (249525)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2335560631_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.35 % (249529)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=677491627:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.35 % (249526)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.35 % (249526)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.35 % (249529)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.35 % Exception at run slice level
% 0.21/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.35 % (249531)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=402095403:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.35 % (249538)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2234591158:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.35 % Exception at run slice level
% 0.21/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.35 % (249530)Instruction limit reached!
% 0.21/0.35 % (249530)------------------------------
% 0.21/0.35 % (249530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (249530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (249530)CaDiCaL version: 2.1.3
% 0.21/0.35 % (249530)Termination reason: Instruction limit
% 0.21/0.35 % (249530)Termination phase: Saturation
% 0.21/0.35 % (249530)Time elapsed: 0.038 s
% 0.21/0.35 % (249530)Peak memory usage: 12 MB
% 0.21/0.35 % (249530)Instructions burned: 135 (million)
% 0.21/0.35 % (249541)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2711428016:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.35 % (249542)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1794762163:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.21/0.35 % (249542)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.35 % (249542)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.35 % (249528)Instruction limit reached!
% 0.21/0.35 % (249528)------------------------------
% 0.21/0.35 % (249528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (249528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (249528)CaDiCaL version: 2.1.3
% 0.21/0.35 % (249528)Termination reason: Instruction limit
% 0.21/0.35 % (249528)Termination phase: Saturation
% 0.21/0.35 % (249528)Time elapsed: 0.054 s
% 0.21/0.35 % (249528)Peak memory usage: 12 MB
% 0.21/0.35 % (249528)Instructions burned: 103 (million)
% 0.21/0.35 % (249526) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-249520-249526"...
% 0.21/0.35 % (249529)Instruction limit reached!
% 0.21/0.35 % (249529)------------------------------
% 0.21/0.35 % (249529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (249529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (249529)CaDiCaL version: 2.1.3
% 0.21/0.35 % (249529)Termination reason: Instruction limit
% 0.21/0.35 % (249529)Termination phase: Saturation
% 0.21/0.35 % (249529)Time elapsed: 0.076 s
% 0.21/0.35 % (249529)Peak memory usage: 12 MB
% 0.21/0.35 % (249529)Instructions burned: 117 (million)
% 0.21/0.35 % (249526)...printing done.
% 0.21/0.35 % (249526)Refutation found. Thanks to Tanya!
% 0.21/0.35 % SZS status Theorem for theBenchmark
% 0.21/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.35 % (249526)------------------------------
% 0.21/0.35 % (249526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (249526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (249526)CaDiCaL version: 2.1.3
% 0.21/0.35 % (249526)Termination reason: Refutation
% 0.21/0.35 % (249526)Time elapsed: 0.078 s
% 0.21/0.35 % (249526)Peak memory usage: 13 MB
% 0.21/0.35 % (249526)Instructions burned: 142 (million)
% 0.21/0.35 % (249520)Success in time 0.115 s
% 0.21/0.35 % Vampire exiting
%------------------------------------------------------------------------------