%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV447^1 : 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 : 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 08:39:31 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 115 ( 18 unt; 0 typ; 11 def)
% Number of atoms : 636 ( 153 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 586 ( 126 ~; 142 |; 0 &; 297 @)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 24 usr; 16 con; 0-4 aty)
% ( 0 !!; 10 ??; 0 @@+; 0 @@-)
% Number of variables : 61 ( 0 sgn 43 !; 6 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_3,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
sK1: sK0 > $o ).
thf(func_def_9,type,
sK2: sK0 > $o ).
thf(func_def_12,type,
sK3: sK0 ).
thf(func_def_13,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK6: 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,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 != X2 )
= ( ? [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_EQUAL_SETS_') ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 != X2 )
= ( ? [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 != X2 )
= ( ? [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 != X2 )
= ( ?? @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 != X2 )
!= ( ?? @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( sK1 != sK2 )
!= ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f12,plain,
( ( sK1 != sK2 )
!= ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( ( ( sK1 != sK2 )
= $true )
| ( ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f16,plain,
( ( ( sK1 != sK2 )
= $false )
| ( ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f17,plain,
( ( ( sK1 = sK2 )
= $true )
| ( ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( sK1 = sK2 )
| ( ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: sK0] :
( ( sK1 = sK2 )
| ( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X1: sK0] :
( ( sK1 = sK2 )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
! [X1: sK0] :
( ( sK1 = sK2 )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK2 )
!= ( ~ ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ) ),
inference(equality_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X1: sK0] :
( ( sK1 = sK2 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( $true
= ( ~ ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ) ),
inference(xor_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X1: sK0] :
( ( sK1 = sK2 )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( $false
= ( ~ ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ) ),
inference(xor_proxy_clausification,[],[f21]) ).
thf(f24,plain,
! [X1: sK0] :
( ( sK1 = sK2 )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X1: sK0] :
( ( sK1 = sK2 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f22]) ).
thf(f26,plain,
( ( ( sK1 = sK2 )
= $false )
| ( ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f15]) ).
thf(f27,plain,
( ( sK1 != sK2 )
| ( ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) )
= $true ) ),
inference(equality_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( sK1 != sK2 )
| ( $true
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( sK1 != sK2 )
| ( $true
= ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
( ( sK1 != sK2 )
| ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) ) ) ),
inference(equality_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( sK1 != sK2 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ( $false
= ( ~ ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) ) ) ),
inference(iff_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( sK1 != sK2 )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ( $true
= ( ~ ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) ) ) ),
inference(iff_proxy_clausification,[],[f30]) ).
thf(f33,plain,
( ( sK1 != sK2 )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( sK1 != sK2 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f31]) ).
thf(f49,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( ( X1 @ X2 )
= $false ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f50,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f52,definition,
( spl5_1
<=> ! [X1: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f53,plain,
( ! [X1: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f55,definition,
( spl5_2
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f56,plain,
( ( sK1 != sK2 )
| spl5_2 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f57,plain,
( ( sK1 = sK2 )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f24,f55,f52]) ).
thf(f60,definition,
( spl5_3
<=> ! [X1: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f61,plain,
( ! [X1: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f62,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f25,f55,f60]) ).
thf(f64,definition,
( spl5_4
<=> ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f66,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f68,definition,
( spl5_5
<=> ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f70,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f71,plain,
( spl5_4
| spl5_5
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f33,f55,f68,f64]) ).
thf(f73,definition,
( spl5_6
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f75,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f77,definition,
( spl5_7
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f79,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f80,plain,
( spl5_6
| spl5_7
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f34,f55,f77,f73]) ).
thf(f90,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl5_2
| ~ spl5_5 ),
inference(constrained_superposition,[],[f70,f57]) ).
thf(f91,plain,
( ( $true = $false )
| ~ spl5_4
| ~ spl5_6 ),
inference(constrained_superposition,[],[f75,f66]) ).
thf(f95,plain,
( $false
| ~ spl5_4
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f96,plain,
( ~ spl5_4
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f95]) ).
thf(f98,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl5_2
| ~ spl5_7 ),
inference(constrained_superposition,[],[f79,f57]) ).
thf(f105,plain,
( spl5_6
| ~ spl5_2
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f98,f77,f55,f73]) ).
thf(f106,plain,
( spl5_4
| ~ spl5_2
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f90,f68,f55,f64]) ).
thf(f107,plain,
( ( ( sK1 @ sK6 )
!= ( sK2 @ sK6 ) )
| spl5_2 ),
inference(negative_extensionality,[],[f56]) ).
thf(f108,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ( $true
= ( sK2 @ sK6 ) )
| spl5_2 ),
inference(xor_proxy_clausification,[],[f107]) ).
thf(f109,plain,
( ( $false
= ( sK1 @ sK6 ) )
| ( $false
= ( sK2 @ sK6 ) )
| spl5_2 ),
inference(xor_proxy_clausification,[],[f107]) ).
thf(f111,definition,
( spl5_8
<=> ( $false
= ( sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f112,plain,
( ( $false
!= ( sK2 @ sK6 ) )
| spl5_8 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f113,plain,
( ( $false
= ( sK2 @ sK6 ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f115,definition,
( spl5_9
<=> ( $false
= ( sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f117,plain,
( ( $false
= ( sK1 @ sK6 ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f115]) ).
thf(f118,plain,
( spl5_8
| spl5_9
| spl5_2 ),
inference(avatar_split_clause,[],[f109,f55,f115,f111]) ).
thf(f120,definition,
( spl5_10
<=> ( $true
= ( sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
thf(f122,plain,
( ( $true
= ( sK2 @ sK6 ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f124,definition,
( spl5_11
<=> ( $true
= ( sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
thf(f126,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f127,plain,
( spl5_10
| spl5_11
| spl5_2 ),
inference(avatar_split_clause,[],[f108,f55,f124,f120]) ).
thf(f128,plain,
( ( $true = $false )
| ~ spl5_8
| ~ spl5_10 ),
inference(constrained_superposition,[],[f122,f113]) ).
thf(f132,plain,
( $false
| ~ spl5_8
| ~ spl5_10 ),
inference(trivial_inequality_removal,[],[f128]) ).
thf(f133,plain,
( ~ spl5_8
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f132]) ).
thf(f182,plain,
( ! [X0: sK0] :
( ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f53,f49]) ).
thf(f187,plain,
( ! [X0: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f182]) ).
thf(f211,plain,
( ! [X0: sK0] :
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f61,f50]) ).
thf(f212,plain,
( ! [X0: sK0] :
( ( $true = $false )
| ( $false
= ( sK2 @ X0 ) )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f187,f50]) ).
thf(f219,plain,
( ! [X0: sK0] :
( ( $false
= ( sK2 @ X0 ) )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f212]) ).
thf(f220,plain,
( ! [X0: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f211]) ).
thf(f233,plain,
( ! [X0: sK0] :
( ( $true = $false )
| ( $false
= ( sK1 @ X0 ) )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f49,f220]) ).
thf(f234,plain,
( ! [X0: sK0] :
( ( $true
= ( sK2 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f233]) ).
thf(f243,plain,
( ( $true = $false )
| ( $false
= ( sK1 @ sK6 ) )
| ~ spl5_3
| ~ spl5_8 ),
inference(constrained_superposition,[],[f113,f234]) ).
thf(f248,plain,
( ( $false
= ( sK1 @ sK6 ) )
| ~ spl5_3
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f243]) ).
thf(f253,plain,
( spl5_9
| ~ spl5_3
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f248,f111,f60,f115]) ).
thf(f257,plain,
( ( $true = $false )
| ~ spl5_9
| ~ spl5_11 ),
inference(constrained_superposition,[],[f126,f117]) ).
thf(f258,plain,
( $false
| ~ spl5_9
| ~ spl5_11 ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f259,plain,
( ~ spl5_9
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f258]) ).
thf(f264,plain,
( ( $false != $false )
| ( $true
= ( sK1 @ sK6 ) )
| ~ spl5_1
| spl5_8 ),
inference(constrained_superposition,[],[f112,f219]) ).
thf(f266,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ~ spl5_1
| spl5_8 ),
inference(trivial_inequality_removal,[],[f264]) ).
thf(f267,plain,
( spl5_11
| ~ spl5_1
| spl5_8 ),
inference(avatar_split_clause,[],[f266,f111,f52,f124]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f58]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f62]) ).
cnf(s3,plain,
( ~ spl5_2
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f71]) ).
cnf(s4,plain,
( ~ spl5_2
| spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f80]) ).
cnf(s7,plain,
( ~ spl5_4
| ~ spl5_6 ),
inference(sat_conversion,[],[f96]) ).
cnf(s10,plain,
( ~ spl5_2
| spl5_6
| ~ spl5_7 ),
inference(sat_conversion,[],[f105]) ).
cnf(s11,plain,
( ~ spl5_2
| spl5_4
| ~ spl5_5 ),
inference(sat_conversion,[],[f106]) ).
cnf(s12,plain,
( spl5_2
| spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f118]) ).
cnf(s13,plain,
( spl5_2
| spl5_10
| spl5_11 ),
inference(sat_conversion,[],[f127]) ).
cnf(s15,plain,
( ~ spl5_8
| ~ spl5_10 ),
inference(sat_conversion,[],[f133]) ).
cnf(s19,plain,
( ~ spl5_3
| ~ spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f253]) ).
cnf(s22,plain,
( ~ spl5_9
| ~ spl5_11 ),
inference(sat_conversion,[],[f259]) ).
cnf(s24,plain,
( ~ spl5_1
| spl5_8
| spl5_11 ),
inference(sat_conversion,[],[f267]) ).
cnf(s25,plain,
( spl5_4
| ~ spl5_2 ),
inference(rat,[],[s3,s11]) ).
cnf(s26,plain,
( spl5_6
| ~ spl5_2 ),
inference(rat,[],[s4,s10]) ).
cnf(s27,plain,
~ spl5_2,
inference(rat,[],[s26,s7,s25]) ).
cnf(s28,plain,
spl5_3,
inference(rat,[],[s2,s27]) ).
cnf(s29,plain,
spl5_1,
inference(rat,[],[s1,s27]) ).
cnf(s30,plain,
spl5_8,
inference(rat,[],[s22,s12,s24,s27,s29]) ).
cnf(s31,plain,
~ spl5_10,
inference(rat,[],[s15,s30]) ).
cnf(s32,plain,
spl5_9,
inference(rat,[],[s19,s28,s30]) ).
cnf(s33,plain,
spl5_11,
inference(rat,[],[s13,s27,s31]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s22,s33,s32]) ).
thf(f268,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV447^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 % Computer : n003.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 15:50:13 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.20/0.30 % (2665174)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (2665183)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=131073696:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (2665183)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (2665180)% WARNING: option uhcvi not known.
% 0.20/0.30 % (2665179)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3639675795_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (2665180)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=940090507:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (2665181)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=645036148:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (2665182)dis+10_1_sil=32000:sp=arity:random_seed=691364258:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (2665180)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (2665180)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.30 % (2665184)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3414447898:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (2665185)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1047302611:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % (2665185) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2665174-2665185"...
% 0.20/0.30 % (2665182) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2665174-2665182"...
% 0.20/0.30 % (2665185)...printing done.
% 0.20/0.30 % (2665182)...printing done.
% 0.20/0.30 % (2665185)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (2665185)------------------------------
% 0.20/0.30 % (2665185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2665185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2665185)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2665185)Termination reason: Refutation
% 0.20/0.30 % (2665185)Time elapsed: 0.009 s
% 0.20/0.30 % (2665185)Peak memory usage: 13 MB
% 0.20/0.30 % (2665185)Instructions burned: 13 (million)
% 0.20/0.30 % (2665174)Success in time 0.062 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------