%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV458^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:38:40 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 137 ( 19 unt; 0 typ; 8 def)
% Number of atoms : 830 ( 177 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 951 ( 130 ~; 183 |; 6 &; 623 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 11 con; 0-4 aty)
% Number of variables : 151 ( 0 sgn 143 !; 8 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
sK1: sK0 > $o ).
thf(func_def_6,type,
sK2: sK0 > $o ).
thf(func_def_7,type,
sK3: sK0 > $o ).
thf(func_def_8,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(func_def_10,type,
sK5: sK0 ).
thf(f1,axiom,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X3: X0,X2: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > $o,X3: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= ( 'const/sets/UNION' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/UNION_ACI_2') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X3: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= ( 'const/sets/UNION' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X3 )
| ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X3: X0 > $o,X2: X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= $true )
<=> ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ X3 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= ( X2 @ X1 ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > $o,X3: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X3 @ X2 ) )
= ( 'const/sets/UNION' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
? [X0: $tType,X3: X0 > $o,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X3 @ X2 ) )
!= ( 'const/sets/UNION' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
!= ( 'const/sets/UNION' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f13]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X3: X0 > $o,X2: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true )
& ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ X3 ) ) ) )
& ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ X3 ) )
| ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > $o,X3: X0 > $o,X2: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true )
& ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ X3 ) ) ) )
& ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ X3 ) )
| ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
!= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
!= $true ) ) )
& ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
!= $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f21,plain,
( ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f22,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f23,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f24,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= ( X2 @ X1 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f33,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) )
| ( $false
= ( X2 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f27]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f27]) ).
thf(f37,plain,
( ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 )
!= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) ),
inference(negative_extensionality,[],[f21]) ).
thf(f38,plain,
( ( $true
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) )
| ( $true
= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) ) ),
inference(xor_proxy_clausification,[],[f37]) ).
thf(f39,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) )
| ( ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 )
= $false ) ),
inference(xor_proxy_clausification,[],[f37]) ).
thf(f41,definition,
( spl6_1
<=> ( ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f42,plain,
( ( ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 )
!= $false )
| spl6_1 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f43,plain,
( ( ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 )
= $false )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f45,definition,
( spl6_2
<=> ( $false
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f47,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f39,f45,f41]) ).
thf(f50,definition,
( spl6_3
<=> ( $true
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f52,plain,
( ( $true
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f54,definition,
( spl6_4
<=> ( $true
= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f56,plain,
( ( $true
= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f57,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f38,f54,f50]) ).
thf(f65,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true != $true )
| ( $false
= ( X2 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(constrained_superposition,[],[f23,f33]) ).
thf(f66,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X3 @ X2 ) )
= $true )
| ( $false
= ( X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f68,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0,X4: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ) )
| ( $true != $true )
| ( ( X3 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f23,f66]) ).
thf(f69,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( X3 @ X1 )
= $false )
| ( $true = $false )
| ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) ) ),
inference(constrained_superposition,[],[f34,f66]) ).
thf(f70,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( ( X3 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f72,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0,X4: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ) )
| ( ( X3 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f74,plain,
( ( $true = $false )
| ( ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 @ sK5 )
= $false )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f43,f70]) ).
thf(f76,plain,
( ( ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 @ sK5 )
= $false )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f79,plain,
( ( ( sK3 @ sK5 )
= $false )
| ( $true = $false )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f70,f76]) ).
thf(f83,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $false
= ( X2 @ X1 ) )
| ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ) ),
inference(constrained_superposition,[],[f24,f33]) ).
thf(f86,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) )
| ( $false
= ( X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f89,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0,X4: X0 > $o] :
( ( $false
= ( X2 @ X1 ) )
| ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ) ) ),
inference(constrained_superposition,[],[f23,f86]) ).
thf(f90,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $false
= ( X2 @ X1 ) )
| ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f34,f86]) ).
thf(f91,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $false
= ( X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f94,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0,X4: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ) )
| ( $false
= ( X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f95,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true = $false )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f91,f43]) ).
thf(f99,plain,
( ( $true = $false )
| ( ( sK2 @ sK5 )
= $false )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f76,f91]) ).
thf(f100,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f102,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f104,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0,X4: X0 > $o] :
( ( $true = $false )
| ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X1 ) )
| ( ( X4 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f72,f34]) ).
thf(f108,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0,X4: X0 > $o] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X1 ) )
| ( ( X4 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f136,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0,X4: X0 > $o] :
( ( ( X3 @ X1 )
= $false )
| ( $true = $false )
| ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X1 ) ) ),
inference(constrained_superposition,[],[f34,f94]) ).
thf(f138,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0,X4: X0 > $o] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X3 @ X4 ) @ X1 ) )
| ( ( X3 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f147,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true )
| ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $false )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f22,f33]) ).
thf(f155,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $false )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f172,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) )
| ( $true = $false )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f52,f155]) ).
thf(f187,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f192,definition,
( spl6_5
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f193,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| spl6_5 ),
inference(avatar_component_clause,[],[f192]) ).
thf(f194,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f192]) ).
thf(f196,definition,
( spl6_6
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f198,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f201,plain,
( spl6_5
| spl6_6
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f187,f50,f196,f192]) ).
thf(f202,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $true = $false )
| ~ spl6_5 ),
inference(constrained_superposition,[],[f194,f34]) ).
thf(f209,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f202]) ).
thf(f213,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_5 ),
inference(forward_demodulation,[],[f209,f102]) ).
thf(f214,plain,
( $false
| ~ spl6_1
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f213]) ).
thf(f215,plain,
( ~ spl6_1
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f214]) ).
thf(f245,plain,
( ( $false != $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| spl6_1 ),
inference(constrained_superposition,[],[f42,f155]) ).
thf(f250,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| spl6_1 ),
inference(trivial_inequality_removal,[],[f245]) ).
thf(f252,plain,
( ( $true = $false )
| ( ( sK2 @ sK5 )
= $false )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f47,f91]) ).
thf(f254,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( $true = $false )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f47,f138]) ).
thf(f260,plain,
( ( $true = $false )
| ( ( sK3 @ sK5 )
= $false )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f108,f47]) ).
thf(f263,plain,
( ( ( sK3 @ sK5 )
= $false )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f260]) ).
thf(f265,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f269,plain,
( ( ( sK2 @ sK5 )
= $false )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f252]) ).
thf(f276,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_5 ),
inference(forward_demodulation,[],[f269,f209]) ).
thf(f277,plain,
( $false
| ~ spl6_2
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f278,plain,
( ~ spl6_2
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f277]) ).
thf(f280,definition,
( spl6_7
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f282,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f284,definition,
( spl6_8
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f285,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| spl6_8 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f286,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f287,plain,
( spl6_7
| spl6_8
| spl6_1 ),
inference(avatar_split_clause,[],[f250,f41,f284,f280]) ).
thf(f294,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK5 ) )
| ~ spl6_8 ),
inference(constrained_superposition,[],[f34,f286]) ).
thf(f298,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f294]) ).
thf(f302,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_8 ),
inference(forward_demodulation,[],[f298,f265]) ).
thf(f303,plain,
( $false
| ~ spl6_2
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f302]) ).
thf(f304,plain,
( ~ spl6_2
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f303]) ).
thf(f320,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ( $true != $true )
| ~ spl6_7 ),
inference(constrained_superposition,[],[f22,f282]) ).
thf(f323,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f326,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| spl6_5
| ~ spl6_7 ),
inference(forward_subsumption_resolution,[],[f323,f193]) ).
thf(f335,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK5 ) )
| spl6_5
| ~ spl6_7 ),
inference(constrained_superposition,[],[f34,f326]) ).
thf(f339,plain,
( ( $true
= ( sK3 @ sK5 ) )
| spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f335]) ).
thf(f343,plain,
( ( $true = $false )
| ~ spl6_2
| spl6_5
| ~ spl6_7 ),
inference(forward_demodulation,[],[f339,f263]) ).
thf(f344,plain,
( $false
| ~ spl6_2
| spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f343]) ).
thf(f345,plain,
( ~ spl6_2
| spl6_5
| ~ spl6_7 ),
inference(avatar_contradiction_clause,[],[f344]) ).
thf(f353,plain,
( ( ( sK3 @ sK5 )
= $false )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f358,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_4 ),
inference(forward_demodulation,[],[f43,f56]) ).
thf(f359,plain,
( $false
| ~ spl6_1
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f358]) ).
thf(f360,plain,
( ~ spl6_1
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f359]) ).
thf(f381,plain,
( ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ~ spl6_6 ),
inference(constrained_superposition,[],[f22,f198]) ).
thf(f384,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f381]) ).
thf(f387,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ~ spl6_6
| spl6_8 ),
inference(forward_subsumption_resolution,[],[f384,f285]) ).
thf(f388,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK5 ) )
| ~ spl6_6
| spl6_8 ),
inference(constrained_superposition,[],[f387,f34]) ).
thf(f394,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl6_6
| spl6_8 ),
inference(trivial_inequality_removal,[],[f388]) ).
thf(f399,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_6
| spl6_8 ),
inference(forward_demodulation,[],[f394,f353]) ).
thf(f400,plain,
( $false
| ~ spl6_1
| ~ spl6_6
| spl6_8 ),
inference(trivial_inequality_removal,[],[f399]) ).
thf(f401,plain,
( ~ spl6_1
| ~ spl6_6
| spl6_8 ),
inference(avatar_contradiction_clause,[],[f400]) ).
thf(f413,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_8 ),
inference(forward_demodulation,[],[f298,f100]) ).
thf(f414,plain,
( $false
| ~ spl6_1
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f413]) ).
thf(f415,plain,
( ~ spl6_1
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f414]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f57]) ).
cnf(s6,plain,
( ~ spl6_3
| spl6_5
| spl6_6 ),
inference(sat_conversion,[],[f201]) ).
cnf(s8,plain,
( ~ spl6_1
| ~ spl6_5 ),
inference(sat_conversion,[],[f215]) ).
cnf(s12,plain,
( ~ spl6_2
| ~ spl6_5 ),
inference(sat_conversion,[],[f278]) ).
cnf(s13,plain,
( spl6_1
| spl6_7
| spl6_8 ),
inference(sat_conversion,[],[f287]) ).
cnf(s15,plain,
( ~ spl6_2
| ~ spl6_8 ),
inference(sat_conversion,[],[f304]) ).
cnf(s17,plain,
( ~ spl6_2
| spl6_5
| ~ spl6_7 ),
inference(sat_conversion,[],[f345]) ).
cnf(s18,plain,
( ~ spl6_1
| ~ spl6_4 ),
inference(sat_conversion,[],[f360]) ).
cnf(s22,plain,
( ~ spl6_1
| ~ spl6_6
| spl6_8 ),
inference(sat_conversion,[],[f401]) ).
cnf(s26,plain,
( ~ spl6_1
| ~ spl6_8 ),
inference(sat_conversion,[],[f415]) ).
cnf(s27,plain,
spl6_1,
inference(rat,[],[s17,s13,s12,s15,s1]) ).
cnf(s28,plain,
~ spl6_8,
inference(rat,[],[s26,s27]) ).
cnf(s29,plain,
~ spl6_6,
inference(rat,[],[s22,s28,s27]) ).
cnf(s30,plain,
~ spl6_4,
inference(rat,[],[s18,s27]) ).
cnf(s31,plain,
~ spl6_5,
inference(rat,[],[s8,s27]) ).
cnf(s32,plain,
spl6_3,
inference(rat,[],[s2,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s6,s29,s31,s32]) ).
thf(f416,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV458^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n001.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 15:54:51 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.32 % (1410449)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.32 % (1410463)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=4156798886: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)
% 0.20/0.32 % (1410466)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.32 % (1410466)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
% 0.20/0.32 % (1410460)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3382206362:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.32 % (1410461)lrs+10_16_si=on:nwc=1.5:random_seed=1400985197:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.32 % (1410465)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1253822860:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.32 % (1410462)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=367551728:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.32 % (1410464)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=977628458:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.32 % (1410466)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=4010097060:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.32 % (1410462)Instruction limit reached!
% 0.20/0.32 % (1410462)------------------------------
% 0.20/0.32 % (1410462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (1410462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (1410462)CaDiCaL version: 2.1.3
% 0.20/0.32 % (1410462)Termination reason: Instruction limit
% 0.20/0.32 % (1410462)Termination phase: Saturation
% 0.20/0.32 % (1410462)Time elapsed: 0.003 s
% 0.20/0.32 % (1410462)Peak memory usage: 12 MB
% 0.20/0.32 % (1410462)Instructions burned: 4 (million)
% 0.20/0.32 % (1410461)Instruction limit reached!
% 0.20/0.32 % (1410461)------------------------------
% 0.20/0.32 % (1410461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (1410461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (1410461)CaDiCaL version: 2.1.3
% 0.20/0.32 % (1410461)Termination reason: Instruction limit
% 0.20/0.32 % (1410461)Termination phase: Saturation
% 0.20/0.32 % (1410461)Time elapsed: 0.012 s
% 0.20/0.32 % (1410461)Peak memory usage: 12 MB
% 0.20/0.32 % (1410461)Instructions burned: 19 (million)
% 0.20/0.32 % (1410464)Instruction limit reached!
% 0.20/0.32 % (1410464)------------------------------
% 0.20/0.32 % (1410464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (1410464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (1410464)CaDiCaL version: 2.1.3
% 0.20/0.32 % (1410464)Termination reason: Instruction limit
% 0.20/0.32 % (1410464)Termination phase: Saturation
% 0.20/0.32 % (1410464)Time elapsed: 0.015 s
% 0.20/0.32 % (1410464)Peak memory usage: 12 MB
% 0.20/0.32 % (1410464)Instructions burned: 25 (million)
% 0.20/0.32 % (1410460) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1410449-1410460"...
% 0.20/0.32 % (1410477)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3132934290:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.32 % (1410460)...printing done.
% 0.20/0.32 % (1410460)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.32 % (1410460)------------------------------
% 0.20/0.32 % (1410460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (1410460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (1410460)CaDiCaL version: 2.1.3
% 0.20/0.32 % (1410460)Termination reason: Refutation
% 0.20/0.32 % (1410460)Time elapsed: 0.022 s
% 0.20/0.32 % (1410460)Peak memory usage: 13 MB
% 0.20/0.32 % (1410460)Instructions burned: 36 (million)
% 0.20/0.32 % (1410449)Success in time 0.055 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------