%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV465^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:41:18 AM UTC 2026
% Result : Theorem 1.80s 1.56s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 6 unt; 0 typ; 6 def)
% Number of atoms : 519 ( 145 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 800 ( 97 ~; 94 |; 30 &; 558 @)
% ( 8 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 10 con; 0-5 aty)
% Number of variables : 149 ( 0 ^; 113 !; 36 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK1: $tType ).
thf(type_def_7,type,
sK2: $tType ).
thf(func_def_0,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/IMAGE':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > $o ) > X1 > $o ) ).
thf(func_def_5,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > $o ) > X0 > X1 ) ).
thf(func_def_6,type,
sK3: sK1 > $o ).
thf(func_def_7,type,
sK4: sK2 > sK1 ).
thf(func_def_8,type,
sK5: sK2 > $o ).
thf(func_def_9,type,
sK6: sK2 ).
thf(func_def_10,type,
sK7: sK1 ).
thf(func_def_12,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f90,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f35,f44,f53,f54,f55,f61,f67,f89]) ).
thf(f89,plain,
( ~ spl8_1
| ~ spl8_4
| spl8_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f88]) ).
thf(f88,plain,
( $false
| ~ spl8_1
| ~ spl8_4
| spl8_6 ),
inference(subsumption_resolution,[status(thm)],[f87,f52]) ).
thf(f52,plain,
( ( $true
!= ( sK3 @ sK7 ) )
| spl8_6 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl8_6
<=> ( $true
= ( sK3 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition]) ).
thf(f87,plain,
( ( $true
= ( sK3 @ sK7 ) )
| ~ spl8_1
| ~ spl8_4 ),
inference(forward_demodulation,[status(thm)],[f85,f72]) ).
thf(f72,plain,
( ( ( sK4 @ ( sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK7 ) )
= sK7 )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ( sK4 @ ( sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK7 ) )
= sK7 )
| ( $true != $true )
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f20,f43]) ).
thf(f43,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl8_4
<=> ( $true
= ( 'const/sets/IN' @ sK1 @ sK7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f20,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ( ( X4 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) )
= X2 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ! [X5: X1] :
( ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
| ( ( X4 @ X5 )
!= X2 ) ) )
& ( ( ( $true
= ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) @ X3 ) )
& ( ( X4 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) )
= X2 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).
thf(f12,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ? [X6: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X6 @ X3 ) )
& ( ( X4 @ X6 )
= X2 ) )
=> ( ( $true
= ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) @ X3 ) )
& ( ( X4 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) )
= X2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ! [X5: X1] :
( ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
| ( ( X4 @ X5 )
!= X2 ) ) )
& ( ? [X6: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X6 @ X3 ) )
& ( ( X4 @ X6 )
= X2 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ! [X5: X1] :
( ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
| ( ( X4 @ X5 )
!= X2 ) ) )
& ( ? [X5: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
& ( ( X4 @ X5 )
= X2 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
<=> ? [X5: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
& ( ( X4 @ X5 )
= X2 ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
? [X5: X1] :
( ( ( ( X4 @ X5 )
= X2 )
& ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $tType,X0: $tType,X2: X1,X3: X0 > $o,X4: X0 > X1] :
? [X5: X0] :
( ( ( ( X4 @ X5 )
= X2 )
& ( 'const/sets/IN' @ X0 @ X5 @ X3 ) )
= ( 'const/sets/IN' @ X1 @ X2 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tAjIH6MiAz/DTF2THF_14612.p','thm/sets/IN_IMAGE_') ).
thf(f85,plain,
( ( ( sK3 @ ( sK4 @ ( sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK7 ) ) )
= $true )
| ~ spl8_1
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $true != $true )
| ( ( sK3 @ ( sK4 @ ( sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK7 ) ) )
= $true )
| ~ spl8_1
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f64,f43]) ).
thf(f64,plain,
( ! [X0: $tType,X2: X0,X1: sK2 > X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK5 ) )
!= $true )
| ( $true
= ( sK3 @ ( sK4 @ ( sK0 @ X0 @ sK2 @ X1 @ sK5 @ X2 ) ) ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ! [X0: $tType,X2: X0,X1: sK2 > X0] :
( ( $true != $true )
| ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK5 ) )
!= $true )
| ( $true
= ( sK3 @ ( sK4 @ ( sK0 @ X0 @ sK2 @ X1 @ sK5 @ X2 ) ) ) ) )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f31,f21]) ).
thf(f21,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( $true
= ( 'const/sets/IN' @ X1 @ ( sK0 @ X0 @ X1 @ X4 @ X3 @ X2 ) @ X3 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f31,plain,
( ! [X7: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X7 @ sK5 ) )
| ( $true
= ( sK3 @ ( sK4 @ X7 ) ) ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl8_1
<=> ! [X7: sK2] :
( ( $true
= ( sK3 @ ( sK4 @ X7 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X7 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f67,plain,
( ~ spl8_1
| ~ spl8_3
| spl8_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
| ~ spl8_1
| ~ spl8_3
| spl8_5 ),
inference(subsumption_resolution,[status(thm)],[f65,f48]) ).
thf(f48,plain,
( ( $true
!= ( sK3 @ ( sK4 @ sK6 ) ) )
| spl8_5 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl8_5
<=> ( $true
= ( sK3 @ ( sK4 @ sK6 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition]) ).
thf(f65,plain,
( ( $true
= ( sK3 @ ( sK4 @ sK6 ) ) )
| ~ spl8_1
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true != $true )
| ( $true
= ( sK3 @ ( sK4 @ sK6 ) ) )
| ~ spl8_1
| ~ spl8_3 ),
inference(superposition,[status(thm)],[f31,f39]) ).
thf(f39,plain,
( ( $true
= ( 'const/sets/IN' @ sK2 @ sK6 @ sK5 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl8_3
<=> ( $true
= ( 'const/sets/IN' @ sK2 @ sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f61,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f60,f33,f30]) ).
thf(f33,definition,
( spl8_2
<=> ! [X8: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X8 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) )
!= $true )
| ( $true
= ( sK3 @ X8 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f60,plain,
( ! [X0: sK2] :
( ( ( sK3 @ ( sK4 @ X0 ) )
= $true )
| ( ( 'const/sets/IN' @ sK2 @ X0 @ sK5 )
!= $true ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ! [X0: sK2] :
( ( ( 'const/sets/IN' @ sK2 @ X0 @ sK5 )
!= $true )
| ( $true != $true )
| ( ( sK3 @ ( sK4 @ X0 ) )
= $true ) )
| ~ spl8_2 ),
inference(superposition,[status(thm)],[f34,f28]) ).
thf(f28,plain,
! [X1: $tType,X0: $tType,X3: X1 > $o,X4: X1 > X0,X5: X1] :
( ( $true
= ( 'const/sets/IN' @ X0 @ ( X4 @ X5 ) @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) ) ),
inference(equality_resolution,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0,X5: X1] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X5 @ X3 ) )
| ( ( X4 @ X5 )
!= X2 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f34,plain,
( ! [X8: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X8 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) )
!= $true )
| ( $true
= ( sK3 @ X8 ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f55,plain,
( ~ spl8_6
| spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f26,f37,f50]) ).
thf(f26,plain,
( ( $true
!= ( sK3 @ sK7 ) )
| ( $true
= ( 'const/sets/IN' @ sK2 @ sK6 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ( $true
= ( 'const/sets/IN' @ sK2 @ sK6 @ sK5 ) )
& ( $true
!= ( sK3 @ ( sK4 @ sK6 ) ) ) )
| ( ( $true
= ( 'const/sets/IN' @ sK1 @ sK7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) )
& ( $true
!= ( sK3 @ sK7 ) ) ) )
& ( ! [X7: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X7 @ sK5 ) )
| ( $true
= ( sK3 @ ( sK4 @ X7 ) ) ) )
| ! [X8: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X8 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) )
!= $true )
| ( $true
= ( sK3 @ X8 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f15,f18,f17,f16]) ).
thf(f16,plain,
( ? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ( ? [X5: X1] :
( ( ( 'const/sets/IN' @ X1 @ X5 @ X4 )
= $true )
& ( $true
!= ( X2 @ ( X3 @ X5 ) ) ) )
| ? [X6: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) )
& ( ( X2 @ X6 )
!= $true ) ) )
& ( ! [X7: X1] :
( ( ( 'const/sets/IN' @ X1 @ X7 @ X4 )
!= $true )
| ( ( X2 @ ( X3 @ X7 ) )
= $true ) )
| ! [X8: X0] :
( ( ( 'const/sets/IN' @ X0 @ X8 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) )
!= $true )
| ( $true
= ( X2 @ X8 ) ) ) ) )
=> ( ( ? [X5: sK2] :
( ( ( 'const/sets/IN' @ sK2 @ X5 @ sK5 )
= $true )
& ( $true
!= ( sK3 @ ( sK4 @ X5 ) ) ) )
| ? [X6: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X6 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) )
= $true )
& ( $true
!= ( sK3 @ X6 ) ) ) )
& ( ! [X7: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X7 @ sK5 ) )
| ( $true
= ( sK3 @ ( sK4 @ X7 ) ) ) )
| ! [X8: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X8 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) )
!= $true )
| ( $true
= ( sK3 @ X8 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X5: sK2] :
( ( ( 'const/sets/IN' @ sK2 @ X5 @ sK5 )
= $true )
& ( $true
!= ( sK3 @ ( sK4 @ X5 ) ) ) )
=> ( ( $true
= ( 'const/sets/IN' @ sK2 @ sK6 @ sK5 ) )
& ( $true
!= ( sK3 @ ( sK4 @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X6: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X6 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) )
= $true )
& ( $true
!= ( sK3 @ X6 ) ) )
=> ( ( $true
= ( 'const/sets/IN' @ sK1 @ sK7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) )
& ( $true
!= ( sK3 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ( ? [X5: X1] :
( ( ( 'const/sets/IN' @ X1 @ X5 @ X4 )
= $true )
& ( $true
!= ( X2 @ ( X3 @ X5 ) ) ) )
| ? [X6: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X6 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) )
& ( ( X2 @ X6 )
!= $true ) ) )
& ( ! [X7: X1] :
( ( ( 'const/sets/IN' @ X1 @ X7 @ X4 )
!= $true )
| ( ( X2 @ ( X3 @ X7 ) )
= $true ) )
| ! [X8: X0] :
( ( ( 'const/sets/IN' @ X0 @ X8 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) )
!= $true )
| ( $true
= ( X2 @ X8 ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ( ? [X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X4 )
= $true )
& ( ( X2 @ ( X3 @ X6 ) )
!= $true ) )
| ? [X5: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) )
& ( $true
!= ( X2 @ X5 ) ) ) )
& ( ! [X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X4 )
!= $true )
| ( ( X2 @ ( X3 @ X6 ) )
= $true ) )
| ! [X5: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) )
| ( $true
= ( X2 @ X5 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ! [X5: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) )
| ( $true
= ( X2 @ X5 ) ) )
<~> ! [X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X4 )
!= $true )
| ( ( X2 @ ( X3 @ X6 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ! [X5: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) ) )
=> ( $true
= ( X2 @ X5 ) ) )
<=> ! [X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X4 )
= $true )
=> ( ( X2 @ ( X3 @ X6 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) )
=> ( X2 @ X5 ) )
= ( ! [X6: X1] :
( ( 'const/sets/IN' @ X1 @ X6 @ X4 )
=> ( X2 @ ( X3 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $tType,X2: $tType,X6: X0 > $o,X3: X2 > X0,X4: X2 > $o,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X2 @ X0 @ X3 @ X4 ) )
=> ( X6 @ X5 ) )
= ( ! [X5: X2] :
( ( 'const/sets/IN' @ X2 @ X5 @ X4 )
=> ( X6 @ ( X3 @ X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $tType,X2: $tType,X6: X0 > $o,X3: X2 > X0,X4: X2 > $o,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X2 @ X0 @ X3 @ X4 ) )
=> ( X6 @ X5 ) )
= ( ! [X5: X2] :
( ( 'const/sets/IN' @ X2 @ X5 @ X4 )
=> ( X6 @ ( X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tAjIH6MiAz/DTF2THF_14612.p','thm/sets/FORALL_IN_IMAGE_') ).
thf(f54,plain,
( spl8_4
| ~ spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f25,f46,f41]) ).
thf(f25,plain,
( ( $true
!= ( sK3 @ ( sK4 @ sK6 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f53,plain,
( ~ spl8_5
| ~ spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f24,f50,f46]) ).
thf(f24,plain,
( ( $true
!= ( sK3 @ sK7 ) )
| ( $true
!= ( sK3 @ ( sK4 @ sK6 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f44,plain,
( spl8_3
| spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f27,f41,f37]) ).
thf(f27,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK7 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK2 @ sK6 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f35,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f23,f33,f30]) ).
thf(f23,plain,
! [X8: sK1,X7: sK2] :
( ( $true
= ( sK3 @ ( sK4 @ X7 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X7 @ sK5 ) )
| ( ( 'const/sets/IN' @ sK1 @ X8 @ ( 'const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5 ) )
!= $true )
| ( $true
= ( sK3 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV465^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:47:51 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SEV465^1 : TPTP v9.2.1. Released v7.0.0.
% 0.33/0.49 % Domain : Analysis
% 0.33/0.49 % Problem : FORALL_IN_IMAGE
% 0.33/0.49 % Version : Especial.
% 0.33/0.49 % English :
% 0.33/0.49
% 0.33/0.49 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.33/0.49 % Source : [Kal16]
% 0.33/0.49 % Names : FORALL_IN_IMAGE_.p [Kal16]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % Rating : 0.00 v7.1.0
% 0.33/0.49 % Syntax : Number of formulae : 4 ( 2 unt; 2 typ; 0 def)
% 0.33/0.49 % Number of atoms : 9 ( 3 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 1 ( 4 avg)
% 0.33/0.49 % Number of connectives : 27 ( 0 ~; 0 |; 1 &; 24 @)
% 0.33/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 6 ( 6 avg)
% 0.33/0.49 % Number of types : 1 ( 0 usr)
% 0.33/0.49 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 3 ( 2 usr; 0 con; 2-5 aty)
% 0.33/0.49 % Number of variables : 16 ( 0 ^; 12 !; 1 ?; 16 :)
% 0.33/0.49 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.33/0.49 % SPC : TH1_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : Exported from core HOL Light.
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf('thf_const_const/sets/IN',type,
% 0.33/0.49 'const/sets/IN':
% 0.33/0.49 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.33/0.49
% 0.33/0.49 thf('thf_const_const/sets/IMAGE',type,
% 0.33/0.49 'const/sets/IMAGE':
% 0.33/0.49 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > $o ) > B > $o ) ).
% 0.33/0.49
% 0.33/0.49 thf('thm/sets/IN_IMAGE_',axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,A0: B,A1: A > $o,A2: A > B] :
% 0.33/0.49 ( ( 'const/sets/IN' @ B @ A0 @ ( 'const/sets/IMAGE' @ A @ B @ A2 @ A1 ) )
% 0.33/0.49 = ( ? [A3: A] :
% 0.33/0.49 ( ( A0
% 0.33/0.49 = ( A2 @ A3 ) )
% 0.33/0.49 & ( 'const/sets/IN' @ A @ A3 @ A1 ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf('thm/sets/FORALL_IN_IMAGE_',conjecture,
% 0.33/0.49 ! [A: $tType,A0: $tType,P: A > $o,A1: A0 > A,A2: A0 > $o] :
% 0.33/0.49 ( ( ! [A3: A] :
% 0.33/0.49 ( ( 'const/sets/IN' @ A @ A3 @ ( 'const/sets/IMAGE' @ A0 @ A @ A1 @ A2 ) )
% 0.33/0.49 => ( P @ A3 ) ) )
% 0.33/0.49 = ( ! [A3: A0] :
% 0.33/0.49 ( ( 'const/sets/IN' @ A0 @ A3 @ A2 )
% 0.33/0.49 => ( P @ ( A1 @ A3 ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.80/1.52 ---- Embedded in THF ---
% 1.80/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.80/1.52 %%% Generated on Tue Feb 24 12:47:52 EST 2026
% 1.80/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 1.80/1.52 %%% Logic specification used:
% 1.80/1.52 %%% thf(spec, logic, $$dhol).
% 1.80/1.52
% 1.80/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tAjIH6MiAz/DTF2DTF14612.p
% See solution above
% 1.80/1.52 ------------------------
% 1.80/1.53 ---- Cleaned THF ---
% 1.80/1.53 thf('thf_const_const/sets/IN',type,
% 1.80/1.53 'const/sets/IN':
% 1.80/1.53 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.80/1.53
% 1.80/1.53 thf('thf_const_const/sets/IMAGE',type,
% 1.80/1.53 'const/sets/IMAGE':
% 1.80/1.53 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > $o ) > B > $o ) ).
% 1.80/1.53
% 1.80/1.53 thf('thm/sets/IN_IMAGE_',axiom,
% 1.80/1.53 ! [B: $tType,A: $tType,A0: B,A1: A > $o,A2: A > B] :
% 1.80/1.53 ( ( 'const/sets/IN' @ B @ A0 @ ( 'const/sets/IMAGE' @ A @ B @ A2 @ A1 ) )
% 1.80/1.53 = ( ? [A3: A] :
% 1.80/1.53 ( ( A0
% 1.80/1.53 = ( A2 @ A3 ) )
% 1.80/1.53 & ( 'const/sets/IN' @ A @ A3 @ A1 ) ) ) ) ).
% 1.80/1.53
% 1.80/1.53 thf('thm/sets/FORALL_IN_IMAGE_',conjecture,
% 1.80/1.53 ! [A: $tType,A0: $tType,P: A > $o,A1: A0 > A,A2: A0 > $o] :
% 1.80/1.53 ( ( ! [A3: A] :
% 1.80/1.53 ( ( 'const/sets/IN' @ A @ A3 @ ( 'const/sets/IMAGE' @ A0 @ A @ A1 @ A2 ) )
% 1.80/1.53 => ( P @ A3 ) ) )
% 1.80/1.53 = ( ! [A3: A0] :
% 1.80/1.53 ( ( 'const/sets/IN' @ A0 @ A3 @ A2 )
% 1.80/1.53 => ( P @ ( A1 @ A3 ) ) ) ) ) ).
% 1.80/1.53 ------------------------
% 1.80/1.55 % (14749)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14612 for (2999ds/2Mi)
% 1.80/1.55 % (14746)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14612 for (2999ds/183Mi)
% 1.80/1.55 % (14747)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_14612 for (2999ds/4Mi)
% 1.80/1.55 % (14752)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14612 for (2999ds/18Mi)
% 1.80/1.55 % (14748)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_14612 for (2999ds/27Mi)
% 1.80/1.55 % (14751)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_14612 for (2999ds/275Mi)
% 1.80/1.55 % (14750)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_14612 for (2999ds/2Mi)
% 1.80/1.55 % Exception at run slice level
% 1.80/1.55 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.80/1.55 % (14749)Instruction limit reached!
% 1.80/1.55 % (14749)------------------------------
% 1.80/1.55 % (14749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.55 % (14749)Termination reason: Unknown
% 1.80/1.55 % (14749)Termination phase: Saturation
% 1.80/1.55
% 1.80/1.55 % (14749)Memory used [KB]: 5500
% 1.80/1.55 % (14749)Time elapsed: 0.003 s
% 1.80/1.55 % (14749)Instructions burned: 2 (million)
% 1.80/1.55 % (14749)------------------------------
% 1.80/1.55 % (14749)------------------------------
% 1.80/1.55 % (14747)Instruction limit reached!
% 1.80/1.55 % (14747)------------------------------
% 1.80/1.55 % (14747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.55 % (14747)Termination reason: Unknown
% 1.80/1.55 % (14747)Termination phase: Saturation
% 1.80/1.55
% 1.80/1.55 % (14747)Memory used [KB]: 5500
% 1.80/1.55 % (14747)Time elapsed: 0.005 s
% 1.80/1.55 % (14747)Instructions burned: 5 (million)
% 1.80/1.55 % (14747)------------------------------
% 1.80/1.55 % (14747)------------------------------
% 1.80/1.56 % (14751)First to succeed.
% 1.80/1.56 % (14752)Instruction limit reached!
% 1.80/1.56 % (14752)------------------------------
% 1.80/1.56 % (14752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.56 % (14752)Termination reason: Unknown
% 1.80/1.56 % (14752)Termination phase: Saturation
% 1.80/1.56
% 1.80/1.56 % (14752)Memory used [KB]: 5756
% 1.80/1.56 % (14752)Time elapsed: 0.012 s
% 1.80/1.56 % (14752)Instructions burned: 19 (million)
% 1.80/1.56 % (14752)------------------------------
% 1.80/1.56 % (14752)------------------------------
% 1.80/1.56 % (14751)Refutation found. Thanks to Tanya!
% 1.80/1.56 % SZS status Theorem for DTF2THF_14612
% 1.80/1.56 % SZS output start Proof for DTF2THF_14612
% 1.80/1.56 thf(type_def_6, type, sK1: $tType).
% 1.80/1.56 thf(type_def_7, type, sK2: $tType).
% 1.80/1.56 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.80/1.56 thf(func_def_1, type, 'const/sets/IMAGE': !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > $o) > X1 > $o)).
% 1.80/1.56 thf(func_def_5, type, sK0: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > $o) > X0 > X1)).
% 1.80/1.56 thf(func_def_6, type, sK3: sK1 > $o).
% 1.80/1.56 thf(func_def_7, type, sK4: sK2 > sK1).
% 1.80/1.56 thf(func_def_8, type, sK5: sK2 > $o).
% 1.80/1.56 thf(func_def_9, type, sK6: sK2).
% 1.80/1.56 thf(func_def_10, type, sK7: sK1).
% 1.80/1.56 thf(func_def_12, type, ph9: !>[X0: $tType]:(X0)).
% 1.80/1.56 thf(f90,plain,(
% 1.80/1.56 $false),
% 1.80/1.56 inference(avatar_sat_refutation,[status(thm)],[f35,f44,f53,f54,f55,f61,f67,f89])).
% 1.80/1.56 thf(f89,plain,(
% 1.80/1.56 ~spl8_1 | ~spl8_4 | spl8_6),
% 1.80/1.56 inference(avatar_contradiction_clause,[status(thm)],[f88])).
% 1.80/1.56 thf(f88,plain,(
% 1.80/1.56 $false | (~spl8_1 | ~spl8_4 | spl8_6)),
% 1.80/1.56 inference(subsumption_resolution,[status(thm)],[f87,f52])).
% 1.80/1.56 thf(f52,plain,(
% 1.80/1.56 ($true != (sK3 @ sK7)) | spl8_6),
% 1.80/1.56 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.80/1.56 thf(f50,definition,(
% 1.80/1.56 spl8_6 <=> ($true = (sK3 @ sK7))),
% 1.80/1.56 introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition])).
% 1.80/1.56 thf(f87,plain,(
% 1.80/1.56 ($true = (sK3 @ sK7)) | (~spl8_1 | ~spl8_4)),
% 1.80/1.56 inference(forward_demodulation,[status(thm)],[f85,f72])).
% 1.80/1.56 thf(f72,plain,(
% 1.80/1.56 ((sK4 @ (sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK7)) = sK7) | ~spl8_4),
% 1.80/1.56 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.80/1.56 thf(f69,plain,(
% 1.80/1.56 ((sK4 @ (sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK7)) = sK7) | ($true != $true) | ~spl8_4),
% 1.80/1.56 inference(superposition,[status(thm)],[f20,f43])).
% 1.80/1.56 thf(f43,plain,(
% 1.80/1.56 ($true = ('const/sets/IN' @ sK1 @ sK7 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5))) | ~spl8_4),
% 1.80/1.56 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.80/1.56 thf(f41,definition,(
% 1.80/1.56 spl8_4 <=> ($true = ('const/sets/IN' @ sK1 @ sK7 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5)))),
% 1.80/1.56 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 1.80/1.56 thf(f20,plain,(
% 1.80/1.56 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > $o,X4 : X1 > X0] : (($true != ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3))) | ((X4 @ (sK0 @ X0 @ X1 @ X4 @ X3 @ X2)) = X2)) )),
% 1.80/1.56 inference(cnf_transformation,[status(thm)],[f13])).
% 1.80/1.56 thf(f13,plain,(
% 1.80/1.56 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1 > $o,X4 : X1 > X0] : ((($true = ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3))) | ! [X5 : X1] : (($true != ('const/sets/IN' @ X1 @ X5 @ X3)) | ((X4 @ X5) != X2))) & ((($true = ('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X4 @ X3 @ X2) @ X3)) & ((X4 @ (sK0 @ X0 @ X1 @ X4 @ X3 @ X2)) = X2)) | ($true != ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3)))))),
% 1.80/1.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12])).
% 1.80/1.56 thf(f12,plain,(
% 1.80/1.56 ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > $o,X4 : X1 > X0] : (? [X6 : X1] : (($true = ('const/sets/IN' @ X1 @ X6 @ X3)) & ((X4 @ X6) = X2)) => (($true = ('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X4 @ X3 @ X2) @ X3)) & ((X4 @ (sK0 @ X0 @ X1 @ X4 @ X3 @ X2)) = X2)))),
% 1.80/1.56 introduced(definition,[],[choice_axiom])).
% 1.80/1.56 thf(f11,plain,(
% 1.80/1.56 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1 > $o,X4 : X1 > X0] : ((($true = ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3))) | ! [X5 : X1] : (($true != ('const/sets/IN' @ X1 @ X5 @ X3)) | ((X4 @ X5) != X2))) & (? [X6 : X1] : (($true = ('const/sets/IN' @ X1 @ X6 @ X3)) & ((X4 @ X6) = X2)) | ($true != ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3)))))),
% 1.80/1.56 inference(rectify,[status(thm)],[f10])).
% 1.80/1.56 thf(f10,plain,(
% 1.80/1.56 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1 > $o,X4 : X1 > X0] : ((($true = ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3))) | ! [X5 : X1] : (($true != ('const/sets/IN' @ X1 @ X5 @ X3)) | ((X4 @ X5) != X2))) & (? [X5 : X1] : (($true = ('const/sets/IN' @ X1 @ X5 @ X3)) & ((X4 @ X5) = X2)) | ($true != ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3)))))),
% 1.80/1.56 inference(nnf_transformation,[status(thm)],[f6])).
% 1.80/1.56 thf(f6,plain,(
% 1.80/1.56 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1 > $o,X4 : X1 > X0] : (($true = ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3))) <=> ? [X5 : X1] : (($true = ('const/sets/IN' @ X1 @ X5 @ X3)) & ((X4 @ X5) = X2)))),
% 1.80/1.56 inference(fool_elimination,[status(thm)],[f5])).
% 1.80/1.56 thf(f5,plain,(
% 1.80/1.56 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1 > $o,X4 : X1 > X0] : (? [X5 : X1] : (((X4 @ X5) = X2) & ('const/sets/IN' @ X1 @ X5 @ X3)) = ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3)))),
% 1.80/1.56 inference(rectify,[status(thm)],[f1])).
% 1.80/1.56 thf(f1,axiom,(
% 1.80/1.56 ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0 > $o,X4 : X0 > X1] : (? [X5 : X0] : (((X4 @ X5) = X2) & ('const/sets/IN' @ X0 @ X5 @ X3)) = ('const/sets/IN' @ X1 @ X2 @ ('const/sets/IMAGE' @ X0 @ X1 @ X4 @ X3)))),
% 1.80/1.56 file('/export/starexec/sandbox/tmp/tmp.tAjIH6MiAz/DTF2THF_14612.p','thm/sets/IN_IMAGE_')).
% 1.80/1.56 thf(f85,plain,(
% 1.80/1.56 ((sK3 @ (sK4 @ (sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK7))) = $true) | (~spl8_1 | ~spl8_4)),
% 1.80/1.56 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.80/1.56 thf(f83,plain,(
% 1.80/1.56 ($true != $true) | ((sK3 @ (sK4 @ (sK0 @ sK1 @ sK2 @ sK4 @ sK5 @ sK7))) = $true) | (~spl8_1 | ~spl8_4)),
% 1.80/1.56 inference(superposition,[status(thm)],[f64,f43])).
% 1.80/1.56 thf(f64,plain,(
% 1.80/1.56 ( ! [X0 : $tType,X2 : X0,X1 : sK2 > X0] : ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK5)) != $true) | ($true = (sK3 @ (sK4 @ (sK0 @ X0 @ sK2 @ X1 @ sK5 @ X2))))) ) | ~spl8_1),
% 1.80/1.56 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.80/1.56 thf(f63,plain,(
% 1.80/1.56 ( ! [X0 : $tType,X2 : X0,X1 : sK2 > X0] : (($true != $true) | (('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ sK2 @ X0 @ X1 @ sK5)) != $true) | ($true = (sK3 @ (sK4 @ (sK0 @ X0 @ sK2 @ X1 @ sK5 @ X2))))) ) | ~spl8_1),
% 1.80/1.56 inference(superposition,[status(thm)],[f31,f21])).
% 1.80/1.56 thf(f21,plain,(
% 1.80/1.56 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > $o,X4 : X1 > X0] : (($true = ('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X4 @ X3 @ X2) @ X3)) | ($true != ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3)))) )),
% 1.80/1.56 inference(cnf_transformation,[status(thm)],[f13])).
% 1.80/1.56 thf(f31,plain,(
% 1.80/1.56 ( ! [X7 : sK2] : (($true != ('const/sets/IN' @ sK2 @ X7 @ sK5)) | ($true = (sK3 @ (sK4 @ X7)))) ) | ~spl8_1),
% 1.80/1.56 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.80/1.56 thf(f30,definition,(
% 1.80/1.56 spl8_1 <=> ! [X7 : sK2] : (($true = (sK3 @ (sK4 @ X7))) | ($true != ('const/sets/IN' @ sK2 @ X7 @ sK5)))),
% 1.80/1.56 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.80/1.56 thf(f67,plain,(
% 1.80/1.56 ~spl8_1 | ~spl8_3 | spl8_5),
% 1.80/1.56 inference(avatar_contradiction_clause,[status(thm)],[f66])).
% 1.80/1.56 thf(f66,plain,(
% 1.80/1.56 $false | (~spl8_1 | ~spl8_3 | spl8_5)),
% 1.80/1.56 inference(subsumption_resolution,[status(thm)],[f65,f48])).
% 1.80/1.56 thf(f48,plain,(
% 1.80/1.56 ($true != (sK3 @ (sK4 @ sK6))) | spl8_5),
% 1.80/1.56 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.80/1.56 thf(f46,definition,(
% 1.80/1.56 spl8_5 <=> ($true = (sK3 @ (sK4 @ sK6)))),
% 1.80/1.56 introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition])).
% 1.80/1.56 thf(f65,plain,(
% 1.80/1.56 ($true = (sK3 @ (sK4 @ sK6))) | (~spl8_1 | ~spl8_3)),
% 1.80/1.56 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.80/1.56 thf(f62,plain,(
% 1.80/1.56 ($true != $true) | ($true = (sK3 @ (sK4 @ sK6))) | (~spl8_1 | ~spl8_3)),
% 1.80/1.56 inference(superposition,[status(thm)],[f31,f39])).
% 1.80/1.56 thf(f39,plain,(
% 1.80/1.56 ($true = ('const/sets/IN' @ sK2 @ sK6 @ sK5)) | ~spl8_3),
% 1.80/1.56 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.80/1.56 thf(f37,definition,(
% 1.80/1.56 spl8_3 <=> ($true = ('const/sets/IN' @ sK2 @ sK6 @ sK5))),
% 1.80/1.56 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.80/1.56 thf(f61,plain,(
% 1.80/1.56 spl8_1 | ~spl8_2),
% 1.80/1.56 inference(avatar_split_clause,[status(thm)],[f60,f33,f30])).
% 1.80/1.56 thf(f33,definition,(
% 1.80/1.56 spl8_2 <=> ! [X8 : sK1] : ((('const/sets/IN' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5)) != $true) | ($true = (sK3 @ X8)))),
% 1.80/1.56 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.80/1.56 thf(f60,plain,(
% 1.80/1.56 ( ! [X0 : sK2] : (((sK3 @ (sK4 @ X0)) = $true) | (('const/sets/IN' @ sK2 @ X0 @ sK5) != $true)) ) | ~spl8_2),
% 1.80/1.56 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.80/1.56 thf(f57,plain,(
% 1.80/1.56 ( ! [X0 : sK2] : ((('const/sets/IN' @ sK2 @ X0 @ sK5) != $true) | ($true != $true) | ((sK3 @ (sK4 @ X0)) = $true)) ) | ~spl8_2),
% 1.80/1.56 inference(superposition,[status(thm)],[f34,f28])).
% 1.80/1.56 thf(f28,plain,(
% 1.80/1.56 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > $o,X4 : X1 > X0,X5 : X1] : (($true = ('const/sets/IN' @ X0 @ (X4 @ X5) @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3))) | ($true != ('const/sets/IN' @ X1 @ X5 @ X3))) )),
% 1.80/1.56 inference(equality_resolution,[status(thm)],[f22])).
% 1.80/1.56 thf(f22,plain,(
% 1.80/1.56 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > $o,X4 : X1 > X0,X5 : X1] : (($true = ('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3))) | ($true != ('const/sets/IN' @ X1 @ X5 @ X3)) | ((X4 @ X5) != X2)) )),
% 1.80/1.56 inference(cnf_transformation,[status(thm)],[f13])).
% 1.80/1.56 thf(f34,plain,(
% 1.80/1.56 ( ! [X8 : sK1] : ((('const/sets/IN' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5)) != $true) | ($true = (sK3 @ X8))) ) | ~spl8_2),
% 1.80/1.56 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.80/1.56 thf(f55,plain,(
% 1.80/1.56 ~spl8_6 | spl8_3),
% 1.80/1.56 inference(avatar_split_clause,[status(thm)],[f26,f37,f50])).
% 1.80/1.56 thf(f26,plain,(
% 1.80/1.56 ($true != (sK3 @ sK7)) | ($true = ('const/sets/IN' @ sK2 @ sK6 @ sK5))),
% 1.80/1.56 inference(cnf_transformation,[status(thm)],[f19])).
% 1.80/1.56 thf(f19,plain,(
% 1.80/1.56 ((($true = ('const/sets/IN' @ sK2 @ sK6 @ sK5)) & ($true != (sK3 @ (sK4 @ sK6)))) | (($true = ('const/sets/IN' @ sK1 @ sK7 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5))) & ($true != (sK3 @ sK7)))) & (! [X7 : sK2] : (($true != ('const/sets/IN' @ sK2 @ X7 @ sK5)) | ($true = (sK3 @ (sK4 @ X7)))) | ! [X8 : sK1] : ((('const/sets/IN' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5)) != $true) | ($true = (sK3 @ X8))))),
% 1.80/1.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f15,f18,f17,f16])).
% 1.80/1.56 thf(f16,plain,(
% 1.80/1.56 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > X0,X4 : X1 > $o] : ((? [X5 : X1] : ((('const/sets/IN' @ X1 @ X5 @ X4) = $true) & ($true != (X2 @ (X3 @ X5)))) | ? [X6 : X0] : (($true = ('const/sets/IN' @ X0 @ X6 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) & ((X2 @ X6) != $true))) & (! [X7 : X1] : ((('const/sets/IN' @ X1 @ X7 @ X4) != $true) | ((X2 @ (X3 @ X7)) = $true)) | ! [X8 : X0] : ((('const/sets/IN' @ X0 @ X8 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)) != $true) | ($true = (X2 @ X8))))) => ((? [X5 : sK2] : ((('const/sets/IN' @ sK2 @ X5 @ sK5) = $true) & ($true != (sK3 @ (sK4 @ X5)))) | ? [X6 : sK1] : ((('const/sets/IN' @ sK1 @ X6 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5)) = $true) & ($true != (sK3 @ X6)))) & (! [X7 : sK2] : (($true != ('const/sets/IN' @ sK2 @ X7 @ sK5)) | ($true = (sK3 @ (sK4 @ X7)))) | ! [X8 : sK1] : ((('const/sets/IN' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5)) != $true) | ($true = (sK3 @ X8)))))),
% 1.80/1.56 introduced(definition,[],[choice_axiom])).
% 1.80/1.56 thf(f17,plain,(
% 1.80/1.56 ? [X5 : sK2] : ((('const/sets/IN' @ sK2 @ X5 @ sK5) = $true) & ($true != (sK3 @ (sK4 @ X5)))) => (($true = ('const/sets/IN' @ sK2 @ sK6 @ sK5)) & ($true != (sK3 @ (sK4 @ sK6))))),
% 1.80/1.56 introduced(definition,[],[choice_axiom])).
% 1.80/1.56 thf(f18,plain,(
% 1.80/1.56 ? [X6 : sK1] : ((('const/sets/IN' @ sK1 @ X6 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5)) = $true) & ($true != (sK3 @ X6))) => (($true = ('const/sets/IN' @ sK1 @ sK7 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5))) & ($true != (sK3 @ sK7)))),
% 1.80/1.56 introduced(definition,[],[choice_axiom])).
% 1.80/1.56 thf(f15,plain,(
% 1.80/1.56 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > X0,X4 : X1 > $o] : ((? [X5 : X1] : ((('const/sets/IN' @ X1 @ X5 @ X4) = $true) & ($true != (X2 @ (X3 @ X5)))) | ? [X6 : X0] : (($true = ('const/sets/IN' @ X0 @ X6 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) & ((X2 @ X6) != $true))) & (! [X7 : X1] : ((('const/sets/IN' @ X1 @ X7 @ X4) != $true) | ((X2 @ (X3 @ X7)) = $true)) | ! [X8 : X0] : ((('const/sets/IN' @ X0 @ X8 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)) != $true) | ($true = (X2 @ X8)))))),
% 1.80/1.56 inference(rectify,[status(thm)],[f14])).
% 1.80/1.56 thf(f14,plain,(
% 1.80/1.56 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > X0,X4 : X1 > $o] : ((? [X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X4) = $true) & ((X2 @ (X3 @ X6)) != $true)) | ? [X5 : X0] : (($true = ('const/sets/IN' @ X0 @ X5 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) & ($true != (X2 @ X5)))) & (! [X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X4) != $true) | ((X2 @ (X3 @ X6)) = $true)) | ! [X5 : X0] : (($true != ('const/sets/IN' @ X0 @ X5 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) | ($true = (X2 @ X5)))))),
% 1.80/1.56 inference(nnf_transformation,[status(thm)],[f9])).
% 1.80/1.56 thf(f9,plain,(
% 1.80/1.56 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > X0,X4 : X1 > $o] : (! [X5 : X0] : (($true != ('const/sets/IN' @ X0 @ X5 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) | ($true = (X2 @ X5))) <~> ! [X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X4) != $true) | ((X2 @ (X3 @ X6)) = $true)))),
% 1.80/1.56 inference(ennf_transformation,[status(thm)],[f8])).
% 1.80/1.56 thf(f8,plain,(
% 1.80/1.56 ~! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > X0,X4 : X1 > $o] : (! [X5 : X0] : (($true = ('const/sets/IN' @ X0 @ X5 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) => ($true = (X2 @ X5))) <=> ! [X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X4) = $true) => ((X2 @ (X3 @ X6)) = $true)))),
% 1.80/1.56 inference(fool_elimination,[status(thm)],[f7])).
% 1.80/1.56 thf(f7,plain,(
% 1.80/1.56 ~! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > X0,X4 : X1 > $o] : (! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)) => (X2 @ X5)) = ! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X4) => (X2 @ (X3 @ X6))))),
% 1.80/1.56 inference(rectify,[status(thm)],[f3])).
% 1.80/1.56 thf(f3,negated_conjecture,(
% 1.80/1.56 ~! [X0 : $tType,X2 : $tType,X6 : X0 > $o,X3 : X2 > X0,X4 : X2 > $o] : (! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ ('const/sets/IMAGE' @ X2 @ X0 @ X3 @ X4)) => (X6 @ X5)) = ! [X5 : X2] : (('const/sets/IN' @ X2 @ X5 @ X4) => (X6 @ (X3 @ X5))))),
% 1.80/1.56 inference(negated_conjecture,[status(cth)],[f2])).
% 1.80/1.56 thf(f2,conjecture,(
% 1.80/1.56 ! [X0 : $tType,X2 : $tType,X6 : X0 > $o,X3 : X2 > X0,X4 : X2 > $o] : (! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ ('const/sets/IMAGE' @ X2 @ X0 @ X3 @ X4)) => (X6 @ X5)) = ! [X5 : X2] : (('const/sets/IN' @ X2 @ X5 @ X4) => (X6 @ (X3 @ X5))))),
% 1.80/1.56 file('/export/starexec/sandbox/tmp/tmp.tAjIH6MiAz/DTF2THF_14612.p','thm/sets/FORALL_IN_IMAGE_')).
% 1.80/1.56 thf(f54,plain,(
% 1.80/1.56 spl8_4 | ~spl8_5),
% 1.80/1.56 inference(avatar_split_clause,[status(thm)],[f25,f46,f41])).
% 1.80/1.56 thf(f25,plain,(
% 1.80/1.56 ($true != (sK3 @ (sK4 @ sK6))) | ($true = ('const/sets/IN' @ sK1 @ sK7 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5)))),
% 1.80/1.56 inference(cnf_transformation,[status(thm)],[f19])).
% 1.80/1.56 thf(f53,plain,(
% 1.80/1.56 ~spl8_5 | ~spl8_6),
% 1.80/1.56 inference(avatar_split_clause,[status(thm)],[f24,f50,f46])).
% 1.80/1.56 thf(f24,plain,(
% 1.80/1.56 ($true != (sK3 @ sK7)) | ($true != (sK3 @ (sK4 @ sK6)))),
% 1.80/1.56 inference(cnf_transformation,[status(thm)],[f19])).
% 1.80/1.56 thf(f44,plain,(
% 1.80/1.56 spl8_3 | spl8_4),
% 1.80/1.56 inference(avatar_split_clause,[status(thm)],[f27,f41,f37])).
% 1.80/1.56 thf(f27,plain,(
% 1.80/1.56 ($true = ('const/sets/IN' @ sK1 @ sK7 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5))) | ($true = ('const/sets/IN' @ sK2 @ sK6 @ sK5))),
% 1.80/1.56 inference(cnf_transformation,[status(thm)],[f19])).
% 1.80/1.56 thf(f35,plain,(
% 1.80/1.56 spl8_1 | spl8_2),
% 1.80/1.56 inference(avatar_split_clause,[status(thm)],[f23,f33,f30])).
% 1.80/1.56 thf(f23,plain,(
% 1.80/1.56 ( ! [X8 : sK1,X7 : sK2] : (($true = (sK3 @ (sK4 @ X7))) | ($true != ('const/sets/IN' @ sK2 @ X7 @ sK5)) | (('const/sets/IN' @ sK1 @ X8 @ ('const/sets/IMAGE' @ sK2 @ sK1 @ sK4 @ sK5)) != $true) | ($true = (sK3 @ X8))) )),
% 1.80/1.56 inference(cnf_transformation,[status(thm)],[f19])).
% 1.80/1.56 % SZS output end Proof for DTF2THF_14612
% 1.80/1.56 % (14751)------------------------------
% 1.80/1.56 % (14751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.56 % (14751)Termination reason: Refutation
% 1.80/1.56
% 1.80/1.56 % (14751)Memory used [KB]: 5628
% 1.80/1.56 % (14751)Time elapsed: 0.012 s
% 1.80/1.56 % (14751)Instructions burned: 14 (million)
% 1.80/1.56 % (14751)------------------------------
% 1.80/1.56 % (14751)------------------------------
% 1.80/1.56 % (14745)Success in time 0.026 s
%------------------------------------------------------------------------------