%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU627^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 09:35:42 AM UTC 2026
% Result : Theorem 1.58s 1.22s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 104 ( 52 unt; 0 typ; 4 def)
% Number of atoms : 907 ( 183 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 1420 ( 34 ~; 67 |; 24 &;1126 @)
% ( 4 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 16 con; 0-2 aty)
% ( 71 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 228 ( 84 ^; 130 !; 14 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(func_def_27,type,
sK5: $i > $i > $i ).
thf(f139,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f94,f112,f118,f125,f138]) ).
thf(f138,plain,
( ~ spl4_1
| spl4_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f137]) ).
thf(f137,plain,
( $false
| ~ spl4_1
| spl4_3 ),
inference(subsumption_resolution,[status(thm)],[f133,f105]) ).
thf(f105,plain,
( ( $false
!= ( in @ sK2 @ sK0 ) )
| spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f104,definition,
( spl4_3
<=> ( $false
= ( in @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f133,plain,
( ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $true = $false )
| ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f129,f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( setadjoin @ Y1 @ emptyset ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( setadjoin @ Y1 @ emptyset ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f33,f27]) ).
thf(f27,plain,
singletoninpowunion = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( upairset2E = $true )
& ( upairinpowunion = $true )
& ( subsetI2 = $true )
& ( singletoninpowunion = $true )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( ( subset @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f21,f20]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true ) ) )
=> ( ( $true
= ( in @ sK2 @ sK0 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( ( subset @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( ( subset @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
!= $true ) )
=> ( ( $true
= ( in @ sK3 @ sK1 ) )
& ( ( subset @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( upairset2E = $true )
& ( upairinpowunion = $true )
& ( subsetI2 = $true )
& ( singletoninpowunion = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true ) ) )
& ( upairinpowunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( subsetI2 = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairinpowunion = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( subsetI2
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairinpowunion
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( subsetI2
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairinpowunion
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( subsetI2
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairinpowunion
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',ubforcartprodlem1) ).
thf(f33,plain,
( singletoninpowunion
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( setadjoin @ Y1 @ emptyset ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( singletoninpowunion
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( setadjoin @ Y1 @ emptyset ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( singletoninpowunion
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ ( binunion @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( singletoninpowunion
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',singletoninpowunion) ).
thf(f129,plain,
( ( $false
= ( in @ ( setadjoin @ sK2 @ emptyset ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) ) )
| ~ spl4_1 ),
inference(subsumption_resolution,[status(thm)],[f128,f24]) ).
thf(f24,plain,
( ( subset @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f128,plain,
( ( $false
= ( in @ ( setadjoin @ sK2 @ emptyset ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) ) )
| ( ( subset @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= $true )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f72,f89]) ).
thf(f89,plain,
( ( ( sK5 @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= ( setadjoin @ sK2 @ emptyset ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl4_1
<=> ( ( sK5 @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= ( setadjoin @ sK2 @ emptyset ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK5 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( subset @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK5 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK5 @ X1 @ X2 ) @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK5 @ X1 @ X2 ) ) )
| ( $true
= ( subset @ X1 @ X2 ) ) ),
inference(sigma_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( $true
= ( subset @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f23]) ).
thf(f23,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetI2
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',subsetI2) ).
thf(f28,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f125,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[status(thm)],[f124]) ).
thf(f124,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $true = $false )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f25,f110]) ).
thf(f110,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl4_4
<=> ( $false
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f25,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f118,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[status(thm)],[f117]) ).
thf(f117,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $true = $false )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f106,f26]) ).
thf(f26,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f106,plain,
( ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f112,plain,
( spl4_3
| spl4_4
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f101,f91,f108,f104]) ).
thf(f91,definition,
( spl4_2
<=> ( ( sK5 @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f101,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $true = $false )
| ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f54,f97]) ).
thf(f97,plain,
( ( ( in @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= $false )
| ~ spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f96,f24]) ).
thf(f96,plain,
( ( ( subset @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= $true )
| ( ( in @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= $false )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f72,f93]) ).
thf(f93,plain,
( ( ( sK5 @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f91]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) )
= $true )
| ( $false
= ( in @ X4 @ X3 ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( ( in @ X4 @ X3 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) )
@ X4 ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y1 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y1 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ Y1 ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ ( setadjoin @ Y3 @ emptyset ) ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ ( setadjoin @ Y3 @ emptyset ) ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f32,f29]) ).
thf(f29,plain,
upairinpowunion = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f32,plain,
( upairinpowunion
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ ( setadjoin @ Y3 @ emptyset ) ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( upairinpowunion
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ ( setadjoin @ Y3 @ emptyset ) ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( upairinpowunion
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( upairinpowunion
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',upairinpowunion) ).
thf(f94,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f85,f91,f87]) ).
thf(f85,plain,
( ( ( sK5 @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ( ( sK5 @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= ( setadjoin @ sK2 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ( sK5 @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= ( setadjoin @ sK2 @ emptyset ) )
| ( $true != $true )
| ( ( sK5 @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK0 @ sK1 ) ) )
= ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) ) ),
inference(superposition,[status(thm)],[f24,f83]) ).
thf(f83,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 ) )
| ( ( sK5 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X1 )
| ( ( sK5 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK5 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X0 )
| ( $true = $false )
| ( $true
= ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 ) )
| ( ( sK5 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X1 ) ),
inference(superposition,[status(thm)],[f73,f64]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( X2 = X3 )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( X1 = X2 )
| ( ( X3 = X2 )
= $true )
| ( $false
= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( $true
= ( X2 = X1 ) )
| ( ( X3 = X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( $true
= ( ( X3 = X2 )
| ( X2 = X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X3 = X2 )
| ( X2 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y0 = X2 )
| ( X2 = X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y0 = X2 )
| ( X2 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y0 = X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y0 = X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f31,f30]) ).
thf(f30,plain,
upairset2E = $true,
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f31,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( upairset2E
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X1 = X2 )
| ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( upairset2E
= ( ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X4 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X3 = X4 )
| ( X2 = X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',upairset2E) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( subset @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU627^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:28:54 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU627^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Ordered Pairs - Cartesian Products
% 0.18/0.45 % Version : Especial > Reduced > Especial.
% 0.18/0.45 % English : (! A:i.! B:i.! x:i.in x A -> (! y:i.in y B -> subset (setadjoin
% 0.18/0.45 % (setadjoin x emptyset) (setadjoin (setadjoin x
% 0.18/0.45 % (setadjoin y emptyset)) emptyset)) (powerset (binunion A B))))
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC129l [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 15 ( 4 unt; 10 typ; 4 def)
% 0.18/0.45 % Number of atoms : 26 ( 6 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 7 ( 5 avg)
% 0.18/0.45 % Number of connectives : 66 ( 0 ~; 1 |; 0 &; 53 @)
% 0.18/0.45 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 19 ( 5 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 11 ( 10 usr; 5 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=184
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyset_type,type,
% 0.18/0.45 emptyset: $i ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoin_type,type,
% 0.18/0.45 setadjoin: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(powerset_type,type,
% 0.18/0.45 powerset: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(subset_type,type,
% 0.18/0.45 subset: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(subsetI2_type,type,
% 0.18/0.45 subsetI2: $o ).
% 0.18/0.45
% 0.18/0.45 thf(subsetI2,definition,
% 0.18/0.45 ( subsetI2
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xx @ B ) )
% 0.18/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(binunion_type,type,
% 0.18/0.45 binunion: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(singletoninpowunion_type,type,
% 0.18/0.45 singletoninpowunion: $o ).
% 0.18/0.45
% 0.18/0.45 thf(singletoninpowunion,definition,
% 0.18/0.45 ( singletoninpowunion
% 0.18/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(upairset2E_type,type,
% 0.18/0.45 upairset2E: $o ).
% 0.18/0.45
% 0.18/0.45 thf(upairset2E,definition,
% 0.18/0.45 ( upairset2E
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.18/0.45 => ( ( Xz = Xx )
% 0.18/0.45 | ( Xz = Xy ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(upairinpowunion_type,type,
% 0.18/0.45 upairinpowunion: $o ).
% 0.18/0.45
% 0.18/0.45 thf(upairinpowunion,definition,
% 0.18/0.45 ( upairinpowunion
% 0.18/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ! [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ B )
% 0.18/0.45 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(ubforcartprodlem1,conjecture,
% 0.18/0.45 ( subsetI2
% 0.18/0.45 => ( singletoninpowunion
% 0.18/0.45 => ( upairset2E
% 0.18/0.45 => ( upairinpowunion
% 0.18/0.45 => ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ! [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ B )
% 0.18/0.45 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.45/1.19 ---- Embedded in THF ---
% 1.45/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.19 %%% Generated on Tue Feb 24 12:28:55 EST 2026
% 1.45/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.19 %%% Logic specification used:
% 1.45/1.19 %%% thf(spec, logic, $$dhol).
% 1.45/1.19
% 1.45/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2DTF10483.p
% See solution above
% 1.45/1.19 ------------------------
% 1.45/1.19 ---- Cleaned THF ---
% 1.45/1.20 thf(in_type,type,
% 1.45/1.20 in: $i > $i > $o ).
% 1.45/1.20
% 1.45/1.20 thf(emptyset_type,type,
% 1.45/1.20 emptyset: $i ).
% 1.45/1.20
% 1.45/1.20 thf(setadjoin_type,type,
% 1.45/1.20 setadjoin: $i > $i > $i ).
% 1.45/1.20
% 1.45/1.20 thf(powerset_type,type,
% 1.45/1.20 powerset: $i > $i ).
% 1.45/1.20
% 1.45/1.20 thf(subset_type,type,
% 1.45/1.20 subset: $i > $i > $o ).
% 1.45/1.20
% 1.45/1.20 thf(subsetI2_type,type,
% 1.45/1.20 subsetI2: $o ).
% 1.45/1.20
% 1.45/1.20 thf(subsetI2,definition,
% 1.45/1.20 ( subsetI2
% 1.45/1.20 = ( ! [A: $i,B: $i] :
% 1.45/1.20 ( ! [Xx: $i] :
% 1.45/1.20 ( ( in @ Xx @ A )
% 1.45/1.20 => ( in @ Xx @ B ) )
% 1.45/1.20 => ( subset @ A @ B ) ) ) ) ).
% 1.45/1.20
% 1.45/1.20 thf(binunion_type,type,
% 1.45/1.20 binunion: $i > $i > $i ).
% 1.45/1.20
% 1.45/1.20 thf(singletoninpowunion_type,type,
% 1.45/1.20 singletoninpowunion: $o ).
% 1.45/1.20
% 1.45/1.20 thf(singletoninpowunion,definition,
% 1.45/1.20 ( singletoninpowunion
% 1.45/1.20 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.45/1.20 ( ( in @ Xx @ A )
% 1.45/1.20 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 1.45/1.20
% 1.45/1.20 thf(upairset2E_type,type,
% 1.45/1.20 upairset2E: $o ).
% 1.45/1.20
% 1.45/1.20 thf(upairset2E,definition,
% 1.45/1.20 ( upairset2E
% 1.45/1.20 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.45/1.20 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 1.45/1.20 => ( ( Xz = Xx )
% 1.45/1.20 | ( Xz = Xy ) ) ) ) ) ).
% 1.45/1.20
% 1.45/1.20 thf(upairinpowunion_type,type,
% 1.45/1.20 upairinpowunion: $o ).
% 1.45/1.20
% 1.45/1.20 thf(upairinpowunion,definition,
% 1.45/1.20 ( upairinpowunion
% 1.45/1.20 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.45/1.20 ( ( in @ Xx @ A )
% 1.45/1.20 => ! [Xy: $i] :
% 1.45/1.20 ( ( in @ Xy @ B )
% 1.45/1.20 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 1.45/1.20
% 1.45/1.20 thf(ubforcartprodlem1,conjecture,
% 1.45/1.20 ( subsetI2
% 1.45/1.20 => ( singletoninpowunion
% 1.45/1.20 => ( upairset2E
% 1.45/1.20 => ( upairinpowunion
% 1.45/1.20 => ! [A: $i,B: $i,Xx: $i] :
% 1.45/1.20 ( ( in @ Xx @ A )
% 1.45/1.20 => ! [Xy: $i] :
% 1.45/1.20 ( ( in @ Xy @ B )
% 1.45/1.20 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ).
% 1.45/1.20 ------------------------
% 1.58/1.21 % (10624)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10483 for (3000ds/183Mi)
% 1.58/1.21 % (10628)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_10483 for (3000ds/2Mi)
% 1.58/1.21 % (10628)Instruction limit reached!
% 1.58/1.21 % (10628)------------------------------
% 1.58/1.21 % (10628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.21 % (10628)Termination reason: Unknown
% 1.58/1.21 % (10628)Termination phase: Property scanning
% 1.58/1.21
% 1.58/1.21 % (10628)Memory used [KB]: 1023
% 1.58/1.21 % (10628)Time elapsed: 0.002 s
% 1.58/1.21 % (10628)Instructions burned: 4 (million)
% 1.58/1.21 % (10628)------------------------------
% 1.58/1.21 % (10628)------------------------------
% 1.58/1.21 % (10627)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10483 for (3000ds/2Mi)
% 1.58/1.21 % (10627)Instruction limit reached!
% 1.58/1.21 % (10627)------------------------------
% 1.58/1.21 % (10627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.21 % (10627)Termination reason: Unknown
% 1.58/1.21 % (10627)Termination phase: Property scanning
% 1.58/1.21
% 1.58/1.21 % (10627)Memory used [KB]: 1023
% 1.58/1.21 % (10627)Time elapsed: 0.003 s
% 1.58/1.21 % (10627)Instructions burned: 3 (million)
% 1.58/1.21 % (10627)------------------------------
% 1.58/1.21 % (10627)------------------------------
% 1.58/1.21 % (10624)First to succeed.
% 1.58/1.22 % (10625)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_10483 for (3000ds/4Mi)
% 1.58/1.22 % (10629)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_10483 for (3000ds/275Mi)
% 1.58/1.22 % (10624)Refutation found. Thanks to Tanya!
% 1.58/1.22 % SZS status Theorem for DTF2THF_10483
% 1.58/1.22 % SZS output start Proof for DTF2THF_10483
% 1.58/1.22 thf(func_def_0, type, in: $i > $i > $o).
% 1.58/1.22 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.58/1.22 thf(func_def_3, type, powerset: $i > $i).
% 1.58/1.22 thf(func_def_4, type, subset: $i > $i > $o).
% 1.58/1.22 thf(func_def_7, type, binunion: $i > $i > $i).
% 1.58/1.22 thf(func_def_27, type, sK5: $i > $i > $i).
% 1.58/1.22 thf(f139,plain,(
% 1.58/1.22 $false),
% 1.58/1.22 inference(avatar_sat_refutation,[status(thm)],[f94,f112,f118,f125,f138])).
% 1.58/1.22 thf(f138,plain,(
% 1.58/1.22 ~spl4_1 | spl4_3),
% 1.58/1.22 inference(avatar_contradiction_clause,[status(thm)],[f137])).
% 1.58/1.22 thf(f137,plain,(
% 1.58/1.22 $false | (~spl4_1 | spl4_3)),
% 1.58/1.22 inference(subsumption_resolution,[status(thm)],[f133,f105])).
% 1.58/1.22 thf(f105,plain,(
% 1.58/1.22 ($false != (in @ sK2 @ sK0)) | spl4_3),
% 1.58/1.22 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.58/1.22 thf(f104,definition,(
% 1.58/1.22 spl4_3 <=> ($false = (in @ sK2 @ sK0))),
% 1.58/1.22 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.58/1.22 thf(f133,plain,(
% 1.58/1.22 ($false = (in @ sK2 @ sK0)) | ~spl4_1),
% 1.58/1.22 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.58/1.22 thf(f131,plain,(
% 1.58/1.22 ($true = $false) | ($false = (in @ sK2 @ sK0)) | ~spl4_1),
% 1.58/1.22 inference(superposition,[status(thm)],[f129,f44])).
% 1.58/1.22 thf(f44,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X3)))) | ((in @ X2 @ X1) = $false)) )),
% 1.58/1.22 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.58/1.22 thf(f43,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X1) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X3)))))) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.58/1.22 thf(f42,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ X1) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ Y0))))) @ X3))) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f41])).
% 1.58/1.22 thf(f41,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ Y0)))))))) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.58/1.22 thf(f40,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ X1 @ Y1))))))) @ X2) = $true)) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f39])).
% 1.58/1.22 thf(f39,plain,(
% 1.58/1.22 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ X1 @ Y1)))))))) = $true)) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.58/1.22 thf(f38,plain,(
% 1.58/1.22 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2))))))))) @ X1))) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f37])).
% 1.58/1.22 thf(f37,plain,(
% 1.58/1.22 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) = $true)),
% 1.58/1.22 inference(definition_unfolding,[status(thm)],[f33,f27])).
% 1.58/1.22 thf(f27,plain,(
% 1.58/1.22 (singletoninpowunion = $true)),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.58/1.22 thf(f22,plain,(
% 1.58/1.22 (upairset2E = $true) & (upairinpowunion = $true) & (subsetI2 = $true) & (singletoninpowunion = $true) & (($true = (in @ sK2 @ sK0)) & (($true = (in @ sK3 @ sK1)) & ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) != $true)))),
% 1.58/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f21,f20])).
% 1.58/1.22 thf(f20,plain,(
% 1.58/1.22 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))) != $true))) => (($true = (in @ sK2 @ sK0)) & ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) != $true)))),
% 1.58/1.22 introduced(definition,[],[choice_axiom])).
% 1.58/1.22 thf(f21,plain,(
% 1.58/1.22 ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) != $true)) => (($true = (in @ sK3 @ sK1)) & ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) != $true))),
% 1.58/1.22 introduced(definition,[],[choice_axiom])).
% 1.58/1.22 thf(f19,plain,(
% 1.58/1.22 (upairset2E = $true) & (upairinpowunion = $true) & (subsetI2 = $true) & (singletoninpowunion = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))) != $true)))),
% 1.58/1.22 inference(flattening,[status(thm)],[f18])).
% 1.58/1.22 thf(f18,plain,(
% 1.58/1.22 (((? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))) != $true))) & (upairinpowunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (subsetI2 = $true)),
% 1.58/1.22 inference(ennf_transformation,[status(thm)],[f17])).
% 1.58/1.22 thf(f17,plain,(
% 1.58/1.22 ~((subsetI2 = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairinpowunion = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => ((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))) = $true)))))))),
% 1.58/1.22 inference(fool_elimination,[status(thm)],[f16])).
% 1.58/1.22 thf(f16,plain,(
% 1.58/1.22 ~(subsetI2 => (singletoninpowunion => (upairset2E => (upairinpowunion => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1)))))))))),
% 1.58/1.22 inference(rectify,[status(thm)],[f6])).
% 1.58/1.22 thf(f6,negated_conjecture,(
% 1.58/1.22 ~(subsetI2 => (singletoninpowunion => (upairset2E => (upairinpowunion => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1)))))))))),
% 1.58/1.22 inference(negated_conjecture,[status(cth)],[f5])).
% 1.58/1.22 thf(f5,conjecture,(
% 1.58/1.22 subsetI2 => (singletoninpowunion => (upairset2E => (upairinpowunion => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))))))),
% 1.58/1.22 file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',ubforcartprodlem1)).
% 1.58/1.22 thf(f33,plain,(
% 1.58/1.22 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))))),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f11])).
% 1.58/1.22 thf(f11,plain,(
% 1.58/1.22 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))))),
% 1.58/1.22 inference(fool_elimination,[status(thm)],[f10])).
% 1.58/1.22 thf(f10,plain,(
% 1.58/1.22 (singletoninpowunion = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X2 @ X0)))))),
% 1.58/1.22 inference(rectify,[status(thm)],[f2])).
% 1.58/1.22 thf(f2,axiom,(
% 1.58/1.22 (singletoninpowunion = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))))),
% 1.58/1.22 file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',singletoninpowunion)).
% 1.58/1.22 thf(f129,plain,(
% 1.58/1.22 ($false = (in @ (setadjoin @ sK2 @ emptyset) @ (powerset @ (binunion @ sK0 @ sK1)))) | ~spl4_1),
% 1.58/1.22 inference(subsumption_resolution,[status(thm)],[f128,f24])).
% 1.58/1.22 thf(f24,plain,(
% 1.58/1.22 ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) != $true)),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.58/1.22 thf(f128,plain,(
% 1.58/1.22 ($false = (in @ (setadjoin @ sK2 @ emptyset) @ (powerset @ (binunion @ sK0 @ sK1)))) | ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = $true) | ~spl4_1),
% 1.58/1.22 inference(superposition,[status(thm)],[f72,f89])).
% 1.58/1.22 thf(f89,plain,(
% 1.58/1.22 ((sK5 @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = (setadjoin @ sK2 @ emptyset)) | ~spl4_1),
% 1.58/1.22 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.58/1.22 thf(f87,definition,(
% 1.58/1.22 spl4_1 <=> ((sK5 @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = (setadjoin @ sK2 @ emptyset))),
% 1.58/1.22 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.58/1.22 thf(f72,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (sK5 @ X1 @ X2) @ X2)) | ($true = (subset @ X1 @ X2))) )),
% 1.58/1.22 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.58/1.22 thf(f71,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK5 @ X1 @ X2) @ X1) => (in @ (sK5 @ X1 @ X2) @ X2))) | ($true = (subset @ X1 @ X2))) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.58/1.22 thf(f70,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK5 @ X1 @ X2))) | ($true = (subset @ X1 @ X2))) )),
% 1.58/1.22 inference(sigma_clausification,[status(thm)],[f69])).
% 1.58/1.22 thf(f69,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))))) | ($true = (subset @ X1 @ X2))) )),
% 1.58/1.22 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 1.58/1.22 thf(f68,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (subset @ X1 @ X2)))) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.58/1.22 thf(f67,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0))) @ X2))) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f66])).
% 1.58/1.22 thf(f66,plain,(
% 1.58/1.22 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0)))) = $true)) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.58/1.22 thf(f65,plain,(
% 1.58/1.22 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))) @ X1))) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f34])).
% 1.58/1.22 thf(f34,plain,(
% 1.58/1.22 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.58/1.22 inference(definition_unfolding,[status(thm)],[f28,f23])).
% 1.58/1.22 thf(f23,plain,(
% 1.58/1.22 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.22 thf(f13,plain,(
% 1.58/1.22 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.58/1.22 inference(fool_elimination,[status(thm)],[f12])).
% 1.58/1.22 thf(f12,plain,(
% 1.58/1.22 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 1.58/1.22 inference(rectify,[status(thm)],[f1])).
% 1.58/1.22 thf(f1,axiom,(
% 1.58/1.22 (subsetI2 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.58/1.22 file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',subsetI2)).
% 1.58/1.22 thf(f28,plain,(
% 1.58/1.22 (subsetI2 = $true)),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.58/1.22 thf(f125,plain,(
% 1.58/1.22 ~spl4_4),
% 1.58/1.22 inference(avatar_contradiction_clause,[status(thm)],[f124])).
% 1.58/1.22 thf(f124,plain,(
% 1.58/1.22 $false | ~spl4_4),
% 1.58/1.22 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.58/1.22 thf(f121,plain,(
% 1.58/1.22 ($true = $false) | ~spl4_4),
% 1.58/1.22 inference(superposition,[status(thm)],[f25,f110])).
% 1.58/1.22 thf(f110,plain,(
% 1.58/1.22 ($false = (in @ sK3 @ sK1)) | ~spl4_4),
% 1.58/1.22 inference(avatar_component_clause,[status(thm)],[f108])).
% 1.58/1.22 thf(f108,definition,(
% 1.58/1.22 spl4_4 <=> ($false = (in @ sK3 @ sK1))),
% 1.58/1.22 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.58/1.22 thf(f25,plain,(
% 1.58/1.22 ($true = (in @ sK3 @ sK1))),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.58/1.22 thf(f118,plain,(
% 1.58/1.22 ~spl4_3),
% 1.58/1.22 inference(avatar_contradiction_clause,[status(thm)],[f117])).
% 1.58/1.22 thf(f117,plain,(
% 1.58/1.22 $false | ~spl4_3),
% 1.58/1.22 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.58/1.22 thf(f113,plain,(
% 1.58/1.22 ($true = $false) | ~spl4_3),
% 1.58/1.22 inference(superposition,[status(thm)],[f106,f26])).
% 1.58/1.22 thf(f26,plain,(
% 1.58/1.22 ($true = (in @ sK2 @ sK0))),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.58/1.22 thf(f106,plain,(
% 1.58/1.22 ($false = (in @ sK2 @ sK0)) | ~spl4_3),
% 1.58/1.22 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.58/1.22 thf(f112,plain,(
% 1.58/1.22 spl4_3 | spl4_4 | ~spl4_2),
% 1.58/1.22 inference(avatar_split_clause,[status(thm)],[f101,f91,f108,f104])).
% 1.58/1.22 thf(f91,definition,(
% 1.58/1.22 spl4_2 <=> ((sK5 @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)))),
% 1.58/1.22 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.58/1.22 thf(f101,plain,(
% 1.58/1.22 ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK2 @ sK0)) | ~spl4_2),
% 1.58/1.22 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.58/1.22 thf(f100,plain,(
% 1.58/1.22 ($true = $false) | ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK2 @ sK0)) | ~spl4_2),
% 1.58/1.22 inference(superposition,[status(thm)],[f54,f97])).
% 1.58/1.22 thf(f97,plain,(
% 1.58/1.22 ((in @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = $false) | ~spl4_2),
% 1.58/1.22 inference(subsumption_resolution,[status(thm)],[f96,f24])).
% 1.58/1.22 thf(f96,plain,(
% 1.58/1.22 ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = $true) | ((in @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = $false) | ~spl4_2),
% 1.58/1.22 inference(superposition,[status(thm)],[f72,f93])).
% 1.58/1.22 thf(f93,plain,(
% 1.58/1.22 ((sK5 @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))) | ~spl4_2),
% 1.58/1.22 inference(avatar_component_clause,[status(thm)],[f91])).
% 1.58/1.22 thf(f54,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ (powerset @ (binunion @ X1 @ X3))) = $true) | ($false = (in @ X4 @ X3)) | ((in @ X2 @ X1) = $false)) )),
% 1.58/1.22 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.58/1.22 thf(f53,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X2 @ X1) = $false) | (((in @ X4 @ X3) => (in @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ (powerset @ (binunion @ X1 @ X3)))) = $true)) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.58/1.22 thf(f52,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ (powerset @ (binunion @ X1 @ X3))))) @ X4)) | ((in @ X2 @ X1) = $false)) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f51])).
% 1.58/1.22 thf(f51,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ (powerset @ (binunion @ X1 @ X3)))))) = $true)) )),
% 1.58/1.22 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.58/1.22 thf(f50,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ (powerset @ (binunion @ X1 @ X3))))))) = $true)) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.58/1.22 thf(f49,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ X2 @ (setadjoin @ Y1 @ emptyset)) @ (powerset @ (binunion @ X1 @ Y0)))))))) @ X3))) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f48])).
% 1.58/1.22 thf(f48,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ X2 @ (setadjoin @ Y1 @ emptyset)) @ (powerset @ (binunion @ X1 @ Y0))))))))))) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.58/1.22 thf(f47,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ (powerset @ (binunion @ X1 @ Y1)))))))))) @ X2) = $true)) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f46])).
% 1.58/1.22 thf(f46,plain,(
% 1.58/1.22 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ (powerset @ (binunion @ X1 @ Y1))))))))))) = $true)) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.58/1.22 thf(f45,plain,(
% 1.58/1.22 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2)))))))))))) @ X1))) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f36])).
% 1.58/1.22 thf(f36,plain,(
% 1.58/1.22 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))))),
% 1.58/1.22 inference(definition_unfolding,[status(thm)],[f32,f29])).
% 1.58/1.22 thf(f29,plain,(
% 1.58/1.22 (upairinpowunion = $true)),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.58/1.22 thf(f32,plain,(
% 1.58/1.22 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))))),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.22 thf(f9,plain,(
% 1.58/1.22 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))))),
% 1.58/1.22 inference(fool_elimination,[status(thm)],[f8])).
% 1.58/1.22 thf(f8,plain,(
% 1.58/1.22 (upairinpowunion = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X2 @ X0))))))),
% 1.58/1.22 inference(rectify,[status(thm)],[f4])).
% 1.58/1.22 thf(f4,axiom,(
% 1.58/1.22 (upairinpowunion = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))))),
% 1.58/1.22 file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',upairinpowunion)).
% 1.58/1.22 thf(f94,plain,(
% 1.58/1.22 spl4_1 | spl4_2),
% 1.58/1.22 inference(avatar_split_clause,[status(thm)],[f85,f91,f87])).
% 1.58/1.22 thf(f85,plain,(
% 1.58/1.22 ((sK5 @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))) | ((sK5 @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = (setadjoin @ sK2 @ emptyset))),
% 1.58/1.22 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.58/1.22 thf(f84,plain,(
% 1.58/1.22 ((sK5 @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = (setadjoin @ sK2 @ emptyset)) | ($true != $true) | ((sK5 @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK0 @ sK1))) = (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)))),
% 1.58/1.22 inference(superposition,[status(thm)],[f24,f83])).
% 1.58/1.22 thf(f83,plain,(
% 1.58/1.22 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2)) | ((sK5 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2) = X1) | ((sK5 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2) = X0)) )),
% 1.58/1.22 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.58/1.22 thf(f81,plain,(
% 1.58/1.22 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((sK5 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2) = X0) | ($true = $false) | ($true = (subset @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2)) | ((sK5 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ X2) = X1)) )),
% 1.58/1.22 inference(superposition,[status(thm)],[f73,f64])).
% 1.58/1.22 thf(f64,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)))) | (X2 = X3) | (X1 = X2)) )),
% 1.58/1.22 inference(equality_proxy_clausification,[status(thm)],[f63])).
% 1.58/1.22 thf(f63,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((X1 = X2) | ((X3 = X2) = $true) | ($false = (in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset))))) )),
% 1.58/1.22 inference(equality_proxy_clausification,[status(thm)],[f62])).
% 1.58/1.22 thf(f62,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)))) | ($true = (X2 = X1)) | ((X3 = X2) = $true)) )),
% 1.58/1.22 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.58/1.22 thf(f61,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)))) | ($true = ((X3 = X2) | (X2 = X1)))) )),
% 1.58/1.22 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.58/1.22 thf(f60,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset))) => ((X3 = X2) | (X2 = X1))) = $true)) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.58/1.22 thf(f59,plain,(
% 1.58/1.22 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset))) => ((Y0 = X2) | (X2 = X1)))) @ X3))) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f58])).
% 1.58/1.22 thf(f58,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset))) => ((Y0 = X2) | (X2 = X1))))) = $true)) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.58/1.22 thf(f57,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ X1 @ emptyset))) => ((Y1 = Y0) | (Y0 = X1)))))) @ X2))) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f56])).
% 1.58/1.22 thf(f56,plain,(
% 1.58/1.22 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ X1 @ emptyset))) => ((Y1 = Y0) | (Y0 = X1))))))) = $true)) )),
% 1.58/1.22 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.58/1.22 thf(f55,plain,(
% 1.58/1.22 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0)))))))) @ X1) = $true)) )),
% 1.58/1.22 inference(pi_clausification,[status(thm)],[f35])).
% 1.58/1.22 thf(f35,plain,(
% 1.58/1.22 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) = $true)),
% 1.58/1.22 inference(definition_unfolding,[status(thm)],[f31,f30])).
% 1.58/1.22 thf(f30,plain,(
% 1.58/1.22 (upairset2E = $true)),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f22])).
% 1.58/1.22 thf(f31,plain,(
% 1.58/1.22 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))))),
% 1.58/1.22 inference(cnf_transformation,[status(thm)],[f15])).
% 1.58/1.22 thf(f15,plain,(
% 1.58/1.22 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))))),
% 1.58/1.22 inference(fool_elimination,[status(thm)],[f14])).
% 1.58/1.22 thf(f14,plain,(
% 1.58/1.22 (upairset2E = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset))) => ((X1 = X2) | (X0 = X1))))),
% 1.58/1.22 inference(rectify,[status(thm)],[f3])).
% 1.58/1.22 thf(f3,axiom,(
% 1.58/1.22 (upairset2E = ! [X2 : $i,X4 : $i,X3 : $i] : ((in @ X4 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) => ((X3 = X4) | (X2 = X4))))),
% 1.58/1.22 file('/export/starexec/sandbox2/tmp/tmp.ZynwDEt9e1/DTF2THF_10483.p',upairset2E)).
% 1.58/1.22 thf(f73,plain,(
% 1.58/1.22 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK5 @ X1 @ X2) @ X1)) | ($true = (subset @ X1 @ X2))) )),
% 1.58/1.22 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.58/1.22 % SZS output end Proof for DTF2THF_10483
% 1.58/1.22 % (10624)------------------------------
% 1.58/1.22 % (10624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.22 % (10624)Termination reason: Refutation
% 1.58/1.22
% 1.58/1.22 % (10624)Memory used [KB]: 5628
% 1.58/1.22 % (10624)Time elapsed: 0.009 s
% 1.58/1.22 % (10624)Instructions burned: 16 (million)
% 1.58/1.22 % (10624)------------------------------
% 1.58/1.22 % (10624)------------------------------
% 1.58/1.22 % (10623)Success in time 0.006 s
%------------------------------------------------------------------------------