%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU792^2 : 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 : n003.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 09:37:14 AM UTC 2026
% Result : Theorem 1.67s 1.34s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 21
% Syntax : Number of formulae : 160 ( 68 unt; 0 typ; 11 def)
% Number of atoms : 1396 ( 305 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 2367 ( 57 ~; 115 |; 39 &;1898 @)
% ( 11 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 24 con; 0-3 aty)
% ( 91 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 289 ( 108 ^; 163 !; 18 ?; 289 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
binunion: $i > $i > $i ).
thf(func_def_1,type,
breln1: $i > $i > $o ).
thf(func_def_2,type,
breln1invset: $i > $i > $i ).
thf(func_def_5,type,
breln1compset: $i > $i > $i > $i ).
thf(f498,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f258,f311,f327,f363,f390,f403,f412,f447,f458,f469,f488,f496]) ).
thf(f496,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f495]) ).
thf(f495,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f489]) ).
thf(f489,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f219,f34]) ).
thf(f34,plain,
( $true
= ( breln1 @ sK0 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( woz2Ex = $true )
& ( breln1compprop = $true )
& ( woz2W = $true )
& ( breln1unionCommutes = $true )
& ( ( breln1 @ sK0 @ sK1 )
= $true )
& ( ( breln1 @ sK0 @ sK2 )
= $true )
& ( $true
= ( breln1 @ sK0 @ sK3 ) )
& ( ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) )
!= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 ) )
& ( breln1invprop = $true )
& ( woz2A = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f28,f27,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( breln1 @ X0 @ X3 )
= $true )
& ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) )
=> ( ( ( breln1 @ sK0 @ sK1 )
= $true )
& ? [X2: $i] :
( ( $true
= ( breln1 @ sK0 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( breln1 @ sK0 @ X3 ) )
& ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ X3 ) @ ( breln1invset @ sK0 @ X2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ X3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X2: $i] :
( ( $true
= ( breln1 @ sK0 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( breln1 @ sK0 @ X3 ) )
& ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ X3 ) @ ( breln1invset @ sK0 @ X2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ X3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) ) ) ) )
=> ( ( ( breln1 @ sK0 @ sK2 )
= $true )
& ? [X3: $i] :
( ( $true
= ( breln1 @ sK0 @ X3 ) )
& ( ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ X3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ X3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) )
!= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X3: $i] :
( ( $true
= ( breln1 @ sK0 @ X3 ) )
& ( ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ X3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ X3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) )
!= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ X3 ) ) )
=> ( ( $true
= ( breln1 @ sK0 @ sK3 ) )
& ( ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) )
!= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( woz2Ex = $true )
& ( breln1compprop = $true )
& ( woz2W = $true )
& ( breln1unionCommutes = $true )
& ? [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( breln1 @ X0 @ X3 )
= $true )
& ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) )
& ( breln1invprop = $true )
& ( woz2A = $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( breln1 @ X0 @ X3 )
= $true )
& ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1compprop = $true )
& ( breln1invprop = $true ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( ( breln1invprop = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( breln1 @ X0 @ X3 )
= $true )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( breln1invprop
=> ( breln1compprop
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( breln1invprop
=> ( breln1compprop
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( breln1invprop
=> ( breln1compprop
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',woz2B) ).
thf(f219,plain,
( ( $false
= ( breln1 @ sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f217]) ).
thf(f217,definition,
( spl4_1
<=> ( $false
= ( breln1 @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f488,plain,
( spl4_1
| spl4_10
| ~ spl4_19 ),
inference(avatar_split_clause,[status(thm)],[f487,f304,f255,f217]) ).
thf(f255,definition,
( spl4_10
<=> ( ( breln1 @ sK0 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition]) ).
thf(f304,definition,
( spl4_19
<=> ( $false
= ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_19])],[avatar_definition]) ).
thf(f487,plain,
( ( $false
= ( breln1 @ sK0 @ sK3 ) )
| spl4_10
| ~ spl4_19 ),
inference(subsumption_resolution,[status(thm)],[f483,f256]) ).
thf(f256,plain,
( ( ( breln1 @ sK0 @ sK1 )
!= $false )
| spl4_10 ),
inference(avatar_component_clause,[status(thm)],[f255]) ).
thf(f483,plain,
( ( $false
= ( breln1 @ sK0 @ sK3 ) )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| ~ spl4_19 ),
inference(trivial_inequality_removal,[status(thm)],[f478]) ).
thf(f478,plain,
( ( $false = $true )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| ( $false
= ( breln1 @ sK0 @ sK3 ) )
| ~ spl4_19 ),
inference(superposition,[status(thm)],[f306,f79]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ X3 ) ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( breln1 @ X2 @ X3 )
=> ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ X3 ) ) ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ Y0 ) ) )
@ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( breln1 @ X2 @ ( breln1compset @ X2 @ X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1compset @ Y0 @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1compset @ Y0 @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( breln1 @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( breln1 @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f39,f30]) ).
thf(f30,plain,
( breln1compprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( breln1 @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( breln1compprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( breln1 @ Y1 @ ( breln1compset @ Y1 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( breln1compprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( breln1compprop
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',breln1compprop) ).
thf(f39,plain,
breln1compprop = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f306,plain,
( ( $false
= ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) )
| ~ spl4_19 ),
inference(avatar_component_clause,[status(thm)],[f304]) ).
thf(f469,plain,
( ~ spl4_3
| spl4_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f468]) ).
thf(f468,plain,
( $false
| ~ spl4_3
| spl4_6 ),
inference(subsumption_resolution,[status(thm)],[f464,f239]) ).
thf(f239,plain,
( ( $false
!= ( breln1 @ sK0 @ sK2 ) )
| spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f238]) ).
thf(f238,definition,
( spl4_6
<=> ( $false
= ( breln1 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f464,plain,
( ( $false
= ( breln1 @ sK0 @ sK2 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f461]) ).
thf(f461,plain,
( ( $false
= ( breln1 @ sK0 @ sK2 ) )
| ( $false = $true )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f71,f227]) ).
thf(f227,plain,
( ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK2 ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f225]) ).
thf(f225,definition,
( spl4_3
<=> ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ ( breln1invset @ X1 @ X2 ) ) )
| ( $false
= ( breln1 @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X1 @ X2 )
=> ( breln1 @ X1 @ ( breln1invset @ X1 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X1 @ Y0 )
=> ( breln1 @ X1 @ ( breln1invset @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X1 @ Y0 )
=> ( breln1 @ X1 @ ( breln1invset @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f41,f32]) ).
thf(f32,plain,
breln1invprop = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f41,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( breln1invprop
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
=> ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
= breln1invprop ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
= breln1invprop ),
file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',breln1invprop) ).
thf(f458,plain,
( spl4_1
| ~ spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f454,f229,f217]) ).
thf(f229,definition,
( spl4_4
<=> ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f454,plain,
( ( $false
= ( breln1 @ sK0 @ sK3 ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f452]) ).
thf(f452,plain,
( ( $false
= ( breln1 @ sK0 @ sK3 ) )
| ( $false = $true )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f71,f231]) ).
thf(f231,plain,
( ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f229]) ).
thf(f447,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[status(thm)],[f446]) ).
thf(f446,plain,
( $false
| ~ spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f439]) ).
thf(f439,plain,
( ( $false = $true )
| ~ spl4_6 ),
inference(superposition,[status(thm)],[f240,f35]) ).
thf(f35,plain,
( ( breln1 @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f240,plain,
( ( $false
= ( breln1 @ sK0 @ sK2 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f238]) ).
thf(f412,plain,
~ spl4_10,
inference(avatar_contradiction_clause,[status(thm)],[f411]) ).
thf(f411,plain,
( $false
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f406]) ).
thf(f406,plain,
( ( $false = $true )
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f36,f257]) ).
thf(f257,plain,
( ( ( breln1 @ sK0 @ sK1 )
= $false )
| ~ spl4_10 ),
inference(avatar_component_clause,[status(thm)],[f255]) ).
thf(f36,plain,
( ( breln1 @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f403,plain,
( spl4_10
| spl4_34 ),
inference(avatar_split_clause,[status(thm)],[f399,f387,f255]) ).
thf(f387,definition,
( spl4_34
<=> ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
= ( breln1compset @ sK0 @ ( binunion @ sK2 @ sK1 ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_34])],[avatar_definition]) ).
thf(f399,plain,
( ( ( breln1 @ sK0 @ sK1 )
= $false )
| spl4_34 ),
inference(trivial_inequality_removal,[status(thm)],[f397]) ).
thf(f397,plain,
( ( ( breln1 @ sK0 @ sK1 )
= $false )
| ( $false = $true )
| spl4_34 ),
inference(superposition,[status(thm)],[f35,f394]) ).
thf(f394,plain,
( ! [X0: $i] :
( ( $false
= ( breln1 @ X0 @ sK2 ) )
| ( $false
= ( breln1 @ X0 @ sK1 ) ) )
| spl4_34 ),
inference(trivial_inequality_removal,[status(thm)],[f392]) ).
thf(f392,plain,
( ! [X0: $i] :
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 ) )
| ( $false
= ( breln1 @ X0 @ sK1 ) )
| ( $false
= ( breln1 @ X0 @ sK2 ) ) )
| spl4_34 ),
inference(superposition,[status(thm)],[f389,f60]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( binunion @ X1 @ X3 )
= ( binunion @ X3 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( binunion @ X1 @ X3 )
= ( binunion @ X3 @ X1 ) ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( breln1 @ X2 @ X3 )
=> ( ( binunion @ X1 @ X3 )
= ( binunion @ X3 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( binunion @ X1 @ Y0 )
= ( binunion @ Y0 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( binunion @ X1 @ Y0 )
= ( binunion @ Y0 @ X1 ) ) ) )
= $true )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( binunion @ X1 @ Y0 )
= ( binunion @ Y0 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( binunion @ X1 @ Y1 )
= ( binunion @ Y1 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( binunion @ X1 @ Y1 )
= ( binunion @ Y1 @ X1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( binunion @ Y0 @ Y2 )
= ( binunion @ Y2 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( binunion @ Y0 @ Y2 )
= ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f45,f37]) ).
thf(f37,plain,
breln1unionCommutes = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f45,plain,
( breln1unionCommutes
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( binunion @ Y0 @ Y2 )
= ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( breln1unionCommutes
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( ( binunion @ Y0 @ Y2 )
= ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( binunion @ X1 @ X2 )
= ( binunion @ X2 @ X1 ) ) ) )
= breln1unionCommutes ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( binunion @ X1 @ X2 )
= ( binunion @ X2 @ X1 ) ) ) )
= breln1unionCommutes ),
file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',breln1unionCommutes) ).
thf(f389,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( breln1compset @ sK0 @ ( binunion @ sK2 @ sK1 ) @ sK3 ) )
| spl4_34 ),
inference(avatar_component_clause,[status(thm)],[f387]) ).
thf(f390,plain,
( spl4_1
| spl4_6
| ~ spl4_34
| spl4_10
| spl4_29 ),
inference(avatar_split_clause,[status(thm)],[f374,f360,f255,f387,f238,f217]) ).
thf(f360,definition,
( spl4_29
<=> ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_29])],[avatar_definition]) ).
thf(f374,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( breln1compset @ sK0 @ ( binunion @ sK2 @ sK1 ) @ sK3 ) )
| ( $false
= ( breln1 @ sK0 @ sK3 ) )
| ( $false
= ( breln1 @ sK0 @ sK2 ) )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| spl4_29 ),
inference(superposition,[status(thm)],[f362,f91]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( binunion @ ( breln1compset @ X2 @ X1 @ X4 ) @ ( breln1compset @ X2 @ X3 @ X4 ) )
= ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ X4 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X4 ) )
| ( $true
= ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ X4 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ X4 ) @ ( breln1compset @ X2 @ X3 @ X4 ) ) ) )
| ( $false
= ( breln1 @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( ( breln1 @ X2 @ X4 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ X4 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ X4 ) @ ( breln1compset @ X2 @ X3 @ X4 ) ) ) ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ Y0 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y0 ) @ ( breln1compset @ X2 @ X3 @ Y0 ) ) ) )
@ X4 ) ) ),
inference(pi_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ Y0 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y0 ) @ ( breln1compset @ X2 @ X3 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( ( breln1 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ X3 ) @ Y0 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y0 ) @ ( breln1compset @ X2 @ X3 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ X2 @ Y1 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ Y0 ) @ Y1 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y1 ) @ ( breln1compset @ X2 @ Y0 @ Y1 ) ) ) ) ) )
@ X3 ) )
| ( $false
= ( breln1 @ X2 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ X2 @ Y1 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ Y0 ) @ Y1 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y1 ) @ ( breln1compset @ X2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ X2 @ Y1 )
=> ( ( breln1compset @ X2 @ ( binunion @ X1 @ Y0 ) @ Y1 )
= ( binunion @ ( breln1compset @ X2 @ X1 @ Y1 ) @ ( breln1compset @ X2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( breln1compset @ Y0 @ ( binunion @ X1 @ Y1 ) @ Y2 )
= ( binunion @ ( breln1compset @ Y0 @ X1 @ Y2 ) @ ( breln1compset @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( breln1compset @ Y0 @ ( binunion @ X1 @ Y1 ) @ Y2 )
= ( binunion @ ( breln1compset @ Y0 @ X1 @ Y2 ) @ ( breln1compset @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln1 @ Y1 @ Y3 )
=> ( ( breln1compset @ Y1 @ ( binunion @ Y0 @ Y2 ) @ Y3 )
= ( binunion @ ( breln1compset @ Y1 @ Y0 @ Y3 ) @ ( breln1compset @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln1 @ Y1 @ Y3 )
=> ( ( breln1compset @ Y1 @ ( binunion @ Y0 @ Y2 ) @ Y3 )
= ( binunion @ ( breln1compset @ Y1 @ Y0 @ Y3 ) @ ( breln1compset @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f44,f31]) ).
thf(f31,plain,
woz2A = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f44,plain,
( woz2A
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln1 @ Y1 @ Y3 )
=> ( ( breln1compset @ Y1 @ ( binunion @ Y0 @ Y2 ) @ Y3 )
= ( binunion @ ( breln1compset @ Y1 @ Y0 @ Y3 ) @ ( breln1compset @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( woz2A
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( breln1 @ Y1 @ Y3 )
=> ( ( breln1compset @ Y1 @ ( binunion @ Y0 @ Y2 ) @ Y3 )
= ( binunion @ ( breln1compset @ Y1 @ Y0 @ Y3 ) @ ( breln1compset @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( woz2A
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( woz2A
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',woz2A) ).
thf(f362,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) )
| spl4_29 ),
inference(avatar_component_clause,[status(thm)],[f360]) ).
thf(f363,plain,
( ~ spl4_29
| spl4_6
| spl4_22 ),
inference(avatar_split_clause,[status(thm)],[f347,f324,f238,f360]) ).
thf(f324,definition,
( spl4_22
<=> ( ( binunion @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK2 ) ) @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) )
= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_22])],[avatar_definition]) ).
thf(f347,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1compset @ sK0 @ sK2 @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) )
| ( $false
= ( breln1 @ sK0 @ sK2 ) )
| spl4_22 ),
inference(superposition,[status(thm)],[f326,f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X2 ) )
= X2 )
| ( $false
= ( breln1 @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $true
= ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X2 ) )
= X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( ( ( breln1 @ X1 @ X2 )
=> ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X2 ) )
= X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( breln1 @ X1 @ Y0 )
=> ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ Y0 ) )
= Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X1 @ Y0 )
=> ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ Y0 ) )
= Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) )
= Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f42,f40]) ).
thf(f40,plain,
woz2Ex = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f42,plain,
( woz2Ex
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( woz2Ex
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( woz2Ex
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( woz2Ex
= ( ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',woz2Ex) ).
thf(f326,plain,
( ( ( binunion @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK2 ) ) @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) )
!= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 ) )
| spl4_22 ),
inference(avatar_component_clause,[status(thm)],[f324]) ).
thf(f327,plain,
( spl4_3
| ~ spl4_22
| spl4_1
| spl4_4
| spl4_20 ),
inference(avatar_split_clause,[status(thm)],[f319,f308,f229,f217,f324,f225]) ).
thf(f308,definition,
( spl4_20
<=> ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_20])],[avatar_definition]) ).
thf(f319,plain,
( ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK2 ) ) )
| ( ( binunion @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ sK2 ) ) @ sK3 ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) )
!= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 ) )
| ( $false
= ( breln1 @ sK0 @ ( breln1invset @ sK0 @ sK3 ) ) )
| ( $false
= ( breln1 @ sK0 @ sK3 ) )
| spl4_20 ),
inference(superposition,[status(thm)],[f310,f114]) ).
thf(f114,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ X1 )
= ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X1 ) @ X2 ) ) )
| ( ( breln1 @ X0 @ X2 )
= $false )
| ( ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
= $false )
| ( ( breln1 @ X0 @ X1 )
= $false ) ),
inference(superposition,[status(thm)],[f100,f66]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1invset @ X1 @ ( breln1compset @ X1 @ X2 @ X3 ) )
= ( breln1compset @ X1 @ ( breln1invset @ X1 @ X3 ) @ ( breln1invset @ X1 @ X2 ) ) )
| ( $false
= ( breln1 @ X1 @ X2 ) )
| ( ( breln1 @ X1 @ X3 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( breln1 @ X1 @ X3 )
= $false )
| ( $true
= ( ( breln1compset @ X1 @ ( breln1invset @ X1 @ X3 ) @ ( breln1invset @ X1 @ X2 ) )
= ( breln1invset @ X1 @ ( breln1compset @ X1 @ X2 @ X3 ) ) ) )
| ( $false
= ( breln1 @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X1 @ X2 ) )
| ( $true
= ( ( breln1 @ X1 @ X3 )
=> ( ( breln1compset @ X1 @ ( breln1invset @ X1 @ X3 ) @ ( breln1invset @ X1 @ X2 ) )
= ( breln1invset @ X1 @ ( breln1compset @ X1 @ X2 @ X3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( breln1 @ X1 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ( breln1 @ X1 @ Y0 )
=> ( ( breln1compset @ X1 @ ( breln1invset @ X1 @ Y0 ) @ ( breln1invset @ X1 @ X2 ) )
= ( breln1invset @ X1 @ ( breln1compset @ X1 @ X2 @ Y0 ) ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X1 @ Y0 )
=> ( ( breln1compset @ X1 @ ( breln1invset @ X1 @ Y0 ) @ ( breln1invset @ X1 @ X2 ) )
= ( breln1invset @ X1 @ ( breln1compset @ X1 @ X2 @ Y0 ) ) ) ) ) )
| ( $false
= ( breln1 @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( breln1 @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X1 @ Y0 )
=> ( ( breln1compset @ X1 @ ( breln1invset @ X1 @ Y0 ) @ ( breln1invset @ X1 @ X2 ) )
= ( breln1invset @ X1 @ ( breln1compset @ X1 @ X2 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( breln1 @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ X1 @ Y1 )
=> ( ( breln1compset @ X1 @ ( breln1invset @ X1 @ Y1 ) @ ( breln1invset @ X1 @ Y0 ) )
= ( breln1invset @ X1 @ ( breln1compset @ X1 @ Y0 @ Y1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( breln1 @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ X1 @ Y1 )
=> ( ( breln1compset @ X1 @ ( breln1invset @ X1 @ Y1 ) @ ( breln1invset @ X1 @ Y0 ) )
= ( breln1invset @ X1 @ ( breln1compset @ X1 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( breln1compset @ Y0 @ ( breln1invset @ Y0 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
= ( breln1invset @ Y0 @ ( breln1compset @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( breln1compset @ Y0 @ ( breln1invset @ Y0 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
= ( breln1invset @ Y0 @ ( breln1compset @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f43,f38]) ).
thf(f38,plain,
woz2W = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f43,plain,
( woz2W
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( breln1compset @ Y0 @ ( breln1invset @ Y0 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
= ( breln1invset @ Y0 @ ( breln1compset @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( woz2W
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( breln1compset @ Y0 @ ( breln1invset @ Y0 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
= ( breln1invset @ Y0 @ ( breln1compset @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( woz2W
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ( ( breln1compset @ X1 @ ( breln1invset @ X1 @ X2 ) @ ( breln1invset @ X1 @ X0 ) )
= ( breln1invset @ X1 @ ( breln1compset @ X1 @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( woz2W
= ( ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',woz2W) ).
thf(f310,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) )
| spl4_20 ),
inference(avatar_component_clause,[status(thm)],[f308]) ).
thf(f311,plain,
( spl4_19
| ~ spl4_20
| spl4_9 ),
inference(avatar_split_clause,[status(thm)],[f279,f251,f308,f304]) ).
thf(f251,definition,
( spl4_9
<=> ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition]) ).
thf(f279,plain,
( ( $false
= ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) )
| ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) )
| spl4_9 ),
inference(superposition,[status(thm)],[f253,f66]) ).
thf(f253,plain,
( ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) ) ) )
| spl4_9 ),
inference(avatar_component_clause,[status(thm)],[f251]) ).
thf(f258,plain,
( spl4_1
| ~ spl4_9
| spl4_10 ),
inference(avatar_split_clause,[status(thm)],[f208,f255,f251,f217]) ).
thf(f208,plain,
( ( $false
= ( breln1 @ sK0 @ sK3 ) )
| ( ( breln1 @ sK0 @ sK1 )
= $false )
| ( ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 )
!= ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK3 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f33,f100]) ).
thf(f33,plain,
( ( binunion @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK2 ) ) ) @ ( breln1invset @ sK0 @ ( breln1compset @ sK0 @ ( breln1invset @ sK0 @ sK3 ) @ ( breln1invset @ sK0 @ sK1 ) ) ) )
!= ( breln1compset @ sK0 @ ( binunion @ sK1 @ sK2 ) @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU792^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:33:55 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU792^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Binary Relations on a Set - Second Wizard of Oz Examples
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S ->
% 0.30/0.46 % (! T:i.breln1 A T -> breln1compset A (binunion R S) T =
% 0.30/0.46 % binunion (breln1invset A (breln1compset A (breln1invset A T)
% 0.30/0.46 % (breln1invset A S))) (breln1invset A (breln1compset A
% 0.30/0.46 % (breln1invset A T) (breln1invset A R))))))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC294l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % 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, 0.40 v6.2.0, 0.29 v6.1.0, 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
% 0.30/0.46 % Syntax : Number of formulae : 17 ( 6 unt; 10 typ; 6 def)
% 0.30/0.46 % Number of atoms : 39 ( 11 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 10 ( 5 avg)
% 0.30/0.46 % Number of connectives : 115 ( 0 ~; 0 |; 0 &; 95 @)
% 0.30/0.46 % ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 16 ( 3 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 11 ( 10 usr; 6 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=357
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(binunion_type,type,
% 0.30/0.46 binunion: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(breln1_type,type,
% 0.30/0.46 breln1: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(breln1invset_type,type,
% 0.30/0.46 breln1invset: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(breln1invprop_type,type,
% 0.30/0.46 breln1invprop: $o ).
% 0.30/0.46
% 0.30/0.46 thf(breln1invprop,definition,
% 0.30/0.46 ( breln1invprop
% 0.30/0.46 = ( ! [A: $i,R: $i] :
% 0.30/0.46 ( ( breln1 @ A @ R )
% 0.30/0.46 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(breln1compset_type,type,
% 0.30/0.46 breln1compset: $i > $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(breln1compprop_type,type,
% 0.30/0.46 breln1compprop: $o ).
% 0.30/0.46
% 0.30/0.46 thf(breln1compprop,definition,
% 0.30/0.46 ( breln1compprop
% 0.30/0.46 = ( ! [A: $i,R: $i] :
% 0.30/0.46 ( ( breln1 @ A @ R )
% 0.30/0.46 => ! [S: $i] :
% 0.30/0.46 ( ( breln1 @ A @ S )
% 0.30/0.46 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(breln1unionCommutes_type,type,
% 0.30/0.46 breln1unionCommutes: $o ).
% 0.30/0.46
% 0.30/0.46 thf(breln1unionCommutes,definition,
% 0.30/0.46 ( breln1unionCommutes
% 0.30/0.46 = ( ! [A: $i,R: $i] :
% 0.30/0.46 ( ( breln1 @ A @ R )
% 0.30/0.46 => ! [S: $i] :
% 0.30/0.46 ( ( breln1 @ A @ S )
% 0.30/0.46 => ( ( binunion @ R @ S )
% 0.30/0.46 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(woz2Ex_type,type,
% 0.30/0.46 woz2Ex: $o ).
% 0.30/0.46
% 0.30/0.46 thf(woz2Ex,definition,
% 0.30/0.46 ( woz2Ex
% 0.30/0.46 = ( ! [A: $i,R: $i] :
% 0.30/0.46 ( ( breln1 @ A @ R )
% 0.30/0.46 => ( R
% 0.30/0.46 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(woz2W_type,type,
% 0.30/0.46 woz2W: $o ).
% 0.30/0.46
% 0.30/0.46 thf(woz2W,definition,
% 0.30/0.46 ( woz2W
% 0.30/0.46 = ( ! [A: $i,R: $i] :
% 0.30/0.46 ( ( breln1 @ A @ R )
% 0.30/0.46 => ! [S: $i] :
% 0.30/0.46 ( ( breln1 @ A @ S )
% 0.30/0.46 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.30/0.46 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(woz2A_type,type,
% 0.30/0.46 woz2A: $o ).
% 0.30/0.46
% 0.30/0.46 thf(woz2A,definition,
% 0.30/0.46 ( woz2A
% 0.30/0.46 = ( ! [A: $i,R: $i] :
% 0.30/0.46 ( ( breln1 @ A @ R )
% 0.30/0.46 => ! [S: $i] :
% 0.30/0.46 ( ( breln1 @ A @ S )
% 0.30/0.46 => ! [T: $i] :
% 0.30/0.46 ( ( breln1 @ A @ T )
% 0.30/0.46 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.30/0.46 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(woz2B,conjecture,
% 0.30/0.46 ( breln1invprop
% 0.30/0.46 => ( breln1compprop
% 0.30/0.46 => ( breln1unionCommutes
% 0.30/0.46 => ( woz2Ex
% 0.30/0.46 => ( woz2W
% 0.30/0.46 => ( woz2A
% 0.30/0.46 => ! [A: $i,R: $i] :
% 0.30/0.46 ( ( breln1 @ A @ R )
% 0.30/0.46 => ! [S: $i] :
% 0.30/0.46 ( ( breln1 @ A @ S )
% 0.30/0.46 => ! [T: $i] :
% 0.30/0.46 ( ( breln1 @ A @ T )
% 0.30/0.46 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.30/0.46 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.56/1.24 ---- Embedded in THF ---
% 1.56/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.24 %%% Generated on Tue Feb 24 12:33:56 EST 2026
% 1.56/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.24 %%% Logic specification used:
% 1.56/1.24 %%% thf(spec, logic, $$dhol).
% 1.56/1.24
% 1.56/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2DTF3734.p
% See solution above
% 1.56/1.24 ------------------------
% 1.56/1.26 ---- Cleaned THF ---
% 1.56/1.26 thf(binunion_type,type,
% 1.56/1.26 binunion: $i > $i > $i ).
% 1.56/1.26
% 1.56/1.26 thf(breln1_type,type,
% 1.56/1.26 breln1: $i > $i > $o ).
% 1.56/1.26
% 1.56/1.26 thf(breln1invset_type,type,
% 1.56/1.26 breln1invset: $i > $i > $i ).
% 1.56/1.26
% 1.56/1.26 thf(breln1invprop_type,type,
% 1.56/1.26 breln1invprop: $o ).
% 1.56/1.26
% 1.56/1.26 thf(breln1invprop,definition,
% 1.56/1.26 ( breln1invprop
% 1.56/1.26 = ( ! [A: $i,R: $i] :
% 1.56/1.26 ( ( breln1 @ A @ R )
% 1.56/1.26 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 1.56/1.26
% 1.56/1.26 thf(breln1compset_type,type,
% 1.56/1.26 breln1compset: $i > $i > $i > $i ).
% 1.56/1.26
% 1.56/1.26 thf(breln1compprop_type,type,
% 1.56/1.26 breln1compprop: $o ).
% 1.56/1.26
% 1.56/1.26 thf(breln1compprop,definition,
% 1.56/1.26 ( breln1compprop
% 1.56/1.26 = ( ! [A: $i,R: $i] :
% 1.56/1.26 ( ( breln1 @ A @ R )
% 1.56/1.26 => ! [S: $i] :
% 1.56/1.26 ( ( breln1 @ A @ S )
% 1.56/1.26 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 1.56/1.26
% 1.56/1.26 thf(breln1unionCommutes_type,type,
% 1.56/1.26 breln1unionCommutes: $o ).
% 1.56/1.26
% 1.56/1.26 thf(breln1unionCommutes,definition,
% 1.56/1.26 ( breln1unionCommutes
% 1.56/1.26 = ( ! [A: $i,R: $i] :
% 1.56/1.26 ( ( breln1 @ A @ R )
% 1.56/1.26 => ! [S: $i] :
% 1.56/1.26 ( ( breln1 @ A @ S )
% 1.56/1.26 => ( ( binunion @ R @ S )
% 1.56/1.26 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 1.56/1.26
% 1.56/1.26 thf(woz2Ex_type,type,
% 1.56/1.26 woz2Ex: $o ).
% 1.56/1.26
% 1.56/1.26 thf(woz2Ex,definition,
% 1.56/1.26 ( woz2Ex
% 1.56/1.26 = ( ! [A: $i,R: $i] :
% 1.56/1.26 ( ( breln1 @ A @ R )
% 1.56/1.26 => ( R
% 1.56/1.26 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 1.56/1.26
% 1.56/1.26 thf(woz2W_type,type,
% 1.56/1.26 woz2W: $o ).
% 1.56/1.26
% 1.56/1.26 thf(woz2W,definition,
% 1.56/1.26 ( woz2W
% 1.56/1.26 = ( ! [A: $i,R: $i] :
% 1.56/1.26 ( ( breln1 @ A @ R )
% 1.56/1.26 => ! [S: $i] :
% 1.56/1.26 ( ( breln1 @ A @ S )
% 1.56/1.26 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 1.56/1.26 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 1.56/1.26
% 1.56/1.26 thf(woz2A_type,type,
% 1.56/1.26 woz2A: $o ).
% 1.56/1.26
% 1.56/1.26 thf(woz2A,definition,
% 1.56/1.26 ( woz2A
% 1.56/1.26 = ( ! [A: $i,R: $i] :
% 1.56/1.26 ( ( breln1 @ A @ R )
% 1.56/1.26 => ! [S: $i] :
% 1.56/1.26 ( ( breln1 @ A @ S )
% 1.56/1.26 => ! [T: $i] :
% 1.56/1.26 ( ( breln1 @ A @ T )
% 1.56/1.26 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 1.56/1.26 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 1.56/1.26
% 1.56/1.26 thf(woz2B,conjecture,
% 1.56/1.26 ( breln1invprop
% 1.56/1.26 => ( breln1compprop
% 1.56/1.26 => ( breln1unionCommutes
% 1.56/1.26 => ( woz2Ex
% 1.56/1.26 => ( woz2W
% 1.56/1.26 => ( woz2A
% 1.56/1.26 => ! [A: $i,R: $i] :
% 1.56/1.26 ( ( breln1 @ A @ R )
% 1.56/1.26 => ! [S: $i] :
% 1.56/1.26 ( ( breln1 @ A @ S )
% 1.56/1.26 => ! [T: $i] :
% 1.56/1.26 ( ( breln1 @ A @ T )
% 1.56/1.26 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 1.56/1.26 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.56/1.26 ------------------------
% 1.56/1.27 % (4012)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/18Mi)
% 1.56/1.27 % (4010)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_3734 for (2999ds/2Mi)
% 1.56/1.27 % (4010)Instruction limit reached!
% 1.56/1.27 % (4010)------------------------------
% 1.56/1.27 % (4010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (4010)Termination reason: Unknown
% 1.56/1.27 % (4010)Termination phase: shuffling
% 1.56/1.27
% 1.56/1.27 % (4010)Memory used [KB]: 1023
% 1.56/1.27 % (4010)Time elapsed: 0.002 s
% 1.56/1.27 % (4010)Instructions burned: 3 (million)
% 1.56/1.27 % (4010)------------------------------
% 1.56/1.27 % (4010)------------------------------
% 1.56/1.28 % (4012)Instruction limit reached!
% 1.56/1.28 % (4012)------------------------------
% 1.56/1.28 % (4012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.28 % (4012)Termination reason: Unknown
% 1.56/1.28 % (4012)Termination phase: Saturation
% 1.56/1.28
% 1.56/1.28 % (4012)Memory used [KB]: 5628
% 1.56/1.28 % (4012)Time elapsed: 0.008 s
% 1.56/1.28 % (4012)Instructions burned: 18 (million)
% 1.56/1.28 % (4012)------------------------------
% 1.56/1.28 % (4012)------------------------------
% 1.56/1.28 % (4006)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/183Mi)
% 1.56/1.28 % (4007)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_3734 for (2999ds/4Mi)
% 1.56/1.28 % (4008)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_3734 for (2999ds/27Mi)
% 1.56/1.28 % (4009)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/2Mi)
% 1.56/1.28 % (4011)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_3734 for (2999ds/275Mi)
% 1.56/1.28 % (4009)Instruction limit reached!
% 1.56/1.28 % (4009)------------------------------
% 1.56/1.28 % (4009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.28 % (4009)Termination reason: Unknown
% 1.56/1.28 % (4009)Termination phase: shuffling
% 1.56/1.28
% 1.56/1.28 % (4009)Memory used [KB]: 895
% 1.56/1.28 % (4009)Time elapsed: 0.003 s
% 1.56/1.28 % (4009)Instructions burned: 2 (million)
% 1.56/1.28 % (4009)------------------------------
% 1.56/1.28 % (4009)------------------------------
% 1.56/1.28 % (4007)Instruction limit reached!
% 1.56/1.28 % (4007)------------------------------
% 1.56/1.28 % (4007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.28 % (4007)Termination reason: Unknown
% 1.56/1.28 % (4007)Termination phase: Property scanning
% 1.56/1.28
% 1.56/1.28 % (4007)Memory used [KB]: 1023
% 1.56/1.28 % (4007)Time elapsed: 0.005 s
% 1.56/1.28 % (4007)Instructions burned: 5 (million)
% 1.56/1.28 % (4007)------------------------------
% 1.56/1.28 % (4007)------------------------------
% 1.56/1.28 % (4013)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/3Mi)
% 1.56/1.28 % (4013)Instruction limit reached!
% 1.56/1.28 % (4013)------------------------------
% 1.56/1.28 % (4013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.28 % (4013)Termination reason: Unknown
% 1.56/1.28 % (4013)Termination phase: Property scanning
% 1.56/1.28
% 1.56/1.28 % (4013)Memory used [KB]: 1023
% 1.56/1.28 % (4013)Time elapsed: 0.003 s
% 1.56/1.28 % (4013)Instructions burned: 4 (million)
% 1.56/1.28 % (4013)------------------------------
% 1.56/1.28 % (4013)------------------------------
% 1.56/1.29 % (4014)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/37Mi)
% 1.56/1.29 % (4017)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/1041Mi)
% 1.56/1.29 % (4008)Instruction limit reached!
% 1.56/1.29 % (4008)------------------------------
% 1.56/1.29 % (4008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.29 % (4008)Termination reason: Unknown
% 1.56/1.29 % (4008)Termination phase: Saturation
% 1.56/1.29
% 1.56/1.29 % (4008)Memory used [KB]: 5628
% 1.56/1.29 % (4008)Time elapsed: 0.018 s
% 1.56/1.29 % (4008)Instructions burned: 27 (million)
% 1.56/1.29 % (4008)------------------------------
% 1.56/1.29 % (4008)------------------------------
% 1.67/1.30 % (4015)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/15Mi)
% 1.67/1.30 % (4014)Instruction limit reached!
% 1.67/1.30 % (4014)------------------------------
% 1.67/1.30 % (4014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.30 % (4014)Termination reason: Unknown
% 1.67/1.30 % (4014)Termination phase: Saturation
% 1.67/1.30
% 1.67/1.30 % (4014)Memory used [KB]: 5756
% 1.67/1.30 % (4014)Time elapsed: 0.012 s
% 1.67/1.30 % (4014)Instructions burned: 37 (million)
% 1.67/1.30 % (4014)------------------------------
% 1.67/1.30 % (4014)------------------------------
% 1.67/1.30 % (4016)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/3Mi)
% 1.67/1.30 % (4016)Instruction limit reached!
% 1.67/1.30 % (4016)------------------------------
% 1.67/1.30 % (4016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.30 % (4016)Termination reason: Unknown
% 1.67/1.30 % (4016)Termination phase: Property scanning
% 1.67/1.30
% 1.67/1.30 % (4016)Memory used [KB]: 1023
% 1.67/1.30 % (4016)Time elapsed: 0.004 s
% 1.67/1.30 % (4016)Instructions burned: 4 (million)
% 1.67/1.30 % (4016)------------------------------
% 1.67/1.30 % (4016)------------------------------
% 1.67/1.31 % (4018)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/7Mi)
% 1.67/1.31 % (4015)Instruction limit reached!
% 1.67/1.31 % (4015)------------------------------
% 1.67/1.31 % (4015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (4015)Termination reason: Unknown
% 1.67/1.31 % (4015)Termination phase: Saturation
% 1.67/1.31
% 1.67/1.31 % (4015)Memory used [KB]: 5628
% 1.67/1.31 % (4015)Time elapsed: 0.011 s
% 1.67/1.31 % (4015)Instructions burned: 15 (million)
% 1.67/1.31 % (4015)------------------------------
% 1.67/1.31 % (4015)------------------------------
% 1.67/1.31 % (4019)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/16Mi)
% 1.67/1.31 % (4018)Instruction limit reached!
% 1.67/1.31 % (4018)------------------------------
% 1.67/1.31 % (4018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (4018)Termination reason: Unknown
% 1.67/1.31 % (4018)Termination phase: Saturation
% 1.67/1.31
% 1.67/1.31 % (4018)Memory used [KB]: 1023
% 1.67/1.31 % (4018)Time elapsed: 0.004 s
% 1.67/1.31 % (4018)Instructions burned: 8 (million)
% 1.67/1.31 % (4018)------------------------------
% 1.67/1.31 % (4018)------------------------------
% 1.67/1.31 % (4019)Instruction limit reached!
% 1.67/1.31 % (4019)------------------------------
% 1.67/1.31 % (4019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (4019)Termination reason: Unknown
% 1.67/1.31 % (4019)Termination phase: Saturation
% 1.67/1.31
% 1.67/1.31 % (4019)Memory used [KB]: 5884
% 1.67/1.31 % (4019)Time elapsed: 0.006 s
% 1.67/1.31 % (4019)Instructions burned: 16 (million)
% 1.67/1.31 % (4019)------------------------------
% 1.67/1.31 % (4019)------------------------------
% 1.67/1.32 % (4022)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/7Mi)
% 1.67/1.32 % (4020)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/3Mi)
% 1.67/1.32 % (4020)Instruction limit reached!
% 1.67/1.32 % (4020)------------------------------
% 1.67/1.32 % (4020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (4020)Termination reason: Unknown
% 1.67/1.32 % (4020)Termination phase: Unused predicate definition removal
% 1.67/1.32
% 1.67/1.32 % (4020)Memory used [KB]: 1023
% 1.67/1.32 % (4020)Time elapsed: 0.003 s
% 1.67/1.32 % (4020)Instructions burned: 4 (million)
% 1.67/1.32 % (4020)------------------------------
% 1.67/1.32 % (4020)------------------------------
% 1.67/1.32 % (4022)Instruction limit reached!
% 1.67/1.32 % (4022)------------------------------
% 1.67/1.32 % (4022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (4022)Termination reason: Unknown
% 1.67/1.32 % (4022)Termination phase: Saturation
% 1.67/1.32
% 1.67/1.32 % (4022)Memory used [KB]: 5500
% 1.67/1.32 % (4022)Time elapsed: 0.004 s
% 1.67/1.32 % (4022)Instructions burned: 7 (million)
% 1.67/1.32 % (4022)------------------------------
% 1.67/1.32 % (4022)------------------------------
% 1.67/1.32 % (4023)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/3Mi)
% 1.67/1.32 % (4023)Instruction limit reached!
% 1.67/1.32 % (4023)------------------------------
% 1.67/1.32 % (4023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (4023)Termination reason: Unknown
% 1.67/1.32 % (4023)Termination phase: Property scanning
% 1.67/1.32
% 1.67/1.32 % (4023)Memory used [KB]: 1023
% 1.67/1.32 % (4023)Time elapsed: 0.002 s
% 1.67/1.32 % (4023)Instructions burned: 4 (million)
% 1.67/1.32 % (4023)------------------------------
% 1.67/1.32 % (4023)------------------------------
% 1.67/1.32 % (4021)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/3Mi)
% 1.67/1.33 % (4021)Instruction limit reached!
% 1.67/1.33 % (4021)------------------------------
% 1.67/1.33 % (4021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (4021)Termination reason: Unknown
% 1.67/1.33 % (4021)Termination phase: Preprocessing 3
% 1.67/1.33
% 1.67/1.33 % (4021)Memory used [KB]: 1023
% 1.67/1.33 % (4021)Time elapsed: 0.004 s
% 1.67/1.33 % (4021)Instructions burned: 4 (million)
% 1.67/1.33 % (4021)------------------------------
% 1.67/1.33 % (4021)------------------------------
% 1.67/1.33 % (4025)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/18Mi)
% 1.67/1.33 % (4024)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/4Mi)
% 1.67/1.33 % (4024)Instruction limit reached!
% 1.67/1.33 % (4024)------------------------------
% 1.67/1.33 % (4024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (4024)Termination reason: Unknown
% 1.67/1.33 % (4024)Termination phase: Property scanning
% 1.67/1.33
% 1.67/1.33 % (4024)Memory used [KB]: 1023
% 1.67/1.33 % (4024)Time elapsed: 0.003 s
% 1.67/1.33 % (4024)Instructions burned: 4 (million)
% 1.67/1.33 % (4024)------------------------------
% 1.67/1.33 % (4024)------------------------------
% 1.67/1.33 % (4026)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/710Mi)
% 1.67/1.34 % (4006)First to succeed.
% 1.67/1.34 % (4025)Instruction limit reached!
% 1.67/1.34 % (4025)------------------------------
% 1.67/1.34 % (4025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (4025)Termination reason: Unknown
% 1.67/1.34 % (4025)Termination phase: Saturation
% 1.67/1.34
% 1.67/1.34 % (4025)Memory used [KB]: 5628
% 1.67/1.34 % (4025)Time elapsed: 0.008 s
% 1.67/1.34 % (4025)Instructions burned: 19 (million)
% 1.67/1.34 % (4025)------------------------------
% 1.67/1.34 % (4025)------------------------------
% 1.67/1.34 % (4028)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/902Mi)
% 1.67/1.34 % (4027)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3734 for (2999ds/6Mi)
% 1.67/1.34 % (4006)Refutation found. Thanks to Tanya!
% 1.67/1.34 % SZS status Theorem for DTF2THF_3734
% 1.67/1.34 % SZS output start Proof for DTF2THF_3734
% 1.67/1.34 thf(func_def_0, type, binunion: $i > $i > $i).
% 1.67/1.34 thf(func_def_1, type, breln1: $i > $i > $o).
% 1.67/1.34 thf(func_def_2, type, breln1invset: $i > $i > $i).
% 1.67/1.34 thf(func_def_5, type, breln1compset: $i > $i > $i > $i).
% 1.67/1.34 thf(f498,plain,(
% 1.67/1.34 $false),
% 1.67/1.34 inference(avatar_sat_refutation,[status(thm)],[f258,f311,f327,f363,f390,f403,f412,f447,f458,f469,f488,f496])).
% 1.67/1.34 thf(f496,plain,(
% 1.67/1.34 ~spl4_1),
% 1.67/1.34 inference(avatar_contradiction_clause,[status(thm)],[f495])).
% 1.67/1.34 thf(f495,plain,(
% 1.67/1.34 $false | ~spl4_1),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f489])).
% 1.67/1.34 thf(f489,plain,(
% 1.67/1.34 ($false = $true) | ~spl4_1),
% 1.67/1.34 inference(superposition,[status(thm)],[f219,f34])).
% 1.67/1.34 thf(f34,plain,(
% 1.67/1.34 ($true = (breln1 @ sK0 @ sK3))),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.34 thf(f29,plain,(
% 1.67/1.34 (woz2Ex = $true) & (breln1compprop = $true) & (woz2W = $true) & (breln1unionCommutes = $true) & (((breln1 @ sK0 @ sK1) = $true) & (((breln1 @ sK0 @ sK2) = $true) & (($true = (breln1 @ sK0 @ sK3)) & ((binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK2))) @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK1)))) != (breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3))))) & (breln1invprop = $true) & (woz2A = $true)),
% 1.67/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f28,f27,f26])).
% 1.67/1.34 thf(f26,plain,(
% 1.67/1.34 ? [X0 : $i,X1 : $i] : (((breln1 @ X0 @ X1) = $true) & ? [X2 : $i] : (((breln1 @ X0 @ X2) = $true) & ? [X3 : $i] : (((breln1 @ X0 @ X3) = $true) & ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) != (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1)))))))) => (((breln1 @ sK0 @ sK1) = $true) & ? [X2 : $i] : (($true = (breln1 @ sK0 @ X2)) & ? [X3 : $i] : (($true = (breln1 @ sK0 @ X3)) & ((breln1compset @ sK0 @ (binunion @ sK1 @ X2) @ X3) != (binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ X3) @ (breln1invset @ sK0 @ X2))) @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ X3) @ (breln1invset @ sK0 @ sK1))))))))),
% 1.67/1.34 introduced(definition,[],[choice_axiom])).
% 1.67/1.34 thf(f27,plain,(
% 1.67/1.34 ? [X2 : $i] : (($true = (breln1 @ sK0 @ X2)) & ? [X3 : $i] : (($true = (breln1 @ sK0 @ X3)) & ((breln1compset @ sK0 @ (binunion @ sK1 @ X2) @ X3) != (binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ X3) @ (breln1invset @ sK0 @ X2))) @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ X3) @ (breln1invset @ sK0 @ sK1))))))) => (((breln1 @ sK0 @ sK2) = $true) & ? [X3 : $i] : (($true = (breln1 @ sK0 @ X3)) & ((binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ X3) @ (breln1invset @ sK0 @ sK2))) @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ X3) @ (breln1invset @ sK0 @ sK1)))) != (breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ X3))))),
% 1.67/1.34 introduced(definition,[],[choice_axiom])).
% 1.67/1.34 thf(f28,plain,(
% 1.67/1.34 ? [X3 : $i] : (($true = (breln1 @ sK0 @ X3)) & ((binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ X3) @ (breln1invset @ sK0 @ sK2))) @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ X3) @ (breln1invset @ sK0 @ sK1)))) != (breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ X3))) => (($true = (breln1 @ sK0 @ sK3)) & ((binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK2))) @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK1)))) != (breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3)))),
% 1.67/1.34 introduced(definition,[],[choice_axiom])).
% 1.67/1.34 thf(f25,plain,(
% 1.67/1.34 (woz2Ex = $true) & (breln1compprop = $true) & (woz2W = $true) & (breln1unionCommutes = $true) & ? [X0 : $i,X1 : $i] : (((breln1 @ X0 @ X1) = $true) & ? [X2 : $i] : (((breln1 @ X0 @ X2) = $true) & ? [X3 : $i] : (((breln1 @ X0 @ X3) = $true) & ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) != (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1)))))))) & (breln1invprop = $true) & (woz2A = $true)),
% 1.67/1.34 inference(flattening,[status(thm)],[f24])).
% 1.67/1.34 thf(f24,plain,(
% 1.67/1.34 (((((? [X0 : $i,X1 : $i] : (((breln1 @ X0 @ X1) = $true) & ? [X2 : $i] : (((breln1 @ X0 @ X2) = $true) & ? [X3 : $i] : (((breln1 @ X0 @ X3) = $true) & ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) != (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1)))))))) & (woz2A = $true)) & (woz2W = $true)) & (woz2Ex = $true)) & (breln1unionCommutes = $true)) & (breln1compprop = $true)) & (breln1invprop = $true)),
% 1.67/1.34 inference(ennf_transformation,[status(thm)],[f19])).
% 1.67/1.34 thf(f19,plain,(
% 1.67/1.34 ~((breln1invprop = $true) => ((breln1compprop = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ! [X0 : $i,X1 : $i] : (((breln1 @ X0 @ X1) = $true) => ! [X2 : $i] : (((breln1 @ X0 @ X2) = $true) => ! [X3 : $i] : (((breln1 @ X0 @ X3) = $true) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1))))))))))))))),
% 1.67/1.34 inference(fool_elimination,[status(thm)],[f18])).
% 1.67/1.34 thf(f18,plain,(
% 1.67/1.34 ~(breln1invprop => (breln1compprop => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((breln1 @ X0 @ X3) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1))))))))))))))),
% 1.67/1.34 inference(rectify,[status(thm)],[f8])).
% 1.67/1.34 thf(f8,negated_conjecture,(
% 1.67/1.34 ~(breln1invprop => (breln1compprop => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((breln1 @ X0 @ X3) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1))))))))))))))),
% 1.67/1.34 inference(negated_conjecture,[status(cth)],[f7])).
% 1.67/1.34 thf(f7,conjecture,(
% 1.67/1.34 breln1invprop => (breln1compprop => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((breln1 @ X0 @ X3) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1)))))))))))))),
% 1.67/1.34 file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',woz2B)).
% 1.67/1.34 thf(f219,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ sK3)) | ~spl4_1),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f217])).
% 1.67/1.34 thf(f217,definition,(
% 1.67/1.34 spl4_1 <=> ($false = (breln1 @ sK0 @ sK3))),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.67/1.34 thf(f488,plain,(
% 1.67/1.34 spl4_1 | spl4_10 | ~spl4_19),
% 1.67/1.34 inference(avatar_split_clause,[status(thm)],[f487,f304,f255,f217])).
% 1.67/1.34 thf(f255,definition,(
% 1.67/1.34 spl4_10 <=> ((breln1 @ sK0 @ sK1) = $false)),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition])).
% 1.67/1.34 thf(f304,definition,(
% 1.67/1.34 spl4_19 <=> ($false = (breln1 @ sK0 @ (breln1compset @ sK0 @ sK1 @ sK3)))),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_19])],[avatar_definition])).
% 1.67/1.34 thf(f487,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ sK3)) | (spl4_10 | ~spl4_19)),
% 1.67/1.34 inference(subsumption_resolution,[status(thm)],[f483,f256])).
% 1.67/1.34 thf(f256,plain,(
% 1.67/1.34 ((breln1 @ sK0 @ sK1) != $false) | spl4_10),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f255])).
% 1.67/1.34 thf(f483,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ sK3)) | ((breln1 @ sK0 @ sK1) = $false) | ~spl4_19),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f478])).
% 1.67/1.34 thf(f478,plain,(
% 1.67/1.34 ($false = $true) | ((breln1 @ sK0 @ sK1) = $false) | ($false = (breln1 @ sK0 @ sK3)) | ~spl4_19),
% 1.67/1.34 inference(superposition,[status(thm)],[f306,f79])).
% 1.67/1.34 thf(f79,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (breln1 @ X2 @ (breln1compset @ X2 @ X1 @ X3))) | ($false = (breln1 @ X2 @ X3)) | ($false = (breln1 @ X2 @ X1))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.67/1.34 thf(f78,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((breln1 @ X2 @ X3) => (breln1 @ X2 @ (breln1compset @ X2 @ X1 @ X3)))) | ($false = (breln1 @ X2 @ X1))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.67/1.34 thf(f77,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (breln1 @ X2 @ (breln1compset @ X2 @ X1 @ Y0)))) @ X3)) | ($false = (breln1 @ X2 @ X1))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f76])).
% 1.67/1.34 thf(f76,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($false = (breln1 @ X2 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (breln1 @ X2 @ (breln1compset @ X2 @ X1 @ Y0))))))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.67/1.34 thf(f75,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : ((((breln1 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (breln1 @ X2 @ (breln1compset @ X2 @ X1 @ Y0)))))) = $true)) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.67/1.34 thf(f74,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (breln1 @ Y0 @ (breln1compset @ Y0 @ X1 @ Y1))))))) @ X2))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f73])).
% 1.67/1.34 thf(f73,plain,(
% 1.67/1.34 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (breln1 @ Y0 @ (breln1compset @ Y0 @ X1 @ Y1)))))))))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.67/1.34 thf(f72,plain,(
% 1.67/1.34 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (breln1 @ Y1 @ (breln1compset @ Y1 @ Y0 @ Y2))))))))) @ X1))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f46])).
% 1.67/1.34 thf(f46,plain,(
% 1.67/1.34 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (breln1 @ Y1 @ (breln1compset @ Y1 @ Y0 @ Y2)))))))))) = $true)),
% 1.67/1.34 inference(definition_unfolding,[status(thm)],[f39,f30])).
% 1.67/1.34 thf(f30,plain,(
% 1.67/1.34 (breln1compprop = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (breln1 @ Y1 @ (breln1compset @ Y1 @ Y0 @ Y2)))))))))))),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f17])).
% 1.67/1.34 thf(f17,plain,(
% 1.67/1.34 (breln1compprop = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (breln1 @ Y1 @ (breln1compset @ Y1 @ Y0 @ Y2)))))))))))),
% 1.67/1.34 inference(fool_elimination,[status(thm)],[f16])).
% 1.67/1.34 thf(f16,plain,(
% 1.67/1.34 (breln1compprop = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2)))))),
% 1.67/1.34 inference(rectify,[status(thm)],[f2])).
% 1.67/1.34 thf(f2,axiom,(
% 1.67/1.34 (breln1compprop = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2)))))),
% 1.67/1.34 file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',breln1compprop)).
% 1.67/1.34 thf(f39,plain,(
% 1.67/1.34 (breln1compprop = $true)),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.34 thf(f306,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ (breln1compset @ sK0 @ sK1 @ sK3))) | ~spl4_19),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f304])).
% 1.67/1.34 thf(f469,plain,(
% 1.67/1.34 ~spl4_3 | spl4_6),
% 1.67/1.34 inference(avatar_contradiction_clause,[status(thm)],[f468])).
% 1.67/1.34 thf(f468,plain,(
% 1.67/1.34 $false | (~spl4_3 | spl4_6)),
% 1.67/1.34 inference(subsumption_resolution,[status(thm)],[f464,f239])).
% 1.67/1.34 thf(f239,plain,(
% 1.67/1.34 ($false != (breln1 @ sK0 @ sK2)) | spl4_6),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f238])).
% 1.67/1.34 thf(f238,definition,(
% 1.67/1.34 spl4_6 <=> ($false = (breln1 @ sK0 @ sK2))),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.67/1.34 thf(f464,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ sK2)) | ~spl4_3),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f461])).
% 1.67/1.34 thf(f461,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ sK2)) | ($false = $true) | ~spl4_3),
% 1.67/1.34 inference(superposition,[status(thm)],[f71,f227])).
% 1.67/1.34 thf(f227,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ (breln1invset @ sK0 @ sK2))) | ~spl4_3),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f225])).
% 1.67/1.34 thf(f225,definition,(
% 1.67/1.34 spl4_3 <=> ($false = (breln1 @ sK0 @ (breln1invset @ sK0 @ sK2)))),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.67/1.34 thf(f71,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($true = (breln1 @ X1 @ (breln1invset @ X1 @ X2))) | ($false = (breln1 @ X1 @ X2))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.67/1.34 thf(f70,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : ((((breln1 @ X1 @ X2) => (breln1 @ X1 @ (breln1invset @ X1 @ X2))) = $true)) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.67/1.34 thf(f69,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((breln1 @ X1 @ Y0) => (breln1 @ X1 @ (breln1invset @ X1 @ Y0)))) @ X2))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f68])).
% 1.67/1.34 thf(f68,plain,(
% 1.67/1.34 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X1 @ Y0) => (breln1 @ X1 @ (breln1invset @ X1 @ Y0))))))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.67/1.34 thf(f67,plain,(
% 1.67/1.34 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (breln1 @ Y0 @ (breln1invset @ Y0 @ Y1)))))) @ X1) = $true)) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f47])).
% 1.67/1.34 thf(f47,plain,(
% 1.67/1.34 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (breln1 @ Y0 @ (breln1invset @ Y0 @ Y1))))))))),
% 1.67/1.34 inference(definition_unfolding,[status(thm)],[f41,f32])).
% 1.67/1.34 thf(f32,plain,(
% 1.67/1.34 (breln1invprop = $true)),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.34 thf(f41,plain,(
% 1.67/1.34 (breln1invprop = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (breln1 @ Y0 @ (breln1invset @ Y0 @ Y1))))))))),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f13])).
% 1.67/1.34 thf(f13,plain,(
% 1.67/1.34 (breln1invprop = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (breln1 @ Y0 @ (breln1invset @ Y0 @ Y1))))))))),
% 1.67/1.34 inference(fool_elimination,[status(thm)],[f12])).
% 1.67/1.34 thf(f12,plain,(
% 1.67/1.34 (! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => (breln1 @ X1 @ (breln1invset @ X1 @ X0))) = breln1invprop)),
% 1.67/1.34 inference(rectify,[status(thm)],[f1])).
% 1.67/1.34 thf(f1,axiom,(
% 1.67/1.34 (! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => (breln1 @ X0 @ (breln1invset @ X0 @ X1))) = breln1invprop)),
% 1.67/1.34 file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',breln1invprop)).
% 1.67/1.34 thf(f458,plain,(
% 1.67/1.34 spl4_1 | ~spl4_4),
% 1.67/1.34 inference(avatar_split_clause,[status(thm)],[f454,f229,f217])).
% 1.67/1.34 thf(f229,definition,(
% 1.67/1.34 spl4_4 <=> ($false = (breln1 @ sK0 @ (breln1invset @ sK0 @ sK3)))),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.67/1.34 thf(f454,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ sK3)) | ~spl4_4),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f452])).
% 1.67/1.34 thf(f452,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ sK3)) | ($false = $true) | ~spl4_4),
% 1.67/1.34 inference(superposition,[status(thm)],[f71,f231])).
% 1.67/1.34 thf(f231,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ (breln1invset @ sK0 @ sK3))) | ~spl4_4),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f229])).
% 1.67/1.34 thf(f447,plain,(
% 1.67/1.34 ~spl4_6),
% 1.67/1.34 inference(avatar_contradiction_clause,[status(thm)],[f446])).
% 1.67/1.34 thf(f446,plain,(
% 1.67/1.34 $false | ~spl4_6),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f439])).
% 1.67/1.34 thf(f439,plain,(
% 1.67/1.34 ($false = $true) | ~spl4_6),
% 1.67/1.34 inference(superposition,[status(thm)],[f240,f35])).
% 1.67/1.34 thf(f35,plain,(
% 1.67/1.34 ((breln1 @ sK0 @ sK2) = $true)),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.34 thf(f240,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ sK2)) | ~spl4_6),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f238])).
% 1.67/1.34 thf(f412,plain,(
% 1.67/1.34 ~spl4_10),
% 1.67/1.34 inference(avatar_contradiction_clause,[status(thm)],[f411])).
% 1.67/1.34 thf(f411,plain,(
% 1.67/1.34 $false | ~spl4_10),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f406])).
% 1.67/1.34 thf(f406,plain,(
% 1.67/1.34 ($false = $true) | ~spl4_10),
% 1.67/1.34 inference(superposition,[status(thm)],[f36,f257])).
% 1.67/1.34 thf(f257,plain,(
% 1.67/1.34 ((breln1 @ sK0 @ sK1) = $false) | ~spl4_10),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f255])).
% 1.67/1.34 thf(f36,plain,(
% 1.67/1.34 ((breln1 @ sK0 @ sK1) = $true)),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.34 thf(f403,plain,(
% 1.67/1.34 spl4_10 | spl4_34),
% 1.67/1.34 inference(avatar_split_clause,[status(thm)],[f399,f387,f255])).
% 1.67/1.34 thf(f387,definition,(
% 1.67/1.34 spl4_34 <=> ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) = (breln1compset @ sK0 @ (binunion @ sK2 @ sK1) @ sK3))),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_34])],[avatar_definition])).
% 1.67/1.34 thf(f399,plain,(
% 1.67/1.34 ((breln1 @ sK0 @ sK1) = $false) | spl4_34),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f397])).
% 1.67/1.34 thf(f397,plain,(
% 1.67/1.34 ((breln1 @ sK0 @ sK1) = $false) | ($false = $true) | spl4_34),
% 1.67/1.34 inference(superposition,[status(thm)],[f35,f394])).
% 1.67/1.34 thf(f394,plain,(
% 1.67/1.34 ( ! [X0 : $i] : (($false = (breln1 @ X0 @ sK2)) | ($false = (breln1 @ X0 @ sK1))) ) | spl4_34),
% 1.67/1.34 inference(trivial_inequality_removal,[status(thm)],[f392])).
% 1.67/1.34 thf(f392,plain,(
% 1.67/1.34 ( ! [X0 : $i] : (((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) != (breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3)) | ($false = (breln1 @ X0 @ sK1)) | ($false = (breln1 @ X0 @ sK2))) ) | spl4_34),
% 1.67/1.34 inference(superposition,[status(thm)],[f389,f60])).
% 1.67/1.34 thf(f60,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((binunion @ X1 @ X3) = (binunion @ X3 @ X1)) | ($false = (breln1 @ X2 @ X3)) | ($false = (breln1 @ X2 @ X1))) )),
% 1.67/1.34 inference(equality_proxy_clausification,[status(thm)],[f59])).
% 1.67/1.34 thf(f59,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((binunion @ X1 @ X3) = (binunion @ X3 @ X1))) | ($false = (breln1 @ X2 @ X3)) | ($false = (breln1 @ X2 @ X1))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.67/1.34 thf(f58,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (breln1 @ X2 @ X1)) | ($true = ((breln1 @ X2 @ X3) => ((binunion @ X1 @ X3) = (binunion @ X3 @ X1))))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.67/1.34 thf(f57,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (breln1 @ X2 @ X1)) | ($true = ((^[Y0 : $i]: ((breln1 @ X2 @ Y0) => ((binunion @ X1 @ Y0) = (binunion @ Y0 @ X1)))) @ X3))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f56])).
% 1.67/1.34 thf(f56,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => ((binunion @ X1 @ Y0) = (binunion @ Y0 @ X1))))) = $true) | ($false = (breln1 @ X2 @ X1))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.67/1.34 thf(f55,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : ((((breln1 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => ((binunion @ X1 @ Y0) = (binunion @ Y0 @ X1)))))) = $true)) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.67/1.34 thf(f54,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((binunion @ X1 @ Y1) = (binunion @ Y1 @ X1))))))) @ X2))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f53])).
% 1.67/1.34 thf(f53,plain,(
% 1.67/1.34 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((binunion @ X1 @ Y1) = (binunion @ Y1 @ X1)))))))) = $true)) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.67/1.34 thf(f52,plain,(
% 1.67/1.34 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((binunion @ Y0 @ Y2) = (binunion @ Y2 @ Y0))))))))) @ X1) = $true)) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f51])).
% 1.67/1.34 thf(f51,plain,(
% 1.67/1.34 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((binunion @ Y0 @ Y2) = (binunion @ Y2 @ Y0)))))))))))),
% 1.67/1.34 inference(definition_unfolding,[status(thm)],[f45,f37])).
% 1.67/1.34 thf(f37,plain,(
% 1.67/1.34 (breln1unionCommutes = $true)),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.34 thf(f45,plain,(
% 1.67/1.34 (breln1unionCommutes = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((binunion @ Y0 @ Y2) = (binunion @ Y2 @ Y0)))))))))))),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f15])).
% 1.67/1.34 thf(f15,plain,(
% 1.67/1.34 (breln1unionCommutes = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((binunion @ Y0 @ Y2) = (binunion @ Y2 @ Y0)))))))))))),
% 1.67/1.34 inference(fool_elimination,[status(thm)],[f14])).
% 1.67/1.34 thf(f14,plain,(
% 1.67/1.34 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ((binunion @ X1 @ X2) = (binunion @ X2 @ X1)))) = breln1unionCommutes)),
% 1.67/1.34 inference(rectify,[status(thm)],[f3])).
% 1.67/1.34 thf(f3,axiom,(
% 1.67/1.34 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ((binunion @ X1 @ X2) = (binunion @ X2 @ X1)))) = breln1unionCommutes)),
% 1.67/1.34 file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',breln1unionCommutes)).
% 1.67/1.34 thf(f389,plain,(
% 1.67/1.34 ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) != (breln1compset @ sK0 @ (binunion @ sK2 @ sK1) @ sK3)) | spl4_34),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f387])).
% 1.67/1.34 thf(f390,plain,(
% 1.67/1.34 spl4_1 | spl4_6 | ~spl4_34 | spl4_10 | spl4_29),
% 1.67/1.34 inference(avatar_split_clause,[status(thm)],[f374,f360,f255,f387,f238,f217])).
% 1.67/1.34 thf(f360,definition,(
% 1.67/1.34 spl4_29 <=> ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) = (binunion @ (breln1compset @ sK0 @ sK2 @ sK3) @ (breln1compset @ sK0 @ sK1 @ sK3)))),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_29])],[avatar_definition])).
% 1.67/1.34 thf(f374,plain,(
% 1.67/1.34 ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) != (breln1compset @ sK0 @ (binunion @ sK2 @ sK1) @ sK3)) | ($false = (breln1 @ sK0 @ sK3)) | ($false = (breln1 @ sK0 @ sK2)) | ((breln1 @ sK0 @ sK1) = $false) | spl4_29),
% 1.67/1.34 inference(superposition,[status(thm)],[f362,f91])).
% 1.67/1.34 thf(f91,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((binunion @ (breln1compset @ X2 @ X1 @ X4) @ (breln1compset @ X2 @ X3 @ X4)) = (breln1compset @ X2 @ (binunion @ X1 @ X3) @ X4)) | ($false = (breln1 @ X2 @ X3)) | ($false = (breln1 @ X2 @ X1)) | ($false = (breln1 @ X2 @ X4))) )),
% 1.67/1.34 inference(equality_proxy_clausification,[status(thm)],[f90])).
% 1.67/1.34 thf(f90,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (breln1 @ X2 @ X1)) | ($false = (breln1 @ X2 @ X4)) | ($true = ((breln1compset @ X2 @ (binunion @ X1 @ X3) @ X4) = (binunion @ (breln1compset @ X2 @ X1 @ X4) @ (breln1compset @ X2 @ X3 @ X4)))) | ($false = (breln1 @ X2 @ X3))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.67/1.34 thf(f89,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (breln1 @ X2 @ X3)) | ($true = ((breln1 @ X2 @ X4) => ((breln1compset @ X2 @ (binunion @ X1 @ X3) @ X4) = (binunion @ (breln1compset @ X2 @ X1 @ X4) @ (breln1compset @ X2 @ X3 @ X4))))) | ($false = (breln1 @ X2 @ X1))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.67/1.34 thf(f88,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (breln1 @ X2 @ X1)) | ($false = (breln1 @ X2 @ X3)) | ($true = ((^[Y0 : $i]: ((breln1 @ X2 @ Y0) => ((breln1compset @ X2 @ (binunion @ X1 @ X3) @ Y0) = (binunion @ (breln1compset @ X2 @ X1 @ Y0) @ (breln1compset @ X2 @ X3 @ Y0))))) @ X4))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f87])).
% 1.67/1.34 thf(f87,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (breln1 @ X2 @ X3)) | ($false = (breln1 @ X2 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => ((breln1compset @ X2 @ (binunion @ X1 @ X3) @ Y0) = (binunion @ (breln1compset @ X2 @ X1 @ Y0) @ (breln1compset @ X2 @ X3 @ Y0)))))))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.67/1.34 thf(f86,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (breln1 @ X2 @ X1)) | ($true = ((breln1 @ X2 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => ((breln1compset @ X2 @ (binunion @ X1 @ X3) @ Y0) = (binunion @ (breln1compset @ X2 @ X1 @ Y0) @ (breln1compset @ X2 @ X3 @ Y0))))))))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.67/1.34 thf(f85,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ X2 @ Y1) => ((breln1compset @ X2 @ (binunion @ X1 @ Y0) @ Y1) = (binunion @ (breln1compset @ X2 @ X1 @ Y1) @ (breln1compset @ X2 @ Y0 @ Y1)))))))) @ X3)) | ($false = (breln1 @ X2 @ X1))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f84])).
% 1.67/1.34 thf(f84,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($false = (breln1 @ X2 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ X2 @ Y1) => ((breln1compset @ X2 @ (binunion @ X1 @ Y0) @ Y1) = (binunion @ (breln1compset @ X2 @ X1 @ Y1) @ (breln1compset @ X2 @ Y0 @ Y1))))))))))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.67/1.34 thf(f83,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((breln1 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ X2 @ Y1) => ((breln1compset @ X2 @ (binunion @ X1 @ Y0) @ Y1) = (binunion @ (breln1compset @ X2 @ X1 @ Y1) @ (breln1compset @ X2 @ Y0 @ Y1)))))))))))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.67/1.34 thf(f82,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((breln1compset @ Y0 @ (binunion @ X1 @ Y1) @ Y2) = (binunion @ (breln1compset @ Y0 @ X1 @ Y2) @ (breln1compset @ Y0 @ Y1 @ Y2))))))))))) @ X2))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f81])).
% 1.67/1.34 thf(f81,plain,(
% 1.67/1.34 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((breln1compset @ Y0 @ (binunion @ X1 @ Y1) @ Y2) = (binunion @ (breln1compset @ Y0 @ X1 @ Y2) @ (breln1compset @ Y0 @ Y1 @ Y2)))))))))))) = $true)) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.67/1.34 thf(f80,plain,(
% 1.67/1.34 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((breln1 @ Y1 @ Y3) => ((breln1compset @ Y1 @ (binunion @ Y0 @ Y2) @ Y3) = (binunion @ (breln1compset @ Y1 @ Y0 @ Y3) @ (breln1compset @ Y1 @ Y2 @ Y3))))))))))))) @ X1) = $true)) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f50])).
% 1.67/1.34 thf(f50,plain,(
% 1.67/1.34 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((breln1 @ Y1 @ Y3) => ((breln1compset @ Y1 @ (binunion @ Y0 @ Y2) @ Y3) = (binunion @ (breln1compset @ Y1 @ Y0 @ Y3) @ (breln1compset @ Y1 @ Y2 @ Y3)))))))))))))))),
% 1.67/1.34 inference(definition_unfolding,[status(thm)],[f44,f31])).
% 1.67/1.34 thf(f31,plain,(
% 1.67/1.34 (woz2A = $true)),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.34 thf(f44,plain,(
% 1.67/1.34 (woz2A = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((breln1 @ Y1 @ Y3) => ((breln1compset @ Y1 @ (binunion @ Y0 @ Y2) @ Y3) = (binunion @ (breln1compset @ Y1 @ Y0 @ Y3) @ (breln1compset @ Y1 @ Y2 @ Y3)))))))))))))))),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f21])).
% 1.67/1.34 thf(f21,plain,(
% 1.67/1.34 (woz2A = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((breln1 @ Y1 @ Y3) => ((breln1compset @ Y1 @ (binunion @ Y0 @ Y2) @ Y3) = (binunion @ (breln1compset @ Y1 @ Y0 @ Y3) @ (breln1compset @ Y1 @ Y2 @ Y3)))))))))))))))),
% 1.67/1.34 inference(fool_elimination,[status(thm)],[f20])).
% 1.67/1.34 thf(f20,plain,(
% 1.67/1.34 (woz2A = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((breln1 @ X0 @ X3) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3)))))))),
% 1.67/1.34 inference(rectify,[status(thm)],[f6])).
% 1.67/1.34 thf(f6,axiom,(
% 1.67/1.34 (woz2A = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((breln1 @ X0 @ X3) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3)))))))),
% 1.67/1.34 file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',woz2A)).
% 1.67/1.34 thf(f362,plain,(
% 1.67/1.34 ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) != (binunion @ (breln1compset @ sK0 @ sK2 @ sK3) @ (breln1compset @ sK0 @ sK1 @ sK3))) | spl4_29),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f360])).
% 1.67/1.34 thf(f363,plain,(
% 1.67/1.34 ~spl4_29 | spl4_6 | spl4_22),
% 1.67/1.34 inference(avatar_split_clause,[status(thm)],[f347,f324,f238,f360])).
% 1.67/1.34 thf(f324,definition,(
% 1.67/1.34 spl4_22 <=> ((binunion @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ (breln1invset @ sK0 @ sK2)) @ sK3) @ (breln1compset @ sK0 @ sK1 @ sK3)) = (breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3))),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_22])],[avatar_definition])).
% 1.67/1.34 thf(f347,plain,(
% 1.67/1.34 ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) != (binunion @ (breln1compset @ sK0 @ sK2 @ sK3) @ (breln1compset @ sK0 @ sK1 @ sK3))) | ($false = (breln1 @ sK0 @ sK2)) | spl4_22),
% 1.67/1.34 inference(superposition,[status(thm)],[f326,f66])).
% 1.67/1.34 thf(f66,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (((breln1invset @ X1 @ (breln1invset @ X1 @ X2)) = X2) | ($false = (breln1 @ X1 @ X2))) )),
% 1.67/1.34 inference(equality_proxy_clausification,[status(thm)],[f65])).
% 1.67/1.34 thf(f65,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($false = (breln1 @ X1 @ X2)) | ($true = ((breln1invset @ X1 @ (breln1invset @ X1 @ X2)) = X2))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.67/1.34 thf(f64,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : ((((breln1 @ X1 @ X2) => ((breln1invset @ X1 @ (breln1invset @ X1 @ X2)) = X2)) = $true)) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.67/1.34 thf(f63,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((breln1 @ X1 @ Y0) => ((breln1invset @ X1 @ (breln1invset @ X1 @ Y0)) = Y0))) @ X2))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f62])).
% 1.67/1.34 thf(f62,plain,(
% 1.67/1.34 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X1 @ Y0) => ((breln1invset @ X1 @ (breln1invset @ X1 @ Y0)) = Y0)))))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.67/1.34 thf(f61,plain,(
% 1.67/1.34 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((breln1invset @ Y0 @ (breln1invset @ Y0 @ Y1)) = Y1))))) @ X1))) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f48])).
% 1.67/1.34 thf(f48,plain,(
% 1.67/1.34 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((breln1invset @ Y0 @ (breln1invset @ Y0 @ Y1)) = Y1)))))))),
% 1.67/1.34 inference(definition_unfolding,[status(thm)],[f42,f40])).
% 1.67/1.34 thf(f40,plain,(
% 1.67/1.34 (woz2Ex = $true)),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.34 thf(f42,plain,(
% 1.67/1.34 (woz2Ex = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((breln1invset @ Y0 @ (breln1invset @ Y0 @ Y1)) = Y1)))))))),
% 1.67/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.34 thf(f23,plain,(
% 1.67/1.34 (woz2Ex = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((breln1invset @ Y0 @ (breln1invset @ Y0 @ Y1)) = Y1)))))))),
% 1.67/1.34 inference(fool_elimination,[status(thm)],[f22])).
% 1.67/1.34 thf(f22,plain,(
% 1.67/1.34 (woz2Ex = ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ((breln1invset @ X1 @ (breln1invset @ X1 @ X0)) = X0)))),
% 1.67/1.34 inference(rectify,[status(thm)],[f4])).
% 1.67/1.34 thf(f4,axiom,(
% 1.67/1.34 (woz2Ex = ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1)))),
% 1.67/1.34 file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',woz2Ex)).
% 1.67/1.34 thf(f326,plain,(
% 1.67/1.34 ((binunion @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ (breln1invset @ sK0 @ sK2)) @ sK3) @ (breln1compset @ sK0 @ sK1 @ sK3)) != (breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3)) | spl4_22),
% 1.67/1.34 inference(avatar_component_clause,[status(thm)],[f324])).
% 1.67/1.34 thf(f327,plain,(
% 1.67/1.34 spl4_3 | ~spl4_22 | spl4_1 | spl4_4 | spl4_20),
% 1.67/1.34 inference(avatar_split_clause,[status(thm)],[f319,f308,f229,f217,f324,f225])).
% 1.67/1.34 thf(f308,definition,(
% 1.67/1.34 spl4_20 <=> ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) = (binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK2))) @ (breln1compset @ sK0 @ sK1 @ sK3)))),
% 1.67/1.34 introduced(definition,[new_symbols(naming,[spl4_20])],[avatar_definition])).
% 1.67/1.34 thf(f319,plain,(
% 1.67/1.34 ($false = (breln1 @ sK0 @ (breln1invset @ sK0 @ sK2))) | ((binunion @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ (breln1invset @ sK0 @ sK2)) @ sK3) @ (breln1compset @ sK0 @ sK1 @ sK3)) != (breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3)) | ($false = (breln1 @ sK0 @ (breln1invset @ sK0 @ sK3))) | ($false = (breln1 @ sK0 @ sK3)) | spl4_20),
% 1.67/1.34 inference(superposition,[status(thm)],[f310,f114])).
% 1.67/1.34 thf(f114,plain,(
% 1.67/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((breln1compset @ X0 @ (breln1invset @ X0 @ X2) @ X1) = (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X1) @ X2))) | ((breln1 @ X0 @ X2) = $false) | ((breln1 @ X0 @ (breln1invset @ X0 @ X1)) = $false) | ((breln1 @ X0 @ X1) = $false)) )),
% 1.67/1.34 inference(superposition,[status(thm)],[f100,f66])).
% 1.67/1.34 thf(f100,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1invset @ X1 @ (breln1compset @ X1 @ X2 @ X3)) = (breln1compset @ X1 @ (breln1invset @ X1 @ X3) @ (breln1invset @ X1 @ X2))) | ($false = (breln1 @ X1 @ X2)) | ((breln1 @ X1 @ X3) = $false)) )),
% 1.67/1.34 inference(equality_proxy_clausification,[status(thm)],[f99])).
% 1.67/1.34 thf(f99,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln1 @ X1 @ X3) = $false) | ($true = ((breln1compset @ X1 @ (breln1invset @ X1 @ X3) @ (breln1invset @ X1 @ X2)) = (breln1invset @ X1 @ (breln1compset @ X1 @ X2 @ X3)))) | ($false = (breln1 @ X1 @ X2))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.67/1.34 thf(f98,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (breln1 @ X1 @ X2)) | ($true = ((breln1 @ X1 @ X3) => ((breln1compset @ X1 @ (breln1invset @ X1 @ X3) @ (breln1invset @ X1 @ X2)) = (breln1invset @ X1 @ (breln1compset @ X1 @ X2 @ X3)))))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.67/1.34 thf(f97,plain,(
% 1.67/1.34 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (breln1 @ X1 @ X2)) | (((^[Y0 : $i]: ((breln1 @ X1 @ Y0) => ((breln1compset @ X1 @ (breln1invset @ X1 @ Y0) @ (breln1invset @ X1 @ X2)) = (breln1invset @ X1 @ (breln1compset @ X1 @ X2 @ Y0))))) @ X3) = $true)) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f96])).
% 1.67/1.34 thf(f96,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X1 @ Y0) => ((breln1compset @ X1 @ (breln1invset @ X1 @ Y0) @ (breln1invset @ X1 @ X2)) = (breln1invset @ X1 @ (breln1compset @ X1 @ X2 @ Y0))))))) | ($false = (breln1 @ X1 @ X2))) )),
% 1.67/1.34 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.67/1.34 thf(f95,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((breln1 @ X1 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X1 @ Y0) => ((breln1compset @ X1 @ (breln1invset @ X1 @ Y0) @ (breln1invset @ X1 @ X2)) = (breln1invset @ X1 @ (breln1compset @ X1 @ X2 @ Y0))))))))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.67/1.34 thf(f94,plain,(
% 1.67/1.34 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((breln1 @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ X1 @ Y1) => ((breln1compset @ X1 @ (breln1invset @ X1 @ Y1) @ (breln1invset @ X1 @ Y0)) = (breln1invset @ X1 @ (breln1compset @ X1 @ Y0 @ Y1)))))))) @ X2) = $true)) )),
% 1.67/1.34 inference(pi_clausification,[status(thm)],[f93])).
% 1.67/1.34 thf(f93,plain,(
% 1.67/1.34 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((breln1 @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ X1 @ Y1) => ((breln1compset @ X1 @ (breln1invset @ X1 @ Y1) @ (breln1invset @ X1 @ Y0)) = (breln1invset @ X1 @ (breln1compset @ X1 @ Y0 @ Y1))))))))))) )),
% 1.67/1.34 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.67/1.34 thf(f92,plain,(
% 1.67/1.34 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((breln1compset @ Y0 @ (breln1invset @ Y0 @ Y2) @ (breln1invset @ Y0 @ Y1)) = (breln1invset @ Y0 @ (breln1compset @ Y0 @ Y1 @ Y2)))))))))) @ X1))) )),
% 1.67/1.35 inference(pi_clausification,[status(thm)],[f49])).
% 1.67/1.35 thf(f49,plain,(
% 1.67/1.35 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((breln1compset @ Y0 @ (breln1invset @ Y0 @ Y2) @ (breln1invset @ Y0 @ Y1)) = (breln1invset @ Y0 @ (breln1compset @ Y0 @ Y1 @ Y2))))))))))))),
% 1.67/1.35 inference(definition_unfolding,[status(thm)],[f43,f38])).
% 1.67/1.35 thf(f38,plain,(
% 1.67/1.35 (woz2W = $true)),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.35 thf(f43,plain,(
% 1.67/1.35 (woz2W = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((breln1compset @ Y0 @ (breln1invset @ Y0 @ Y2) @ (breln1invset @ Y0 @ Y1)) = (breln1invset @ Y0 @ (breln1compset @ Y0 @ Y1 @ Y2))))))))))))),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f11])).
% 1.67/1.35 thf(f11,plain,(
% 1.67/1.35 (woz2W = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((breln1compset @ Y0 @ (breln1invset @ Y0 @ Y2) @ (breln1invset @ Y0 @ Y1)) = (breln1invset @ Y0 @ (breln1compset @ Y0 @ Y1 @ Y2))))))))))))),
% 1.67/1.35 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.35 thf(f10,plain,(
% 1.67/1.35 (woz2W = ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => ((breln1compset @ X1 @ (breln1invset @ X1 @ X2) @ (breln1invset @ X1 @ X0)) = (breln1invset @ X1 @ (breln1compset @ X1 @ X0 @ X2))))))),
% 1.67/1.35 inference(rectify,[status(thm)],[f5])).
% 1.67/1.35 thf(f5,axiom,(
% 1.67/1.35 (woz2W = ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ((breln1invset @ X0 @ (breln1compset @ X0 @ X1 @ X2)) = (breln1compset @ X0 @ (breln1invset @ X0 @ X2) @ (breln1invset @ X0 @ X1))))))),
% 1.67/1.35 file('/export/starexec/sandbox2/tmp/tmp.kWcbtiotMz/DTF2THF_3734.p',woz2W)).
% 1.67/1.35 thf(f310,plain,(
% 1.67/1.35 ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) != (binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK2))) @ (breln1compset @ sK0 @ sK1 @ sK3))) | spl4_20),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f308])).
% 1.67/1.35 thf(f311,plain,(
% 1.67/1.35 spl4_19 | ~spl4_20 | spl4_9),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f279,f251,f308,f304])).
% 1.67/1.35 thf(f251,definition,(
% 1.67/1.35 spl4_9 <=> ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) = (binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK2))) @ (breln1invset @ sK0 @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ sK1 @ sK3)))))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 1.67/1.35 thf(f279,plain,(
% 1.67/1.35 ($false = (breln1 @ sK0 @ (breln1compset @ sK0 @ sK1 @ sK3))) | ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) != (binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK2))) @ (breln1compset @ sK0 @ sK1 @ sK3))) | spl4_9),
% 1.67/1.35 inference(superposition,[status(thm)],[f253,f66])).
% 1.67/1.35 thf(f253,plain,(
% 1.67/1.35 ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) != (binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK2))) @ (breln1invset @ sK0 @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ sK1 @ sK3))))) | spl4_9),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f251])).
% 1.67/1.35 thf(f258,plain,(
% 1.67/1.35 spl4_1 | ~spl4_9 | spl4_10),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f208,f255,f251,f217])).
% 1.67/1.35 thf(f208,plain,(
% 1.67/1.35 ($false = (breln1 @ sK0 @ sK3)) | ((breln1 @ sK0 @ sK1) = $false) | ((breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3) != (binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK2))) @ (breln1invset @ sK0 @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ sK1 @ sK3)))))),
% 1.67/1.35 inference(superposition,[status(thm)],[f33,f100])).
% 1.67/1.35 thf(f33,plain,(
% 1.67/1.35 ((binunion @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK2))) @ (breln1invset @ sK0 @ (breln1compset @ sK0 @ (breln1invset @ sK0 @ sK3) @ (breln1invset @ sK0 @ sK1)))) != (breln1compset @ sK0 @ (binunion @ sK1 @ sK2) @ sK3))),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.35 % SZS output end Proof for DTF2THF_3734
% 1.67/1.35 % (4006)------------------------------
% 1.67/1.35 % (4006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (4006)Termination reason: Refutation
% 1.67/1.35
% 1.67/1.35 % (4006)Memory used [KB]: 6140
% 1.67/1.35 % (4006)Time elapsed: 0.065 s
% 1.67/1.35 % (4006)Instructions burned: 97 (million)
% 1.67/1.35 % (4006)------------------------------
% 1.67/1.35 % (4006)------------------------------
% 1.67/1.35 % (4005)Success in time 0.071 s
%------------------------------------------------------------------------------