%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU744^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:51 AM UTC 2026
% Result : Theorem 1.43s 1.20s
% Output : Refutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 76 ( 32 unt; 0 typ; 4 def)
% Number of atoms : 720 ( 156 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 1031 ( 72 ~; 56 |; 36 &; 725 @)
% ( 4 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 13 con; 0-2 aty)
% ( 42 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 164 ( 49 ^; 97 !; 18 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(f104,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f69,f75,f90,f96,f103]) ).
thf(f103,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $false = $true )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f84,f21]) ).
thf(f21,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( binunionTILcontra = $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( setminusER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f17,f16,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) )
& ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) )
& ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ X3 @ sK0 ) ) )
=> ( ( ( in @ sK3 @ sK1 )
= $true )
& ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( ( in @ sK3 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( binunionTILcontra = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( setminusER = $true ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionTILcontra = $true )
& ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( setminusER = $true )
=> ( ( binunionTILcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setminusER = $true )
=> ( ( binunionTILcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setminusER
=> ( binunionTILcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setminusER
=> ( binunionTILcontra
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) )
=> ~ ( in @ X2 @ X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setminusER
=> ( binunionTILcontra
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) )
=> ~ ( in @ X2 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OqKGAiXEPd/DTF2THF_30386.p',inComplementUnionImpNotIn1) ).
thf(f84,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f82]) ).
thf(f82,definition,
( spl4_3
<=> ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f96,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $false = $true )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f23,f88]) ).
thf(f88,plain,
( ( $false
= ( in @ sK3 @ sK0 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f86,definition,
( spl4_4
<=> ( $false
= ( in @ sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f23,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f90,plain,
( spl4_4
| spl4_3
| ~ spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f79,f62,f82,f86]) ).
thf(f62,definition,
( spl4_1
<=> ! [X0: $i] :
( ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( ( in @ sK3 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f79,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $false = $true )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f63,f22]) ).
thf(f22,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f63,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( ( in @ sK3 @ X0 )
= $false )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f75,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f74]) ).
thf(f74,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $false = $true )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f67,f25]) ).
thf(f25,plain,
( ( in @ sK3 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f67,plain,
( ( ( in @ sK3 @ sK1 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl4_2
<=> ( ( in @ sK3 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f69,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f59,f62,f65]) ).
thf(f59,plain,
! [X0: $i] :
( ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( ( in @ sK3 @ sK1 )
= $false )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( ( in @ sK3 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( in @ sK3 @ sK1 )
= $false )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( ( in @ sK3 @ X0 )
= $false )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f43,f55]) ).
thf(f55,plain,
( $false
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $false = $true )
| ( $false
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(superposition,[status(thm)],[f51,f24]) ).
thf(f24,plain,
( $true
= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( in @ X3 @ X2 ) )
= $true )
| ( $false
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ Y0 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setminus @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setminus @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f27,f20]) ).
thf(f20,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f27,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
=> ~ ( in @ X0 @ X1 ) )
= setminusER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/tmp/tmp.OqKGAiXEPd/DTF2THF_30386.p',setminusER) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( $false
= ( in @ X4 @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X4 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) )
| ( $false
= ( in @ X4 @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( ~ ( in @ X4 @ X2 ) )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X4 @ X1 ) )
| ( $true
= ( ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) )
=> ~ ( in @ X4 @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( in @ X4 @ X1 )
=> ( ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) )
=> ~ ( in @ X4 @ X2 ) ) )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ~ ( in @ Y0 @ ( binunion @ X2 @ X3 ) )
=> ~ ( in @ Y0 @ X2 ) ) )
@ X4 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ~ ( in @ Y0 @ ( binunion @ X2 @ X3 ) )
=> ~ ( in @ Y0 @ X2 ) ) ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ~ ( in @ Y0 @ ( binunion @ X2 @ X3 ) )
=> ~ ( in @ Y0 @ X2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ~ ( in @ Y1 @ ( binunion @ X2 @ Y0 ) )
=> ~ ( in @ Y1 @ X2 ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ~ ( in @ Y1 @ ( binunion @ X2 @ Y0 ) )
=> ~ ( in @ Y1 @ X2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ~ ( in @ Y1 @ ( binunion @ X2 @ Y0 ) )
=> ~ ( in @ Y1 @ X2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ~ ( in @ Y2 @ ( binunion @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y0 ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ~ ( in @ Y2 @ ( binunion @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ ( in @ Y3 @ ( binunion @ Y1 @ Y2 ) )
=> ~ ( in @ Y3 @ Y1 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ ( in @ Y3 @ ( binunion @ Y1 @ Y2 ) )
=> ~ ( in @ Y3 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f26,f19]) ).
thf(f19,plain,
( binunionTILcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ ( in @ Y3 @ ( binunion @ Y1 @ Y2 ) )
=> ~ ( in @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( binunionTILcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ~ ( in @ Y3 @ ( binunion @ Y1 @ Y2 ) )
=> ~ ( in @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ~ ( in @ X3 @ X0 ) ) ) ) )
= binunionTILcontra ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X3: $i,X0: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ ( binunion @ X3 @ X4 ) )
=> ~ ( in @ X2 @ X3 ) ) ) ) )
= binunionTILcontra ),
file('/export/starexec/sandbox/tmp/tmp.OqKGAiXEPd/DTF2THF_30386.p',binunionTILcontra) ).
thf(f26,plain,
binunionTILcontra = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU744^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:33:21 EST 2026
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEU744^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.42 % Domain : Set Theory
% 0.16/0.42 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.16/0.42 % Version : Especial > Reduced > Especial.
% 0.16/0.42 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.16/0.42 % (! x:i.in x A -> in x (setminus A (binunion X Y)) -> ~(in x X))))
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.42 % Source : [Bro08]
% 0.16/0.42 % Names : ZFC246l [Bro08]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.16/0.42 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.16/0.42 % Number of atoms : 18 ( 2 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 7 ( 6 avg)
% 0.16/0.42 % Number of connectives : 51 ( 4 ~; 0 |; 0 &; 36 @)
% 0.16/0.42 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 15 ( 6 avg)
% 0.16/0.42 % Number of types : 2 ( 0 usr)
% 0.16/0.42 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.16/0.42 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : http://mathgate.info/detsetitem.php?id=306
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(in_type,type,
% 0.16/0.42 in: $i > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(powerset_type,type,
% 0.16/0.42 powerset: $i > $i ).
% 0.16/0.42
% 0.16/0.42 thf(binunion_type,type,
% 0.16/0.42 binunion: $i > $i > $i ).
% 0.16/0.42
% 0.16/0.42 thf(setminus_type,type,
% 0.16/0.42 setminus: $i > $i > $i ).
% 0.16/0.42
% 0.16/0.42 thf(setminusER_type,type,
% 0.16/0.42 setminusER: $o ).
% 0.16/0.42
% 0.16/0.42 thf(setminusER,definition,
% 0.16/0.42 ( setminusER
% 0.16/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.42 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.42 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(binunionTILcontra_type,type,
% 0.16/0.42 binunionTILcontra: $o ).
% 0.16/0.42
% 0.16/0.42 thf(binunionTILcontra,definition,
% 0.16/0.42 ( binunionTILcontra
% 0.16/0.42 = ( ! [A: $i,X: $i] :
% 0.16/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.16/0.42 => ! [Y: $i] :
% 0.16/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.16/0.42 => ! [Xx: $i] :
% 0.16/0.42 ( ( in @ Xx @ A )
% 0.16/0.42 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.16/0.42 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(inComplementUnionImpNotIn1,conjecture,
% 0.16/0.42 ( setminusER
% 0.16/0.42 => ( binunionTILcontra
% 0.16/0.42 => ! [A: $i,X: $i] :
% 0.16/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.16/0.42 => ! [Y: $i] :
% 0.16/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.16/0.42 => ! [Xx: $i] :
% 0.16/0.42 ( ( in @ Xx @ A )
% 0.16/0.42 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.16/0.42 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.30/1.17 ---- Embedded in THF ---
% 1.30/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.30/1.17 %%% Generated on Tue Feb 24 12:33:21 EST 2026
% 1.30/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.30/1.17 %%% Logic specification used:
% 1.30/1.17 %%% thf(spec, logic, $$dhol).
% 1.30/1.17
% 1.30/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OqKGAiXEPd/DTF2DTF30386.p
% See solution above
% 1.30/1.17 ------------------------
% 1.30/1.18 ---- Cleaned THF ---
% 1.30/1.18 thf(in_type,type,
% 1.30/1.18 in: $i > $i > $o ).
% 1.30/1.18
% 1.30/1.18 thf(powerset_type,type,
% 1.30/1.18 powerset: $i > $i ).
% 1.30/1.18
% 1.30/1.18 thf(binunion_type,type,
% 1.30/1.18 binunion: $i > $i > $i ).
% 1.30/1.18
% 1.30/1.18 thf(setminus_type,type,
% 1.30/1.18 setminus: $i > $i > $i ).
% 1.30/1.18
% 1.30/1.18 thf(setminusER_type,type,
% 1.30/1.18 setminusER: $o ).
% 1.30/1.18
% 1.30/1.18 thf(setminusER,definition,
% 1.30/1.18 ( setminusER
% 1.30/1.18 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.30/1.18 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.30/1.18 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.30/1.18
% 1.30/1.18 thf(binunionTILcontra_type,type,
% 1.30/1.18 binunionTILcontra: $o ).
% 1.30/1.18
% 1.30/1.18 thf(binunionTILcontra,definition,
% 1.30/1.18 ( binunionTILcontra
% 1.30/1.18 = ( ! [A: $i,X: $i] :
% 1.30/1.18 ( ( in @ X @ ( powerset @ A ) )
% 1.30/1.18 => ! [Y: $i] :
% 1.30/1.18 ( ( in @ Y @ ( powerset @ A ) )
% 1.30/1.18 => ! [Xx: $i] :
% 1.30/1.18 ( ( in @ Xx @ A )
% 1.30/1.18 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 1.30/1.18 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 1.30/1.18
% 1.30/1.18 thf(inComplementUnionImpNotIn1,conjecture,
% 1.30/1.18 ( setminusER
% 1.30/1.18 => ( binunionTILcontra
% 1.30/1.18 => ! [A: $i,X: $i] :
% 1.30/1.18 ( ( in @ X @ ( powerset @ A ) )
% 1.30/1.18 => ! [Y: $i] :
% 1.30/1.18 ( ( in @ Y @ ( powerset @ A ) )
% 1.30/1.18 => ! [Xx: $i] :
% 1.30/1.18 ( ( in @ Xx @ A )
% 1.30/1.18 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 1.30/1.18 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 1.30/1.18 ------------------------
% 1.30/1.19 % (30485)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30386 for (3000ds/183Mi)
% 1.30/1.19 % (30485)First to succeed.
% 1.30/1.20 % (30488)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30386 for (3000ds/2Mi)
% 1.30/1.20 % (30489)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_30386 for (3000ds/2Mi)
% 1.30/1.20 % (30487)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_30386 for (3000ds/27Mi)
% 1.30/1.20 % (30490)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_30386 for (3000ds/275Mi)
% 1.30/1.20 % (30486)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_30386 for (3000ds/4Mi)
% 1.30/1.20 % (30491)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30386 for (3000ds/18Mi)
% 1.43/1.20 % (30485)Refutation found. Thanks to Tanya!
% 1.43/1.20 % SZS status Theorem for DTF2THF_30386
% 1.43/1.20 % SZS output start Proof for DTF2THF_30386
% 1.43/1.20 thf(func_def_0, type, in: $i > $i > $o).
% 1.43/1.20 thf(func_def_1, type, powerset: $i > $i).
% 1.43/1.20 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.43/1.20 thf(func_def_3, type, setminus: $i > $i > $i).
% 1.43/1.20 thf(f104,plain,(
% 1.43/1.20 $false),
% 1.43/1.20 inference(avatar_sat_refutation,[status(thm)],[f69,f75,f90,f96,f103])).
% 1.43/1.20 thf(f103,plain,(
% 1.43/1.20 ~spl4_3),
% 1.43/1.20 inference(avatar_contradiction_clause,[status(thm)],[f102])).
% 1.43/1.20 thf(f102,plain,(
% 1.43/1.20 $false | ~spl4_3),
% 1.43/1.20 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.43/1.20 thf(f98,plain,(
% 1.43/1.20 ($false = $true) | ~spl4_3),
% 1.43/1.20 inference(superposition,[status(thm)],[f84,f21])).
% 1.43/1.20 thf(f21,plain,(
% 1.43/1.20 ($true = (in @ sK1 @ (powerset @ sK0)))),
% 1.43/1.20 inference(cnf_transformation,[status(thm)],[f18])).
% 1.43/1.20 thf(f18,plain,(
% 1.43/1.20 (binunionTILcontra = $true) & (((((in @ sK3 @ sK1) = $true) & ($true = (in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)))) & ((in @ sK3 @ sK0) = $true)) & ($true = (in @ sK2 @ (powerset @ sK0)))) & ($true = (in @ sK1 @ (powerset @ sK0)))) & (setminusER = $true)),
% 1.43/1.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f17,f16,f15])).
% 1.43/1.20 thf(f15,plain,(
% 1.43/1.20 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ($true = (in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ X2)))) & ($true = (in @ X3 @ sK0))) & ((in @ X2 @ (powerset @ sK0)) = $true)) & ($true = (in @ sK1 @ (powerset @ sK0))))),
% 1.43/1.20 introduced(definition,[],[choice_axiom])).
% 1.43/1.20 thf(f16,plain,(
% 1.43/1.20 ? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ($true = (in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ X2)))) & ($true = (in @ X3 @ sK0))) & ((in @ X2 @ (powerset @ sK0)) = $true)) => (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ($true = (in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)))) & ($true = (in @ X3 @ sK0))) & ($true = (in @ sK2 @ (powerset @ sK0))))),
% 1.43/1.20 introduced(definition,[],[choice_axiom])).
% 1.43/1.20 thf(f17,plain,(
% 1.43/1.20 ? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ($true = (in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)))) & ($true = (in @ X3 @ sK0))) => (((in @ sK3 @ sK1) = $true) & ($true = (in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)))) & ((in @ sK3 @ sK0) = $true))),
% 1.43/1.20 introduced(definition,[],[choice_axiom])).
% 1.43/1.20 thf(f14,plain,(
% 1.43/1.20 (binunionTILcontra = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (setminusER = $true)),
% 1.43/1.20 inference(flattening,[status(thm)],[f13])).
% 1.43/1.20 thf(f13,plain,(
% 1.43/1.20 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X1) = $true) & ($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))))) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binunionTILcontra = $true)) & (setminusER = $true)),
% 1.43/1.20 inference(ennf_transformation,[status(thm)],[f12])).
% 1.43/1.20 thf(f12,plain,(
% 1.43/1.20 ~((setminusER = $true) => ((binunionTILcontra = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) => ((in @ X3 @ X1) != $true)))))))),
% 1.43/1.20 inference(flattening,[status(thm)],[f11])).
% 1.43/1.20 thf(f11,plain,(
% 1.43/1.20 ~((setminusER = $true) => ((binunionTILcontra = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) => ~((in @ X3 @ X1) = $true)))))))),
% 1.43/1.20 inference(fool_elimination,[status(thm)],[f10])).
% 1.43/1.20 thf(f10,plain,(
% 1.43/1.20 ~(setminusER => (binunionTILcontra => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => ~(in @ X3 @ X1)))))))),
% 1.43/1.20 inference(rectify,[status(thm)],[f4])).
% 1.43/1.20 thf(f4,negated_conjecture,(
% 1.43/1.20 ~(setminusER => (binunionTILcontra => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4))) => ~(in @ X2 @ X3)))))))),
% 1.43/1.20 inference(negated_conjecture,[status(cth)],[f3])).
% 1.43/1.20 thf(f3,conjecture,(
% 1.43/1.20 setminusER => (binunionTILcontra => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4))) => ~(in @ X2 @ X3))))))),
% 1.43/1.20 file('/export/starexec/sandbox/tmp/tmp.OqKGAiXEPd/DTF2THF_30386.p',inComplementUnionImpNotIn1)).
% 1.43/1.20 thf(f84,plain,(
% 1.43/1.20 ($false = (in @ sK1 @ (powerset @ sK0))) | ~spl4_3),
% 1.43/1.20 inference(avatar_component_clause,[status(thm)],[f82])).
% 1.43/1.20 thf(f82,definition,(
% 1.43/1.20 spl4_3 <=> ($false = (in @ sK1 @ (powerset @ sK0)))),
% 1.43/1.20 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.43/1.20 thf(f96,plain,(
% 1.43/1.20 ~spl4_4),
% 1.43/1.20 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 1.43/1.20 thf(f95,plain,(
% 1.43/1.20 $false | ~spl4_4),
% 1.43/1.20 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.43/1.20 thf(f92,plain,(
% 1.43/1.20 ($false = $true) | ~spl4_4),
% 1.43/1.20 inference(superposition,[status(thm)],[f23,f88])).
% 1.43/1.20 thf(f88,plain,(
% 1.43/1.20 ($false = (in @ sK3 @ sK0)) | ~spl4_4),
% 1.43/1.20 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.43/1.20 thf(f86,definition,(
% 1.43/1.20 spl4_4 <=> ($false = (in @ sK3 @ sK0))),
% 1.43/1.20 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.43/1.20 thf(f23,plain,(
% 1.43/1.20 ((in @ sK3 @ sK0) = $true)),
% 1.43/1.20 inference(cnf_transformation,[status(thm)],[f18])).
% 1.43/1.20 thf(f90,plain,(
% 1.43/1.20 spl4_4 | spl4_3 | ~spl4_1),
% 1.43/1.20 inference(avatar_split_clause,[status(thm)],[f79,f62,f82,f86])).
% 1.43/1.20 thf(f62,definition,(
% 1.43/1.20 spl4_1 <=> ! [X0 : $i] : (($false = (in @ sK1 @ (powerset @ X0))) | ($false = (in @ sK2 @ (powerset @ X0))) | ((in @ sK3 @ X0) = $false))),
% 1.43/1.20 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.43/1.20 thf(f79,plain,(
% 1.43/1.20 ($false = (in @ sK1 @ (powerset @ sK0))) | ($false = (in @ sK3 @ sK0)) | ~spl4_1),
% 1.43/1.20 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.43/1.20 thf(f77,plain,(
% 1.43/1.20 ($false = $true) | ($false = (in @ sK1 @ (powerset @ sK0))) | ($false = (in @ sK3 @ sK0)) | ~spl4_1),
% 1.43/1.20 inference(superposition,[status(thm)],[f63,f22])).
% 1.43/1.20 thf(f22,plain,(
% 1.43/1.20 ($true = (in @ sK2 @ (powerset @ sK0)))),
% 1.43/1.20 inference(cnf_transformation,[status(thm)],[f18])).
% 1.43/1.20 thf(f63,plain,(
% 1.43/1.20 ( ! [X0 : $i] : (($false = (in @ sK2 @ (powerset @ X0))) | ((in @ sK3 @ X0) = $false) | ($false = (in @ sK1 @ (powerset @ X0)))) ) | ~spl4_1),
% 1.43/1.20 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.43/1.20 thf(f75,plain,(
% 1.43/1.20 ~spl4_2),
% 1.43/1.20 inference(avatar_contradiction_clause,[status(thm)],[f74])).
% 1.43/1.20 thf(f74,plain,(
% 1.43/1.20 $false | ~spl4_2),
% 1.43/1.20 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.43/1.20 thf(f70,plain,(
% 1.43/1.20 ($false = $true) | ~spl4_2),
% 1.43/1.20 inference(superposition,[status(thm)],[f67,f25])).
% 1.43/1.20 thf(f25,plain,(
% 1.43/1.20 ((in @ sK3 @ sK1) = $true)),
% 1.43/1.20 inference(cnf_transformation,[status(thm)],[f18])).
% 1.43/1.20 thf(f67,plain,(
% 1.43/1.20 ((in @ sK3 @ sK1) = $false) | ~spl4_2),
% 1.43/1.20 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.43/1.20 thf(f65,definition,(
% 1.43/1.20 spl4_2 <=> ((in @ sK3 @ sK1) = $false)),
% 1.43/1.20 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.43/1.20 thf(f69,plain,(
% 1.43/1.20 spl4_2 | spl4_1),
% 1.43/1.20 inference(avatar_split_clause,[status(thm)],[f59,f62,f65])).
% 1.43/1.20 thf(f59,plain,(
% 1.43/1.20 ( ! [X0 : $i] : (($false = (in @ sK2 @ (powerset @ X0))) | ((in @ sK3 @ sK1) = $false) | ($false = (in @ sK1 @ (powerset @ X0))) | ((in @ sK3 @ X0) = $false)) )),
% 1.43/1.20 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.43/1.20 thf(f56,plain,(
% 1.43/1.20 ( ! [X0 : $i] : (($false = $true) | ((in @ sK3 @ sK1) = $false) | ($false = (in @ sK2 @ (powerset @ X0))) | ((in @ sK3 @ X0) = $false) | ($false = (in @ sK1 @ (powerset @ X0)))) )),
% 1.43/1.20 inference(superposition,[status(thm)],[f43,f55])).
% 1.43/1.20 thf(f55,plain,(
% 1.43/1.20 ($false = (in @ sK3 @ (binunion @ sK1 @ sK2)))),
% 1.43/1.20 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.43/1.20 thf(f52,plain,(
% 1.43/1.20 ($false = $true) | ($false = (in @ sK3 @ (binunion @ sK1 @ sK2)))),
% 1.43/1.20 inference(superposition,[status(thm)],[f51,f24])).
% 1.43/1.20 thf(f24,plain,(
% 1.43/1.20 ($true = (in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))))),
% 1.43/1.20 inference(cnf_transformation,[status(thm)],[f18])).
% 1.43/1.20 thf(f51,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (setminus @ X1 @ X2))) | ((in @ X3 @ X2) = $false)) )),
% 1.43/1.20 inference(not_proxy_clausification,[status(thm)],[f50])).
% 1.43/1.20 thf(f50,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (in @ X3 @ X2)) = $true) | ($false = (in @ X3 @ (setminus @ X1 @ X2)))) )),
% 1.43/1.20 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.43/1.20 thf(f49,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ (setminus @ X1 @ X2)) => (~ (in @ X3 @ X2))) = $true)) )),
% 1.43/1.20 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.43/1.20 thf(f48,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (setminus @ X1 @ X2)) => (~ (in @ Y0 @ X2)))) @ X3) = $true)) )),
% 1.43/1.20 inference(pi_clausification,[status(thm)],[f47])).
% 1.43/1.20 thf(f47,plain,(
% 1.43/1.20 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setminus @ X1 @ X2)) => (~ (in @ Y0 @ X2))))) = $true)) )),
% 1.43/1.20 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.43/1.20 thf(f46,plain,(
% 1.43/1.20 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setminus @ X1 @ Y0)) => (~ (in @ Y1 @ Y0)))))) @ X2))) )),
% 1.43/1.20 inference(pi_clausification,[status(thm)],[f45])).
% 1.43/1.20 thf(f45,plain,(
% 1.43/1.20 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setminus @ X1 @ Y0)) => (~ (in @ Y1 @ Y0))))))) = $true)) )),
% 1.43/1.20 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.43/1.20 thf(f44,plain,(
% 1.43/1.20 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (~ (in @ Y2 @ Y1)))))))) @ X1) = $true)) )),
% 1.43/1.20 inference(pi_clausification,[status(thm)],[f29])).
% 1.43/1.20 thf(f29,plain,(
% 1.43/1.20 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (~ (in @ Y2 @ Y1))))))))))),
% 1.43/1.20 inference(definition_unfolding,[status(thm)],[f27,f20])).
% 1.43/1.20 thf(f20,plain,(
% 1.43/1.20 (setminusER = $true)),
% 1.43/1.20 inference(cnf_transformation,[status(thm)],[f18])).
% 1.43/1.20 thf(f27,plain,(
% 1.43/1.20 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (~ (in @ Y2 @ Y1))))))))))),
% 1.43/1.20 inference(cnf_transformation,[status(thm)],[f9])).
% 1.43/1.20 thf(f9,plain,(
% 1.43/1.20 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (~ (in @ Y2 @ Y1))))))))))),
% 1.43/1.20 inference(fool_elimination,[status(thm)],[f8])).
% 1.43/1.20 thf(f8,plain,(
% 1.43/1.20 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => ~(in @ X0 @ X1)) = setminusER)),
% 1.43/1.20 inference(rectify,[status(thm)],[f1])).
% 1.43/1.20 thf(f1,axiom,(
% 1.43/1.20 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.43/1.20 file('/export/starexec/sandbox/tmp/tmp.OqKGAiXEPd/DTF2THF_30386.p',setminusER)).
% 1.43/1.20 thf(f43,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X4 @ (binunion @ X2 @ X3)) = $true) | ($false = (in @ X4 @ X1)) | ($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1))) | ($false = (in @ X4 @ X2))) )),
% 1.43/1.20 inference(not_proxy_clausification,[status(thm)],[f42])).
% 1.43/1.20 thf(f42,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X4 @ X2)) | ($false = (~ (in @ X4 @ (binunion @ X2 @ X3)))) | ($false = (in @ X4 @ X1)) | ($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.43/1.20 inference(not_proxy_clausification,[status(thm)],[f41])).
% 1.43/1.20 thf(f41,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X4 @ X1)) | ($false = (in @ X3 @ (powerset @ X1))) | ((~ (in @ X4 @ X2)) = $true) | ($false = (in @ X2 @ (powerset @ X1))) | ($false = (~ (in @ X4 @ (binunion @ X2 @ X3))))) )),
% 1.43/1.20 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.43/1.20 thf(f40,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X4 @ X1)) | ($true = ((~ (in @ X4 @ (binunion @ X2 @ X3))) => (~ (in @ X4 @ X2)))) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.43/1.20 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.43/1.20 thf(f39,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ X1) => ((~ (in @ X4 @ (binunion @ X2 @ X3))) => (~ (in @ X4 @ X2)))) = $true) | ($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.43/1.20 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.43/1.20 thf(f38,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => ((~ (in @ Y0 @ (binunion @ X2 @ X3))) => (~ (in @ Y0 @ X2))))) @ X4)) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.43/1.20 inference(pi_clausification,[status(thm)],[f37])).
% 1.43/1.20 thf(f37,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((~ (in @ Y0 @ (binunion @ X2 @ X3))) => (~ (in @ Y0 @ X2))))))) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.43/1.20 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.43/1.20 thf(f36,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($true = ((in @ X3 @ (powerset @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((~ (in @ Y0 @ (binunion @ X2 @ X3))) => (~ (in @ Y0 @ X2))))))))) )),
% 1.43/1.20 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.43/1.20 thf(f35,plain,(
% 1.43/1.20 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((~ (in @ Y1 @ (binunion @ X2 @ Y0))) => (~ (in @ Y1 @ X2)))))))) @ X3) = $true)) )),
% 1.43/1.20 inference(pi_clausification,[status(thm)],[f34])).
% 1.43/1.20 thf(f34,plain,(
% 1.43/1.20 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((~ (in @ Y1 @ (binunion @ X2 @ Y0))) => (~ (in @ Y1 @ X2))))))))))) )),
% 1.43/1.20 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.43/1.20 thf(f33,plain,(
% 1.43/1.20 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (powerset @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((~ (in @ Y1 @ (binunion @ X2 @ Y0))) => (~ (in @ Y1 @ X2)))))))))))) )),
% 1.43/1.20 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.43/1.20 thf(f32,plain,(
% 1.43/1.20 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((~ (in @ Y2 @ (binunion @ Y0 @ Y1))) => (~ (in @ Y2 @ Y0))))))))))) @ X2) = $true)) )),
% 1.43/1.20 inference(pi_clausification,[status(thm)],[f31])).
% 1.43/1.20 thf(f31,plain,(
% 1.43/1.20 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((~ (in @ Y2 @ (binunion @ Y0 @ Y1))) => (~ (in @ Y2 @ Y0)))))))))))) = $true)) )),
% 1.43/1.20 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.43/1.20 thf(f30,plain,(
% 1.43/1.20 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ (in @ Y3 @ (binunion @ Y1 @ Y2))) => (~ (in @ Y3 @ Y1))))))))))))) @ X1))) )),
% 1.43/1.20 inference(pi_clausification,[status(thm)],[f28])).
% 1.43/1.20 thf(f28,plain,(
% 1.43/1.20 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ (in @ Y3 @ (binunion @ Y1 @ Y2))) => (~ (in @ Y3 @ Y1)))))))))))))) = $true)),
% 1.43/1.20 inference(definition_unfolding,[status(thm)],[f26,f19])).
% 1.43/1.20 thf(f19,plain,(
% 1.43/1.20 (binunionTILcontra = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ (in @ Y3 @ (binunion @ Y1 @ Y2))) => (~ (in @ Y3 @ Y1)))))))))))))))),
% 1.43/1.20 inference(cnf_transformation,[status(thm)],[f7])).
% 1.43/1.20 thf(f7,plain,(
% 1.43/1.20 (binunionTILcontra = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ (in @ Y3 @ (binunion @ Y1 @ Y2))) => (~ (in @ Y3 @ Y1)))))))))))))))),
% 1.43/1.20 inference(fool_elimination,[status(thm)],[f6])).
% 1.43/1.20 thf(f6,plain,(
% 1.43/1.20 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => (~(in @ X3 @ (binunion @ X0 @ X2)) => ~(in @ X3 @ X0))))) = binunionTILcontra)),
% 1.43/1.20 inference(rectify,[status(thm)],[f2])).
% 1.43/1.20 thf(f2,axiom,(
% 1.43/1.20 (! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (binunion @ X3 @ X4)) => ~(in @ X2 @ X3))))) = binunionTILcontra)),
% 1.43/1.20 file('/export/starexec/sandbox/tmp/tmp.OqKGAiXEPd/DTF2THF_30386.p',binunionTILcontra)).
% 1.43/1.20 thf(f26,plain,(
% 1.43/1.20 (binunionTILcontra = $true)),
% 1.43/1.20 inference(cnf_transformation,[status(thm)],[f18])).
% 1.43/1.20 % SZS output end Proof for DTF2THF_30386
% 1.43/1.20 % (30485)------------------------------
% 1.43/1.20 % (30485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.20 % (30485)Termination reason: Refutation
% 1.43/1.20
% 1.43/1.20 % (30485)Memory used [KB]: 5628
% 1.43/1.20 % (30485)Time elapsed: 0.006 s
% 1.43/1.20 % (30485)Instructions burned: 9 (million)
% 1.43/1.20 % (30485)------------------------------
% 1.43/1.20 % (30485)------------------------------
% 1.43/1.20 % (30484)Success in time 0.015 s
%------------------------------------------------------------------------------