%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU745^2 : 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 : n013.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 1.50s 1.21s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 31 unt; 0 typ; 5 def)
% Number of atoms : 713 ( 144 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 1081 ( 64 ~; 55 |; 36 &; 777 @)
% ( 5 <=>; 102 =>; 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 : 19 ( 15 usr; 14 con; 0-2 aty)
% ( 42 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 155 ( 49 ^; 88 !; 18 ?; 155 :)
% 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(f112,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f61,f85,f91,f98,f105,f111]) ).
thf(f111,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f60,f75]) ).
thf(f75,plain,
( ( ( in @ sK3 @ sK1 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f73,definition,
( spl4_3
<=> ( ( in @ sK3 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f60,plain,
( ( ( in @ sK3 @ sK1 )
= $true )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl4_2
<=> ( ( in @ sK3 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f105,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[status(thm)],[f104]) ).
thf(f104,plain,
( $false
| ~ spl4_5 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $false = $true )
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f19,f83]) ).
thf(f83,plain,
( ( $false
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl4_5
<=> ( $false
= ( in @ sK2 @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f19,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( setminusI = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
!= $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f13,f16,f15,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ X2 ) ) ) )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK1 ) )
!= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ X2 ) ) ) )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK1 ) )
!= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK1 ) )
!= $true ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK0 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true )
& ( ( in @ X3 @ ( setminus @ sK0 @ sK1 ) )
!= $true ) )
=> ( ( ( in @ sK3 @ sK0 )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( setminusI = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( inComplementUnionImpNotIn1 = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( setminusI = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( setminusI
=> ( inComplementUnionImpNotIn1
=> ! [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 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( inComplementUnionImpNotIn1
=> ! [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 @ ( setminus @ X0 @ X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setminusI
=> ( inComplementUnionImpNotIn1
=> ! [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 @ ( setminus @ X0 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ewj5LQToEf/DTF2THF_21477.p',inComplementUnionImpInComplement1) ).
thf(f98,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[status(thm)],[f97]) ).
thf(f97,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $false = $true )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f79,f23]) ).
thf(f23,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f79,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl4_4
<=> ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f91,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f90]) ).
thf(f90,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f56,f22]) ).
thf(f22,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f56,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl4_1
<=> ( ( in @ sK3 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f85,plain,
( spl4_5
| spl4_4
| spl4_3
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f68,f54,f73,f77,f81]) ).
thf(f68,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK3 @ sK1 )
= $false )
| ( $false
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK3 @ sK1 )
= $false )
| ( $false
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f21,f50]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false
= ( in @ X4 @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( in @ X4 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
= $false )
| ( ( ~ ( in @ X4 @ X1 ) )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( in @ X4 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( ( in @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ~ ( in @ X4 @ X1 ) )
= $true )
| ( ( in @ X4 @ X2 )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ( in @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ~ ( in @ X4 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ~ ( in @ Y0 @ X1 ) ) )
@ X4 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ~ ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
=> ~ ( in @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( setminus @ X2 @ ( binunion @ X1 @ Y0 ) ) )
=> ~ ( in @ Y1 @ X1 ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( setminus @ X2 @ ( binunion @ X1 @ Y0 ) ) )
=> ~ ( in @ Y1 @ X1 ) ) ) ) ) ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ ( setminus @ X2 @ ( binunion @ X1 @ Y0 ) ) )
=> ~ ( in @ Y1 @ X1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( binunion @ X1 @ Y1 ) ) )
=> ~ ( in @ Y2 @ X1 ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( binunion @ X1 @ Y1 ) ) )
=> ~ ( in @ Y2 @ X1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) ) )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) ) )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f18]) ).
thf(f18,plain,
( inComplementUnionImpNotIn1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) ) )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( inComplementUnionImpNotIn1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ ( setminus @ Y1 @ ( binunion @ Y0 @ Y2 ) ) )
=> ~ ( in @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [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 ) ) ) ) )
= inComplementUnionImpNotIn1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [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 ) ) ) ) )
= inComplementUnionImpNotIn1 ),
file('/export/starexec/sandbox/tmp/tmp.Ewj5LQToEf/DTF2THF_21477.p',inComplementUnionImpNotIn1) ).
thf(f24,plain,
inComplementUnionImpNotIn1 = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f21,plain,
( ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f61,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f52,f58,f54]) ).
thf(f52,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( ( in @ sK3 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ( $true != $true )
| ( ( in @ sK3 @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f20,f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X3 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X2 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X2 @ ( setminus @ X1 @ X3 ) )
= $true )
| ( $false
= ( ~ ( in @ X2 @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( ~ ( in @ X2 @ X3 )
=> ( in @ X2 @ ( setminus @ X1 @ X3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X3 )
=> ( in @ X2 @ ( setminus @ X1 @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( setminus @ X1 @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( setminus @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ X1 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ X1 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( setminus @ Y0 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( setminus @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f26,f25]) ).
thf(f25,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f26,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( setminus @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( setminus @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ~ ( in @ X1 @ X0 )
=> ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setminusI
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ewj5LQToEf/DTF2THF_21477.p',setminusI) ).
thf(f20,plain,
( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU745^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n013.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:36:23 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SEU745^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.27/0.46 % Version : Especial > Reduced > Especial.
% 0.27/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.27/0.46 % (! x:i.in x A -> in x (setminus A (binunion X Y)) ->
% 0.27/0.46 % in x (setminus A X))))
% 0.27/0.46
% 0.27/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.46 % Source : [Bro08]
% 0.27/0.46 % Names : ZFC247l [Bro08]
% 0.27/0.46 % : ZFC250l [Bro08]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 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 v3.7.0
% 0.27/0.46 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.27/0.46 % Number of atoms : 19 ( 2 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 7 ( 6 avg)
% 0.27/0.46 % Number of connectives : 56 ( 2 ~; 0 |; 0 &; 42 @)
% 0.27/0.46 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 15 ( 6 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.27/0.46 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : http://mathgate.info/detsetitem.php?id=307
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(in_type,type,
% 0.27/0.46 in: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(powerset_type,type,
% 0.27/0.46 powerset: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(binunion_type,type,
% 0.27/0.46 binunion: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(setminus_type,type,
% 0.27/0.46 setminus: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(setminusI_type,type,
% 0.27/0.46 setminusI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setminusI,definition,
% 0.27/0.46 ( setminusI
% 0.27/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ~ ( in @ Xx @ B )
% 0.27/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(inComplementUnionImpNotIn1_type,type,
% 0.27/0.46 inComplementUnionImpNotIn1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(inComplementUnionImpNotIn1,definition,
% 0.27/0.46 ( inComplementUnionImpNotIn1
% 0.27/0.46 = ( ! [A: $i,X: $i] :
% 0.27/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.46 => ! [Y: $i] :
% 0.27/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.27/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(inComplementUnionImpInComplement1,conjecture,
% 0.27/0.46 ( setminusI
% 0.27/0.46 => ( inComplementUnionImpNotIn1
% 0.27/0.46 => ! [A: $i,X: $i] :
% 0.27/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.46 => ! [Y: $i] :
% 0.27/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.27/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.36/1.18 ---- Embedded in THF ---
% 1.36/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.18 %%% Generated on Tue Feb 24 12:36:23 EST 2026
% 1.36/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.18 %%% Logic specification used:
% 1.36/1.18 %%% thf(spec, logic, $$dhol).
% 1.36/1.18
% 1.36/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ewj5LQToEf/DTF2DTF21477.p
% See solution above
% 1.36/1.18 ------------------------
% 1.36/1.19 ---- Cleaned THF ---
% 1.36/1.19 thf(in_type,type,
% 1.36/1.19 in: $i > $i > $o ).
% 1.36/1.19
% 1.36/1.19 thf(powerset_type,type,
% 1.36/1.19 powerset: $i > $i ).
% 1.36/1.19
% 1.36/1.19 thf(binunion_type,type,
% 1.36/1.19 binunion: $i > $i > $i ).
% 1.36/1.19
% 1.36/1.19 thf(setminus_type,type,
% 1.36/1.19 setminus: $i > $i > $i ).
% 1.36/1.19
% 1.36/1.19 thf(setminusI_type,type,
% 1.36/1.19 setminusI: $o ).
% 1.36/1.19
% 1.36/1.19 thf(setminusI,definition,
% 1.36/1.19 ( setminusI
% 1.36/1.19 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.36/1.19 ( ( in @ Xx @ A )
% 1.36/1.19 => ( ~ ( in @ Xx @ B )
% 1.36/1.19 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.36/1.19
% 1.36/1.19 thf(inComplementUnionImpNotIn1_type,type,
% 1.36/1.19 inComplementUnionImpNotIn1: $o ).
% 1.36/1.19
% 1.36/1.19 thf(inComplementUnionImpNotIn1,definition,
% 1.36/1.19 ( inComplementUnionImpNotIn1
% 1.36/1.19 = ( ! [A: $i,X: $i] :
% 1.36/1.19 ( ( in @ X @ ( powerset @ A ) )
% 1.36/1.19 => ! [Y: $i] :
% 1.36/1.19 ( ( in @ Y @ ( powerset @ A ) )
% 1.36/1.19 => ! [Xx: $i] :
% 1.36/1.19 ( ( in @ Xx @ A )
% 1.36/1.19 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 1.36/1.19 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 1.36/1.19
% 1.36/1.19 thf(inComplementUnionImpInComplement1,conjecture,
% 1.36/1.19 ( setminusI
% 1.36/1.19 => ( inComplementUnionImpNotIn1
% 1.36/1.19 => ! [A: $i,X: $i] :
% 1.36/1.19 ( ( in @ X @ ( powerset @ A ) )
% 1.36/1.19 => ! [Y: $i] :
% 1.36/1.19 ( ( in @ Y @ ( powerset @ A ) )
% 1.36/1.19 => ! [Xx: $i] :
% 1.36/1.19 ( ( in @ Xx @ A )
% 1.36/1.19 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 1.36/1.19 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 1.36/1.19 ------------------------
% 1.50/1.20 % (21575)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_21477 for (3000ds/4Mi)
% 1.50/1.20 % (21574)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21477 for (3000ds/183Mi)
% 1.50/1.20 % (21575)Instruction limit reached!
% 1.50/1.20 % (21575)------------------------------
% 1.50/1.20 % (21575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.20 % (21575)Termination reason: Unknown
% 1.50/1.20 % (21575)Termination phase: Saturation
% 1.50/1.20
% 1.50/1.20 % (21575)Memory used [KB]: 5500
% 1.50/1.20 % (21575)Time elapsed: 0.003 s
% 1.50/1.20 % (21575)Instructions burned: 4 (million)
% 1.50/1.20 % (21575)------------------------------
% 1.50/1.20 % (21575)------------------------------
% 1.50/1.21 % (21574)First to succeed.
% 1.50/1.21 % (21574)Refutation found. Thanks to Tanya!
% 1.50/1.21 % SZS status Theorem for DTF2THF_21477
% 1.50/1.21 % SZS output start Proof for DTF2THF_21477
% 1.50/1.21 thf(func_def_0, type, in: $i > $i > $o).
% 1.50/1.21 thf(func_def_1, type, powerset: $i > $i).
% 1.50/1.21 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.50/1.21 thf(func_def_3, type, setminus: $i > $i > $i).
% 1.50/1.21 thf(f112,plain,(
% 1.50/1.21 $false),
% 1.50/1.21 inference(avatar_sat_refutation,[status(thm)],[f61,f85,f91,f98,f105,f111])).
% 1.50/1.21 thf(f111,plain,(
% 1.50/1.21 ~spl4_2 | ~spl4_3),
% 1.50/1.21 inference(avatar_contradiction_clause,[status(thm)],[f110])).
% 1.50/1.21 thf(f110,plain,(
% 1.50/1.21 $false | (~spl4_2 | ~spl4_3)),
% 1.50/1.21 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.50/1.21 thf(f107,plain,(
% 1.50/1.21 ($false = $true) | (~spl4_2 | ~spl4_3)),
% 1.50/1.21 inference(superposition,[status(thm)],[f60,f75])).
% 1.50/1.21 thf(f75,plain,(
% 1.50/1.21 ((in @ sK3 @ sK1) = $false) | ~spl4_3),
% 1.50/1.21 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.50/1.21 thf(f73,definition,(
% 1.50/1.21 spl4_3 <=> ((in @ sK3 @ sK1) = $false)),
% 1.50/1.21 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.50/1.21 thf(f60,plain,(
% 1.50/1.21 ((in @ sK3 @ sK1) = $true) | ~spl4_2),
% 1.50/1.21 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.50/1.21 thf(f58,definition,(
% 1.50/1.21 spl4_2 <=> ((in @ sK3 @ sK1) = $true)),
% 1.50/1.21 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.50/1.21 thf(f105,plain,(
% 1.50/1.21 ~spl4_5),
% 1.50/1.21 inference(avatar_contradiction_clause,[status(thm)],[f104])).
% 1.50/1.21 thf(f104,plain,(
% 1.50/1.21 $false | ~spl4_5),
% 1.50/1.21 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.50/1.21 thf(f101,plain,(
% 1.50/1.21 ($false = $true) | ~spl4_5),
% 1.50/1.21 inference(superposition,[status(thm)],[f19,f83])).
% 1.50/1.21 thf(f83,plain,(
% 1.50/1.21 ($false = (in @ sK2 @ (powerset @ sK0))) | ~spl4_5),
% 1.50/1.21 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.50/1.21 thf(f81,definition,(
% 1.50/1.21 spl4_5 <=> ($false = (in @ sK2 @ (powerset @ sK0)))),
% 1.50/1.21 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.50/1.21 thf(f19,plain,(
% 1.50/1.21 ($true = (in @ sK2 @ (powerset @ sK0)))),
% 1.50/1.21 inference(cnf_transformation,[status(thm)],[f17])).
% 1.50/1.21 thf(f17,plain,(
% 1.50/1.21 (setminusI = $true) & (inComplementUnionImpNotIn1 = $true) & (($true = (in @ sK1 @ (powerset @ sK0))) & ((((in @ sK3 @ sK0) = $true) & ((in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true) & ((in @ sK3 @ (setminus @ sK0 @ sK1)) != $true)) & ($true = (in @ sK2 @ (powerset @ sK0)))))),
% 1.50/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f13,f16,f15,f14])).
% 1.50/1.21 thf(f14,plain,(
% 1.50/1.21 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X0)) & ($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) & ((in @ X3 @ (setminus @ X0 @ X1)) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true))) => (($true = (in @ sK1 @ (powerset @ sK0))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ($true = (in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ X2)))) & ((in @ X3 @ (setminus @ sK0 @ sK1)) != $true)) & ($true = (in @ X2 @ (powerset @ sK0)))))),
% 1.50/1.21 introduced(definition,[],[choice_axiom])).
% 1.50/1.21 thf(f15,plain,(
% 1.50/1.21 ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ($true = (in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ X2)))) & ((in @ X3 @ (setminus @ sK0 @ sK1)) != $true)) & ($true = (in @ X2 @ (powerset @ sK0)))) => (? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true) & ((in @ X3 @ (setminus @ sK0 @ sK1)) != $true)) & ($true = (in @ sK2 @ (powerset @ sK0))))),
% 1.50/1.21 introduced(definition,[],[choice_axiom])).
% 1.50/1.21 thf(f16,plain,(
% 1.50/1.21 ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ((in @ X3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true) & ((in @ X3 @ (setminus @ sK0 @ sK1)) != $true)) => (((in @ sK3 @ sK0) = $true) & ((in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true) & ((in @ sK3 @ (setminus @ sK0 @ sK1)) != $true))),
% 1.50/1.21 introduced(definition,[],[choice_axiom])).
% 1.50/1.21 thf(f13,plain,(
% 1.50/1.21 (setminusI = $true) & (inComplementUnionImpNotIn1 = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X0)) & ($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) & ((in @ X3 @ (setminus @ X0 @ X1)) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true)))),
% 1.50/1.21 inference(flattening,[status(thm)],[f12])).
% 1.50/1.21 thf(f12,plain,(
% 1.50/1.21 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ X1)) != $true) & ($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))))) & ($true = (in @ X3 @ X0))) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (inComplementUnionImpNotIn1 = $true)) & (setminusI = $true)),
% 1.50/1.21 inference(ennf_transformation,[status(thm)],[f9])).
% 1.50/1.21 thf(f9,plain,(
% 1.50/1.21 ~((setminusI = $true) => ((inComplementUnionImpNotIn1 = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => (($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) => ((in @ X3 @ (setminus @ X0 @ X1)) = $true)))))))),
% 1.50/1.21 inference(fool_elimination,[status(thm)],[f8])).
% 1.50/1.21 thf(f8,plain,(
% 1.50/1.21 ~(setminusI => (inComplementUnionImpNotIn1 => ! [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 @ (setminus @ X0 @ X1))))))))),
% 1.50/1.21 inference(rectify,[status(thm)],[f4])).
% 1.50/1.21 thf(f4,negated_conjecture,(
% 1.50/1.21 ~(setminusI => (inComplementUnionImpNotIn1 => ! [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 @ (setminus @ X0 @ X3))))))))),
% 1.50/1.21 inference(negated_conjecture,[status(cth)],[f3])).
% 1.50/1.21 thf(f3,conjecture,(
% 1.50/1.21 setminusI => (inComplementUnionImpNotIn1 => ! [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 @ (setminus @ X0 @ X3)))))))),
% 1.50/1.21 file('/export/starexec/sandbox/tmp/tmp.Ewj5LQToEf/DTF2THF_21477.p',inComplementUnionImpInComplement1)).
% 1.50/1.21 thf(f98,plain,(
% 1.50/1.21 ~spl4_4),
% 1.50/1.21 inference(avatar_contradiction_clause,[status(thm)],[f97])).
% 1.50/1.21 thf(f97,plain,(
% 1.50/1.21 $false | ~spl4_4),
% 1.50/1.21 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.50/1.21 thf(f93,plain,(
% 1.50/1.21 ($false = $true) | ~spl4_4),
% 1.50/1.21 inference(superposition,[status(thm)],[f79,f23])).
% 1.50/1.21 thf(f23,plain,(
% 1.50/1.21 ($true = (in @ sK1 @ (powerset @ sK0)))),
% 1.50/1.21 inference(cnf_transformation,[status(thm)],[f17])).
% 1.50/1.21 thf(f79,plain,(
% 1.50/1.21 ($false = (in @ sK1 @ (powerset @ sK0))) | ~spl4_4),
% 1.50/1.21 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.50/1.21 thf(f77,definition,(
% 1.50/1.21 spl4_4 <=> ($false = (in @ sK1 @ (powerset @ sK0)))),
% 1.50/1.21 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.50/1.21 thf(f91,plain,(
% 1.50/1.21 ~spl4_1),
% 1.50/1.21 inference(avatar_contradiction_clause,[status(thm)],[f90])).
% 1.50/1.21 thf(f90,plain,(
% 1.50/1.21 $false | ~spl4_1),
% 1.50/1.21 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.50/1.21 thf(f86,plain,(
% 1.50/1.21 ($false = $true) | ~spl4_1),
% 1.50/1.21 inference(superposition,[status(thm)],[f56,f22])).
% 1.50/1.21 thf(f22,plain,(
% 1.50/1.21 ((in @ sK3 @ sK0) = $true)),
% 1.50/1.21 inference(cnf_transformation,[status(thm)],[f17])).
% 1.50/1.21 thf(f56,plain,(
% 1.50/1.21 ((in @ sK3 @ sK0) = $false) | ~spl4_1),
% 1.50/1.21 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.50/1.21 thf(f54,definition,(
% 1.50/1.21 spl4_1 <=> ((in @ sK3 @ sK0) = $false)),
% 1.50/1.21 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.50/1.21 thf(f85,plain,(
% 1.50/1.21 spl4_5 | spl4_4 | spl4_3 | spl4_1),
% 1.50/1.21 inference(avatar_split_clause,[status(thm)],[f68,f54,f73,f77,f81])).
% 1.50/1.21 thf(f68,plain,(
% 1.50/1.21 ($false = (in @ sK1 @ (powerset @ sK0))) | ((in @ sK3 @ sK1) = $false) | ($false = (in @ sK2 @ (powerset @ sK0))) | ((in @ sK3 @ sK0) = $false)),
% 1.50/1.21 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.50/1.21 thf(f64,plain,(
% 1.50/1.21 ((in @ sK3 @ sK0) = $false) | ($false = (in @ sK2 @ (powerset @ sK0))) | ((in @ sK3 @ sK1) = $false) | ($false = (in @ sK1 @ (powerset @ sK0))) | ($false = $true)),
% 1.50/1.21 inference(superposition,[status(thm)],[f21,f50])).
% 1.50/1.21 thf(f50,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X4 @ (setminus @ X2 @ (binunion @ X1 @ X3))) = $false) | ((in @ X1 @ (powerset @ X2)) = $false) | ($false = (in @ X4 @ X1)) | ($false = (in @ X3 @ (powerset @ X2))) | ((in @ X4 @ X2) = $false)) )),
% 1.50/1.21 inference(not_proxy_clausification,[status(thm)],[f49])).
% 1.50/1.21 thf(f49,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | ((in @ X4 @ (setminus @ X2 @ (binunion @ X1 @ X3))) = $false) | ((~ (in @ X4 @ X1)) = $true) | ($false = (in @ X3 @ (powerset @ X2))) | ((in @ X4 @ X2) = $false)) )),
% 1.50/1.21 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.50/1.21 thf(f48,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | (((in @ X4 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (~ (in @ X4 @ X1))) = $true) | ((in @ X4 @ X2) = $false) | ($false = (in @ X3 @ (powerset @ X2)))) )),
% 1.50/1.21 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.50/1.21 thf(f47,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | ($false = (in @ X3 @ (powerset @ X2))) | ($true = ((in @ X4 @ X2) => ((in @ X4 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (~ (in @ X4 @ X1)))))) )),
% 1.50/1.21 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.50/1.21 thf(f46,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (~ (in @ Y0 @ X1))))) @ X4)) | ($false = (in @ X3 @ (powerset @ X2)))) )),
% 1.50/1.21 inference(pi_clausification,[status(thm)],[f45])).
% 1.50/1.21 thf(f45,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | ($false = (in @ X3 @ (powerset @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (~ (in @ Y0 @ X1)))))))) )),
% 1.50/1.21 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.50/1.21 thf(f44,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | ($true = ((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (~ (in @ Y0 @ X1))))))))) )),
% 1.50/1.21 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.50/1.21 thf(f43,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X2)) = $false) | (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (setminus @ X2 @ (binunion @ X1 @ Y0))) => (~ (in @ Y1 @ X1)))))))) @ X3) = $true)) )),
% 1.50/1.21 inference(pi_clausification,[status(thm)],[f42])).
% 1.50/1.21 thf(f42,plain,(
% 1.50/1.21 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (setminus @ X2 @ (binunion @ X1 @ Y0))) => (~ (in @ Y1 @ X1)))))))))) | ((in @ X1 @ (powerset @ X2)) = $false)) )),
% 1.50/1.21 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.50/1.21 thf(f41,plain,(
% 1.50/1.21 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (setminus @ X2 @ (binunion @ X1 @ Y0))) => (~ (in @ Y1 @ X1)))))))))))) )),
% 1.50/1.21 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.50/1.21 thf(f40,plain,(
% 1.50/1.21 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (binunion @ X1 @ Y1))) => (~ (in @ Y2 @ X1))))))))))) @ X2) = $true)) )),
% 1.50/1.21 inference(pi_clausification,[status(thm)],[f39])).
% 1.50/1.21 thf(f39,plain,(
% 1.50/1.21 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (binunion @ X1 @ Y1))) => (~ (in @ Y2 @ X1)))))))))))) = $true)) )),
% 1.50/1.21 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.50/1.21 thf(f38,plain,(
% 1.50/1.21 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0))))))))))))) @ X1) = $true)) )),
% 1.50/1.21 inference(pi_clausification,[status(thm)],[f27])).
% 1.50/1.21 thf(f27,plain,(
% 1.50/1.21 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0)))))))))))))))),
% 1.50/1.21 inference(definition_unfolding,[status(thm)],[f24,f18])).
% 1.50/1.21 thf(f18,plain,(
% 1.50/1.21 (inComplementUnionImpNotIn1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0)))))))))))))))),
% 1.50/1.21 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.21 thf(f11,plain,(
% 1.50/1.21 (inComplementUnionImpNotIn1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0)))))))))))))))),
% 1.50/1.21 inference(fool_elimination,[status(thm)],[f10])).
% 1.50/1.21 thf(f10,plain,(
% 1.50/1.21 (! [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))))) = inComplementUnionImpNotIn1)),
% 1.50/1.21 inference(rectify,[status(thm)],[f2])).
% 1.50/1.21 thf(f2,axiom,(
% 1.50/1.21 (! [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))))) = inComplementUnionImpNotIn1)),
% 1.50/1.21 file('/export/starexec/sandbox/tmp/tmp.Ewj5LQToEf/DTF2THF_21477.p',inComplementUnionImpNotIn1)).
% 1.50/1.21 thf(f24,plain,(
% 1.50/1.21 (inComplementUnionImpNotIn1 = $true)),
% 1.50/1.21 inference(cnf_transformation,[status(thm)],[f17])).
% 1.50/1.21 thf(f21,plain,(
% 1.50/1.21 ((in @ sK3 @ (setminus @ sK0 @ (binunion @ sK1 @ sK2))) = $true)),
% 1.50/1.21 inference(cnf_transformation,[status(thm)],[f17])).
% 1.50/1.21 thf(f61,plain,(
% 1.50/1.21 spl4_1 | spl4_2),
% 1.50/1.21 inference(avatar_split_clause,[status(thm)],[f52,f58,f54])).
% 1.50/1.21 thf(f52,plain,(
% 1.50/1.21 ((in @ sK3 @ sK0) = $false) | ((in @ sK3 @ sK1) = $true)),
% 1.50/1.21 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.50/1.21 thf(f51,plain,(
% 1.50/1.21 ((in @ sK3 @ sK0) = $false) | ($true != $true) | ((in @ sK3 @ sK1) = $true)),
% 1.50/1.21 inference(superposition,[status(thm)],[f20,f37])).
% 1.50/1.21 thf(f37,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (setminus @ X1 @ X3)) = $true) | ((in @ X2 @ X1) = $false) | ((in @ X2 @ X3) = $true)) )),
% 1.50/1.21 inference(not_proxy_clausification,[status(thm)],[f36])).
% 1.50/1.21 thf(f36,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ X1) = $false) | ((in @ X2 @ (setminus @ X1 @ X3)) = $true) | ($false = (~ (in @ X2 @ X3)))) )),
% 1.50/1.21 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.50/1.21 thf(f35,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ X1) = $false) | (((~ (in @ X2 @ X3)) => (in @ X2 @ (setminus @ X1 @ X3))) = $true)) )),
% 1.50/1.21 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.50/1.21 thf(f34,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X1) => ((~ (in @ X2 @ X3)) => (in @ X2 @ (setminus @ X1 @ X3)))))) )),
% 1.50/1.21 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.50/1.21 thf(f33,plain,(
% 1.50/1.21 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ X1) => ((~ (in @ X2 @ Y0)) => (in @ X2 @ (setminus @ X1 @ Y0))))) @ X3) = $true)) )),
% 1.50/1.21 inference(pi_clausification,[status(thm)],[f32])).
% 1.50/1.21 thf(f32,plain,(
% 1.50/1.21 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => ((~ (in @ X2 @ Y0)) => (in @ X2 @ (setminus @ X1 @ Y0)))))))) )),
% 1.50/1.21 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.50/1.21 thf(f31,plain,(
% 1.50/1.21 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ X1 @ Y1))))))) @ X2) = $true)) )),
% 1.50/1.21 inference(pi_clausification,[status(thm)],[f30])).
% 1.50/1.21 thf(f30,plain,(
% 1.50/1.21 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ X1 @ Y1)))))))) = $true)) )),
% 1.50/1.21 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.50/1.21 thf(f29,plain,(
% 1.50/1.21 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (in @ Y1 @ (setminus @ Y0 @ Y2))))))))) @ X1) = $true)) )),
% 1.50/1.21 inference(pi_clausification,[status(thm)],[f28])).
% 1.50/1.21 thf(f28,plain,(
% 1.50/1.21 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))))),
% 1.50/1.21 inference(definition_unfolding,[status(thm)],[f26,f25])).
% 1.50/1.21 thf(f25,plain,(
% 1.50/1.21 (setminusI = $true)),
% 1.50/1.21 inference(cnf_transformation,[status(thm)],[f17])).
% 1.50/1.21 thf(f26,plain,(
% 1.50/1.21 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))))),
% 1.50/1.21 inference(cnf_transformation,[status(thm)],[f7])).
% 1.50/1.21 thf(f7,plain,(
% 1.50/1.21 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))))),
% 1.50/1.21 inference(fool_elimination,[status(thm)],[f6])).
% 1.50/1.21 thf(f6,plain,(
% 1.50/1.21 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (~(in @ X1 @ X0) => (in @ X1 @ (setminus @ X2 @ X0)))))),
% 1.50/1.21 inference(rectify,[status(thm)],[f1])).
% 1.50/1.21 thf(f1,axiom,(
% 1.50/1.21 (setminusI = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 1.50/1.21 file('/export/starexec/sandbox/tmp/tmp.Ewj5LQToEf/DTF2THF_21477.p',setminusI)).
% 1.50/1.21 thf(f20,plain,(
% 1.50/1.21 ((in @ sK3 @ (setminus @ sK0 @ sK1)) != $true)),
% 1.50/1.21 inference(cnf_transformation,[status(thm)],[f17])).
% 1.50/1.21 % SZS output end Proof for DTF2THF_21477
% 1.50/1.21 % (21574)------------------------------
% 1.50/1.21 % (21574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.21 % (21574)Termination reason: Refutation
% 1.50/1.21
% 1.50/1.21 % (21574)Memory used [KB]: 5628
% 1.50/1.21 % (21574)Time elapsed: 0.007 s
% 1.50/1.21 % (21574)Instructions burned: 9 (million)
% 1.50/1.21 % (21574)------------------------------
% 1.50/1.21 % (21574)------------------------------
% 1.50/1.21 % (21573)Success in time 0.016 s
%------------------------------------------------------------------------------