%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU751^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n022.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 09:36:54 AM UTC 2026
% Result : Theorem 1.69s 1.33s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 26
% Syntax : Number of formulae : 142 ( 26 unt; 0 typ; 5 def)
% Number of atoms : 2174 ( 572 equ; 0 cnn)
% Maximal formula atoms : 12 ( 15 avg)
% Number of connectives : 2443 ( 304 ~; 240 |; 165 &;1598 @)
% ( 25 <=>; 111 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 36 con; 0-2 aty)
% Number of variables : 329 ( 0 ^; 240 !; 89 ?; 329 :)
% 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,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
setminus: $i > $i > $i ).
thf(f199,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f156,f167,f173,f185,f190,f198]) ).
thf(f198,plain,
( spl23_2
| spl23_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f197]) ).
thf(f197,plain,
( $false
| spl23_2
| spl23_5 ),
inference(subsumption_resolution,[status(thm)],[f196,f93]) ).
thf(f93,plain,
( $true
= ( in @ sK14 @ sK11 ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
( ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( complementT_lem = $true )
& ( binintersectI = $true )
& ( $true
= ( in @ sK12 @ ( powerset @ sK11 ) ) )
& ( $true
= ( in @ sK14 @ sK11 ) )
& ( $true
= ( in @ sK14 @ ( setminus @ sK11 @ ( binintersect @ sK12 @ sK13 ) ) ) )
& ( $true
!= ( in @ sK14 @ ( binunion @ ( setminus @ sK11 @ sK12 ) @ ( setminus @ sK11 @ sK13 ) ) ) )
& ( $true
= ( in @ sK13 @ ( powerset @ sK11 ) ) )
& ( binunionTILcontra = $true )
& ( complementTE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f36,f59,f58,f57]) ).
thf(f57,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
& ( $true
!= ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK12 @ ( powerset @ sK11 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ sK11 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK11 @ ( binintersect @ sK12 @ X2 ) ) ) )
& ( $true
!= ( in @ X3 @ ( binunion @ ( setminus @ sK11 @ sK12 ) @ ( setminus @ sK11 @ X2 ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ sK11 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f58,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ sK11 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK11 @ ( binintersect @ sK12 @ X2 ) ) ) )
& ( $true
!= ( in @ X3 @ ( binunion @ ( setminus @ sK11 @ sK12 ) @ ( setminus @ sK11 @ X2 ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ sK11 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ sK11 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK11 @ ( binintersect @ sK12 @ sK13 ) ) )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ sK11 @ sK12 ) @ ( setminus @ sK11 @ sK13 ) ) )
!= $true ) )
& ( $true
= ( in @ sK13 @ ( powerset @ sK11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f59,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK11 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK11 @ ( binintersect @ sK12 @ sK13 ) ) )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ sK11 @ sK12 ) @ ( setminus @ sK11 @ sK13 ) ) )
!= $true ) )
=> ( ( $true
= ( in @ sK14 @ sK11 ) )
& ( $true
= ( in @ sK14 @ ( setminus @ sK11 @ ( binintersect @ sK12 @ sK13 ) ) ) )
& ( $true
!= ( in @ sK14 @ ( binunion @ ( setminus @ sK11 @ sK12 ) @ ( setminus @ sK11 @ sK13 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( complementT_lem = $true )
& ( binintersectI = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
& ( $true
!= ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
& ( binunionTILcontra = $true )
& ( complementTE1 = $true ) ),
inference(flattening,[status(thm)],[f35]) ).
thf(f35,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTE1 = $true )
& ( complementT_lem = $true )
& ( setminusER = $true )
& ( binintersectI = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ( binintersectI = $true )
=> ( ( setminusER = $true )
=> ( ( complementT_lem = $true )
=> ( ( complementTE1 = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
=> ( $true
= ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( binintersectI
=> ( setminusER
=> ( complementT_lem
=> ( complementTE1
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( binintersectI
=> ( setminusER
=> ( complementT_lem
=> ( complementTE1
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( binintersect @ X3 @ X4 ) ) )
=> ( in @ X2 @ ( binunion @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( binintersectI
=> ( setminusER
=> ( complementT_lem
=> ( complementTE1
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( binintersect @ X3 @ X4 ) ) )
=> ( in @ X2 @ ( binunion @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',demorgan1a) ).
thf(f196,plain,
( ( $true
!= ( in @ sK14 @ sK11 ) )
| spl23_2
| spl23_5 ),
inference(subsumption_resolution,[status(thm)],[f195,f90]) ).
thf(f90,plain,
( $true
= ( in @ sK13 @ ( powerset @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f195,plain,
( ( $true
!= ( in @ sK13 @ ( powerset @ sK11 ) ) )
| ( $true
!= ( in @ sK14 @ sK11 ) )
| spl23_2
| spl23_5 ),
inference(subsumption_resolution,[status(thm)],[f194,f155]) ).
thf(f155,plain,
( ( $true
!= ( in @ sK14 @ sK13 ) )
| spl23_2 ),
inference(avatar_component_clause,[status(thm)],[f153]) ).
thf(f153,definition,
( spl23_2
<=> ( $true
= ( in @ sK14 @ sK13 ) ) ),
introduced(definition,[new_symbols(naming,[spl23_2])],[avatar_definition]) ).
thf(f194,plain,
( ( $true
= ( in @ sK14 @ sK13 ) )
| ( $true
!= ( in @ sK13 @ ( powerset @ sK11 ) ) )
| ( $true
!= ( in @ sK14 @ sK11 ) )
| spl23_5 ),
inference(trivial_inequality_removal,[status(thm)],[f193]) ).
thf(f193,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK14 @ sK11 ) )
| ( $true
!= ( in @ sK13 @ ( powerset @ sK11 ) ) )
| ( $true
= ( in @ sK14 @ sK13 ) )
| spl23_5 ),
inference(superposition,[status(thm)],[f189,f140]) ).
thf(f140,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f83,f88]) ).
thf(f88,plain,
complementTE1 = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f83,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( complementTE1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( complementTE1 != $true ) )
& ( ( complementTE1 = $true )
| ( ( $true
= ( in @ sK7 @ sK6 ) )
& ( $true
!= ( in @ sK7 @ ( setminus @ sK6 @ sK5 ) ) )
& ( ( in @ sK7 @ sK5 )
!= $true )
& ( $true
= ( in @ sK5 @ ( powerset @ sK6 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f49,f51,f50]) ).
thf(f50,plain,
( ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( $true
!= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) )
& ( $true
!= ( in @ X5 @ X3 ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X4 ) ) ) )
=> ( ? [X5: $i] :
( ( $true
= ( in @ X5 @ sK6 ) )
& ( $true
!= ( in @ X5 @ ( setminus @ sK6 @ sK5 ) ) )
& ( ( in @ X5 @ sK5 )
!= $true ) )
& ( $true
= ( in @ sK5 @ ( powerset @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ sK6 ) )
& ( $true
!= ( in @ X5 @ ( setminus @ sK6 @ sK5 ) ) )
& ( ( in @ X5 @ sK5 )
!= $true ) )
=> ( ( $true
= ( in @ sK7 @ sK6 ) )
& ( $true
!= ( in @ sK7 @ ( setminus @ sK6 @ sK5 ) ) )
& ( ( in @ sK7 @ sK5 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f49,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( complementTE1 != $true ) )
& ( ( complementTE1 = $true )
| ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( $true
!= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) )
& ( $true
!= ( in @ X5 @ X3 ) ) )
& ( $true
= ( in @ X3 @ ( powerset @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( complementTE1 != $true ) )
& ( ( complementTE1 = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( complementTE1 = $true ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
( ( complementTE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( complementTE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) )
<=> ( complementTE1 = $true ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) )
= complementTE1 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ ( setminus @ X0 @ X3 ) )
=> ( in @ X2 @ X3 ) ) ) )
= complementTE1 ),
file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',complementTE1) ).
thf(f189,plain,
( ( ( in @ sK14 @ ( setminus @ sK11 @ sK13 ) )
!= $true )
| spl23_5 ),
inference(avatar_component_clause,[status(thm)],[f187]) ).
thf(f187,definition,
( spl23_5
<=> ( ( in @ sK14 @ ( setminus @ sK11 @ sK13 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl23_5])],[avatar_definition]) ).
thf(f190,plain,
( ~ spl23_5
| spl23_4 ),
inference(avatar_split_clause,[status(thm)],[f175,f165,f187]) ).
thf(f165,definition,
( spl23_4
<=> ! [X0: $i] :
( ( $true
!= ( in @ ( setminus @ sK11 @ sK13 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK14 @ X0 ) )
| ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ X0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl23_4])],[avatar_definition]) ).
thf(f175,plain,
! [X0: $i] :
( ( ( in @ sK14 @ ( setminus @ sK11 @ sK13 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ sK11 @ sK13 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK14 @ X0 ) )
| ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f174]) ).
thf(f174,plain,
! [X0: $i] :
( ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ ( setminus @ sK11 @ sK13 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK14 @ X0 ) )
| ( ( in @ sK14 @ ( setminus @ sK11 @ sK13 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f91,f142]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
!= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f110,f98]) ).
thf(f98,plain,
binunionTIRcontra = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f110,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( binunionTIRcontra != $true ) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ( ( ( in @ sK21 @ ( powerset @ sK19 ) )
= $true )
& ( $true
= ( in @ sK22 @ sK21 ) )
& ( $true
= ( in @ sK22 @ sK19 ) )
& ( $true
!= ( in @ sK22 @ ( binunion @ sK20 @ sK21 ) ) )
& ( $true
= ( in @ sK20 @ ( powerset @ sK19 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22])],[f68,f71,f70,f69]) ).
thf(f69,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
= $true )
& ? [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
& ( $true
= ( in @ X7 @ X4 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) ) ) )
& ( $true
= ( in @ X5 @ ( powerset @ X4 ) ) ) )
=> ( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ sK19 ) ) )
& ? [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
& ( $true
= ( in @ X7 @ sK19 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK20 @ X6 ) ) ) ) )
& ( $true
= ( in @ sK20 @ ( powerset @ sK19 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f70,plain,
( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ sK19 ) ) )
& ? [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
& ( $true
= ( in @ X7 @ sK19 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK20 @ X6 ) ) ) ) )
=> ( ( ( in @ sK21 @ ( powerset @ sK19 ) )
= $true )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK21 ) )
& ( $true
= ( in @ X7 @ sK19 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK20 @ sK21 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f71,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK21 ) )
& ( $true
= ( in @ X7 @ sK19 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK20 @ sK21 ) ) ) )
=> ( ( $true
= ( in @ sK22 @ sK21 ) )
& ( $true
= ( in @ sK22 @ sK19 ) )
& ( $true
!= ( in @ sK22 @ ( binunion @ sK20 @ sK21 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f68,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
= $true )
& ? [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
& ( $true
= ( in @ X7 @ X4 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) ) ) )
& ( $true
= ( in @ X5 @ ( powerset @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( ( in @ X3 @ X0 )
= $true )
& ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( binunionTIRcontra = $true ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( binunionTIRcontra = $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 @ ( binunion @ X1 @ X2 ) ) )
=> ( $true
!= ( in @ X3 @ X2 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ( binunionTIRcontra = $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 @ ( binunion @ X1 @ X2 ) ) )
=> ( $true
!= ( in @ X3 @ X2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( binunionTIRcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( binunionTIRcontra
= ( ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ ( binunion @ X3 @ X4 ) )
=> ~ ( in @ X2 @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',binunionTIRcontra) ).
thf(f91,plain,
( $true
!= ( in @ sK14 @ ( binunion @ ( setminus @ sK11 @ sK12 ) @ ( setminus @ sK11 @ sK13 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f185,plain,
~ spl23_4,
inference(avatar_contradiction_clause,[status(thm)],[f184]) ).
thf(f184,plain,
( $false
| ~ spl23_4 ),
inference(subsumption_resolution,[status(thm)],[f183,f94]) ).
thf(f94,plain,
( $true
= ( in @ sK12 @ ( powerset @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f183,plain,
( ( $true
!= ( in @ sK12 @ ( powerset @ sK11 ) ) )
| ~ spl23_4 ),
inference(trivial_inequality_removal,[status(thm)],[f182]) ).
thf(f182,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK12 @ ( powerset @ sK11 ) ) )
| ~ spl23_4 ),
inference(superposition,[status(thm)],[f181,f143]) ).
thf(f143,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f75,f96]) ).
thf(f96,plain,
complementT_lem = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f75,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( complementT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ( ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( $true
!= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f41,f42]) ).
thf(f42,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X2 ) ) )
& ( ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X2 ) )
!= $true ) )
=> ( ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( $true
!= ( in @ ( setminus @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X2 ) ) )
& ( ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X2 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true ) )
<=> ( complementT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ( ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) )
= $true ) )
<=> ( complementT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( complementT_lem
= ( ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X3 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',complementT_lem) ).
thf(f181,plain,
( ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ sK11 ) )
!= $true )
| ~ spl23_4 ),
inference(subsumption_resolution,[status(thm)],[f180,f90]) ).
thf(f180,plain,
( ( $true
!= ( in @ sK13 @ ( powerset @ sK11 ) ) )
| ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ sK11 ) )
!= $true )
| ~ spl23_4 ),
inference(subsumption_resolution,[status(thm)],[f179,f93]) ).
thf(f179,plain,
( ( $true
!= ( in @ sK14 @ sK11 ) )
| ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ sK11 ) )
!= $true )
| ( $true
!= ( in @ sK13 @ ( powerset @ sK11 ) ) )
| ~ spl23_4 ),
inference(trivial_inequality_removal,[status(thm)],[f178]) ).
thf(f178,plain,
( ( $true != $true )
| ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ sK11 ) )
!= $true )
| ( $true
!= ( in @ sK14 @ sK11 ) )
| ( $true
!= ( in @ sK13 @ ( powerset @ sK11 ) ) )
| ~ spl23_4 ),
inference(superposition,[status(thm)],[f166,f143]) ).
thf(f166,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( setminus @ sK11 @ sK13 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK14 @ X0 ) )
| ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ X0 ) )
!= $true ) )
| ~ spl23_4 ),
inference(avatar_component_clause,[status(thm)],[f165]) ).
thf(f173,plain,
( spl23_1
| spl23_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f172]) ).
thf(f172,plain,
( $false
| spl23_1
| spl23_3 ),
inference(subsumption_resolution,[status(thm)],[f171,f93]) ).
thf(f171,plain,
( ( $true
!= ( in @ sK14 @ sK11 ) )
| spl23_1
| spl23_3 ),
inference(subsumption_resolution,[status(thm)],[f170,f94]) ).
thf(f170,plain,
( ( $true
!= ( in @ sK12 @ ( powerset @ sK11 ) ) )
| ( $true
!= ( in @ sK14 @ sK11 ) )
| spl23_1
| spl23_3 ),
inference(subsumption_resolution,[status(thm)],[f169,f151]) ).
thf(f151,plain,
( ( $true
!= ( in @ sK14 @ sK12 ) )
| spl23_1 ),
inference(avatar_component_clause,[status(thm)],[f149]) ).
thf(f149,definition,
( spl23_1
<=> ( $true
= ( in @ sK14 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl23_1])],[avatar_definition]) ).
thf(f169,plain,
( ( $true
= ( in @ sK14 @ sK12 ) )
| ( $true
!= ( in @ sK12 @ ( powerset @ sK11 ) ) )
| ( $true
!= ( in @ sK14 @ sK11 ) )
| spl23_3 ),
inference(trivial_inequality_removal,[status(thm)],[f168]) ).
thf(f168,plain,
( ( $true
!= ( in @ sK12 @ ( powerset @ sK11 ) ) )
| ( $true
!= ( in @ sK14 @ sK11 ) )
| ( $true
= ( in @ sK14 @ sK12 ) )
| ( $true != $true )
| spl23_3 ),
inference(superposition,[status(thm)],[f163,f140]) ).
thf(f163,plain,
( ( ( in @ sK14 @ ( setminus @ sK11 @ sK12 ) )
!= $true )
| spl23_3 ),
inference(avatar_component_clause,[status(thm)],[f161]) ).
thf(f161,definition,
( spl23_3
<=> ( ( in @ sK14 @ ( setminus @ sK11 @ sK12 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl23_3])],[avatar_definition]) ).
thf(f167,plain,
( ~ spl23_3
| spl23_4 ),
inference(avatar_split_clause,[status(thm)],[f159,f165,f161]) ).
thf(f159,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( setminus @ sK11 @ sK13 ) @ ( powerset @ X0 ) ) )
| ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK14 @ ( setminus @ sK11 @ sK12 ) )
!= $true )
| ( $true
!= ( in @ sK14 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
! [X0: $i] :
( ( ( in @ sK14 @ ( setminus @ sK11 @ sK12 ) )
!= $true )
| ( ( in @ ( setminus @ sK11 @ sK12 ) @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK14 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( in @ ( setminus @ sK11 @ sK13 ) @ ( powerset @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f91,f138]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f104,f89]) ).
thf(f89,plain,
binunionTILcontra = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( binunionTILcontra != $true ) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binunionTILcontra != $true ) )
& ( ( binunionTILcontra = $true )
| ( ( $true
= ( in @ sK18 @ sK16 ) )
& ( ( in @ sK18 @ sK15 )
= $true )
& ( $true
!= ( in @ sK18 @ ( binunion @ sK15 @ sK17 ) ) )
& ( ( in @ sK17 @ ( powerset @ sK16 ) )
= $true )
& ( $true
= ( in @ sK15 @ ( powerset @ sK16 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18])],[f62,f65,f64,f63]) ).
thf(f63,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( $true
= ( in @ X7 @ X4 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) )
=> ( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK16 ) )
& ( $true
= ( in @ X7 @ sK15 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK15 @ X6 ) ) ) )
& ( ( in @ X6 @ ( powerset @ sK16 ) )
= $true ) )
& ( $true
= ( in @ sK15 @ ( powerset @ sK16 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f64,plain,
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK16 ) )
& ( $true
= ( in @ X7 @ sK15 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK15 @ X6 ) ) ) )
& ( ( in @ X6 @ ( powerset @ sK16 ) )
= $true ) )
=> ( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK16 ) )
& ( $true
= ( in @ X7 @ sK15 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK15 @ sK17 ) ) ) )
& ( ( in @ sK17 @ ( powerset @ sK16 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f65,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK16 ) )
& ( $true
= ( in @ X7 @ sK15 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK15 @ sK17 ) ) ) )
=> ( ( $true
= ( in @ sK18 @ sK16 ) )
& ( ( in @ sK18 @ sK15 )
= $true )
& ( $true
!= ( in @ sK18 @ ( binunion @ sK15 @ sK17 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f62,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binunionTILcontra != $true ) )
& ( ( binunionTILcontra = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( $true
= ( in @ X7 @ X4 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionTILcontra != $true ) )
& ( ( binunionTILcontra = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( binunionTILcontra = $true ) ),
inference(flattening,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( binunionTILcontra = $true ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
=> ( $true
!= ( in @ X3 @ X1 ) ) ) ) ) )
<=> ( binunionTILcontra = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [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 @ ( binunion @ X1 @ X2 ) ) )
=> ( $true
!= ( in @ X3 @ X1 ) ) ) ) ) )
<=> ( binunionTILcontra = $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) )
= binunionTILcontra ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: $i,X3: $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/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',binunionTILcontra) ).
thf(f156,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(avatar_split_clause,[status(thm)],[f147,f153,f149]) ).
thf(f147,plain,
( ( $true
!= ( in @ sK14 @ sK12 ) )
| ( $true
!= ( in @ sK14 @ sK13 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK14 @ sK12 ) )
| ( $true
!= ( in @ sK14 @ sK13 ) ) ),
inference(superposition,[status(thm)],[f145,f141]) ).
thf(f141,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true != $true )
| ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X1 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f87,f95]) ).
thf(f95,plain,
binintersectI = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f87,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( binintersectI != $true ) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ( ( ( in @ sK8 @ sK9 )
= $true )
& ( $true
= ( in @ sK8 @ sK10 ) )
& ( ( in @ sK8 @ ( binintersect @ sK9 @ sK10 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f54,f55]) ).
thf(f55,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
& ( $true
= ( in @ X3 @ X5 ) )
& ( $true
!= ( in @ X3 @ ( binintersect @ X4 @ X5 ) ) ) )
=> ( ( ( in @ sK8 @ sK9 )
= $true )
& ( $true
= ( in @ sK8 @ sK10 ) )
& ( ( in @ sK8 @ ( binintersect @ sK9 @ sK10 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
& ( $true
= ( in @ X3 @ X5 ) )
& ( $true
!= ( in @ X3 @ ( binintersect @ X4 @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ X2 ) )
& ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
<=> ( binintersectI = $true ) ),
inference(flattening,[status(thm)],[f32]) ).
thf(f32,plain,
( ( binintersectI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( binintersectI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( $true
= ( in @ X1 @ X2 ) )
=> ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
= binintersectI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectI ),
file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',binintersectI) ).
thf(f145,plain,
( ( in @ sK14 @ ( binintersect @ sK12 @ sK13 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $true != $true )
| ( ( in @ sK14 @ ( binintersect @ sK12 @ sK13 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f139,f92]) ).
thf(f92,plain,
( $true
= ( in @ sK14 @ ( setminus @ sK11 @ ( binintersect @ sK12 @ sK13 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f139,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f76,f97]) ).
thf(f97,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f76,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( setminusER = $true )
| ( ( ( in @ sK2 @ ( setminus @ sK3 @ sK4 ) )
= $true )
& ( $true
= ( in @ sK2 @ sK4 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) ) )
| ( setminusER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f45,f46]) ).
thf(f46,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( $true
= ( in @ X0 @ X2 ) ) )
=> ( ( ( in @ sK2 @ ( setminus @ sK3 @ sK4 ) )
= $true )
& ( $true
= ( in @ sK2 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( $true
= ( in @ X0 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) ) )
| ( setminusER != $true ) ) ),
inference(rectify,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( setminusER = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X0 )
= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( setminusER = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( ( in @ X2 @ X0 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( ( in @ X2 @ X0 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
=> ~ ( in @ X2 @ X0 ) )
= setminusER ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',setminusER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU751^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:32:51 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SEU751^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.46 % Domain : Set Theory
% 0.26/0.46 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.26/0.46 % Version : Especial > Reduced > Especial.
% 0.26/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.26/0.46 % (! x:i.in x A -> in x (setminus A (binintersect X Y)) ->
% 0.26/0.46 % in x (binunion (setminus A X) (setminus A Y)))))
% 0.26/0.46
% 0.26/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.46 % Source : [Bro08]
% 0.26/0.46 % Names : ZFC253l [Bro08]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.26/0.46 % Syntax : Number of formulae : 18 ( 6 unt; 11 typ; 6 def)
% 0.26/0.46 % Number of atoms : 44 ( 6 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 11 ( 6 avg)
% 0.26/0.46 % Number of connectives : 114 ( 6 ~; 0 |; 0 &; 83 @)
% 0.26/0.46 % ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 20 ( 4 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 12 ( 11 usr; 6 con; 0-2 aty)
% 0.26/0.46 % Number of variables : 23 ( 0 ^; 23 !; 0 ?; 23 :)
% 0.26/0.46 % SPC : TH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : http://mathgate.info/detsetitem.php?id=312
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(in_type,type,
% 0.26/0.46 in: $i > $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(powerset_type,type,
% 0.26/0.46 powerset: $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(binunion_type,type,
% 0.26/0.46 binunion: $i > $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(binintersect_type,type,
% 0.26/0.46 binintersect: $i > $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(binintersectI_type,type,
% 0.26/0.46 binintersectI: $o ).
% 0.26/0.46
% 0.26/0.46 thf(binintersectI,definition,
% 0.26/0.46 ( binintersectI
% 0.26/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( ( in @ Xx @ B )
% 0.26/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(setminus_type,type,
% 0.26/0.46 setminus: $i > $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(setminusER_type,type,
% 0.26/0.46 setminusER: $o ).
% 0.26/0.46
% 0.26/0.46 thf(setminusER,definition,
% 0.26/0.46 ( setminusER
% 0.26/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.26/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(complementT_lem_type,type,
% 0.26/0.46 complementT_lem: $o ).
% 0.26/0.46
% 0.26/0.46 thf(complementT_lem,definition,
% 0.26/0.46 ( complementT_lem
% 0.26/0.46 = ( ! [A: $i,X: $i] :
% 0.26/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(complementTE1_type,type,
% 0.26/0.46 complementTE1: $o ).
% 0.26/0.46
% 0.26/0.46 thf(complementTE1,definition,
% 0.26/0.46 ( complementTE1
% 0.26/0.46 = ( ! [A: $i,X: $i] :
% 0.26/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.46 => ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.26/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(binunionTILcontra_type,type,
% 0.26/0.46 binunionTILcontra: $o ).
% 0.26/0.46
% 0.26/0.46 thf(binunionTILcontra,definition,
% 0.26/0.46 ( binunionTILcontra
% 0.26/0.46 = ( ! [A: $i,X: $i] :
% 0.26/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.46 => ! [Y: $i] :
% 0.26/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.46 => ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.26/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(binunionTIRcontra_type,type,
% 0.26/0.46 binunionTIRcontra: $o ).
% 0.26/0.46
% 0.26/0.46 thf(binunionTIRcontra,definition,
% 0.26/0.46 ( binunionTIRcontra
% 0.26/0.46 = ( ! [A: $i,X: $i] :
% 0.26/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.46 => ! [Y: $i] :
% 0.26/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.46 => ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.26/0.46 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(demorgan1a,conjecture,
% 0.26/0.46 ( binintersectI
% 0.26/0.46 => ( setminusER
% 0.26/0.46 => ( complementT_lem
% 0.26/0.46 => ( complementTE1
% 0.26/0.46 => ( binunionTILcontra
% 0.26/0.46 => ( binunionTIRcontra
% 0.26/0.46 => ! [A: $i,X: $i] :
% 0.26/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.46 => ! [Y: $i] :
% 0.26/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.46 => ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.26/0.46 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.51/1.29 ---- Embedded in THF ---
% 1.51/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.29 %%% Generated on Tue Feb 24 12:32:52 EST 2026
% 1.51/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.29 %%% Logic specification used:
% 1.51/1.29 %%% thf(spec, logic, $$dhol).
% 1.51/1.29
% 1.51/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2DTF25864.p
% See solution above
% 1.51/1.29 ------------------------
% 1.69/1.30 ---- Cleaned THF ---
% 1.69/1.30 thf(in_type,type,
% 1.69/1.30 in: $i > $i > $o ).
% 1.69/1.30
% 1.69/1.30 thf(powerset_type,type,
% 1.69/1.30 powerset: $i > $i ).
% 1.69/1.30
% 1.69/1.30 thf(binunion_type,type,
% 1.69/1.30 binunion: $i > $i > $i ).
% 1.69/1.30
% 1.69/1.30 thf(binintersect_type,type,
% 1.69/1.30 binintersect: $i > $i > $i ).
% 1.69/1.30
% 1.69/1.30 thf(binintersectI_type,type,
% 1.69/1.30 binintersectI: $o ).
% 1.69/1.30
% 1.69/1.30 thf(binintersectI,definition,
% 1.69/1.30 ( binintersectI
% 1.69/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ A )
% 1.69/1.30 => ( ( in @ Xx @ B )
% 1.69/1.30 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(setminus_type,type,
% 1.69/1.30 setminus: $i > $i > $i ).
% 1.69/1.30
% 1.69/1.30 thf(setminusER_type,type,
% 1.69/1.30 setminusER: $o ).
% 1.69/1.30
% 1.69/1.30 thf(setminusER,definition,
% 1.69/1.30 ( setminusER
% 1.69/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.69/1.30 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(complementT_lem_type,type,
% 1.69/1.30 complementT_lem: $o ).
% 1.69/1.30
% 1.69/1.30 thf(complementT_lem,definition,
% 1.69/1.30 ( complementT_lem
% 1.69/1.30 = ( ! [A: $i,X: $i] :
% 1.69/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.30 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(complementTE1_type,type,
% 1.69/1.30 complementTE1: $o ).
% 1.69/1.30
% 1.69/1.30 thf(complementTE1,definition,
% 1.69/1.30 ( complementTE1
% 1.69/1.30 = ( ! [A: $i,X: $i] :
% 1.69/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.30 => ! [Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ A )
% 1.69/1.30 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 1.69/1.30 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(binunionTILcontra_type,type,
% 1.69/1.30 binunionTILcontra: $o ).
% 1.69/1.30
% 1.69/1.30 thf(binunionTILcontra,definition,
% 1.69/1.30 ( binunionTILcontra
% 1.69/1.30 = ( ! [A: $i,X: $i] :
% 1.69/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.30 => ! [Y: $i] :
% 1.69/1.30 ( ( in @ Y @ ( powerset @ A ) )
% 1.69/1.30 => ! [Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ A )
% 1.69/1.30 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 1.69/1.30 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(binunionTIRcontra_type,type,
% 1.69/1.30 binunionTIRcontra: $o ).
% 1.69/1.30
% 1.69/1.30 thf(binunionTIRcontra,definition,
% 1.69/1.30 ( binunionTIRcontra
% 1.69/1.30 = ( ! [A: $i,X: $i] :
% 1.69/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.30 => ! [Y: $i] :
% 1.69/1.30 ( ( in @ Y @ ( powerset @ A ) )
% 1.69/1.30 => ! [Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ A )
% 1.69/1.30 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 1.69/1.30 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(demorgan1a,conjecture,
% 1.69/1.30 ( binintersectI
% 1.69/1.30 => ( setminusER
% 1.69/1.30 => ( complementT_lem
% 1.69/1.30 => ( complementTE1
% 1.69/1.30 => ( binunionTILcontra
% 1.69/1.30 => ( binunionTIRcontra
% 1.69/1.30 => ! [A: $i,X: $i] :
% 1.69/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.69/1.30 => ! [Y: $i] :
% 1.69/1.30 ( ( in @ Y @ ( powerset @ A ) )
% 1.69/1.30 => ! [Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ A )
% 1.69/1.30 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 1.69/1.30 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.69/1.30 ------------------------
% 1.69/1.32 % (26138)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_25864 for (2999ds/275Mi)
% 1.69/1.32 % (26137)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_25864 for (2999ds/2Mi)
% 1.69/1.32 % (26137)Instruction limit reached!
% 1.69/1.32 % (26137)------------------------------
% 1.69/1.32 % (26137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (26137)Termination reason: Unknown
% 1.69/1.32 % (26137)Termination phase: Property scanning
% 1.69/1.32
% 1.69/1.32 % (26137)Memory used [KB]: 1023
% 1.69/1.32 % (26137)Time elapsed: 0.002 s
% 1.69/1.32 % (26137)Instructions burned: 3 (million)
% 1.69/1.32 % (26137)------------------------------
% 1.69/1.32 % (26137)------------------------------
% 1.69/1.32 % (26138)First to succeed.
% 1.69/1.32 % (26134)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_25864 for (2999ds/4Mi)
% 1.69/1.32 % (26133)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25864 for (2999ds/183Mi)
% 1.69/1.32 % (26135)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_25864 for (2999ds/27Mi)
% 1.69/1.32 % (26136)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25864 for (2999ds/2Mi)
% 1.69/1.32 % (26139)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25864 for (2999ds/18Mi)
% 1.69/1.32 % (26136)Instruction limit reached!
% 1.69/1.32 % (26136)------------------------------
% 1.69/1.32 % (26136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (26136)Termination reason: Unknown
% 1.69/1.32 % (26136)Termination phase: shuffling
% 1.69/1.32
% 1.69/1.32 % (26136)Memory used [KB]: 1023
% 1.69/1.32 % (26136)Time elapsed: 0.003 s
% 1.69/1.32 % (26136)Instructions burned: 2 (million)
% 1.69/1.32 % (26136)------------------------------
% 1.69/1.32 % (26136)------------------------------
% 1.69/1.33 % (26134)Instruction limit reached!
% 1.69/1.33 % (26134)------------------------------
% 1.69/1.33 % (26134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (26134)Termination reason: Unknown
% 1.69/1.33 % (26134)Termination phase: Preprocessing 3
% 1.69/1.33
% 1.69/1.33 % (26134)Memory used [KB]: 1023
% 1.69/1.33 % (26134)Time elapsed: 0.004 s
% 1.69/1.33 % (26134)Instructions burned: 4 (million)
% 1.69/1.33 % (26134)------------------------------
% 1.69/1.33 % (26134)------------------------------
% 1.69/1.33 % (26138)Refutation found. Thanks to Tanya!
% 1.69/1.33 % SZS status Theorem for DTF2THF_25864
% 1.69/1.33 % SZS output start Proof for DTF2THF_25864
% 1.69/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.33 thf(func_def_1, type, powerset: $i > $i).
% 1.69/1.33 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.69/1.33 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.69/1.33 thf(func_def_6, type, setminus: $i > $i > $i).
% 1.69/1.33 thf(f199,plain,(
% 1.69/1.33 $false),
% 1.69/1.33 inference(avatar_sat_refutation,[status(thm)],[f156,f167,f173,f185,f190,f198])).
% 1.69/1.33 thf(f198,plain,(
% 1.69/1.33 spl23_2 | spl23_5),
% 1.69/1.33 inference(avatar_contradiction_clause,[status(thm)],[f197])).
% 1.69/1.33 thf(f197,plain,(
% 1.69/1.33 $false | (spl23_2 | spl23_5)),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f196,f93])).
% 1.69/1.33 thf(f93,plain,(
% 1.69/1.33 ($true = (in @ sK14 @ sK11))),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f60,plain,(
% 1.69/1.33 (binunionTIRcontra = $true) & (setminusER = $true) & (complementT_lem = $true) & (binintersectI = $true) & (($true = (in @ sK12 @ (powerset @ sK11))) & ((($true = (in @ sK14 @ sK11)) & ($true = (in @ sK14 @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)))) & ($true != (in @ sK14 @ (binunion @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ sK13))))) & ($true = (in @ sK13 @ (powerset @ sK11))))) & (binunionTILcontra = $true) & (complementTE1 = $true)),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f36,f59,f58,f57])).
% 1.69/1.33 thf(f57,plain,(
% 1.69/1.33 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ($true = (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) & ($true != (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) & ((in @ X2 @ (powerset @ X0)) = $true))) => (($true = (in @ sK12 @ (powerset @ sK11))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ sK11) = $true) & ($true = (in @ X3 @ (setminus @ sK11 @ (binintersect @ sK12 @ X2)))) & ($true != (in @ X3 @ (binunion @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ X2))))) & ((in @ X2 @ (powerset @ sK11)) = $true)))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f58,plain,(
% 1.69/1.33 ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ sK11) = $true) & ($true = (in @ X3 @ (setminus @ sK11 @ (binintersect @ sK12 @ X2)))) & ($true != (in @ X3 @ (binunion @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ X2))))) & ((in @ X2 @ (powerset @ sK11)) = $true)) => (? [X3 : $i] : (((in @ X3 @ sK11) = $true) & ((in @ X3 @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13))) = $true) & ((in @ X3 @ (binunion @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ sK13))) != $true)) & ($true = (in @ sK13 @ (powerset @ sK11))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f59,plain,(
% 1.69/1.33 ? [X3 : $i] : (((in @ X3 @ sK11) = $true) & ((in @ X3 @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13))) = $true) & ((in @ X3 @ (binunion @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ sK13))) != $true)) => (($true = (in @ sK14 @ sK11)) & ($true = (in @ sK14 @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)))) & ($true != (in @ sK14 @ (binunion @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ sK13)))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f36,plain,(
% 1.69/1.33 (binunionTIRcontra = $true) & (setminusER = $true) & (complementT_lem = $true) & (binintersectI = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ($true = (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) & ($true != (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) & ((in @ X2 @ (powerset @ X0)) = $true))) & (binunionTILcontra = $true) & (complementTE1 = $true)),
% 1.69/1.33 inference(flattening,[status(thm)],[f35])).
% 1.69/1.33 thf(f35,plain,(
% 1.69/1.33 (((((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((($true != (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) & ($true = (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTE1 = $true)) & (complementT_lem = $true)) & (setminusER = $true)) & (binintersectI = $true)),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f13])).
% 1.69/1.33 thf(f13,plain,(
% 1.69/1.33 ~((binintersectI = $true) => ((setminusER = $true) => ((complementT_lem = $true) => ((complementTE1 = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (($true = (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) => ($true = (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))))))))))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f12])).
% 1.69/1.33 thf(f12,plain,(
% 1.69/1.33 ~(binintersectI => (setminusER => (complementT_lem => (complementTE1 => (binunionTILcontra => (binunionTIRcontra => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))))))))),
% 1.69/1.33 inference(rectify,[status(thm)],[f8])).
% 1.69/1.33 thf(f8,negated_conjecture,(
% 1.69/1.33 ~(binintersectI => (setminusER => (complementT_lem => (complementTE1 => (binunionTILcontra => (binunionTIRcontra => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (binintersect @ X3 @ X4))) => (in @ X2 @ (binunion @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4)))))))))))))),
% 1.69/1.33 inference(negated_conjecture,[status(cth)],[f7])).
% 1.69/1.33 thf(f7,conjecture,(
% 1.69/1.33 binintersectI => (setminusER => (complementT_lem => (complementTE1 => (binunionTILcontra => (binunionTIRcontra => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (binintersect @ X3 @ X4))) => (in @ X2 @ (binunion @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4))))))))))))),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',demorgan1a)).
% 1.69/1.33 thf(f196,plain,(
% 1.69/1.33 ($true != (in @ sK14 @ sK11)) | (spl23_2 | spl23_5)),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f195,f90])).
% 1.69/1.33 thf(f90,plain,(
% 1.69/1.33 ($true = (in @ sK13 @ (powerset @ sK11)))),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f195,plain,(
% 1.69/1.33 ($true != (in @ sK13 @ (powerset @ sK11))) | ($true != (in @ sK14 @ sK11)) | (spl23_2 | spl23_5)),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f194,f155])).
% 1.69/1.33 thf(f155,plain,(
% 1.69/1.33 ($true != (in @ sK14 @ sK13)) | spl23_2),
% 1.69/1.33 inference(avatar_component_clause,[status(thm)],[f153])).
% 1.69/1.33 thf(f153,definition,(
% 1.69/1.33 spl23_2 <=> ($true = (in @ sK14 @ sK13))),
% 1.69/1.33 introduced(definition,[new_symbols(naming,[spl23_2])],[avatar_definition])).
% 1.69/1.33 thf(f194,plain,(
% 1.69/1.33 ($true = (in @ sK14 @ sK13)) | ($true != (in @ sK13 @ (powerset @ sK11))) | ($true != (in @ sK14 @ sK11)) | spl23_5),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f193])).
% 1.69/1.33 thf(f193,plain,(
% 1.69/1.33 ($true != $true) | ($true != (in @ sK14 @ sK11)) | ($true != (in @ sK13 @ (powerset @ sK11))) | ($true = (in @ sK14 @ sK13)) | spl23_5),
% 1.69/1.33 inference(superposition,[status(thm)],[f189,f140])).
% 1.69/1.33 thf(f140,plain,(
% 1.69/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.69/1.33 thf(f117,plain,(
% 1.69/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X1) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != $true)) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f83,f88])).
% 1.69/1.33 thf(f88,plain,(
% 1.69/1.33 (complementTE1 = $true)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f83,plain,(
% 1.69/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X0) = $true) | ($true != (in @ X0 @ (powerset @ X1))) | (complementTE1 != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f52])).
% 1.69/1.33 thf(f52,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X0) = $true)) | ($true != (in @ X0 @ (powerset @ X1)))) | (complementTE1 != $true)) & ((complementTE1 = $true) | ((($true = (in @ sK7 @ sK6)) & ($true != (in @ sK7 @ (setminus @ sK6 @ sK5))) & ((in @ sK7 @ sK5) != $true)) & ($true = (in @ sK5 @ (powerset @ sK6)))))),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f49,f51,f50])).
% 1.69/1.33 thf(f50,plain,(
% 1.69/1.33 ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true = (in @ X5 @ X4)) & ($true != (in @ X5 @ (setminus @ X4 @ X3))) & ($true != (in @ X5 @ X3))) & ($true = (in @ X3 @ (powerset @ X4)))) => (? [X5 : $i] : (($true = (in @ X5 @ sK6)) & ($true != (in @ X5 @ (setminus @ sK6 @ sK5))) & ((in @ X5 @ sK5) != $true)) & ($true = (in @ sK5 @ (powerset @ sK6))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f51,plain,(
% 1.69/1.33 ? [X5 : $i] : (($true = (in @ X5 @ sK6)) & ($true != (in @ X5 @ (setminus @ sK6 @ sK5))) & ((in @ X5 @ sK5) != $true)) => (($true = (in @ sK7 @ sK6)) & ($true != (in @ sK7 @ (setminus @ sK6 @ sK5))) & ((in @ sK7 @ sK5) != $true))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f49,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X0) = $true)) | ($true != (in @ X0 @ (powerset @ X1)))) | (complementTE1 != $true)) & ((complementTE1 = $true) | ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true = (in @ X5 @ X4)) & ($true != (in @ X5 @ (setminus @ X4 @ X3))) & ($true != (in @ X5 @ X3))) & ($true = (in @ X3 @ (powerset @ X4)))))),
% 1.69/1.33 inference(rectify,[status(thm)],[f48])).
% 1.69/1.33 thf(f48,plain,(
% 1.69/1.33 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ (setminus @ X0 @ X1)) = $true) | ((in @ X2 @ X1) = $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (complementTE1 != $true)) & ((complementTE1 = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ (setminus @ X0 @ X1)) != $true) & ((in @ X2 @ X1) != $true)) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 1.69/1.33 inference(nnf_transformation,[status(thm)],[f31])).
% 1.69/1.33 thf(f31,plain,(
% 1.69/1.33 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ (setminus @ X0 @ X1)) = $true) | ((in @ X2 @ X1) = $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (complementTE1 = $true)),
% 1.69/1.33 inference(flattening,[status(thm)],[f30])).
% 1.69/1.33 thf(f30,plain,(
% 1.69/1.33 (complementTE1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1) = $true) | ((in @ X2 @ (setminus @ X0 @ X1)) = $true)) | ((in @ X2 @ X0) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f25])).
% 1.69/1.33 thf(f25,plain,(
% 1.69/1.33 (complementTE1 = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ X0) = $true) => (((in @ X2 @ (setminus @ X0 @ X1)) != $true) => ((in @ X2 @ X1) = $true))))),
% 1.69/1.33 inference(flattening,[status(thm)],[f19])).
% 1.69/1.33 thf(f19,plain,(
% 1.69/1.33 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ X0) = $true) => (~((in @ X2 @ (setminus @ X0 @ X1)) = $true) => ((in @ X2 @ X1) = $true)))) <=> (complementTE1 = $true)),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f18])).
% 1.69/1.33 thf(f18,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X1)))) = complementTE1)),
% 1.69/1.33 inference(rectify,[status(thm)],[f4])).
% 1.69/1.33 thf(f4,axiom,(
% 1.69/1.33 (! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (setminus @ X0 @ X3)) => (in @ X2 @ X3)))) = complementTE1)),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',complementTE1)).
% 1.69/1.33 thf(f189,plain,(
% 1.69/1.33 ((in @ sK14 @ (setminus @ sK11 @ sK13)) != $true) | spl23_5),
% 1.69/1.33 inference(avatar_component_clause,[status(thm)],[f187])).
% 1.69/1.33 thf(f187,definition,(
% 1.69/1.33 spl23_5 <=> ((in @ sK14 @ (setminus @ sK11 @ sK13)) = $true)),
% 1.69/1.33 introduced(definition,[new_symbols(naming,[spl23_5])],[avatar_definition])).
% 1.69/1.33 thf(f190,plain,(
% 1.69/1.33 ~spl23_5 | spl23_4),
% 1.69/1.33 inference(avatar_split_clause,[status(thm)],[f175,f165,f187])).
% 1.69/1.33 thf(f165,definition,(
% 1.69/1.33 spl23_4 <=> ! [X0 : $i] : (($true != (in @ (setminus @ sK11 @ sK13) @ (powerset @ X0))) | ($true != (in @ sK14 @ X0)) | ((in @ (setminus @ sK11 @ sK12) @ (powerset @ X0)) != $true))),
% 1.69/1.33 introduced(definition,[new_symbols(naming,[spl23_4])],[avatar_definition])).
% 1.69/1.33 thf(f175,plain,(
% 1.69/1.33 ( ! [X0 : $i] : (((in @ sK14 @ (setminus @ sK11 @ sK13)) != $true) | ($true != (in @ (setminus @ sK11 @ sK13) @ (powerset @ X0))) | ($true != (in @ sK14 @ X0)) | ((in @ (setminus @ sK11 @ sK12) @ (powerset @ X0)) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f174])).
% 1.69/1.33 thf(f174,plain,(
% 1.69/1.33 ( ! [X0 : $i] : (((in @ (setminus @ sK11 @ sK12) @ (powerset @ X0)) != $true) | ($true != $true) | ($true != (in @ (setminus @ sK11 @ sK13) @ (powerset @ X0))) | ($true != (in @ sK14 @ X0)) | ((in @ sK14 @ (setminus @ sK11 @ sK13)) != $true)) )),
% 1.69/1.33 inference(superposition,[status(thm)],[f91,f142])).
% 1.69/1.33 thf(f142,plain,(
% 1.69/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ X3 @ (binunion @ X1 @ X2))) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != (in @ X3 @ X2)) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X3 @ X0) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.69/1.33 thf(f132,plain,(
% 1.69/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X3 @ X0) != $true) | ($true != (in @ X3 @ X2)) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f110,f98])).
% 1.69/1.33 thf(f98,plain,(
% 1.69/1.33 (binunionTIRcontra = $true)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f110,plain,(
% 1.69/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))) | ((in @ X1 @ (powerset @ X0)) != $true) | (binunionTIRcontra != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f72])).
% 1.69/1.33 thf(f72,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (($true != (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionTIRcontra != $true)) & ((binunionTIRcontra = $true) | ((((in @ sK21 @ (powerset @ sK19)) = $true) & (($true = (in @ sK22 @ sK21)) & ($true = (in @ sK22 @ sK19)) & ($true != (in @ sK22 @ (binunion @ sK20 @ sK21))))) & ($true = (in @ sK20 @ (powerset @ sK19)))))),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22])],[f68,f71,f70,f69])).
% 1.69/1.33 thf(f69,plain,(
% 1.69/1.33 ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ (powerset @ X4)) = $true) & ? [X7 : $i] : (((in @ X7 @ X6) = $true) & ($true = (in @ X7 @ X4)) & ($true != (in @ X7 @ (binunion @ X5 @ X6))))) & ($true = (in @ X5 @ (powerset @ X4)))) => (? [X6 : $i] : (($true = (in @ X6 @ (powerset @ sK19))) & ? [X7 : $i] : (((in @ X7 @ X6) = $true) & ($true = (in @ X7 @ sK19)) & ($true != (in @ X7 @ (binunion @ sK20 @ X6))))) & ($true = (in @ sK20 @ (powerset @ sK19))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f70,plain,(
% 1.69/1.33 ? [X6 : $i] : (($true = (in @ X6 @ (powerset @ sK19))) & ? [X7 : $i] : (((in @ X7 @ X6) = $true) & ($true = (in @ X7 @ sK19)) & ($true != (in @ X7 @ (binunion @ sK20 @ X6))))) => (((in @ sK21 @ (powerset @ sK19)) = $true) & ? [X7 : $i] : (($true = (in @ X7 @ sK21)) & ($true = (in @ X7 @ sK19)) & ($true != (in @ X7 @ (binunion @ sK20 @ sK21)))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f71,plain,(
% 1.69/1.33 ? [X7 : $i] : (($true = (in @ X7 @ sK21)) & ($true = (in @ X7 @ sK19)) & ($true != (in @ X7 @ (binunion @ sK20 @ sK21)))) => (($true = (in @ sK22 @ sK21)) & ($true = (in @ sK22 @ sK19)) & ($true != (in @ sK22 @ (binunion @ sK20 @ sK21))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f68,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (($true != (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionTIRcontra != $true)) & ((binunionTIRcontra = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ (powerset @ X4)) = $true) & ? [X7 : $i] : (((in @ X7 @ X6) = $true) & ($true = (in @ X7 @ X4)) & ($true != (in @ X7 @ (binunion @ X5 @ X6))))) & ($true = (in @ X5 @ (powerset @ X4)))))),
% 1.69/1.33 inference(rectify,[status(thm)],[f67])).
% 1.69/1.33 thf(f67,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (($true != (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionTIRcontra != $true)) & ((binunionTIRcontra = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ((in @ X3 @ X0) = $true) & ($true != (in @ X3 @ (binunion @ X1 @ X2))))) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 1.69/1.33 inference(nnf_transformation,[status(thm)],[f29])).
% 1.69/1.33 thf(f29,plain,(
% 1.69/1.33 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (($true != (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))))) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (binunionTIRcontra = $true)),
% 1.69/1.33 inference(flattening,[status(thm)],[f28])).
% 1.69/1.33 thf(f28,plain,(
% 1.69/1.33 (binunionTIRcontra = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((($true != (in @ X3 @ X2)) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f27])).
% 1.69/1.33 thf(f27,plain,(
% 1.69/1.33 (binunionTIRcontra = $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 @ (binunion @ X1 @ X2))) => ($true != (in @ X3 @ X2))))))),
% 1.69/1.33 inference(flattening,[status(thm)],[f21])).
% 1.69/1.33 thf(f21,plain,(
% 1.69/1.33 (binunionTIRcontra = $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 @ (binunion @ X1 @ X2))) => ~($true = (in @ X3 @ X2))))))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f20])).
% 1.69/1.33 thf(f20,plain,(
% 1.69/1.33 (binunionTIRcontra = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ (binunion @ X1 @ X2)) => ~(in @ X3 @ X2))))))),
% 1.69/1.33 inference(rectify,[status(thm)],[f6])).
% 1.69/1.33 thf(f6,axiom,(
% 1.69/1.33 (binunionTIRcontra = ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (binunion @ X3 @ X4)) => ~(in @ X2 @ X4))))))),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',binunionTIRcontra)).
% 1.69/1.33 thf(f91,plain,(
% 1.69/1.33 ($true != (in @ sK14 @ (binunion @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ sK13))))),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f185,plain,(
% 1.69/1.33 ~spl23_4),
% 1.69/1.33 inference(avatar_contradiction_clause,[status(thm)],[f184])).
% 1.69/1.33 thf(f184,plain,(
% 1.69/1.33 $false | ~spl23_4),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f183,f94])).
% 1.69/1.33 thf(f94,plain,(
% 1.69/1.33 ($true = (in @ sK12 @ (powerset @ sK11)))),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f183,plain,(
% 1.69/1.33 ($true != (in @ sK12 @ (powerset @ sK11))) | ~spl23_4),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f182])).
% 1.69/1.33 thf(f182,plain,(
% 1.69/1.33 ($true != $true) | ($true != (in @ sK12 @ (powerset @ sK11))) | ~spl23_4),
% 1.69/1.33 inference(superposition,[status(thm)],[f181,f143])).
% 1.69/1.33 thf(f143,plain,(
% 1.69/1.33 ( ! [X0 : $i,X1 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.69/1.33 thf(f111,plain,(
% 1.69/1.33 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true) | ($true != $true)) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f75,f96])).
% 1.69/1.33 thf(f96,plain,(
% 1.69/1.33 (complementT_lem = $true)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f75,plain,(
% 1.69/1.33 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true) | (complementT_lem != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f43])).
% 1.69/1.33 thf(f43,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | (($true = (in @ sK1 @ (powerset @ sK0))) & ($true != (in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))))),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f41,f42])).
% 1.69/1.33 thf(f42,plain,(
% 1.69/1.33 ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (powerset @ X2))) & ((in @ (setminus @ X2 @ X3) @ (powerset @ X2)) != $true)) => (($true = (in @ sK1 @ (powerset @ sK0))) & ($true != (in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f41,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (powerset @ X2))) & ((in @ (setminus @ X2 @ X3) @ (powerset @ X2)) != $true)))),
% 1.69/1.33 inference(rectify,[status(thm)],[f40])).
% 1.69/1.33 thf(f40,plain,(
% 1.69/1.33 (! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) != $true)))),
% 1.69/1.33 inference(nnf_transformation,[status(thm)],[f37])).
% 1.69/1.33 thf(f37,plain,(
% 1.69/1.33 ! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true)) <=> (complementT_lem = $true)),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f17])).
% 1.69/1.33 thf(f17,plain,(
% 1.69/1.33 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true)) <=> (complementT_lem = $true)),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.33 thf(f16,plain,(
% 1.69/1.33 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))))),
% 1.69/1.33 inference(rectify,[status(thm)],[f3])).
% 1.69/1.33 thf(f3,axiom,(
% 1.69/1.33 (complementT_lem = ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X3) @ (powerset @ X0))))),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',complementT_lem)).
% 1.69/1.33 thf(f181,plain,(
% 1.69/1.33 ((in @ (setminus @ sK11 @ sK12) @ (powerset @ sK11)) != $true) | ~spl23_4),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f180,f90])).
% 1.69/1.33 thf(f180,plain,(
% 1.69/1.33 ($true != (in @ sK13 @ (powerset @ sK11))) | ((in @ (setminus @ sK11 @ sK12) @ (powerset @ sK11)) != $true) | ~spl23_4),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f179,f93])).
% 1.69/1.33 thf(f179,plain,(
% 1.69/1.33 ($true != (in @ sK14 @ sK11)) | ((in @ (setminus @ sK11 @ sK12) @ (powerset @ sK11)) != $true) | ($true != (in @ sK13 @ (powerset @ sK11))) | ~spl23_4),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f178])).
% 1.69/1.33 thf(f178,plain,(
% 1.69/1.33 ($true != $true) | ((in @ (setminus @ sK11 @ sK12) @ (powerset @ sK11)) != $true) | ($true != (in @ sK14 @ sK11)) | ($true != (in @ sK13 @ (powerset @ sK11))) | ~spl23_4),
% 1.69/1.33 inference(superposition,[status(thm)],[f166,f143])).
% 1.69/1.33 thf(f166,plain,(
% 1.69/1.33 ( ! [X0 : $i] : (($true != (in @ (setminus @ sK11 @ sK13) @ (powerset @ X0))) | ($true != (in @ sK14 @ X0)) | ((in @ (setminus @ sK11 @ sK12) @ (powerset @ X0)) != $true)) ) | ~spl23_4),
% 1.69/1.33 inference(avatar_component_clause,[status(thm)],[f165])).
% 1.69/1.33 thf(f173,plain,(
% 1.69/1.33 spl23_1 | spl23_3),
% 1.69/1.33 inference(avatar_contradiction_clause,[status(thm)],[f172])).
% 1.69/1.33 thf(f172,plain,(
% 1.69/1.33 $false | (spl23_1 | spl23_3)),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f171,f93])).
% 1.69/1.33 thf(f171,plain,(
% 1.69/1.33 ($true != (in @ sK14 @ sK11)) | (spl23_1 | spl23_3)),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f170,f94])).
% 1.69/1.33 thf(f170,plain,(
% 1.69/1.33 ($true != (in @ sK12 @ (powerset @ sK11))) | ($true != (in @ sK14 @ sK11)) | (spl23_1 | spl23_3)),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f169,f151])).
% 1.69/1.33 thf(f151,plain,(
% 1.69/1.33 ($true != (in @ sK14 @ sK12)) | spl23_1),
% 1.69/1.33 inference(avatar_component_clause,[status(thm)],[f149])).
% 1.69/1.33 thf(f149,definition,(
% 1.69/1.33 spl23_1 <=> ($true = (in @ sK14 @ sK12))),
% 1.69/1.33 introduced(definition,[new_symbols(naming,[spl23_1])],[avatar_definition])).
% 1.69/1.33 thf(f169,plain,(
% 1.69/1.33 ($true = (in @ sK14 @ sK12)) | ($true != (in @ sK12 @ (powerset @ sK11))) | ($true != (in @ sK14 @ sK11)) | spl23_3),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f168])).
% 1.69/1.33 thf(f168,plain,(
% 1.69/1.33 ($true != (in @ sK12 @ (powerset @ sK11))) | ($true != (in @ sK14 @ sK11)) | ($true = (in @ sK14 @ sK12)) | ($true != $true) | spl23_3),
% 1.69/1.33 inference(superposition,[status(thm)],[f163,f140])).
% 1.69/1.33 thf(f163,plain,(
% 1.69/1.33 ((in @ sK14 @ (setminus @ sK11 @ sK12)) != $true) | spl23_3),
% 1.69/1.33 inference(avatar_component_clause,[status(thm)],[f161])).
% 1.69/1.33 thf(f161,definition,(
% 1.69/1.33 spl23_3 <=> ((in @ sK14 @ (setminus @ sK11 @ sK12)) = $true)),
% 1.69/1.33 introduced(definition,[new_symbols(naming,[spl23_3])],[avatar_definition])).
% 1.69/1.33 thf(f167,plain,(
% 1.69/1.33 ~spl23_3 | spl23_4),
% 1.69/1.33 inference(avatar_split_clause,[status(thm)],[f159,f165,f161])).
% 1.69/1.33 thf(f159,plain,(
% 1.69/1.33 ( ! [X0 : $i] : (($true != (in @ (setminus @ sK11 @ sK13) @ (powerset @ X0))) | ((in @ (setminus @ sK11 @ sK12) @ (powerset @ X0)) != $true) | ((in @ sK14 @ (setminus @ sK11 @ sK12)) != $true) | ($true != (in @ sK14 @ X0))) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 1.69/1.33 thf(f158,plain,(
% 1.69/1.33 ( ! [X0 : $i] : (((in @ sK14 @ (setminus @ sK11 @ sK12)) != $true) | ((in @ (setminus @ sK11 @ sK12) @ (powerset @ X0)) != $true) | ($true != (in @ sK14 @ X0)) | ($true != $true) | ($true != (in @ (setminus @ sK11 @ sK13) @ (powerset @ X0)))) )),
% 1.69/1.33 inference(superposition,[status(thm)],[f91,f138])).
% 1.69/1.33 thf(f138,plain,(
% 1.69/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ X3 @ (binunion @ X0 @ X2))) | ($true != (in @ X2 @ (powerset @ X1))) | ((in @ X3 @ X0) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != (in @ X3 @ X1))) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.69/1.33 thf(f126,plain,(
% 1.69/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ((in @ X3 @ X0) != $true) | ($true != $true) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ (binunion @ X0 @ X2))) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f104,f89])).
% 1.69/1.33 thf(f89,plain,(
% 1.69/1.33 (binunionTILcontra = $true)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f104,plain,(
% 1.69/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X3 @ X1)) | ((in @ X3 @ X0) != $true) | ($true = (in @ X3 @ (binunion @ X0 @ X2))) | ($true != (in @ X2 @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1))) | (binunionTILcontra != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f66])).
% 1.69/1.33 thf(f66,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X1)) | ((in @ X3 @ X0) != $true) | ($true = (in @ X3 @ (binunion @ X0 @ X2)))) | ($true != (in @ X2 @ (powerset @ X1)))) | ($true != (in @ X0 @ (powerset @ X1)))) | (binunionTILcontra != $true)) & ((binunionTILcontra = $true) | (((($true = (in @ sK18 @ sK16)) & ((in @ sK18 @ sK15) = $true) & ($true != (in @ sK18 @ (binunion @ sK15 @ sK17)))) & ((in @ sK17 @ (powerset @ sK16)) = $true)) & ($true = (in @ sK15 @ (powerset @ sK16)))))),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18])],[f62,f65,f64,f63])).
% 1.69/1.33 thf(f63,plain,(
% 1.69/1.33 ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X5)) & ($true = (in @ X7 @ X4)) & ($true != (in @ X7 @ (binunion @ X4 @ X6)))) & ($true = (in @ X6 @ (powerset @ X5)))) & ((in @ X4 @ (powerset @ X5)) = $true)) => (? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ sK16)) & ($true = (in @ X7 @ sK15)) & ($true != (in @ X7 @ (binunion @ sK15 @ X6)))) & ((in @ X6 @ (powerset @ sK16)) = $true)) & ($true = (in @ sK15 @ (powerset @ sK16))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f64,plain,(
% 1.69/1.33 ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ sK16)) & ($true = (in @ X7 @ sK15)) & ($true != (in @ X7 @ (binunion @ sK15 @ X6)))) & ((in @ X6 @ (powerset @ sK16)) = $true)) => (? [X7 : $i] : (($true = (in @ X7 @ sK16)) & ($true = (in @ X7 @ sK15)) & ($true != (in @ X7 @ (binunion @ sK15 @ sK17)))) & ((in @ sK17 @ (powerset @ sK16)) = $true))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f65,plain,(
% 1.69/1.33 ? [X7 : $i] : (($true = (in @ X7 @ sK16)) & ($true = (in @ X7 @ sK15)) & ($true != (in @ X7 @ (binunion @ sK15 @ sK17)))) => (($true = (in @ sK18 @ sK16)) & ((in @ sK18 @ sK15) = $true) & ($true != (in @ sK18 @ (binunion @ sK15 @ sK17))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f62,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X1)) | ((in @ X3 @ X0) != $true) | ($true = (in @ X3 @ (binunion @ X0 @ X2)))) | ($true != (in @ X2 @ (powerset @ X1)))) | ($true != (in @ X0 @ (powerset @ X1)))) | (binunionTILcontra != $true)) & ((binunionTILcontra = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X5)) & ($true = (in @ X7 @ X4)) & ($true != (in @ X7 @ (binunion @ X4 @ X6)))) & ($true = (in @ X6 @ (powerset @ X5)))) & ((in @ X4 @ (powerset @ X5)) = $true)))),
% 1.69/1.33 inference(rectify,[status(thm)],[f61])).
% 1.69/1.33 thf(f61,plain,(
% 1.69/1.33 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionTILcontra != $true)) & ((binunionTILcontra = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ($true = (in @ X3 @ X1)) & ($true != (in @ X3 @ (binunion @ X1 @ X2)))) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 1.69/1.33 inference(nnf_transformation,[status(thm)],[f39])).
% 1.69/1.33 thf(f39,plain,(
% 1.69/1.33 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (binunionTILcontra = $true)),
% 1.69/1.33 inference(flattening,[status(thm)],[f38])).
% 1.69/1.33 thf(f38,plain,(
% 1.69/1.33 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (binunionTILcontra = $true)),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f26])).
% 1.69/1.33 thf(f26,plain,(
% 1.69/1.33 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (($true != (in @ X3 @ (binunion @ X1 @ X2))) => ($true != (in @ X3 @ X1)))))) <=> (binunionTILcontra = $true)),
% 1.69/1.33 inference(flattening,[status(thm)],[f15])).
% 1.69/1.33 thf(f15,plain,(
% 1.69/1.33 ! [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 @ (binunion @ X1 @ X2))) => ~($true = (in @ X3 @ X1)))))) <=> (binunionTILcontra = $true)),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f14])).
% 1.69/1.33 thf(f14,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ (binunion @ X1 @ X2)) => ~(in @ X3 @ X1))))) = binunionTILcontra)),
% 1.69/1.33 inference(rectify,[status(thm)],[f5])).
% 1.69/1.33 thf(f5,axiom,(
% 1.69/1.33 (! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (binunion @ X3 @ X4)) => ~(in @ X2 @ X3))))) = binunionTILcontra)),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',binunionTILcontra)).
% 1.69/1.33 thf(f156,plain,(
% 1.69/1.33 ~spl23_1 | ~spl23_2),
% 1.69/1.33 inference(avatar_split_clause,[status(thm)],[f147,f153,f149])).
% 1.69/1.33 thf(f147,plain,(
% 1.69/1.33 ($true != (in @ sK14 @ sK12)) | ($true != (in @ sK14 @ sK13))),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f146])).
% 1.69/1.33 thf(f146,plain,(
% 1.69/1.33 ($true != $true) | ($true != (in @ sK14 @ sK12)) | ($true != (in @ sK14 @ sK13))),
% 1.69/1.33 inference(superposition,[status(thm)],[f145,f141])).
% 1.69/1.33 thf(f141,plain,(
% 1.69/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (binintersect @ X1 @ X2))) | ($true != (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.69/1.33 thf(f122,plain,(
% 1.69/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X2)) | ($true != $true) | ($true = (in @ X0 @ (binintersect @ X1 @ X2))) | ((in @ X0 @ X1) != $true)) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f87,f95])).
% 1.69/1.33 thf(f95,plain,(
% 1.69/1.33 (binintersectI = $true)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f87,plain,(
% 1.69/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ (binintersect @ X1 @ X2))) | (binintersectI != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f56])).
% 1.69/1.33 thf(f56,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) | ($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ (binintersect @ X1 @ X2)))) | (binintersectI != $true)) & ((binintersectI = $true) | (((in @ sK8 @ sK9) = $true) & ($true = (in @ sK8 @ sK10)) & ((in @ sK8 @ (binintersect @ sK9 @ sK10)) != $true)))),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f54,f55])).
% 1.69/1.33 thf(f55,plain,(
% 1.69/1.33 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) & ($true = (in @ X3 @ X5)) & ($true != (in @ X3 @ (binintersect @ X4 @ X5)))) => (((in @ sK8 @ sK9) = $true) & ($true = (in @ sK8 @ sK10)) & ((in @ sK8 @ (binintersect @ sK9 @ sK10)) != $true))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f54,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) | ($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ (binintersect @ X1 @ X2)))) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) & ($true = (in @ X3 @ X5)) & ($true != (in @ X3 @ (binintersect @ X4 @ X5)))))),
% 1.69/1.33 inference(rectify,[status(thm)],[f53])).
% 1.69/1.33 thf(f53,plain,(
% 1.69/1.33 (! [X1 : $i,X0 : $i,X2 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true = (in @ X1 @ (binintersect @ X0 @ X2)))) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) & ($true = (in @ X1 @ X2)) & ($true != (in @ X1 @ (binintersect @ X0 @ X2)))))),
% 1.69/1.33 inference(nnf_transformation,[status(thm)],[f33])).
% 1.69/1.33 thf(f33,plain,(
% 1.69/1.33 ! [X1 : $i,X0 : $i,X2 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X1 @ X2)) | ($true = (in @ X1 @ (binintersect @ X0 @ X2)))) <=> (binintersectI = $true)),
% 1.69/1.33 inference(flattening,[status(thm)],[f32])).
% 1.69/1.33 thf(f32,plain,(
% 1.69/1.33 (binintersectI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : ((($true = (in @ X1 @ (binintersect @ X0 @ X2))) | ($true != (in @ X1 @ X2))) | ($true != (in @ X1 @ X0)))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 1.69/1.33 thf(f11,plain,(
% 1.69/1.33 (binintersectI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => (($true = (in @ X1 @ X2)) => ($true = (in @ X1 @ (binintersect @ X0 @ X2)))))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.69/1.33 thf(f10,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ X0 @ X2)))) = binintersectI)),
% 1.69/1.33 inference(rectify,[status(thm)],[f1])).
% 1.69/1.33 thf(f1,axiom,(
% 1.69/1.33 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))) = binintersectI)),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',binintersectI)).
% 1.69/1.33 thf(f145,plain,(
% 1.69/1.33 ((in @ sK14 @ (binintersect @ sK12 @ sK13)) != $true)),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.69/1.33 thf(f144,plain,(
% 1.69/1.33 ($true != $true) | ((in @ sK14 @ (binintersect @ sK12 @ sK13)) != $true)),
% 1.69/1.33 inference(superposition,[status(thm)],[f139,f92])).
% 1.69/1.33 thf(f92,plain,(
% 1.69/1.33 ($true = (in @ sK14 @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13))))),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f139,plain,(
% 1.69/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != (in @ X3 @ X5))) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.69/1.33 thf(f116,plain,(
% 1.69/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != (in @ X3 @ X5)) | ($true != $true)) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f76,f97])).
% 1.69/1.33 thf(f97,plain,(
% 1.69/1.33 (setminusER = $true)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f60])).
% 1.69/1.33 thf(f76,plain,(
% 1.69/1.33 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != (in @ X3 @ X5)) | (setminusER != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f47])).
% 1.69/1.33 thf(f47,plain,(
% 1.69/1.33 ((setminusER = $true) | (((in @ sK2 @ (setminus @ sK3 @ sK4)) = $true) & ($true = (in @ sK2 @ sK4)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != (in @ X3 @ X5))) | (setminusER != $true))),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f45,f46])).
% 1.69/1.33 thf(f46,plain,(
% 1.69/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) & ($true = (in @ X0 @ X2))) => (((in @ sK2 @ (setminus @ sK3 @ sK4)) = $true) & ($true = (in @ sK2 @ sK4)))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f45,plain,(
% 1.69/1.33 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) & ($true = (in @ X0 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != (in @ X3 @ X5))) | (setminusER != $true))),
% 1.69/1.33 inference(rectify,[status(thm)],[f44])).
% 1.69/1.33 thf(f44,plain,(
% 1.69/1.33 ((setminusER = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) & ((in @ X2 @ X0) = $true))) & (! [X2 : $i,X1 : $i,X0 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X0) != $true)) | (setminusER != $true))),
% 1.69/1.33 inference(nnf_transformation,[status(thm)],[f34])).
% 1.69/1.33 thf(f34,plain,(
% 1.69/1.33 (setminusER = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X0) != $true))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f24])).
% 1.69/1.33 thf(f24,plain,(
% 1.69/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ((in @ X2 @ X0) != $true)) <=> (setminusER = $true)),
% 1.69/1.33 inference(flattening,[status(thm)],[f23])).
% 1.69/1.33 thf(f23,plain,(
% 1.69/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ~((in @ X2 @ X0) = $true)) <=> (setminusER = $true)),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f22])).
% 1.69/1.33 thf(f22,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X1 @ X0)) => ~(in @ X2 @ X0)) = setminusER)),
% 1.69/1.33 inference(rectify,[status(thm)],[f2])).
% 1.69/1.33 thf(f2,axiom,(
% 1.69/1.33 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.IaPG4XmqaW/DTF2THF_25864.p',setminusER)).
% 1.69/1.33 % SZS output end Proof for DTF2THF_25864
% 1.69/1.33 % (26138)------------------------------
% 1.69/1.33 % (26138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (26138)Termination reason: Refutation
% 1.69/1.33
% 1.69/1.33 % (26138)Memory used [KB]: 5628
% 1.69/1.33 % (26138)Time elapsed: 0.010 s
% 1.69/1.33 % (26138)Instructions burned: 16 (million)
% 1.69/1.33 % (26138)------------------------------
% 1.69/1.33 % (26138)------------------------------
% 1.69/1.33 % (26132)Success in time 0.018 s
%------------------------------------------------------------------------------