%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU754^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 09:36:56 AM UTC 2026
% Result : Theorem 1.56s 1.27s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 121 ( 23 unt; 0 typ; 4 def)
% Number of atoms : 1851 ( 494 equ; 0 cnn)
% Maximal formula atoms : 12 ( 15 avg)
% Number of connectives : 2060 ( 256 ~; 197 |; 145 &;1342 @)
% ( 22 <=>; 98 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 32 con; 0-2 aty)
% Number of variables : 302 ( 0 ^; 221 !; 81 ?; 302 :)
% 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(f173,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f137,f151,f155,f160,f172]) ).
thf(f172,plain,
( spl21_2
| spl21_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f171]) ).
thf(f171,plain,
( $false
| spl21_2
| spl21_3 ),
inference(subsumption_resolution,[status(thm)],[f170,f147]) ).
thf(f147,plain,
( ( $true
!= ( in @ sK13 @ sK12 ) )
| spl21_3 ),
inference(avatar_component_clause,[status(thm)],[f145]) ).
thf(f145,definition,
( spl21_3
<=> ( $true
= ( in @ sK13 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl21_3])],[avatar_definition]) ).
thf(f170,plain,
( ( $true
= ( in @ sK13 @ sK12 ) )
| spl21_2 ),
inference(subsumption_resolution,[status(thm)],[f169,f81]) ).
thf(f81,plain,
( $true
= ( in @ sK13 @ sK11 ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( ( setminusER = $true )
& ( setminusI = $true )
& ( binintersectI = $true )
& ( binunionTILcontra = $true )
& ( $true
= ( in @ sK12 @ ( powerset @ sK11 ) ) )
& ( $true
= ( in @ sK13 @ ( setminus @ sK11 @ ( binunion @ sK10 @ sK12 ) ) ) )
& ( $true
= ( in @ sK13 @ sK11 ) )
& ( $true
!= ( in @ sK13 @ ( binintersect @ ( setminus @ sK11 @ sK10 ) @ ( setminus @ sK11 @ sK12 ) ) ) )
& ( $true
= ( in @ sK10 @ ( powerset @ sK11 ) ) )
& ( binunionTIRcontra = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f34,f52,f51,f50]) ).
thf(f50,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK11 ) )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ sK11 @ ( binunion @ sK10 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK11 ) )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ sK11 @ sK10 ) @ ( setminus @ sK11 @ X2 ) ) )
!= $true ) ) )
& ( $true
= ( in @ sK10 @ ( powerset @ sK11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK11 ) )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ sK11 @ ( binunion @ sK10 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK11 ) )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ sK11 @ sK10 ) @ ( setminus @ sK11 @ X2 ) ) )
!= $true ) ) )
=> ( ( $true
= ( in @ sK12 @ ( powerset @ sK11 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ sK11 @ ( binunion @ sK10 @ sK12 ) ) ) )
& ( $true
= ( in @ X3 @ sK11 ) )
& ( $true
!= ( in @ X3 @ ( binintersect @ ( setminus @ sK11 @ sK10 ) @ ( setminus @ sK11 @ sK12 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f52,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ sK11 @ ( binunion @ sK10 @ sK12 ) ) ) )
& ( $true
= ( in @ X3 @ sK11 ) )
& ( $true
!= ( in @ X3 @ ( binintersect @ ( setminus @ sK11 @ sK10 ) @ ( setminus @ sK11 @ sK12 ) ) ) ) )
=> ( ( $true
= ( in @ sK13 @ ( setminus @ sK11 @ ( binunion @ sK10 @ sK12 ) ) ) )
& ( $true
= ( in @ sK13 @ sK11 ) )
& ( $true
!= ( in @ sK13 @ ( binintersect @ ( setminus @ sK11 @ sK10 ) @ ( setminus @ sK11 @ sK12 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ( setminusER = $true )
& ( setminusI = $true )
& ( binintersectI = $true )
& ( binunionTILcontra = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionTIRcontra = $true ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binintersectI = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( ( binintersectI = $true )
=> ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
=> ( $true
= ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( binintersectI
=> ( setminusI
=> ( setminusER
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( binintersectI
=> ( setminusI
=> ( setminusER
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) )
=> ( in @ X2 @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( binintersectI
=> ( setminusI
=> ( setminusER
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( binunion @ X3 @ X4 ) ) )
=> ( in @ X2 @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',demorgan2a) ).
thf(f169,plain,
( ( $true
!= ( in @ sK13 @ sK11 ) )
| ( $true
= ( in @ sK13 @ sK12 ) )
| spl21_2 ),
inference(trivial_inequality_removal,[status(thm)],[f168]) ).
thf(f168,plain,
( ( $true
!= ( in @ sK13 @ sK11 ) )
| ( $true
= ( in @ sK13 @ sK12 ) )
| ( $true != $true )
| spl21_2 ),
inference(superposition,[status(thm)],[f136,f123]) ).
thf(f123,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
= ( in @ X4 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true != $true )
| ( $true
!= ( in @ X4 @ X5 ) ) ),
inference(definition_unfolding,[status(thm)],[f74,f86]) ).
thf(f86,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f74,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( setminusI = $true )
| ( ( $true
!= ( in @ sK8 @ ( setminus @ sK9 @ sK7 ) ) )
& ( $true
!= ( in @ sK8 @ sK7 ) )
& ( ( in @ sK8 @ sK9 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true
!= ( in @ X4 @ X5 ) ) )
| ( setminusI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f47,f48]) ).
thf(f48,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
=> ( ( $true
!= ( in @ sK8 @ ( setminus @ sK9 @ sK7 ) ) )
& ( $true
!= ( in @ sK8 @ sK7 ) )
& ( ( in @ sK8 @ sK9 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true
!= ( in @ X4 @ X5 ) ) )
| ( setminusI != $true ) ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( setminusI = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( setminusI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
= setminusI ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',setminusI) ).
thf(f136,plain,
( ( $true
!= ( in @ sK13 @ ( setminus @ sK11 @ sK12 ) ) )
| spl21_2 ),
inference(avatar_component_clause,[status(thm)],[f134]) ).
thf(f134,definition,
( spl21_2
<=> ( $true
= ( in @ sK13 @ ( setminus @ sK11 @ sK12 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl21_2])],[avatar_definition]) ).
thf(f160,plain,
~ spl21_4,
inference(avatar_contradiction_clause,[status(thm)],[f159]) ).
thf(f159,plain,
( $false
| ~ spl21_4 ),
inference(subsumption_resolution,[status(thm)],[f158,f81]) ).
thf(f158,plain,
( ( $true
!= ( in @ sK13 @ sK11 ) )
| ~ spl21_4 ),
inference(subsumption_resolution,[status(thm)],[f157,f79]) ).
thf(f79,plain,
( $true
= ( in @ sK10 @ ( powerset @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f157,plain,
( ( $true
!= ( in @ sK10 @ ( powerset @ sK11 ) ) )
| ( $true
!= ( in @ sK13 @ sK11 ) )
| ~ spl21_4 ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $true
!= ( in @ sK10 @ ( powerset @ sK11 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK13 @ sK11 ) )
| ~ spl21_4 ),
inference(superposition,[status(thm)],[f150,f83]) ).
thf(f83,plain,
( $true
= ( in @ sK12 @ ( powerset @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f150,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK12 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK13 @ X0 ) )
| ( ( in @ sK10 @ ( powerset @ X0 ) )
!= $true ) )
| ~ spl21_4 ),
inference(avatar_component_clause,[status(thm)],[f149]) ).
thf(f149,definition,
( spl21_4
<=> ! [X0: $i] :
( ( $true
!= ( in @ sK12 @ ( powerset @ X0 ) ) )
| ( ( in @ sK10 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK13 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl21_4])],[avatar_definition]) ).
thf(f155,plain,
( spl21_4
| spl21_1 ),
inference(avatar_split_clause,[status(thm)],[f154,f130,f149]) ).
thf(f130,definition,
( spl21_1
<=> ( $true
= ( in @ sK13 @ ( setminus @ sK11 @ sK10 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl21_1])],[avatar_definition]) ).
thf(f154,plain,
( ! [X0: $i] :
( ( ( in @ sK10 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK13 @ X0 ) )
| ( $true
!= ( in @ sK12 @ ( powerset @ X0 ) ) ) )
| spl21_1 ),
inference(subsumption_resolution,[status(thm)],[f153,f141]) ).
thf(f141,plain,
( ( $true
= ( in @ sK13 @ sK10 ) )
| spl21_1 ),
inference(subsumption_resolution,[status(thm)],[f140,f81]) ).
thf(f140,plain,
( ( $true
= ( in @ sK13 @ sK10 ) )
| ( $true
!= ( in @ sK13 @ sK11 ) )
| spl21_1 ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
( ( $true
!= ( in @ sK13 @ sK11 ) )
| ( $true != $true )
| ( $true
= ( in @ sK13 @ sK10 ) )
| spl21_1 ),
inference(superposition,[status(thm)],[f132,f123]) ).
thf(f132,plain,
( ( $true
!= ( in @ sK13 @ ( setminus @ sK11 @ sK10 ) ) )
| spl21_1 ),
inference(avatar_component_clause,[status(thm)],[f130]) ).
thf(f153,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK12 @ ( powerset @ X0 ) ) )
| ( ( in @ sK10 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK13 @ X0 ) )
| ( $true
!= ( in @ sK13 @ sK10 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f152]) ).
thf(f152,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK13 @ sK10 ) )
| ( $true
!= ( in @ sK12 @ ( powerset @ X0 ) ) )
| ( $true != $true )
| ( ( in @ sK10 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK13 @ X0 ) ) ),
inference(superposition,[status(thm)],[f126,f124]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f93,f84]) ).
thf(f84,plain,
binunionTILcontra = $true,
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( binunionTILcontra != $true ) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) ) )
| ( binunionTILcontra != $true ) )
& ( ( binunionTILcontra = $true )
| ( ( $true
= ( in @ sK15 @ ( powerset @ sK14 ) ) )
& ( $true
= ( in @ sK17 @ sK15 ) )
& ( ( in @ sK17 @ ( binunion @ sK15 @ sK16 ) )
!= $true )
& ( $true
= ( in @ sK17 @ sK14 ) )
& ( $true
= ( in @ sK16 @ ( powerset @ sK14 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f55,f58,f57,f56]) ).
thf(f56,plain,
( ? [X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ X4 ) ) )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( ( in @ X7 @ ( binunion @ X5 @ X6 ) )
!= $true )
& ( $true
= ( in @ X7 @ X4 ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X4 ) ) ) ) )
=> ( ( $true
= ( in @ sK15 @ ( powerset @ sK14 ) ) )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK15 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK15 @ X6 ) ) )
& ( $true
= ( in @ X7 @ sK14 ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ sK14 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f57,plain,
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK15 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK15 @ X6 ) ) )
& ( $true
= ( in @ X7 @ sK14 ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ sK14 ) ) ) )
=> ( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK15 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK15 @ sK16 ) ) )
& ( $true
= ( in @ X7 @ sK14 ) ) )
& ( $true
= ( in @ sK16 @ ( powerset @ sK14 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f58,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK15 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK15 @ sK16 ) ) )
& ( $true
= ( in @ X7 @ sK14 ) ) )
=> ( ( $true
= ( in @ sK17 @ sK15 ) )
& ( ( in @ sK17 @ ( binunion @ sK15 @ sK16 ) )
!= $true )
& ( $true
= ( in @ sK17 @ sK14 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f55,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) ) )
| ( binunionTILcontra != $true ) )
& ( ( binunionTILcontra = $true )
| ? [X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ X4 ) ) )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( ( in @ X7 @ ( binunion @ X5 @ X6 ) )
!= $true )
& ( $true
= ( in @ X7 @ X4 ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X4 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) ) )
| ( binunionTILcontra != $true ) )
& ( ( binunionTILcontra = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) ) )
<=> ( binunionTILcontra = $true ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ( binunionTILcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( binunionTILcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) )
<=> ( binunionTILcontra = $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,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)],[f4]) ).
thf(f4,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/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',binunionTILcontra) ).
thf(f126,plain,
( $true
!= ( in @ sK13 @ ( binunion @ sK10 @ sK12 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK13 @ ( binunion @ sK10 @ sK12 ) ) ) ),
inference(superposition,[status(thm)],[f120,f82]) ).
thf(f82,plain,
( $true
= ( in @ sK13 @ ( setminus @ sK11 @ ( binunion @ sK10 @ sK12 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f120,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X5 ) )
| ( $true
!= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f94,f87]) ).
thf(f87,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f94,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( setminusER = $true )
| ( ( $true
= ( in @ sK18 @ ( setminus @ sK19 @ sK20 ) ) )
& ( $true
= ( in @ sK18 @ sK20 ) ) ) )
& ( ! [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,[sK18,sK19,sK20])],[f61,f62]) ).
thf(f62,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X2 )
= $true ) )
=> ( ( $true
= ( in @ sK18 @ ( setminus @ sK19 @ sK20 ) ) )
& ( $true
= ( in @ sK18 @ sK20 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f61,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) ) )
| ( setminusER != $true ) ) ),
inference(rectify,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X2 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
=> ( ( in @ X0 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
=> ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X0 @ X2 ) )
= setminusER ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',setminusER) ).
thf(f151,plain,
( ~ spl21_3
| spl21_4 ),
inference(avatar_split_clause,[status(thm)],[f143,f149,f145]) ).
thf(f143,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK12 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK13 @ X0 ) )
| ( ( in @ sK10 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK13 @ sK12 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK13 @ sK12 ) )
| ( ( in @ sK10 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ sK13 @ X0 ) )
| ( $true
!= ( in @ sK12 @ ( powerset @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f126,f122]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f73,f78]) ).
thf(f78,plain,
binunionTIRcontra = $true,
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( binunionTIRcontra != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ( ( ( in @ sK6 @ sK3 )
= $true )
& ( ( in @ sK6 @ sK5 )
= $true )
& ( $true
!= ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) ) )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f41,f44,f43,f42]) ).
thf(f42,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X4 ) )
& ( $true
= ( in @ X7 @ X6 ) )
& ( ( in @ X7 @ ( binunion @ X5 @ X6 ) )
!= $true ) )
& ( $true
= ( in @ X6 @ ( powerset @ X4 ) ) ) )
& ( $true
= ( in @ X5 @ ( powerset @ X4 ) ) ) )
=> ( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK3 ) )
& ( $true
= ( in @ X7 @ X6 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK4 @ X6 ) ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ sK3 ) ) ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f43,plain,
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK3 ) )
& ( $true
= ( in @ X7 @ X6 ) )
& ( $true
!= ( in @ X7 @ ( binunion @ sK4 @ X6 ) ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ sK3 ) ) ) )
=> ( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK3 ) )
& ( $true
= ( in @ X7 @ sK5 ) )
& ( ( in @ X7 @ ( binunion @ sK4 @ sK5 ) )
!= $true ) )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK3 ) )
& ( $true
= ( in @ X7 @ sK5 ) )
& ( ( in @ X7 @ ( binunion @ sK4 @ sK5 ) )
!= $true ) )
=> ( ( ( in @ sK6 @ sK3 )
= $true )
& ( ( in @ sK6 @ sK5 )
= $true )
& ( $true
!= ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X4 ) )
& ( $true
= ( in @ X7 @ X6 ) )
& ( ( in @ X7 @ ( binunion @ X5 @ X6 ) )
!= $true ) )
& ( $true
= ( in @ X6 @ ( powerset @ X4 ) ) ) )
& ( $true
= ( in @ X5 @ ( powerset @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
& ( ( in @ X3 @ X2 )
= $true )
& ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) )
<=> ( binunionTIRcontra = $true ) ),
inference(flattening,[status(thm)],[f29]) ).
thf(f29,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) )
<=> ( binunionTIRcontra = $true ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,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 @ X2 ) ) ) ) )
= binunionTIRcontra ),
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 @ X4 ) ) ) ) )
= binunionTIRcontra ),
file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',binunionTIRcontra) ).
thf(f137,plain,
( ~ spl21_1
| ~ spl21_2 ),
inference(avatar_split_clause,[status(thm)],[f128,f134,f130]) ).
thf(f128,plain,
( ( $true
!= ( in @ sK13 @ ( setminus @ sK11 @ sK10 ) ) )
| ( $true
!= ( in @ sK13 @ ( setminus @ sK11 @ sK12 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $true
!= ( in @ sK13 @ ( setminus @ sK11 @ sK12 ) ) )
| ( $true
!= ( in @ sK13 @ ( setminus @ sK11 @ sK10 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f80,f121]) ).
thf(f121,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f64,f85]) ).
thf(f85,plain,
binintersectI = $true,
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f64,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) )
| ( binintersectI != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( binintersectI = $true )
| ( ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
!= ( in @ sK2 @ ( binintersect @ sK1 @ sK0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) ) )
| ( binintersectI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f37,f38]) ).
thf(f38,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true ) )
=> ( ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
!= ( in @ sK2 @ ( binintersect @ sK1 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( ( binintersectI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ ( binintersect @ X4 @ X3 ) ) ) )
| ( binintersectI != $true ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( binintersectI = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X2 ) )
& ( $true
!= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) ) )
| ( binintersectI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( binintersectI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f31]) ).
thf(f31,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) )
<=> ( binintersectI = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true
= ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ) )
<=> ( binintersectI = $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binintersectI
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',binintersectI) ).
thf(f80,plain,
( $true
!= ( in @ sK13 @ ( binintersect @ ( setminus @ sK11 @ sK10 ) @ ( setminus @ sK11 @ sK12 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU754^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:33:50 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEU754^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.19/0.47 % Version : Especial > Reduced > Especial.
% 0.19/0.47 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.19/0.47 % (! x:i.in x A -> in x (setminus A (binunion X Y)) ->
% 0.19/0.47 % in x (binintersect (setminus A X) (setminus A Y)))))
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.47 % Source : [Bro08]
% 0.19/0.47 % Names : ZFC256l [Bro08]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % 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, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.19/0.47 % Syntax : Number of formulae : 16 ( 5 unt; 10 typ; 5 def)
% 0.19/0.47 % Number of atoms : 38 ( 5 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 10 ( 6 avg)
% 0.19/0.47 % Number of connectives : 100 ( 6 ~; 0 |; 0 &; 72 @)
% 0.19/0.47 % ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 19 ( 4 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 11 ( 10 usr; 5 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : http://mathgate.info/detsetitem.php?id=315
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(in_type,type,
% 0.19/0.47 in: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(powerset_type,type,
% 0.19/0.47 powerset: $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(binunion_type,type,
% 0.19/0.47 binunion: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(binintersect_type,type,
% 0.19/0.47 binintersect: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectI_type,type,
% 0.19/0.47 binintersectI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectI,definition,
% 0.19/0.47 ( binintersectI
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminus_type,type,
% 0.19/0.47 setminus: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(setminusI_type,type,
% 0.19/0.47 setminusI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusI,definition,
% 0.19/0.47 ( setminusI
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusER_type,type,
% 0.19/0.47 setminusER: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusER,definition,
% 0.19/0.47 ( setminusER
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionTILcontra_type,type,
% 0.19/0.47 binunionTILcontra: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionTILcontra,definition,
% 0.19/0.47 ( binunionTILcontra
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.19/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionTIRcontra_type,type,
% 0.19/0.47 binunionTIRcontra: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionTIRcontra,definition,
% 0.19/0.47 ( binunionTIRcontra
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.19/0.47 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(demorgan2a,conjecture,
% 0.19/0.47 ( binintersectI
% 0.19/0.47 => ( setminusI
% 0.19/0.47 => ( setminusER
% 0.19/0.47 => ( binunionTILcontra
% 0.19/0.47 => ( binunionTIRcontra
% 0.19/0.47 => ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.19/0.47 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.56/1.23 ---- Embedded in THF ---
% 1.56/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.23 %%% Generated on Tue Feb 24 12:33:51 EST 2026
% 1.56/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.23 %%% Logic specification used:
% 1.56/1.23 %%% thf(spec, logic, $$dhol).
% 1.56/1.23
% 1.56/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2DTF10310.p
% See solution above
% 1.56/1.23 ------------------------
% 1.56/1.24 ---- Cleaned THF ---
% 1.56/1.24 thf(in_type,type,
% 1.56/1.24 in: $i > $i > $o ).
% 1.56/1.24
% 1.56/1.24 thf(powerset_type,type,
% 1.56/1.24 powerset: $i > $i ).
% 1.56/1.24
% 1.56/1.24 thf(binunion_type,type,
% 1.56/1.24 binunion: $i > $i > $i ).
% 1.56/1.24
% 1.56/1.24 thf(binintersect_type,type,
% 1.56/1.24 binintersect: $i > $i > $i ).
% 1.56/1.24
% 1.56/1.24 thf(binintersectI_type,type,
% 1.56/1.24 binintersectI: $o ).
% 1.56/1.24
% 1.56/1.24 thf(binintersectI,definition,
% 1.56/1.24 ( binintersectI
% 1.56/1.24 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.56/1.24 ( ( in @ Xx @ A )
% 1.56/1.24 => ( ( in @ Xx @ B )
% 1.56/1.24 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf(setminus_type,type,
% 1.56/1.24 setminus: $i > $i > $i ).
% 1.56/1.24
% 1.56/1.24 thf(setminusI_type,type,
% 1.56/1.24 setminusI: $o ).
% 1.56/1.24
% 1.56/1.24 thf(setminusI,definition,
% 1.56/1.24 ( setminusI
% 1.56/1.24 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.56/1.24 ( ( in @ Xx @ A )
% 1.56/1.24 => ( ~ ( in @ Xx @ B )
% 1.56/1.24 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf(setminusER_type,type,
% 1.56/1.24 setminusER: $o ).
% 1.56/1.24
% 1.56/1.24 thf(setminusER,definition,
% 1.56/1.24 ( setminusER
% 1.56/1.24 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.56/1.24 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.56/1.24 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf(binunionTILcontra_type,type,
% 1.56/1.24 binunionTILcontra: $o ).
% 1.56/1.24
% 1.56/1.24 thf(binunionTILcontra,definition,
% 1.56/1.24 ( binunionTILcontra
% 1.56/1.24 = ( ! [A: $i,X: $i] :
% 1.56/1.24 ( ( in @ X @ ( powerset @ A ) )
% 1.56/1.24 => ! [Y: $i] :
% 1.56/1.24 ( ( in @ Y @ ( powerset @ A ) )
% 1.56/1.24 => ! [Xx: $i] :
% 1.56/1.24 ( ( in @ Xx @ A )
% 1.56/1.24 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 1.56/1.24 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf(binunionTIRcontra_type,type,
% 1.56/1.24 binunionTIRcontra: $o ).
% 1.56/1.24
% 1.56/1.24 thf(binunionTIRcontra,definition,
% 1.56/1.24 ( binunionTIRcontra
% 1.56/1.24 = ( ! [A: $i,X: $i] :
% 1.56/1.24 ( ( in @ X @ ( powerset @ A ) )
% 1.56/1.24 => ! [Y: $i] :
% 1.56/1.24 ( ( in @ Y @ ( powerset @ A ) )
% 1.56/1.24 => ! [Xx: $i] :
% 1.56/1.24 ( ( in @ Xx @ A )
% 1.56/1.24 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 1.56/1.24 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 1.56/1.24
% 1.56/1.24 thf(demorgan2a,conjecture,
% 1.56/1.24 ( binintersectI
% 1.56/1.24 => ( setminusI
% 1.56/1.24 => ( setminusER
% 1.56/1.24 => ( binunionTILcontra
% 1.56/1.24 => ( binunionTIRcontra
% 1.56/1.24 => ! [A: $i,X: $i] :
% 1.56/1.24 ( ( in @ X @ ( powerset @ A ) )
% 1.56/1.24 => ! [Y: $i] :
% 1.56/1.24 ( ( in @ Y @ ( powerset @ A ) )
% 1.56/1.24 => ! [Xx: $i] :
% 1.56/1.24 ( ( in @ Xx @ A )
% 1.56/1.24 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 1.56/1.24 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.56/1.24 ------------------------
% 1.56/1.25 % (10501)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_10310 for (2999ds/4Mi)
% 1.56/1.25 % (10501)Instruction limit reached!
% 1.56/1.25 % (10501)------------------------------
% 1.56/1.25 % (10501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.25 % (10501)Termination reason: Unknown
% 1.56/1.25 % (10501)Termination phase: Saturation
% 1.56/1.25
% 1.56/1.25 % (10501)Memory used [KB]: 5500
% 1.56/1.25 % (10501)Time elapsed: 0.003 s
% 1.56/1.25 % (10501)Instructions burned: 5 (million)
% 1.56/1.25 % (10501)------------------------------
% 1.56/1.25 % (10501)------------------------------
% 1.56/1.25 % (10503)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10310 for (2999ds/2Mi)
% 1.56/1.26 % (10503)Instruction limit reached!
% 1.56/1.26 % (10503)------------------------------
% 1.56/1.26 % (10503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.26 % (10503)Termination reason: Unknown
% 1.56/1.26 % (10503)Termination phase: Preprocessing 3
% 1.56/1.26
% 1.56/1.26 % (10503)Memory used [KB]: 1023
% 1.56/1.26 % (10503)Time elapsed: 0.002 s
% 1.56/1.26 % (10503)Instructions burned: 3 (million)
% 1.56/1.26 % (10503)------------------------------
% 1.56/1.26 % (10503)------------------------------
% 1.56/1.26 % (10505)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_10310 for (2999ds/275Mi)
% 1.56/1.26 % (10500)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10310 for (2999ds/183Mi)
% 1.56/1.26 % (10502)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_10310 for (2999ds/27Mi)
% 1.56/1.27 % (10507)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10310 for (2999ds/3Mi)
% 1.56/1.27 % (10507)Instruction limit reached!
% 1.56/1.27 % (10507)------------------------------
% 1.56/1.27 % (10507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (10507)Termination reason: Unknown
% 1.56/1.27 % (10507)Termination phase: Preprocessing 3
% 1.56/1.27
% 1.56/1.27 % (10507)Memory used [KB]: 1023
% 1.56/1.27 % (10507)Time elapsed: 0.002 s
% 1.56/1.27 % (10507)Instructions burned: 3 (million)
% 1.56/1.27 % (10507)------------------------------
% 1.56/1.27 % (10507)------------------------------
% 1.56/1.27 % (10505)First to succeed.
% 1.56/1.27 % (10508)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_10310 for (2999ds/37Mi)
% 1.56/1.27 % (10504)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_10310 for (2999ds/2Mi)
% 1.56/1.27 % (10504)Instruction limit reached!
% 1.56/1.27 % (10504)------------------------------
% 1.56/1.27 % (10504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (10504)Termination reason: Unknown
% 1.56/1.27 % (10504)Termination phase: shuffling
% 1.56/1.27
% 1.56/1.27 % (10504)Memory used [KB]: 895
% 1.56/1.27 % (10504)Time elapsed: 0.003 s
% 1.56/1.27 % (10504)Instructions burned: 2 (million)
% 1.56/1.27 % (10504)------------------------------
% 1.56/1.27 % (10504)------------------------------
% 1.56/1.27 % (10506)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10310 for (2999ds/18Mi)
% 1.56/1.27 % (10505)Refutation found. Thanks to Tanya!
% 1.56/1.27 % SZS status Theorem for DTF2THF_10310
% 1.56/1.27 % SZS output start Proof for DTF2THF_10310
% 1.56/1.27 thf(func_def_0, type, in: $i > $i > $o).
% 1.56/1.27 thf(func_def_1, type, powerset: $i > $i).
% 1.56/1.27 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.56/1.27 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.56/1.27 thf(func_def_6, type, setminus: $i > $i > $i).
% 1.56/1.27 thf(f173,plain,(
% 1.56/1.27 $false),
% 1.56/1.27 inference(avatar_sat_refutation,[status(thm)],[f137,f151,f155,f160,f172])).
% 1.56/1.27 thf(f172,plain,(
% 1.56/1.27 spl21_2 | spl21_3),
% 1.56/1.27 inference(avatar_contradiction_clause,[status(thm)],[f171])).
% 1.56/1.27 thf(f171,plain,(
% 1.56/1.27 $false | (spl21_2 | spl21_3)),
% 1.56/1.27 inference(subsumption_resolution,[status(thm)],[f170,f147])).
% 1.56/1.27 thf(f147,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ sK12)) | spl21_3),
% 1.56/1.27 inference(avatar_component_clause,[status(thm)],[f145])).
% 1.56/1.27 thf(f145,definition,(
% 1.56/1.27 spl21_3 <=> ($true = (in @ sK13 @ sK12))),
% 1.56/1.27 introduced(definition,[new_symbols(naming,[spl21_3])],[avatar_definition])).
% 1.56/1.27 thf(f170,plain,(
% 1.56/1.27 ($true = (in @ sK13 @ sK12)) | spl21_2),
% 1.56/1.27 inference(subsumption_resolution,[status(thm)],[f169,f81])).
% 1.56/1.27 thf(f81,plain,(
% 1.56/1.27 ($true = (in @ sK13 @ sK11))),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 thf(f53,plain,(
% 1.56/1.27 (setminusER = $true) & (setminusI = $true) & (binintersectI = $true) & (binunionTILcontra = $true) & ((($true = (in @ sK12 @ (powerset @ sK11))) & (($true = (in @ sK13 @ (setminus @ sK11 @ (binunion @ sK10 @ sK12)))) & ($true = (in @ sK13 @ sK11)) & ($true != (in @ sK13 @ (binintersect @ (setminus @ sK11 @ sK10) @ (setminus @ sK11 @ sK12)))))) & ($true = (in @ sK10 @ (powerset @ sK11)))) & (binunionTIRcontra = $true)),
% 1.56/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f34,f52,f51,f50])).
% 1.56/1.27 thf(f50,plain,(
% 1.56/1.27 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))))) & ($true = (in @ X0 @ (powerset @ X1)))) => (? [X2 : $i] : (((in @ X2 @ (powerset @ sK11)) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ sK11 @ (binunion @ sK10 @ X2)))) & ($true = (in @ X3 @ sK11)) & ((in @ X3 @ (binintersect @ (setminus @ sK11 @ sK10) @ (setminus @ sK11 @ X2))) != $true))) & ($true = (in @ sK10 @ (powerset @ sK11))))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f51,plain,(
% 1.56/1.27 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK11)) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ sK11 @ (binunion @ sK10 @ X2)))) & ($true = (in @ X3 @ sK11)) & ((in @ X3 @ (binintersect @ (setminus @ sK11 @ sK10) @ (setminus @ sK11 @ X2))) != $true))) => (($true = (in @ sK12 @ (powerset @ sK11))) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ sK11 @ (binunion @ sK10 @ sK12)))) & ($true = (in @ X3 @ sK11)) & ($true != (in @ X3 @ (binintersect @ (setminus @ sK11 @ sK10) @ (setminus @ sK11 @ sK12))))))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f52,plain,(
% 1.56/1.27 ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ sK11 @ (binunion @ sK10 @ sK12)))) & ($true = (in @ X3 @ sK11)) & ($true != (in @ X3 @ (binintersect @ (setminus @ sK11 @ sK10) @ (setminus @ sK11 @ sK12))))) => (($true = (in @ sK13 @ (setminus @ sK11 @ (binunion @ sK10 @ sK12)))) & ($true = (in @ sK13 @ sK11)) & ($true != (in @ sK13 @ (binintersect @ (setminus @ sK11 @ sK10) @ (setminus @ sK11 @ sK12)))))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f34,plain,(
% 1.56/1.27 (setminusER = $true) & (setminusI = $true) & (binintersectI = $true) & (binunionTILcontra = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))))) & ($true = (in @ X0 @ (powerset @ X1)))) & (binunionTIRcontra = $true)),
% 1.56/1.27 inference(flattening,[status(thm)],[f33])).
% 1.56/1.27 thf(f33,plain,(
% 1.56/1.27 ((((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((($true != (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) & ($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ($true = (in @ X0 @ (powerset @ X1)))) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (setminusER = $true)) & (setminusI = $true)) & (binintersectI = $true)),
% 1.56/1.27 inference(ennf_transformation,[status(thm)],[f20])).
% 1.56/1.27 thf(f20,plain,(
% 1.56/1.27 ~((binintersectI = $true) => ((setminusI = $true) => ((setminusER = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) => ($true = (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))))))))))))),
% 1.56/1.27 inference(fool_elimination,[status(thm)],[f19])).
% 1.56/1.27 thf(f19,plain,(
% 1.56/1.27 ~(binintersectI => (setminusI => (setminusER => (binunionTILcontra => (binunionTIRcontra => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) => (in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))))))))))))),
% 1.56/1.27 inference(rectify,[status(thm)],[f7])).
% 1.56/1.27 thf(f7,negated_conjecture,(
% 1.56/1.27 ~(binintersectI => (setminusI => (setminusER => (binunionTILcontra => (binunionTIRcontra => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4))) => (in @ X2 @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4))))))))))))),
% 1.56/1.27 inference(negated_conjecture,[status(cth)],[f6])).
% 1.56/1.27 thf(f6,conjecture,(
% 1.56/1.27 binintersectI => (setminusI => (setminusER => (binunionTILcontra => (binunionTIRcontra => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4))) => (in @ X2 @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4)))))))))))),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',demorgan2a)).
% 1.56/1.27 thf(f169,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ sK11)) | ($true = (in @ sK13 @ sK12)) | spl21_2),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f168])).
% 1.56/1.27 thf(f168,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ sK11)) | ($true = (in @ sK13 @ sK12)) | ($true != $true) | spl21_2),
% 1.56/1.27 inference(superposition,[status(thm)],[f136,f123])).
% 1.56/1.27 thf(f123,plain,(
% 1.56/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ($true != (in @ X4 @ X5)) | ($true = (in @ X4 @ X3))) )),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.56/1.27 thf(f110,plain,(
% 1.56/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ($true = (in @ X4 @ X3)) | ($true != $true) | ($true != (in @ X4 @ X5))) )),
% 1.56/1.27 inference(definition_unfolding,[status(thm)],[f74,f86])).
% 1.56/1.27 thf(f86,plain,(
% 1.56/1.27 (setminusI = $true)),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 thf(f74,plain,(
% 1.56/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ($true = (in @ X4 @ X3)) | ($true != (in @ X4 @ X5)) | (setminusI != $true)) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f49])).
% 1.56/1.27 thf(f49,plain,(
% 1.56/1.27 ((setminusI = $true) | (($true != (in @ sK8 @ (setminus @ sK9 @ sK7))) & ($true != (in @ sK8 @ sK7)) & ((in @ sK8 @ sK9) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ($true = (in @ X4 @ X3)) | ($true != (in @ X4 @ X5))) | (setminusI != $true))),
% 1.56/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f47,f48])).
% 1.56/1.27 thf(f48,plain,(
% 1.56/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) & ((in @ X1 @ X0) != $true) & ($true = (in @ X1 @ X2))) => (($true != (in @ sK8 @ (setminus @ sK9 @ sK7))) & ($true != (in @ sK8 @ sK7)) & ((in @ sK8 @ sK9) = $true))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f47,plain,(
% 1.56/1.27 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) & ((in @ X1 @ X0) != $true) & ($true = (in @ X1 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ($true = (in @ X4 @ X3)) | ($true != (in @ X4 @ X5))) | (setminusI != $true))),
% 1.56/1.27 inference(rectify,[status(thm)],[f46])).
% 1.56/1.27 thf(f46,plain,(
% 1.56/1.27 ((setminusI = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (($true != (in @ X0 @ (setminus @ X2 @ X1))) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ X2) = $true))) & (! [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true)) | (setminusI != $true))),
% 1.56/1.27 inference(nnf_transformation,[status(thm)],[f26])).
% 1.56/1.27 thf(f26,plain,(
% 1.56/1.27 (setminusI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true))),
% 1.56/1.27 inference(flattening,[status(thm)],[f25])).
% 1.56/1.27 thf(f25,plain,(
% 1.56/1.27 ! [X0 : $i,X2 : $i,X1 : $i] : ((($true = (in @ X0 @ (setminus @ X2 @ X1))) | ((in @ X0 @ X1) = $true)) | ((in @ X0 @ X2) != $true)) <=> (setminusI = $true)),
% 1.56/1.27 inference(ennf_transformation,[status(thm)],[f21])).
% 1.56/1.27 thf(f21,plain,(
% 1.56/1.27 ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X0 @ X2) = $true) => (((in @ X0 @ X1) != $true) => ($true = (in @ X0 @ (setminus @ X2 @ X1))))) <=> (setminusI = $true)),
% 1.56/1.27 inference(flattening,[status(thm)],[f12])).
% 1.56/1.27 thf(f12,plain,(
% 1.56/1.27 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => (~((in @ X0 @ X1) = $true) => ($true = (in @ X0 @ (setminus @ X2 @ X1))))) <=> (setminusI = $true)),
% 1.56/1.27 inference(fool_elimination,[status(thm)],[f11])).
% 1.56/1.27 thf(f11,plain,(
% 1.56/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => (in @ X0 @ (setminus @ X2 @ X1)))) = setminusI)),
% 1.56/1.27 inference(rectify,[status(thm)],[f2])).
% 1.56/1.27 thf(f2,axiom,(
% 1.56/1.27 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',setminusI)).
% 1.56/1.27 thf(f136,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ (setminus @ sK11 @ sK12))) | spl21_2),
% 1.56/1.27 inference(avatar_component_clause,[status(thm)],[f134])).
% 1.56/1.27 thf(f134,definition,(
% 1.56/1.27 spl21_2 <=> ($true = (in @ sK13 @ (setminus @ sK11 @ sK12)))),
% 1.56/1.27 introduced(definition,[new_symbols(naming,[spl21_2])],[avatar_definition])).
% 1.56/1.27 thf(f160,plain,(
% 1.56/1.27 ~spl21_4),
% 1.56/1.27 inference(avatar_contradiction_clause,[status(thm)],[f159])).
% 1.56/1.27 thf(f159,plain,(
% 1.56/1.27 $false | ~spl21_4),
% 1.56/1.27 inference(subsumption_resolution,[status(thm)],[f158,f81])).
% 1.56/1.27 thf(f158,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ sK11)) | ~spl21_4),
% 1.56/1.27 inference(subsumption_resolution,[status(thm)],[f157,f79])).
% 1.56/1.27 thf(f79,plain,(
% 1.56/1.27 ($true = (in @ sK10 @ (powerset @ sK11)))),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 thf(f157,plain,(
% 1.56/1.27 ($true != (in @ sK10 @ (powerset @ sK11))) | ($true != (in @ sK13 @ sK11)) | ~spl21_4),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.56/1.27 thf(f156,plain,(
% 1.56/1.27 ($true != (in @ sK10 @ (powerset @ sK11))) | ($true != $true) | ($true != (in @ sK13 @ sK11)) | ~spl21_4),
% 1.56/1.27 inference(superposition,[status(thm)],[f150,f83])).
% 1.56/1.27 thf(f83,plain,(
% 1.56/1.27 ($true = (in @ sK12 @ (powerset @ sK11)))),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 thf(f150,plain,(
% 1.56/1.27 ( ! [X0 : $i] : (($true != (in @ sK12 @ (powerset @ X0))) | ($true != (in @ sK13 @ X0)) | ((in @ sK10 @ (powerset @ X0)) != $true)) ) | ~spl21_4),
% 1.56/1.27 inference(avatar_component_clause,[status(thm)],[f149])).
% 1.56/1.27 thf(f149,definition,(
% 1.56/1.27 spl21_4 <=> ! [X0 : $i] : (($true != (in @ sK12 @ (powerset @ X0))) | ((in @ sK10 @ (powerset @ X0)) != $true) | ($true != (in @ sK13 @ X0)))),
% 1.56/1.27 introduced(definition,[new_symbols(naming,[spl21_4])],[avatar_definition])).
% 1.56/1.27 thf(f155,plain,(
% 1.56/1.27 spl21_4 | spl21_1),
% 1.56/1.27 inference(avatar_split_clause,[status(thm)],[f154,f130,f149])).
% 1.56/1.27 thf(f130,definition,(
% 1.56/1.27 spl21_1 <=> ($true = (in @ sK13 @ (setminus @ sK11 @ sK10)))),
% 1.56/1.27 introduced(definition,[new_symbols(naming,[spl21_1])],[avatar_definition])).
% 1.56/1.27 thf(f154,plain,(
% 1.56/1.27 ( ! [X0 : $i] : (((in @ sK10 @ (powerset @ X0)) != $true) | ($true != (in @ sK13 @ X0)) | ($true != (in @ sK12 @ (powerset @ X0)))) ) | spl21_1),
% 1.56/1.27 inference(subsumption_resolution,[status(thm)],[f153,f141])).
% 1.56/1.27 thf(f141,plain,(
% 1.56/1.27 ($true = (in @ sK13 @ sK10)) | spl21_1),
% 1.56/1.27 inference(subsumption_resolution,[status(thm)],[f140,f81])).
% 1.56/1.27 thf(f140,plain,(
% 1.56/1.27 ($true = (in @ sK13 @ sK10)) | ($true != (in @ sK13 @ sK11)) | spl21_1),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.56/1.27 thf(f139,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ sK11)) | ($true != $true) | ($true = (in @ sK13 @ sK10)) | spl21_1),
% 1.56/1.27 inference(superposition,[status(thm)],[f132,f123])).
% 1.56/1.27 thf(f132,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ (setminus @ sK11 @ sK10))) | spl21_1),
% 1.56/1.27 inference(avatar_component_clause,[status(thm)],[f130])).
% 1.56/1.27 thf(f153,plain,(
% 1.56/1.27 ( ! [X0 : $i] : (($true != (in @ sK12 @ (powerset @ X0))) | ((in @ sK10 @ (powerset @ X0)) != $true) | ($true != (in @ sK13 @ X0)) | ($true != (in @ sK13 @ sK10))) )),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f152])).
% 1.56/1.27 thf(f152,plain,(
% 1.56/1.27 ( ! [X0 : $i] : (($true != (in @ sK13 @ sK10)) | ($true != (in @ sK12 @ (powerset @ X0))) | ($true != $true) | ((in @ sK10 @ (powerset @ X0)) != $true) | ($true != (in @ sK13 @ X0))) )),
% 1.56/1.27 inference(superposition,[status(thm)],[f126,f124])).
% 1.56/1.27 thf(f124,plain,(
% 1.56/1.27 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ X3 @ (binunion @ X1 @ X2))) | ((in @ X3 @ X1) != $true) | ($true != (in @ X3 @ X0)) | ($true != (in @ X2 @ (powerset @ X0))) | ($true != (in @ X1 @ (powerset @ X0)))) )),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.56/1.27 thf(f111,plain,(
% 1.56/1.27 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X3 @ X0)) | ($true != (in @ X2 @ (powerset @ X0))) | ($true = (in @ X3 @ (binunion @ X1 @ X2))) | ((in @ X3 @ X1) != $true) | ($true != $true) | ($true != (in @ X1 @ (powerset @ X0)))) )),
% 1.56/1.27 inference(definition_unfolding,[status(thm)],[f93,f84])).
% 1.56/1.27 thf(f84,plain,(
% 1.56/1.27 (binunionTILcontra = $true)),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 thf(f93,plain,(
% 1.56/1.27 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))) | ($true != (in @ X3 @ X0)) | ($true != (in @ X2 @ (powerset @ X0))) | (binunionTILcontra != $true)) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f59])).
% 1.56/1.27 thf(f59,plain,(
% 1.56/1.27 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))) | ($true != (in @ X3 @ X0))) | ($true != (in @ X2 @ (powerset @ X0))))) | (binunionTILcontra != $true)) & ((binunionTILcontra = $true) | (($true = (in @ sK15 @ (powerset @ sK14))) & ((($true = (in @ sK17 @ sK15)) & ((in @ sK17 @ (binunion @ sK15 @ sK16)) != $true) & ($true = (in @ sK17 @ sK14))) & ($true = (in @ sK16 @ (powerset @ sK14))))))),
% 1.56/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f55,f58,f57,f56])).
% 1.56/1.27 thf(f56,plain,(
% 1.56/1.27 ? [X4 : $i,X5 : $i] : (($true = (in @ X5 @ (powerset @ X4))) & ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X5)) & ((in @ X7 @ (binunion @ X5 @ X6)) != $true) & ($true = (in @ X7 @ X4))) & ($true = (in @ X6 @ (powerset @ X4))))) => (($true = (in @ sK15 @ (powerset @ sK14))) & ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ sK15)) & ($true != (in @ X7 @ (binunion @ sK15 @ X6))) & ($true = (in @ X7 @ sK14))) & ($true = (in @ X6 @ (powerset @ sK14)))))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f57,plain,(
% 1.56/1.27 ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ sK15)) & ($true != (in @ X7 @ (binunion @ sK15 @ X6))) & ($true = (in @ X7 @ sK14))) & ($true = (in @ X6 @ (powerset @ sK14)))) => (? [X7 : $i] : (($true = (in @ X7 @ sK15)) & ($true != (in @ X7 @ (binunion @ sK15 @ sK16))) & ($true = (in @ X7 @ sK14))) & ($true = (in @ sK16 @ (powerset @ sK14))))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f58,plain,(
% 1.56/1.27 ? [X7 : $i] : (($true = (in @ X7 @ sK15)) & ($true != (in @ X7 @ (binunion @ sK15 @ sK16))) & ($true = (in @ X7 @ sK14))) => (($true = (in @ sK17 @ sK15)) & ((in @ sK17 @ (binunion @ sK15 @ sK16)) != $true) & ($true = (in @ sK17 @ sK14)))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f55,plain,(
% 1.56/1.27 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))) | ($true != (in @ X3 @ X0))) | ($true != (in @ X2 @ (powerset @ X0))))) | (binunionTILcontra != $true)) & ((binunionTILcontra = $true) | ? [X4 : $i,X5 : $i] : (($true = (in @ X5 @ (powerset @ X4))) & ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X5)) & ((in @ X7 @ (binunion @ X5 @ X6)) != $true) & ($true = (in @ X7 @ X4))) & ($true = (in @ X6 @ (powerset @ X4))))))),
% 1.56/1.27 inference(rectify,[status(thm)],[f54])).
% 1.56/1.27 thf(f54,plain,(
% 1.56/1.27 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))) | ($true != (in @ X3 @ X0))) | ($true != (in @ X2 @ (powerset @ X0))))) | (binunionTILcontra != $true)) & ((binunionTILcontra = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ (binunion @ X1 @ X2))) & ($true = (in @ X3 @ X0))) & ($true = (in @ X2 @ (powerset @ X0))))))),
% 1.56/1.27 inference(nnf_transformation,[status(thm)],[f28])).
% 1.56/1.27 thf(f28,plain,(
% 1.56/1.27 ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))) | ($true != (in @ X3 @ X0))) | ($true != (in @ X2 @ (powerset @ X0))))) <=> (binunionTILcontra = $true)),
% 1.56/1.27 inference(flattening,[status(thm)],[f27])).
% 1.56/1.27 thf(f27,plain,(
% 1.56/1.27 (binunionTILcontra = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ($true != (in @ X3 @ X0))) | ($true != (in @ X2 @ (powerset @ X0)))) | ($true != (in @ X1 @ (powerset @ X0))))),
% 1.56/1.27 inference(ennf_transformation,[status(thm)],[f23])).
% 1.56/1.27 thf(f23,plain,(
% 1.56/1.27 (binunionTILcontra = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => (($true != (in @ X3 @ (binunion @ X1 @ X2))) => ((in @ X3 @ X1) != $true)))))),
% 1.56/1.27 inference(flattening,[status(thm)],[f10])).
% 1.56/1.27 thf(f10,plain,(
% 1.56/1.27 ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => (~($true = (in @ X3 @ (binunion @ X1 @ X2))) => ~((in @ X3 @ X1) = $true))))) <=> (binunionTILcontra = $true)),
% 1.56/1.27 inference(fool_elimination,[status(thm)],[f9])).
% 1.56/1.27 thf(f9,plain,(
% 1.56/1.27 (! [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)),
% 1.56/1.27 inference(rectify,[status(thm)],[f4])).
% 1.56/1.27 thf(f4,axiom,(
% 1.56/1.27 (! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (binunion @ X3 @ X4)) => ~(in @ X2 @ X3))))) = binunionTILcontra)),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',binunionTILcontra)).
% 1.56/1.27 thf(f126,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ (binunion @ sK10 @ sK12)))),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.56/1.27 thf(f125,plain,(
% 1.56/1.27 ($true != $true) | ($true != (in @ sK13 @ (binunion @ sK10 @ sK12)))),
% 1.56/1.27 inference(superposition,[status(thm)],[f120,f82])).
% 1.56/1.27 thf(f82,plain,(
% 1.56/1.27 ($true = (in @ sK13 @ (setminus @ sK11 @ (binunion @ sK10 @ sK12))))),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 thf(f120,plain,(
% 1.56/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != (in @ X3 @ X5))) )),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.56/1.27 thf(f119,plain,(
% 1.56/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ X5)) | ($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != $true)) )),
% 1.56/1.27 inference(definition_unfolding,[status(thm)],[f94,f87])).
% 1.56/1.27 thf(f87,plain,(
% 1.56/1.27 (setminusER = $true)),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 thf(f94,plain,(
% 1.56/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != (in @ X3 @ X5)) | (setminusER != $true)) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f63])).
% 1.56/1.27 thf(f63,plain,(
% 1.56/1.27 ((setminusER = $true) | (($true = (in @ sK18 @ (setminus @ sK19 @ sK20))) & ($true = (in @ sK18 @ sK20)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != (in @ X3 @ X5))) | (setminusER != $true))),
% 1.56/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f61,f62])).
% 1.56/1.27 thf(f62,plain,(
% 1.56/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X1 @ X2))) & ((in @ X0 @ X2) = $true)) => (($true = (in @ sK18 @ (setminus @ sK19 @ sK20))) & ($true = (in @ sK18 @ sK20)))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f61,plain,(
% 1.56/1.27 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X1 @ X2))) & ((in @ X0 @ X2) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (setminus @ X4 @ X5))) | ($true != (in @ X3 @ X5))) | (setminusER != $true))),
% 1.56/1.27 inference(rectify,[status(thm)],[f60])).
% 1.56/1.27 thf(f60,plain,(
% 1.56/1.27 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X1 @ X2))) & ((in @ X0 @ X2) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (setminus @ X1 @ X2))) | ((in @ X0 @ X2) != $true)) | (setminusER != $true))),
% 1.56/1.27 inference(nnf_transformation,[status(thm)],[f35])).
% 1.56/1.27 thf(f35,plain,(
% 1.56/1.27 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (setminus @ X1 @ X2))) | ((in @ X0 @ X2) != $true))),
% 1.56/1.27 inference(ennf_transformation,[status(thm)],[f22])).
% 1.56/1.27 thf(f22,plain,(
% 1.56/1.27 (setminusER = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X0 @ (setminus @ X1 @ X2))) => ((in @ X0 @ X2) != $true))),
% 1.56/1.27 inference(flattening,[status(thm)],[f14])).
% 1.56/1.27 thf(f14,plain,(
% 1.56/1.27 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setminus @ X1 @ X2))) => ~((in @ X0 @ X2) = $true)) <=> (setminusER = $true)),
% 1.56/1.27 inference(fool_elimination,[status(thm)],[f13])).
% 1.56/1.27 thf(f13,plain,(
% 1.56/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X1 @ X2)) => ~(in @ X0 @ X2)) = setminusER)),
% 1.56/1.27 inference(rectify,[status(thm)],[f3])).
% 1.56/1.27 thf(f3,axiom,(
% 1.56/1.27 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',setminusER)).
% 1.56/1.27 thf(f151,plain,(
% 1.56/1.27 ~spl21_3 | spl21_4),
% 1.56/1.27 inference(avatar_split_clause,[status(thm)],[f143,f149,f145])).
% 1.56/1.27 thf(f143,plain,(
% 1.56/1.27 ( ! [X0 : $i] : (($true != (in @ sK12 @ (powerset @ X0))) | ($true != (in @ sK13 @ X0)) | ((in @ sK10 @ (powerset @ X0)) != $true) | ($true != (in @ sK13 @ sK12))) )),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.56/1.27 thf(f142,plain,(
% 1.56/1.27 ( ! [X0 : $i] : (($true != (in @ sK13 @ sK12)) | ((in @ sK10 @ (powerset @ X0)) != $true) | ($true != $true) | ($true != (in @ sK13 @ X0)) | ($true != (in @ sK12 @ (powerset @ X0)))) )),
% 1.56/1.27 inference(superposition,[status(thm)],[f126,f122])).
% 1.56/1.27 thf(f122,plain,(
% 1.56/1.27 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ X3 @ (binunion @ X1 @ X2))) | ((in @ X3 @ X2) != $true) | ($true != (in @ X3 @ X0)) | ($true != (in @ X1 @ (powerset @ X0))) | ($true != (in @ X2 @ (powerset @ X0)))) )),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.56/1.27 thf(f101,plain,(
% 1.56/1.27 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X2 @ (powerset @ X0))) | ($true != (in @ X1 @ (powerset @ X0))) | ((in @ X3 @ X2) != $true) | ($true != (in @ X3 @ X0)) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) )),
% 1.56/1.27 inference(definition_unfolding,[status(thm)],[f73,f78])).
% 1.56/1.27 thf(f78,plain,(
% 1.56/1.27 (binunionTIRcontra = $true)),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 thf(f73,plain,(
% 1.56/1.27 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X3 @ X0)) | ((in @ X3 @ X2) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2))) | ($true != (in @ X2 @ (powerset @ X0))) | ($true != (in @ X1 @ (powerset @ X0))) | (binunionTIRcontra != $true)) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f45])).
% 1.56/1.27 thf(f45,plain,(
% 1.56/1.27 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ((in @ X3 @ X2) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ($true != (in @ X2 @ (powerset @ X0)))) | ($true != (in @ X1 @ (powerset @ X0)))) | (binunionTIRcontra != $true)) & ((binunionTIRcontra = $true) | (((((in @ sK6 @ sK3) = $true) & ((in @ sK6 @ sK5) = $true) & ($true != (in @ sK6 @ (binunion @ sK4 @ sK5)))) & ($true = (in @ sK5 @ (powerset @ sK3)))) & ($true = (in @ sK4 @ (powerset @ sK3)))))),
% 1.56/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f41,f44,f43,f42])).
% 1.56/1.27 thf(f42,plain,(
% 1.56/1.27 ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X4)) & ($true = (in @ X7 @ X6)) & ((in @ X7 @ (binunion @ X5 @ X6)) != $true)) & ($true = (in @ X6 @ (powerset @ X4)))) & ($true = (in @ X5 @ (powerset @ X4)))) => (? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ sK3)) & ($true = (in @ X7 @ X6)) & ($true != (in @ X7 @ (binunion @ sK4 @ X6)))) & ($true = (in @ X6 @ (powerset @ sK3)))) & ($true = (in @ sK4 @ (powerset @ sK3))))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f43,plain,(
% 1.56/1.27 ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ sK3)) & ($true = (in @ X7 @ X6)) & ($true != (in @ X7 @ (binunion @ sK4 @ X6)))) & ($true = (in @ X6 @ (powerset @ sK3)))) => (? [X7 : $i] : (($true = (in @ X7 @ sK3)) & ($true = (in @ X7 @ sK5)) & ((in @ X7 @ (binunion @ sK4 @ sK5)) != $true)) & ($true = (in @ sK5 @ (powerset @ sK3))))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f44,plain,(
% 1.56/1.27 ? [X7 : $i] : (($true = (in @ X7 @ sK3)) & ($true = (in @ X7 @ sK5)) & ((in @ X7 @ (binunion @ sK4 @ sK5)) != $true)) => (((in @ sK6 @ sK3) = $true) & ((in @ sK6 @ sK5) = $true) & ($true != (in @ sK6 @ (binunion @ sK4 @ sK5))))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f41,plain,(
% 1.56/1.27 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ((in @ X3 @ X2) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ($true != (in @ X2 @ (powerset @ X0)))) | ($true != (in @ X1 @ (powerset @ X0)))) | (binunionTIRcontra != $true)) & ((binunionTIRcontra = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X4)) & ($true = (in @ X7 @ X6)) & ((in @ X7 @ (binunion @ X5 @ X6)) != $true)) & ($true = (in @ X6 @ (powerset @ X4)))) & ($true = (in @ X5 @ (powerset @ X4)))))),
% 1.56/1.27 inference(rectify,[status(thm)],[f40])).
% 1.56/1.27 thf(f40,plain,(
% 1.56/1.27 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ((in @ X3 @ X2) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ($true != (in @ X2 @ (powerset @ X0)))) | ($true != (in @ X1 @ (powerset @ X0)))) | (binunionTIRcontra != $true)) & ((binunionTIRcontra = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X0)) & ((in @ X3 @ X2) = $true) & ($true != (in @ X3 @ (binunion @ X1 @ X2)))) & ($true = (in @ X2 @ (powerset @ X0)))) & ($true = (in @ X1 @ (powerset @ X0)))))),
% 1.56/1.27 inference(nnf_transformation,[status(thm)],[f30])).
% 1.56/1.27 thf(f30,plain,(
% 1.56/1.27 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ((in @ X3 @ X2) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ($true != (in @ X2 @ (powerset @ X0)))) | ($true != (in @ X1 @ (powerset @ X0)))) <=> (binunionTIRcontra = $true)),
% 1.56/1.27 inference(flattening,[status(thm)],[f29])).
% 1.56/1.27 thf(f29,plain,(
% 1.56/1.27 (binunionTIRcontra = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2) != $true) | ($true = (in @ X3 @ (binunion @ X1 @ X2)))) | ($true != (in @ X3 @ X0))) | ($true != (in @ X2 @ (powerset @ X0)))) | ($true != (in @ X1 @ (powerset @ X0))))),
% 1.56/1.27 inference(ennf_transformation,[status(thm)],[f24])).
% 1.56/1.27 thf(f24,plain,(
% 1.56/1.27 (binunionTIRcontra = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => (($true != (in @ X3 @ (binunion @ X1 @ X2))) => ((in @ X3 @ X2) != $true)))))),
% 1.56/1.27 inference(flattening,[status(thm)],[f16])).
% 1.56/1.27 thf(f16,plain,(
% 1.56/1.27 ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => (~($true = (in @ X3 @ (binunion @ X1 @ X2))) => ~((in @ X3 @ X2) = $true))))) <=> (binunionTIRcontra = $true)),
% 1.56/1.27 inference(fool_elimination,[status(thm)],[f15])).
% 1.56/1.27 thf(f15,plain,(
% 1.56/1.27 (! [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))))) = binunionTIRcontra)),
% 1.56/1.27 inference(rectify,[status(thm)],[f5])).
% 1.56/1.27 thf(f5,axiom,(
% 1.56/1.27 (! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (binunion @ X3 @ X4)) => ~(in @ X2 @ X4))))) = binunionTIRcontra)),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',binunionTIRcontra)).
% 1.56/1.27 thf(f137,plain,(
% 1.56/1.27 ~spl21_1 | ~spl21_2),
% 1.56/1.27 inference(avatar_split_clause,[status(thm)],[f128,f134,f130])).
% 1.56/1.27 thf(f128,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ (setminus @ sK11 @ sK10))) | ($true != (in @ sK13 @ (setminus @ sK11 @ sK12)))),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.56/1.27 thf(f127,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ (setminus @ sK11 @ sK12))) | ($true != (in @ sK13 @ (setminus @ sK11 @ sK10))) | ($true != $true)),
% 1.56/1.27 inference(superposition,[status(thm)],[f80,f121])).
% 1.56/1.27 thf(f121,plain,(
% 1.56/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (binintersect @ X4 @ X3))) | ($true != (in @ X5 @ X3)) | ((in @ X5 @ X4) != $true)) )),
% 1.56/1.27 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.56/1.27 thf(f100,plain,(
% 1.56/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (binintersect @ X4 @ X3))) | ($true != (in @ X5 @ X3)) | ((in @ X5 @ X4) != $true) | ($true != $true)) )),
% 1.56/1.27 inference(definition_unfolding,[status(thm)],[f64,f85])).
% 1.56/1.27 thf(f85,plain,(
% 1.56/1.27 (binintersectI = $true)),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 thf(f64,plain,(
% 1.56/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ (binintersect @ X4 @ X3))) | (binintersectI != $true)) )),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f39])).
% 1.56/1.27 thf(f39,plain,(
% 1.56/1.27 ((binintersectI = $true) | (($true = (in @ sK2 @ sK0)) & ($true = (in @ sK2 @ sK1)) & ($true != (in @ sK2 @ (binintersect @ sK1 @ sK0))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ (binintersect @ X4 @ X3)))) | (binintersectI != $true))),
% 1.56/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f37,f38])).
% 1.56/1.27 thf(f38,plain,(
% 1.56/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ (binintersect @ X1 @ X0)) != $true)) => (($true = (in @ sK2 @ sK0)) & ($true = (in @ sK2 @ sK1)) & ($true != (in @ sK2 @ (binintersect @ sK1 @ sK0))))),
% 1.56/1.27 introduced(definition,[],[choice_axiom])).
% 1.56/1.27 thf(f37,plain,(
% 1.56/1.27 ((binintersectI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ (binintersect @ X1 @ X0)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ (binintersect @ X4 @ X3)))) | (binintersectI != $true))),
% 1.56/1.27 inference(rectify,[status(thm)],[f36])).
% 1.56/1.27 thf(f36,plain,(
% 1.56/1.27 ((binintersectI = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ X0) = $true) & ($true = (in @ X1 @ X2)) & ($true != (in @ X1 @ (binintersect @ X2 @ X0))))) & (! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ X2)) | ($true = (in @ X1 @ (binintersect @ X2 @ X0)))) | (binintersectI != $true))),
% 1.56/1.27 inference(nnf_transformation,[status(thm)],[f32])).
% 1.56/1.27 thf(f32,plain,(
% 1.56/1.27 (binintersectI = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ X2)) | ($true = (in @ X1 @ (binintersect @ X2 @ X0))))),
% 1.56/1.27 inference(flattening,[status(thm)],[f31])).
% 1.56/1.27 thf(f31,plain,(
% 1.56/1.27 ! [X0 : $i,X2 : $i,X1 : $i] : ((($true = (in @ X1 @ (binintersect @ X2 @ X0))) | ((in @ X1 @ X0) != $true)) | ($true != (in @ X1 @ X2))) <=> (binintersectI = $true)),
% 1.56/1.27 inference(ennf_transformation,[status(thm)],[f18])).
% 1.56/1.27 thf(f18,plain,(
% 1.56/1.27 ! [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X1 @ X2)) => (((in @ X1 @ X0) = $true) => ($true = (in @ X1 @ (binintersect @ X2 @ X0))))) <=> (binintersectI = $true)),
% 1.56/1.27 inference(fool_elimination,[status(thm)],[f17])).
% 1.56/1.27 thf(f17,plain,(
% 1.56/1.27 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ (binintersect @ X2 @ X0)))))),
% 1.56/1.27 inference(rectify,[status(thm)],[f1])).
% 1.56/1.27 thf(f1,axiom,(
% 1.56/1.27 (binintersectI = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 1.56/1.27 file('/export/starexec/sandbox/tmp/tmp.oIkT34Gjzy/DTF2THF_10310.p',binintersectI)).
% 1.56/1.27 thf(f80,plain,(
% 1.56/1.27 ($true != (in @ sK13 @ (binintersect @ (setminus @ sK11 @ sK10) @ (setminus @ sK11 @ sK12))))),
% 1.56/1.27 inference(cnf_transformation,[status(thm)],[f53])).
% 1.56/1.27 % SZS output end Proof for DTF2THF_10310
% 1.56/1.27 % (10505)------------------------------
% 1.56/1.27 % (10505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (10505)Termination reason: Refutation
% 1.56/1.27
% 1.56/1.27 % (10505)Memory used [KB]: 5628
% 1.56/1.27 % (10505)Time elapsed: 0.014 s
% 1.56/1.27 % (10505)Instructions burned: 12 (million)
% 1.56/1.27 % (10505)------------------------------
% 1.56/1.27 % (10505)------------------------------
% 1.56/1.27 % (10498)Success in time 0.034 s
%------------------------------------------------------------------------------