%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU752^2 : 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 : n026.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 09:36:55 AM UTC 2026
% Result : Theorem 1.74s 1.48s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of formulae : 121 ( 23 unt; 0 typ; 5 def)
% Number of atoms : 1830 ( 489 equ; 0 cnn)
% Maximal formula atoms : 12 ( 15 avg)
% Number of connectives : 2038 ( 249 ~; 194 |; 145 &;1332 @)
% ( 23 <=>; 95 =>; 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 : 39 ( 36 usr; 33 con; 0-2 aty)
% Number of variables : 301 ( 0 ^; 220 !; 81 ?; 301 :)
% 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_5,type,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
setminus: $i > $i > $i ).
thf(f171,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f139,f149,f156,f160,f163,f170]) ).
thf(f170,plain,
~ spl21_4,
inference(avatar_contradiction_clause,[status(thm)],[f169]) ).
thf(f169,plain,
( $false
| ~ spl21_4 ),
inference(subsumption_resolution,[status(thm)],[f168,f73]) ).
thf(f73,plain,
( ( in @ sK9 @ sK7 )
= $true ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( ( setminusER = $true )
& ( binunionE = $true )
& ( binintersectTELcontra = $true )
& ( binintersectTERcontra = $true )
& ( ( in @ sK6 @ ( powerset @ sK7 ) )
= $true )
& ( ( in @ sK9 @ ( setminus @ sK7 @ ( binintersect @ sK6 @ sK8 ) ) )
!= $true )
& ( $true
= ( in @ sK9 @ ( binunion @ ( setminus @ sK7 @ sK6 ) @ ( setminus @ sK7 @ sK8 ) ) ) )
& ( ( in @ sK9 @ sK7 )
= $true )
& ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) )
& ( setminusI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f31,f46,f45,f44]) ).
thf(f44,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) )
=> ( ( ( in @ sK6 @ ( powerset @ sK7 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ sK7 @ ( binintersect @ sK6 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( binunion @ ( setminus @ sK7 @ sK6 ) @ ( setminus @ sK7 @ X2 ) ) ) )
& ( ( in @ X3 @ sK7 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK7 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ sK7 @ ( binintersect @ sK6 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( binunion @ ( setminus @ sK7 @ sK6 ) @ ( setminus @ sK7 @ X2 ) ) ) )
& ( ( in @ X3 @ sK7 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK7 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK7 @ ( binintersect @ sK6 @ sK8 ) ) )
!= $true )
& ( $true
= ( in @ X3 @ ( binunion @ ( setminus @ sK7 @ sK6 ) @ ( setminus @ sK7 @ sK8 ) ) ) )
& ( ( in @ X3 @ sK7 )
= $true ) )
& ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f46,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK7 @ ( binintersect @ sK6 @ sK8 ) ) )
!= $true )
& ( $true
= ( in @ X3 @ ( binunion @ ( setminus @ sK7 @ sK6 ) @ ( setminus @ sK7 @ sK8 ) ) ) )
& ( ( in @ X3 @ sK7 )
= $true ) )
=> ( ( ( in @ sK9 @ ( setminus @ sK7 @ ( binintersect @ sK6 @ sK8 ) ) )
!= $true )
& ( $true
= ( in @ sK9 @ ( binunion @ ( setminus @ sK7 @ sK6 ) @ ( setminus @ sK7 @ sK8 ) ) ) )
& ( ( in @ sK9 @ sK7 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( setminusER = $true )
& ( binunionE = $true )
& ( binintersectTELcontra = $true )
& ( binintersectTERcontra = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) )
& ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binunionE = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( ( binunionE = $true )
=> ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
=> ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binunion @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) )
=> ( in @ X2 @ ( setminus @ X0 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binunion @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) )
=> ( in @ X2 @ ( setminus @ X0 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',demorgan1b) ).
thf(f168,plain,
( ( ( in @ sK9 @ sK7 )
!= $true )
| ~ spl21_4 ),
inference(subsumption_resolution,[status(thm)],[f167,f76]) ).
thf(f76,plain,
( ( in @ sK6 @ ( powerset @ sK7 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f167,plain,
( ( ( in @ sK6 @ ( powerset @ sK7 ) )
!= $true )
| ( ( in @ sK9 @ sK7 )
!= $true )
| ~ spl21_4 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ( ( in @ sK9 @ sK7 )
!= $true )
| ( $true != $true )
| ( ( in @ sK6 @ ( powerset @ sK7 ) )
!= $true )
| ~ spl21_4 ),
inference(superposition,[status(thm)],[f148,f72]) ).
thf(f72,plain,
( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f148,plain,
( ! [X0: $i] :
( ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK9 @ X0 )
!= $true ) )
| ~ spl21_4 ),
inference(avatar_component_clause,[status(thm)],[f147]) ).
thf(f147,definition,
( spl21_4
<=> ! [X0: $i] :
( ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK9 @ X0 )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl21_4])],[avatar_definition]) ).
thf(f163,plain,
( ~ spl21_5
| ~ spl21_1 ),
inference(avatar_split_clause,[status(thm)],[f162,f132,f153]) ).
thf(f153,definition,
( spl21_5
<=> ( $true
= ( in @ sK9 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl21_5])],[avatar_definition]) ).
thf(f132,definition,
( spl21_1
<=> ( ( in @ sK9 @ ( setminus @ sK7 @ sK8 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl21_1])],[avatar_definition]) ).
thf(f162,plain,
( ( $true
!= ( in @ sK9 @ sK8 ) )
| ~ spl21_1 ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK9 @ sK8 ) )
| ~ spl21_1 ),
inference(superposition,[status(thm)],[f122,f134]) ).
thf(f134,plain,
( ( ( in @ sK9 @ ( setminus @ sK7 @ sK8 ) )
= $true )
| ~ spl21_1 ),
inference(avatar_component_clause,[status(thm)],[f132]) ).
thf(f122,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f70,f80]) ).
thf(f80,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f70,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( ( in @ sK4 @ sK3 )
= $true )
& ( $true
= ( in @ sK4 @ ( setminus @ sK5 @ sK3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f41,f42]) ).
thf(f42,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
= $true )
& ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true ) )
=> ( ( ( in @ sK4 @ sK3 )
= $true )
& ( $true
= ( in @ sK4 @ ( setminus @ sK5 @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
= $true )
& ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',setminusER) ).
thf(f160,plain,
( ~ spl21_2
| ~ spl21_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f159]) ).
thf(f159,plain,
( $false
| ~ spl21_2
| ~ spl21_3 ),
inference(subsumption_resolution,[status(thm)],[f158,f145]) ).
thf(f145,plain,
( ( $true
= ( in @ sK9 @ sK6 ) )
| ~ spl21_3 ),
inference(avatar_component_clause,[status(thm)],[f143]) ).
thf(f143,definition,
( spl21_3
<=> ( $true
= ( in @ sK9 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl21_3])],[avatar_definition]) ).
thf(f158,plain,
( ( $true
!= ( in @ sK9 @ sK6 ) )
| ~ spl21_2 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK9 @ sK6 ) )
| ~ spl21_2 ),
inference(superposition,[status(thm)],[f122,f138]) ).
thf(f138,plain,
( ( $true
= ( in @ sK9 @ ( setminus @ sK7 @ sK6 ) ) )
| ~ spl21_2 ),
inference(avatar_component_clause,[status(thm)],[f136]) ).
thf(f136,definition,
( spl21_2
<=> ( $true
= ( in @ sK9 @ ( setminus @ sK7 @ sK6 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl21_2])],[avatar_definition]) ).
thf(f156,plain,
( spl21_4
| spl21_5 ),
inference(avatar_split_clause,[status(thm)],[f151,f153,f147]) ).
thf(f151,plain,
! [X0: $i] :
( ( ( in @ sK9 @ X0 )
!= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( in @ sK9 @ sK8 ) )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
! [X0: $i] :
( ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( in @ sK9 @ sK8 ) )
| ( $true != $true )
| ( ( in @ sK9 @ X0 )
!= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f123,f128]) ).
thf(f128,plain,
( ( in @ sK9 @ ( binintersect @ sK6 @ sK8 ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f127,f73]) ).
thf(f127,plain,
( ( ( in @ sK9 @ ( binintersect @ sK6 @ sK8 ) )
= $true )
| ( ( in @ sK9 @ sK7 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ( ( in @ sK9 @ ( binintersect @ sK6 @ sK8 ) )
= $true )
| ( $true != $true )
| ( ( in @ sK9 @ sK7 )
!= $true ) ),
inference(superposition,[status(thm)],[f75,f121]) ).
thf(f121,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
= $true )
| ( $true
= ( in @ X3 @ X4 ) )
| ( ( in @ X3 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X3 @ X5 )
!= $true )
| ( $true
= ( in @ X3 @ X4 ) )
| ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f87,f71]) ).
thf(f71,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f87,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ X4 ) )
| ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( setminusI = $true )
| ( ( ( in @ sK14 @ sK15 )
!= $true )
& ( ( in @ sK14 @ sK16 )
= $true )
& ( ( in @ sK14 @ ( setminus @ sK16 @ sK15 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ X4 ) )
| ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f55,f56]) ).
thf(f56,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) )
=> ( ( ( in @ sK14 @ sK15 )
!= $true )
& ( ( in @ sK14 @ sK16 )
= $true )
& ( ( in @ sK14 @ ( setminus @ sK16 @ sK15 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f55,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ X4 ) )
| ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( setminusI = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( setminusI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f32]) ).
thf(f32,plain,
( ( setminusI = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( setminusI = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ~ ( in @ X1 @ X0 )
=> ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setminusI
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',setminusI) ).
thf(f75,plain,
( ( in @ sK9 @ ( setminus @ sK7 @ ( binintersect @ sK6 @ sK8 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f96,f77]) ).
thf(f77,plain,
binintersectTERcontra = $true,
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( binintersectTERcontra != $true ) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( binintersectTERcontra != $true ) )
& ( ( binintersectTERcontra = $true )
| ( ( ( in @ sK17 @ ( powerset @ sK18 ) )
= $true )
& ( $true
= ( in @ sK20 @ ( binintersect @ sK17 @ sK19 ) ) )
& ( ( in @ sK20 @ sK18 )
= $true )
& ( $true
!= ( in @ sK20 @ sK19 ) )
& ( ( in @ sK19 @ ( powerset @ sK18 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20])],[f59,f62,f61,f60]) ).
thf(f60,plain,
( ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( binintersect @ X4 @ X6 ) ) )
& ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ X7 @ X6 ) ) )
& ( ( in @ X6 @ ( powerset @ X5 ) )
= $true ) ) )
=> ( ( ( in @ sK17 @ ( powerset @ sK18 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( binintersect @ sK17 @ X6 ) ) )
& ( ( in @ X7 @ sK18 )
= $true )
& ( $true
!= ( in @ X7 @ X6 ) ) )
& ( ( in @ X6 @ ( powerset @ sK18 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f61,plain,
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( binintersect @ sK17 @ X6 ) ) )
& ( ( in @ X7 @ sK18 )
= $true )
& ( $true
!= ( in @ X7 @ X6 ) ) )
& ( ( in @ X6 @ ( powerset @ sK18 ) )
= $true ) )
=> ( ? [X7: $i] :
( ( ( in @ X7 @ ( binintersect @ sK17 @ sK19 ) )
= $true )
& ( ( in @ X7 @ sK18 )
= $true )
& ( ( in @ X7 @ sK19 )
!= $true ) )
& ( ( in @ sK19 @ ( powerset @ sK18 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f62,plain,
( ? [X7: $i] :
( ( ( in @ X7 @ ( binintersect @ sK17 @ sK19 ) )
= $true )
& ( ( in @ X7 @ sK18 )
= $true )
& ( ( in @ X7 @ sK19 )
!= $true ) )
=> ( ( $true
= ( in @ sK20 @ ( binintersect @ sK17 @ sK19 ) ) )
& ( ( in @ sK20 @ sK18 )
= $true )
& ( $true
!= ( in @ sK20 @ sK19 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f59,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( binintersectTERcontra != $true ) )
& ( ( binintersectTERcontra = $true )
| ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( binintersect @ X4 @ X6 ) ) )
& ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ X7 @ X6 ) ) )
& ( ( in @ X6 @ ( powerset @ X5 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( binintersectTERcontra != $true ) )
& ( ( binintersectTERcontra = $true )
| ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
<=> ( binintersectTERcontra = $true ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) )
<=> ( binintersectTERcontra = $true ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X2 )
!= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) )
<=> ( binintersectTERcontra = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( binintersectTERcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X2 )
!= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( binintersectTERcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( binintersectTERcontra
= ( ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',binintersectTERcontra) ).
thf(f149,plain,
( spl21_3
| spl21_4 ),
inference(avatar_split_clause,[status(thm)],[f141,f147,f143]) ).
thf(f141,plain,
! [X0: $i] :
( ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK9 @ X0 )
!= $true )
| ( $true
= ( in @ sK9 @ sK6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
! [X0: $i] :
( ( $true
= ( in @ sK9 @ sK6 ) )
| ( ( in @ sK9 @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f120,f128]) ).
thf(f120,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f86,f78]) ).
thf(f78,plain,
binintersectTELcontra = $true,
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( binintersectTELcontra != $true ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( binintersectTELcontra != $true ) )
& ( ( binintersectTELcontra = $true )
| ( ( ( in @ sK11 @ ( powerset @ sK10 ) )
= $true )
& ( $true
= ( in @ sK13 @ ( binintersect @ sK11 @ sK12 ) ) )
& ( ( in @ sK13 @ sK11 )
!= $true )
& ( $true
= ( in @ sK13 @ sK10 ) )
& ( ( in @ sK12 @ ( powerset @ sK10 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f49,f52,f51,f50]) ).
thf(f50,plain,
( ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ ( binintersect @ X5 @ X6 ) )
= $true )
& ( $true
!= ( in @ X7 @ X5 ) )
& ( $true
= ( in @ X7 @ X4 ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X4 ) ) ) ) )
=> ( ( ( in @ sK11 @ ( powerset @ sK10 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ ( binintersect @ sK11 @ X6 ) )
= $true )
& ( ( in @ X7 @ sK11 )
!= $true )
& ( ( in @ X7 @ sK10 )
= $true ) )
& ( ( in @ X6 @ ( powerset @ sK10 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
( ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ ( binintersect @ sK11 @ X6 ) )
= $true )
& ( ( in @ X7 @ sK11 )
!= $true )
& ( ( in @ X7 @ sK10 )
= $true ) )
& ( ( in @ X6 @ ( powerset @ sK10 ) )
= $true ) )
=> ( ? [X7: $i] :
( ( ( in @ X7 @ ( binintersect @ sK11 @ sK12 ) )
= $true )
& ( ( in @ X7 @ sK11 )
!= $true )
& ( ( in @ X7 @ sK10 )
= $true ) )
& ( ( in @ sK12 @ ( powerset @ sK10 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f52,plain,
( ? [X7: $i] :
( ( ( in @ X7 @ ( binintersect @ sK11 @ sK12 ) )
= $true )
& ( ( in @ X7 @ sK11 )
!= $true )
& ( ( in @ X7 @ sK10 )
= $true ) )
=> ( ( $true
= ( in @ sK13 @ ( binintersect @ sK11 @ sK12 ) ) )
& ( ( in @ sK13 @ sK11 )
!= $true )
& ( $true
= ( in @ sK13 @ sK10 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f49,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( binintersectTELcontra != $true ) )
& ( ( binintersectTELcontra = $true )
| ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ ( binintersect @ X5 @ X6 ) )
= $true )
& ( $true
!= ( in @ X7 @ X5 ) )
& ( $true
= ( in @ X7 @ X4 ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X4 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( binintersectTELcontra != $true ) )
& ( ( binintersectTELcontra = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X3 @ X1 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
<=> ( binintersectTELcontra = $true ) ),
inference(flattening,[status(thm)],[f34]) ).
thf(f34,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) )
<=> ( binintersectTELcontra = $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X1 )
!= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) )
<=> ( binintersectTELcontra = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X1 )
!= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) )
<=> ( binintersectTELcontra = $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 @ X1 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) )
= binintersectTELcontra ),
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 @ X3 )
=> ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ) ) ) )
= binintersectTELcontra ),
file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',binintersectTELcontra) ).
thf(f139,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[status(thm)],[f130,f136,f132]) ).
thf(f130,plain,
( ( ( in @ sK9 @ ( setminus @ sK7 @ sK8 ) )
= $true )
| ( $true
= ( in @ sK9 @ ( setminus @ sK7 @ sK6 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
( ( ( in @ sK9 @ ( setminus @ sK7 @ sK8 ) )
= $true )
| ( $true != $true )
| ( $true
= ( in @ sK9 @ ( setminus @ sK7 @ sK6 ) ) ) ),
inference(superposition,[status(thm)],[f124,f74]) ).
thf(f74,plain,
( $true
= ( in @ sK9 @ ( binunion @ ( setminus @ sK7 @ sK6 ) @ ( setminus @ sK7 @ sK8 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f124,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f67,f79]) ).
thf(f79,plain,
binunionE = $true,
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f67,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( $true
= ( in @ X0 @ X2 ) )
| ( binunionE != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ sK2 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f37,f38]) ).
thf(f38,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X4 @ X5 ) ) )
& ( $true
!= ( in @ X3 @ X4 ) )
& ( ( in @ X3 @ X5 )
!= $true ) )
=> ( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X4 @ X5 ) ) )
& ( $true
!= ( in @ X3 @ X4 ) )
& ( ( in @ X3 @ X5 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
<=> ( binunionE = $true ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binunionE
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',binunionE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU752^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:33:10 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.47 ---- Original DTF file ---
% 0.18/0.48 thf(spec,logic,$$dhol).
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 % File : SEU752^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.48 % Domain : Set Theory
% 0.18/0.48 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.18/0.48 % Version : Especial > Reduced > Especial.
% 0.18/0.48 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.18/0.48 % (! x:i.in x A -> in x (binunion (setminus A X) (setminus A Y)) ->
% 0.18/0.48 % in x (setminus A (binintersect X Y)))))
% 0.18/0.48
% 0.18/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.48 % Source : [Bro08]
% 0.18/0.48 % Names : ZFC254l [Bro08]
% 0.18/0.48
% 0.18/0.48 % Status : Theorem
% 0.18/0.48 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 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 v5.1.0, 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
% 0.18/0.48 % Syntax : Number of formulae : 16 ( 5 unt; 10 typ; 5 def)
% 0.18/0.48 % Number of atoms : 38 ( 5 equ; 0 cnn)
% 0.18/0.48 % Maximal formula atoms : 10 ( 6 avg)
% 0.18/0.48 % Number of connectives : 100 ( 6 ~; 1 |; 0 &; 72 @)
% 0.18/0.48 % ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% 0.18/0.48 % Maximal formula depth : 19 ( 4 avg)
% 0.18/0.48 % Number of types : 2 ( 0 usr)
% 0.18/0.48 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.18/0.48 % Number of symbols : 11 ( 10 usr; 5 con; 0-2 aty)
% 0.18/0.48 % Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% 0.18/0.48 % SPC : TH0_THM_EQU_NAR
% 0.18/0.48
% 0.18/0.48 % Comments : http://mathgate.info/detsetitem.php?id=313
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 thf(in_type,type,
% 0.18/0.48 in: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(powerset_type,type,
% 0.18/0.48 powerset: $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(binunion_type,type,
% 0.18/0.48 binunion: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(binunionE_type,type,
% 0.18/0.48 binunionE: $o ).
% 0.18/0.48
% 0.18/0.48 thf(binunionE,definition,
% 0.18/0.48 ( binunionE
% 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.18/0.48 => ( ( in @ Xx @ A )
% 0.18/0.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(binintersect_type,type,
% 0.18/0.48 binintersect: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(setminus_type,type,
% 0.18/0.48 setminus: $i > $i > $i ).
% 0.18/0.48
% 0.18/0.48 thf(setminusI_type,type,
% 0.18/0.48 setminusI: $o ).
% 0.18/0.48
% 0.18/0.48 thf(setminusI,definition,
% 0.18/0.48 ( setminusI
% 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.48 ( ( in @ Xx @ A )
% 0.18/0.48 => ( ~ ( in @ Xx @ B )
% 0.18/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(setminusER_type,type,
% 0.18/0.48 setminusER: $o ).
% 0.18/0.48
% 0.18/0.48 thf(setminusER,definition,
% 0.18/0.48 ( setminusER
% 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(binintersectTELcontra_type,type,
% 0.18/0.48 binintersectTELcontra: $o ).
% 0.18/0.48
% 0.18/0.48 thf(binintersectTELcontra,definition,
% 0.18/0.48 ( binintersectTELcontra
% 0.18/0.48 = ( ! [A: $i,X: $i] :
% 0.18/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.18/0.48 => ! [Y: $i] :
% 0.18/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.18/0.48 => ! [Xx: $i] :
% 0.18/0.48 ( ( in @ Xx @ A )
% 0.18/0.48 => ( ~ ( in @ Xx @ X )
% 0.18/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(binintersectTERcontra_type,type,
% 0.18/0.48 binintersectTERcontra: $o ).
% 0.18/0.48
% 0.18/0.48 thf(binintersectTERcontra,definition,
% 0.18/0.48 ( binintersectTERcontra
% 0.18/0.48 = ( ! [A: $i,X: $i] :
% 0.18/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.18/0.48 => ! [Y: $i] :
% 0.18/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.18/0.48 => ! [Xx: $i] :
% 0.18/0.48 ( ( in @ Xx @ A )
% 0.18/0.48 => ( ~ ( in @ Xx @ Y )
% 0.18/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(demorgan1b,conjecture,
% 0.18/0.48 ( binunionE
% 0.18/0.48 => ( setminusI
% 0.18/0.48 => ( setminusER
% 0.18/0.48 => ( binintersectTELcontra
% 0.18/0.48 => ( binintersectTERcontra
% 0.18/0.48 => ! [A: $i,X: $i] :
% 0.18/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.18/0.48 => ! [Y: $i] :
% 0.18/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.18/0.48 => ! [Xx: $i] :
% 0.18/0.48 ( ( in @ Xx @ A )
% 0.18/0.48 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.18/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 ------------------------
% 1.74/1.43 ---- Embedded in THF ---
% 1.74/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.74/1.44 %%% Generated on Tue Feb 24 12:33:11 EST 2026
% 1.74/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.74/1.44 %%% Logic specification used:
% 1.74/1.44 %%% thf(spec, logic, $$dhol).
% 1.74/1.44
% 1.74/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2DTF21928.p
% See solution above
% 1.74/1.44 ------------------------
% 1.74/1.44 ---- Cleaned THF ---
% 1.74/1.45 thf(in_type,type,
% 1.74/1.45 in: $i > $i > $o ).
% 1.74/1.45
% 1.74/1.45 thf(powerset_type,type,
% 1.74/1.45 powerset: $i > $i ).
% 1.74/1.45
% 1.74/1.45 thf(binunion_type,type,
% 1.74/1.45 binunion: $i > $i > $i ).
% 1.74/1.45
% 1.74/1.45 thf(binunionE_type,type,
% 1.74/1.45 binunionE: $o ).
% 1.74/1.45
% 1.74/1.45 thf(binunionE,definition,
% 1.74/1.45 ( binunionE
% 1.74/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.74/1.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 1.74/1.45 => ( ( in @ Xx @ A )
% 1.74/1.45 | ( in @ Xx @ B ) ) ) ) ) ).
% 1.74/1.45
% 1.74/1.45 thf(binintersect_type,type,
% 1.74/1.45 binintersect: $i > $i > $i ).
% 1.74/1.45
% 1.74/1.45 thf(setminus_type,type,
% 1.74/1.45 setminus: $i > $i > $i ).
% 1.74/1.45
% 1.74/1.45 thf(setminusI_type,type,
% 1.74/1.45 setminusI: $o ).
% 1.74/1.45
% 1.74/1.45 thf(setminusI,definition,
% 1.74/1.45 ( setminusI
% 1.74/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.74/1.45 ( ( in @ Xx @ A )
% 1.74/1.45 => ( ~ ( in @ Xx @ B )
% 1.74/1.45 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.74/1.45
% 1.74/1.45 thf(setminusER_type,type,
% 1.74/1.45 setminusER: $o ).
% 1.74/1.45
% 1.74/1.45 thf(setminusER,definition,
% 1.74/1.45 ( setminusER
% 1.74/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.74/1.45 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.74/1.45 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.74/1.45
% 1.74/1.45 thf(binintersectTELcontra_type,type,
% 1.74/1.45 binintersectTELcontra: $o ).
% 1.74/1.45
% 1.74/1.45 thf(binintersectTELcontra,definition,
% 1.74/1.45 ( binintersectTELcontra
% 1.74/1.45 = ( ! [A: $i,X: $i] :
% 1.74/1.45 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.45 => ! [Y: $i] :
% 1.74/1.45 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.45 => ! [Xx: $i] :
% 1.74/1.45 ( ( in @ Xx @ A )
% 1.74/1.45 => ( ~ ( in @ Xx @ X )
% 1.74/1.45 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 1.74/1.45
% 1.74/1.45 thf(binintersectTERcontra_type,type,
% 1.74/1.45 binintersectTERcontra: $o ).
% 1.74/1.45
% 1.74/1.45 thf(binintersectTERcontra,definition,
% 1.74/1.45 ( binintersectTERcontra
% 1.74/1.45 = ( ! [A: $i,X: $i] :
% 1.74/1.45 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.45 => ! [Y: $i] :
% 1.74/1.45 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.45 => ! [Xx: $i] :
% 1.74/1.45 ( ( in @ Xx @ A )
% 1.74/1.45 => ( ~ ( in @ Xx @ Y )
% 1.74/1.45 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 1.74/1.45
% 1.74/1.45 thf(demorgan1b,conjecture,
% 1.74/1.45 ( binunionE
% 1.74/1.45 => ( setminusI
% 1.74/1.45 => ( setminusER
% 1.74/1.45 => ( binintersectTELcontra
% 1.74/1.45 => ( binintersectTERcontra
% 1.74/1.45 => ! [A: $i,X: $i] :
% 1.74/1.45 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.45 => ! [Y: $i] :
% 1.74/1.45 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.45 => ! [Xx: $i] :
% 1.74/1.45 ( ( in @ Xx @ A )
% 1.74/1.45 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 1.74/1.45 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.74/1.45 ------------------------
% 1.74/1.47 % (22064)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21928 for (2999ds/2Mi)
% 1.74/1.47 % (22063)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_21928 for (2999ds/27Mi)
% 1.74/1.47 % (22065)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_21928 for (2999ds/2Mi)
% 1.74/1.47 % (22061)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21928 for (2999ds/183Mi)
% 1.74/1.47 % (22067)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21928 for (2999ds/18Mi)
% 1.74/1.47 % (22062)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_21928 for (2999ds/4Mi)
% 1.74/1.47 % (22066)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_21928 for (2999ds/275Mi)
% 1.74/1.47 % (22064)Instruction limit reached!
% 1.74/1.47 % (22064)------------------------------
% 1.74/1.47 % (22064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (22064)Termination reason: Unknown
% 1.74/1.47 % (22064)Termination phase: Property scanning
% 1.74/1.47 % (22065)Instruction limit reached!
% 1.74/1.47 % (22065)------------------------------
% 1.74/1.47 % (22065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (22065)Termination reason: Unknown
% 1.74/1.47 % (22065)Termination phase: Property scanning
% 1.74/1.47
% 1.74/1.47 % (22065)Memory used [KB]: 1023
% 1.74/1.47 % (22065)Time elapsed: 0.003 s
% 1.74/1.47 % (22065)Instructions burned: 3 (million)
% 1.74/1.47 % (22065)------------------------------
% 1.74/1.47 % (22065)------------------------------
% 1.74/1.47
% 1.74/1.47 % (22064)Memory used [KB]: 1023
% 1.74/1.47 % (22064)Time elapsed: 0.003 s
% 1.74/1.47 % (22064)Instructions burned: 3 (million)
% 1.74/1.47 % (22064)------------------------------
% 1.74/1.47 % (22064)------------------------------
% 1.74/1.47 % (22062)Instruction limit reached!
% 1.74/1.47 % (22062)------------------------------
% 1.74/1.47 % (22062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (22062)Termination reason: Unknown
% 1.74/1.47 % (22062)Termination phase: Property scanning
% 1.74/1.47
% 1.74/1.47 % (22062)Memory used [KB]: 1023
% 1.74/1.47 % (22062)Time elapsed: 0.004 s
% 1.74/1.47 % (22062)Instructions burned: 5 (million)
% 1.74/1.47 % (22062)------------------------------
% 1.74/1.47 % (22062)------------------------------
% 1.74/1.47 % (22066)First to succeed.
% 1.74/1.47 % (22067)Instruction limit reached!
% 1.74/1.47 % (22067)------------------------------
% 1.74/1.47 % (22067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (22067)Termination reason: Unknown
% 1.74/1.47 % (22067)Termination phase: Saturation
% 1.74/1.48
% 1.74/1.48 % (22067)Memory used [KB]: 5628
% 1.74/1.48 % (22067)Time elapsed: 0.011 s
% 1.74/1.48 % (22067)Instructions burned: 18 (million)
% 1.74/1.48 % (22067)------------------------------
% 1.74/1.48 % (22067)------------------------------
% 1.74/1.48 % (22066)Refutation found. Thanks to Tanya!
% 1.74/1.48 % SZS status Theorem for DTF2THF_21928
% 1.74/1.48 % SZS output start Proof for DTF2THF_21928
% 1.74/1.48 thf(func_def_0, type, in: $i > $i > $o).
% 1.74/1.48 thf(func_def_1, type, powerset: $i > $i).
% 1.74/1.48 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.74/1.48 thf(func_def_5, type, binintersect: $i > $i > $i).
% 1.74/1.48 thf(func_def_6, type, setminus: $i > $i > $i).
% 1.74/1.48 thf(f171,plain,(
% 1.74/1.48 $false),
% 1.74/1.48 inference(avatar_sat_refutation,[status(thm)],[f139,f149,f156,f160,f163,f170])).
% 1.74/1.48 thf(f170,plain,(
% 1.74/1.48 ~spl21_4),
% 1.74/1.48 inference(avatar_contradiction_clause,[status(thm)],[f169])).
% 1.74/1.48 thf(f169,plain,(
% 1.74/1.48 $false | ~spl21_4),
% 1.74/1.48 inference(subsumption_resolution,[status(thm)],[f168,f73])).
% 1.74/1.48 thf(f73,plain,(
% 1.74/1.48 ((in @ sK9 @ sK7) = $true)),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f47,plain,(
% 1.74/1.48 (setminusER = $true) & (binunionE = $true) & (binintersectTELcontra = $true) & (binintersectTERcontra = $true) & (((in @ sK6 @ (powerset @ sK7)) = $true) & ((((in @ sK9 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true) & ($true = (in @ sK9 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8)))) & ((in @ sK9 @ sK7) = $true)) & ($true = (in @ sK8 @ (powerset @ sK7))))) & (setminusI = $true)),
% 1.74/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f31,f46,f45,f44])).
% 1.74/1.48 thf(f44,plain,(
% 1.74/1.48 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (($true != (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) & ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true))) => (((in @ sK6 @ (powerset @ sK7)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (($true != (in @ X3 @ (setminus @ sK7 @ (binintersect @ sK6 @ X2)))) & ($true = (in @ X3 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ X2)))) & ((in @ X3 @ sK7) = $true)) & ((in @ X2 @ (powerset @ sK7)) = $true)))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f45,plain,(
% 1.74/1.48 ? [X2 : $i] : (? [X3 : $i] : (($true != (in @ X3 @ (setminus @ sK7 @ (binintersect @ sK6 @ X2)))) & ($true = (in @ X3 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ X2)))) & ((in @ X3 @ sK7) = $true)) & ((in @ X2 @ (powerset @ sK7)) = $true)) => (? [X3 : $i] : (((in @ X3 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true) & ($true = (in @ X3 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8)))) & ((in @ X3 @ sK7) = $true)) & ($true = (in @ sK8 @ (powerset @ sK7))))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f46,plain,(
% 1.74/1.48 ? [X3 : $i] : (((in @ X3 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true) & ($true = (in @ X3 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8)))) & ((in @ X3 @ sK7) = $true)) => (((in @ sK9 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true) & ($true = (in @ sK9 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8)))) & ((in @ sK9 @ sK7) = $true))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f31,plain,(
% 1.74/1.48 (setminusER = $true) & (binunionE = $true) & (binintersectTELcontra = $true) & (binintersectTERcontra = $true) & ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (($true != (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) & ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true))) & (setminusI = $true)),
% 1.74/1.48 inference(flattening,[status(thm)],[f30])).
% 1.74/1.48 thf(f30,plain,(
% 1.74/1.48 ((((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((($true != (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) & ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true)) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ($true = (in @ X0 @ (powerset @ X1)))) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (setminusER = $true)) & (setminusI = $true)) & (binunionE = $true)),
% 1.74/1.48 inference(ennf_transformation,[status(thm)],[f20])).
% 1.74/1.48 thf(f20,plain,(
% 1.74/1.48 ~((binunionE = $true) => ((setminusI = $true) => ((setminusER = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) => ($true = (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))))))))))))),
% 1.74/1.48 inference(fool_elimination,[status(thm)],[f19])).
% 1.74/1.48 thf(f19,plain,(
% 1.74/1.48 ~(binunionE => (setminusI => (setminusER => (binintersectTELcontra => (binintersectTERcontra => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) => (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))))))))))))),
% 1.74/1.48 inference(rectify,[status(thm)],[f7])).
% 1.74/1.48 thf(f7,negated_conjecture,(
% 1.74/1.48 ~(binunionE => (setminusI => (setminusER => (binintersectTELcontra => (binintersectTERcontra => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binunion @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4))) => (in @ X2 @ (setminus @ X0 @ (binintersect @ X3 @ X4))))))))))))),
% 1.74/1.48 inference(negated_conjecture,[status(cth)],[f6])).
% 1.74/1.48 thf(f6,conjecture,(
% 1.74/1.48 binunionE => (setminusI => (setminusER => (binintersectTELcontra => (binintersectTERcontra => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binunion @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4))) => (in @ X2 @ (setminus @ X0 @ (binintersect @ X3 @ X4)))))))))))),
% 1.74/1.48 file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',demorgan1b)).
% 1.74/1.48 thf(f168,plain,(
% 1.74/1.48 ((in @ sK9 @ sK7) != $true) | ~spl21_4),
% 1.74/1.48 inference(subsumption_resolution,[status(thm)],[f167,f76])).
% 1.74/1.48 thf(f76,plain,(
% 1.74/1.48 ((in @ sK6 @ (powerset @ sK7)) = $true)),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f167,plain,(
% 1.74/1.48 ((in @ sK6 @ (powerset @ sK7)) != $true) | ((in @ sK9 @ sK7) != $true) | ~spl21_4),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.74/1.48 thf(f166,plain,(
% 1.74/1.48 ((in @ sK9 @ sK7) != $true) | ($true != $true) | ((in @ sK6 @ (powerset @ sK7)) != $true) | ~spl21_4),
% 1.74/1.48 inference(superposition,[status(thm)],[f148,f72])).
% 1.74/1.48 thf(f72,plain,(
% 1.74/1.48 ($true = (in @ sK8 @ (powerset @ sK7)))),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f148,plain,(
% 1.74/1.48 ( ! [X0 : $i] : (((in @ sK8 @ (powerset @ X0)) != $true) | ((in @ sK6 @ (powerset @ X0)) != $true) | ((in @ sK9 @ X0) != $true)) ) | ~spl21_4),
% 1.74/1.48 inference(avatar_component_clause,[status(thm)],[f147])).
% 1.74/1.48 thf(f147,definition,(
% 1.74/1.48 spl21_4 <=> ! [X0 : $i] : (((in @ sK6 @ (powerset @ X0)) != $true) | ((in @ sK9 @ X0) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true))),
% 1.74/1.48 introduced(definition,[new_symbols(naming,[spl21_4])],[avatar_definition])).
% 1.74/1.48 thf(f163,plain,(
% 1.74/1.48 ~spl21_5 | ~spl21_1),
% 1.74/1.48 inference(avatar_split_clause,[status(thm)],[f162,f132,f153])).
% 1.74/1.48 thf(f153,definition,(
% 1.74/1.48 spl21_5 <=> ($true = (in @ sK9 @ sK8))),
% 1.74/1.48 introduced(definition,[new_symbols(naming,[spl21_5])],[avatar_definition])).
% 1.74/1.48 thf(f132,definition,(
% 1.74/1.48 spl21_1 <=> ((in @ sK9 @ (setminus @ sK7 @ sK8)) = $true)),
% 1.74/1.48 introduced(definition,[new_symbols(naming,[spl21_1])],[avatar_definition])).
% 1.74/1.48 thf(f162,plain,(
% 1.74/1.48 ($true != (in @ sK9 @ sK8)) | ~spl21_1),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 1.74/1.48 thf(f161,plain,(
% 1.74/1.48 ($true != $true) | ($true != (in @ sK9 @ sK8)) | ~spl21_1),
% 1.74/1.48 inference(superposition,[status(thm)],[f122,f134])).
% 1.74/1.48 thf(f134,plain,(
% 1.74/1.48 ((in @ sK9 @ (setminus @ sK7 @ sK8)) = $true) | ~spl21_1),
% 1.74/1.48 inference(avatar_component_clause,[status(thm)],[f132])).
% 1.74/1.48 thf(f122,plain,(
% 1.74/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) | ((in @ X1 @ X0) != $true)) )),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.74/1.48 thf(f101,plain,(
% 1.74/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X1 @ (setminus @ X2 @ X0)) != $true) | ((in @ X1 @ X0) != $true)) )),
% 1.74/1.48 inference(definition_unfolding,[status(thm)],[f70,f80])).
% 1.74/1.48 thf(f80,plain,(
% 1.74/1.48 (setminusER = $true)),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f70,plain,(
% 1.74/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (setminus @ X2 @ X0)) != $true) | (setminusER != $true)) )),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f43])).
% 1.74/1.48 thf(f43,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (setminus @ X2 @ X0)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | (((in @ sK4 @ sK3) = $true) & ($true = (in @ sK4 @ (setminus @ sK5 @ sK3)))))),
% 1.74/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f41,f42])).
% 1.74/1.48 thf(f42,plain,(
% 1.74/1.48 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) = $true) & ((in @ X4 @ (setminus @ X5 @ X3)) = $true)) => (((in @ sK4 @ sK3) = $true) & ($true = (in @ sK4 @ (setminus @ sK5 @ sK3))))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f41,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (setminus @ X2 @ X0)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) = $true) & ((in @ X4 @ (setminus @ X5 @ X3)) = $true)))),
% 1.74/1.48 inference(rectify,[status(thm)],[f40])).
% 1.74/1.48 thf(f40,plain,(
% 1.74/1.48 (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ (setminus @ X0 @ X1)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ (setminus @ X0 @ X1)) = $true)))),
% 1.74/1.48 inference(nnf_transformation,[status(thm)],[f27])).
% 1.74/1.48 thf(f27,plain,(
% 1.74/1.48 ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ (setminus @ X0 @ X1)) != $true)) <=> (setminusER = $true)),
% 1.74/1.48 inference(ennf_transformation,[status(thm)],[f22])).
% 1.74/1.48 thf(f22,plain,(
% 1.74/1.48 ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (setminus @ X0 @ X1)) = $true) => ((in @ X2 @ X1) != $true)) <=> (setminusER = $true)),
% 1.74/1.48 inference(flattening,[status(thm)],[f14])).
% 1.74/1.48 thf(f14,plain,(
% 1.74/1.48 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setminus @ X0 @ X1)) = $true) => ~((in @ X2 @ X1) = $true)) <=> (setminusER = $true)),
% 1.74/1.48 inference(fool_elimination,[status(thm)],[f13])).
% 1.74/1.48 thf(f13,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.74/1.48 inference(rectify,[status(thm)],[f3])).
% 1.74/1.48 thf(f3,axiom,(
% 1.74/1.48 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.74/1.48 file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',setminusER)).
% 1.74/1.48 thf(f160,plain,(
% 1.74/1.48 ~spl21_2 | ~spl21_3),
% 1.74/1.48 inference(avatar_contradiction_clause,[status(thm)],[f159])).
% 1.74/1.48 thf(f159,plain,(
% 1.74/1.48 $false | (~spl21_2 | ~spl21_3)),
% 1.74/1.48 inference(subsumption_resolution,[status(thm)],[f158,f145])).
% 1.74/1.48 thf(f145,plain,(
% 1.74/1.48 ($true = (in @ sK9 @ sK6)) | ~spl21_3),
% 1.74/1.48 inference(avatar_component_clause,[status(thm)],[f143])).
% 1.74/1.48 thf(f143,definition,(
% 1.74/1.48 spl21_3 <=> ($true = (in @ sK9 @ sK6))),
% 1.74/1.48 introduced(definition,[new_symbols(naming,[spl21_3])],[avatar_definition])).
% 1.74/1.48 thf(f158,plain,(
% 1.74/1.48 ($true != (in @ sK9 @ sK6)) | ~spl21_2),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.74/1.48 thf(f157,plain,(
% 1.74/1.48 ($true != $true) | ($true != (in @ sK9 @ sK6)) | ~spl21_2),
% 1.74/1.48 inference(superposition,[status(thm)],[f122,f138])).
% 1.74/1.48 thf(f138,plain,(
% 1.74/1.48 ($true = (in @ sK9 @ (setminus @ sK7 @ sK6))) | ~spl21_2),
% 1.74/1.48 inference(avatar_component_clause,[status(thm)],[f136])).
% 1.74/1.48 thf(f136,definition,(
% 1.74/1.48 spl21_2 <=> ($true = (in @ sK9 @ (setminus @ sK7 @ sK6)))),
% 1.74/1.48 introduced(definition,[new_symbols(naming,[spl21_2])],[avatar_definition])).
% 1.74/1.48 thf(f156,plain,(
% 1.74/1.48 spl21_4 | spl21_5),
% 1.74/1.48 inference(avatar_split_clause,[status(thm)],[f151,f153,f147])).
% 1.74/1.48 thf(f151,plain,(
% 1.74/1.48 ( ! [X0 : $i] : (((in @ sK9 @ X0) != $true) | ((in @ sK6 @ (powerset @ X0)) != $true) | ($true = (in @ sK9 @ sK8)) | ((in @ sK8 @ (powerset @ X0)) != $true)) )),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.74/1.48 thf(f150,plain,(
% 1.74/1.48 ( ! [X0 : $i] : (((in @ sK8 @ (powerset @ X0)) != $true) | ($true = (in @ sK9 @ sK8)) | ($true != $true) | ((in @ sK9 @ X0) != $true) | ((in @ sK6 @ (powerset @ X0)) != $true)) )),
% 1.74/1.48 inference(superposition,[status(thm)],[f123,f128])).
% 1.74/1.48 thf(f128,plain,(
% 1.74/1.48 ((in @ sK9 @ (binintersect @ sK6 @ sK8)) = $true)),
% 1.74/1.48 inference(subsumption_resolution,[status(thm)],[f127,f73])).
% 1.74/1.48 thf(f127,plain,(
% 1.74/1.48 ((in @ sK9 @ (binintersect @ sK6 @ sK8)) = $true) | ((in @ sK9 @ sK7) != $true)),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.74/1.48 thf(f126,plain,(
% 1.74/1.48 ((in @ sK9 @ (binintersect @ sK6 @ sK8)) = $true) | ($true != $true) | ((in @ sK9 @ sK7) != $true)),
% 1.74/1.48 inference(superposition,[status(thm)],[f75,f121])).
% 1.74/1.48 thf(f121,plain,(
% 1.74/1.48 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X5 @ X4)) = $true) | ($true = (in @ X3 @ X4)) | ((in @ X3 @ X5) != $true)) )),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.74/1.48 thf(f113,plain,(
% 1.74/1.48 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X3 @ X5) != $true) | ($true = (in @ X3 @ X4)) | ((in @ X3 @ (setminus @ X5 @ X4)) = $true)) )),
% 1.74/1.48 inference(definition_unfolding,[status(thm)],[f87,f71])).
% 1.74/1.48 thf(f71,plain,(
% 1.74/1.48 (setminusI = $true)),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f87,plain,(
% 1.74/1.48 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ X4)) | ((in @ X3 @ X5) != $true) | ((in @ X3 @ (setminus @ X5 @ X4)) = $true) | (setminusI != $true)) )),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f57])).
% 1.74/1.48 thf(f57,plain,(
% 1.74/1.48 ((setminusI = $true) | (((in @ sK14 @ sK15) != $true) & ((in @ sK14 @ sK16) = $true) & ((in @ sK14 @ (setminus @ sK16 @ sK15)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ X4)) | ((in @ X3 @ X5) != $true) | ((in @ X3 @ (setminus @ X5 @ X4)) = $true)) | (setminusI != $true))),
% 1.74/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f55,f56])).
% 1.74/1.48 thf(f56,plain,(
% 1.74/1.48 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) & ($true = (in @ X0 @ X2)) & ((in @ X0 @ (setminus @ X2 @ X1)) != $true)) => (((in @ sK14 @ sK15) != $true) & ((in @ sK14 @ sK16) = $true) & ((in @ sK14 @ (setminus @ sK16 @ sK15)) != $true))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f55,plain,(
% 1.74/1.48 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) & ($true = (in @ X0 @ X2)) & ((in @ X0 @ (setminus @ X2 @ X1)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ X4)) | ((in @ X3 @ X5) != $true) | ((in @ X3 @ (setminus @ X5 @ X4)) = $true)) | (setminusI != $true))),
% 1.74/1.48 inference(rectify,[status(thm)],[f54])).
% 1.74/1.48 thf(f54,plain,(
% 1.74/1.48 ((setminusI = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ X0) != $true) & ((in @ X1 @ X2) = $true) & ((in @ X1 @ (setminus @ X2 @ X0)) != $true))) & (! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) | ((in @ X1 @ X2) != $true) | ((in @ X1 @ (setminus @ X2 @ X0)) = $true)) | (setminusI != $true))),
% 1.74/1.48 inference(nnf_transformation,[status(thm)],[f33])).
% 1.74/1.48 thf(f33,plain,(
% 1.74/1.48 (setminusI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) | ((in @ X1 @ X2) != $true) | ((in @ X1 @ (setminus @ X2 @ X0)) = $true))),
% 1.74/1.48 inference(flattening,[status(thm)],[f32])).
% 1.74/1.48 thf(f32,plain,(
% 1.74/1.48 (setminusI = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X1 @ (setminus @ X2 @ X0)) = $true) | ((in @ X1 @ X0) = $true)) | ((in @ X1 @ X2) != $true))),
% 1.74/1.48 inference(ennf_transformation,[status(thm)],[f21])).
% 1.74/1.48 thf(f21,plain,(
% 1.74/1.48 (setminusI = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ X2) = $true) => (((in @ X1 @ X0) != $true) => ((in @ X1 @ (setminus @ X2 @ X0)) = $true)))),
% 1.74/1.48 inference(flattening,[status(thm)],[f18])).
% 1.74/1.48 thf(f18,plain,(
% 1.74/1.48 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) => (~((in @ X1 @ X0) = $true) => ((in @ X1 @ (setminus @ X2 @ X0)) = $true)))),
% 1.74/1.48 inference(fool_elimination,[status(thm)],[f17])).
% 1.74/1.48 thf(f17,plain,(
% 1.74/1.48 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (~(in @ X1 @ X0) => (in @ X1 @ (setminus @ X2 @ X0)))))),
% 1.74/1.48 inference(rectify,[status(thm)],[f2])).
% 1.74/1.48 thf(f2,axiom,(
% 1.74/1.48 (setminusI = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 1.74/1.48 file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',setminusI)).
% 1.74/1.48 thf(f75,plain,(
% 1.74/1.48 ((in @ sK9 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true)),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f123,plain,(
% 1.74/1.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X3 @ X1) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true) | ((in @ X3 @ X2) = $true)) )),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.74/1.48 thf(f114,plain,(
% 1.74/1.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != $true)) )),
% 1.74/1.48 inference(definition_unfolding,[status(thm)],[f96,f77])).
% 1.74/1.48 thf(f77,plain,(
% 1.74/1.48 (binintersectTERcontra = $true)),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f96,plain,(
% 1.74/1.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | (binintersectTERcontra != $true)) )),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f63])).
% 1.74/1.48 thf(f63,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X1)) != $true))) | (binintersectTERcontra != $true)) & ((binintersectTERcontra = $true) | (((in @ sK17 @ (powerset @ sK18)) = $true) & ((($true = (in @ sK20 @ (binintersect @ sK17 @ sK19))) & ((in @ sK20 @ sK18) = $true) & ($true != (in @ sK20 @ sK19))) & ((in @ sK19 @ (powerset @ sK18)) = $true))))),
% 1.74/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20])],[f59,f62,f61,f60])).
% 1.74/1.48 thf(f60,plain,(
% 1.74/1.48 ? [X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X5)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ (binintersect @ X4 @ X6))) & ($true = (in @ X7 @ X5)) & ($true != (in @ X7 @ X6))) & ((in @ X6 @ (powerset @ X5)) = $true))) => (((in @ sK17 @ (powerset @ sK18)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ (binintersect @ sK17 @ X6))) & ((in @ X7 @ sK18) = $true) & ($true != (in @ X7 @ X6))) & ((in @ X6 @ (powerset @ sK18)) = $true)))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f61,plain,(
% 1.74/1.48 ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ (binintersect @ sK17 @ X6))) & ((in @ X7 @ sK18) = $true) & ($true != (in @ X7 @ X6))) & ((in @ X6 @ (powerset @ sK18)) = $true)) => (? [X7 : $i] : (((in @ X7 @ (binintersect @ sK17 @ sK19)) = $true) & ((in @ X7 @ sK18) = $true) & ((in @ X7 @ sK19) != $true)) & ((in @ sK19 @ (powerset @ sK18)) = $true))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f62,plain,(
% 1.74/1.48 ? [X7 : $i] : (((in @ X7 @ (binintersect @ sK17 @ sK19)) = $true) & ((in @ X7 @ sK18) = $true) & ((in @ X7 @ sK19) != $true)) => (($true = (in @ sK20 @ (binintersect @ sK17 @ sK19))) & ((in @ sK20 @ sK18) = $true) & ($true != (in @ sK20 @ sK19)))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f59,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X1)) != $true))) | (binintersectTERcontra != $true)) & ((binintersectTERcontra = $true) | ? [X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X5)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ (binintersect @ X4 @ X6))) & ($true = (in @ X7 @ X5)) & ($true != (in @ X7 @ X6))) & ((in @ X6 @ (powerset @ X5)) = $true))))),
% 1.74/1.48 inference(rectify,[status(thm)],[f58])).
% 1.74/1.48 thf(f58,plain,(
% 1.74/1.48 (! [X1 : $i,X0 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectTERcontra != $true)) & ((binintersectTERcontra = $true) | ? [X1 : $i,X0 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) = $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true))))),
% 1.74/1.48 inference(nnf_transformation,[status(thm)],[f26])).
% 1.74/1.48 thf(f26,plain,(
% 1.74/1.48 ! [X1 : $i,X0 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) <=> (binintersectTERcontra = $true)),
% 1.74/1.48 inference(flattening,[status(thm)],[f25])).
% 1.74/1.48 thf(f25,plain,(
% 1.74/1.48 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ($true != (in @ X1 @ (powerset @ X0)))) <=> (binintersectTERcontra = $true)),
% 1.74/1.48 inference(ennf_transformation,[status(thm)],[f24])).
% 1.74/1.48 thf(f24,plain,(
% 1.74/1.48 ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ X2) != $true) => ((in @ X3 @ (binintersect @ X1 @ X2)) != $true))))) <=> (binintersectTERcontra = $true)),
% 1.74/1.48 inference(flattening,[status(thm)],[f12])).
% 1.74/1.48 thf(f12,plain,(
% 1.74/1.48 (binintersectTERcontra = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (~((in @ X3 @ X2) = $true) => ~((in @ X3 @ (binintersect @ X1 @ X2)) = $true)))))),
% 1.74/1.48 inference(fool_elimination,[status(thm)],[f11])).
% 1.74/1.48 thf(f11,plain,(
% 1.74/1.48 (binintersectTERcontra = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ X2) => ~(in @ X3 @ (binintersect @ X1 @ X2)))))))),
% 1.74/1.48 inference(rectify,[status(thm)],[f5])).
% 1.74/1.48 thf(f5,axiom,(
% 1.74/1.48 (binintersectTERcontra = ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X4) => ~(in @ X2 @ (binintersect @ X3 @ X4)))))))),
% 1.74/1.48 file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',binintersectTERcontra)).
% 1.74/1.48 thf(f149,plain,(
% 1.74/1.48 spl21_3 | spl21_4),
% 1.74/1.48 inference(avatar_split_clause,[status(thm)],[f141,f147,f143])).
% 1.74/1.48 thf(f141,plain,(
% 1.74/1.48 ( ! [X0 : $i] : (((in @ sK6 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true) | ((in @ sK9 @ X0) != $true) | ($true = (in @ sK9 @ sK6))) )),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.74/1.48 thf(f140,plain,(
% 1.74/1.48 ( ! [X0 : $i] : (($true = (in @ sK9 @ sK6)) | ((in @ sK9 @ X0) != $true) | ($true != $true) | ((in @ sK8 @ (powerset @ X0)) != $true) | ((in @ sK6 @ (powerset @ X0)) != $true)) )),
% 1.74/1.48 inference(superposition,[status(thm)],[f120,f128])).
% 1.74/1.48 thf(f120,plain,(
% 1.74/1.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ X1 @ (powerset @ X0)))) )),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.74/1.48 thf(f104,plain,(
% 1.74/1.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X3 @ X0) != $true) | ($true != (in @ X1 @ (powerset @ X0))) | ((in @ X3 @ X1) = $true)) )),
% 1.74/1.48 inference(definition_unfolding,[status(thm)],[f86,f78])).
% 1.74/1.48 thf(f78,plain,(
% 1.74/1.48 (binintersectTELcontra = $true)),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f86,plain,(
% 1.74/1.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | (binintersectTELcontra != $true)) )),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f53])).
% 1.74/1.48 thf(f53,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectTELcontra != $true)) & ((binintersectTELcontra = $true) | (((in @ sK11 @ (powerset @ sK10)) = $true) & ((($true = (in @ sK13 @ (binintersect @ sK11 @ sK12))) & ((in @ sK13 @ sK11) != $true) & ($true = (in @ sK13 @ sK10))) & ((in @ sK12 @ (powerset @ sK10)) = $true))))),
% 1.74/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f49,f52,f51,f50])).
% 1.74/1.48 thf(f50,plain,(
% 1.74/1.48 ? [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ (binintersect @ X5 @ X6)) = $true) & ($true != (in @ X7 @ X5)) & ($true = (in @ X7 @ X4))) & ($true = (in @ X6 @ (powerset @ X4))))) => (((in @ sK11 @ (powerset @ sK10)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ (binintersect @ sK11 @ X6)) = $true) & ((in @ X7 @ sK11) != $true) & ((in @ X7 @ sK10) = $true)) & ((in @ X6 @ (powerset @ sK10)) = $true)))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f51,plain,(
% 1.74/1.48 ? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ (binintersect @ sK11 @ X6)) = $true) & ((in @ X7 @ sK11) != $true) & ((in @ X7 @ sK10) = $true)) & ((in @ X6 @ (powerset @ sK10)) = $true)) => (? [X7 : $i] : (((in @ X7 @ (binintersect @ sK11 @ sK12)) = $true) & ((in @ X7 @ sK11) != $true) & ((in @ X7 @ sK10) = $true)) & ((in @ sK12 @ (powerset @ sK10)) = $true))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f52,plain,(
% 1.74/1.48 ? [X7 : $i] : (((in @ X7 @ (binintersect @ sK11 @ sK12)) = $true) & ((in @ X7 @ sK11) != $true) & ((in @ X7 @ sK10) = $true)) => (($true = (in @ sK13 @ (binintersect @ sK11 @ sK12))) & ((in @ sK13 @ sK11) != $true) & ($true = (in @ sK13 @ sK10)))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f49,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectTELcontra != $true)) & ((binintersectTELcontra = $true) | ? [X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6 : $i] : (? [X7 : $i] : (((in @ X7 @ (binintersect @ X5 @ X6)) = $true) & ($true != (in @ X7 @ X5)) & ($true = (in @ X7 @ X4))) & ($true = (in @ X6 @ (powerset @ X4))))))),
% 1.74/1.48 inference(rectify,[status(thm)],[f48])).
% 1.74/1.48 thf(f48,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectTELcontra != $true)) & ((binintersectTELcontra = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) = $true) & ((in @ X3 @ X1) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))))),
% 1.74/1.48 inference(nnf_transformation,[status(thm)],[f35])).
% 1.74/1.48 thf(f35,plain,(
% 1.74/1.48 ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) <=> (binintersectTELcontra = $true)),
% 1.74/1.48 inference(flattening,[status(thm)],[f34])).
% 1.74/1.48 thf(f34,plain,(
% 1.74/1.48 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X1) = $true)) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ($true != (in @ X1 @ (powerset @ X0)))) <=> (binintersectTELcontra = $true)),
% 1.74/1.48 inference(ennf_transformation,[status(thm)],[f23])).
% 1.74/1.48 thf(f23,plain,(
% 1.74/1.48 ! [X1 : $i,X0 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ X1) != $true) => ((in @ X3 @ (binintersect @ X1 @ X2)) != $true))))) <=> (binintersectTELcontra = $true)),
% 1.74/1.48 inference(flattening,[status(thm)],[f10])).
% 1.74/1.48 thf(f10,plain,(
% 1.74/1.48 ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (~((in @ X3 @ X1) = $true) => ~((in @ X3 @ (binintersect @ X1 @ X2)) = $true))))) <=> (binintersectTELcontra = $true)),
% 1.74/1.48 inference(fool_elimination,[status(thm)],[f9])).
% 1.74/1.48 thf(f9,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ X1) => ~(in @ X3 @ (binintersect @ X1 @ X2)))))) = binintersectTELcontra)),
% 1.74/1.48 inference(rectify,[status(thm)],[f4])).
% 1.74/1.48 thf(f4,axiom,(
% 1.74/1.48 (! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X3) => ~(in @ X2 @ (binintersect @ X3 @ X4)))))) = binintersectTELcontra)),
% 1.74/1.48 file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',binintersectTELcontra)).
% 1.74/1.48 thf(f139,plain,(
% 1.74/1.48 spl21_1 | spl21_2),
% 1.74/1.48 inference(avatar_split_clause,[status(thm)],[f130,f136,f132])).
% 1.74/1.48 thf(f130,plain,(
% 1.74/1.48 ((in @ sK9 @ (setminus @ sK7 @ sK8)) = $true) | ($true = (in @ sK9 @ (setminus @ sK7 @ sK6)))),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.74/1.48 thf(f129,plain,(
% 1.74/1.48 ((in @ sK9 @ (setminus @ sK7 @ sK8)) = $true) | ($true != $true) | ($true = (in @ sK9 @ (setminus @ sK7 @ sK6)))),
% 1.74/1.48 inference(superposition,[status(thm)],[f124,f74])).
% 1.74/1.48 thf(f74,plain,(
% 1.74/1.48 ($true = (in @ sK9 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8))))),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f124,plain,(
% 1.74/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (binunion @ X1 @ X2))) | ($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) = $true)) )),
% 1.74/1.48 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.74/1.48 thf(f97,plain,(
% 1.74/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (binunion @ X1 @ X2))) | ($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) = $true) | ($true != $true)) )),
% 1.74/1.48 inference(definition_unfolding,[status(thm)],[f67,f79])).
% 1.74/1.48 thf(f79,plain,(
% 1.74/1.48 (binunionE = $true)),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.48 thf(f67,plain,(
% 1.74/1.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (binunion @ X1 @ X2))) | ((in @ X0 @ X1) = $true) | ($true = (in @ X0 @ X2)) | (binunionE != $true)) )),
% 1.74/1.48 inference(cnf_transformation,[status(thm)],[f39])).
% 1.74/1.48 thf(f39,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (binunion @ X1 @ X2))) | ((in @ X0 @ X1) = $true) | ($true = (in @ X0 @ X2))) | (binunionE != $true)) & ((binunionE = $true) | (((in @ sK0 @ (binunion @ sK1 @ sK2)) = $true) & ((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ sK2) != $true)))),
% 1.74/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f37,f38])).
% 1.74/1.48 thf(f38,plain,(
% 1.74/1.48 ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ (binunion @ X4 @ X5))) & ($true != (in @ X3 @ X4)) & ((in @ X3 @ X5) != $true)) => (((in @ sK0 @ (binunion @ sK1 @ sK2)) = $true) & ((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ sK2) != $true))),
% 1.74/1.48 introduced(definition,[],[choice_axiom])).
% 1.74/1.48 thf(f37,plain,(
% 1.74/1.48 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (binunion @ X1 @ X2))) | ((in @ X0 @ X1) = $true) | ($true = (in @ X0 @ X2))) | (binunionE != $true)) & ((binunionE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ (binunion @ X4 @ X5))) & ($true != (in @ X3 @ X4)) & ((in @ X3 @ X5) != $true)))),
% 1.74/1.48 inference(rectify,[status(thm)],[f36])).
% 1.74/1.48 thf(f36,plain,(
% 1.74/1.48 (! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ (binunion @ X1 @ X0)) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) = $true)) | (binunionE != $true)) & ((binunionE = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ (binunion @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) != $true)))),
% 1.74/1.48 inference(nnf_transformation,[status(thm)],[f29])).
% 1.74/1.48 thf(f29,plain,(
% 1.74/1.48 ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ (binunion @ X1 @ X0)) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) = $true)) <=> (binunionE = $true)),
% 1.74/1.48 inference(flattening,[status(thm)],[f28])).
% 1.74/1.48 thf(f28,plain,(
% 1.74/1.48 (binunionE = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) = $true)) | ((in @ X2 @ (binunion @ X1 @ X0)) != $true))),
% 1.74/1.48 inference(ennf_transformation,[status(thm)],[f16])).
% 1.74/1.48 thf(f16,plain,(
% 1.74/1.48 (binunionE = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ (binunion @ X1 @ X0)) = $true) => (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) = $true)))),
% 1.74/1.48 inference(fool_elimination,[status(thm)],[f15])).
% 1.74/1.48 thf(f15,plain,(
% 1.74/1.48 (binunionE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binunion @ X1 @ X0)) => ((in @ X2 @ X0) | (in @ X2 @ X1))))),
% 1.74/1.48 inference(rectify,[status(thm)],[f1])).
% 1.74/1.48 thf(f1,axiom,(
% 1.74/1.48 (binunionE = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X1) | (in @ X2 @ X0))))),
% 1.74/1.48 file('/export/starexec/sandbox/tmp/tmp.e5nrnikOT8/DTF2THF_21928.p',binunionE)).
% 1.74/1.48 % SZS output end Proof for DTF2THF_21928
% 1.74/1.48 % (22066)------------------------------
% 1.74/1.48 % (22066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.48 % (22066)Termination reason: Refutation
% 1.74/1.48
% 1.74/1.48 % (22066)Memory used [KB]: 5628
% 1.74/1.48 % (22066)Time elapsed: 0.013 s
% 1.74/1.48 % (22066)Instructions burned: 13 (million)
% 1.74/1.48 % (22066)------------------------------
% 1.74/1.48 % (22066)------------------------------
% 1.74/1.48 % (22060)Success in time 0.024 s
%------------------------------------------------------------------------------