%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU764^2 : 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 : n014.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 09:37:00 AM UTC 2026
% Result : Theorem 1.74s 1.34s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 80 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 1127 ( 281 equ; 0 cnn)
% Maximal formula atoms : 10 ( 14 avg)
% Number of connectives : 1849 ( 127 ~; 92 |; 93 &;1473 @)
% ( 8 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 21 con; 0-2 aty)
% Number of variables : 175 ( 0 ^; 110 !; 65 ?; 175 :)
% 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_4,type,
setminus: $i > $i > $i ).
thf(f110,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f97,f103,f109]) ).
thf(f109,plain,
spl14_2,
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
| spl14_2 ),
inference(subsumption_resolution,[status(thm)],[f107,f60]) ).
thf(f60,plain,
( ( in @ sK12 @ ( powerset @ sK10 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( in @ sK12 @ ( powerset @ sK10 ) )
= $true )
& ( ( in @ sK13 @ ( powerset @ sK10 ) )
= $true )
& ( ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( binintersect @ ( setminus @ sK10 @ sK12 ) @ ( setminus @ sK10 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) )
& ( ( in @ sK11 @ ( powerset @ sK10 ) )
= $true )
& ( $true
= ( in @ sK9 @ ( powerset @ sK10 ) ) )
& ( binunionT_lem = $true )
& ( demorgan2 = $true )
& ( demorgan1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f35,f39,f38,f37,f36]) ).
thf(f36,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X1 ) ) )
& ( ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) )
!= ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ sK10 ) ) )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK10 ) )
= $true )
& ( ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ X2 ) ) @ ( binintersect @ ( setminus @ sK10 @ X3 ) @ ( setminus @ sK10 @ X4 ) ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ sK10 ) )
= $true ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK10 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ sK10 ) ) )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK10 ) )
= $true )
& ( ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ X2 ) ) @ ( binintersect @ ( setminus @ sK10 @ X3 ) @ ( setminus @ sK10 @ X4 ) ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ sK10 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ sK10 ) ) )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK10 ) )
= $true )
& ( ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( binintersect @ ( setminus @ sK10 @ X3 ) @ ( setminus @ sK10 @ X4 ) ) ) ) ) )
& ( ( in @ sK11 @ ( powerset @ sK10 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ sK10 ) ) )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK10 ) )
= $true )
& ( ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( binintersect @ ( setminus @ sK10 @ X3 ) @ ( setminus @ sK10 @ X4 ) ) ) ) ) )
=> ( ( ( in @ sK12 @ ( powerset @ sK10 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK10 ) )
= $true )
& ( ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( binintersect @ ( setminus @ sK10 @ sK12 ) @ ( setminus @ sK10 @ X4 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ X4 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK10 ) )
= $true )
& ( ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( binintersect @ ( setminus @ sK10 @ sK12 ) @ ( setminus @ sK10 @ X4 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ X4 ) ) ) ) )
=> ( ( ( in @ sK13 @ ( powerset @ sK10 ) )
= $true )
& ( ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( binintersect @ ( setminus @ sK10 @ sK12 ) @ ( setminus @ sK10 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X1 ) ) )
& ( ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) )
!= ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionT_lem = $true )
& ( demorgan2 = $true )
& ( demorgan1 = $true ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X0 ) )
= $true )
& ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionT_lem = $true )
& ( demorgan2 = $true )
& ( demorgan1 = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X0 ) )
= $true )
& ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( demorgan2 = $true )
& ( demorgan1 = $true )
& ( binunionT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( binunionT_lem = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X0 ) )
= $true )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VRLqFJpPNV/DTF2THF_9901.p',woz1_2) ).
thf(f107,plain,
( ( ( in @ sK12 @ ( powerset @ sK10 ) )
!= $true )
| spl14_2 ),
inference(subsumption_resolution,[status(thm)],[f106,f59]) ).
thf(f59,plain,
( ( in @ sK13 @ ( powerset @ sK10 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f106,plain,
( ( ( in @ sK13 @ ( powerset @ sK10 ) )
!= $true )
| ( ( in @ sK12 @ ( powerset @ sK10 ) )
!= $true )
| spl14_2 ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ( ( in @ sK12 @ ( powerset @ sK10 ) )
!= $true )
| ( $true != $true )
| ( ( in @ sK13 @ ( powerset @ sK10 ) )
!= $true )
| spl14_2 ),
inference(superposition,[status(thm)],[f96,f73]) ).
thf(f73,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f48,f55]) ).
thf(f55,plain,
binunionT_lem = $true,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f48,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( binunionT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ( ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true )
& ( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true )
& ( ( in @ ( binunion @ sK4 @ sK5 ) @ ( powerset @ sK3 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f26,f28,f27]) ).
thf(f27,plain,
( ? [X3: $i,X4: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) )
& ? [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
= $true )
& ( $true
!= ( in @ ( binunion @ X4 @ X5 ) @ ( powerset @ X3 ) ) ) ) )
=> ( ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true )
& ? [X5: $i] :
( ( ( in @ X5 @ ( powerset @ sK3 ) )
= $true )
& ( $true
!= ( in @ ( binunion @ sK4 @ X5 ) @ ( powerset @ sK3 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X5: $i] :
( ( ( in @ X5 @ ( powerset @ sK3 ) )
= $true )
& ( $true
!= ( in @ ( binunion @ sK4 @ X5 ) @ ( powerset @ sK3 ) ) ) )
=> ( ( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true )
& ( ( in @ ( binunion @ sK4 @ sK5 ) @ ( powerset @ sK3 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ? [X3: $i,X4: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) )
& ? [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
= $true )
& ( $true
!= ( in @ ( binunion @ X4 @ X5 ) @ ( powerset @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) )
<=> ( binunionT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( binunionT_lem = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) )
= binunionT_lem ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) )
= binunionT_lem ),
file('/export/starexec/sandbox/tmp/tmp.VRLqFJpPNV/DTF2THF_9901.p',binunionT_lem) ).
thf(f96,plain,
( ( ( in @ ( binunion @ sK12 @ sK13 ) @ ( powerset @ sK10 ) )
!= $true )
| spl14_2 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f94,definition,
( spl14_2
<=> ( ( in @ ( binunion @ sK12 @ sK13 ) @ ( powerset @ sK10 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl14_2])],[avatar_definition]) ).
thf(f103,plain,
spl14_1,
inference(avatar_contradiction_clause,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
| spl14_1 ),
inference(subsumption_resolution,[status(thm)],[f101,f56]) ).
thf(f56,plain,
( $true
= ( in @ sK9 @ ( powerset @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f101,plain,
( ( $true
!= ( in @ sK9 @ ( powerset @ sK10 ) ) )
| spl14_1 ),
inference(subsumption_resolution,[status(thm)],[f100,f57]) ).
thf(f57,plain,
( ( in @ sK11 @ ( powerset @ sK10 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f100,plain,
( ( ( in @ sK11 @ ( powerset @ sK10 ) )
!= $true )
| ( $true
!= ( in @ sK9 @ ( powerset @ sK10 ) ) )
| spl14_1 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true != $true )
| ( ( in @ sK11 @ ( powerset @ sK10 ) )
!= $true )
| ( $true
!= ( in @ sK9 @ ( powerset @ sK10 ) ) )
| spl14_1 ),
inference(superposition,[status(thm)],[f92,f73]) ).
thf(f92,plain,
( ( ( in @ ( binunion @ sK9 @ sK11 ) @ ( powerset @ sK10 ) )
!= $true )
| spl14_1 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl14_1
<=> ( ( in @ ( binunion @ sK9 @ sK11 ) @ ( powerset @ sK10 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl14_1])],[avatar_definition]) ).
thf(f97,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[status(thm)],[f88,f94,f90]) ).
thf(f88,plain,
( ( ( in @ ( binunion @ sK12 @ sK13 ) @ ( powerset @ sK10 ) )
!= $true )
| ( ( in @ ( binunion @ sK9 @ sK11 ) @ ( powerset @ sK10 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ( in @ ( binunion @ sK9 @ sK11 ) @ ( powerset @ sK10 ) )
!= $true )
| ( ( in @ ( binunion @ sK12 @ sK13 ) @ ( powerset @ sK10 ) )
!= $true )
| ( ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) ) ),
inference(superposition,[status(thm)],[f85,f74]) ).
thf(f74,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f44,f53]) ).
thf(f53,plain,
demorgan1 = $true,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f44,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( demorgan1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( demorgan1 != $true ) )
& ( ( demorgan1 = $true )
| ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( ( binunion @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) )
!= ( setminus @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f23,f22]) ).
thf(f22,plain,
( ? [X3: $i,X4: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) )
& ? [X5: $i] :
( ( ( setminus @ X3 @ ( binintersect @ X4 @ X5 ) )
!= ( binunion @ ( setminus @ X3 @ X4 ) @ ( setminus @ X3 @ X5 ) ) )
& ( ( in @ X5 @ ( powerset @ X3 ) )
= $true ) ) )
=> ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ? [X5: $i] :
( ( ( setminus @ sK0 @ ( binintersect @ sK1 @ X5 ) )
!= ( binunion @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ X5 ) ) )
& ( ( in @ X5 @ ( powerset @ sK0 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X5: $i] :
( ( ( setminus @ sK0 @ ( binintersect @ sK1 @ X5 ) )
!= ( binunion @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ X5 ) ) )
& ( ( in @ X5 @ ( powerset @ sK0 ) )
= $true ) )
=> ( ( ( binunion @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) )
!= ( setminus @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( demorgan1 != $true ) )
& ( ( demorgan1 = $true )
| ? [X3: $i,X4: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) )
& ? [X5: $i] :
( ( ( setminus @ X3 @ ( binintersect @ X4 @ X5 ) )
!= ( binunion @ ( setminus @ X3 @ X4 ) @ ( setminus @ X3 @ X5 ) ) )
& ( ( in @ X5 @ ( powerset @ X3 ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
= ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( demorgan1 != $true ) )
& ( ( demorgan1 = $true )
| ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
!= ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
= ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
<=> ( demorgan1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
= ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) )
<=> ( demorgan1 = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( demorgan1
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
= ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( demorgan1
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VRLqFJpPNV/DTF2THF_9901.p',demorgan1) ).
thf(f85,plain,
( ( binunion @ ( setminus @ sK10 @ ( binunion @ sK9 @ sK11 ) ) @ ( setminus @ sK10 @ ( binunion @ sK12 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f84,f57]) ).
thf(f84,plain,
( ( ( in @ sK11 @ ( powerset @ sK10 ) )
!= $true )
| ( ( binunion @ ( setminus @ sK10 @ ( binunion @ sK9 @ sK11 ) ) @ ( setminus @ sK10 @ ( binunion @ sK12 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f83,f56]) ).
thf(f83,plain,
( ( $true
!= ( in @ sK9 @ ( powerset @ sK10 ) ) )
| ( ( binunion @ ( setminus @ sK10 @ ( binunion @ sK9 @ sK11 ) ) @ ( setminus @ sK10 @ ( binunion @ sK12 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) )
| ( ( in @ sK11 @ ( powerset @ sK10 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f80,f75]) ).
thf(f75,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f52,f54]) ).
thf(f54,plain,
demorgan2 = $true,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f52,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( demorgan2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( demorgan2 != $true ) )
& ( ( demorgan2 = $true )
| ( ( ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) )
!= ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) )
& ( ( in @ sK8 @ ( powerset @ sK6 ) )
= $true )
& ( $true
= ( in @ sK7 @ ( powerset @ sK6 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f31,f33,f32]) ).
thf(f32,plain,
( ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( binintersect @ ( setminus @ X3 @ X4 ) @ ( setminus @ X3 @ X5 ) )
!= ( setminus @ X3 @ ( binunion @ X4 @ X5 ) ) )
& ( ( in @ X5 @ ( powerset @ X3 ) )
= $true ) )
& ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) ) )
=> ( ? [X5: $i] :
( ( ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ X5 ) )
!= ( setminus @ sK6 @ ( binunion @ sK7 @ X5 ) ) )
& ( ( in @ X5 @ ( powerset @ sK6 ) )
= $true ) )
& ( $true
= ( in @ sK7 @ ( powerset @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X5: $i] :
( ( ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ X5 ) )
!= ( setminus @ sK6 @ ( binunion @ sK7 @ X5 ) ) )
& ( ( in @ X5 @ ( powerset @ sK6 ) )
= $true ) )
=> ( ( ( setminus @ sK6 @ ( binunion @ sK7 @ sK8 ) )
!= ( binintersect @ ( setminus @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK8 ) ) )
& ( ( in @ sK8 @ ( powerset @ sK6 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( demorgan2 != $true ) )
& ( ( demorgan2 = $true )
| ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( binintersect @ ( setminus @ X3 @ X4 ) @ ( setminus @ X3 @ X5 ) )
!= ( setminus @ X3 @ ( binunion @ X4 @ X5 ) ) )
& ( ( in @ X5 @ ( powerset @ X3 ) )
= $true ) )
& ( $true
= ( in @ X4 @ ( powerset @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( demorgan2 != $true ) )
& ( ( demorgan2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
!= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( demorgan2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
<=> ( demorgan2 = $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
= demorgan2 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
= demorgan2 ),
file('/export/starexec/sandbox/tmp/tmp.VRLqFJpPNV/DTF2THF_9901.p',demorgan2) ).
thf(f80,plain,
( ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( setminus @ sK10 @ ( binunion @ sK12 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f79,f59]) ).
thf(f79,plain,
( ( ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( setminus @ sK10 @ ( binunion @ sK12 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) )
| ( ( in @ sK13 @ ( powerset @ sK10 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f77,f60]) ).
thf(f77,plain,
( ( ( in @ sK12 @ ( powerset @ sK10 ) )
!= $true )
| ( ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( setminus @ sK10 @ ( binunion @ sK12 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) )
| ( ( in @ sK13 @ ( powerset @ sK10 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f58,f75]) ).
thf(f58,plain,
( ( binunion @ ( binintersect @ ( setminus @ sK10 @ sK9 ) @ ( setminus @ sK10 @ sK11 ) ) @ ( binintersect @ ( setminus @ sK10 @ sK12 ) @ ( setminus @ sK10 @ sK13 ) ) )
!= ( setminus @ sK10 @ ( binintersect @ ( binunion @ sK9 @ sK11 ) @ ( binunion @ sK12 @ sK13 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU764^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n014.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:33:27 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : SEU764^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.46 % Domain : Set Theory
% 0.21/0.46 % Problem : Typed Set Theory - First Wizard of Oz Examples - WoZ1 Problems
% 0.21/0.46 % Version : Especial > Reduced > Especial.
% 0.21/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.21/0.46 % (! Z:i.in Z (powerset A) -> (! W:i.in W (powerset A) ->
% 0.21/0.46 % setminus A (binintersect (binunion X Y) (binunion Z W)) =
% 0.21/0.46 % binunion (binintersect (setminus A X) (setminus A Y))
% 0.21/0.46 % (binintersect (setminus A Z) (setminus A W))))))
% 0.21/0.46
% 0.21/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.46 % Source : [Bro08]
% 0.21/0.46 % Names : ZFC266l [Bro08]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 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 v3.7.0
% 0.21/0.46 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 3 def)
% 0.21/0.46 % Number of atoms : 23 ( 6 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 8 ( 5 avg)
% 0.21/0.46 % Number of connectives : 90 ( 0 ~; 0 |; 0 &; 77 @)
% 0.21/0.46 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 15 ( 5 avg)
% 0.21/0.46 % Number of types : 2 ( 0 usr)
% 0.21/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% 0.21/0.46 % Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 0.21/0.46 % SPC : TH0_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : http://mathgate.info/detsetitem.php?id=325
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(in_type,type,
% 0.21/0.46 in: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(powerset_type,type,
% 0.21/0.46 powerset: $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(binunion_type,type,
% 0.21/0.46 binunion: $i > $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(binintersect_type,type,
% 0.21/0.46 binintersect: $i > $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(setminus_type,type,
% 0.21/0.46 setminus: $i > $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(binunionT_lem_type,type,
% 0.21/0.46 binunionT_lem: $o ).
% 0.21/0.46
% 0.21/0.46 thf(binunionT_lem,definition,
% 0.21/0.46 ( binunionT_lem
% 0.21/0.46 = ( ! [A: $i,X: $i] :
% 0.21/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.46 => ! [Y: $i] :
% 0.21/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.46 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(demorgan1_type,type,
% 0.21/0.46 demorgan1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(demorgan1,definition,
% 0.21/0.46 ( demorgan1
% 0.21/0.46 = ( ! [A: $i,X: $i] :
% 0.21/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.46 => ! [Y: $i] :
% 0.21/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.46 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.21/0.46 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(demorgan2_type,type,
% 0.21/0.46 demorgan2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(demorgan2,definition,
% 0.21/0.46 ( demorgan2
% 0.21/0.46 = ( ! [A: $i,X: $i] :
% 0.21/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.46 => ! [Y: $i] :
% 0.21/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.46 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.21/0.46 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(woz1_2,conjecture,
% 0.21/0.46 ( binunionT_lem
% 0.21/0.46 => ( demorgan1
% 0.21/0.46 => ( demorgan2
% 0.21/0.46 => ! [A: $i,X: $i] :
% 0.21/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.46 => ! [Y: $i] :
% 0.21/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.46 => ! [Z: $i] :
% 0.21/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.21/0.46 => ! [W: $i] :
% 0.21/0.46 ( ( in @ W @ ( powerset @ A ) )
% 0.21/0.46 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.21/0.46 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 ------------------------
% 1.57/1.29 ---- Embedded in THF ---
% 1.57/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.29 %%% Generated on Tue Feb 24 12:33:28 EST 2026
% 1.57/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.29 %%% Logic specification used:
% 1.57/1.29 %%% thf(spec, logic, $$dhol).
% 1.57/1.29
% 1.57/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VRLqFJpPNV/DTF2DTF9901.p
% See solution above
% 1.57/1.29 ------------------------
% 1.74/1.30 ---- Cleaned THF ---
% 1.74/1.31 thf(in_type,type,
% 1.74/1.31 in: $i > $i > $o ).
% 1.74/1.31
% 1.74/1.31 thf(powerset_type,type,
% 1.74/1.31 powerset: $i > $i ).
% 1.74/1.31
% 1.74/1.31 thf(binunion_type,type,
% 1.74/1.31 binunion: $i > $i > $i ).
% 1.74/1.31
% 1.74/1.31 thf(binintersect_type,type,
% 1.74/1.31 binintersect: $i > $i > $i ).
% 1.74/1.31
% 1.74/1.31 thf(setminus_type,type,
% 1.74/1.31 setminus: $i > $i > $i ).
% 1.74/1.31
% 1.74/1.31 thf(binunionT_lem_type,type,
% 1.74/1.31 binunionT_lem: $o ).
% 1.74/1.31
% 1.74/1.31 thf(binunionT_lem,definition,
% 1.74/1.31 ( binunionT_lem
% 1.74/1.31 = ( ! [A: $i,X: $i] :
% 1.74/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.31 => ! [Y: $i] :
% 1.74/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.31 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.74/1.31
% 1.74/1.31 thf(demorgan1_type,type,
% 1.74/1.31 demorgan1: $o ).
% 1.74/1.31
% 1.74/1.31 thf(demorgan1,definition,
% 1.74/1.31 ( demorgan1
% 1.74/1.31 = ( ! [A: $i,X: $i] :
% 1.74/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.31 => ! [Y: $i] :
% 1.74/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.31 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 1.74/1.31 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 1.74/1.31
% 1.74/1.31 thf(demorgan2_type,type,
% 1.74/1.31 demorgan2: $o ).
% 1.74/1.31
% 1.74/1.31 thf(demorgan2,definition,
% 1.74/1.31 ( demorgan2
% 1.74/1.31 = ( ! [A: $i,X: $i] :
% 1.74/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.31 => ! [Y: $i] :
% 1.74/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.31 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 1.74/1.31 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 1.74/1.31
% 1.74/1.31 thf(woz1_2,conjecture,
% 1.74/1.31 ( binunionT_lem
% 1.74/1.31 => ( demorgan1
% 1.74/1.31 => ( demorgan2
% 1.74/1.31 => ! [A: $i,X: $i] :
% 1.74/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.74/1.31 => ! [Y: $i] :
% 1.74/1.31 ( ( in @ Y @ ( powerset @ A ) )
% 1.74/1.31 => ! [Z: $i] :
% 1.74/1.31 ( ( in @ Z @ ( powerset @ A ) )
% 1.74/1.31 => ! [W: $i] :
% 1.74/1.31 ( ( in @ W @ ( powerset @ A ) )
% 1.74/1.31 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 1.74/1.31 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ) ).
% 1.74/1.31 ------------------------
% 1.74/1.33 % (10097)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9901 for (2999ds/18Mi)
% 1.74/1.33 % (10096)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_9901 for (2999ds/275Mi)
% 1.74/1.33 % (10092)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_9901 for (2999ds/4Mi)
% 1.74/1.33 % (10094)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9901 for (2999ds/2Mi)
% 1.74/1.33 % (10093)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_9901 for (2999ds/27Mi)
% 1.74/1.33 % (10094)Instruction limit reached!
% 1.74/1.33 % (10094)------------------------------
% 1.74/1.33 % (10094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.33 % (10094)Termination reason: Unknown
% 1.74/1.33 % (10094)Termination phase: Preprocessing 3
% 1.74/1.33
% 1.74/1.33 % (10094)Memory used [KB]: 1023
% 1.74/1.33 % (10094)Time elapsed: 0.004 s
% 1.74/1.33 % (10094)Instructions burned: 3 (million)
% 1.74/1.33 % (10094)------------------------------
% 1.74/1.33 % (10094)------------------------------
% 1.74/1.33 % (10092)Instruction limit reached!
% 1.74/1.33 % (10092)------------------------------
% 1.74/1.33 % (10092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.33 % (10092)Termination reason: Unknown
% 1.74/1.33 % (10092)Termination phase: Saturation
% 1.74/1.33
% 1.74/1.33 % (10092)Memory used [KB]: 5500
% 1.74/1.33 % (10092)Time elapsed: 0.005 s
% 1.74/1.33 % (10092)Instructions burned: 5 (million)
% 1.74/1.33 % (10092)------------------------------
% 1.74/1.33 % (10092)------------------------------
% 1.74/1.34 % (10095)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_9901 for (2999ds/2Mi)
% 1.74/1.34 % (10095)Instruction limit reached!
% 1.74/1.34 % (10095)------------------------------
% 1.74/1.34 % (10095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (10095)Termination reason: Unknown
% 1.74/1.34 % (10095)Termination phase: shuffling
% 1.74/1.34
% 1.74/1.34 % (10095)Memory used [KB]: 1023
% 1.74/1.34 % (10095)Time elapsed: 0.003 s
% 1.74/1.34 % (10097)Instruction limit reached!
% 1.74/1.34 % (10097)------------------------------
% 1.74/1.34 % (10097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (10097)Termination reason: Unknown
% 1.74/1.34 % (10097)Termination phase: Saturation
% 1.74/1.34
% 1.74/1.34 % (10097)Memory used [KB]: 5628
% 1.74/1.34 % (10097)Time elapsed: 0.012 s
% 1.74/1.34 % (10097)Instructions burned: 18 (million)
% 1.74/1.34 % (10097)------------------------------
% 1.74/1.34 % (10097)------------------------------
% 1.74/1.34 % (10095)Instructions burned: 2 (million)
% 1.74/1.34 % (10095)------------------------------
% 1.74/1.34 % (10095)------------------------------
% 1.74/1.34 % (10096)First to succeed.
% 1.74/1.34 % (10093)Also succeeded, but the first one will report.
% 1.74/1.34 % (10096)Refutation found. Thanks to Tanya!
% 1.74/1.34 % SZS status Theorem for DTF2THF_9901
% 1.74/1.34 % SZS output start Proof for DTF2THF_9901
% 1.74/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.74/1.34 thf(func_def_1, type, powerset: $i > $i).
% 1.74/1.34 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.74/1.34 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.74/1.34 thf(func_def_4, type, setminus: $i > $i > $i).
% 1.74/1.34 thf(f110,plain,(
% 1.74/1.34 $false),
% 1.74/1.34 inference(avatar_sat_refutation,[status(thm)],[f97,f103,f109])).
% 1.74/1.34 thf(f109,plain,(
% 1.74/1.34 spl14_2),
% 1.74/1.34 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 1.74/1.34 thf(f108,plain,(
% 1.74/1.34 $false | spl14_2),
% 1.74/1.34 inference(subsumption_resolution,[status(thm)],[f107,f60])).
% 1.74/1.34 thf(f60,plain,(
% 1.74/1.34 ((in @ sK12 @ (powerset @ sK10)) = $true)),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 1.74/1.34 thf(f40,plain,(
% 1.74/1.34 (((((in @ sK12 @ (powerset @ sK10)) = $true) & (((in @ sK13 @ (powerset @ sK10)) = $true) & ((binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (binintersect @ (setminus @ sK10 @ sK12) @ (setminus @ sK10 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13)))))) & ((in @ sK11 @ (powerset @ sK10)) = $true)) & ($true = (in @ sK9 @ (powerset @ sK10)))) & (binunionT_lem = $true) & (demorgan2 = $true) & (demorgan1 = $true)),
% 1.74/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f35,f39,f38,f37,f36])).
% 1.74/1.34 thf(f36,plain,(
% 1.74/1.34 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ (powerset @ X1))) & ? [X4 : $i] : (($true = (in @ X4 @ (powerset @ X1))) & ((binunion @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) @ (binintersect @ (setminus @ X1 @ X3) @ (setminus @ X1 @ X4))) != (setminus @ X1 @ (binintersect @ (binunion @ X0 @ X2) @ (binunion @ X3 @ X4)))))) & ($true = (in @ X2 @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) => (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ (powerset @ sK10))) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK10)) = $true) & ((setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ X2) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ X2)) @ (binintersect @ (setminus @ sK10 @ X3) @ (setminus @ sK10 @ X4)))))) & ((in @ X2 @ (powerset @ sK10)) = $true)) & ($true = (in @ sK9 @ (powerset @ sK10))))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f37,plain,(
% 1.74/1.34 ? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ (powerset @ sK10))) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK10)) = $true) & ((setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ X2) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ X2)) @ (binintersect @ (setminus @ sK10 @ X3) @ (setminus @ sK10 @ X4)))))) & ((in @ X2 @ (powerset @ sK10)) = $true)) => (? [X3 : $i] : (($true = (in @ X3 @ (powerset @ sK10))) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK10)) = $true) & ((setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (binintersect @ (setminus @ sK10 @ X3) @ (setminus @ sK10 @ X4)))))) & ((in @ sK11 @ (powerset @ sK10)) = $true))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f38,plain,(
% 1.74/1.34 ? [X3 : $i] : (($true = (in @ X3 @ (powerset @ sK10))) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK10)) = $true) & ((setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (binintersect @ (setminus @ sK10 @ X3) @ (setminus @ sK10 @ X4)))))) => (((in @ sK12 @ (powerset @ sK10)) = $true) & ? [X4 : $i] : (((in @ X4 @ (powerset @ sK10)) = $true) & ((binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (binintersect @ (setminus @ sK10 @ sK12) @ (setminus @ sK10 @ X4))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ X4))))))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f39,plain,(
% 1.74/1.34 ? [X4 : $i] : (((in @ X4 @ (powerset @ sK10)) = $true) & ((binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (binintersect @ (setminus @ sK10 @ sK12) @ (setminus @ sK10 @ X4))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ X4))))) => (((in @ sK13 @ (powerset @ sK10)) = $true) & ((binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (binintersect @ (setminus @ sK10 @ sK12) @ (setminus @ sK10 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13)))))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f35,plain,(
% 1.74/1.34 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ (powerset @ X1))) & ? [X4 : $i] : (($true = (in @ X4 @ (powerset @ X1))) & ((binunion @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) @ (binintersect @ (setminus @ X1 @ X3) @ (setminus @ X1 @ X4))) != (setminus @ X1 @ (binintersect @ (binunion @ X0 @ X2) @ (binunion @ X3 @ X4)))))) & ($true = (in @ X2 @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) & (binunionT_lem = $true) & (demorgan2 = $true) & (demorgan1 = $true)),
% 1.74/1.34 inference(rectify,[status(thm)],[f19])).
% 1.74/1.34 thf(f19,plain,(
% 1.74/1.34 ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) & ? [X4 : $i] : (((in @ X4 @ (powerset @ X0)) = $true) & ((setminus @ X0 @ (binintersect @ (binunion @ X1 @ X2) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4)))))) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binunionT_lem = $true) & (demorgan2 = $true) & (demorgan1 = $true)),
% 1.74/1.34 inference(flattening,[status(thm)],[f18])).
% 1.74/1.34 thf(f18,plain,(
% 1.74/1.34 ((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) & ? [X4 : $i] : (((in @ X4 @ (powerset @ X0)) = $true) & ((setminus @ X0 @ (binintersect @ (binunion @ X1 @ X2) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4)))))) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (demorgan2 = $true)) & (demorgan1 = $true)) & (binunionT_lem = $true)),
% 1.74/1.34 inference(ennf_transformation,[status(thm)],[f8])).
% 1.74/1.34 thf(f8,plain,(
% 1.74/1.34 ~((binunionT_lem = $true) => ((demorgan1 = $true) => ((demorgan2 = $true) => ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) => ! [X4 : $i] : (((in @ X4 @ (powerset @ X0)) = $true) => ((setminus @ X0 @ (binintersect @ (binunion @ X1 @ X2) @ (binunion @ X3 @ X4))) = (binunion @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4)))))))))))),
% 1.74/1.34 inference(fool_elimination,[status(thm)],[f7])).
% 1.74/1.34 thf(f7,plain,(
% 1.74/1.34 ~(binunionT_lem => (demorgan1 => (demorgan2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((setminus @ X0 @ (binintersect @ (binunion @ X1 @ X2) @ (binunion @ X3 @ X4))) = (binunion @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4)))))))))))),
% 1.74/1.34 inference(rectify,[status(thm)],[f5])).
% 1.74/1.34 thf(f5,negated_conjecture,(
% 1.74/1.34 ~(binunionT_lem => (demorgan1 => (demorgan2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((setminus @ X0 @ (binintersect @ (binunion @ X1 @ X2) @ (binunion @ X3 @ X4))) = (binunion @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4)))))))))))),
% 1.74/1.34 inference(negated_conjecture,[status(cth)],[f4])).
% 1.74/1.34 thf(f4,conjecture,(
% 1.74/1.34 binunionT_lem => (demorgan1 => (demorgan2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((setminus @ X0 @ (binintersect @ (binunion @ X1 @ X2) @ (binunion @ X3 @ X4))) = (binunion @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (binintersect @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4))))))))))),
% 1.74/1.34 file('/export/starexec/sandbox/tmp/tmp.VRLqFJpPNV/DTF2THF_9901.p',woz1_2)).
% 1.74/1.34 thf(f107,plain,(
% 1.74/1.34 ((in @ sK12 @ (powerset @ sK10)) != $true) | spl14_2),
% 1.74/1.34 inference(subsumption_resolution,[status(thm)],[f106,f59])).
% 1.74/1.34 thf(f59,plain,(
% 1.74/1.34 ((in @ sK13 @ (powerset @ sK10)) = $true)),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 1.74/1.34 thf(f106,plain,(
% 1.74/1.34 ((in @ sK13 @ (powerset @ sK10)) != $true) | ((in @ sK12 @ (powerset @ sK10)) != $true) | spl14_2),
% 1.74/1.34 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.74/1.34 thf(f105,plain,(
% 1.74/1.34 ((in @ sK12 @ (powerset @ sK10)) != $true) | ($true != $true) | ((in @ sK13 @ (powerset @ sK10)) != $true) | spl14_2),
% 1.74/1.34 inference(superposition,[status(thm)],[f96,f73])).
% 1.74/1.34 thf(f73,plain,(
% 1.74/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.74/1.34 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.74/1.34 thf(f65,plain,(
% 1.74/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true)) )),
% 1.74/1.34 inference(definition_unfolding,[status(thm)],[f48,f55])).
% 1.74/1.34 thf(f55,plain,(
% 1.74/1.34 (binunionT_lem = $true)),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 1.74/1.34 thf(f48,plain,(
% 1.74/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | (binunionT_lem != $true)) )),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.74/1.34 thf(f29,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true))) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | (((in @ sK4 @ (powerset @ sK3)) = $true) & (((in @ sK5 @ (powerset @ sK3)) = $true) & ((in @ (binunion @ sK4 @ sK5) @ (powerset @ sK3)) != $true))))),
% 1.74/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f26,f28,f27])).
% 1.74/1.34 thf(f27,plain,(
% 1.74/1.34 ? [X3 : $i,X4 : $i] : (($true = (in @ X4 @ (powerset @ X3))) & ? [X5 : $i] : (((in @ X5 @ (powerset @ X3)) = $true) & ($true != (in @ (binunion @ X4 @ X5) @ (powerset @ X3))))) => (((in @ sK4 @ (powerset @ sK3)) = $true) & ? [X5 : $i] : (((in @ X5 @ (powerset @ sK3)) = $true) & ($true != (in @ (binunion @ sK4 @ X5) @ (powerset @ sK3)))))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f28,plain,(
% 1.74/1.34 ? [X5 : $i] : (((in @ X5 @ (powerset @ sK3)) = $true) & ($true != (in @ (binunion @ sK4 @ X5) @ (powerset @ sK3)))) => (((in @ sK5 @ (powerset @ sK3)) = $true) & ((in @ (binunion @ sK4 @ sK5) @ (powerset @ sK3)) != $true))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f26,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true))) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X3 : $i,X4 : $i] : (($true = (in @ X4 @ (powerset @ X3))) & ? [X5 : $i] : (((in @ X5 @ (powerset @ X3)) = $true) & ($true != (in @ (binunion @ X4 @ X5) @ (powerset @ X3))))))),
% 1.74/1.34 inference(rectify,[status(thm)],[f25])).
% 1.74/1.34 thf(f25,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true))) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) != $true))))),
% 1.74/1.34 inference(nnf_transformation,[status(thm)],[f15])).
% 1.74/1.34 thf(f15,plain,(
% 1.74/1.34 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true))) <=> (binunionT_lem = $true)),
% 1.74/1.34 inference(ennf_transformation,[status(thm)],[f12])).
% 1.74/1.34 thf(f12,plain,(
% 1.74/1.34 (binunionT_lem = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true)))),
% 1.74/1.34 inference(fool_elimination,[status(thm)],[f11])).
% 1.74/1.34 thf(f11,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))) = binunionT_lem)),
% 1.74/1.34 inference(rectify,[status(thm)],[f1])).
% 1.74/1.34 thf(f1,axiom,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))) = binunionT_lem)),
% 1.74/1.34 file('/export/starexec/sandbox/tmp/tmp.VRLqFJpPNV/DTF2THF_9901.p',binunionT_lem)).
% 1.74/1.34 thf(f96,plain,(
% 1.74/1.34 ((in @ (binunion @ sK12 @ sK13) @ (powerset @ sK10)) != $true) | spl14_2),
% 1.74/1.34 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.74/1.34 thf(f94,definition,(
% 1.74/1.34 spl14_2 <=> ((in @ (binunion @ sK12 @ sK13) @ (powerset @ sK10)) = $true)),
% 1.74/1.34 introduced(definition,[new_symbols(naming,[spl14_2])],[avatar_definition])).
% 1.74/1.34 thf(f103,plain,(
% 1.74/1.34 spl14_1),
% 1.74/1.34 inference(avatar_contradiction_clause,[status(thm)],[f102])).
% 1.74/1.34 thf(f102,plain,(
% 1.74/1.34 $false | spl14_1),
% 1.74/1.34 inference(subsumption_resolution,[status(thm)],[f101,f56])).
% 1.74/1.34 thf(f56,plain,(
% 1.74/1.34 ($true = (in @ sK9 @ (powerset @ sK10)))),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 1.74/1.34 thf(f101,plain,(
% 1.74/1.34 ($true != (in @ sK9 @ (powerset @ sK10))) | spl14_1),
% 1.74/1.34 inference(subsumption_resolution,[status(thm)],[f100,f57])).
% 1.74/1.34 thf(f57,plain,(
% 1.74/1.34 ((in @ sK11 @ (powerset @ sK10)) = $true)),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 1.74/1.34 thf(f100,plain,(
% 1.74/1.34 ((in @ sK11 @ (powerset @ sK10)) != $true) | ($true != (in @ sK9 @ (powerset @ sK10))) | spl14_1),
% 1.74/1.34 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.74/1.34 thf(f99,plain,(
% 1.74/1.34 ($true != $true) | ((in @ sK11 @ (powerset @ sK10)) != $true) | ($true != (in @ sK9 @ (powerset @ sK10))) | spl14_1),
% 1.74/1.34 inference(superposition,[status(thm)],[f92,f73])).
% 1.74/1.34 thf(f92,plain,(
% 1.74/1.34 ((in @ (binunion @ sK9 @ sK11) @ (powerset @ sK10)) != $true) | spl14_1),
% 1.74/1.34 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.74/1.34 thf(f90,definition,(
% 1.74/1.34 spl14_1 <=> ((in @ (binunion @ sK9 @ sK11) @ (powerset @ sK10)) = $true)),
% 1.74/1.34 introduced(definition,[new_symbols(naming,[spl14_1])],[avatar_definition])).
% 1.74/1.34 thf(f97,plain,(
% 1.74/1.34 ~spl14_1 | ~spl14_2),
% 1.74/1.34 inference(avatar_split_clause,[status(thm)],[f88,f94,f90])).
% 1.74/1.34 thf(f88,plain,(
% 1.74/1.34 ((in @ (binunion @ sK12 @ sK13) @ (powerset @ sK10)) != $true) | ((in @ (binunion @ sK9 @ sK11) @ (powerset @ sK10)) != $true)),
% 1.74/1.34 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.74/1.34 thf(f87,plain,(
% 1.74/1.34 ((in @ (binunion @ sK9 @ sK11) @ (powerset @ sK10)) != $true) | ((in @ (binunion @ sK12 @ sK13) @ (powerset @ sK10)) != $true) | ((setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13))))),
% 1.74/1.34 inference(superposition,[status(thm)],[f85,f74])).
% 1.74/1.34 thf(f74,plain,(
% 1.74/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.74/1.34 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.74/1.34 thf(f61,plain,(
% 1.74/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) )),
% 1.74/1.34 inference(definition_unfolding,[status(thm)],[f44,f53])).
% 1.74/1.34 thf(f53,plain,(
% 1.74/1.34 (demorgan1 = $true)),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 1.74/1.34 thf(f44,plain,(
% 1.74/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true) | (demorgan1 != $true)) )),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f24])).
% 1.74/1.34 thf(f24,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true))) | (demorgan1 != $true)) & ((demorgan1 = $true) | (((in @ sK1 @ (powerset @ sK0)) = $true) & (((binunion @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ sK2)) != (setminus @ sK0 @ (binintersect @ sK1 @ sK2))) & ($true = (in @ sK2 @ (powerset @ sK0))))))),
% 1.74/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f23,f22])).
% 1.74/1.34 thf(f22,plain,(
% 1.74/1.34 ? [X3 : $i,X4 : $i] : (($true = (in @ X4 @ (powerset @ X3))) & ? [X5 : $i] : (((setminus @ X3 @ (binintersect @ X4 @ X5)) != (binunion @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X5))) & ((in @ X5 @ (powerset @ X3)) = $true))) => (((in @ sK1 @ (powerset @ sK0)) = $true) & ? [X5 : $i] : (((setminus @ sK0 @ (binintersect @ sK1 @ X5)) != (binunion @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ X5))) & ((in @ X5 @ (powerset @ sK0)) = $true)))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f23,plain,(
% 1.74/1.34 ? [X5 : $i] : (((setminus @ sK0 @ (binintersect @ sK1 @ X5)) != (binunion @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ X5))) & ((in @ X5 @ (powerset @ sK0)) = $true)) => (((binunion @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ sK2)) != (setminus @ sK0 @ (binintersect @ sK1 @ sK2))) & ($true = (in @ sK2 @ (powerset @ sK0))))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f21,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true))) | (demorgan1 != $true)) & ((demorgan1 = $true) | ? [X3 : $i,X4 : $i] : (($true = (in @ X4 @ (powerset @ X3))) & ? [X5 : $i] : (((setminus @ X3 @ (binintersect @ X4 @ X5)) != (binunion @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X5))) & ((in @ X5 @ (powerset @ X3)) = $true))))),
% 1.74/1.34 inference(rectify,[status(thm)],[f20])).
% 1.74/1.34 thf(f20,plain,(
% 1.74/1.34 (! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) = (setminus @ X1 @ (binintersect @ X0 @ X2))) | ($true != (in @ X2 @ (powerset @ X1))))) | (demorgan1 != $true)) & ((demorgan1 = $true) | ? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) != (setminus @ X1 @ (binintersect @ X0 @ X2))) & ($true = (in @ X2 @ (powerset @ X1))))))),
% 1.74/1.34 inference(nnf_transformation,[status(thm)],[f16])).
% 1.74/1.34 thf(f16,plain,(
% 1.74/1.34 ! [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) = (setminus @ X1 @ (binintersect @ X0 @ X2))) | ($true != (in @ X2 @ (powerset @ X1))))) <=> (demorgan1 = $true)),
% 1.74/1.34 inference(ennf_transformation,[status(thm)],[f14])).
% 1.74/1.34 thf(f14,plain,(
% 1.74/1.34 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) = (setminus @ X1 @ (binintersect @ X0 @ X2))))) <=> (demorgan1 = $true)),
% 1.74/1.34 inference(fool_elimination,[status(thm)],[f13])).
% 1.74/1.34 thf(f13,plain,(
% 1.74/1.34 (demorgan1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) = (setminus @ X1 @ (binintersect @ X0 @ X2))))))),
% 1.74/1.34 inference(rectify,[status(thm)],[f2])).
% 1.74/1.34 thf(f2,axiom,(
% 1.74/1.34 (demorgan1 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((setminus @ X0 @ (binintersect @ X1 @ X2)) = (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))),
% 1.74/1.34 file('/export/starexec/sandbox/tmp/tmp.VRLqFJpPNV/DTF2THF_9901.p',demorgan1)).
% 1.74/1.34 thf(f85,plain,(
% 1.74/1.34 ((binunion @ (setminus @ sK10 @ (binunion @ sK9 @ sK11)) @ (setminus @ sK10 @ (binunion @ sK12 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13))))),
% 1.74/1.34 inference(subsumption_resolution,[status(thm)],[f84,f57])).
% 1.74/1.34 thf(f84,plain,(
% 1.74/1.34 ((in @ sK11 @ (powerset @ sK10)) != $true) | ((binunion @ (setminus @ sK10 @ (binunion @ sK9 @ sK11)) @ (setminus @ sK10 @ (binunion @ sK12 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13))))),
% 1.74/1.34 inference(subsumption_resolution,[status(thm)],[f83,f56])).
% 1.74/1.34 thf(f83,plain,(
% 1.74/1.34 ($true != (in @ sK9 @ (powerset @ sK10))) | ((binunion @ (setminus @ sK10 @ (binunion @ sK9 @ sK11)) @ (setminus @ sK10 @ (binunion @ sK12 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13)))) | ((in @ sK11 @ (powerset @ sK10)) != $true)),
% 1.74/1.34 inference(superposition,[status(thm)],[f80,f75])).
% 1.74/1.34 thf(f75,plain,(
% 1.74/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.74/1.34 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.74/1.34 thf(f69,plain,(
% 1.74/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) )),
% 1.74/1.34 inference(definition_unfolding,[status(thm)],[f52,f54])).
% 1.74/1.34 thf(f54,plain,(
% 1.74/1.34 (demorgan2 = $true)),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 1.74/1.34 thf(f52,plain,(
% 1.74/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | (demorgan2 != $true)) )),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f34])).
% 1.74/1.34 thf(f34,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (demorgan2 != $true)) & ((demorgan2 = $true) | ((((setminus @ sK6 @ (binunion @ sK7 @ sK8)) != (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8))) & ((in @ sK8 @ (powerset @ sK6)) = $true)) & ($true = (in @ sK7 @ (powerset @ sK6)))))),
% 1.74/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f31,f33,f32])).
% 1.74/1.34 thf(f32,plain,(
% 1.74/1.34 ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (((binintersect @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X5)) != (setminus @ X3 @ (binunion @ X4 @ X5))) & ((in @ X5 @ (powerset @ X3)) = $true)) & ($true = (in @ X4 @ (powerset @ X3)))) => (? [X5 : $i] : (((binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ X5)) != (setminus @ sK6 @ (binunion @ sK7 @ X5))) & ((in @ X5 @ (powerset @ sK6)) = $true)) & ($true = (in @ sK7 @ (powerset @ sK6))))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f33,plain,(
% 1.74/1.34 ? [X5 : $i] : (((binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ X5)) != (setminus @ sK6 @ (binunion @ sK7 @ X5))) & ((in @ X5 @ (powerset @ sK6)) = $true)) => (((setminus @ sK6 @ (binunion @ sK7 @ sK8)) != (binintersect @ (setminus @ sK6 @ sK7) @ (setminus @ sK6 @ sK8))) & ((in @ sK8 @ (powerset @ sK6)) = $true))),
% 1.74/1.34 introduced(definition,[],[choice_axiom])).
% 1.74/1.34 thf(f31,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (demorgan2 != $true)) & ((demorgan2 = $true) | ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (((binintersect @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X5)) != (setminus @ X3 @ (binunion @ X4 @ X5))) & ((in @ X5 @ (powerset @ X3)) = $true)) & ($true = (in @ X4 @ (powerset @ X3)))))),
% 1.74/1.34 inference(rectify,[status(thm)],[f30])).
% 1.74/1.34 thf(f30,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (demorgan2 != $true)) & ((demorgan2 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) != (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 1.74/1.34 inference(nnf_transformation,[status(thm)],[f17])).
% 1.74/1.34 thf(f17,plain,(
% 1.74/1.34 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (demorgan2 = $true)),
% 1.74/1.34 inference(ennf_transformation,[status(thm)],[f10])).
% 1.74/1.34 thf(f10,plain,(
% 1.74/1.34 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) <=> (demorgan2 = $true)),
% 1.74/1.34 inference(fool_elimination,[status(thm)],[f9])).
% 1.74/1.34 thf(f9,plain,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) = demorgan2)),
% 1.74/1.34 inference(rectify,[status(thm)],[f3])).
% 1.74/1.34 thf(f3,axiom,(
% 1.74/1.34 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((setminus @ X0 @ (binunion @ X1 @ X2)) = (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) = demorgan2)),
% 1.74/1.34 file('/export/starexec/sandbox/tmp/tmp.VRLqFJpPNV/DTF2THF_9901.p',demorgan2)).
% 1.74/1.34 thf(f80,plain,(
% 1.74/1.34 ((binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (setminus @ sK10 @ (binunion @ sK12 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13))))),
% 1.74/1.34 inference(subsumption_resolution,[status(thm)],[f79,f59])).
% 1.74/1.34 thf(f79,plain,(
% 1.74/1.34 ((binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (setminus @ sK10 @ (binunion @ sK12 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13)))) | ((in @ sK13 @ (powerset @ sK10)) != $true)),
% 1.74/1.34 inference(subsumption_resolution,[status(thm)],[f77,f60])).
% 1.74/1.34 thf(f77,plain,(
% 1.74/1.34 ((in @ sK12 @ (powerset @ sK10)) != $true) | ((binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (setminus @ sK10 @ (binunion @ sK12 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13)))) | ((in @ sK13 @ (powerset @ sK10)) != $true)),
% 1.74/1.34 inference(superposition,[status(thm)],[f58,f75])).
% 1.74/1.34 thf(f58,plain,(
% 1.74/1.34 ((binunion @ (binintersect @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ sK11)) @ (binintersect @ (setminus @ sK10 @ sK12) @ (setminus @ sK10 @ sK13))) != (setminus @ sK10 @ (binintersect @ (binunion @ sK9 @ sK11) @ (binunion @ sK12 @ sK13))))),
% 1.74/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 1.74/1.34 % SZS output end Proof for DTF2THF_9901
% 1.74/1.34 % (10096)------------------------------
% 1.74/1.34 % (10096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (10096)Termination reason: Refutation
% 1.74/1.34
% 1.74/1.34 % (10096)Memory used [KB]: 5628
% 1.74/1.34 % (10096)Time elapsed: 0.015 s
% 1.74/1.34 % (10096)Instructions burned: 16 (million)
% 1.74/1.34 % (10096)------------------------------
% 1.74/1.34 % (10096)------------------------------
% 1.74/1.34 % (10090)Success in time 0.031 s
%------------------------------------------------------------------------------