%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU749^2 : 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 : n008.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 09:36:53 AM UTC 2026
% Result : Theorem 1.56s 1.29s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 92 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 1584 ( 451 equ; 0 cnn)
% Maximal formula atoms : 14 ( 17 avg)
% Number of connectives : 2246 ( 236 ~; 208 |; 116 &;1605 @)
% ( 10 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 21 con; 0-3 aty)
% Number of variables : 266 ( 0 ^; 204 !; 62 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(func_def_26,type,
sK15: $i > $i > $i > $i ).
thf(f168,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f167,f61]) ).
thf(f61,plain,
( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( complementT_lem = $true )
& ( $true
!= ( in @ ( setminus @ sK5 @ ( binunion @ sK6 @ sK7 ) ) @ ( powerset @ ( setminus @ sK5 @ sK6 ) ) ) )
& ( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) )
& ( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) )
& ( binunionT_lem = $true )
& ( demorgan2a1 = $true )
& ( powersetTI1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f20,f36,f35]) ).
thf(f35,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( $true
!= ( in @ ( setminus @ sK5 @ ( binunion @ sK6 @ X2 ) ) @ ( powerset @ ( setminus @ sK5 @ sK6 ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK5 ) ) ) )
& ( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ? [X2: $i] :
( ( $true
!= ( in @ ( setminus @ sK5 @ ( binunion @ sK6 @ X2 ) ) @ ( powerset @ ( setminus @ sK5 @ sK6 ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK5 ) ) ) )
=> ( ( $true
!= ( in @ ( setminus @ sK5 @ ( binunion @ sK6 @ sK7 ) ) @ ( powerset @ ( setminus @ sK5 @ sK6 ) ) ) )
& ( $true
= ( in @ sK7 @ ( powerset @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ( complementT_lem = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionT_lem = $true )
& ( demorgan2a1 = $true )
& ( powersetTI1 = $true ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( demorgan2a1 = $true )
& ( powersetTI1 = $true )
& ( complementT_lem = $true )
& ( binunionT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( binunionT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( powersetTI1 = $true )
=> ( ( demorgan2a1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( binunionT_lem
=> ( complementT_lem
=> ( powersetTI1
=> ( demorgan2a1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( binunionT_lem
=> ( complementT_lem
=> ( powersetTI1
=> ( demorgan2a1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( binunionT_lem
=> ( complementT_lem
=> ( powersetTI1
=> ( demorgan2a1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',complementUnionInPowersetComplement) ).
thf(f167,plain,
( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) ),
inference(subsumption_resolution,[status(thm)],[f166,f60]) ).
thf(f60,plain,
( $true
= ( in @ sK6 @ ( powerset @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f166,plain,
( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) ) ),
inference(superposition,[status(thm)],[f154,f101]) ).
thf(f101,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f53,f59]) ).
thf(f59,plain,
binunionT_lem = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f53,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) )
| ( $true
= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( binunionT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( binunionT_lem = $true )
| ( ( $true
= ( in @ sK2 @ ( powerset @ sK3 ) ) )
& ( $true
!= ( in @ ( binunion @ sK2 @ sK4 ) @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) )
| ! [X5: $i] :
( ( $true
= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) ) )
| ( binunionT_lem != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f31,f33,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
!= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK2 @ ( powerset @ sK3 ) ) )
& ? [X2: $i] :
( ( $true
!= ( in @ ( binunion @ sK2 @ X2 ) @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK3 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X2: $i] :
( ( $true
!= ( in @ ( binunion @ sK2 @ X2 ) @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK3 ) ) ) )
=> ( ( $true
!= ( in @ ( binunion @ sK2 @ sK4 ) @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( binunionT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
!= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) )
| ! [X5: $i] :
( ( $true
= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) ) )
| ( binunionT_lem != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( binunionT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
!= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( binunionT_lem != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( binunionT_lem = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( binunionT_lem = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( $true
= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binunionT_lem
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',binunionT_lem) ).
thf(f154,plain,
( $true
!= ( in @ ( binunion @ sK6 @ sK7 ) @ ( powerset @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
( ( $true
!= ( in @ ( binunion @ sK6 @ sK7 ) @ ( powerset @ sK5 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f142,f99]) ).
thf(f99,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true != $true )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f52,f63]) ).
thf(f63,plain,
complementT_lem = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f52,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( complementT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ( ( $true
!= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f28]) ).
thf(f28,plain,
( ? [X2: $i,X3: $i] :
( ( $true
!= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) ) )
=> ( ( $true
!= ( in @ ( setminus @ sK1 @ sK0 ) @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X2: $i,X3: $i] :
( ( $true
!= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( complementT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) )
<=> ( complementT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( complementT_lem
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',complementT_lem) ).
thf(f142,plain,
( $true
!= ( in @ ( setminus @ sK5 @ ( binunion @ sK6 @ sK7 ) ) @ ( powerset @ sK5 ) ) ),
inference(subsumption_resolution,[status(thm)],[f141,f61]) ).
thf(f141,plain,
( ( $true
!= ( in @ ( setminus @ sK5 @ ( binunion @ sK6 @ sK7 ) ) @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f140,f60]) ).
thf(f140,plain,
( ( $true
!= ( in @ ( setminus @ sK5 @ ( binunion @ sK6 @ sK7 ) ) @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
( ( $true
!= ( in @ sK6 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ sK7 @ ( powerset @ sK5 ) ) )
| ( $true
!= ( in @ ( setminus @ sK5 @ ( binunion @ sK6 @ sK7 ) ) @ ( powerset @ sK5 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f62,f132]) ).
thf(f132,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f131,f99]) ).
thf(f131,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f127]) ).
thf(f127,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) ) )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f117,f102]) ).
thf(f102,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X4 )
= $true )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true != $true )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f71,f57]) ).
thf(f57,plain,
powersetTI1 = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f71,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X4 )
= $true )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( powersetTI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( powersetTI1 = $true )
| ( ( ( in @ sK14 @ ( powerset @ sK12 ) )
= $true )
& ( ( in @ sK13 @ ( powerset @ sK14 ) )
!= $true )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ sK14 ) )
| ( $true
!= ( in @ X3 @ sK12 ) )
| ( ( in @ X3 @ sK13 )
!= $true ) )
& ( $true
= ( in @ sK13 @ ( powerset @ sK12 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ( ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X6 )
!= $true )
& ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X4 )
= $true )
& ( $true
= ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X5 ) ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) )
| ( powersetTI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f45,f48,f47,f46]) ).
thf(f46,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK12 ) )
= $true )
& ( ( in @ sK13 @ ( powerset @ X2 ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( $true
!= ( in @ X3 @ sK12 ) )
| ( ( in @ X3 @ sK13 )
!= $true ) ) )
& ( $true
= ( in @ sK13 @ ( powerset @ sK12 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK12 ) )
= $true )
& ( ( in @ sK13 @ ( powerset @ X2 ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( $true
!= ( in @ X3 @ sK12 ) )
| ( ( in @ X3 @ sK13 )
!= $true ) ) )
=> ( ( ( in @ sK14 @ ( powerset @ sK12 ) )
= $true )
& ( ( in @ sK13 @ ( powerset @ sK14 ) )
!= $true )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ sK14 ) )
| ( $true
!= ( in @ X3 @ sK12 ) )
| ( ( in @ X3 @ sK13 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f48,plain,
! [X4: $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
& ( $true
= ( in @ X7 @ X4 ) )
& ( $true
= ( in @ X7 @ X5 ) ) )
=> ( ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X6 )
!= $true )
& ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X4 )
= $true )
& ( $true
= ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ( ( powersetTI1 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ? [X7: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
& ( $true
= ( in @ X7 @ X4 ) )
& ( $true
= ( in @ X7 @ X5 ) ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) )
| ( powersetTI1 != $true ) ) ),
inference(rectify,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( powersetTI1 = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( $true
!= ( in @ X0 @ ( powerset @ X2 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
= ( in @ X0 @ ( powerset @ X2 ) ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( powersetTI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( powersetTI1 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
= ( in @ X0 @ ( powerset @ X2 ) ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ( powersetTI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X2 ) ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( powersetTI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( $true
= ( in @ X0 @ ( powerset @ X2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( powersetTI1
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( in @ X0 @ ( powerset @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( powersetTI1
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( in @ X1 @ ( powerset @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',powersetTI1) ).
thf(f117,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK15 @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X3 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X3 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( sK15 @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X3 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X3 ) ) )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f113]) ).
thf(f113,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X3 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X3 ) ) )
| ( $true
!= ( in @ ( sK15 @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ X3 ) @ X0 ) )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X3 ) )
!= $true )
| ( $true
!= ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X3 ) ) )
| ( ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f98,f110]) ).
thf(f110,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK15 @ X0 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X4 ) ) )
| ( ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ ( sK15 @ X0 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ X4 ) @ X1 )
!= $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X0 ) )
= $true )
| ( $true
= ( in @ ( sK15 @ X0 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ X4 ) @ ( setminus @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ ( sK15 @ X0 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ X4 ) @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X4 ) ) ) ),
inference(superposition,[status(thm)],[f100,f97]) ).
thf(f97,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X5 ) )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
= ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X5 ) )
| ( $true != $true )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f70,f57]) ).
thf(f70,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ( $true
= ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X5 ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( powersetTI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f100,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) )
| ( $true
= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f64,f58]) ).
thf(f58,plain,
demorgan2a1 = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f64,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( $true
= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( demorgan2a1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( demorgan2a1 = $true )
| ( ( ( in @ sK8 @ ( powerset @ sK9 ) )
= $true )
& ( ( in @ sK10 @ ( powerset @ sK9 ) )
= $true )
& ( $true
!= ( in @ sK11 @ ( setminus @ sK9 @ sK8 ) ) )
& ( $true
= ( in @ sK11 @ ( setminus @ sK9 @ ( binunion @ sK8 @ sK10 ) ) ) )
& ( $true
= ( in @ sK11 @ sK9 ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ! [X7: $i] :
( ( $true
= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) )
| ( $true
!= ( in @ X7 @ X5 ) ) ) ) )
| ( demorgan2a1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f39,f42,f41,f40]) ).
thf(f40,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ) )
=> ( ( ( in @ sK8 @ ( powerset @ sK9 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK9 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK9 @ sK8 ) )
!= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK9 @ ( binunion @ sK8 @ X2 ) ) ) )
& ( ( in @ X3 @ sK9 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK9 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK9 @ sK8 ) )
!= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK9 @ ( binunion @ sK8 @ X2 ) ) ) )
& ( ( in @ X3 @ sK9 )
= $true ) ) )
=> ( ( ( in @ sK10 @ ( powerset @ sK9 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK9 @ sK8 ) )
!= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK9 @ ( binunion @ sK8 @ sK10 ) ) ) )
& ( ( in @ X3 @ sK9 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK9 @ sK8 ) )
!= $true )
& ( $true
= ( in @ X3 @ ( setminus @ sK9 @ ( binunion @ sK8 @ sK10 ) ) ) )
& ( ( in @ X3 @ sK9 )
= $true ) )
=> ( ( $true
!= ( in @ sK11 @ ( setminus @ sK9 @ sK8 ) ) )
& ( $true
= ( in @ sK11 @ ( setminus @ sK9 @ ( binunion @ sK8 @ sK10 ) ) ) )
& ( $true
= ( in @ sK11 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ( ( demorgan2a1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ! [X7: $i] :
( ( $true
= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X5 @ ( binunion @ X4 @ X6 ) ) ) )
| ( $true
!= ( in @ X7 @ X5 ) ) ) ) )
| ( demorgan2a1 != $true ) ) ),
inference(rectify,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( demorgan2a1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) )
| ( demorgan2a1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( demorgan2a1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( demorgan2a1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ) )
<=> ( demorgan2a1 = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( demorgan2a1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( demorgan2a1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',demorgan2a1) ).
thf(f98,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X6 )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X6 )
!= $true )
| ( $true != $true )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f72,f57]) ).
thf(f72,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
= ( in @ X5 @ ( powerset @ X6 ) ) )
| ( ( in @ ( sK15 @ X6 @ X5 @ X4 ) @ X6 )
!= $true )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( powersetTI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f62,plain,
( $true
!= ( in @ ( setminus @ sK5 @ ( binunion @ sK6 @ sK7 ) ) @ ( powerset @ ( setminus @ sK5 @ sK6 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU749^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:32:54 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.44 ---- Original DTF file ---
% 0.26/0.44 thf(spec,logic,$$dhol).
% 0.26/0.44 %------------------------------------------------------------------------------
% 0.26/0.44 % File : SEU749^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.44 % Domain : Set Theory
% 0.26/0.44 % Problem : Typed Set Theory - Laws for Typed Sets - DeMorgan Laws
% 0.26/0.44 % Version : Especial > Reduced > Especial.
% 0.26/0.44 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.26/0.44 % in (setminus A (binunion X Y)) (powerset (setminus A X))))
% 0.26/0.44
% 0.26/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.44 % Source : [Bro08]
% 0.26/0.44 % Names : ZFC251l [Bro08]
% 0.26/0.44 % : ZFC269l [Bro08]
% 0.26/0.44
% 0.26/0.44 % Status : Theorem
% 0.26/0.44 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 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
% 0.26/0.44 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.26/0.44 % Number of atoms : 31 ( 4 equ; 0 cnn)
% 0.26/0.44 % Maximal formula atoms : 7 ( 6 avg)
% 0.26/0.44 % Number of connectives : 85 ( 0 ~; 0 |; 0 &; 67 @)
% 0.26/0.44 % ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% 0.26/0.44 % Maximal formula depth : 15 ( 4 avg)
% 0.26/0.44 % Number of types : 2 ( 0 usr)
% 0.26/0.44 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.26/0.44 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.26/0.44 % Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 0.26/0.44 % SPC : TH0_THM_EQU_NAR
% 0.26/0.44
% 0.26/0.44 % Comments : http://mathgate.info/detsetitem.php?id=379
% 0.26/0.44 %------------------------------------------------------------------------------
% 0.26/0.44 thf(in_type,type,
% 0.26/0.44 in: $i > $i > $o ).
% 0.26/0.44
% 0.26/0.44 thf(powerset_type,type,
% 0.26/0.44 powerset: $i > $i ).
% 0.26/0.44
% 0.26/0.44 thf(binunion_type,type,
% 0.26/0.44 binunion: $i > $i > $i ).
% 0.26/0.44
% 0.26/0.44 thf(setminus_type,type,
% 0.26/0.44 setminus: $i > $i > $i ).
% 0.26/0.44
% 0.26/0.44 thf(binunionT_lem_type,type,
% 0.26/0.44 binunionT_lem: $o ).
% 0.26/0.44
% 0.26/0.44 thf(binunionT_lem,definition,
% 0.26/0.44 ( binunionT_lem
% 0.26/0.44 = ( ! [A: $i,X: $i] :
% 0.26/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.44 => ! [Y: $i] :
% 0.26/0.44 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.44 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.26/0.44
% 0.26/0.44 thf(complementT_lem_type,type,
% 0.26/0.44 complementT_lem: $o ).
% 0.26/0.44
% 0.26/0.44 thf(complementT_lem,definition,
% 0.26/0.44 ( complementT_lem
% 0.26/0.44 = ( ! [A: $i,X: $i] :
% 0.26/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.44 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.26/0.44
% 0.26/0.44 thf(powersetTI1_type,type,
% 0.26/0.44 powersetTI1: $o ).
% 0.26/0.44
% 0.26/0.44 thf(powersetTI1,definition,
% 0.26/0.44 ( powersetTI1
% 0.26/0.44 = ( ! [A: $i,X: $i] :
% 0.26/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.44 => ! [Y: $i] :
% 0.26/0.44 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.44 => ( ! [Xx: $i] :
% 0.26/0.44 ( ( in @ Xx @ A )
% 0.26/0.44 => ( ( in @ Xx @ X )
% 0.26/0.44 => ( in @ Xx @ Y ) ) )
% 0.26/0.44 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.26/0.44
% 0.26/0.44 thf(demorgan2a1_type,type,
% 0.26/0.44 demorgan2a1: $o ).
% 0.26/0.44
% 0.26/0.44 thf(demorgan2a1,definition,
% 0.26/0.44 ( demorgan2a1
% 0.26/0.44 = ( ! [A: $i,X: $i] :
% 0.26/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.44 => ! [Y: $i] :
% 0.26/0.44 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.44 => ! [Xx: $i] :
% 0.26/0.44 ( ( in @ Xx @ A )
% 0.26/0.44 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.26/0.44 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.44
% 0.26/0.44 thf(complementUnionInPowersetComplement,conjecture,
% 0.26/0.44 ( binunionT_lem
% 0.26/0.44 => ( complementT_lem
% 0.26/0.44 => ( powersetTI1
% 0.26/0.44 => ( demorgan2a1
% 0.26/0.44 => ! [A: $i,X: $i] :
% 0.26/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.44 => ! [Y: $i] :
% 0.26/0.44 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.44 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.26/0.44
% 0.26/0.44 %------------------------------------------------------------------------------
% 0.26/0.44 ------------------------
% 1.56/1.24 ---- Embedded in THF ---
% 1.56/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.24 %%% Generated on Tue Feb 24 12:32:55 EST 2026
% 1.56/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.24 %%% Logic specification used:
% 1.56/1.24 %%% thf(spec, logic, $$dhol).
% 1.56/1.24
% 1.56/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2DTF13172.p
% See solution above
% 1.56/1.24 ------------------------
% 1.56/1.25 ---- Cleaned THF ---
% 1.56/1.25 thf(in_type,type,
% 1.56/1.25 in: $i > $i > $o ).
% 1.56/1.25
% 1.56/1.25 thf(powerset_type,type,
% 1.56/1.25 powerset: $i > $i ).
% 1.56/1.25
% 1.56/1.25 thf(binunion_type,type,
% 1.56/1.25 binunion: $i > $i > $i ).
% 1.56/1.25
% 1.56/1.25 thf(setminus_type,type,
% 1.56/1.25 setminus: $i > $i > $i ).
% 1.56/1.25
% 1.56/1.25 thf(binunionT_lem_type,type,
% 1.56/1.25 binunionT_lem: $o ).
% 1.56/1.25
% 1.56/1.25 thf(binunionT_lem,definition,
% 1.56/1.25 ( binunionT_lem
% 1.56/1.25 = ( ! [A: $i,X: $i] :
% 1.56/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.56/1.25 => ! [Y: $i] :
% 1.56/1.25 ( ( in @ Y @ ( powerset @ A ) )
% 1.56/1.25 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(complementT_lem_type,type,
% 1.56/1.25 complementT_lem: $o ).
% 1.56/1.25
% 1.56/1.25 thf(complementT_lem,definition,
% 1.56/1.25 ( complementT_lem
% 1.56/1.25 = ( ! [A: $i,X: $i] :
% 1.56/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.56/1.25 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(powersetTI1_type,type,
% 1.56/1.25 powersetTI1: $o ).
% 1.56/1.25
% 1.56/1.25 thf(powersetTI1,definition,
% 1.56/1.25 ( powersetTI1
% 1.56/1.25 = ( ! [A: $i,X: $i] :
% 1.56/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.56/1.25 => ! [Y: $i] :
% 1.56/1.25 ( ( in @ Y @ ( powerset @ A ) )
% 1.56/1.25 => ( ! [Xx: $i] :
% 1.56/1.25 ( ( in @ Xx @ A )
% 1.56/1.25 => ( ( in @ Xx @ X )
% 1.56/1.25 => ( in @ Xx @ Y ) ) )
% 1.56/1.25 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(demorgan2a1_type,type,
% 1.56/1.25 demorgan2a1: $o ).
% 1.56/1.25
% 1.56/1.25 thf(demorgan2a1,definition,
% 1.56/1.25 ( demorgan2a1
% 1.56/1.25 = ( ! [A: $i,X: $i] :
% 1.56/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.56/1.25 => ! [Y: $i] :
% 1.56/1.25 ( ( in @ Y @ ( powerset @ A ) )
% 1.56/1.25 => ! [Xx: $i] :
% 1.56/1.25 ( ( in @ Xx @ A )
% 1.56/1.25 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 1.56/1.25 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 1.56/1.25
% 1.56/1.25 thf(complementUnionInPowersetComplement,conjecture,
% 1.56/1.25 ( binunionT_lem
% 1.56/1.25 => ( complementT_lem
% 1.56/1.25 => ( powersetTI1
% 1.56/1.25 => ( demorgan2a1
% 1.56/1.25 => ! [A: $i,X: $i] :
% 1.56/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.56/1.25 => ! [Y: $i] :
% 1.56/1.25 ( ( in @ Y @ ( powerset @ A ) )
% 1.56/1.25 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 1.56/1.25 ------------------------
% 1.56/1.26 % (13364)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_13172 for (3000ds/2Mi)
% 1.56/1.26 % (13360)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13172 for (3000ds/183Mi)
% 1.56/1.26 % (13364)Instruction limit reached!
% 1.56/1.26 % (13364)------------------------------
% 1.56/1.26 % (13364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.26 % (13364)Termination reason: Unknown
% 1.56/1.26 % (13364)Termination phase: Property scanning
% 1.56/1.26
% 1.56/1.26 % (13364)Memory used [KB]: 1023
% 1.56/1.26 % (13364)Time elapsed: 0.002 s
% 1.56/1.26 % (13364)Instructions burned: 3 (million)
% 1.56/1.26 % (13364)------------------------------
% 1.56/1.26 % (13364)------------------------------
% 1.56/1.27 % (13361)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_13172 for (3000ds/4Mi)
% 1.56/1.27 % (13363)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13172 for (3000ds/2Mi)
% 1.56/1.27 % (13362)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_13172 for (3000ds/27Mi)
% 1.56/1.27 % (13363)Instruction limit reached!
% 1.56/1.27 % (13363)------------------------------
% 1.56/1.27 % (13363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (13363)Termination reason: Unknown
% 1.56/1.27 % (13363)Termination phase: shuffling
% 1.56/1.27
% 1.56/1.27 % (13363)Memory used [KB]: 1023
% 1.56/1.27 % (13363)Time elapsed: 0.003 s
% 1.56/1.27 % (13363)Instructions burned: 2 (million)
% 1.56/1.27 % (13363)------------------------------
% 1.56/1.27 % (13363)------------------------------
% 1.56/1.27 % (13366)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13172 for (3000ds/18Mi)
% 1.56/1.27 % (13361)Instruction limit reached!
% 1.56/1.27 % (13361)------------------------------
% 1.56/1.27 % (13361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.27 % (13361)Termination reason: Unknown
% 1.56/1.27 % (13361)Termination phase: Property scanning
% 1.56/1.27
% 1.56/1.27 % (13361)Memory used [KB]: 1023
% 1.56/1.27 % (13361)Time elapsed: 0.004 s
% 1.56/1.27 % (13361)Instructions burned: 4 (million)
% 1.56/1.27 % (13361)------------------------------
% 1.56/1.27 % (13361)------------------------------
% 1.56/1.27 % (13365)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_13172 for (3000ds/275Mi)
% 1.56/1.28 % (13366)Instruction limit reached!
% 1.56/1.28 % (13366)------------------------------
% 1.56/1.28 % (13366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.28 % (13366)Termination reason: Unknown
% 1.56/1.28 % (13366)Termination phase: Saturation
% 1.56/1.28
% 1.56/1.28 % (13366)Memory used [KB]: 5628
% 1.56/1.28 % (13366)Time elapsed: 0.011 s
% 1.56/1.28 % (13366)Instructions burned: 18 (million)
% 1.56/1.28 % (13366)------------------------------
% 1.56/1.28 % (13366)------------------------------
% 1.56/1.29 % (13362)Instruction limit reached!
% 1.56/1.29 % (13362)------------------------------
% 1.56/1.29 % (13362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.29 % (13362)Termination reason: Unknown
% 1.56/1.29 % (13362)Termination phase: Saturation
% 1.56/1.29
% 1.56/1.29 % (13362)Memory used [KB]: 5628
% 1.56/1.29 % (13362)Time elapsed: 0.019 s
% 1.56/1.29 % (13362)Instructions burned: 28 (million)
% 1.56/1.29 % (13362)------------------------------
% 1.56/1.29 % (13362)------------------------------
% 1.56/1.29 % (13365)First to succeed.
% 1.56/1.29 % (13369)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_13172 for (2999ds/37Mi)
% 1.56/1.29 % (13370)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_13172 for (2999ds/15Mi)
% 1.56/1.29 % (13365)Refutation found. Thanks to Tanya!
% 1.56/1.29 % SZS status Theorem for DTF2THF_13172
% 1.56/1.29 % SZS output start Proof for DTF2THF_13172
% 1.56/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.56/1.29 thf(func_def_1, type, powerset: $i > $i).
% 1.56/1.29 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.56/1.29 thf(func_def_3, type, setminus: $i > $i > $i).
% 1.56/1.29 thf(func_def_26, type, sK15: $i > $i > $i > $i).
% 1.56/1.29 thf(f168,plain,(
% 1.56/1.29 $false),
% 1.56/1.29 inference(subsumption_resolution,[status(thm)],[f167,f61])).
% 1.56/1.29 thf(f61,plain,(
% 1.56/1.29 ($true = (in @ sK7 @ (powerset @ sK5)))),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f37])).
% 1.56/1.29 thf(f37,plain,(
% 1.56/1.29 (complementT_lem = $true) & ((($true != (in @ (setminus @ sK5 @ (binunion @ sK6 @ sK7)) @ (powerset @ (setminus @ sK5 @ sK6)))) & ($true = (in @ sK7 @ (powerset @ sK5)))) & ($true = (in @ sK6 @ (powerset @ sK5)))) & (binunionT_lem = $true) & (demorgan2a1 = $true) & (powersetTI1 = $true)),
% 1.56/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f20,f36,f35])).
% 1.56/1.29 thf(f35,plain,(
% 1.56/1.29 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (($true != (in @ (setminus @ sK5 @ (binunion @ sK6 @ X2)) @ (powerset @ (setminus @ sK5 @ sK6)))) & ($true = (in @ X2 @ (powerset @ sK5)))) & ($true = (in @ sK6 @ (powerset @ sK5))))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f36,plain,(
% 1.56/1.29 ? [X2 : $i] : (($true != (in @ (setminus @ sK5 @ (binunion @ sK6 @ X2)) @ (powerset @ (setminus @ sK5 @ sK6)))) & ($true = (in @ X2 @ (powerset @ sK5)))) => (($true != (in @ (setminus @ sK5 @ (binunion @ sK6 @ sK7)) @ (powerset @ (setminus @ sK5 @ sK6)))) & ($true = (in @ sK7 @ (powerset @ sK5))))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f20,plain,(
% 1.56/1.29 (complementT_lem = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binunionT_lem = $true) & (demorgan2a1 = $true) & (powersetTI1 = $true)),
% 1.56/1.29 inference(flattening,[status(thm)],[f19])).
% 1.56/1.29 thf(f19,plain,(
% 1.56/1.29 (((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (demorgan2a1 = $true)) & (powersetTI1 = $true)) & (complementT_lem = $true)) & (binunionT_lem = $true)),
% 1.56/1.29 inference(ennf_transformation,[status(thm)],[f17])).
% 1.56/1.29 thf(f17,plain,(
% 1.56/1.29 ~((binunionT_lem = $true) => ((complementT_lem = $true) => ((powersetTI1 = $true) => ((demorgan2a1 = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true)))))))),
% 1.56/1.29 inference(fool_elimination,[status(thm)],[f16])).
% 1.56/1.29 thf(f16,plain,(
% 1.56/1.29 ~(binunionT_lem => (complementT_lem => (powersetTI1 => (demorgan2a1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))))))))),
% 1.56/1.29 inference(rectify,[status(thm)],[f6])).
% 1.56/1.29 thf(f6,negated_conjecture,(
% 1.56/1.29 ~(binunionT_lem => (complementT_lem => (powersetTI1 => (demorgan2a1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))))))))),
% 1.56/1.29 inference(negated_conjecture,[status(cth)],[f5])).
% 1.56/1.29 thf(f5,conjecture,(
% 1.56/1.29 binunionT_lem => (complementT_lem => (powersetTI1 => (demorgan2a1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))))))))),
% 1.56/1.29 file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',complementUnionInPowersetComplement)).
% 1.56/1.29 thf(f167,plain,(
% 1.56/1.29 ($true != (in @ sK7 @ (powerset @ sK5)))),
% 1.56/1.29 inference(subsumption_resolution,[status(thm)],[f166,f60])).
% 1.56/1.29 thf(f60,plain,(
% 1.56/1.29 ($true = (in @ sK6 @ (powerset @ sK5)))),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f37])).
% 1.56/1.29 thf(f166,plain,(
% 1.56/1.29 ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK7 @ (powerset @ sK5)))),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 1.56/1.29 thf(f165,plain,(
% 1.56/1.29 ($true != $true) | ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK7 @ (powerset @ sK5)))),
% 1.56/1.29 inference(superposition,[status(thm)],[f154,f101])).
% 1.56/1.29 thf(f101,plain,(
% 1.56/1.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ (binunion @ X3 @ X5) @ (powerset @ X4))) | ($true != (in @ X3 @ (powerset @ X4))) | ($true != (in @ X5 @ (powerset @ X4)))) )),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.56/1.29 thf(f83,plain,(
% 1.56/1.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ (binunion @ X3 @ X5) @ (powerset @ X4))) | ($true != (in @ X5 @ (powerset @ X4))) | ($true != $true) | ($true != (in @ X3 @ (powerset @ X4)))) )),
% 1.56/1.29 inference(definition_unfolding,[status(thm)],[f53,f59])).
% 1.56/1.29 thf(f59,plain,(
% 1.56/1.29 (binunionT_lem = $true)),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f37])).
% 1.56/1.29 thf(f53,plain,(
% 1.56/1.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (powerset @ X4))) | ($true = (in @ (binunion @ X3 @ X5) @ (powerset @ X4))) | ($true != (in @ X5 @ (powerset @ X4))) | (binunionT_lem != $true)) )),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f34])).
% 1.56/1.29 thf(f34,plain,(
% 1.56/1.29 ((binunionT_lem = $true) | (($true = (in @ sK2 @ (powerset @ sK3))) & (($true != (in @ (binunion @ sK2 @ sK4) @ (powerset @ sK3))) & ($true = (in @ sK4 @ (powerset @ sK3)))))) & (! [X3 : $i,X4 : $i] : (($true != (in @ X3 @ (powerset @ X4))) | ! [X5 : $i] : (($true = (in @ (binunion @ X3 @ X5) @ (powerset @ X4))) | ($true != (in @ X5 @ (powerset @ X4))))) | (binunionT_lem != $true))),
% 1.56/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f31,f33,f32])).
% 1.56/1.29 thf(f32,plain,(
% 1.56/1.29 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (($true != (in @ (binunion @ X0 @ X2) @ (powerset @ X1))) & ((in @ X2 @ (powerset @ X1)) = $true))) => (($true = (in @ sK2 @ (powerset @ sK3))) & ? [X2 : $i] : (($true != (in @ (binunion @ sK2 @ X2) @ (powerset @ sK3))) & ($true = (in @ X2 @ (powerset @ sK3)))))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f33,plain,(
% 1.56/1.29 ? [X2 : $i] : (($true != (in @ (binunion @ sK2 @ X2) @ (powerset @ sK3))) & ($true = (in @ X2 @ (powerset @ sK3)))) => (($true != (in @ (binunion @ sK2 @ sK4) @ (powerset @ sK3))) & ($true = (in @ sK4 @ (powerset @ sK3))))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f31,plain,(
% 1.56/1.29 ((binunionT_lem = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (($true != (in @ (binunion @ X0 @ X2) @ (powerset @ X1))) & ((in @ X2 @ (powerset @ X1)) = $true)))) & (! [X3 : $i,X4 : $i] : (($true != (in @ X3 @ (powerset @ X4))) | ! [X5 : $i] : (($true = (in @ (binunion @ X3 @ X5) @ (powerset @ X4))) | ($true != (in @ X5 @ (powerset @ X4))))) | (binunionT_lem != $true))),
% 1.56/1.29 inference(rectify,[status(thm)],[f30])).
% 1.56/1.29 thf(f30,plain,(
% 1.56/1.29 ((binunionT_lem = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (($true != (in @ (binunion @ X0 @ X2) @ (powerset @ X1))) & ((in @ X2 @ (powerset @ X1)) = $true)))) & (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (($true = (in @ (binunion @ X0 @ X2) @ (powerset @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true))) | (binunionT_lem != $true))),
% 1.56/1.29 inference(nnf_transformation,[status(thm)],[f18])).
% 1.56/1.29 thf(f18,plain,(
% 1.56/1.29 (binunionT_lem = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (($true = (in @ (binunion @ X0 @ X2) @ (powerset @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true)))),
% 1.56/1.29 inference(ennf_transformation,[status(thm)],[f9])).
% 1.56/1.29 thf(f9,plain,(
% 1.56/1.29 (binunionT_lem = $true) <=> ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ($true = (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))))),
% 1.56/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.56/1.29 thf(f8,plain,(
% 1.56/1.29 (binunionT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))))),
% 1.56/1.29 inference(rectify,[status(thm)],[f1])).
% 1.56/1.29 thf(f1,axiom,(
% 1.56/1.29 (binunionT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))))),
% 1.56/1.29 file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',binunionT_lem)).
% 1.56/1.29 thf(f154,plain,(
% 1.56/1.29 ($true != (in @ (binunion @ sK6 @ sK7) @ (powerset @ sK5)))),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 1.56/1.29 thf(f153,plain,(
% 1.56/1.29 ($true != (in @ (binunion @ sK6 @ sK7) @ (powerset @ sK5))) | ($true != $true)),
% 1.56/1.29 inference(superposition,[status(thm)],[f142,f99])).
% 1.56/1.29 thf(f99,plain,(
% 1.56/1.29 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.56/1.29 thf(f77,plain,(
% 1.56/1.29 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true != $true) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) )),
% 1.56/1.29 inference(definition_unfolding,[status(thm)],[f52,f63])).
% 1.56/1.29 thf(f63,plain,(
% 1.56/1.29 (complementT_lem = $true)),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f37])).
% 1.56/1.29 thf(f52,plain,(
% 1.56/1.29 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1))) | (complementT_lem != $true)) )),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f29])).
% 1.56/1.29 thf(f29,plain,(
% 1.56/1.29 (! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | (($true != (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) & ($true = (in @ sK0 @ (powerset @ sK1)))))),
% 1.56/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f28])).
% 1.56/1.29 thf(f28,plain,(
% 1.56/1.29 ? [X2 : $i,X3 : $i] : (($true != (in @ (setminus @ X3 @ X2) @ (powerset @ X3))) & ($true = (in @ X2 @ (powerset @ X3)))) => (($true != (in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))) & ($true = (in @ sK0 @ (powerset @ sK1))))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f27,plain,(
% 1.56/1.29 (! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : (($true != (in @ (setminus @ X3 @ X2) @ (powerset @ X3))) & ($true = (in @ X2 @ (powerset @ X3)))))),
% 1.56/1.29 inference(rectify,[status(thm)],[f26])).
% 1.56/1.29 thf(f26,plain,(
% 1.56/1.29 (! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : (($true != (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) & ($true = (in @ X0 @ (powerset @ X1)))))),
% 1.56/1.29 inference(nnf_transformation,[status(thm)],[f21])).
% 1.56/1.29 thf(f21,plain,(
% 1.56/1.29 ! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (complementT_lem = $true)),
% 1.56/1.29 inference(ennf_transformation,[status(thm)],[f15])).
% 1.56/1.29 thf(f15,plain,(
% 1.56/1.29 ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) <=> (complementT_lem = $true)),
% 1.56/1.29 inference(fool_elimination,[status(thm)],[f14])).
% 1.56/1.29 thf(f14,plain,(
% 1.56/1.29 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))))),
% 1.56/1.29 inference(rectify,[status(thm)],[f2])).
% 1.56/1.29 thf(f2,axiom,(
% 1.56/1.29 (complementT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 1.56/1.29 file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',complementT_lem)).
% 1.56/1.29 thf(f142,plain,(
% 1.56/1.29 ($true != (in @ (setminus @ sK5 @ (binunion @ sK6 @ sK7)) @ (powerset @ sK5)))),
% 1.56/1.29 inference(subsumption_resolution,[status(thm)],[f141,f61])).
% 1.56/1.29 thf(f141,plain,(
% 1.56/1.29 ($true != (in @ (setminus @ sK5 @ (binunion @ sK6 @ sK7)) @ (powerset @ sK5))) | ($true != (in @ sK7 @ (powerset @ sK5)))),
% 1.56/1.29 inference(subsumption_resolution,[status(thm)],[f140,f60])).
% 1.56/1.29 thf(f140,plain,(
% 1.56/1.29 ($true != (in @ (setminus @ sK5 @ (binunion @ sK6 @ sK7)) @ (powerset @ sK5))) | ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK7 @ (powerset @ sK5)))),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.56/1.29 thf(f139,plain,(
% 1.56/1.29 ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK7 @ (powerset @ sK5))) | ($true != (in @ (setminus @ sK5 @ (binunion @ sK6 @ sK7)) @ (powerset @ sK5))) | ($true != $true)),
% 1.56/1.29 inference(superposition,[status(thm)],[f62,f132])).
% 1.56/1.29 thf(f132,plain,(
% 1.56/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true) | ($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.56/1.29 inference(subsumption_resolution,[status(thm)],[f131,f99])).
% 1.56/1.29 thf(f131,plain,(
% 1.56/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true)) )),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 1.56/1.29 thf(f130,plain,(
% 1.56/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true)) )),
% 1.56/1.29 inference(duplicate_literal_removal,[status(thm)],[f127])).
% 1.56/1.29 thf(f127,plain,(
% 1.56/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ($true != (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true)) )),
% 1.56/1.29 inference(superposition,[status(thm)],[f117,f102])).
% 1.56/1.29 thf(f102,plain,(
% 1.56/1.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK15 @ X6 @ X5 @ X4) @ X4) = $true) | ($true = (in @ X5 @ (powerset @ X6))) | ((in @ X6 @ (powerset @ X4)) != $true) | ($true != (in @ X5 @ (powerset @ X4)))) )),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.56/1.29 thf(f95,plain,(
% 1.56/1.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (powerset @ X4))) | ($true != $true) | ($true = (in @ X5 @ (powerset @ X6))) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ (sK15 @ X6 @ X5 @ X4) @ X4) = $true)) )),
% 1.56/1.29 inference(definition_unfolding,[status(thm)],[f71,f57])).
% 1.56/1.29 thf(f57,plain,(
% 1.56/1.29 (powersetTI1 = $true)),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f37])).
% 1.56/1.29 thf(f71,plain,(
% 1.56/1.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ($true = (in @ X5 @ (powerset @ X6))) | ((in @ (sK15 @ X6 @ X5 @ X4) @ X4) = $true) | ($true != (in @ X5 @ (powerset @ X4))) | (powersetTI1 != $true)) )),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f49])).
% 1.56/1.29 thf(f49,plain,(
% 1.56/1.29 ((powersetTI1 = $true) | ((((in @ sK14 @ (powerset @ sK12)) = $true) & ((in @ sK13 @ (powerset @ sK14)) != $true) & ! [X3 : $i] : (($true = (in @ X3 @ sK14)) | ($true != (in @ X3 @ sK12)) | ((in @ X3 @ sK13) != $true))) & ($true = (in @ sK13 @ (powerset @ sK12))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ($true = (in @ X5 @ (powerset @ X6))) | (((in @ (sK15 @ X6 @ X5 @ X4) @ X6) != $true) & ((in @ (sK15 @ X6 @ X5 @ X4) @ X4) = $true) & ($true = (in @ (sK15 @ X6 @ X5 @ X4) @ X5)))) | ($true != (in @ X5 @ (powerset @ X4)))) | (powersetTI1 != $true))),
% 1.56/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f45,f48,f47,f46])).
% 1.56/1.29 thf(f46,plain,(
% 1.56/1.29 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ((in @ X1 @ (powerset @ X2)) != $true) & ! [X3 : $i] : (((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (((in @ X2 @ (powerset @ sK12)) = $true) & ((in @ sK13 @ (powerset @ X2)) != $true) & ! [X3 : $i] : (((in @ X3 @ X2) = $true) | ($true != (in @ X3 @ sK12)) | ((in @ X3 @ sK13) != $true))) & ($true = (in @ sK13 @ (powerset @ sK12))))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f47,plain,(
% 1.56/1.29 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK12)) = $true) & ((in @ sK13 @ (powerset @ X2)) != $true) & ! [X3 : $i] : (((in @ X3 @ X2) = $true) | ($true != (in @ X3 @ sK12)) | ((in @ X3 @ sK13) != $true))) => (((in @ sK14 @ (powerset @ sK12)) = $true) & ((in @ sK13 @ (powerset @ sK14)) != $true) & ! [X3 : $i] : (($true = (in @ X3 @ sK14)) | ($true != (in @ X3 @ sK12)) | ((in @ X3 @ sK13) != $true)))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f48,plain,(
% 1.56/1.29 ! [X4 : $i,X5 : $i,X6 : $i] : (? [X7 : $i] : (($true != (in @ X7 @ X6)) & ($true = (in @ X7 @ X4)) & ($true = (in @ X7 @ X5))) => (((in @ (sK15 @ X6 @ X5 @ X4) @ X6) != $true) & ((in @ (sK15 @ X6 @ X5 @ X4) @ X4) = $true) & ($true = (in @ (sK15 @ X6 @ X5 @ X4) @ X5))))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f45,plain,(
% 1.56/1.29 ((powersetTI1 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ((in @ X1 @ (powerset @ X2)) != $true) & ! [X3 : $i] : (((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true))) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ($true = (in @ X5 @ (powerset @ X6))) | ? [X7 : $i] : (($true != (in @ X7 @ X6)) & ($true = (in @ X7 @ X4)) & ($true = (in @ X7 @ X5)))) | ($true != (in @ X5 @ (powerset @ X4)))) | (powersetTI1 != $true))),
% 1.56/1.29 inference(rectify,[status(thm)],[f44])).
% 1.56/1.29 thf(f44,plain,(
% 1.56/1.29 ((powersetTI1 = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ($true != (in @ X0 @ (powerset @ X2))) & ! [X3 : $i] : (((in @ X3 @ X2) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) != $true))) & ($true = (in @ X0 @ (powerset @ X1))))) & (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ($true = (in @ X0 @ (powerset @ X2))) | ? [X3 : $i] : (((in @ X3 @ X2) != $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true))) | ($true != (in @ X0 @ (powerset @ X1)))) | (powersetTI1 != $true))),
% 1.56/1.29 inference(nnf_transformation,[status(thm)],[f25])).
% 1.56/1.29 thf(f25,plain,(
% 1.56/1.29 (powersetTI1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ($true = (in @ X0 @ (powerset @ X2))) | ? [X3 : $i] : (((in @ X3 @ X2) != $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true))) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.56/1.29 inference(flattening,[status(thm)],[f24])).
% 1.56/1.29 thf(f24,plain,(
% 1.56/1.29 (powersetTI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((($true = (in @ X0 @ (powerset @ X2))) | ? [X3 : $i] : ((((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X3 @ X1) = $true))) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.56/1.29 inference(ennf_transformation,[status(thm)],[f13])).
% 1.56/1.29 thf(f13,plain,(
% 1.56/1.29 (powersetTI1 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => (! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X0) = $true) => ((in @ X3 @ X2) = $true))) => ($true = (in @ X0 @ (powerset @ X2))))))),
% 1.56/1.29 inference(fool_elimination,[status(thm)],[f12])).
% 1.56/1.29 thf(f12,plain,(
% 1.56/1.29 (powersetTI1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (in @ X0 @ (powerset @ X2))))))),
% 1.56/1.29 inference(rectify,[status(thm)],[f3])).
% 1.56/1.29 thf(f3,axiom,(
% 1.56/1.29 (powersetTI1 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2))))))),
% 1.56/1.29 file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',powersetTI1)).
% 1.56/1.29 thf(f117,plain,(
% 1.56/1.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK15 @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) @ X0)) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ (setminus @ X0 @ X1) @ (powerset @ X3))) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)) != $true)) )),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.56/1.29 thf(f116,plain,(
% 1.56/1.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ (sK15 @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) @ X0)) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != $true) | ($true != (in @ (setminus @ X0 @ X1) @ (powerset @ X3))) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true)) )),
% 1.56/1.29 inference(duplicate_literal_removal,[status(thm)],[f113])).
% 1.56/1.29 thf(f113,plain,(
% 1.56/1.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)) != $true) | ($true != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ (setminus @ X0 @ X1) @ (powerset @ X3))) | ($true != (in @ (sK15 @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) @ X0)) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)) != $true) | ($true != (in @ (setminus @ X0 @ X1) @ (powerset @ X3))) | ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))) = $true)) )),
% 1.56/1.29 inference(superposition,[status(thm)],[f98,f110])).
% 1.56/1.29 thf(f110,plain,(
% 1.56/1.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true = (in @ (sK15 @ X0 @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ X4) @ (setminus @ X1 @ X2))) | ($true != (in @ X0 @ (powerset @ X4))) | ((in @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ (powerset @ X0)) = $true) | ((in @ (sK15 @ X0 @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ X4) @ X1) != $true) | ($true != (in @ X3 @ (powerset @ X1))) | ($true != (in @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ (powerset @ X4))) | ((in @ X2 @ (powerset @ X1)) != $true)) )),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.56/1.29 thf(f108,plain,(
% 1.56/1.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ (powerset @ X0)) = $true) | ($true = (in @ (sK15 @ X0 @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ X4) @ (setminus @ X1 @ X2))) | ($true != (in @ X3 @ (powerset @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true) | ((in @ (sK15 @ X0 @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ X4) @ X1) != $true) | ($true != $true) | ($true != (in @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ (powerset @ X4))) | ($true != (in @ X0 @ (powerset @ X4)))) )),
% 1.56/1.29 inference(superposition,[status(thm)],[f100,f97])).
% 1.56/1.29 thf(f97,plain,(
% 1.56/1.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = (in @ (sK15 @ X6 @ X5 @ X4) @ X5)) | ($true = (in @ X5 @ (powerset @ X6))) | ((in @ X6 @ (powerset @ X4)) != $true) | ($true != (in @ X5 @ (powerset @ X4)))) )),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.56/1.29 thf(f96,plain,(
% 1.56/1.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (powerset @ X4))) | ($true = (in @ (sK15 @ X6 @ X5 @ X4) @ X5)) | ($true != $true) | ($true = (in @ X5 @ (powerset @ X6))) | ((in @ X6 @ (powerset @ X4)) != $true)) )),
% 1.56/1.29 inference(definition_unfolding,[status(thm)],[f70,f57])).
% 1.56/1.29 thf(f70,plain,(
% 1.56/1.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ($true = (in @ X5 @ (powerset @ X6))) | ($true = (in @ (sK15 @ X6 @ X5 @ X4) @ X5)) | ($true != (in @ X5 @ (powerset @ X4))) | (powersetTI1 != $true)) )),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f49])).
% 1.56/1.29 thf(f100,plain,(
% 1.56/1.29 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6)))) | ($true = (in @ X7 @ (setminus @ X5 @ X4))) | ((in @ X6 @ (powerset @ X5)) != $true) | ($true != (in @ X7 @ X5)) | ($true != (in @ X4 @ (powerset @ X5)))) )),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.56/1.29 thf(f89,plain,(
% 1.56/1.29 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6)))) | ($true != (in @ X4 @ (powerset @ X5))) | ($true != (in @ X7 @ X5)) | ($true = (in @ X7 @ (setminus @ X5 @ X4))) | ((in @ X6 @ (powerset @ X5)) != $true)) )),
% 1.56/1.29 inference(definition_unfolding,[status(thm)],[f64,f58])).
% 1.56/1.29 thf(f58,plain,(
% 1.56/1.29 (demorgan2a1 = $true)),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f37])).
% 1.56/1.29 thf(f64,plain,(
% 1.56/1.29 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (powerset @ X5))) | ((in @ X6 @ (powerset @ X5)) != $true) | ($true = (in @ X7 @ (setminus @ X5 @ X4))) | ($true != (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6)))) | ($true != (in @ X7 @ X5)) | (demorgan2a1 != $true)) )),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f43])).
% 1.56/1.29 thf(f43,plain,(
% 1.56/1.29 ((demorgan2a1 = $true) | (((in @ sK8 @ (powerset @ sK9)) = $true) & (((in @ sK10 @ (powerset @ sK9)) = $true) & (($true != (in @ sK11 @ (setminus @ sK9 @ sK8))) & ($true = (in @ sK11 @ (setminus @ sK9 @ (binunion @ sK8 @ sK10)))) & ($true = (in @ sK11 @ sK9)))))) & (! [X4 : $i,X5 : $i] : (($true != (in @ X4 @ (powerset @ X5))) | ! [X6 : $i] : (((in @ X6 @ (powerset @ X5)) != $true) | ! [X7 : $i] : (($true = (in @ X7 @ (setminus @ X5 @ X4))) | ($true != (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6)))) | ($true != (in @ X7 @ X5))))) | (demorgan2a1 != $true))),
% 1.56/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f39,f42,f41,f40])).
% 1.56/1.29 thf(f40,plain,(
% 1.56/1.29 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ X1 @ X0)) != $true) & ($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ X1) = $true)))) => (((in @ sK8 @ (powerset @ sK9)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK9))) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK9 @ sK8)) != $true) & ($true = (in @ X3 @ (setminus @ sK9 @ (binunion @ sK8 @ X2)))) & ((in @ X3 @ sK9) = $true))))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f41,plain,(
% 1.56/1.29 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK9))) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK9 @ sK8)) != $true) & ($true = (in @ X3 @ (setminus @ sK9 @ (binunion @ sK8 @ X2)))) & ((in @ X3 @ sK9) = $true))) => (((in @ sK10 @ (powerset @ sK9)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK9 @ sK8)) != $true) & ($true = (in @ X3 @ (setminus @ sK9 @ (binunion @ sK8 @ sK10)))) & ((in @ X3 @ sK9) = $true)))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f42,plain,(
% 1.56/1.29 ? [X3 : $i] : (((in @ X3 @ (setminus @ sK9 @ sK8)) != $true) & ($true = (in @ X3 @ (setminus @ sK9 @ (binunion @ sK8 @ sK10)))) & ((in @ X3 @ sK9) = $true)) => (($true != (in @ sK11 @ (setminus @ sK9 @ sK8))) & ($true = (in @ sK11 @ (setminus @ sK9 @ (binunion @ sK8 @ sK10)))) & ($true = (in @ sK11 @ sK9)))),
% 1.56/1.29 introduced(definition,[],[choice_axiom])).
% 1.56/1.29 thf(f39,plain,(
% 1.56/1.29 ((demorgan2a1 = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ X1 @ X0)) != $true) & ($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ X1) = $true))))) & (! [X4 : $i,X5 : $i] : (($true != (in @ X4 @ (powerset @ X5))) | ! [X6 : $i] : (((in @ X6 @ (powerset @ X5)) != $true) | ! [X7 : $i] : (($true = (in @ X7 @ (setminus @ X5 @ X4))) | ($true != (in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6)))) | ($true != (in @ X7 @ X5))))) | (demorgan2a1 != $true))),
% 1.56/1.29 inference(rectify,[status(thm)],[f38])).
% 1.56/1.29 thf(f38,plain,(
% 1.56/1.29 ((demorgan2a1 = $true) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ X1)) != $true) & ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) = $true) & ((in @ X3 @ X0) = $true))))) & (! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ X1)) = $true) | ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true) | ((in @ X3 @ X0) != $true)))) | (demorgan2a1 != $true))),
% 1.56/1.29 inference(nnf_transformation,[status(thm)],[f23])).
% 1.56/1.29 thf(f23,plain,(
% 1.56/1.29 (demorgan2a1 = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ X1)) = $true) | ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true) | ((in @ X3 @ X0) != $true))))),
% 1.56/1.29 inference(flattening,[status(thm)],[f22])).
% 1.56/1.29 thf(f22,plain,(
% 1.56/1.29 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ X1)) = $true) | ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) != $true)) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (demorgan2a1 = $true)),
% 1.56/1.29 inference(ennf_transformation,[status(thm)],[f11])).
% 1.56/1.29 thf(f11,plain,(
% 1.56/1.29 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) = $true) => ((in @ X3 @ (setminus @ X0 @ X1)) = $true))))) <=> (demorgan2a1 = $true)),
% 1.56/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.56/1.29 thf(f10,plain,(
% 1.56/1.29 (demorgan2a1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (setminus @ X0 @ X1)))))))),
% 1.56/1.29 inference(rectify,[status(thm)],[f4])).
% 1.56/1.29 thf(f4,axiom,(
% 1.56/1.29 (demorgan2a1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (setminus @ X0 @ X1)))))))),
% 1.56/1.29 file('/export/starexec/sandbox/tmp/tmp.Ik5OJbq7U9/DTF2THF_13172.p',demorgan2a1)).
% 1.56/1.29 thf(f98,plain,(
% 1.56/1.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK15 @ X6 @ X5 @ X4) @ X6) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ($true != (in @ X5 @ (powerset @ X4))) | ($true = (in @ X5 @ (powerset @ X6)))) )),
% 1.56/1.29 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.56/1.29 thf(f94,plain,(
% 1.56/1.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ((in @ (sK15 @ X6 @ X5 @ X4) @ X6) != $true) | ($true != $true) | ($true = (in @ X5 @ (powerset @ X6))) | ($true != (in @ X5 @ (powerset @ X4)))) )),
% 1.56/1.29 inference(definition_unfolding,[status(thm)],[f72,f57])).
% 1.56/1.29 thf(f72,plain,(
% 1.56/1.29 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ($true = (in @ X5 @ (powerset @ X6))) | ((in @ (sK15 @ X6 @ X5 @ X4) @ X6) != $true) | ($true != (in @ X5 @ (powerset @ X4))) | (powersetTI1 != $true)) )),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f49])).
% 1.56/1.29 thf(f62,plain,(
% 1.56/1.29 ($true != (in @ (setminus @ sK5 @ (binunion @ sK6 @ sK7)) @ (powerset @ (setminus @ sK5 @ sK6))))),
% 1.56/1.29 inference(cnf_transformation,[status(thm)],[f37])).
% 1.56/1.29 % SZS output end Proof for DTF2THF_13172
% 1.56/1.29 % (13365)------------------------------
% 1.56/1.29 % (13365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.29 % (13365)Termination reason: Refutation
% 1.56/1.29
% 1.56/1.29 % (13365)Memory used [KB]: 5756
% 1.56/1.29 % (13365)Time elapsed: 0.019 s
% 1.56/1.29 % (13365)Instructions burned: 46 (million)
% 1.56/1.29 % (13365)------------------------------
% 1.56/1.29 % (13365)------------------------------
% 1.56/1.29 % (13359)Success in time 0.042 s
%------------------------------------------------------------------------------