%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU730^2 : 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 : n006.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 09:36:44 AM UTC 2026
% Result : Theorem 1.69s 1.32s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 1133 ( 337 equ; 0 cnn)
% Maximal formula atoms : 14 ( 15 avg)
% Number of connectives : 1548 ( 175 ~; 162 |; 80 &;1073 @)
% ( 8 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 15 con; 0-3 aty)
% Number of variables : 193 ( 0 ^; 154 !; 39 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(func_def_16,type,
sK6: $i > $i > $i > $i ).
thf(f155,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f154,f55]) ).
thf(f55,plain,
( $true
= ( in @ sK9 @ ( powerset @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( subsetTI = $true )
& ( doubleComplementE1 = $true )
& ( complementT_lem = $true )
& ( $true
= ( in @ sK9 @ ( powerset @ sK10 ) ) )
& ( ( subset @ ( setminus @ sK10 @ ( setminus @ sK10 @ sK9 ) ) @ sK9 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f16,f37]) ).
thf(f37,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ( ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 )
!= $true ) )
=> ( ( $true
= ( in @ sK9 @ ( powerset @ sK10 ) ) )
& ( ( subset @ ( setminus @ sK10 @ ( setminus @ sK10 @ sK9 ) ) @ sK9 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( subsetTI = $true )
& ( doubleComplementE1 = $true )
& ( complementT_lem = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ( ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ( ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 )
!= $true ) )
& ( doubleComplementE1 = $true )
& ( subsetTI = $true )
& ( complementT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( complementT_lem = $true )
=> ( ( subsetTI = $true )
=> ( ( doubleComplementE1 = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ( ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( complementT_lem
=> ( subsetTI
=> ( doubleComplementE1
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( complementT_lem
=> ( subsetTI
=> ( doubleComplementE1
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( complementT_lem
=> ( subsetTI
=> ( doubleComplementE1
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5GjDdpBbum/DTF2THF_11417.p',doubleComplementSub2) ).
thf(f154,plain,
( $true
!= ( in @ sK9 @ ( powerset @ sK10 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
( ( $true
!= ( in @ sK9 @ ( powerset @ sK10 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f54,f143]) ).
thf(f143,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f142,f75]) ).
thf(f75,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f53,f56]) ).
thf(f56,plain,
complementT_lem = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f53,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)],[f36]) ).
thf(f36,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 @ sK8 @ sK7 ) @ ( powerset @ sK8 ) ) )
& ( $true
= ( in @ sK7 @ ( powerset @ sK8 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f34,f35]) ).
thf(f35,plain,
( ? [X2: $i,X3: $i] :
( ( $true
!= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) ) )
=> ( ( $true
!= ( in @ ( setminus @ sK8 @ sK7 ) @ ( powerset @ sK8 ) ) )
& ( $true
= ( in @ sK7 @ ( powerset @ sK8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,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)],[f33]) ).
thf(f33,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( complementT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
<=> ( complementT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5GjDdpBbum/DTF2THF_11417.p',complementT_lem) ).
thf(f142,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f141]) ).
thf(f141,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f138,f75]) ).
thf(f138,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f137]) ).
thf(f137,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X1 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f132]) ).
thf(f132,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 )
= $true )
| ( ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f122,f77]) ).
thf(f77,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
= ( subset @ X4 @ X6 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true != $true )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
= ( subset @ X4 @ X6 ) ) ),
inference(definition_unfolding,[status(thm)],[f46,f58]) ).
thf(f58,plain,
subsetTI = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f46,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
| ( $true
= ( subset @ X4 @ X6 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( subsetTI = $true )
| ( ( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK4 ) )
| ( ( in @ X3 @ sK3 )
!= $true )
| ( $true
= ( in @ X3 @ sK5 ) ) )
& ( $true
!= ( subset @ sK3 @ sK5 ) )
& ( $true
= ( in @ sK3 @ ( powerset @ sK4 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
& ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
& ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) ) )
| ( $true
= ( subset @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( subsetTI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f28,f31,f30,f29]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
!= ( subset @ X0 @ X2 ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK4 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK4 ) )
| ( ( in @ X3 @ sK3 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
!= ( subset @ sK3 @ X2 ) ) )
& ( $true
= ( in @ sK3 @ ( powerset @ sK4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK4 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK4 ) )
| ( ( in @ X3 @ sK3 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
!= ( subset @ sK3 @ X2 ) ) )
=> ( ( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK4 ) )
| ( ( in @ X3 @ sK3 )
!= $true )
| ( $true
= ( in @ X3 @ sK5 ) ) )
& ( $true
!= ( subset @ sK3 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
! [X4: $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( $true
= ( in @ X7 @ X4 ) )
& ( ( in @ X7 @ X6 )
!= $true ) )
=> ( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
& ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
& ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( ( subsetTI = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
!= ( subset @ X0 @ X2 ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( $true
= ( in @ X7 @ X4 ) )
& ( ( in @ X7 @ X6 )
!= $true ) )
| ( $true
= ( subset @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( subsetTI != $true ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( subsetTI = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
!= ( subset @ X0 @ X2 ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
= ( subset @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( subsetTI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( subsetTI = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
= ( subset @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ( subsetTI = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( $true
= ( subset @ X0 @ X2 ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( subsetTI = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( $true
= ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( subsetTI
= ( ! [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 ) ) )
=> ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( subsetTI
= ( ! [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 ) ) )
=> ( subset @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5GjDdpBbum/DTF2THF_11417.p',subsetTI) ).
thf(f122,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) ) @ X2 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) @ X0 ) )
| ( $true
!= ( in @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) @ X0 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) ) @ X2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f114]) ).
thf(f114,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) @ X0 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) ) @ X2 ) )
| ( $true
= ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) @ X0 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X2 ) ) )
| ( $true
!= ( in @ ( setminus @ X2 @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f74,f81]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK6 @ X0 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) ) @ X3 ) )
| ( $true
!= ( in @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) ) @ X2 ) )
| ( $true
= ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK6 @ X0 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) ) @ X2 ) )
| ( $true
!= ( in @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK6 @ X0 @ X1 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) ) @ X3 ) )
| ( $true
= ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) @ X0 ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f78,f76]) ).
thf(f76,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true
= ( subset @ X4 @ X6 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X4 @ X6 ) )
| ( $true != $true )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) ) ),
inference(definition_unfolding,[status(thm)],[f45,f58]) ).
thf(f45,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
| ( $true
= ( subset @ X4 @ X6 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f78,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f43,f57]) ).
thf(f57,plain,
doubleComplementE1 = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f43,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) )
| ( doubleComplementE1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) ) ) )
| ( doubleComplementE1 != $true ) )
& ( ( doubleComplementE1 = $true )
| ( ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
!= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f25,f24]) ).
thf(f24,plain,
( ? [X3: $i,X4: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X4 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( $true
!= ( in @ X5 @ X3 ) )
& ( $true
= ( in @ X5 @ ( setminus @ X4 @ ( setminus @ X4 @ X3 ) ) ) ) ) )
=> ( ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ sK1 ) )
& ( $true
!= ( in @ X5 @ sK0 ) )
& ( $true
= ( in @ X5 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ sK1 ) )
& ( $true
!= ( in @ X5 @ sK0 ) )
& ( $true
= ( in @ X5 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) ) ) )
=> ( ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
!= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) ) ) )
| ( doubleComplementE1 != $true ) )
& ( ( doubleComplementE1 = $true )
| ? [X3: $i,X4: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X4 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( $true
!= ( in @ X5 @ X3 ) )
& ( $true
= ( in @ X5 @ ( setminus @ X4 @ ( setminus @ X4 @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( $true
= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) )
| ( doubleComplementE1 != $true ) )
& ( ( doubleComplementE1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
!= ( in @ X2 @ X1 ) )
& ( $true
= ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( $true
= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) )
<=> ( doubleComplementE1 = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ( doubleComplementE1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( doubleComplementE1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
=> ( ( $true
= ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
=> ( $true
= ( in @ X2 @ X1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( doubleComplementE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( doubleComplementE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X3 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5GjDdpBbum/DTF2THF_11417.p',doubleComplementE1) ).
thf(f74,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
= ( subset @ X4 @ X6 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X4 @ X6 ) )
| ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f44,f58]) ).
thf(f44,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) )
| ( $true
= ( subset @ X4 @ X6 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f54,plain,
( ( subset @ ( setminus @ sK10 @ ( setminus @ sK10 @ sK9 ) ) @ sK9 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU730^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:32:15 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEU730^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.47 % Domain : Set Theory
% 0.27/0.47 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.27/0.47 % Version : Especial > Reduced > Especial.
% 0.27/0.47 % English : (! A:i.! X:i.in X (powerset A) ->
% 0.27/0.47 % subset (setminus A (setminus A X)) X)
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.47 % Source : [Bro08]
% 0.27/0.47 % Names : ZFC232l [Bro08]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.27/0.47 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.27/0.47 % Number of atoms : 23 ( 3 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 5 ( 5 avg)
% 0.27/0.47 % Number of connectives : 57 ( 0 ~; 0 |; 0 &; 44 @)
% 0.27/0.47 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 12 ( 4 avg)
% 0.27/0.47 % Number of types : 2 ( 0 usr)
% 0.27/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.27/0.47 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : http://mathgate.info/detsetitem.php?id=290
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(in_type,type,
% 0.27/0.47 in: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(powerset_type,type,
% 0.27/0.47 powerset: $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(subset_type,type,
% 0.27/0.47 subset: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminus_type,type,
% 0.27/0.47 setminus: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(complementT_lem_type,type,
% 0.27/0.47 complementT_lem: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementT_lem,definition,
% 0.27/0.47 ( complementT_lem
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetTI_type,type,
% 0.27/0.47 subsetTI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetTI,definition,
% 0.27/0.47 ( subsetTI
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ X )
% 0.27/0.47 => ( in @ Xx @ Y ) ) )
% 0.27/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementE1_type,type,
% 0.27/0.47 doubleComplementE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementE1,definition,
% 0.27/0.47 ( doubleComplementE1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.27/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementSub2,conjecture,
% 0.27/0.47 ( complementT_lem
% 0.27/0.47 => ( subsetTI
% 0.27/0.47 => ( doubleComplementE1
% 0.27/0.47 => ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.28 %%% Generated on Tue Feb 24 12:32:16 EST 2026
% 1.49/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.28 %%% Logic specification used:
% 1.49/1.28 %%% thf(spec, logic, $$dhol).
% 1.49/1.28
% 1.49/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5GjDdpBbum/DTF2DTF11417.p
% See solution above
% 1.49/1.28 ------------------------
% 1.49/1.29 ---- Cleaned THF ---
% 1.49/1.30 thf(in_type,type,
% 1.49/1.30 in: $i > $i > $o ).
% 1.49/1.30
% 1.49/1.30 thf(powerset_type,type,
% 1.49/1.30 powerset: $i > $i ).
% 1.49/1.30
% 1.49/1.30 thf(subset_type,type,
% 1.49/1.30 subset: $i > $i > $o ).
% 1.49/1.30
% 1.49/1.30 thf(setminus_type,type,
% 1.49/1.30 setminus: $i > $i > $i ).
% 1.49/1.30
% 1.49/1.30 thf(complementT_lem_type,type,
% 1.49/1.30 complementT_lem: $o ).
% 1.49/1.30
% 1.49/1.30 thf(complementT_lem,definition,
% 1.49/1.30 ( complementT_lem
% 1.49/1.30 = ( ! [A: $i,X: $i] :
% 1.49/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.49/1.30 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(subsetTI_type,type,
% 1.49/1.30 subsetTI: $o ).
% 1.49/1.30
% 1.49/1.30 thf(subsetTI,definition,
% 1.49/1.30 ( subsetTI
% 1.49/1.30 = ( ! [A: $i,X: $i] :
% 1.49/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.49/1.30 => ! [Y: $i] :
% 1.49/1.30 ( ( in @ Y @ ( powerset @ A ) )
% 1.49/1.30 => ( ! [Xx: $i] :
% 1.49/1.30 ( ( in @ Xx @ A )
% 1.49/1.30 => ( ( in @ Xx @ X )
% 1.49/1.30 => ( in @ Xx @ Y ) ) )
% 1.49/1.30 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(doubleComplementE1_type,type,
% 1.49/1.30 doubleComplementE1: $o ).
% 1.49/1.30
% 1.49/1.30 thf(doubleComplementE1,definition,
% 1.49/1.30 ( doubleComplementE1
% 1.49/1.30 = ( ! [A: $i,X: $i] :
% 1.49/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.49/1.30 => ! [Xx: $i] :
% 1.49/1.30 ( ( in @ Xx @ A )
% 1.49/1.30 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 1.49/1.30 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(doubleComplementSub2,conjecture,
% 1.49/1.30 ( complementT_lem
% 1.49/1.30 => ( subsetTI
% 1.49/1.30 => ( doubleComplementE1
% 1.49/1.30 => ! [A: $i,X: $i] :
% 1.49/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.49/1.30 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ) ).
% 1.49/1.30 ------------------------
% 1.69/1.31 % (11613)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_11417 for (3000ds/275Mi)
% 1.69/1.32 % (11611)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11417 for (3000ds/2Mi)
% 1.69/1.32 % (11608)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11417 for (3000ds/183Mi)
% 1.69/1.32 % (11610)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_11417 for (3000ds/27Mi)
% 1.69/1.32 % (11609)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_11417 for (3000ds/4Mi)
% 1.69/1.32 % (11611)Instruction limit reached!
% 1.69/1.32 % (11611)------------------------------
% 1.69/1.32 % (11611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (11611)Termination reason: Unknown
% 1.69/1.32 % (11611)Termination phase: Property scanning
% 1.69/1.32
% 1.69/1.32 % (11611)Memory used [KB]: 1023
% 1.69/1.32 % (11611)Time elapsed: 0.003 s
% 1.69/1.32 % (11611)Instructions burned: 3 (million)
% 1.69/1.32 % (11611)------------------------------
% 1.69/1.32 % (11611)------------------------------
% 1.69/1.32 % (11609)Instruction limit reached!
% 1.69/1.32 % (11609)------------------------------
% 1.69/1.32 % (11609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (11609)Termination reason: Unknown
% 1.69/1.32 % (11609)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (11609)Memory used [KB]: 5500
% 1.69/1.32 % (11609)Time elapsed: 0.005 s
% 1.69/1.32 % (11609)Instructions burned: 5 (million)
% 1.69/1.32 % (11609)------------------------------
% 1.69/1.32 % (11609)------------------------------
% 1.69/1.32 % (11613)First to succeed.
% 1.69/1.32 % (11613)Refutation found. Thanks to Tanya!
% 1.69/1.32 % SZS status Theorem for DTF2THF_11417
% 1.69/1.32 % SZS output start Proof for DTF2THF_11417
% 1.69/1.32 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.32 thf(func_def_1, type, powerset: $i > $i).
% 1.69/1.32 thf(func_def_2, type, subset: $i > $i > $o).
% 1.69/1.32 thf(func_def_3, type, setminus: $i > $i > $i).
% 1.69/1.32 thf(func_def_16, type, sK6: $i > $i > $i > $i).
% 1.69/1.32 thf(f155,plain,(
% 1.69/1.32 $false),
% 1.69/1.32 inference(subsumption_resolution,[status(thm)],[f154,f55])).
% 1.69/1.32 thf(f55,plain,(
% 1.69/1.32 ($true = (in @ sK9 @ (powerset @ sK10)))),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f38])).
% 1.69/1.32 thf(f38,plain,(
% 1.69/1.32 (subsetTI = $true) & (doubleComplementE1 = $true) & (complementT_lem = $true) & (($true = (in @ sK9 @ (powerset @ sK10))) & ((subset @ (setminus @ sK10 @ (setminus @ sK10 @ sK9)) @ sK9) != $true))),
% 1.69/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f16,f37])).
% 1.69/1.32 thf(f37,plain,(
% 1.69/1.32 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0) != $true)) => (($true = (in @ sK9 @ (powerset @ sK10))) & ((subset @ (setminus @ sK10 @ (setminus @ sK10 @ sK9)) @ sK9) != $true))),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f16,plain,(
% 1.69/1.32 (subsetTI = $true) & (doubleComplementE1 = $true) & (complementT_lem = $true) & ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0) != $true))),
% 1.69/1.32 inference(flattening,[status(thm)],[f15])).
% 1.69/1.32 thf(f15,plain,(
% 1.69/1.32 ((? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0) != $true)) & (doubleComplementE1 = $true)) & (subsetTI = $true)) & (complementT_lem = $true)),
% 1.69/1.32 inference(ennf_transformation,[status(thm)],[f12])).
% 1.69/1.32 thf(f12,plain,(
% 1.69/1.32 ~((complementT_lem = $true) => ((subsetTI = $true) => ((doubleComplementE1 = $true) => ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0) = $true)))))),
% 1.69/1.32 inference(fool_elimination,[status(thm)],[f11])).
% 1.69/1.32 thf(f11,plain,(
% 1.69/1.32 ~(complementT_lem => (subsetTI => (doubleComplementE1 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)))))),
% 1.69/1.32 inference(rectify,[status(thm)],[f5])).
% 1.69/1.32 thf(f5,negated_conjecture,(
% 1.69/1.32 ~(complementT_lem => (subsetTI => (doubleComplementE1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1)))))),
% 1.69/1.32 inference(negated_conjecture,[status(cth)],[f4])).
% 1.69/1.32 thf(f4,conjecture,(
% 1.69/1.32 complementT_lem => (subsetTI => (doubleComplementE1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1))))),
% 1.69/1.32 file('/export/starexec/sandbox/tmp/tmp.5GjDdpBbum/DTF2THF_11417.p',doubleComplementSub2)).
% 1.69/1.32 thf(f154,plain,(
% 1.69/1.32 ($true != (in @ sK9 @ (powerset @ sK10)))),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 1.69/1.32 thf(f153,plain,(
% 1.69/1.32 ($true != (in @ sK9 @ (powerset @ sK10))) | ($true != $true)),
% 1.69/1.32 inference(superposition,[status(thm)],[f54,f143])).
% 1.69/1.32 thf(f143,plain,(
% 1.69/1.32 ( ! [X0 : $i,X1 : $i] : (((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.69/1.32 inference(subsumption_resolution,[status(thm)],[f142,f75])).
% 1.69/1.32 thf(f75,plain,(
% 1.69/1.32 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.69/1.32 thf(f71,plain,(
% 1.69/1.32 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != $true)) )),
% 1.69/1.32 inference(definition_unfolding,[status(thm)],[f53,f56])).
% 1.69/1.32 thf(f56,plain,(
% 1.69/1.32 (complementT_lem = $true)),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f38])).
% 1.69/1.32 thf(f53,plain,(
% 1.69/1.32 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1))) | (complementT_lem != $true)) )),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f36])).
% 1.69/1.32 thf(f36,plain,(
% 1.69/1.32 (! [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 @ sK8 @ sK7) @ (powerset @ sK8))) & ($true = (in @ sK7 @ (powerset @ sK8)))))),
% 1.69/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f34,f35])).
% 1.69/1.32 thf(f35,plain,(
% 1.69/1.32 ? [X2 : $i,X3 : $i] : (($true != (in @ (setminus @ X3 @ X2) @ (powerset @ X3))) & ($true = (in @ X2 @ (powerset @ X3)))) => (($true != (in @ (setminus @ sK8 @ sK7) @ (powerset @ sK8))) & ($true = (in @ sK7 @ (powerset @ sK8))))),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f34,plain,(
% 1.69/1.32 (! [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)))))),
% 1.69/1.32 inference(rectify,[status(thm)],[f33])).
% 1.69/1.32 thf(f33,plain,(
% 1.69/1.32 (! [X1 : $i,X0 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X1 : $i,X0 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 1.69/1.32 inference(nnf_transformation,[status(thm)],[f17])).
% 1.69/1.32 thf(f17,plain,(
% 1.69/1.32 ! [X1 : $i,X0 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (complementT_lem = $true)),
% 1.69/1.32 inference(ennf_transformation,[status(thm)],[f10])).
% 1.69/1.32 thf(f10,plain,(
% 1.69/1.32 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) <=> (complementT_lem = $true)),
% 1.69/1.32 inference(fool_elimination,[status(thm)],[f9])).
% 1.69/1.32 thf(f9,plain,(
% 1.69/1.32 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 1.69/1.32 inference(rectify,[status(thm)],[f1])).
% 1.69/1.32 thf(f1,axiom,(
% 1.69/1.32 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 1.69/1.32 file('/export/starexec/sandbox/tmp/tmp.5GjDdpBbum/DTF2THF_11417.p',complementT_lem)).
% 1.69/1.32 thf(f142,plain,(
% 1.69/1.32 ( ! [X0 : $i,X1 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f141])).
% 1.69/1.32 thf(f141,plain,(
% 1.69/1.32 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ($true != $true)) )),
% 1.69/1.32 inference(superposition,[status(thm)],[f138,f75])).
% 1.69/1.32 thf(f138,plain,(
% 1.69/1.32 ( ! [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ (powerset @ X1)) != $true) | ((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0) = $true) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f137])).
% 1.69/1.32 thf(f137,plain,(
% 1.69/1.32 ( ! [X0 : $i,X1 : $i] : (((in @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ (powerset @ X1)) != $true) | ($true != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0) = $true)) )),
% 1.69/1.32 inference(duplicate_literal_removal,[status(thm)],[f132])).
% 1.69/1.32 thf(f132,plain,(
% 1.69/1.32 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0) = $true) | ((in @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ (powerset @ X1)) != $true) | ((subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0) = $true) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.69/1.32 inference(superposition,[status(thm)],[f122,f77])).
% 1.69/1.32 thf(f77,plain,(
% 1.69/1.32 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) | ($true != (in @ X6 @ (powerset @ X5))) | ($true = (subset @ X4 @ X6)) | ($true != (in @ X4 @ (powerset @ X5)))) )),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.69/1.32 thf(f68,plain,(
% 1.69/1.32 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (powerset @ X5))) | ($true != $true) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) | ($true != (in @ X6 @ (powerset @ X5))) | ($true = (subset @ X4 @ X6))) )),
% 1.69/1.32 inference(definition_unfolding,[status(thm)],[f46,f58])).
% 1.69/1.32 thf(f58,plain,(
% 1.69/1.32 (subsetTI = $true)),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f38])).
% 1.69/1.32 thf(f46,plain,(
% 1.69/1.32 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X5))) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) | ($true = (subset @ X4 @ X6)) | ($true != (in @ X4 @ (powerset @ X5))) | (subsetTI != $true)) )),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f32])).
% 1.69/1.32 thf(f32,plain,(
% 1.69/1.32 ((subsetTI = $true) | ((($true = (in @ sK5 @ (powerset @ sK4))) & ! [X3 : $i] : (($true != (in @ X3 @ sK4)) | ((in @ X3 @ sK3) != $true) | ($true = (in @ X3 @ sK5))) & ($true != (subset @ sK3 @ sK5))) & ($true = (in @ sK3 @ (powerset @ sK4))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (($true != (in @ X6 @ (powerset @ X5))) | (($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) & ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) & ($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6))) | ($true = (subset @ X4 @ X6))) | ($true != (in @ X4 @ (powerset @ X5)))) | (subsetTI != $true))),
% 1.69/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f28,f31,f30,f29])).
% 1.69/1.32 thf(f29,plain,(
% 1.69/1.32 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) = $true)) & ($true != (subset @ X0 @ X2))) & ($true = (in @ X0 @ (powerset @ X1)))) => (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK4))) & ! [X3 : $i] : (($true != (in @ X3 @ sK4)) | ((in @ X3 @ sK3) != $true) | ((in @ X3 @ X2) = $true)) & ($true != (subset @ sK3 @ X2))) & ($true = (in @ sK3 @ (powerset @ sK4))))),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f30,plain,(
% 1.69/1.32 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK4))) & ! [X3 : $i] : (($true != (in @ X3 @ sK4)) | ((in @ X3 @ sK3) != $true) | ((in @ X3 @ X2) = $true)) & ($true != (subset @ sK3 @ X2))) => (($true = (in @ sK5 @ (powerset @ sK4))) & ! [X3 : $i] : (($true != (in @ X3 @ sK4)) | ((in @ X3 @ sK3) != $true) | ($true = (in @ X3 @ sK5))) & ($true != (subset @ sK3 @ sK5)))),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f31,plain,(
% 1.69/1.32 ! [X4 : $i,X5 : $i,X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X5)) & ($true = (in @ X7 @ X4)) & ((in @ X7 @ X6) != $true)) => (($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) & ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) & ($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6))))),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f28,plain,(
% 1.69/1.32 ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) = $true)) & ($true != (subset @ X0 @ X2))) & ($true = (in @ X0 @ (powerset @ X1))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (($true != (in @ X6 @ (powerset @ X5))) | ? [X7 : $i] : (($true = (in @ X7 @ X5)) & ($true = (in @ X7 @ X4)) & ((in @ X7 @ X6) != $true)) | ($true = (subset @ X4 @ X6))) | ($true != (in @ X4 @ (powerset @ X5)))) | (subsetTI != $true))),
% 1.69/1.32 inference(rectify,[status(thm)],[f27])).
% 1.69/1.32 thf(f27,plain,(
% 1.69/1.32 ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) = $true)) & ($true != (subset @ X0 @ X2))) & ($true = (in @ X0 @ (powerset @ X1))))) & (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) != $true)) | ($true = (subset @ X0 @ X2))) | ($true != (in @ X0 @ (powerset @ X1)))) | (subsetTI != $true))),
% 1.69/1.32 inference(nnf_transformation,[status(thm)],[f21])).
% 1.69/1.32 thf(f21,plain,(
% 1.69/1.32 (subsetTI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) != $true)) | ($true = (subset @ X0 @ X2))) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.69/1.32 inference(flattening,[status(thm)],[f20])).
% 1.69/1.32 thf(f20,plain,(
% 1.69/1.32 (subsetTI = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((($true = (subset @ X0 @ X2)) | ? [X3 : $i] : ((((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X3 @ X1) = $true))) | ($true != (in @ X2 @ (powerset @ X1)))) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.69/1.32 inference(ennf_transformation,[status(thm)],[f8])).
% 1.69/1.32 thf(f8,plain,(
% 1.69/1.32 (subsetTI = $true) <=> ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => (! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X0) = $true) => ((in @ X3 @ X2) = $true))) => ($true = (subset @ X0 @ X2)))))),
% 1.69/1.32 inference(fool_elimination,[status(thm)],[f7])).
% 1.69/1.32 thf(f7,plain,(
% 1.69/1.32 (subsetTI = ! [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))) => (subset @ X0 @ X2)))))),
% 1.69/1.32 inference(rectify,[status(thm)],[f2])).
% 1.69/1.32 thf(f2,axiom,(
% 1.69/1.32 (subsetTI = ! [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))) => (subset @ X1 @ X2)))))),
% 1.69/1.32 file('/export/starexec/sandbox/tmp/tmp.5GjDdpBbum/DTF2THF_11417.p',subsetTI)).
% 1.69/1.32 thf(f122,plain,(
% 1.69/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK6 @ X0 @ X1 @ (setminus @ X2 @ (setminus @ X2 @ X0))) @ X2)) | ($true != (in @ X0 @ (powerset @ X2))) | ($true = (subset @ (setminus @ X2 @ (setminus @ X2 @ X0)) @ X0)) | ($true != (in @ (setminus @ X2 @ (setminus @ X2 @ X0)) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.69/1.32 thf(f121,plain,(
% 1.69/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (setminus @ X2 @ (setminus @ X2 @ X0)) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X2))) | ($true = (subset @ (setminus @ X2 @ (setminus @ X2 @ X0)) @ X0)) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != $true) | ($true != (in @ (sK6 @ X0 @ X1 @ (setminus @ X2 @ (setminus @ X2 @ X0))) @ X2))) )),
% 1.69/1.32 inference(duplicate_literal_removal,[status(thm)],[f114])).
% 1.69/1.32 thf(f114,plain,(
% 1.69/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ (setminus @ X2 @ (setminus @ X2 @ X0)) @ (powerset @ X1))) | ($true = (subset @ (setminus @ X2 @ (setminus @ X2 @ X0)) @ X0)) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != (in @ (sK6 @ X0 @ X1 @ (setminus @ X2 @ (setminus @ X2 @ X0))) @ X2)) | ($true = (subset @ (setminus @ X2 @ (setminus @ X2 @ X0)) @ X0)) | ($true != (in @ X0 @ (powerset @ X2))) | ($true != (in @ (setminus @ X2 @ (setminus @ X2 @ X0)) @ (powerset @ X1)))) )),
% 1.69/1.32 inference(superposition,[status(thm)],[f74,f81])).
% 1.69/1.32 thf(f81,plain,(
% 1.69/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK6 @ X0 @ X1 @ (setminus @ X2 @ (setminus @ X2 @ X3))) @ X3)) | ($true != (in @ (setminus @ X2 @ (setminus @ X2 @ X3)) @ (powerset @ X1))) | ($true != (in @ X3 @ (powerset @ X2))) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != (in @ (sK6 @ X0 @ X1 @ (setminus @ X2 @ (setminus @ X2 @ X3))) @ X2)) | ($true = (subset @ (setminus @ X2 @ (setminus @ X2 @ X3)) @ X0))) )),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.69/1.32 thf(f79,plain,(
% 1.69/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK6 @ X0 @ X1 @ (setminus @ X2 @ (setminus @ X2 @ X3))) @ X2)) | ($true != (in @ (setminus @ X2 @ (setminus @ X2 @ X3)) @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (sK6 @ X0 @ X1 @ (setminus @ X2 @ (setminus @ X2 @ X3))) @ X3)) | ($true = (subset @ (setminus @ X2 @ (setminus @ X2 @ X3)) @ X0)) | ($true != (in @ X3 @ (powerset @ X2))) | ($true != $true)) )),
% 1.69/1.32 inference(superposition,[status(thm)],[f78,f76])).
% 1.69/1.32 thf(f76,plain,(
% 1.69/1.32 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) | ($true != (in @ X4 @ (powerset @ X5))) | ($true = (subset @ X4 @ X6)) | ($true != (in @ X6 @ (powerset @ X5)))) )),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.69/1.32 thf(f69,plain,(
% 1.69/1.32 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = (subset @ X4 @ X6)) | ($true != $true) | ($true != (in @ X6 @ (powerset @ X5))) | ($true != (in @ X4 @ (powerset @ X5))) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4))) )),
% 1.69/1.32 inference(definition_unfolding,[status(thm)],[f45,f58])).
% 1.69/1.32 thf(f45,plain,(
% 1.69/1.32 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X5))) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) | ($true = (subset @ X4 @ X6)) | ($true != (in @ X4 @ (powerset @ X5))) | (subsetTI != $true)) )),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f32])).
% 1.69/1.32 thf(f78,plain,(
% 1.69/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) | ($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ X0)) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.69/1.32 thf(f59,plain,(
% 1.69/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != $true) | ($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ X0))) )),
% 1.69/1.32 inference(definition_unfolding,[status(thm)],[f43,f57])).
% 1.69/1.32 thf(f57,plain,(
% 1.69/1.32 (doubleComplementE1 = $true)),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f38])).
% 1.69/1.32 thf(f43,plain,(
% 1.69/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ X0)) | ($true != (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) | (doubleComplementE1 != $true)) )),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f26])).
% 1.69/1.32 thf(f26,plain,(
% 1.69/1.32 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ X0)) | ($true != (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))))) | (doubleComplementE1 != $true)) & ((doubleComplementE1 = $true) | (($true = (in @ sK0 @ (powerset @ sK1))) & (($true = (in @ sK2 @ sK1)) & ($true != (in @ sK2 @ sK0)) & ($true = (in @ sK2 @ (setminus @ sK1 @ (setminus @ sK1 @ sK0)))))))),
% 1.69/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f25,f24])).
% 1.69/1.32 thf(f24,plain,(
% 1.69/1.32 ? [X3 : $i,X4 : $i] : (($true = (in @ X3 @ (powerset @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ X4)) & ($true != (in @ X5 @ X3)) & ($true = (in @ X5 @ (setminus @ X4 @ (setminus @ X4 @ X3)))))) => (($true = (in @ sK0 @ (powerset @ sK1))) & ? [X5 : $i] : (($true = (in @ X5 @ sK1)) & ($true != (in @ X5 @ sK0)) & ($true = (in @ X5 @ (setminus @ sK1 @ (setminus @ sK1 @ sK0))))))),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f25,plain,(
% 1.69/1.32 ? [X5 : $i] : (($true = (in @ X5 @ sK1)) & ($true != (in @ X5 @ sK0)) & ($true = (in @ X5 @ (setminus @ sK1 @ (setminus @ sK1 @ sK0))))) => (($true = (in @ sK2 @ sK1)) & ($true != (in @ sK2 @ sK0)) & ($true = (in @ sK2 @ (setminus @ sK1 @ (setminus @ sK1 @ sK0)))))),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f23,plain,(
% 1.69/1.32 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ X0)) | ($true != (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))))) | (doubleComplementE1 != $true)) & ((doubleComplementE1 = $true) | ? [X3 : $i,X4 : $i] : (($true = (in @ X3 @ (powerset @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ X4)) & ($true != (in @ X5 @ X3)) & ($true = (in @ X5 @ (setminus @ X4 @ (setminus @ X4 @ X3)))))))),
% 1.69/1.32 inference(rectify,[status(thm)],[f22])).
% 1.69/1.32 thf(f22,plain,(
% 1.69/1.32 (! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (($true != (in @ X2 @ X0)) | ($true = (in @ X2 @ X1)) | ($true != (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))) | (doubleComplementE1 != $true)) & ((doubleComplementE1 = $true) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ X0)) & ($true != (in @ X2 @ X1)) & ($true = (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))))),
% 1.69/1.32 inference(nnf_transformation,[status(thm)],[f19])).
% 1.69/1.32 thf(f19,plain,(
% 1.69/1.32 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2 : $i] : (($true != (in @ X2 @ X0)) | ($true = (in @ X2 @ X1)) | ($true != (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))) <=> (doubleComplementE1 = $true)),
% 1.69/1.32 inference(flattening,[status(thm)],[f18])).
% 1.69/1.32 thf(f18,plain,(
% 1.69/1.32 (doubleComplementE1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((($true = (in @ X2 @ X1)) | ($true != (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1))))) | ($true != (in @ X2 @ X0))) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 1.69/1.32 inference(ennf_transformation,[status(thm)],[f14])).
% 1.69/1.32 thf(f14,plain,(
% 1.69/1.32 (doubleComplementE1 = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ X0)) => (($true = (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) => ($true = (in @ X2 @ X1)))))),
% 1.69/1.32 inference(fool_elimination,[status(thm)],[f13])).
% 1.69/1.32 thf(f13,plain,(
% 1.69/1.32 (doubleComplementE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1))) => (in @ X2 @ X1)))))),
% 1.69/1.32 inference(rectify,[status(thm)],[f3])).
% 1.69/1.32 thf(f3,axiom,(
% 1.69/1.32 (doubleComplementE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (setminus @ X0 @ X1))) => (in @ X3 @ X1)))))),
% 1.69/1.32 file('/export/starexec/sandbox/tmp/tmp.5GjDdpBbum/DTF2THF_11417.p',doubleComplementE1)).
% 1.69/1.32 thf(f74,plain,(
% 1.69/1.32 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6)) | ($true != (in @ X6 @ (powerset @ X5))) | ($true = (subset @ X4 @ X6)) | ($true != (in @ X4 @ (powerset @ X5)))) )),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.69/1.32 thf(f70,plain,(
% 1.69/1.32 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = (subset @ X4 @ X6)) | ($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6)) | ($true != (in @ X6 @ (powerset @ X5))) | ($true != (in @ X4 @ (powerset @ X5))) | ($true != $true)) )),
% 1.69/1.32 inference(definition_unfolding,[status(thm)],[f44,f58])).
% 1.69/1.32 thf(f44,plain,(
% 1.69/1.32 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X5))) | ($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6)) | ($true = (subset @ X4 @ X6)) | ($true != (in @ X4 @ (powerset @ X5))) | (subsetTI != $true)) )),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f32])).
% 1.69/1.32 thf(f54,plain,(
% 1.69/1.32 ((subset @ (setminus @ sK10 @ (setminus @ sK10 @ sK9)) @ sK9) != $true)),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f38])).
% 1.69/1.32 % SZS output end Proof for DTF2THF_11417
% 1.69/1.32 % (11613)------------------------------
% 1.69/1.32 % (11613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (11613)Termination reason: Refutation
% 1.69/1.32
% 1.69/1.32 % (11613)Memory used [KB]: 5628
% 1.69/1.32 % (11613)Time elapsed: 0.015 s
% 1.69/1.32 % (11613)Instructions burned: 38 (million)
% 1.69/1.32 % (11613)------------------------------
% 1.69/1.32 % (11613)------------------------------
% 1.69/1.32 % (11607)Success in time 0.007 s
%------------------------------------------------------------------------------