%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU717^2 : 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 : n020.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 09:36:38 AM UTC 2026
% Result : Theorem 1.63s 1.32s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 1059 ( 293 equ; 0 cnn)
% Maximal formula atoms : 14 ( 17 avg)
% Number of connectives : 1171 ( 153 ~; 138 |; 74 &; 749 @)
% ( 5 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 12 con; 0-3 aty)
% Number of variables : 153 ( 0 ^; 117 !; 36 ?; 153 :)
% 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_10,type,
sK2: $i > $i > $i > $i ).
thf(f132,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f131,f45]) ).
thf(f45,plain,
( ( in @ sK8 @ ( powerset @ sK6 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( in @ sK7 @ ( powerset @ sK8 ) )
!= $true )
& ( ( in @ sK8 @ ( powerset @ sK6 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK7 )
!= $true )
| ( ( in @ X3 @ sK8 )
= $true )
| ( ( in @ X3 @ sK6 )
!= $true ) )
& ( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true )
& ( powersetI1 = $true )
& ( subsetTI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f27,f29,f28]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( in @ sK7 @ ( powerset @ X2 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ sK6 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK7 )
!= $true )
| ( $true
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ sK6 )
!= $true ) ) )
& ( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X2: $i] :
( ( ( in @ sK7 @ ( powerset @ X2 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ sK6 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK7 )
!= $true )
| ( $true
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ sK6 )
!= $true ) ) )
=> ( ( ( in @ sK7 @ ( powerset @ sK8 ) )
!= $true )
& ( ( in @ sK8 @ ( powerset @ sK6 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK7 )
!= $true )
| ( ( in @ X3 @ sK8 )
= $true )
| ( ( in @ X3 @ sK6 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( powersetI1 = $true )
& ( subsetTI = $true ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X0 @ ( powerset @ X2 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( powersetI1 = $true )
& ( subsetTI = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X0 @ ( powerset @ X2 ) )
!= $true )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( subsetTI = $true )
& ( powersetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( powersetI1 = $true )
=> ( ( subsetTI = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ X0 )
= $true )
=> ( $true
= ( in @ X3 @ X2 ) ) ) )
=> ( ( in @ X0 @ ( powerset @ X2 ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( powersetI1
=> ( 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 ) ) )
=> ( in @ X0 @ ( powerset @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( powersetI1
=> ( subsetTI
=> ! [X2: $i,X0: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( in @ X2 @ ( powerset @ X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( powersetI1
=> ( subsetTI
=> ! [X2: $i,X0: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( in @ X2 @ ( powerset @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FCAu3b3gbN/DTF2THF_6691.p',powersetTI1) ).
thf(f131,plain,
( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f130,f62]) ).
thf(f62,plain,
( ( subset @ sK7 @ sK8 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true != $true )
| ( ( subset @ sK7 @ sK8 )
!= $true ) ),
inference(superposition,[status(thm)],[f46,f60]) ).
thf(f60,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f33,f42]) ).
thf(f42,plain,
powersetI1 = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( powersetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ( ( ( subset @ sK0 @ sK1 )
= $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19]) ).
thf(f19,plain,
( ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
& ( ( in @ X2 @ ( powerset @ X3 ) )
!= $true ) )
=> ( ( ( subset @ sK0 @ sK1 )
= $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
& ( ( in @ X2 @ ( powerset @ X3 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
<=> ( powersetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
<=> ( powersetI1 = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( powersetI1
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( powersetI1
= ( ! [X1: $i,X0: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FCAu3b3gbN/DTF2THF_6691.p',powersetI1) ).
thf(f46,plain,
( ( in @ sK7 @ ( powerset @ sK8 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f130,plain,
( ( ( subset @ sK7 @ sK8 )
= $true )
| ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f129,f43]) ).
thf(f43,plain,
( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f129,plain,
( ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ( ( subset @ sK7 @ sK8 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ( ( subset @ sK7 @ sK8 )
= $true )
| ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| ( $true != $true )
| ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f127]) ).
thf(f127,plain,
( ( ( subset @ sK7 @ sK8 )
= $true )
| ( ( subset @ sK7 @ sK8 )
= $true )
| ( $true != $true )
| ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ sK7 @ ( powerset @ sK6 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f114,f58]) ).
thf(f58,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( $true != $true )
| ( ( subset @ X0 @ X2 )
= $true )
| ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f40,f41]) ).
thf(f41,plain,
subsetTI = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f40,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true )
| ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true )
| ( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
!= $true ) ) ) )
| ( subsetTI != $true ) )
& ( ( subsetTI = $true )
| ( ( $true
= ( in @ sK3 @ ( powerset @ sK4 ) ) )
& ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ sK5 )
!= $true )
& ! [X7: $i] :
( ( ( in @ X7 @ sK3 )
!= $true )
| ( ( in @ X7 @ sK4 )
!= $true )
| ( $true
= ( in @ X7 @ sK5 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f22,f25,f24,f23]) ).
thf(f23,plain,
! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( in @ X3 @ X2 ) ) )
=> ( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
= $true )
& ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
= $true )
& ( $true
!= ( subset @ X4 @ X6 ) )
& ! [X7: $i] :
( ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X6 )
= $true ) ) ) )
=> ( ( $true
= ( in @ sK3 @ ( powerset @ sK4 ) ) )
& ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ X6 )
!= $true )
& ! [X7: $i] :
( ( ( in @ X7 @ sK3 )
!= $true )
| ( ( in @ X7 @ sK4 )
!= $true )
| ( ( in @ X7 @ X6 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ X6 )
!= $true )
& ! [X7: $i] :
( ( ( in @ X7 @ sK3 )
!= $true )
| ( ( in @ X7 @ sK4 )
!= $true )
| ( ( in @ X7 @ X6 )
= $true ) ) )
=> ( ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ sK5 )
!= $true )
& ! [X7: $i] :
( ( ( in @ X7 @ sK3 )
!= $true )
| ( ( in @ X7 @ sK4 )
!= $true )
| ( $true
= ( in @ X7 @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( in @ X3 @ X2 ) ) ) ) )
| ( subsetTI != $true ) )
& ( ( subsetTI = $true )
| ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
= $true )
& ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
= $true )
& ( $true
!= ( subset @ X4 @ X6 ) )
& ! [X7: $i] :
( ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X6 )
= $true ) ) ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( in @ X3 @ X2 ) ) ) ) )
| ( subsetTI != $true ) )
& ( ( subsetTI = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ X2 )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ X3 @ X2 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( in @ X3 @ X2 ) ) ) ) )
<=> ( subsetTI = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
| ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
<=> ( subsetTI = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ X0 )
= $true )
=> ( $true
= ( in @ X3 @ X2 ) ) ) )
=> ( ( subset @ X0 @ X2 )
= $true ) ) ) )
<=> ( subsetTI = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [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 ) ) ) )
= subsetTI ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X0: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) )
= subsetTI ),
file('/export/starexec/sandbox/tmp/tmp.FCAu3b3gbN/DTF2THF_6691.p',subsetTI) ).
thf(f114,plain,
! [X0: $i] :
( ( ( in @ ( sK2 @ sK8 @ sK6 @ X0 ) @ sK7 )
!= $true )
| ( ( in @ X0 @ ( powerset @ sK6 ) )
!= $true )
| ( ( subset @ X0 @ sK8 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f113,f45]) ).
thf(f113,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ ( sK2 @ sK8 @ sK6 @ X0 ) @ sK7 )
!= $true )
| ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ( ( subset @ X0 @ sK8 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
! [X0: $i] :
( ( ( in @ ( sK2 @ sK8 @ sK6 @ X0 ) @ sK7 )
!= $true )
| ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ( ( subset @ X0 @ sK8 )
= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ sK6 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f108]) ).
thf(f108,plain,
! [X0: $i] :
( ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ X0 @ ( powerset @ sK6 ) )
!= $true )
| ( ( subset @ X0 @ sK8 )
= $true )
| ( ( subset @ X0 @ sK8 )
= $true )
| ( ( in @ X0 @ ( powerset @ sK6 ) )
!= $true )
| ( $true != $true )
| ( ( in @ ( sK2 @ sK8 @ sK6 @ X0 ) @ sK7 )
!= $true ) ),
inference(superposition,[status(thm)],[f66,f59]) ).
thf(f59,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f39,f41]) ).
thf(f39,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true )
| ( $true
= ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f66,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK2 @ sK8 @ X0 @ X1 ) @ sK6 ) )
| ( ( in @ ( sK2 @ sK8 @ X0 @ X1 ) @ sK7 )
!= $true )
| ( ( subset @ X1 @ sK8 )
= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK8 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ ( sK2 @ sK8 @ X0 @ X1 ) @ sK6 ) )
| ( ( subset @ X1 @ sK8 )
= $true )
| ( ( in @ ( sK2 @ sK8 @ X0 @ X1 ) @ sK7 )
!= $true ) ),
inference(superposition,[status(thm)],[f57,f44]) ).
thf(f44,plain,
! [X3: $i] :
( ( ( in @ X3 @ sK8 )
= $true )
| ( ( in @ X3 @ sK7 )
!= $true )
| ( ( in @ X3 @ sK6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f57,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f38,f41]) ).
thf(f38,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X2 )
= $true )
| ( ( in @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU717^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n020.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 12:31:57 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
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU717^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.28/0.47 % Version : Especial > Reduced > Especial.
% 0.28/0.47 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.28/0.47 % (! x:i.in x A -> in x X -> in x Y) -> in X (powerset Y)))
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.47 % Source : [Bro08]
% 0.28/0.47 % Names : ZFC219l [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.28/0.47 % Number of atoms : 20 ( 2 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 8 ( 6 avg)
% 0.28/0.47 % Number of connectives : 47 ( 0 ~; 0 |; 0 &; 34 @)
% 0.28/0.47 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 14 ( 5 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=275
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(in_type,type,
% 0.28/0.47 in: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(powerset_type,type,
% 0.28/0.47 powerset: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(subset_type,type,
% 0.28/0.47 subset: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1_type,type,
% 0.28/0.47 powersetI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1,definition,
% 0.28/0.47 ( powersetI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ B @ A )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTI_type,type,
% 0.28/0.47 subsetTI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTI,definition,
% 0.28/0.47 ( subsetTI
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ X )
% 0.28/0.47 => ( in @ Xx @ Y ) ) )
% 0.28/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetTI1,conjecture,
% 0.28/0.47 ( powersetI1
% 0.28/0.47 => ( subsetTI
% 0.28/0.47 => ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ X )
% 0.28/0.47 => ( in @ Xx @ Y ) ) )
% 0.28/0.47 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.47/1.28 ---- Embedded in THF ---
% 1.47/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.28 %%% Generated on Tue Feb 24 12:31:58 EST 2026
% 1.47/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.28 %%% Logic specification used:
% 1.47/1.28 %%% thf(spec, logic, $$dhol).
% 1.47/1.28
% 1.47/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FCAu3b3gbN/DTF2DTF6691.p
% See solution above
% 1.47/1.28 ------------------------
% 1.47/1.29 ---- Cleaned THF ---
% 1.47/1.29 thf(in_type,type,
% 1.47/1.29 in: $i > $i > $o ).
% 1.47/1.29
% 1.47/1.29 thf(powerset_type,type,
% 1.47/1.29 powerset: $i > $i ).
% 1.47/1.29
% 1.47/1.29 thf(subset_type,type,
% 1.47/1.29 subset: $i > $i > $o ).
% 1.47/1.29
% 1.47/1.29 thf(powersetI1_type,type,
% 1.47/1.29 powersetI1: $o ).
% 1.47/1.29
% 1.47/1.29 thf(powersetI1,definition,
% 1.47/1.29 ( powersetI1
% 1.47/1.29 = ( ! [A: $i,B: $i] :
% 1.47/1.29 ( ( subset @ B @ A )
% 1.47/1.29 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(subsetTI_type,type,
% 1.47/1.29 subsetTI: $o ).
% 1.47/1.29
% 1.47/1.29 thf(subsetTI,definition,
% 1.47/1.29 ( subsetTI
% 1.47/1.29 = ( ! [A: $i,X: $i] :
% 1.47/1.29 ( ( in @ X @ ( powerset @ A ) )
% 1.47/1.29 => ! [Y: $i] :
% 1.47/1.29 ( ( in @ Y @ ( powerset @ A ) )
% 1.47/1.29 => ( ! [Xx: $i] :
% 1.47/1.29 ( ( in @ Xx @ A )
% 1.47/1.29 => ( ( in @ Xx @ X )
% 1.47/1.29 => ( in @ Xx @ Y ) ) )
% 1.47/1.29 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(powersetTI1,conjecture,
% 1.47/1.29 ( powersetI1
% 1.47/1.29 => ( subsetTI
% 1.47/1.29 => ! [A: $i,X: $i] :
% 1.47/1.29 ( ( in @ X @ ( powerset @ A ) )
% 1.47/1.29 => ! [Y: $i] :
% 1.47/1.29 ( ( in @ Y @ ( powerset @ A ) )
% 1.47/1.29 => ( ! [Xx: $i] :
% 1.47/1.29 ( ( in @ Xx @ A )
% 1.47/1.30 => ( ( in @ Xx @ X )
% 1.47/1.30 => ( in @ Xx @ Y ) ) )
% 1.47/1.30 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 1.47/1.30 ------------------------
% 1.63/1.31 % (6978)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_6691 for (2999ds/275Mi)
% 1.63/1.31 % (6976)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6691 for (2999ds/2Mi)
% 1.63/1.31 % (6976)Instruction limit reached!
% 1.63/1.31 % (6976)------------------------------
% 1.63/1.31 % (6976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (6976)Termination reason: Unknown
% 1.63/1.31 % (6976)Termination phase: Preprocessing 3
% 1.63/1.31
% 1.63/1.31 % (6976)Memory used [KB]: 895
% 1.63/1.31 % (6976)Time elapsed: 0.002 s
% 1.63/1.31 % (6976)Instructions burned: 2 (million)
% 1.63/1.31 % (6976)------------------------------
% 1.63/1.31 % (6976)------------------------------
% 1.63/1.32 % (6978)First to succeed.
% 1.63/1.32 % (6974)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_6691 for (2999ds/4Mi)
% 1.63/1.32 % (6973)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6691 for (2999ds/183Mi)
% 1.63/1.32 % (6975)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_6691 for (2999ds/27Mi)
% 1.63/1.32 % (6977)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_6691 for (2999ds/2Mi)
% 1.63/1.32 % (6979)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6691 for (2999ds/18Mi)
% 1.63/1.32 % (6977)Instruction limit reached!
% 1.63/1.32 % (6977)------------------------------
% 1.63/1.32 % (6977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (6977)Termination reason: Unknown
% 1.63/1.32 % (6977)Termination phase: shuffling
% 1.63/1.32
% 1.63/1.32 % (6977)Memory used [KB]: 895
% 1.63/1.32 % (6977)Time elapsed: 0.003 s
% 1.63/1.32 % (6977)Instructions burned: 2 (million)
% 1.63/1.32 % (6977)------------------------------
% 1.63/1.32 % (6977)------------------------------
% 1.63/1.32 % (6978)Refutation found. Thanks to Tanya!
% 1.63/1.32 % SZS status Theorem for DTF2THF_6691
% 1.63/1.32 % SZS output start Proof for DTF2THF_6691
% 1.63/1.32 thf(func_def_0, type, in: $i > $i > $o).
% 1.63/1.32 thf(func_def_1, type, powerset: $i > $i).
% 1.63/1.32 thf(func_def_2, type, subset: $i > $i > $o).
% 1.63/1.32 thf(func_def_10, type, sK2: $i > $i > $i > $i).
% 1.63/1.32 thf(f132,plain,(
% 1.63/1.32 $false),
% 1.63/1.32 inference(subsumption_resolution,[status(thm)],[f131,f45])).
% 1.63/1.32 thf(f45,plain,(
% 1.63/1.32 ((in @ sK8 @ (powerset @ sK6)) = $true)),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f30])).
% 1.63/1.32 thf(f30,plain,(
% 1.63/1.32 ((((in @ sK7 @ (powerset @ sK8)) != $true) & ((in @ sK8 @ (powerset @ sK6)) = $true) & ! [X3 : $i] : (((in @ X3 @ sK7) != $true) | ((in @ X3 @ sK8) = $true) | ((in @ X3 @ sK6) != $true))) & ((in @ sK7 @ (powerset @ sK6)) = $true)) & (powersetI1 = $true) & (subsetTI = $true)),
% 1.63/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f27,f29,f28])).
% 1.63/1.32 thf(f28,plain,(
% 1.63/1.32 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X1 @ (powerset @ X2)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (((in @ sK7 @ (powerset @ X2)) != $true) & ((in @ X2 @ (powerset @ sK6)) = $true) & ! [X3 : $i] : (((in @ X3 @ sK7) != $true) | ($true = (in @ X3 @ X2)) | ((in @ X3 @ sK6) != $true))) & ((in @ sK7 @ (powerset @ sK6)) = $true))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f29,plain,(
% 1.63/1.32 ? [X2 : $i] : (((in @ sK7 @ (powerset @ X2)) != $true) & ((in @ X2 @ (powerset @ sK6)) = $true) & ! [X3 : $i] : (((in @ X3 @ sK7) != $true) | ($true = (in @ X3 @ X2)) | ((in @ X3 @ sK6) != $true))) => (((in @ sK7 @ (powerset @ sK8)) != $true) & ((in @ sK8 @ (powerset @ sK6)) = $true) & ! [X3 : $i] : (((in @ X3 @ sK7) != $true) | ((in @ X3 @ sK8) = $true) | ((in @ X3 @ sK6) != $true)))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f27,plain,(
% 1.63/1.32 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X1 @ (powerset @ X2)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (powersetI1 = $true) & (subsetTI = $true)),
% 1.63/1.32 inference(rectify,[status(thm)],[f13])).
% 1.63/1.32 thf(f13,plain,(
% 1.63/1.32 ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X0 @ (powerset @ X2)) != $true) & ((in @ X2 @ (powerset @ X1)) = $true) & ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ($true = (in @ X3 @ X2)) | ((in @ X3 @ X1) != $true))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (powersetI1 = $true) & (subsetTI = $true)),
% 1.63/1.32 inference(flattening,[status(thm)],[f12])).
% 1.63/1.32 thf(f12,plain,(
% 1.63/1.32 (? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X0 @ (powerset @ X2)) != $true) & ! [X3 : $i] : ((($true = (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true)) | ((in @ X3 @ X1) != $true))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (subsetTI = $true)) & (powersetI1 = $true)),
% 1.63/1.32 inference(ennf_transformation,[status(thm)],[f11])).
% 1.63/1.32 thf(f11,plain,(
% 1.63/1.32 ~((powersetI1 = $true) => ((subsetTI = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => (! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X0) = $true) => ($true = (in @ X3 @ X2)))) => ((in @ X0 @ (powerset @ X2)) = $true))))))),
% 1.63/1.32 inference(fool_elimination,[status(thm)],[f10])).
% 1.63/1.32 thf(f10,plain,(
% 1.63/1.32 ~(powersetI1 => (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))) => (in @ X0 @ (powerset @ X2)))))))),
% 1.63/1.32 inference(rectify,[status(thm)],[f4])).
% 1.63/1.32 thf(f4,negated_conjecture,(
% 1.63/1.32 ~(powersetI1 => (subsetTI => ! [X2 : $i,X0 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ X2) => (in @ X4 @ X3))) => (in @ X2 @ (powerset @ X3)))))))),
% 1.63/1.32 inference(negated_conjecture,[status(cth)],[f3])).
% 1.63/1.32 thf(f3,conjecture,(
% 1.63/1.32 powersetI1 => (subsetTI => ! [X2 : $i,X0 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ X2) => (in @ X4 @ X3))) => (in @ X2 @ (powerset @ X3))))))),
% 1.63/1.32 file('/export/starexec/sandbox/tmp/tmp.FCAu3b3gbN/DTF2THF_6691.p',powersetTI1)).
% 1.63/1.32 thf(f131,plain,(
% 1.63/1.32 ((in @ sK8 @ (powerset @ sK6)) != $true)),
% 1.63/1.32 inference(subsumption_resolution,[status(thm)],[f130,f62])).
% 1.63/1.32 thf(f62,plain,(
% 1.63/1.32 ((subset @ sK7 @ sK8) != $true)),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.63/1.32 thf(f61,plain,(
% 1.63/1.32 ($true != $true) | ((subset @ sK7 @ sK8) != $true)),
% 1.63/1.32 inference(superposition,[status(thm)],[f46,f60])).
% 1.63/1.32 thf(f60,plain,(
% 1.63/1.32 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) | ((subset @ X0 @ X1) != $true)) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.63/1.32 thf(f47,plain,(
% 1.63/1.32 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ($true != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) )),
% 1.63/1.32 inference(definition_unfolding,[status(thm)],[f33,f42])).
% 1.63/1.32 thf(f42,plain,(
% 1.63/1.32 (powersetI1 = $true)),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f30])).
% 1.63/1.32 thf(f33,plain,(
% 1.63/1.32 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true) | (powersetI1 != $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f20])).
% 1.63/1.32 thf(f20,plain,(
% 1.63/1.32 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | (((subset @ sK0 @ sK1) = $true) & ((in @ sK0 @ (powerset @ sK1)) != $true)))),
% 1.63/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19])).
% 1.63/1.32 thf(f19,plain,(
% 1.63/1.32 ? [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) = $true) & ((in @ X2 @ (powerset @ X3)) != $true)) => (((subset @ sK0 @ sK1) = $true) & ((in @ sK0 @ (powerset @ sK1)) != $true))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f18,plain,(
% 1.63/1.32 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) = $true) & ((in @ X2 @ (powerset @ X3)) != $true)))),
% 1.63/1.32 inference(rectify,[status(thm)],[f17])).
% 1.63/1.32 thf(f17,plain,(
% 1.63/1.32 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((in @ X0 @ (powerset @ X1)) != $true)))),
% 1.63/1.32 inference(nnf_transformation,[status(thm)],[f16])).
% 1.63/1.32 thf(f16,plain,(
% 1.63/1.32 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) <=> (powersetI1 = $true)),
% 1.63/1.32 inference(ennf_transformation,[status(thm)],[f9])).
% 1.63/1.32 thf(f9,plain,(
% 1.63/1.32 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => ((in @ X0 @ (powerset @ X1)) = $true)) <=> (powersetI1 = $true)),
% 1.63/1.32 inference(fool_elimination,[status(thm)],[f8])).
% 1.63/1.32 thf(f8,plain,(
% 1.63/1.32 (powersetI1 = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 1.63/1.32 inference(rectify,[status(thm)],[f1])).
% 1.63/1.32 thf(f1,axiom,(
% 1.63/1.32 (powersetI1 = ! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 1.63/1.32 file('/export/starexec/sandbox/tmp/tmp.FCAu3b3gbN/DTF2THF_6691.p',powersetI1)).
% 1.63/1.32 thf(f46,plain,(
% 1.63/1.32 ((in @ sK7 @ (powerset @ sK8)) != $true)),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f30])).
% 1.63/1.32 thf(f130,plain,(
% 1.63/1.32 ((subset @ sK7 @ sK8) = $true) | ((in @ sK8 @ (powerset @ sK6)) != $true)),
% 1.63/1.32 inference(subsumption_resolution,[status(thm)],[f129,f43])).
% 1.63/1.32 thf(f43,plain,(
% 1.63/1.32 ((in @ sK7 @ (powerset @ sK6)) = $true)),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f30])).
% 1.63/1.32 thf(f129,plain,(
% 1.63/1.32 ((in @ sK7 @ (powerset @ sK6)) != $true) | ((in @ sK8 @ (powerset @ sK6)) != $true) | ((subset @ sK7 @ sK8) = $true)),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.63/1.32 thf(f128,plain,(
% 1.63/1.32 ((subset @ sK7 @ sK8) = $true) | ((in @ sK7 @ (powerset @ sK6)) != $true) | ($true != $true) | ((in @ sK8 @ (powerset @ sK6)) != $true)),
% 1.63/1.32 inference(duplicate_literal_removal,[status(thm)],[f127])).
% 1.63/1.32 thf(f127,plain,(
% 1.63/1.32 ((subset @ sK7 @ sK8) = $true) | ((subset @ sK7 @ sK8) = $true) | ($true != $true) | ((in @ sK7 @ (powerset @ sK6)) != $true) | ((in @ sK8 @ (powerset @ sK6)) != $true) | ((in @ sK7 @ (powerset @ sK6)) != $true)),
% 1.63/1.32 inference(superposition,[status(thm)],[f114,f58])).
% 1.63/1.32 thf(f58,plain,(
% 1.63/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X2 @ X1 @ X0) @ X0) = $true) | ((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true)) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.63/1.32 thf(f50,plain,(
% 1.63/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ($true != $true) | ((subset @ X0 @ X2) = $true) | ((in @ (sK2 @ X2 @ X1 @ X0) @ X0) = $true) | ((in @ X2 @ (powerset @ X1)) != $true)) )),
% 1.63/1.32 inference(definition_unfolding,[status(thm)],[f40,f41])).
% 1.63/1.32 thf(f41,plain,(
% 1.63/1.32 (subsetTI = $true)),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f30])).
% 1.63/1.32 thf(f40,plain,(
% 1.63/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true) | ((in @ (sK2 @ X2 @ X1 @ X0) @ X0) = $true) | (subsetTI != $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f26])).
% 1.63/1.32 thf(f26,plain,(
% 1.63/1.32 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true) | (((in @ (sK2 @ X2 @ X1 @ X0) @ X0) = $true) & ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) & ((in @ (sK2 @ X2 @ X1 @ X0) @ X2) != $true)))) | (subsetTI != $true)) & ((subsetTI = $true) | (($true = (in @ sK3 @ (powerset @ sK4))) & (((in @ sK5 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ sK5) != $true) & ! [X7 : $i] : (((in @ X7 @ sK3) != $true) | ((in @ X7 @ sK4) != $true) | ($true = (in @ X7 @ sK5))))))),
% 1.63/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f22,f25,f24,f23])).
% 1.63/1.32 thf(f23,plain,(
% 1.63/1.32 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ X2))) => (((in @ (sK2 @ X2 @ X1 @ X0) @ X0) = $true) & ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) & ((in @ (sK2 @ X2 @ X1 @ X0) @ X2) != $true)))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f24,plain,(
% 1.63/1.32 ? [X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X5)) = $true) & ? [X6 : $i] : (((in @ X6 @ (powerset @ X5)) = $true) & ($true != (subset @ X4 @ X6)) & ! [X7 : $i] : (((in @ X7 @ X4) != $true) | ((in @ X7 @ X5) != $true) | ((in @ X7 @ X6) = $true)))) => (($true = (in @ sK3 @ (powerset @ sK4))) & ? [X6 : $i] : (((in @ X6 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ X6) != $true) & ! [X7 : $i] : (((in @ X7 @ sK3) != $true) | ((in @ X7 @ sK4) != $true) | ((in @ X7 @ X6) = $true))))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f25,plain,(
% 1.63/1.32 ? [X6 : $i] : (((in @ X6 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ X6) != $true) & ! [X7 : $i] : (((in @ X7 @ sK3) != $true) | ((in @ X7 @ sK4) != $true) | ((in @ X7 @ X6) = $true))) => (((in @ sK5 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ sK5) != $true) & ! [X7 : $i] : (((in @ X7 @ sK3) != $true) | ((in @ X7 @ sK4) != $true) | ($true = (in @ X7 @ sK5))))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f22,plain,(
% 1.63/1.32 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true) | ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ X2))))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X5)) = $true) & ? [X6 : $i] : (((in @ X6 @ (powerset @ X5)) = $true) & ($true != (subset @ X4 @ X6)) & ! [X7 : $i] : (((in @ X7 @ X4) != $true) | ((in @ X7 @ X5) != $true) | ((in @ X7 @ X6) = $true)))))),
% 1.63/1.32 inference(rectify,[status(thm)],[f21])).
% 1.63/1.32 thf(f21,plain,(
% 1.63/1.32 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true) | ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ X2))))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((subset @ X0 @ X2) != $true) & ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true) | ($true = (in @ X3 @ X2))))))),
% 1.63/1.32 inference(nnf_transformation,[status(thm)],[f15])).
% 1.63/1.32 thf(f15,plain,(
% 1.63/1.32 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true) | ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ X2))))) <=> (subsetTI = $true)),
% 1.63/1.32 inference(flattening,[status(thm)],[f14])).
% 1.63/1.32 thf(f14,plain,(
% 1.63/1.32 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((subset @ X0 @ X2) = $true) | ? [X3 : $i] : ((($true != (in @ X3 @ X2)) & ((in @ X3 @ X0) = $true)) & ((in @ X3 @ X1) = $true))) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) <=> (subsetTI = $true)),
% 1.63/1.32 inference(ennf_transformation,[status(thm)],[f7])).
% 1.63/1.32 thf(f7,plain,(
% 1.63/1.32 ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => (! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X0) = $true) => ($true = (in @ X3 @ X2)))) => ((subset @ X0 @ X2) = $true)))) <=> (subsetTI = $true)),
% 1.63/1.32 inference(fool_elimination,[status(thm)],[f6])).
% 1.63/1.32 thf(f6,plain,(
% 1.63/1.32 (! [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)))) = subsetTI)),
% 1.63/1.32 inference(rectify,[status(thm)],[f2])).
% 1.63/1.32 thf(f2,axiom,(
% 1.63/1.32 (! [X2 : $i,X0 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ X2) => (in @ X4 @ X3))) => (subset @ X2 @ X3)))) = subsetTI)),
% 1.63/1.32 file('/export/starexec/sandbox/tmp/tmp.FCAu3b3gbN/DTF2THF_6691.p',subsetTI)).
% 1.63/1.32 thf(f114,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (((in @ (sK2 @ sK8 @ sK6 @ X0) @ sK7) != $true) | ((in @ X0 @ (powerset @ sK6)) != $true) | ((subset @ X0 @ sK8) = $true)) )),
% 1.63/1.32 inference(subsumption_resolution,[status(thm)],[f113,f45])).
% 1.63/1.32 thf(f113,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (((in @ X0 @ (powerset @ sK6)) != $true) | ((in @ (sK2 @ sK8 @ sK6 @ X0) @ sK7) != $true) | ((in @ sK8 @ (powerset @ sK6)) != $true) | ((subset @ X0 @ sK8) = $true)) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.63/1.32 thf(f112,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (((in @ (sK2 @ sK8 @ sK6 @ X0) @ sK7) != $true) | ((in @ sK8 @ (powerset @ sK6)) != $true) | ((subset @ X0 @ sK8) = $true) | ($true != $true) | ((in @ X0 @ (powerset @ sK6)) != $true)) )),
% 1.63/1.32 inference(duplicate_literal_removal,[status(thm)],[f108])).
% 1.63/1.32 thf(f108,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (((in @ sK8 @ (powerset @ sK6)) != $true) | ((in @ sK8 @ (powerset @ sK6)) != $true) | ((in @ X0 @ (powerset @ sK6)) != $true) | ((subset @ X0 @ sK8) = $true) | ((subset @ X0 @ sK8) = $true) | ((in @ X0 @ (powerset @ sK6)) != $true) | ($true != $true) | ((in @ (sK2 @ sK8 @ sK6 @ X0) @ sK7) != $true)) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f66,f59])).
% 1.63/1.32 thf(f59,plain,(
% 1.63/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) | ((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true)) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.63/1.32 thf(f51,plain,(
% 1.63/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X0 @ X2) = $true) | ((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) | ($true != $true)) )),
% 1.63/1.32 inference(definition_unfolding,[status(thm)],[f39,f41])).
% 1.63/1.32 thf(f39,plain,(
% 1.63/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true) | ($true = (in @ (sK2 @ X2 @ X1 @ X0) @ X1)) | (subsetTI != $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f26])).
% 1.63/1.32 thf(f66,plain,(
% 1.63/1.32 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK2 @ sK8 @ X0 @ X1) @ sK6)) | ((in @ (sK2 @ sK8 @ X0 @ X1) @ sK7) != $true) | ((subset @ X1 @ sK8) = $true) | ((in @ sK8 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.63/1.32 thf(f64,plain,(
% 1.63/1.32 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true) | ($true != $true) | ($true != (in @ (sK2 @ sK8 @ X0 @ X1) @ sK6)) | ((subset @ X1 @ sK8) = $true) | ((in @ (sK2 @ sK8 @ X0 @ X1) @ sK7) != $true)) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f57,f44])).
% 1.63/1.32 thf(f44,plain,(
% 1.63/1.32 ( ! [X3 : $i] : (((in @ X3 @ sK8) = $true) | ((in @ X3 @ sK7) != $true) | ((in @ X3 @ sK6) != $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f30])).
% 1.63/1.32 thf(f57,plain,(
% 1.63/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X2 @ X1 @ X0) @ X2) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true) | ((in @ X0 @ (powerset @ X1)) != $true)) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.63/1.32 thf(f52,plain,(
% 1.63/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X2 @ X1 @ X0) @ X2) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true)) )),
% 1.63/1.32 inference(definition_unfolding,[status(thm)],[f38,f41])).
% 1.63/1.32 thf(f38,plain,(
% 1.63/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true) | ((in @ (sK2 @ X2 @ X1 @ X0) @ X2) != $true) | (subsetTI != $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f26])).
% 1.63/1.32 % SZS output end Proof for DTF2THF_6691
% 1.63/1.32 % (6978)------------------------------
% 1.63/1.32 % (6978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (6978)Termination reason: Refutation
% 1.63/1.32
% 1.63/1.32 % (6978)Memory used [KB]: 5628
% 1.63/1.32 % (6978)Time elapsed: 0.009 s
% 1.63/1.32 % (6978)Instructions burned: 17 (million)
% 1.63/1.32 % (6978)------------------------------
% 1.63/1.32 % (6978)------------------------------
% 1.63/1.32 % (6972)Success in time 0.019 s
%------------------------------------------------------------------------------