%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU579^2 : 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 : n004.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 09:35:23 AM UTC 2026
% Result : Theorem 1.62s 1.37s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 90 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 1081 ( 330 equ; 0 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 1136 ( 148 ~; 143 |; 71 &; 713 @)
% ( 10 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 18 con; 0-2 aty)
% Number of variables : 239 ( 0 ^; 195 !; 44 ?; 239 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_12,type,
sK2: $i > $i > $i ).
thf(func_def_21,type,
sK11: $i > $i > $i ).
thf(f354,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f350,f51]) ).
thf(f51,plain,
( ( subset @ sK4 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( powersetE = $true )
& ( subsetI2 = $true )
& ( powersetI = $true )
& ( subsetE = $true )
& ( ( subset @ sK4 @ sK3 )
= $true )
& ( ( subset @ ( powerset @ sK4 ) @ ( powerset @ sK3 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f25,f31]) ).
thf(f31,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
!= $true ) )
=> ( ( ( subset @ sK4 @ sK3 )
= $true )
& ( ( subset @ ( powerset @ sK4 ) @ ( powerset @ sK3 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( powersetE = $true )
& ( subsetI2 = $true )
& ( powersetI = $true )
& ( subsetE = $true )
& ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
!= $true ) )
& ( subsetE = $true )
& ( subsetI2 = $true )
& ( powersetE = $true )
& ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( powersetI = $true )
=> ( ( powersetE = $true )
=> ( ( subsetI2 = $true )
=> ( ( subsetE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( powersetI
=> ( powersetE
=> ( subsetI2
=> ( subsetE
=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( powersetI
=> ( powersetE
=> ( subsetI2
=> ( subsetE
=> ! [X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( powersetI
=> ( powersetE
=> ( subsetI2
=> ( subsetE
=> ! [X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( subset @ ( powerset @ X0 ) @ ( powerset @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',powersetsubset) ).
thf(f350,plain,
( ( subset @ sK4 @ sK3 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f340]) ).
thf(f340,plain,
( ( ( subset @ sK4 @ sK3 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f50,f326]) ).
thf(f326,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f325]) ).
thf(f325,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f317]) ).
thf(f317,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ ( powerset @ X1 ) @ ( powerset @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f129,f215]) ).
thf(f215,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ ( sK11 @ X1 @ ( powerset @ X2 ) ) @ X0 )
= $true )
| ( ( subset @ ( powerset @ X2 ) @ X1 )
= $true )
| ( ( subset @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f214]) ).
thf(f214,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ ( powerset @ X2 ) @ X1 )
= $true )
| ( ( subset @ X2 @ X0 )
!= $true )
| ( ( subset @ ( sK11 @ X1 @ ( powerset @ X2 ) ) @ X0 )
= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f204]) ).
thf(f204,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ ( sK11 @ X1 @ ( powerset @ X2 ) ) @ X0 )
= $true )
| ( ( subset @ ( sK11 @ X1 @ ( powerset @ X2 ) ) @ X0 )
= $true )
| ( ( subset @ ( powerset @ X2 ) @ X1 )
= $true )
| ( $true != $true )
| ( ( subset @ X2 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f94,f136]) ).
thf(f136,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK11 @ X0 @ ( sK11 @ X1 @ ( powerset @ X2 ) ) ) @ X2 )
= $true )
| ( ( subset @ ( sK11 @ X1 @ ( powerset @ X2 ) ) @ X0 )
= $true )
| ( ( subset @ ( powerset @ X2 ) @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ ( powerset @ X2 ) @ X1 )
= $true )
| ( ( subset @ ( sK11 @ X1 @ ( powerset @ X2 ) ) @ X0 )
= $true )
| ( ( in @ ( sK11 @ X0 @ ( sK11 @ X1 @ ( powerset @ X2 ) ) ) @ X2 )
= $true ) ),
inference(superposition,[status(thm)],[f104,f88]) ).
thf(f88,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK11 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ ( sK11 @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f67,f54]) ).
thf(f54,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f67,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ ( sK11 @ X1 @ X0 ) @ X0 )
= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( ( in @ ( sK11 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
!= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ( ( ( subset @ sK12 @ sK13 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK12 )
!= $true )
| ( ( in @ X5 @ sK13 )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f42,f44,f43]) ).
thf(f43,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
=> ( ( ( in @ ( sK11 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ? [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) ) )
=> ( ( ( subset @ sK12 @ sK13 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK12 )
!= $true )
| ( ( in @ X5 @ sK13 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( subsetI2 = $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( subsetI2
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',subsetI2) ).
thf(f104,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( sK11 @ X0 @ ( powerset @ X1 ) ) )
!= $true )
| ( ( subset @ ( powerset @ X1 ) @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( sK11 @ X0 @ ( powerset @ X1 ) ) )
!= $true )
| ( ( subset @ ( powerset @ X1 ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f84,f88]) ).
thf(f84,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f63,f55]) ).
thf(f55,plain,
powersetE = $true,
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f63,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( powersetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ( ( ( in @ sK10 @ sK9 )
!= $true )
& ( ( in @ sK10 @ sK8 )
= $true )
& ( ( in @ sK8 @ ( powerset @ sK9 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f38,f39]) ).
thf(f39,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X5 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ X4 ) )
= $true ) )
=> ( ( ( in @ sK10 @ sK9 )
!= $true )
& ( ( in @ sK10 @ sK8 )
= $true )
& ( ( in @ sK8 @ ( powerset @ sK9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X5 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ X4 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X1 @ ( powerset @ X2 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) )
<=> ( powersetE = $true ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
!= $true ) )
<=> ( powersetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $true )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) )
<=> ( powersetE = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) )
= powersetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= powersetE ),
file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',powersetE) ).
thf(f94,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK11 @ X0 @ X1 ) @ X2 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true )
| ( ( subset @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK11 @ X0 @ X1 ) @ X2 )
!= $true )
| ( ( subset @ X2 @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f87,f89]) ).
thf(f89,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f56,f52]) ).
thf(f52,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f56,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( subsetE = $true )
| ( ( ( subset @ sK6 @ sK5 )
= $true )
& ( ( in @ sK7 @ sK6 )
= $true )
& ( ( in @ sK7 @ sK5 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f34,f35]) ).
thf(f35,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
=> ( ( ( subset @ sK6 @ sK5 )
= $true )
& ( ( in @ sK7 @ sK6 )
= $true )
& ( ( in @ sK7 @ sK5 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
= $true ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',subsetE) ).
thf(f87,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f66,f54]) ).
thf(f66,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ ( sK11 @ X1 @ X0 ) @ X1 )
!= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f129,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( sK11 @ ( powerset @ X0 ) @ X1 ) @ X0 )
!= $true )
| ( ( subset @ X1 @ ( powerset @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( sK11 @ ( powerset @ X0 ) @ X1 ) @ X0 )
!= $true )
| ( $true != $true )
| ( ( subset @ X1 @ ( powerset @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f87,f118]) ).
thf(f118,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f114]) ).
thf(f114,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( $true != $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f99,f85]) ).
thf(f85,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f47,f53]) ).
thf(f53,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f47,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( powersetI = $true )
| ( ! [X2: $i] :
( ( ( in @ X2 @ sK1 )
!= $true )
| ( ( in @ X2 @ sK0 )
= $true ) )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true ) )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) )
| ( powersetI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f29,f28]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
=> ( ! [X2: $i] :
( ( ( in @ X2 @ sK1 )
!= $true )
| ( ( in @ X2 @ sK0 )
= $true ) )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
!= $true ) )
=> ( ( ( in @ ( sK2 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
!= $true ) )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) )
| ( powersetI != $true ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( powersetI = $true )
| ? [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( powersetI = $true )
<=> ! [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( powersetI = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI ),
file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',powersetI) ).
thf(f99,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X0 @ X1 ) @ X2 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X0 @ X1 ) @ X2 )
!= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f86,f89]) ).
thf(f86,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f46,f53]) ).
thf(f46,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK2 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f50,plain,
( ( subset @ ( powerset @ sK4 ) @ ( powerset @ sK3 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU579^2 : 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 : n004.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 12:27:26 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
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SEU579^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.46 % Domain : Set Theory
% 0.26/0.46 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.26/0.46 % Version : Especial > Reduced > Especial.
% 0.26/0.46 % English : (! A:i.! B:i.subset A B -> subset (powerset A) (powerset B))
% 0.26/0.46
% 0.26/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.46 % Source : [Bro08]
% 0.26/0.46 % Names : ZFC081l [Bro08]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 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 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.26/0.46 % Syntax : Number of formulae : 12 ( 4 unt; 7 typ; 4 def)
% 0.26/0.46 % Number of atoms : 26 ( 4 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 6 ( 5 avg)
% 0.26/0.46 % Number of connectives : 45 ( 0 ~; 0 |; 0 &; 32 @)
% 0.26/0.46 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 11 ( 3 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% 0.26/0.46 % Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% 0.26/0.46 % SPC : TH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : http://mathgate.info/detsetitem.php?id=156
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(in_type,type,
% 0.26/0.46 in: $i > $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(powerset_type,type,
% 0.26/0.46 powerset: $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(powersetI_type,type,
% 0.26/0.46 powersetI: $o ).
% 0.26/0.46
% 0.26/0.46 thf(powersetI,definition,
% 0.26/0.46 ( powersetI
% 0.26/0.46 = ( ! [A: $i,B: $i] :
% 0.26/0.46 ( ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ B )
% 0.26/0.46 => ( in @ Xx @ A ) )
% 0.26/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(powersetE_type,type,
% 0.26/0.46 powersetE: $o ).
% 0.26/0.46
% 0.26/0.46 thf(powersetE,definition,
% 0.26/0.46 ( powersetE
% 0.26/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.26/0.46 => ( ( in @ Xx @ B )
% 0.26/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(subset_type,type,
% 0.26/0.46 subset: $i > $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(subsetI2_type,type,
% 0.26/0.46 subsetI2: $o ).
% 0.26/0.46
% 0.26/0.46 thf(subsetI2,definition,
% 0.26/0.46 ( subsetI2
% 0.26/0.46 = ( ! [A: $i,B: $i] :
% 0.26/0.46 ( ! [Xx: $i] :
% 0.26/0.46 ( ( in @ Xx @ A )
% 0.26/0.46 => ( in @ Xx @ B ) )
% 0.26/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(subsetE_type,type,
% 0.26/0.46 subsetE: $o ).
% 0.26/0.46
% 0.26/0.46 thf(subsetE,definition,
% 0.26/0.46 ( subsetE
% 0.26/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.46 ( ( subset @ A @ B )
% 0.26/0.46 => ( ( in @ Xx @ A )
% 0.26/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(powersetsubset,conjecture,
% 0.26/0.46 ( powersetI
% 0.26/0.46 => ( powersetE
% 0.26/0.46 => ( subsetI2
% 0.26/0.46 => ( subsetE
% 0.26/0.46 => ! [A: $i,B: $i] :
% 0.26/0.46 ( ( subset @ A @ B )
% 0.26/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 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 12:27:27 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.7dLhMdGokl/DTF2DTF528.p
% See solution above
% 1.47/1.28 ------------------------
% 1.47/1.29 ---- Cleaned THF ---
% 1.47/1.30 thf(in_type,type,
% 1.47/1.30 in: $i > $i > $o ).
% 1.47/1.30
% 1.47/1.30 thf(powerset_type,type,
% 1.47/1.30 powerset: $i > $i ).
% 1.47/1.30
% 1.47/1.30 thf(powersetI_type,type,
% 1.47/1.30 powersetI: $o ).
% 1.47/1.30
% 1.47/1.30 thf(powersetI,definition,
% 1.47/1.30 ( powersetI
% 1.47/1.30 = ( ! [A: $i,B: $i] :
% 1.47/1.30 ( ! [Xx: $i] :
% 1.47/1.30 ( ( in @ Xx @ B )
% 1.47/1.30 => ( in @ Xx @ A ) )
% 1.47/1.30 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.47/1.30
% 1.47/1.30 thf(powersetE_type,type,
% 1.47/1.30 powersetE: $o ).
% 1.47/1.30
% 1.47/1.30 thf(powersetE,definition,
% 1.47/1.30 ( powersetE
% 1.47/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.47/1.30 ( ( in @ B @ ( powerset @ A ) )
% 1.47/1.30 => ( ( in @ Xx @ B )
% 1.47/1.30 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.47/1.30
% 1.47/1.30 thf(subset_type,type,
% 1.47/1.30 subset: $i > $i > $o ).
% 1.47/1.30
% 1.47/1.30 thf(subsetI2_type,type,
% 1.47/1.30 subsetI2: $o ).
% 1.47/1.30
% 1.47/1.30 thf(subsetI2,definition,
% 1.47/1.30 ( subsetI2
% 1.47/1.30 = ( ! [A: $i,B: $i] :
% 1.47/1.30 ( ! [Xx: $i] :
% 1.47/1.30 ( ( in @ Xx @ A )
% 1.47/1.30 => ( in @ Xx @ B ) )
% 1.47/1.30 => ( subset @ A @ B ) ) ) ) ).
% 1.47/1.30
% 1.47/1.30 thf(subsetE_type,type,
% 1.47/1.30 subsetE: $o ).
% 1.47/1.30
% 1.47/1.30 thf(subsetE,definition,
% 1.47/1.30 ( subsetE
% 1.47/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.47/1.30 ( ( subset @ A @ B )
% 1.47/1.30 => ( ( in @ Xx @ A )
% 1.47/1.30 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.47/1.30
% 1.47/1.30 thf(powersetsubset,conjecture,
% 1.47/1.30 ( powersetI
% 1.47/1.30 => ( powersetE
% 1.47/1.30 => ( subsetI2
% 1.47/1.30 => ( subsetE
% 1.47/1.30 => ! [A: $i,B: $i] :
% 1.47/1.30 ( ( subset @ A @ B )
% 1.47/1.30 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ) ) ).
% 1.47/1.30 ------------------------
% 1.62/1.31 % (844)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/2Mi)
% 1.62/1.31 % (844)Instruction limit reached!
% 1.62/1.31 % (844)------------------------------
% 1.62/1.31 % (844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (844)Termination reason: Unknown
% 1.62/1.31 % (844)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (844)Memory used [KB]: 5500
% 1.62/1.31 % (844)Time elapsed: 0.003 s
% 1.62/1.31 % (844)Instructions burned: 4 (million)
% 1.62/1.31 % (844)------------------------------
% 1.62/1.31 % (844)------------------------------
% 1.62/1.32 % (841)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/183Mi)
% 1.62/1.32 % (842)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_528 for (2999ds/4Mi)
% 1.62/1.32 % (843)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_528 for (2999ds/27Mi)
% 1.62/1.32 % (845)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_528 for (2999ds/2Mi)
% 1.62/1.32 % (846)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_528 for (2999ds/275Mi)
% 1.62/1.32 % (847)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/18Mi)
% 1.62/1.32 % (845)Instruction limit reached!
% 1.62/1.32 % (845)------------------------------
% 1.62/1.32 % (845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (845)Termination reason: Unknown
% 1.62/1.32 % (845)Termination phase: Property scanning
% 1.62/1.32
% 1.62/1.32 % (845)Memory used [KB]: 895
% 1.62/1.32 % (845)Time elapsed: 0.003 s
% 1.62/1.32 % (845)Instructions burned: 2 (million)
% 1.62/1.32 % (845)------------------------------
% 1.62/1.32 % (845)------------------------------
% 1.62/1.32 % (842)Instruction limit reached!
% 1.62/1.32 % (842)------------------------------
% 1.62/1.32 % (842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (842)Termination reason: Unknown
% 1.62/1.32 % (842)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (842)Memory used [KB]: 5500
% 1.62/1.32 % (842)Time elapsed: 0.005 s
% 1.62/1.32 % (842)Instructions burned: 5 (million)
% 1.62/1.32 % (842)------------------------------
% 1.62/1.32 % (842)------------------------------
% 1.62/1.32 % (848)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/3Mi)
% 1.62/1.32 % (848)Instruction limit reached!
% 1.62/1.32 % (848)------------------------------
% 1.62/1.32 % (848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (848)Termination reason: Unknown
% 1.62/1.32 % (848)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (848)Memory used [KB]: 5500
% 1.62/1.32 % (848)Time elapsed: 0.002 s
% 1.62/1.32 % (848)Instructions burned: 3 (million)
% 1.62/1.32 % (848)------------------------------
% 1.62/1.32 % (848)------------------------------
% 1.62/1.33 % (847)Instruction limit reached!
% 1.62/1.33 % (847)------------------------------
% 1.62/1.33 % (847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (847)Termination reason: Unknown
% 1.62/1.33 % (847)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (847)Memory used [KB]: 5628
% 1.62/1.33 % (847)Time elapsed: 0.014 s
% 1.62/1.33 % (847)Instructions burned: 18 (million)
% 1.62/1.33 % (847)------------------------------
% 1.62/1.33 % (847)------------------------------
% 1.62/1.33 % (851)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/3Mi)
% 1.62/1.33 % (851)Instruction limit reached!
% 1.62/1.33 % (851)------------------------------
% 1.62/1.33 % (851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (851)Termination reason: Unknown
% 1.62/1.33 % (851)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (851)Memory used [KB]: 5500
% 1.62/1.33 % (851)Time elapsed: 0.002 s
% 1.62/1.33 % (851)Instructions burned: 4 (million)
% 1.62/1.33 % (851)------------------------------
% 1.62/1.33 % (851)------------------------------
% 1.62/1.34 % (843)Instruction limit reached!
% 1.62/1.34 % (843)------------------------------
% 1.62/1.34 % (843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (843)Termination reason: Unknown
% 1.62/1.34 % (843)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (843)Memory used [KB]: 5628
% 1.62/1.34 % (843)Time elapsed: 0.019 s
% 1.62/1.34 % (843)Instructions burned: 27 (million)
% 1.62/1.34 % (843)------------------------------
% 1.62/1.34 % (843)------------------------------
% 1.62/1.34 % (849)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/37Mi)
% 1.62/1.34 % (850)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/15Mi)
% 1.62/1.34 % (853)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/7Mi)
% 1.62/1.35 % (853)Instruction limit reached!
% 1.62/1.35 % (853)------------------------------
% 1.62/1.35 % (853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (853)Termination reason: Unknown
% 1.62/1.35 % (853)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (853)Memory used [KB]: 1023
% 1.62/1.35 % (853)Time elapsed: 0.004 s
% 1.62/1.35 % (853)Instructions burned: 9 (million)
% 1.62/1.35 % (853)------------------------------
% 1.62/1.35 % (853)------------------------------
% 1.62/1.35 % (852)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/1041Mi)
% 1.62/1.35 % (850)Instruction limit reached!
% 1.62/1.35 % (850)------------------------------
% 1.62/1.35 % (850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (850)Termination reason: Unknown
% 1.62/1.35 % (850)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (850)Memory used [KB]: 5628
% 1.62/1.35 % (850)Time elapsed: 0.012 s
% 1.62/1.35 % (850)Instructions burned: 16 (million)
% 1.62/1.35 % (850)------------------------------
% 1.62/1.35 % (850)------------------------------
% 1.62/1.35 % (854)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/16Mi)
% 1.62/1.35 % (855)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/3Mi)
% 1.62/1.36 % (855)Instruction limit reached!
% 1.62/1.36 % (855)------------------------------
% 1.62/1.36 % (855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (855)Termination reason: Unknown
% 1.62/1.36 % (855)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (855)Memory used [KB]: 1023
% 1.62/1.36 % (855)Time elapsed: 0.002 s
% 1.62/1.36 % (855)Instructions burned: 4 (million)
% 1.62/1.36 % (855)------------------------------
% 1.62/1.36 % (855)------------------------------
% 1.62/1.36 % (849)Instruction limit reached!
% 1.62/1.36 % (849)------------------------------
% 1.62/1.36 % (849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (849)Termination reason: Unknown
% 1.62/1.36 % (849)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (849)Memory used [KB]: 5628
% 1.62/1.36 % (849)Time elapsed: 0.024 s
% 1.62/1.36 % (849)Instructions burned: 38 (million)
% 1.62/1.36 % (849)------------------------------
% 1.62/1.36 % (849)------------------------------
% 1.62/1.36 % (854)Instruction limit reached!
% 1.62/1.36 % (854)------------------------------
% 1.62/1.36 % (854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (854)Termination reason: Unknown
% 1.62/1.36 % (854)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (854)Memory used [KB]: 5756
% 1.62/1.36 % (854)Time elapsed: 0.010 s
% 1.62/1.36 % (854)Instructions burned: 17 (million)
% 1.62/1.36 % (854)------------------------------
% 1.62/1.36 % (854)------------------------------
% 1.62/1.36 % (856)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/3Mi)
% 1.62/1.36 % (857)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/7Mi)
% 1.62/1.36 % (856)Instruction limit reached!
% 1.62/1.36 % (856)------------------------------
% 1.62/1.36 % (856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (856)Termination reason: Unknown
% 1.62/1.36 % (856)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (856)Memory used [KB]: 1023
% 1.62/1.36 % (856)Time elapsed: 0.003 s
% 1.62/1.36 % (856)Instructions burned: 4 (million)
% 1.62/1.36 % (856)------------------------------
% 1.62/1.36 % (856)------------------------------
% 1.62/1.37 % (857)Refutation not found, incomplete strategy
% 1.62/1.37 % (857)------------------------------
% 1.62/1.37 % (857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (857)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.37
% 1.62/1.37
% 1.62/1.37 % (857)Memory used [KB]: 5500
% 1.62/1.37 % (857)Time elapsed: 0.002 s
% 1.62/1.37 % (857)Instructions burned: 4 (million)
% 1.62/1.37 % (857)------------------------------
% 1.62/1.37 % (857)------------------------------
% 1.62/1.37 % (846)First to succeed.
% 1.62/1.37 % (860)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_528 for (2999ds/4Mi)
% 1.62/1.37 % (860)Instruction limit reached!
% 1.62/1.37 % (860)------------------------------
% 1.62/1.37 % (860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (860)Termination reason: Unknown
% 1.62/1.37 % (860)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (860)Memory used [KB]: 5500
% 1.62/1.37 % (860)Time elapsed: 0.003 s
% 1.62/1.37 % (860)Instructions burned: 4 (million)
% 1.62/1.37 % (860)------------------------------
% 1.62/1.37 % (860)------------------------------
% 1.62/1.37 % (846)Refutation found. Thanks to Tanya!
% 1.62/1.37 % SZS status Theorem for DTF2THF_528
% 1.62/1.37 % SZS output start Proof for DTF2THF_528
% 1.62/1.37 thf(func_def_0, type, in: $i > $i > $o).
% 1.62/1.37 thf(func_def_1, type, powerset: $i > $i).
% 1.62/1.37 thf(func_def_5, type, subset: $i > $i > $o).
% 1.62/1.37 thf(func_def_12, type, sK2: $i > $i > $i).
% 1.62/1.37 thf(func_def_21, type, sK11: $i > $i > $i).
% 1.62/1.37 thf(f354,plain,(
% 1.62/1.37 $false),
% 1.62/1.37 inference(subsumption_resolution,[status(thm)],[f350,f51])).
% 1.62/1.37 thf(f51,plain,(
% 1.62/1.37 ((subset @ sK4 @ sK3) = $true)),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f32])).
% 1.62/1.37 thf(f32,plain,(
% 1.62/1.37 (powersetE = $true) & (subsetI2 = $true) & (powersetI = $true) & (subsetE = $true) & (((subset @ sK4 @ sK3) = $true) & ((subset @ (powerset @ sK4) @ (powerset @ sK3)) != $true))),
% 1.62/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f25,f31])).
% 1.62/1.37 thf(f31,plain,(
% 1.62/1.37 ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) & ((subset @ (powerset @ X1) @ (powerset @ X0)) != $true)) => (((subset @ sK4 @ sK3) = $true) & ((subset @ (powerset @ sK4) @ (powerset @ sK3)) != $true))),
% 1.62/1.37 introduced(definition,[],[choice_axiom])).
% 1.62/1.37 thf(f25,plain,(
% 1.62/1.37 (powersetE = $true) & (subsetI2 = $true) & (powersetI = $true) & (subsetE = $true) & ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) & ((subset @ (powerset @ X1) @ (powerset @ X0)) != $true))),
% 1.62/1.37 inference(flattening,[status(thm)],[f24])).
% 1.62/1.37 thf(f24,plain,(
% 1.62/1.37 (((? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) & ((subset @ (powerset @ X1) @ (powerset @ X0)) != $true)) & (subsetE = $true)) & (subsetI2 = $true)) & (powersetE = $true)) & (powersetI = $true)),
% 1.62/1.37 inference(ennf_transformation,[status(thm)],[f11])).
% 1.62/1.37 thf(f11,plain,(
% 1.62/1.37 ~((powersetI = $true) => ((powersetE = $true) => ((subsetI2 = $true) => ((subsetE = $true) => ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => ((subset @ (powerset @ X1) @ (powerset @ X0)) = $true))))))),
% 1.62/1.37 inference(fool_elimination,[status(thm)],[f10])).
% 1.62/1.37 thf(f10,plain,(
% 1.62/1.37 ~(powersetI => (powersetE => (subsetI2 => (subsetE => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (subset @ (powerset @ X1) @ (powerset @ X0)))))))),
% 1.62/1.37 inference(rectify,[status(thm)],[f6])).
% 1.62/1.37 thf(f6,negated_conjecture,(
% 1.62/1.37 ~(powersetI => (powersetE => (subsetI2 => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1)))))))),
% 1.62/1.37 inference(negated_conjecture,[status(cth)],[f5])).
% 1.62/1.37 thf(f5,conjecture,(
% 1.62/1.37 powersetI => (powersetE => (subsetI2 => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1))))))),
% 1.62/1.37 file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',powersetsubset)).
% 1.62/1.37 thf(f350,plain,(
% 1.62/1.37 ((subset @ sK4 @ sK3) != $true)),
% 1.62/1.37 inference(trivial_inequality_removal,[status(thm)],[f340])).
% 1.62/1.37 thf(f340,plain,(
% 1.62/1.37 ((subset @ sK4 @ sK3) != $true) | ($true != $true)),
% 1.62/1.37 inference(superposition,[status(thm)],[f50,f326])).
% 1.62/1.37 thf(f326,plain,(
% 1.62/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ (powerset @ X1) @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true)) )),
% 1.62/1.37 inference(trivial_inequality_removal,[status(thm)],[f325])).
% 1.62/1.37 thf(f325,plain,(
% 1.62/1.37 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((subset @ X1 @ X0) != $true) | ((subset @ (powerset @ X1) @ (powerset @ X0)) = $true)) )),
% 1.62/1.37 inference(duplicate_literal_removal,[status(thm)],[f317])).
% 1.62/1.37 thf(f317,plain,(
% 1.62/1.37 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((subset @ X1 @ X0) != $true) | ((subset @ (powerset @ X1) @ (powerset @ X0)) = $true) | ((subset @ (powerset @ X1) @ (powerset @ X0)) = $true)) )),
% 1.62/1.37 inference(superposition,[status(thm)],[f129,f215])).
% 1.62/1.37 thf(f215,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (sK11 @ X1 @ (powerset @ X2)) @ X0) = $true) | ((subset @ (powerset @ X2) @ X1) = $true) | ((subset @ X2 @ X0) != $true)) )),
% 1.62/1.37 inference(trivial_inequality_removal,[status(thm)],[f214])).
% 1.62/1.37 thf(f214,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (powerset @ X2) @ X1) = $true) | ((subset @ X2 @ X0) != $true) | ((subset @ (sK11 @ X1 @ (powerset @ X2)) @ X0) = $true) | ($true != $true)) )),
% 1.62/1.37 inference(duplicate_literal_removal,[status(thm)],[f204])).
% 1.62/1.37 thf(f204,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (sK11 @ X1 @ (powerset @ X2)) @ X0) = $true) | ((subset @ (sK11 @ X1 @ (powerset @ X2)) @ X0) = $true) | ((subset @ (powerset @ X2) @ X1) = $true) | ($true != $true) | ((subset @ X2 @ X0) != $true)) )),
% 1.62/1.37 inference(superposition,[status(thm)],[f94,f136])).
% 1.62/1.37 thf(f136,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK11 @ X0 @ (sK11 @ X1 @ (powerset @ X2))) @ X2) = $true) | ((subset @ (sK11 @ X1 @ (powerset @ X2)) @ X0) = $true) | ((subset @ (powerset @ X2) @ X1) = $true)) )),
% 1.62/1.37 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.62/1.37 thf(f132,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((subset @ (powerset @ X2) @ X1) = $true) | ((subset @ (sK11 @ X1 @ (powerset @ X2)) @ X0) = $true) | ((in @ (sK11 @ X0 @ (sK11 @ X1 @ (powerset @ X2))) @ X2) = $true)) )),
% 1.62/1.37 inference(superposition,[status(thm)],[f104,f88])).
% 1.62/1.37 thf(f88,plain,(
% 1.62/1.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK11 @ X1 @ X0) @ X0) = $true) | ((subset @ X0 @ X1) = $true)) )),
% 1.62/1.37 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.62/1.37 thf(f80,plain,(
% 1.62/1.37 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((subset @ X0 @ X1) = $true) | ((in @ (sK11 @ X1 @ X0) @ X0) = $true)) )),
% 1.62/1.37 inference(definition_unfolding,[status(thm)],[f67,f54])).
% 1.62/1.37 thf(f54,plain,(
% 1.62/1.37 (subsetI2 = $true)),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f32])).
% 1.62/1.37 thf(f67,plain,(
% 1.62/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK11 @ X1 @ X0) @ X0) = $true) | (subsetI2 != $true)) )),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f45])).
% 1.62/1.37 thf(f45,plain,(
% 1.62/1.37 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (((in @ (sK11 @ X1 @ X0) @ X0) = $true) & ((in @ (sK11 @ X1 @ X0) @ X1) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | (((subset @ sK12 @ sK13) != $true) & ! [X5 : $i] : (((in @ X5 @ sK12) != $true) | ((in @ X5 @ sK13) = $true))))),
% 1.62/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f42,f44,f43])).
% 1.62/1.37 thf(f43,plain,(
% 1.62/1.37 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) => (((in @ (sK11 @ X1 @ X0) @ X0) = $true) & ((in @ (sK11 @ X1 @ X0) @ X1) != $true)))),
% 1.62/1.37 introduced(definition,[],[choice_axiom])).
% 1.62/1.37 thf(f44,plain,(
% 1.62/1.37 ? [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) != $true) & ! [X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true))) => (((subset @ sK12 @ sK13) != $true) & ! [X5 : $i] : (((in @ X5 @ sK12) != $true) | ((in @ X5 @ sK13) = $true)))),
% 1.62/1.37 introduced(definition,[],[choice_axiom])).
% 1.62/1.37 thf(f42,plain,(
% 1.62/1.37 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) != $true) & ! [X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true))))),
% 1.62/1.37 inference(rectify,[status(thm)],[f41])).
% 1.62/1.37 thf(f41,plain,(
% 1.62/1.37 (! [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))))),
% 1.62/1.37 inference(nnf_transformation,[status(thm)],[f19])).
% 1.62/1.37 thf(f19,plain,(
% 1.62/1.37 ! [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) <=> (subsetI2 = $true)),
% 1.62/1.37 inference(ennf_transformation,[status(thm)],[f15])).
% 1.62/1.37 thf(f15,plain,(
% 1.62/1.37 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((subset @ X1 @ X0) = $true)) <=> (subsetI2 = $true)),
% 1.62/1.37 inference(fool_elimination,[status(thm)],[f14])).
% 1.62/1.37 thf(f14,plain,(
% 1.62/1.37 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 1.62/1.37 inference(rectify,[status(thm)],[f3])).
% 1.62/1.37 thf(f3,axiom,(
% 1.62/1.37 (subsetI2 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.62/1.37 file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',subsetI2)).
% 1.62/1.37 thf(f104,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (sK11 @ X0 @ (powerset @ X1))) != $true) | ((subset @ (powerset @ X1) @ X0) = $true) | ((in @ X2 @ X1) = $true)) )),
% 1.62/1.37 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.62/1.37 thf(f101,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ (sK11 @ X0 @ (powerset @ X1))) != $true) | ((subset @ (powerset @ X1) @ X0) = $true)) )),
% 1.62/1.37 inference(superposition,[status(thm)],[f84,f88])).
% 1.62/1.37 thf(f84,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) )),
% 1.62/1.37 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.62/1.37 thf(f76,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true) | ($true != $true) | ((in @ X0 @ (powerset @ X1)) != $true)) )),
% 1.62/1.37 inference(definition_unfolding,[status(thm)],[f63,f55])).
% 1.62/1.37 thf(f55,plain,(
% 1.62/1.37 (powersetE = $true)),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f32])).
% 1.62/1.37 thf(f63,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | (powersetE != $true)) )),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f40])).
% 1.62/1.37 thf(f40,plain,(
% 1.62/1.37 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X0 @ (powerset @ X1)) != $true)) | (powersetE != $true)) & ((powersetE = $true) | (((in @ sK10 @ sK9) != $true) & ((in @ sK10 @ sK8) = $true) & ((in @ sK8 @ (powerset @ sK9)) = $true)))),
% 1.62/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f38,f39])).
% 1.62/1.37 thf(f39,plain,(
% 1.62/1.37 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) != $true) & ((in @ X5 @ X3) = $true) & ((in @ X3 @ (powerset @ X4)) = $true)) => (((in @ sK10 @ sK9) != $true) & ((in @ sK10 @ sK8) = $true) & ((in @ sK8 @ (powerset @ sK9)) = $true))),
% 1.62/1.37 introduced(definition,[],[choice_axiom])).
% 1.62/1.37 thf(f38,plain,(
% 1.62/1.37 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X0 @ (powerset @ X1)) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) != $true) & ((in @ X5 @ X3) = $true) & ((in @ X3 @ (powerset @ X4)) = $true)))),
% 1.62/1.37 inference(rectify,[status(thm)],[f37])).
% 1.62/1.37 thf(f37,plain,(
% 1.62/1.37 (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true) | ((in @ X1 @ (powerset @ X2)) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true) & ((in @ X1 @ (powerset @ X2)) = $true)))),
% 1.62/1.37 inference(nnf_transformation,[status(thm)],[f21])).
% 1.62/1.37 thf(f21,plain,(
% 1.62/1.37 ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true) | ((in @ X1 @ (powerset @ X2)) != $true)) <=> (powersetE = $true)),
% 1.62/1.37 inference(flattening,[status(thm)],[f20])).
% 1.62/1.37 thf(f20,plain,(
% 1.62/1.37 ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) | ((in @ X1 @ (powerset @ X2)) != $true)) <=> (powersetE = $true)),
% 1.62/1.37 inference(ennf_transformation,[status(thm)],[f9])).
% 1.62/1.37 thf(f9,plain,(
% 1.62/1.37 ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X2)) = $true) => (((in @ X0 @ X1) = $true) => ((in @ X0 @ X2) = $true))) <=> (powersetE = $true)),
% 1.62/1.37 inference(fool_elimination,[status(thm)],[f8])).
% 1.62/1.37 thf(f8,plain,(
% 1.62/1.37 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X2)) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = powersetE)),
% 1.62/1.37 inference(rectify,[status(thm)],[f2])).
% 1.62/1.37 thf(f2,axiom,(
% 1.62/1.37 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetE)),
% 1.62/1.37 file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',powersetE)).
% 1.62/1.37 thf(f94,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK11 @ X0 @ X1) @ X2) != $true) | ((subset @ X1 @ X0) = $true) | ((subset @ X2 @ X0) != $true)) )),
% 1.62/1.37 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.62/1.37 thf(f93,plain,(
% 1.62/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK11 @ X0 @ X1) @ X2) != $true) | ((subset @ X2 @ X0) != $true) | ((subset @ X1 @ X0) = $true) | ($true != $true)) )),
% 1.62/1.37 inference(superposition,[status(thm)],[f87,f89])).
% 1.62/1.37 thf(f89,plain,(
% 1.62/1.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ((subset @ X4 @ X3) != $true) | ((in @ X5 @ X4) != $true)) )),
% 1.62/1.37 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.62/1.37 thf(f75,plain,(
% 1.62/1.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((subset @ X4 @ X3) != $true) | ((in @ X5 @ X4) != $true) | ((in @ X5 @ X3) = $true)) )),
% 1.62/1.37 inference(definition_unfolding,[status(thm)],[f56,f52])).
% 1.62/1.37 thf(f52,plain,(
% 1.62/1.37 (subsetE = $true)),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f32])).
% 1.62/1.37 thf(f56,plain,(
% 1.62/1.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X3) != $true) | ((in @ X5 @ X4) != $true) | ((in @ X5 @ X3) = $true) | (subsetE != $true)) )),
% 1.62/1.37 inference(cnf_transformation,[status(thm)],[f36])).
% 1.62/1.37 thf(f36,plain,(
% 1.62/1.37 ((subsetE = $true) | (((subset @ sK6 @ sK5) = $true) & ((in @ sK7 @ sK6) = $true) & ((in @ sK7 @ sK5) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X3) != $true) | ((in @ X5 @ X4) != $true) | ((in @ X5 @ X3) = $true)) | (subsetE != $true))),
% 1.62/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f34,f35])).
% 1.62/1.37 thf(f35,plain,(
% 1.62/1.37 ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) = $true) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) => (((subset @ sK6 @ sK5) = $true) & ((in @ sK7 @ sK6) = $true) & ((in @ sK7 @ sK5) != $true))),
% 1.62/1.37 introduced(definition,[],[choice_axiom])).
% 1.62/1.37 thf(f34,plain,(
% 1.62/1.37 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) = $true) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X3) != $true) | ((in @ X5 @ X4) != $true) | ((in @ X5 @ X3) = $true)) | (subsetE != $true))),
% 1.62/1.37 inference(rectify,[status(thm)],[f33])).
% 1.62/1.37 thf(f33,plain,(
% 1.62/1.37 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) = $true) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) | (subsetE != $true))),
% 1.62/1.37 inference(nnf_transformation,[status(thm)],[f23])).
% 1.62/1.38 thf(f23,plain,(
% 1.62/1.38 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))),
% 1.62/1.38 inference(flattening,[status(thm)],[f22])).
% 1.62/1.38 thf(f22,plain,(
% 1.62/1.38 ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) | ((subset @ X1 @ X0) != $true)) <=> (subsetE = $true)),
% 1.62/1.38 inference(ennf_transformation,[status(thm)],[f13])).
% 1.62/1.38 thf(f13,plain,(
% 1.62/1.38 ! [X0 : $i,X2 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true))) <=> (subsetE = $true)),
% 1.62/1.38 inference(fool_elimination,[status(thm)],[f12])).
% 1.62/1.38 thf(f12,plain,(
% 1.62/1.38 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = subsetE)),
% 1.62/1.38 inference(rectify,[status(thm)],[f4])).
% 1.62/1.38 thf(f4,axiom,(
% 1.62/1.38 (! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.62/1.38 file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',subsetE)).
% 1.62/1.38 thf(f87,plain,(
% 1.62/1.38 ( ! [X0 : $i,X1 : $i] : (((in @ (sK11 @ X1 @ X0) @ X1) != $true) | ((subset @ X0 @ X1) = $true)) )),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.62/1.38 thf(f81,plain,(
% 1.62/1.38 ( ! [X0 : $i,X1 : $i] : (((in @ (sK11 @ X1 @ X0) @ X1) != $true) | ((subset @ X0 @ X1) = $true) | ($true != $true)) )),
% 1.62/1.38 inference(definition_unfolding,[status(thm)],[f66,f54])).
% 1.62/1.38 thf(f66,plain,(
% 1.62/1.38 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK11 @ X1 @ X0) @ X1) != $true) | (subsetI2 != $true)) )),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f45])).
% 1.62/1.38 thf(f129,plain,(
% 1.62/1.38 ( ! [X0 : $i,X1 : $i] : (((subset @ (sK11 @ (powerset @ X0) @ X1) @ X0) != $true) | ((subset @ X1 @ (powerset @ X0)) = $true)) )),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.62/1.38 thf(f120,plain,(
% 1.62/1.38 ( ! [X0 : $i,X1 : $i] : (((subset @ (sK11 @ (powerset @ X0) @ X1) @ X0) != $true) | ($true != $true) | ((subset @ X1 @ (powerset @ X0)) = $true)) )),
% 1.62/1.38 inference(superposition,[status(thm)],[f87,f118])).
% 1.62/1.38 thf(f118,plain,(
% 1.62/1.38 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) | ((subset @ X0 @ X1) != $true)) )),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.62/1.38 thf(f117,plain,(
% 1.62/1.38 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true) | ($true != $true)) )),
% 1.62/1.38 inference(duplicate_literal_removal,[status(thm)],[f114])).
% 1.62/1.38 thf(f114,plain,(
% 1.62/1.38 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) | ($true != $true) | ((subset @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) )),
% 1.62/1.38 inference(superposition,[status(thm)],[f99,f85])).
% 1.62/1.38 thf(f85,plain,(
% 1.62/1.38 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X4) = $true) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.62/1.38 thf(f70,plain,(
% 1.62/1.38 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ((in @ (sK2 @ X4 @ X3) @ X4) = $true) | ($true != $true)) )),
% 1.62/1.38 inference(definition_unfolding,[status(thm)],[f47,f53])).
% 1.62/1.38 thf(f53,plain,(
% 1.62/1.38 (powersetI = $true)),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f32])).
% 1.62/1.38 thf(f47,plain,(
% 1.62/1.38 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X4) = $true) | ((in @ X4 @ (powerset @ X3)) = $true) | (powersetI != $true)) )),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f30])).
% 1.62/1.38 thf(f30,plain,(
% 1.62/1.38 ((powersetI = $true) | (! [X2 : $i] : (((in @ X2 @ sK1) != $true) | ((in @ X2 @ sK0) = $true)) & ((in @ sK1 @ (powerset @ sK0)) != $true))) & (! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X4) = $true) & ((in @ (sK2 @ X4 @ X3) @ X3) != $true)) | ((in @ X4 @ (powerset @ X3)) = $true)) | (powersetI != $true))),
% 1.62/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f29,f28])).
% 1.62/1.38 thf(f28,plain,(
% 1.62/1.38 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ((in @ X1 @ (powerset @ X0)) != $true)) => (! [X2 : $i] : (((in @ X2 @ sK1) != $true) | ((in @ X2 @ sK0) = $true)) & ((in @ sK1 @ (powerset @ sK0)) != $true))),
% 1.62/1.38 introduced(definition,[],[choice_axiom])).
% 1.62/1.38 thf(f29,plain,(
% 1.62/1.38 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) != $true)) => (((in @ (sK2 @ X4 @ X3) @ X4) = $true) & ((in @ (sK2 @ X4 @ X3) @ X3) != $true)))),
% 1.62/1.38 introduced(definition,[],[choice_axiom])).
% 1.62/1.38 thf(f27,plain,(
% 1.62/1.38 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ((in @ X1 @ (powerset @ X0)) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) != $true)) | ((in @ X4 @ (powerset @ X3)) = $true)) | (powersetI != $true))),
% 1.62/1.38 inference(rectify,[status(thm)],[f26])).
% 1.62/1.38 thf(f26,plain,(
% 1.62/1.38 ((powersetI = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)) & ((in @ X0 @ (powerset @ X1)) != $true))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI != $true))),
% 1.62/1.38 inference(nnf_transformation,[status(thm)],[f18])).
% 1.62/1.38 thf(f18,plain,(
% 1.62/1.38 (powersetI = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) | ((in @ X0 @ (powerset @ X1)) = $true))),
% 1.62/1.38 inference(ennf_transformation,[status(thm)],[f17])).
% 1.62/1.38 thf(f17,plain,(
% 1.62/1.38 (powersetI = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((in @ X0 @ (powerset @ X1)) = $true))),
% 1.62/1.38 inference(fool_elimination,[status(thm)],[f16])).
% 1.62/1.38 thf(f16,plain,(
% 1.62/1.38 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))) = powersetI)),
% 1.62/1.38 inference(rectify,[status(thm)],[f1])).
% 1.62/1.38 thf(f1,axiom,(
% 1.62/1.38 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 1.62/1.38 file('/export/starexec/sandbox/tmp/tmp.7dLhMdGokl/DTF2THF_528.p',powersetI)).
% 1.62/1.38 thf(f99,plain,(
% 1.62/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X0 @ X1) @ X2) != $true) | ((in @ X0 @ (powerset @ X1)) = $true) | ((subset @ X2 @ X1) != $true)) )),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.62/1.38 thf(f95,plain,(
% 1.62/1.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X0 @ X1) @ X2) != $true) | ((subset @ X2 @ X1) != $true) | ($true != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) )),
% 1.62/1.38 inference(superposition,[status(thm)],[f86,f89])).
% 1.62/1.38 thf(f86,plain,(
% 1.62/1.38 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != $true) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 1.62/1.38 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.62/1.38 thf(f71,plain,(
% 1.62/1.38 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ (sK2 @ X4 @ X3) @ X3) != $true) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 1.62/1.38 inference(definition_unfolding,[status(thm)],[f46,f53])).
% 1.62/1.38 thf(f46,plain,(
% 1.62/1.38 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) != $true) | ((in @ X4 @ (powerset @ X3)) = $true) | (powersetI != $true)) )),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f30])).
% 1.62/1.38 thf(f50,plain,(
% 1.62/1.38 ((subset @ (powerset @ sK4) @ (powerset @ sK3)) != $true)),
% 1.62/1.38 inference(cnf_transformation,[status(thm)],[f32])).
% 1.62/1.38 % SZS output end Proof for DTF2THF_528
% 1.62/1.38 % (846)------------------------------
% 1.62/1.38 % (846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (846)Termination reason: Refutation
% 1.62/1.38
% 1.62/1.38 % (846)Memory used [KB]: 5756
% 1.62/1.38 % (846)Time elapsed: 0.057 s
% 1.62/1.38 % (846)Instructions burned: 87 (million)
% 1.62/1.38 % (846)------------------------------
% 1.62/1.38 % (846)------------------------------
% 1.62/1.38 % (840)Success in time 0.066 s
%------------------------------------------------------------------------------