%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU725^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:41 AM UTC 2026
% Result : Theorem 1.69s 1.79s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 15
% Syntax : Number of formulae : 114 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 1716 ( 450 equ; 0 cnn)
% Maximal formula atoms : 14 ( 15 avg)
% Number of connectives : 1881 ( 196 ~; 182 |; 112 &;1299 @)
% ( 15 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 24 con; 0-3 aty)
% Number of variables : 266 ( 0 ^; 206 !; 60 ?; 266 :)
% 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_5,type,
setminus: $i > $i > $i ).
thf(func_def_18,type,
sK6: $i > $i > $i > $i ).
thf(f2758,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f2757,f910]) ).
thf(f910,plain,
( $true
!= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK9 ) ),
inference(trivial_inequality_removal,[status(thm)],[f908]) ).
thf(f908,plain,
( ( $true
!= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f109,f451]) ).
thf(f451,plain,
( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ ( setminus @ sK7 @ sK9 ) ) ),
inference(subsumption_resolution,[status(thm)],[f402,f72]) ).
thf(f72,plain,
( $true
!= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( ( complementT_lem = $true )
& ( setminusI = $true )
& ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK7 ) ) )
& ( $true
= ( subset @ sK8 @ sK9 ) )
& ( $true
!= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) )
& ( setminusER = $true )
& ( subsetTI = $true )
& ( subsetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f26,f44,f43]) ).
thf(f43,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ( $true
= ( subset @ X1 @ X2 ) )
& ( $true
!= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) ) )
=> ( ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK7 ) ) )
& ( $true
= ( subset @ sK8 @ X2 ) )
& ( ( subset @ ( setminus @ sK7 @ X2 ) @ ( setminus @ sK7 @ sK8 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK7 ) ) )
& ( $true
= ( subset @ sK8 @ X2 ) )
& ( ( subset @ ( setminus @ sK7 @ X2 ) @ ( setminus @ sK7 @ sK8 ) )
!= $true ) )
=> ( ( $true
= ( in @ sK9 @ ( powerset @ sK7 ) ) )
& ( $true
= ( subset @ sK8 @ sK9 ) )
& ( $true
!= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( complementT_lem = $true )
& ( setminusI = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ( $true
= ( subset @ X1 @ X2 ) )
& ( $true
!= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) ) )
& ( setminusER = $true )
& ( subsetTI = $true )
& ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( $true
!= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) )
& ( $true
= ( subset @ X1 @ X2 ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
& ( subsetTI = $true )
& ( complementT_lem = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ( subsetE = $true )
=> ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( complementT_lem = $true )
=> ( ( subsetTI = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ( ( $true
= ( subset @ X1 @ X2 ) )
=> ( $true
= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( subsetE
=> ( setminusI
=> ( setminusER
=> ( complementT_lem
=> ( subsetTI
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( subsetE
=> ( setminusI
=> ( setminusER
=> ( complementT_lem
=> ( subsetTI
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( setminus @ X0 @ X4 ) @ ( setminus @ X0 @ X3 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( subsetE
=> ( setminusI
=> ( setminusER
=> ( complementT_lem
=> ( subsetTI
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ X3 @ X4 )
=> ( subset @ ( setminus @ X0 @ X4 ) @ ( setminus @ X0 @ X3 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',contrasubsetT2) ).
thf(f402,plain,
( ( $true
= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ ( setminus @ sK7 @ sK9 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f397]) ).
thf(f397,plain,
( ( $true
= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ ( setminus @ sK7 @ sK9 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f134,f121]) ).
thf(f121,plain,
( $true
= ( in @ ( setminus @ sK7 @ sK9 ) @ ( powerset @ sK7 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $true
= ( in @ ( setminus @ sK7 @ sK9 ) @ ( powerset @ sK7 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f112,f74]) ).
thf(f74,plain,
( $true
= ( in @ sK9 @ ( powerset @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f112,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f80,f77]) ).
thf(f77,plain,
complementT_lem = $true,
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f80,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
| ( complementT_lem != $true ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ( ( $true
= ( in @ sK10 @ ( powerset @ sK11 ) ) )
& ( ( in @ ( setminus @ sK11 @ sK10 ) @ ( powerset @ sK11 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f47,f48]) ).
thf(f48,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) )
& ( $true
!= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) ) )
=> ( ( $true
= ( in @ sK10 @ ( powerset @ sK11 ) ) )
& ( ( in @ ( setminus @ sK11 @ sK10 ) @ ( powerset @ sK11 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) )
& ( $true
!= ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ( $true
!= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) )
<=> ( complementT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ( $true
= ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) )
<=> ( complementT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) )
= complementT_lem ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: $i,X0: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X3 ) @ ( powerset @ X0 ) ) )
= complementT_lem ),
file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',complementT_lem) ).
thf(f134,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ sK7 ) ) )
| ( $true
= ( subset @ X0 @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ X0 @ sK7 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ X0 @ sK7 ) @ X0 ) )
| ( $true
= ( subset @ X0 @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ sK7 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f111,f120]) ).
thf(f120,plain,
( $true
= ( in @ ( setminus @ sK7 @ sK8 ) @ ( powerset @ sK7 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $true
= ( in @ ( setminus @ sK7 @ sK8 ) @ ( powerset @ sK7 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f112,f75]) ).
thf(f75,plain,
( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f111,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
| ( $true
= ( subset @ X5 @ X6 ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f63,f70]) ).
thf(f70,plain,
subsetTI = $true,
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f63,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( subsetTI = $true )
| ( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK3 ) )
| ( $true
!= ( in @ X3 @ sK4 ) )
| ( $true
= ( in @ X3 @ sK5 ) ) )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
& ( $true
!= ( subset @ sK4 @ sK5 ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
& ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
& ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) )
| ( subsetTI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f38,f41,f40,f39]) ).
thf(f39,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ( $true
!= ( subset @ X1 @ X2 ) ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
=> ( ? [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK3 ) )
| ( $true
!= ( in @ X3 @ sK4 ) )
| ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK3 ) ) )
& ( $true
!= ( subset @ sK4 @ X2 ) ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ? [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK3 ) )
| ( $true
!= ( in @ X3 @ sK4 ) )
| ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK3 ) ) )
& ( $true
!= ( subset @ sK4 @ X2 ) ) )
=> ( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK3 ) )
| ( $true
!= ( in @ X3 @ sK4 ) )
| ( $true
= ( in @ X3 @ sK5 ) ) )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
& ( $true
!= ( subset @ sK4 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
! [X4: $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X4 ) )
& ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ X7 @ X6 ) ) )
=> ( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
& ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X5 ) )
& ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ( ( subsetTI = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ( $true
!= ( subset @ X1 @ X2 ) ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X4 ) )
& ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ X7 @ X6 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) )
| ( subsetTI != $true ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( subsetTI = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ( $true
!= ( subset @ X0 @ X2 ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X3 @ X0 ) )
& ( $true
!= ( in @ X3 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( subsetTI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( subsetTI = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X3 @ X0 ) )
& ( $true
!= ( in @ X3 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ( subsetTI = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( subset @ X0 @ X2 ) )
| ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ X0 ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( subsetTI = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( in @ X3 @ X2 ) ) ) )
=> ( $true
= ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( subsetTI
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( subsetTI
= ( ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X4 ) ) )
=> ( subset @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',subsetTI) ).
thf(f109,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) )
| ( ( in @ X5 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f81,f71]) ).
thf(f71,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f81,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( $true
!= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( setminusER = $true )
| ( ( $true
= ( in @ sK14 @ sK12 ) )
& ( $true
= ( in @ sK14 @ ( setminus @ sK13 @ sK12 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( $true
!= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) ) )
| ( setminusER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f51,f52]) ).
thf(f52,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
=> ( ( $true
= ( in @ sK14 @ sK12 ) )
& ( $true
= ( in @ sK14 @ ( setminus @ sK13 @ sK12 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( $true
!= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) ) )
| ( setminusER != $true ) ) ),
inference(rectify,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( ( in @ X2 @ X0 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
=> ~ ( in @ X2 @ X0 ) )
= setminusER ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',setminusER) ).
thf(f2757,plain,
( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK9 ) ),
inference(trivial_inequality_removal,[status(thm)],[f2751]) ).
thf(f2751,plain,
( ( $true != $true )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK9 ) ) ),
inference(superposition,[status(thm)],[f117,f2651]) ).
thf(f2651,plain,
( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK8 ) ),
inference(subsumption_resolution,[status(thm)],[f2603,f72]) ).
thf(f2603,plain,
( ( $true
= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK8 ) ) ),
inference(subsumption_resolution,[status(thm)],[f2602,f120]) ).
thf(f2602,plain,
( ( $true
!= ( in @ ( setminus @ sK7 @ sK8 ) @ ( powerset @ sK7 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK8 ) )
| ( $true
= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f2595,f121]) ).
thf(f2595,plain,
( ( $true
!= ( in @ ( setminus @ sK7 @ sK9 ) @ ( powerset @ sK7 ) ) )
| ( $true
= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK8 ) )
| ( $true
!= ( in @ ( setminus @ sK7 @ sK8 ) @ ( powerset @ sK7 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2590]) ).
thf(f2590,plain,
( ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK8 ) )
| ( $true
!= ( in @ ( setminus @ sK7 @ sK9 ) @ ( powerset @ sK7 ) ) )
| ( $true
= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true
!= ( in @ ( setminus @ sK7 @ sK8 ) @ ( powerset @ sK7 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f114,f905]) ).
thf(f905,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ ( setminus @ sK7 @ X0 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f904]) ).
thf(f904,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ ( setminus @ sK7 @ X0 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f110,f538]) ).
thf(f538,plain,
( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK7 ) ),
inference(subsumption_resolution,[status(thm)],[f522,f72]) ).
thf(f522,plain,
( ( $true
= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK7 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f519]) ).
thf(f519,plain,
( ( $true != $true )
| ( $true
= ( subset @ ( setminus @ sK7 @ sK9 ) @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ ( setminus @ sK7 @ sK9 ) @ sK7 ) @ sK7 ) ) ),
inference(superposition,[status(thm)],[f154,f121]) ).
thf(f154,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ sK7 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ X0 @ sK7 ) @ sK7 ) )
| ( $true
= ( subset @ X0 @ ( setminus @ sK7 @ sK8 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
! [X0: $i] :
( ( $true
= ( subset @ X0 @ ( setminus @ sK7 @ sK8 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ ( powerset @ sK7 ) ) )
| ( $true
= ( in @ ( sK6 @ ( setminus @ sK7 @ sK8 ) @ X0 @ sK7 ) @ sK7 ) ) ),
inference(superposition,[status(thm)],[f115,f120]) ).
thf(f115,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
| ( $true != $true )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f64,f70]) ).
thf(f64,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f110,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ X4 @ X5 ) )
| ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true )
| ( $true
= ( in @ X4 @ X5 ) )
| ( $true
!= ( in @ X4 @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f58,f76]) ).
thf(f76,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f58,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true )
| ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ X4 @ X5 ) )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( setminusI = $true )
| ( ( $true
!= ( in @ sK1 @ ( setminus @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( $true
!= ( in @ sK1 @ sK2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true )
| ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ X4 @ X5 ) ) )
| ( setminusI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f34,f35]) ).
thf(f35,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
& ( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( in @ X1 @ X2 ) ) )
=> ( ( $true
!= ( in @ sK1 @ ( setminus @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( $true
!= ( in @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
& ( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( in @ X1 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true )
| ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ X4 @ X5 ) ) )
| ( setminusI != $true ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( setminusI = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
& ( $true
= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ X1 ) ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setminusI
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',setminusI) ).
thf(f114,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f62,f70]) ).
thf(f62,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( subset @ X5 @ X6 ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f117,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK8 ) )
| ( $true
= ( in @ X0 @ sK9 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK8 ) )
| ( $true
= ( in @ X0 @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f113,f73]) ).
thf(f73,plain,
( $true
= ( subset @ sK8 @ sK9 ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f113,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( $true != $true )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f87,f69]) ).
thf(f69,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f87,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( $true
= ( subset @ sK16 @ sK15 ) )
& ( $true
= ( in @ sK17 @ sK16 ) )
& ( $true
!= ( in @ sK17 @ sK15 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f55,f56]) ).
thf(f56,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
& ( $true
= ( in @ X5 @ X4 ) )
& ( ( in @ X5 @ X3 )
!= $true ) )
=> ( ( $true
= ( subset @ sK16 @ sK15 ) )
& ( $true
= ( in @ sK17 @ sK16 ) )
& ( $true
!= ( in @ sK17 @ sK15 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f55,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
& ( $true
= ( in @ X5 @ X4 ) )
& ( ( in @ X5 @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( subset @ X2 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X0 ) )
& ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( subset @ X2 @ X0 ) )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
= $true ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X0 ) ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X0 ) )
=> ( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( in @ X1 @ X0 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',subsetE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU725^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n006.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 12:32:00 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SEU725^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.39 % Domain : Set Theory
% 0.17/0.39 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.17/0.39 % Version : Especial > Reduced > Especial.
% 0.17/0.39 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.17/0.39 % subset X Y -> subset (setminus A Y) (setminus A X)))
% 0.17/0.39
% 0.17/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.39 % Source : [Bro08]
% 0.17/0.39 % Names : ZFC227l [Bro08]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 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
% 0.17/0.39 % Syntax : Number of formulae : 15 ( 5 unt; 9 typ; 5 def)
% 0.17/0.39 % Number of atoms : 35 ( 5 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 9 ( 5 avg)
% 0.17/0.39 % Number of connectives : 77 ( 2 ~; 0 |; 0 &; 56 @)
% 0.17/0.39 % ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 16 ( 4 avg)
% 0.17/0.39 % Number of types : 2 ( 0 usr)
% 0.17/0.39 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 10 ( 9 usr; 5 con; 0-2 aty)
% 0.17/0.39 % Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : http://mathgate.info/detsetitem.php?id=285
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(in_type,type,
% 0.17/0.39 in: $i > $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(powerset_type,type,
% 0.17/0.39 powerset: $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(subset_type,type,
% 0.17/0.39 subset: $i > $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(subsetE_type,type,
% 0.17/0.39 subsetE: $o ).
% 0.17/0.39
% 0.17/0.39 thf(subsetE,definition,
% 0.17/0.39 ( subsetE
% 0.17/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.39 ( ( subset @ A @ B )
% 0.17/0.39 => ( ( in @ Xx @ A )
% 0.17/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setminus_type,type,
% 0.17/0.39 setminus: $i > $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(setminusI_type,type,
% 0.17/0.39 setminusI: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setminusI,definition,
% 0.17/0.39 ( setminusI
% 0.17/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( ~ ( in @ Xx @ B )
% 0.17/0.39 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setminusER_type,type,
% 0.17/0.39 setminusER: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setminusER,definition,
% 0.17/0.39 ( setminusER
% 0.17/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.39 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(complementT_lem_type,type,
% 0.17/0.39 complementT_lem: $o ).
% 0.17/0.39
% 0.17/0.39 thf(complementT_lem,definition,
% 0.17/0.39 ( complementT_lem
% 0.17/0.39 = ( ! [A: $i,X: $i] :
% 0.17/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.39 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(subsetTI_type,type,
% 0.17/0.39 subsetTI: $o ).
% 0.17/0.39
% 0.17/0.39 thf(subsetTI,definition,
% 0.17/0.39 ( subsetTI
% 0.17/0.39 = ( ! [A: $i,X: $i] :
% 0.17/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.39 => ! [Y: $i] :
% 0.17/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.39 => ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( ( in @ Xx @ X )
% 0.17/0.39 => ( in @ Xx @ Y ) ) )
% 0.17/0.39 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(contrasubsetT2,conjecture,
% 0.17/0.39 ( subsetE
% 0.17/0.39 => ( setminusI
% 0.17/0.39 => ( setminusER
% 0.17/0.39 => ( complementT_lem
% 0.17/0.39 => ( subsetTI
% 0.17/0.39 => ! [A: $i,X: $i] :
% 0.17/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.39 => ! [Y: $i] :
% 0.17/0.39 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.39 => ( ( subset @ X @ Y )
% 0.17/0.39 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.58/1.35 ---- Embedded in THF ---
% 1.58/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.58/1.35 %%% Generated on Tue Feb 24 12:32:01 EST 2026
% 1.58/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.58/1.35 %%% Logic specification used:
% 1.58/1.35 %%% thf(spec, logic, $$dhol).
% 1.58/1.35
% 1.58/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2DTF10052.p
% See solution above
% 1.58/1.36 ------------------------
% 1.58/1.36 ---- Cleaned THF ---
% 1.58/1.37 thf(in_type,type,
% 1.58/1.37 in: $i > $i > $o ).
% 1.58/1.37
% 1.58/1.37 thf(powerset_type,type,
% 1.58/1.37 powerset: $i > $i ).
% 1.58/1.37
% 1.58/1.37 thf(subset_type,type,
% 1.58/1.37 subset: $i > $i > $o ).
% 1.58/1.37
% 1.58/1.37 thf(subsetE_type,type,
% 1.58/1.37 subsetE: $o ).
% 1.58/1.37
% 1.58/1.37 thf(subsetE,definition,
% 1.58/1.37 ( subsetE
% 1.58/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.58/1.37 ( ( subset @ A @ B )
% 1.58/1.37 => ( ( in @ Xx @ A )
% 1.58/1.37 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.58/1.37
% 1.58/1.37 thf(setminus_type,type,
% 1.58/1.37 setminus: $i > $i > $i ).
% 1.58/1.37
% 1.58/1.37 thf(setminusI_type,type,
% 1.58/1.37 setminusI: $o ).
% 1.58/1.37
% 1.58/1.37 thf(setminusI,definition,
% 1.58/1.37 ( setminusI
% 1.58/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.58/1.37 ( ( in @ Xx @ A )
% 1.58/1.37 => ( ~ ( in @ Xx @ B )
% 1.58/1.37 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.58/1.37
% 1.58/1.37 thf(setminusER_type,type,
% 1.58/1.37 setminusER: $o ).
% 1.58/1.37
% 1.58/1.37 thf(setminusER,definition,
% 1.58/1.37 ( setminusER
% 1.58/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.58/1.37 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.58/1.37 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.58/1.37
% 1.58/1.37 thf(complementT_lem_type,type,
% 1.58/1.37 complementT_lem: $o ).
% 1.58/1.37
% 1.58/1.37 thf(complementT_lem,definition,
% 1.58/1.37 ( complementT_lem
% 1.58/1.37 = ( ! [A: $i,X: $i] :
% 1.58/1.37 ( ( in @ X @ ( powerset @ A ) )
% 1.58/1.37 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 1.58/1.37
% 1.58/1.37 thf(subsetTI_type,type,
% 1.58/1.37 subsetTI: $o ).
% 1.58/1.37
% 1.58/1.37 thf(subsetTI,definition,
% 1.58/1.37 ( subsetTI
% 1.58/1.37 = ( ! [A: $i,X: $i] :
% 1.58/1.37 ( ( in @ X @ ( powerset @ A ) )
% 1.58/1.37 => ! [Y: $i] :
% 1.58/1.37 ( ( in @ Y @ ( powerset @ A ) )
% 1.58/1.37 => ( ! [Xx: $i] :
% 1.58/1.37 ( ( in @ Xx @ A )
% 1.58/1.37 => ( ( in @ Xx @ X )
% 1.58/1.37 => ( in @ Xx @ Y ) ) )
% 1.58/1.37 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 1.58/1.37
% 1.58/1.37 thf(contrasubsetT2,conjecture,
% 1.58/1.37 ( subsetE
% 1.58/1.37 => ( setminusI
% 1.58/1.37 => ( setminusER
% 1.58/1.37 => ( complementT_lem
% 1.58/1.37 => ( subsetTI
% 1.58/1.37 => ! [A: $i,X: $i] :
% 1.58/1.37 ( ( in @ X @ ( powerset @ A ) )
% 1.58/1.37 => ! [Y: $i] :
% 1.58/1.37 ( ( in @ Y @ ( powerset @ A ) )
% 1.58/1.37 => ( ( subset @ X @ Y )
% 1.58/1.37 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ).
% 1.58/1.37 ------------------------
% 1.58/1.39 % (10149)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/183Mi)
% 1.58/1.39 % (10153)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_10052 for (2999ds/2Mi)
% 1.58/1.39 % (10152)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/2Mi)
% 1.58/1.39 % (10150)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_10052 for (2999ds/4Mi)
% 1.58/1.39 % (10155)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/18Mi)
% 1.58/1.39 % (10151)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_10052 for (2999ds/27Mi)
% 1.58/1.39 % (10152)Instruction limit reached!
% 1.58/1.39 % (10152)------------------------------
% 1.58/1.39 % (10152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (10152)Termination reason: Unknown
% 1.58/1.39 % (10153)Instruction limit reached!
% 1.58/1.39 % (10153)------------------------------
% 1.58/1.39 % (10153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (10152)Termination phase: Property scanning
% 1.58/1.39
% 1.58/1.39 % (10152)Memory used [KB]: 1023
% 1.58/1.39 % (10152)Time elapsed: 0.003 s
% 1.58/1.39 % (10152)Instructions burned: 3 (million)
% 1.58/1.39 % (10152)------------------------------
% 1.58/1.39 % (10152)------------------------------
% 1.58/1.39 % (10153)Termination reason: Unknown
% 1.58/1.39 % (10153)Termination phase: Naming
% 1.58/1.39
% 1.58/1.39 % (10153)Memory used [KB]: 1023
% 1.58/1.39 % (10153)Time elapsed: 0.003 s
% 1.58/1.39 % (10153)Instructions burned: 3 (million)
% 1.58/1.39 % (10153)------------------------------
% 1.58/1.39 % (10153)------------------------------
% 1.58/1.39 % (10150)Instruction limit reached!
% 1.58/1.39 % (10150)------------------------------
% 1.58/1.39 % (10150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (10150)Termination reason: Unknown
% 1.58/1.39 % (10150)Termination phase: Saturation
% 1.58/1.39
% 1.58/1.39 % (10150)Memory used [KB]: 1023
% 1.58/1.39 % (10150)Time elapsed: 0.004 s
% 1.58/1.39 % (10150)Instructions burned: 4 (million)
% 1.58/1.39 % (10150)------------------------------
% 1.58/1.39 % (10150)------------------------------
% 1.58/1.39 % (10154)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_10052 for (2999ds/275Mi)
% 1.69/1.40 % (10155)Instruction limit reached!
% 1.69/1.40 % (10155)------------------------------
% 1.69/1.40 % (10155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (10155)Termination reason: Unknown
% 1.69/1.40 % (10155)Termination phase: Saturation
% 1.69/1.40
% 1.69/1.40 % (10155)Memory used [KB]: 5628
% 1.69/1.40 % (10155)Time elapsed: 0.012 s
% 1.69/1.40 % (10155)Instructions burned: 19 (million)
% 1.69/1.40 % (10155)------------------------------
% 1.69/1.40 % (10155)------------------------------
% 1.69/1.40 % (10151)Instruction limit reached!
% 1.69/1.40 % (10151)------------------------------
% 1.69/1.40 % (10151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (10151)Termination reason: Unknown
% 1.69/1.40 % (10151)Termination phase: Saturation
% 1.69/1.40
% 1.69/1.40 % (10151)Memory used [KB]: 5628
% 1.69/1.40 % (10151)Time elapsed: 0.016 s
% 1.69/1.40 % (10151)Instructions burned: 28 (million)
% 1.69/1.40 % (10151)------------------------------
% 1.69/1.40 % (10151)------------------------------
% 1.69/1.40 % (10156)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/3Mi)
% 1.69/1.40 % (10157)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_10052 for (2999ds/37Mi)
% 1.69/1.40 % (10158)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_10052 for (2999ds/15Mi)
% 1.69/1.40 % (10156)Instruction limit reached!
% 1.69/1.40 % (10156)------------------------------
% 1.69/1.40 % (10156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (10156)Termination reason: Unknown
% 1.69/1.40 % (10156)Termination phase: Property scanning
% 1.69/1.40
% 1.69/1.40 % (10156)Memory used [KB]: 1023
% 1.69/1.40 % (10156)Time elapsed: 0.003 s
% 1.69/1.41 % (10156)Instructions burned: 3 (million)
% 1.69/1.41 % (10156)------------------------------
% 1.69/1.41 % (10156)------------------------------
% 1.69/1.41 % (10158)Instruction limit reached!
% 1.69/1.41 % (10158)------------------------------
% 1.69/1.41 % (10158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (10158)Termination reason: Unknown
% 1.69/1.41 % (10158)Termination phase: Saturation
% 1.69/1.41
% 1.69/1.41 % (10158)Memory used [KB]: 5628
% 1.69/1.41 % (10158)Time elapsed: 0.010 s
% 1.69/1.41 % (10158)Instructions burned: 15 (million)
% 1.69/1.41 % (10158)------------------------------
% 1.69/1.41 % (10158)------------------------------
% 1.69/1.41 % (10159)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_10052 for (2999ds/3Mi)
% 1.69/1.42 % (10159)Instruction limit reached!
% 1.69/1.42 % (10159)------------------------------
% 1.69/1.42 % (10159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.42 % (10159)Termination reason: Unknown
% 1.69/1.42 % (10159)Termination phase: Property scanning
% 1.69/1.42
% 1.69/1.42 % (10159)Memory used [KB]: 1023
% 1.69/1.42 % (10159)Time elapsed: 0.004 s
% 1.69/1.42 % (10159)Instructions burned: 4 (million)
% 1.69/1.42 % (10159)------------------------------
% 1.69/1.42 % (10159)------------------------------
% 1.69/1.42 % (10160)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_10052 for (2999ds/1041Mi)
% 1.69/1.42 % (10161)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/7Mi)
% 1.69/1.42 % (10157)Instruction limit reached!
% 1.69/1.42 % (10157)------------------------------
% 1.69/1.42 % (10157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.42 % (10157)Termination reason: Unknown
% 1.69/1.42 % (10157)Termination phase: Saturation
% 1.69/1.42
% 1.69/1.42 % (10157)Memory used [KB]: 5628
% 1.69/1.42 % (10157)Time elapsed: 0.020 s
% 1.69/1.42 % (10157)Instructions burned: 37 (million)
% 1.69/1.42 % (10157)------------------------------
% 1.69/1.42 % (10157)------------------------------
% 1.69/1.43 % (10161)Instruction limit reached!
% 1.69/1.43 % (10161)------------------------------
% 1.69/1.43 % (10161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.43 % (10161)Termination reason: Unknown
% 1.69/1.43 % (10161)Termination phase: Saturation
% 1.69/1.43
% 1.69/1.43 % (10161)Memory used [KB]: 1023
% 1.69/1.43 % (10161)Time elapsed: 0.006 s
% 1.69/1.43 % (10161)Instructions burned: 8 (million)
% 1.69/1.43 % (10161)------------------------------
% 1.69/1.43 % (10161)------------------------------
% 1.69/1.43 % (10162)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/16Mi)
% 1.69/1.43 % (10163)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_10052 for (2999ds/3Mi)
% 1.69/1.43 % (10163)Instruction limit reached!
% 1.69/1.43 % (10163)------------------------------
% 1.69/1.43 % (10163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.43 % (10163)Termination reason: Unknown
% 1.69/1.43 % (10163)Termination phase: Property scanning
% 1.69/1.43
% 1.69/1.43 % (10163)Memory used [KB]: 1023
% 1.69/1.43 % (10163)Time elapsed: 0.003 s
% 1.69/1.43 % (10163)Instructions burned: 3 (million)
% 1.69/1.43 % (10163)------------------------------
% 1.69/1.43 % (10163)------------------------------
% 1.69/1.44 % (10162)Instruction limit reached!
% 1.69/1.44 % (10162)------------------------------
% 1.69/1.44 % (10162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.44 % (10162)Termination reason: Unknown
% 1.69/1.44 % (10162)Termination phase: Saturation
% 1.69/1.44
% 1.69/1.44 % (10162)Memory used [KB]: 5884
% 1.69/1.44 % (10162)Time elapsed: 0.010 s
% 1.69/1.44 % (10162)Instructions burned: 16 (million)
% 1.69/1.44 % (10162)------------------------------
% 1.69/1.44 % (10162)------------------------------
% 1.69/1.44 % (10164)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_10052 for (2999ds/3Mi)
% 1.69/1.44 % (10164)Instruction limit reached!
% 1.69/1.44 % (10164)------------------------------
% 1.69/1.44 % (10164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.44 % (10164)Termination reason: Unknown
% 1.69/1.44 % (10164)Termination phase: Unused predicate definition removal
% 1.69/1.44
% 1.69/1.44 % (10164)Memory used [KB]: 1023
% 1.69/1.44 % (10164)Time elapsed: 0.003 s
% 1.69/1.44 % (10164)Instructions burned: 3 (million)
% 1.69/1.44 % (10164)------------------------------
% 1.69/1.44 % (10164)------------------------------
% 1.69/1.44 % (10165)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/7Mi)
% 1.69/1.44 % (10165)Refutation not found, incomplete strategy
% 1.69/1.44 % (10165)------------------------------
% 1.69/1.44 % (10165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.44 % (10165)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.44
% 1.69/1.45
% 1.69/1.45 % (10165)Memory used [KB]: 5500
% 1.69/1.45 % (10165)Time elapsed: 0.004 s
% 1.69/1.45 % (10165)Instructions burned: 4 (million)
% 1.69/1.45 % (10165)------------------------------
% 1.69/1.45 % (10165)------------------------------
% 1.69/1.45 % (10166)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/3Mi)
% 1.69/1.45 % (10166)Instruction limit reached!
% 1.69/1.45 % (10166)------------------------------
% 1.69/1.45 % (10166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.45 % (10166)Termination reason: Unknown
% 1.69/1.45 % (10166)Termination phase: Property scanning
% 1.69/1.45
% 1.69/1.45 % (10166)Memory used [KB]: 1023
% 1.69/1.45 % (10166)Time elapsed: 0.003 s
% 1.69/1.45 % (10166)Instructions burned: 3 (million)
% 1.69/1.45 % (10166)------------------------------
% 1.69/1.45 % (10166)------------------------------
% 1.69/1.45 % (10167)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/4Mi)
% 1.69/1.45 % (10167)Instruction limit reached!
% 1.69/1.45 % (10167)------------------------------
% 1.69/1.45 % (10167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.45 % (10167)Termination reason: Unknown
% 1.69/1.45 % (10167)Termination phase: Saturation
% 1.69/1.46
% 1.69/1.46 % (10167)Memory used [KB]: 5500
% 1.69/1.46 % (10167)Time elapsed: 0.004 s
% 1.69/1.46 % (10167)Instructions burned: 5 (million)
% 1.69/1.46 % (10167)------------------------------
% 1.69/1.46 % (10167)------------------------------
% 1.69/1.46 % (10168)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/18Mi)
% 1.69/1.46 % (10169)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/710Mi)
% 1.69/1.47 % (10168)Instruction limit reached!
% 1.69/1.47 % (10168)------------------------------
% 1.69/1.47 % (10168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.47 % (10168)Termination reason: Unknown
% 1.69/1.47 % (10168)Termination phase: Saturation
% 1.69/1.47
% 1.69/1.47 % (10168)Memory used [KB]: 5628
% 1.69/1.47 % (10168)Time elapsed: 0.011 s
% 1.69/1.47 % (10168)Instructions burned: 18 (million)
% 1.69/1.47 % (10168)------------------------------
% 1.69/1.47 % (10168)------------------------------
% 1.69/1.47 % (10170)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/6Mi)
% 1.69/1.47 % (10170)Instruction limit reached!
% 1.69/1.47 % (10170)------------------------------
% 1.69/1.47 % (10170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.47 % (10170)Termination reason: Unknown
% 1.69/1.47 % (10170)Termination phase: Saturation
% 1.69/1.47
% 1.69/1.47 % (10170)Memory used [KB]: 5500
% 1.69/1.47 % (10170)Time elapsed: 0.005 s
% 1.69/1.47 % (10170)Instructions burned: 7 (million)
% 1.69/1.47 % (10170)------------------------------
% 1.69/1.47 % (10170)------------------------------
% 1.69/1.47 % (10171)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/902Mi)
% 1.69/1.47 % (10171)Refutation not found, incomplete strategy
% 1.69/1.47 % (10171)------------------------------
% 1.69/1.47 % (10171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.47 % (10171)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.47
% 1.69/1.47
% 1.69/1.47 % (10171)Memory used [KB]: 5500
% 1.69/1.47 % (10171)Time elapsed: 0.005 s
% 1.69/1.47 % (10171)Instructions burned: 6 (million)
% 1.69/1.47 % (10171)------------------------------
% 1.69/1.47 % (10171)------------------------------
% 1.69/1.47 % (10149)Instruction limit reached!
% 1.69/1.47 % (10149)------------------------------
% 1.69/1.47 % (10149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.47 % (10149)Termination reason: Unknown
% 1.69/1.47 % (10149)Termination phase: Saturation
% 1.69/1.47
% 1.69/1.48 % (10149)Memory used [KB]: 6396
% 1.69/1.48 % (10149)Time elapsed: 0.091 s
% 1.69/1.48 % (10149)Instructions burned: 184 (million)
% 1.69/1.48 % (10149)------------------------------
% 1.69/1.48 % (10149)------------------------------
% 1.69/1.48 % (10172)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/21Mi)
% 1.69/1.49 % (10173)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/5Mi)
% 1.69/1.49 % (10173)Instruction limit reached!
% 1.69/1.49 % (10173)------------------------------
% 1.69/1.49 % (10173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.49 % (10173)Termination reason: Unknown
% 1.69/1.49 % (10173)Termination phase: Saturation
% 1.69/1.49
% 1.69/1.49 % (10173)Memory used [KB]: 5500
% 1.69/1.49 % (10173)Time elapsed: 0.004 s
% 1.69/1.49 % (10173)Instructions burned: 5 (million)
% 1.69/1.49 % (10173)------------------------------
% 1.69/1.49 % (10173)------------------------------
% 1.69/1.49 % (10174)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/6Mi)
% 1.69/1.49 % (10175)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10052 for (2999ds/377Mi)
% 1.69/1.49 % (10172)Instruction limit reached!
% 1.69/1.49 % (10172)------------------------------
% 1.69/1.49 % (10172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.49 % (10172)Termination reason: Unknown
% 1.69/1.49 % (10172)Termination phase: Saturation
% 1.69/1.49
% 1.69/1.49 % (10172)Memory used [KB]: 5628
% 1.69/1.49 % (10172)Time elapsed: 0.013 s
% 1.69/1.49 % (10172)Instructions burned: 21 (million)
% 1.69/1.49 % (10172)------------------------------
% 1.69/1.49 % (10172)------------------------------
% 1.69/1.49 % (10174)Instruction limit reached!
% 1.69/1.49 % (10174)------------------------------
% 1.69/1.49 % (10174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.49 % (10174)Termination reason: Unknown
% 1.69/1.49 % (10174)Termination phase: Saturation
% 1.69/1.49
% 1.69/1.49 % (10174)Memory used [KB]: 5500
% 1.69/1.49 % (10174)Time elapsed: 0.005 s
% 1.69/1.49 % (10174)Instructions burned: 7 (million)
% 1.69/1.49 % (10174)------------------------------
% 1.69/1.49 % (10174)------------------------------
% 1.69/1.51 % (10176)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_10052 for (2998ds/779Mi)
% 1.69/1.51 % (10177)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_10052 for (2998ds/19Mi)
% 1.69/1.51 % (10178)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10052 for (2998ds/879Mi)
% 1.69/1.52 % (10177)Refutation not found, incomplete strategy
% 1.69/1.52 % (10177)------------------------------
% 1.69/1.52 % (10177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.52 % (10177)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.52
% 1.69/1.52
% 1.69/1.52 % (10177)Memory used [KB]: 5628
% 1.69/1.52 % (10177)Time elapsed: 0.034 s
% 1.69/1.52 % (10177)Instructions burned: 18 (million)
% 1.69/1.52 % (10177)------------------------------
% 1.69/1.52 % (10177)------------------------------
% 1.69/1.54 % (10179)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10052 for (2998ds/17Mi)
% 1.69/1.54 % (10154)Instruction limit reached!
% 1.69/1.54 % (10154)------------------------------
% 1.69/1.54 % (10154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.54 % (10154)Termination reason: Unknown
% 1.69/1.54 % (10154)Termination phase: Saturation
% 1.69/1.54
% 1.69/1.54 % (10154)Memory used [KB]: 6140
% 1.69/1.54 % (10154)Time elapsed: 0.155 s
% 1.69/1.54 % (10154)Instructions burned: 276 (million)
% 1.69/1.54 % (10154)------------------------------
% 1.69/1.54 % (10154)------------------------------
% 1.69/1.55 % (10179)Instruction limit reached!
% 1.69/1.55 % (10179)------------------------------
% 1.69/1.55 % (10179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.55 % (10179)Termination reason: Unknown
% 1.69/1.55 % (10179)Termination phase: Saturation
% 1.69/1.55
% 1.69/1.55 % (10179)Memory used [KB]: 5628
% 1.69/1.55 % (10179)Time elapsed: 0.011 s
% 1.69/1.55 % (10179)Instructions burned: 17 (million)
% 1.69/1.55 % (10179)------------------------------
% 1.69/1.55 % (10179)------------------------------
% 1.69/1.56 % (10181)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10052 for (2998ds/30Mi)
% 1.69/1.56 % (10180)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10052 for (2998ds/3Mi)
% 1.69/1.56 % (10180)Instruction limit reached!
% 1.69/1.56 % (10180)------------------------------
% 1.69/1.56 % (10180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.56 % (10180)Termination reason: Unknown
% 1.69/1.57 % (10180)Termination phase: Preprocessing 3
% 1.69/1.57
% 1.69/1.57 % (10180)Memory used [KB]: 1023
% 1.69/1.57 % (10180)Time elapsed: 0.003 s
% 1.69/1.57 % (10180)Instructions burned: 3 (million)
% 1.69/1.57 % (10180)------------------------------
% 1.69/1.57 % (10180)------------------------------
% 1.69/1.57 % (10181)Refutation not found, incomplete strategy
% 1.69/1.57 % (10181)------------------------------
% 1.69/1.57 % (10181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.57 % (10181)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.57
% 1.69/1.57
% 1.69/1.57 % (10181)Memory used [KB]: 5500
% 1.69/1.57 % (10181)Time elapsed: 0.007 s
% 1.69/1.57 % (10181)Instructions burned: 10 (million)
% 1.69/1.57 % (10181)------------------------------
% 1.69/1.57 % (10181)------------------------------
% 1.69/1.59 % (10182)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10052 for (2997ds/127Mi)
% 1.69/1.59 % (10183)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10052 for (2997ds/100Mi)
% 1.69/1.64 % (10183)Instruction limit reached!
% 1.69/1.64 % (10183)------------------------------
% 1.69/1.64 % (10183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.64 % (10183)Termination reason: Unknown
% 1.69/1.64 % (10183)Termination phase: Saturation
% 1.69/1.64
% 1.69/1.64 % (10183)Memory used [KB]: 6012
% 1.69/1.64 % (10183)Time elapsed: 0.051 s
% 1.69/1.64 % (10183)Instructions burned: 100 (million)
% 1.69/1.64 % (10183)------------------------------
% 1.69/1.64 % (10183)------------------------------
% 1.69/1.65 % (10184)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_10052 for (2997ds/3Mi)
% 1.69/1.65 % (10184)Instruction limit reached!
% 1.69/1.65 % (10184)------------------------------
% 1.69/1.65 % (10184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.65 % (10184)Termination reason: Unknown
% 1.69/1.65 % (10184)Termination phase: Saturation
% 1.69/1.65
% 1.69/1.65 % (10184)Memory used [KB]: 1023
% 1.69/1.65 % (10184)Time elapsed: 0.004 s
% 1.69/1.65 % (10184)Instructions burned: 4 (million)
% 1.69/1.65 % (10184)------------------------------
% 1.69/1.65 % (10184)------------------------------
% 1.69/1.66 % (10182)Instruction limit reached!
% 1.69/1.66 % (10182)------------------------------
% 1.69/1.66 % (10182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.66 % (10182)Termination reason: Unknown
% 1.69/1.66 % (10182)Termination phase: Saturation
% 1.69/1.66
% 1.69/1.66 % (10182)Memory used [KB]: 5756
% 1.69/1.66 % (10182)Time elapsed: 0.075 s
% 1.69/1.66 % (10182)Instructions burned: 128 (million)
% 1.69/1.66 % (10182)------------------------------
% 1.69/1.66 % (10182)------------------------------
% 1.69/1.67 % (10185)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_10052 for (2997ds/20Mi)
% 1.69/1.67 % (10175)Instruction limit reached!
% 1.69/1.67 % (10175)------------------------------
% 1.69/1.67 % (10175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.67 % (10175)Termination reason: Unknown
% 1.69/1.67 % (10175)Termination phase: Saturation
% 1.69/1.67
% 1.69/1.67 % (10175)Memory used [KB]: 6268
% 1.69/1.67 % (10175)Time elapsed: 0.203 s
% 1.69/1.67 % (10175)Instructions burned: 378 (million)
% 1.69/1.67 % (10175)------------------------------
% 1.69/1.67 % (10175)------------------------------
% 1.69/1.68 % (10186)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_10052 for (2997ds/86Mi)
% 1.69/1.68 % (10185)Instruction limit reached!
% 1.69/1.68 % (10185)------------------------------
% 1.69/1.68 % (10185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.68 % (10185)Termination reason: Unknown
% 1.69/1.68 % (10185)Termination phase: Saturation
% 1.69/1.68
% 1.69/1.68 % (10185)Memory used [KB]: 5628
% 1.69/1.68 % (10185)Time elapsed: 0.013 s
% 1.69/1.68 % (10185)Instructions burned: 21 (million)
% 1.69/1.68 % (10185)------------------------------
% 1.69/1.68 % (10185)------------------------------
% 1.69/1.69 % (10187)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_10052 for (2996ds/107Mi)
% 1.69/1.70 % (10188)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_10052 for (2996ds/39Mi)
% 1.69/1.72 % (10188)Instruction limit reached!
% 1.69/1.72 % (10188)------------------------------
% 1.69/1.72 % (10188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.72 % (10188)Termination reason: Unknown
% 1.69/1.72 % (10188)Termination phase: Saturation
% 1.69/1.72
% 1.69/1.72 % (10188)Memory used [KB]: 5628
% 1.69/1.72 % (10188)Time elapsed: 0.021 s
% 1.69/1.72 % (10188)Instructions burned: 39 (million)
% 1.69/1.72 % (10188)------------------------------
% 1.69/1.72 % (10188)------------------------------
% 1.69/1.73 % (10186)Instruction limit reached!
% 1.69/1.73 % (10186)------------------------------
% 1.69/1.73 % (10186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.73 % (10186)Termination reason: Unknown
% 1.69/1.73 % (10186)Termination phase: Saturation
% 1.69/1.73
% 1.69/1.73 % (10186)Memory used [KB]: 5884
% 1.69/1.73 % (10186)Time elapsed: 0.053 s
% 1.69/1.73 % (10186)Instructions burned: 87 (million)
% 1.69/1.73 % (10186)------------------------------
% 1.69/1.73 % (10186)------------------------------
% 1.69/1.74 % (10189)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_10052 for (2996ds/448Mi)
% 1.69/1.74 % (10187)Instruction limit reached!
% 1.69/1.74 % (10187)------------------------------
% 1.69/1.74 % (10187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.74 % (10187)Termination reason: Unknown
% 1.69/1.74 % (10187)Termination phase: Saturation
% 1.69/1.74
% 1.69/1.74 % (10187)Memory used [KB]: 5884
% 1.69/1.74 % (10187)Time elapsed: 0.054 s
% 1.69/1.74 % (10187)Instructions burned: 107 (million)
% 1.69/1.74 % (10187)------------------------------
% 1.69/1.74 % (10187)------------------------------
% 1.69/1.75 % (10190)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_10052 for (2996ds/46Mi)
% 1.69/1.76 % (10191)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_10052 for (2996ds/98Mi)
% 1.69/1.78 % (10190)Instruction limit reached!
% 1.69/1.78 % (10190)------------------------------
% 1.69/1.78 % (10190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.78 % (10190)Termination reason: Unknown
% 1.69/1.78 % (10190)Termination phase: Saturation
% 1.69/1.78
% 1.69/1.78 % (10190)Memory used [KB]: 5756
% 1.69/1.78 % (10190)Time elapsed: 0.030 s
% 1.69/1.78 % (10190)Instructions burned: 47 (million)
% 1.69/1.78 % (10190)------------------------------
% 1.69/1.78 % (10190)------------------------------
% 1.69/1.78 % (10169)First to succeed.
% 1.69/1.79 % (10169)Refutation found. Thanks to Tanya!
% 1.69/1.79 % SZS status Theorem for DTF2THF_10052
% 1.69/1.79 % SZS output start Proof for DTF2THF_10052
% 1.69/1.79 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.79 thf(func_def_1, type, powerset: $i > $i).
% 1.69/1.79 thf(func_def_2, type, subset: $i > $i > $o).
% 1.69/1.79 thf(func_def_5, type, setminus: $i > $i > $i).
% 1.69/1.79 thf(func_def_18, type, sK6: $i > $i > $i > $i).
% 1.69/1.79 thf(f2758,plain,(
% 1.69/1.79 $false),
% 1.69/1.79 inference(subsumption_resolution,[status(thm)],[f2757,f910])).
% 1.69/1.79 thf(f910,plain,(
% 1.69/1.79 ($true != (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK9))),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f908])).
% 1.69/1.79 thf(f908,plain,(
% 1.69/1.79 ($true != (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK9)) | ($true != $true)),
% 1.69/1.79 inference(superposition,[status(thm)],[f109,f451])).
% 1.69/1.79 thf(f451,plain,(
% 1.69/1.79 ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ (setminus @ sK7 @ sK9)))),
% 1.69/1.79 inference(subsumption_resolution,[status(thm)],[f402,f72])).
% 1.69/1.79 thf(f72,plain,(
% 1.69/1.79 ($true != (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8)))),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f45])).
% 1.69/1.79 thf(f45,plain,(
% 1.69/1.79 (complementT_lem = $true) & (setminusI = $true) & (($true = (in @ sK8 @ (powerset @ sK7))) & (($true = (in @ sK9 @ (powerset @ sK7))) & ($true = (subset @ sK8 @ sK9)) & ($true != (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))))) & (setminusER = $true) & (subsetTI = $true) & (subsetE = $true)),
% 1.69/1.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f26,f44,f43])).
% 1.69/1.79 thf(f43,plain,(
% 1.69/1.79 ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ($true = (subset @ X1 @ X2)) & ($true != (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))))) => (($true = (in @ sK8 @ (powerset @ sK7))) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK7))) & ($true = (subset @ sK8 @ X2)) & ((subset @ (setminus @ sK7 @ X2) @ (setminus @ sK7 @ sK8)) != $true)))),
% 1.69/1.79 introduced(definition,[],[choice_axiom])).
% 1.69/1.79 thf(f44,plain,(
% 1.69/1.79 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK7))) & ($true = (subset @ sK8 @ X2)) & ((subset @ (setminus @ sK7 @ X2) @ (setminus @ sK7 @ sK8)) != $true)) => (($true = (in @ sK9 @ (powerset @ sK7))) & ($true = (subset @ sK8 @ sK9)) & ($true != (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))))),
% 1.69/1.79 introduced(definition,[],[choice_axiom])).
% 1.69/1.79 thf(f26,plain,(
% 1.69/1.79 (complementT_lem = $true) & (setminusI = $true) & ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ($true = (subset @ X1 @ X2)) & ($true != (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))))) & (setminusER = $true) & (subsetTI = $true) & (subsetE = $true)),
% 1.69/1.79 inference(flattening,[status(thm)],[f25])).
% 1.69/1.79 thf(f25,plain,(
% 1.69/1.79 ((((? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((($true != (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) & ($true = (subset @ X1 @ X2))) & ($true = (in @ X2 @ (powerset @ X0)))) & ($true = (in @ X1 @ (powerset @ X0)))) & (subsetTI = $true)) & (complementT_lem = $true)) & (setminusER = $true)) & (setminusI = $true)) & (subsetE = $true)),
% 1.69/1.79 inference(ennf_transformation,[status(thm)],[f16])).
% 1.69/1.79 thf(f16,plain,(
% 1.69/1.79 ~((subsetE = $true) => ((setminusI = $true) => ((setminusER = $true) => ((complementT_lem = $true) => ((subsetTI = $true) => ! [X1 : $i,X0 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => (($true = (subset @ X1 @ X2)) => ($true = (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)))))))))))),
% 1.69/1.79 inference(fool_elimination,[status(thm)],[f15])).
% 1.69/1.79 thf(f15,plain,(
% 1.69/1.79 ~(subsetE => (setminusI => (setminusER => (complementT_lem => (subsetTI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ X2) => (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))))))))))),
% 1.69/1.79 inference(rectify,[status(thm)],[f7])).
% 1.69/1.79 thf(f7,negated_conjecture,(
% 1.69/1.79 ~(subsetE => (setminusI => (setminusER => (complementT_lem => (subsetTI => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X3 @ X4) => (subset @ (setminus @ X0 @ X4) @ (setminus @ X0 @ X3))))))))))),
% 1.69/1.79 inference(negated_conjecture,[status(cth)],[f6])).
% 1.69/1.79 thf(f6,conjecture,(
% 1.69/1.79 subsetE => (setminusI => (setminusER => (complementT_lem => (subsetTI => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X3 @ X4) => (subset @ (setminus @ X0 @ X4) @ (setminus @ X0 @ X3)))))))))),
% 1.69/1.79 file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',contrasubsetT2)).
% 1.69/1.79 thf(f402,plain,(
% 1.69/1.79 ($true = (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ (setminus @ sK7 @ sK9)))),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f397])).
% 1.69/1.79 thf(f397,plain,(
% 1.69/1.79 ($true = (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ (setminus @ sK7 @ sK9))) | ($true != $true)),
% 1.69/1.79 inference(superposition,[status(thm)],[f134,f121])).
% 1.69/1.79 thf(f121,plain,(
% 1.69/1.79 ($true = (in @ (setminus @ sK7 @ sK9) @ (powerset @ sK7)))),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.69/1.79 thf(f118,plain,(
% 1.69/1.79 ($true = (in @ (setminus @ sK7 @ sK9) @ (powerset @ sK7))) | ($true != $true)),
% 1.69/1.79 inference(superposition,[status(thm)],[f112,f74])).
% 1.69/1.79 thf(f74,plain,(
% 1.69/1.79 ($true = (in @ sK9 @ (powerset @ sK7)))),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f45])).
% 1.69/1.79 thf(f112,plain,(
% 1.69/1.79 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.69/1.79 thf(f99,plain,(
% 1.69/1.79 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | ($true != $true)) )),
% 1.69/1.79 inference(definition_unfolding,[status(thm)],[f80,f77])).
% 1.69/1.79 thf(f77,plain,(
% 1.69/1.79 (complementT_lem = $true)),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f45])).
% 1.69/1.79 thf(f80,plain,(
% 1.69/1.79 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) | (complementT_lem != $true)) )),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f49])).
% 1.69/1.79 thf(f49,plain,(
% 1.69/1.79 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | (($true = (in @ sK10 @ (powerset @ sK11))) & ((in @ (setminus @ sK11 @ sK10) @ (powerset @ sK11)) != $true)))),
% 1.69/1.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f47,f48])).
% 1.69/1.79 thf(f48,plain,(
% 1.69/1.79 ? [X2 : $i,X3 : $i] : (($true = (in @ X2 @ (powerset @ X3))) & ($true != (in @ (setminus @ X3 @ X2) @ (powerset @ X3)))) => (($true = (in @ sK10 @ (powerset @ sK11))) & ((in @ (setminus @ sK11 @ sK10) @ (powerset @ sK11)) != $true))),
% 1.69/1.79 introduced(definition,[],[choice_axiom])).
% 1.69/1.79 thf(f47,plain,(
% 1.69/1.79 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : (($true = (in @ X2 @ (powerset @ X3))) & ($true != (in @ (setminus @ X3 @ X2) @ (powerset @ X3)))))),
% 1.69/1.79 inference(rectify,[status(thm)],[f46])).
% 1.69/1.79 thf(f46,plain,(
% 1.69/1.79 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ($true != (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))))),
% 1.69/1.79 inference(nnf_transformation,[status(thm)],[f32])).
% 1.69/1.79 thf(f32,plain,(
% 1.69/1.79 ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) <=> (complementT_lem = $true)),
% 1.69/1.79 inference(ennf_transformation,[status(thm)],[f10])).
% 1.69/1.79 thf(f10,plain,(
% 1.69/1.79 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ($true = (in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) <=> (complementT_lem = $true)),
% 1.69/1.79 inference(fool_elimination,[status(thm)],[f9])).
% 1.69/1.79 thf(f9,plain,(
% 1.69/1.79 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = complementT_lem)),
% 1.69/1.79 inference(rectify,[status(thm)],[f4])).
% 1.69/1.79 thf(f4,axiom,(
% 1.69/1.79 (! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X3) @ (powerset @ X0))) = complementT_lem)),
% 1.69/1.79 file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',complementT_lem)).
% 1.69/1.79 thf(f134,plain,(
% 1.69/1.79 ( ! [X0 : $i] : (($true != (in @ X0 @ (powerset @ sK7))) | ($true = (subset @ X0 @ (setminus @ sK7 @ sK8))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ X0 @ sK7) @ X0))) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.69/1.79 thf(f132,plain,(
% 1.69/1.79 ( ! [X0 : $i] : (($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ X0 @ sK7) @ X0)) | ($true = (subset @ X0 @ (setminus @ sK7 @ sK8))) | ($true != (in @ X0 @ (powerset @ sK7))) | ($true != $true)) )),
% 1.69/1.79 inference(superposition,[status(thm)],[f111,f120])).
% 1.69/1.79 thf(f120,plain,(
% 1.69/1.79 ($true = (in @ (setminus @ sK7 @ sK8) @ (powerset @ sK7)))),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.69/1.79 thf(f119,plain,(
% 1.69/1.79 ($true = (in @ (setminus @ sK7 @ sK8) @ (powerset @ sK7))) | ($true != $true)),
% 1.69/1.79 inference(superposition,[status(thm)],[f112,f75])).
% 1.69/1.79 thf(f75,plain,(
% 1.69/1.79 ($true = (in @ sK8 @ (powerset @ sK7)))),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f45])).
% 1.69/1.79 thf(f111,plain,(
% 1.69/1.79 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X4))) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) | ($true != (in @ X5 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6))) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.69/1.79 thf(f97,plain,(
% 1.69/1.79 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X4))) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) | ($true = (subset @ X5 @ X6)) | ($true != (in @ X5 @ (powerset @ X4))) | ($true != $true)) )),
% 1.69/1.79 inference(definition_unfolding,[status(thm)],[f63,f70])).
% 1.69/1.79 thf(f70,plain,(
% 1.69/1.79 (subsetTI = $true)),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f45])).
% 1.69/1.79 thf(f63,plain,(
% 1.69/1.79 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) | ($true != (in @ X6 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6)) | ($true != (in @ X5 @ (powerset @ X4))) | (subsetTI != $true)) )),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f42])).
% 1.69/1.79 thf(f42,plain,(
% 1.69/1.79 ((subsetTI = $true) | ((! [X3 : $i] : (($true != (in @ X3 @ sK3)) | ($true != (in @ X3 @ sK4)) | ($true = (in @ X3 @ sK5))) & ($true = (in @ sK5 @ (powerset @ sK3))) & ($true != (subset @ sK4 @ sK5))) & ($true = (in @ sK4 @ (powerset @ sK3))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : ((($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) & ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) & ($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6))) | ($true != (in @ X6 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6))) | ($true != (in @ X5 @ (powerset @ X4)))) | (subsetTI != $true))),
% 1.69/1.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f38,f41,f40,f39])).
% 1.69/1.79 thf(f39,plain,(
% 1.69/1.79 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X2))) & ($true = (in @ X2 @ (powerset @ X0))) & ($true != (subset @ X1 @ X2))) & ($true = (in @ X1 @ (powerset @ X0)))) => (? [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ sK3)) | ($true != (in @ X3 @ sK4)) | ($true = (in @ X3 @ X2))) & ($true = (in @ X2 @ (powerset @ sK3))) & ($true != (subset @ sK4 @ X2))) & ($true = (in @ sK4 @ (powerset @ sK3))))),
% 1.69/1.79 introduced(definition,[],[choice_axiom])).
% 1.69/1.79 thf(f40,plain,(
% 1.69/1.79 ? [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ sK3)) | ($true != (in @ X3 @ sK4)) | ($true = (in @ X3 @ X2))) & ($true = (in @ X2 @ (powerset @ sK3))) & ($true != (subset @ sK4 @ X2))) => (! [X3 : $i] : (($true != (in @ X3 @ sK3)) | ($true != (in @ X3 @ sK4)) | ($true = (in @ X3 @ sK5))) & ($true = (in @ sK5 @ (powerset @ sK3))) & ($true != (subset @ sK4 @ sK5)))),
% 1.69/1.79 introduced(definition,[],[choice_axiom])).
% 1.69/1.79 thf(f41,plain,(
% 1.69/1.79 ! [X4 : $i,X5 : $i,X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X4)) & ($true = (in @ X7 @ X5)) & ($true != (in @ X7 @ X6))) => (($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) & ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X5)) & ($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6))))),
% 1.69/1.79 introduced(definition,[],[choice_axiom])).
% 1.69/1.79 thf(f38,plain,(
% 1.69/1.79 ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X2))) & ($true = (in @ X2 @ (powerset @ X0))) & ($true != (subset @ X1 @ X2))) & ($true = (in @ X1 @ (powerset @ X0))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X4)) & ($true = (in @ X7 @ X5)) & ($true != (in @ X7 @ X6))) | ($true != (in @ X6 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6))) | ($true != (in @ X5 @ (powerset @ X4)))) | (subsetTI != $true))),
% 1.69/1.79 inference(rectify,[status(thm)],[f37])).
% 1.69/1.79 thf(f37,plain,(
% 1.69/1.79 ((subsetTI = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true != (in @ X3 @ X0)) | ($true = (in @ X3 @ X2))) & ($true = (in @ X2 @ (powerset @ X1))) & ($true != (subset @ X0 @ X2))) & ($true = (in @ X0 @ (powerset @ X1))))) & (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ($true = (in @ X3 @ X0)) & ($true != (in @ X3 @ X2))) | ($true != (in @ X2 @ (powerset @ X1))) | ($true = (subset @ X0 @ X2))) | ($true != (in @ X0 @ (powerset @ X1)))) | (subsetTI != $true))),
% 1.69/1.79 inference(nnf_transformation,[status(thm)],[f24])).
% 1.69/1.79 thf(f24,plain,(
% 1.69/1.79 (subsetTI = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ($true = (in @ X3 @ X0)) & ($true != (in @ X3 @ X2))) | ($true != (in @ X2 @ (powerset @ X1))) | ($true = (subset @ X0 @ X2))) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.69/1.79 inference(flattening,[status(thm)],[f23])).
% 1.69/1.79 thf(f23,plain,(
% 1.69/1.79 (subsetTI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((($true = (subset @ X0 @ X2)) | ? [X3 : $i] : ((($true != (in @ X3 @ X2)) & ($true = (in @ X3 @ X0))) & ($true = (in @ X3 @ X1)))) | ($true != (in @ X2 @ (powerset @ X1)))) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.69/1.79 inference(ennf_transformation,[status(thm)],[f20])).
% 1.69/1.79 thf(f20,plain,(
% 1.69/1.79 (subsetTI = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => (! [X3 : $i] : (($true = (in @ X3 @ X1)) => (($true = (in @ X3 @ X0)) => ($true = (in @ X3 @ X2)))) => ($true = (subset @ X0 @ X2)))))),
% 1.69/1.79 inference(fool_elimination,[status(thm)],[f19])).
% 1.69/1.79 thf(f19,plain,(
% 1.69/1.79 (subsetTI = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (subset @ X0 @ X2)))))),
% 1.69/1.79 inference(rectify,[status(thm)],[f5])).
% 1.69/1.79 thf(f5,axiom,(
% 1.69/1.79 (subsetTI = ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => (! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X3) => (in @ X2 @ X4))) => (subset @ X3 @ X4)))))),
% 1.69/1.79 file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',subsetTI)).
% 1.69/1.79 thf(f109,plain,(
% 1.69/1.79 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (setminus @ X4 @ X3))) | ((in @ X5 @ X3) != $true)) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.69/1.79 thf(f104,plain,(
% 1.69/1.79 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ($true != $true) | ($true != (in @ X5 @ (setminus @ X4 @ X3)))) )),
% 1.69/1.79 inference(definition_unfolding,[status(thm)],[f81,f71])).
% 1.69/1.79 thf(f71,plain,(
% 1.69/1.79 (setminusER = $true)),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f45])).
% 1.69/1.79 thf(f81,plain,(
% 1.69/1.79 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ($true != (in @ X5 @ (setminus @ X4 @ X3))) | (setminusER != $true)) )),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f53])).
% 1.69/1.79 thf(f53,plain,(
% 1.69/1.79 ((setminusER = $true) | (($true = (in @ sK14 @ sK12)) & ($true = (in @ sK14 @ (setminus @ sK13 @ sK12))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ($true != (in @ X5 @ (setminus @ X4 @ X3)))) | (setminusER != $true))),
% 1.69/1.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f51,f52])).
% 1.69/1.79 thf(f52,plain,(
% 1.69/1.79 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))) => (($true = (in @ sK14 @ sK12)) & ($true = (in @ sK14 @ (setminus @ sK13 @ sK12))))),
% 1.69/1.79 introduced(definition,[],[choice_axiom])).
% 1.69/1.79 thf(f51,plain,(
% 1.69/1.79 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X2 @ (setminus @ X1 @ X0))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ($true != (in @ X5 @ (setminus @ X4 @ X3)))) | (setminusER != $true))),
% 1.69/1.79 inference(rectify,[status(thm)],[f50])).
% 1.69/1.79 thf(f50,plain,(
% 1.69/1.79 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ($true = (in @ X2 @ (setminus @ X1 @ X0))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ($true != (in @ X2 @ (setminus @ X1 @ X0)))) | (setminusER != $true))),
% 1.69/1.79 inference(nnf_transformation,[status(thm)],[f31])).
% 1.69/1.79 thf(f31,plain,(
% 1.69/1.79 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ($true != (in @ X2 @ (setminus @ X1 @ X0))))),
% 1.69/1.79 inference(ennf_transformation,[status(thm)],[f22])).
% 1.69/1.79 thf(f22,plain,(
% 1.69/1.79 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ((in @ X2 @ X0) != $true))),
% 1.69/1.79 inference(flattening,[status(thm)],[f12])).
% 1.69/1.79 thf(f12,plain,(
% 1.69/1.79 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ~((in @ X2 @ X0) = $true)) <=> (setminusER = $true)),
% 1.69/1.79 inference(fool_elimination,[status(thm)],[f11])).
% 1.69/1.79 thf(f11,plain,(
% 1.69/1.79 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X1 @ X0)) => ~(in @ X2 @ X0)) = setminusER)),
% 1.69/1.79 inference(rectify,[status(thm)],[f3])).
% 1.69/1.79 thf(f3,axiom,(
% 1.69/1.79 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.69/1.79 file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',setminusER)).
% 1.69/1.79 thf(f2757,plain,(
% 1.69/1.79 ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK9))),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f2751])).
% 1.69/1.79 thf(f2751,plain,(
% 1.69/1.79 ($true != $true) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK9))),
% 1.69/1.79 inference(superposition,[status(thm)],[f117,f2651])).
% 1.69/1.79 thf(f2651,plain,(
% 1.69/1.79 ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK8))),
% 1.69/1.79 inference(subsumption_resolution,[status(thm)],[f2603,f72])).
% 1.69/1.79 thf(f2603,plain,(
% 1.69/1.79 ($true = (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK8))),
% 1.69/1.79 inference(subsumption_resolution,[status(thm)],[f2602,f120])).
% 1.69/1.79 thf(f2602,plain,(
% 1.69/1.79 ($true != (in @ (setminus @ sK7 @ sK8) @ (powerset @ sK7))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK8)) | ($true = (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8)))),
% 1.69/1.79 inference(subsumption_resolution,[status(thm)],[f2595,f121])).
% 1.69/1.79 thf(f2595,plain,(
% 1.69/1.79 ($true != (in @ (setminus @ sK7 @ sK9) @ (powerset @ sK7))) | ($true = (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK8)) | ($true != (in @ (setminus @ sK7 @ sK8) @ (powerset @ sK7)))),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f2590])).
% 1.69/1.79 thf(f2590,plain,(
% 1.69/1.79 ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK8)) | ($true != (in @ (setminus @ sK7 @ sK9) @ (powerset @ sK7))) | ($true = (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))) | ($true != (in @ (setminus @ sK7 @ sK8) @ (powerset @ sK7))) | ($true != $true)),
% 1.69/1.79 inference(superposition,[status(thm)],[f114,f905])).
% 1.69/1.79 thf(f905,plain,(
% 1.69/1.79 ( ! [X0 : $i] : (($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ (setminus @ sK7 @ X0))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ X0))) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f904])).
% 1.69/1.79 thf(f904,plain,(
% 1.69/1.79 ( ! [X0 : $i] : (($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ (setminus @ sK7 @ X0))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ X0)) | ($true != $true)) )),
% 1.69/1.79 inference(superposition,[status(thm)],[f110,f538])).
% 1.69/1.79 thf(f538,plain,(
% 1.69/1.79 ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK7))),
% 1.69/1.79 inference(subsumption_resolution,[status(thm)],[f522,f72])).
% 1.69/1.79 thf(f522,plain,(
% 1.69/1.79 ($true = (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK7))),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f519])).
% 1.69/1.79 thf(f519,plain,(
% 1.69/1.79 ($true != $true) | ($true = (subset @ (setminus @ sK7 @ sK9) @ (setminus @ sK7 @ sK8))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ (setminus @ sK7 @ sK9) @ sK7) @ sK7))),
% 1.69/1.79 inference(superposition,[status(thm)],[f154,f121])).
% 1.69/1.79 thf(f154,plain,(
% 1.69/1.79 ( ! [X0 : $i] : (($true != (in @ X0 @ (powerset @ sK7))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ X0 @ sK7) @ sK7)) | ($true = (subset @ X0 @ (setminus @ sK7 @ sK8)))) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.69/1.79 thf(f150,plain,(
% 1.69/1.79 ( ! [X0 : $i] : (($true = (subset @ X0 @ (setminus @ sK7 @ sK8))) | ($true != $true) | ($true != (in @ X0 @ (powerset @ sK7))) | ($true = (in @ (sK6 @ (setminus @ sK7 @ sK8) @ X0 @ sK7) @ sK7))) )),
% 1.69/1.79 inference(superposition,[status(thm)],[f115,f120])).
% 1.69/1.79 thf(f115,plain,(
% 1.69/1.79 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X4))) | ($true != (in @ X5 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6)) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4))) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.69/1.79 thf(f96,plain,(
% 1.69/1.79 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6)) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) | ($true != $true) | ($true != (in @ X5 @ (powerset @ X4)))) )),
% 1.69/1.79 inference(definition_unfolding,[status(thm)],[f64,f70])).
% 1.69/1.79 thf(f64,plain,(
% 1.69/1.79 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) | ($true != (in @ X6 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6)) | ($true != (in @ X5 @ (powerset @ X4))) | (subsetTI != $true)) )),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f42])).
% 1.69/1.79 thf(f110,plain,(
% 1.69/1.79 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X3)) | ($true = (in @ X4 @ X5)) | ((in @ X4 @ (setminus @ X3 @ X5)) = $true)) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.69/1.79 thf(f91,plain,(
% 1.69/1.79 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X4 @ (setminus @ X3 @ X5)) = $true) | ($true = (in @ X4 @ X5)) | ($true != (in @ X4 @ X3))) )),
% 1.69/1.79 inference(definition_unfolding,[status(thm)],[f58,f76])).
% 1.69/1.79 thf(f76,plain,(
% 1.69/1.79 (setminusI = $true)),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f45])).
% 1.69/1.79 thf(f58,plain,(
% 1.69/1.79 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X3 @ X5)) = $true) | ($true != (in @ X4 @ X3)) | ($true = (in @ X4 @ X5)) | (setminusI != $true)) )),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f36])).
% 1.69/1.79 thf(f36,plain,(
% 1.69/1.79 ((setminusI = $true) | (($true != (in @ sK1 @ (setminus @ sK0 @ sK2))) & ($true = (in @ sK1 @ sK0)) & ($true != (in @ sK1 @ sK2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X3 @ X5)) = $true) | ($true != (in @ X4 @ X3)) | ($true = (in @ X4 @ X5))) | (setminusI != $true))),
% 1.69/1.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f34,f35])).
% 1.69/1.79 thf(f35,plain,(
% 1.69/1.79 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setminus @ X0 @ X2))) & ((in @ X1 @ X0) = $true) & ($true != (in @ X1 @ X2))) => (($true != (in @ sK1 @ (setminus @ sK0 @ sK2))) & ($true = (in @ sK1 @ sK0)) & ($true != (in @ sK1 @ sK2)))),
% 1.69/1.79 introduced(definition,[],[choice_axiom])).
% 1.69/1.79 thf(f34,plain,(
% 1.69/1.79 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setminus @ X0 @ X2))) & ((in @ X1 @ X0) = $true) & ($true != (in @ X1 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X3 @ X5)) = $true) | ($true != (in @ X4 @ X3)) | ($true = (in @ X4 @ X5))) | (setminusI != $true))),
% 1.69/1.79 inference(rectify,[status(thm)],[f33])).
% 1.69/1.79 thf(f33,plain,(
% 1.69/1.79 ((setminusI = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setminus @ X2 @ X1))) & ($true = (in @ X0 @ X2)) & ($true != (in @ X0 @ X1)))) & (! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) | ($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ X1))) | (setminusI != $true))),
% 1.69/1.79 inference(nnf_transformation,[status(thm)],[f28])).
% 1.69/1.79 thf(f28,plain,(
% 1.69/1.79 (setminusI = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (setminus @ X2 @ X1))) | ($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ X1)))),
% 1.69/1.79 inference(flattening,[status(thm)],[f27])).
% 1.69/1.79 thf(f27,plain,(
% 1.69/1.79 (setminusI = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((($true = (in @ X0 @ (setminus @ X2 @ X1))) | ($true = (in @ X0 @ X1))) | ($true != (in @ X0 @ X2)))),
% 1.69/1.79 inference(ennf_transformation,[status(thm)],[f21])).
% 1.69/1.79 thf(f21,plain,(
% 1.69/1.79 (setminusI = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X2)) => (($true != (in @ X0 @ X1)) => ($true = (in @ X0 @ (setminus @ X2 @ X1)))))),
% 1.69/1.79 inference(flattening,[status(thm)],[f14])).
% 1.69/1.79 thf(f14,plain,(
% 1.69/1.79 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) => (~($true = (in @ X0 @ X1)) => ($true = (in @ X0 @ (setminus @ X2 @ X1)))))),
% 1.69/1.79 inference(fool_elimination,[status(thm)],[f13])).
% 1.69/1.79 thf(f13,plain,(
% 1.69/1.79 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => (in @ X0 @ (setminus @ X2 @ X1)))))),
% 1.69/1.79 inference(rectify,[status(thm)],[f2])).
% 1.69/1.79 thf(f2,axiom,(
% 1.69/1.79 (setminusI = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 1.69/1.79 file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',setminusI)).
% 1.69/1.79 thf(f114,plain,(
% 1.69/1.79 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6)) | ($true != (in @ X5 @ (powerset @ X4))) | ($true != (in @ X6 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6))) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.69/1.79 thf(f98,plain,(
% 1.69/1.79 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X4))) | ($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6)) | ($true != (in @ X5 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6)) | ($true != $true)) )),
% 1.69/1.79 inference(definition_unfolding,[status(thm)],[f62,f70])).
% 1.69/1.79 thf(f62,plain,(
% 1.69/1.79 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ (sK6 @ X6 @ X5 @ X4) @ X6)) | ($true != (in @ X6 @ (powerset @ X4))) | ($true = (subset @ X5 @ X6)) | ($true != (in @ X5 @ (powerset @ X4))) | (subsetTI != $true)) )),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f42])).
% 1.69/1.79 thf(f117,plain,(
% 1.69/1.79 ( ! [X0 : $i] : (($true != (in @ X0 @ sK8)) | ($true = (in @ X0 @ sK9))) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.69/1.79 thf(f116,plain,(
% 1.69/1.79 ( ! [X0 : $i] : (($true != (in @ X0 @ sK8)) | ($true = (in @ X0 @ sK9)) | ($true != $true)) )),
% 1.69/1.79 inference(superposition,[status(thm)],[f113,f73])).
% 1.69/1.79 thf(f73,plain,(
% 1.69/1.79 ($true = (subset @ sK8 @ sK9))),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f45])).
% 1.69/1.79 thf(f113,plain,(
% 1.69/1.79 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) )),
% 1.69/1.79 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.69/1.79 thf(f105,plain,(
% 1.69/1.79 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ($true != (subset @ X1 @ X0)) | ($true != $true) | ((in @ X2 @ X0) = $true)) )),
% 1.69/1.79 inference(definition_unfolding,[status(thm)],[f87,f69])).
% 1.69/1.79 thf(f69,plain,(
% 1.69/1.79 (subsetE = $true)),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f45])).
% 1.69/1.79 thf(f87,plain,(
% 1.69/1.79 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true) | (subsetE != $true)) )),
% 1.69/1.79 inference(cnf_transformation,[status(thm)],[f57])).
% 1.69/1.79 thf(f57,plain,(
% 1.69/1.79 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X1 @ X0)) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) | (subsetE != $true)) & ((subsetE = $true) | (($true = (subset @ sK16 @ sK15)) & ($true = (in @ sK17 @ sK16)) & ($true != (in @ sK17 @ sK15))))),
% 1.69/1.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f55,f56])).
% 1.69/1.79 thf(f56,plain,(
% 1.69/1.79 ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (subset @ X4 @ X3)) & ($true = (in @ X5 @ X4)) & ((in @ X5 @ X3) != $true)) => (($true = (subset @ sK16 @ sK15)) & ($true = (in @ sK17 @ sK16)) & ($true != (in @ sK17 @ sK15)))),
% 1.69/1.79 introduced(definition,[],[choice_axiom])).
% 1.69/1.79 thf(f55,plain,(
% 1.69/1.79 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X1 @ X0)) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (subset @ X4 @ X3)) & ($true = (in @ X5 @ X4)) & ((in @ X5 @ X3) != $true)))),
% 1.69/1.79 inference(rectify,[status(thm)],[f54])).
% 1.69/1.79 thf(f54,plain,(
% 1.69/1.79 (! [X0 : $i,X2 : $i,X1 : $i] : (($true != (subset @ X2 @ X0)) | ($true != (in @ X1 @ X2)) | ((in @ X1 @ X0) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (($true = (subset @ X2 @ X0)) & ($true = (in @ X1 @ X2)) & ((in @ X1 @ X0) != $true)))),
% 1.69/1.79 inference(nnf_transformation,[status(thm)],[f30])).
% 1.69/1.79 thf(f30,plain,(
% 1.69/1.79 ! [X0 : $i,X2 : $i,X1 : $i] : (($true != (subset @ X2 @ X0)) | ($true != (in @ X1 @ X2)) | ((in @ X1 @ X0) = $true)) <=> (subsetE = $true)),
% 1.69/1.79 inference(flattening,[status(thm)],[f29])).
% 1.69/1.79 thf(f29,plain,(
% 1.69/1.79 ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ X0) = $true) | ($true != (in @ X1 @ X2))) | ($true != (subset @ X2 @ X0))) <=> (subsetE = $true)),
% 1.69/1.79 inference(ennf_transformation,[status(thm)],[f18])).
% 1.69/1.79 thf(f18,plain,(
% 1.69/1.79 ! [X0 : $i,X2 : $i,X1 : $i] : (($true = (subset @ X2 @ X0)) => (($true = (in @ X1 @ X2)) => ((in @ X1 @ X0) = $true))) <=> (subsetE = $true)),
% 1.69/1.79 inference(fool_elimination,[status(thm)],[f17])).
% 1.69/1.79 thf(f17,plain,(
% 1.69/1.79 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ X0))) = subsetE)),
% 1.69/1.79 inference(rectify,[status(thm)],[f1])).
% 1.69/1.79 thf(f1,axiom,(
% 1.69/1.79 (! [X1 : $i,X2 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.69/1.79 file('/export/starexec/sandbox2/tmp/tmp.WUy7ugVKxJ/DTF2THF_10052.p',subsetE)).
% 1.69/1.79 % SZS output end Proof for DTF2THF_10052
% 1.69/1.79 % (10169)------------------------------
% 1.69/1.79 % (10169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.79 % (10169)Termination reason: Refutation
% 1.69/1.79
% 1.69/1.79 % (10169)Memory used [KB]: 7291
% 1.69/1.79 % (10169)Time elapsed: 0.323 s
% 1.69/1.79 % (10169)Instructions burned: 609 (million)
% 1.69/1.79 % (10169)------------------------------
% 1.69/1.79 % (10169)------------------------------
% 1.69/1.79 % (10148)Success in time 0.418 s
%------------------------------------------------------------------------------