%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU736^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:47 AM UTC 2026
% Result : Theorem 1.71s 1.33s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 1042 ( 279 equ; 0 cnn)
% Maximal formula atoms : 14 ( 18 avg)
% Number of connectives : 1124 ( 124 ~; 92 |; 98 &; 739 @)
% ( 8 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 149 ( 0 ^; 104 !; 45 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(f76,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f75,f50]) ).
thf(f50,plain,
( ( in @ sK10 @ sK9 )
= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( in @ sK9 @ ( powerset @ sK7 ) )
= $true )
& ( ( in @ sK10 @ ( setminus @ sK7 @ sK8 ) )
!= $true )
& ( ( in @ sK10 @ sK9 )
= $true )
& ( ( in @ sK10 @ sK7 )
= $true )
& ( ( subset @ sK8 @ ( setminus @ sK7 @ sK9 ) )
= $true )
& ( ( in @ sK8 @ ( powerset @ sK7 ) )
= $true )
& ( contrasubsetT = $true )
& ( setminusI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f15,f32,f31,f30]) ).
thf(f30,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK7 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK7 @ sK8 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( $true
= ( in @ X3 @ sK7 ) ) )
& ( ( subset @ sK8 @ ( setminus @ sK7 @ X2 ) )
= $true ) )
& ( ( in @ sK8 @ ( powerset @ sK7 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK7 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK7 @ sK8 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( $true
= ( in @ X3 @ sK7 ) ) )
& ( ( subset @ sK8 @ ( setminus @ sK7 @ X2 ) )
= $true ) )
=> ( ( ( in @ sK9 @ ( powerset @ sK7 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK7 @ sK8 ) )
!= $true )
& ( ( in @ X3 @ sK9 )
= $true )
& ( $true
= ( in @ X3 @ sK7 ) ) )
& ( ( subset @ sK8 @ ( setminus @ sK7 @ sK9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK7 @ sK8 ) )
!= $true )
& ( ( in @ X3 @ sK9 )
= $true )
& ( $true
= ( in @ X3 @ sK7 ) ) )
=> ( ( ( in @ sK10 @ ( setminus @ sK7 @ sK8 ) )
!= $true )
& ( ( in @ sK10 @ sK9 )
= $true )
& ( ( in @ sK10 @ sK7 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( contrasubsetT = $true )
& ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( contrasubsetT = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setminusI = $true )
=> ( ( contrasubsetT = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setminusI
=> ( contrasubsetT
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( contrasubsetT
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ X3 @ ( setminus @ X0 @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( setminus @ X0 @ X3 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setminusI
=> ( contrasubsetT
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ X3 @ ( setminus @ X0 @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( setminus @ X0 @ X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UPFCvlpbuE/DTF2THF_11698.p',contraSubsetComplement) ).
thf(f75,plain,
( ( in @ sK10 @ sK9 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f74,f49]) ).
thf(f49,plain,
( ( in @ sK10 @ sK7 )
= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f74,plain,
( ( ( in @ sK10 @ sK7 )
!= $true )
| ( ( in @ sK10 @ sK9 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( in @ sK10 @ sK9 )
!= $true )
| ( ( in @ sK10 @ sK7 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f72,f68]) ).
thf(f68,plain,
( ( in @ sK10 @ sK8 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f67,f49]) ).
thf(f67,plain,
( ( ( in @ sK10 @ sK8 )
= $true )
| ( ( in @ sK10 @ sK7 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true != $true )
| ( ( in @ sK10 @ sK8 )
= $true )
| ( ( in @ sK10 @ sK7 )
!= $true ) ),
inference(superposition,[status(thm)],[f51,f65]) ).
thf(f65,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true != $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f37,f45]) ).
thf(f45,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f37,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ( ( ( in @ sK2 @ sK0 )
!= $true )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f22]) ).
thf(f22,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
!= $true ) )
=> ( ( ( in @ sK2 @ sK0 )
!= $true )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) )
<=> ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
= setminusI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox/tmp/tmp.UPFCvlpbuE/DTF2THF_11698.p',setminusI) ).
thf(f51,plain,
( ( in @ sK10 @ ( setminus @ sK7 @ sK8 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f72,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK8 ) )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( ( in @ X0 @ sK9 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f71,f47]) ).
thf(f47,plain,
( ( in @ sK8 @ ( powerset @ sK7 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f71,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK9 )
!= $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( $true
!= ( in @ X0 @ sK8 ) )
| ( ( in @ sK8 @ ( powerset @ sK7 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f70,f52]) ).
thf(f52,plain,
( ( in @ sK9 @ ( powerset @ sK7 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f70,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK7 )
!= $true )
| ( ( in @ sK9 @ ( powerset @ sK7 ) )
!= $true )
| ( ( in @ X0 @ sK9 )
!= $true )
| ( $true
!= ( in @ X0 @ sK8 ) )
| ( ( in @ sK8 @ ( powerset @ sK7 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK8 @ ( powerset @ sK7 ) )
!= $true )
| ( $true
!= ( in @ X0 @ sK8 ) )
| ( ( in @ X0 @ sK9 )
!= $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( ( in @ sK9 @ ( powerset @ sK7 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f64,f48]) ).
thf(f48,plain,
( ( subset @ sK8 @ ( setminus @ sK7 @ sK9 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f44,f46]) ).
thf(f46,plain,
contrasubsetT = $true,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( contrasubsetT != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( contrasubsetT != $true ) )
& ( ( contrasubsetT = $true )
| ( ( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true )
& ( ( in @ sK6 @ sK3 )
= $true )
& ( ( in @ sK6 @ sK5 )
= $true )
& ( ( subset @ sK4 @ ( setminus @ sK3 @ sK5 ) )
= $true )
& ( ( in @ sK6 @ sK4 )
= $true )
& ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f25,f28,f27,f26]) ).
thf(f26,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
= $true )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ X4 ) )
& ( $true
= ( in @ X7 @ X6 ) )
& ( $true
= ( subset @ X5 @ ( setminus @ X4 @ X6 ) ) )
& ( ( in @ X7 @ X5 )
= $true ) ) )
& ( ( in @ X5 @ ( powerset @ X4 ) )
= $true ) )
=> ( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ sK3 ) )
= $true )
& ? [X7: $i] :
( ( ( in @ X7 @ sK3 )
= $true )
& ( $true
= ( in @ X7 @ X6 ) )
& ( ( subset @ sK4 @ ( setminus @ sK3 @ X6 ) )
= $true )
& ( ( in @ X7 @ sK4 )
= $true ) ) )
& ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ sK3 ) )
= $true )
& ? [X7: $i] :
( ( ( in @ X7 @ sK3 )
= $true )
& ( $true
= ( in @ X7 @ X6 ) )
& ( ( subset @ sK4 @ ( setminus @ sK3 @ X6 ) )
= $true )
& ( ( in @ X7 @ sK4 )
= $true ) ) )
=> ( ( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true )
& ? [X7: $i] :
( ( ( in @ X7 @ sK3 )
= $true )
& ( ( in @ X7 @ sK5 )
= $true )
& ( ( subset @ sK4 @ ( setminus @ sK3 @ sK5 ) )
= $true )
& ( ( in @ X7 @ sK4 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X7: $i] :
( ( ( in @ X7 @ sK3 )
= $true )
& ( ( in @ X7 @ sK5 )
= $true )
& ( ( subset @ sK4 @ ( setminus @ sK3 @ sK5 ) )
= $true )
& ( ( in @ X7 @ sK4 )
= $true ) )
=> ( ( ( in @ sK6 @ sK3 )
= $true )
& ( ( in @ sK6 @ sK5 )
= $true )
& ( ( subset @ sK4 @ ( setminus @ sK3 @ sK5 ) )
= $true )
& ( ( in @ sK6 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( contrasubsetT != $true ) )
& ( ( contrasubsetT = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
= $true )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ X4 ) )
& ( $true
= ( in @ X7 @ X6 ) )
& ( $true
= ( subset @ X5 @ ( setminus @ X4 @ X6 ) ) )
& ( ( in @ X7 @ X5 )
= $true ) ) )
& ( ( in @ X5 @ ( powerset @ X4 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( contrasubsetT != $true ) )
& ( ( contrasubsetT = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X3 @ X1 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( contrasubsetT = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( contrasubsetT = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( $true
!= ( in @ X3 @ X1 ) ) ) ) ) ) )
<=> ( contrasubsetT = $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( contrasubsetT = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( $true
!= ( in @ X3 @ X1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( contrasubsetT
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( contrasubsetT
= ( ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( subset @ X3 @ ( setminus @ X0 @ X4 ) )
=> ( ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UPFCvlpbuE/DTF2THF_11698.p',contrasubsetT) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU736^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:32:39 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU736^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.31/0.47 % Version : Especial > Reduced > Especial.
% 0.31/0.47 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.31/0.47 % subset X (setminus A Y) -> (! x:i.in x A -> in x Y ->
% 0.31/0.47 % in x (setminus A X))))
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC238l [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.31/0.47 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.31/0.47 % Number of atoms : 21 ( 2 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 8 ( 7 avg)
% 0.31/0.47 % Number of connectives : 58 ( 2 ~; 0 |; 0 &; 42 @)
% 0.31/0.47 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 15 ( 6 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=298
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(powerset_type,type,
% 0.31/0.47 powerset: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(subset_type,type,
% 0.31/0.47 subset: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(setminus_type,type,
% 0.31/0.47 setminus: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setminusI_type,type,
% 0.31/0.47 setminusI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setminusI,definition,
% 0.31/0.47 ( setminusI
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT_type,type,
% 0.31/0.47 contrasubsetT: $o ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT,definition,
% 0.31/0.47 ( contrasubsetT
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.47 => ( ( in @ Xx @ Y )
% 0.31/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(contraSubsetComplement,conjecture,
% 0.31/0.47 ( setminusI
% 0.31/0.47 => ( contrasubsetT
% 0.31/0.47 => ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ Y )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.52/1.29 ---- Embedded in THF ---
% 1.52/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.29 %%% Generated on Tue Feb 24 12:32:40 EST 2026
% 1.52/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.29 %%% Logic specification used:
% 1.52/1.29 %%% thf(spec, logic, $$dhol).
% 1.52/1.29
% 1.52/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.UPFCvlpbuE/DTF2DTF11698.p
% See solution above
% 1.52/1.29 ------------------------
% 1.71/1.30 ---- Cleaned THF ---
% 1.71/1.30 thf(in_type,type,
% 1.71/1.30 in: $i > $i > $o ).
% 1.71/1.30
% 1.71/1.30 thf(powerset_type,type,
% 1.71/1.30 powerset: $i > $i ).
% 1.71/1.30
% 1.71/1.30 thf(subset_type,type,
% 1.71/1.30 subset: $i > $i > $o ).
% 1.71/1.30
% 1.71/1.30 thf(setminus_type,type,
% 1.71/1.30 setminus: $i > $i > $i ).
% 1.71/1.30
% 1.71/1.30 thf(setminusI_type,type,
% 1.71/1.30 setminusI: $o ).
% 1.71/1.30
% 1.71/1.30 thf(setminusI,definition,
% 1.71/1.30 ( setminusI
% 1.71/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.71/1.30 ( ( in @ Xx @ A )
% 1.71/1.30 => ( ~ ( in @ Xx @ B )
% 1.71/1.30 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.71/1.30
% 1.71/1.30 thf(contrasubsetT_type,type,
% 1.71/1.30 contrasubsetT: $o ).
% 1.71/1.30
% 1.71/1.30 thf(contrasubsetT,definition,
% 1.71/1.30 ( contrasubsetT
% 1.71/1.30 = ( ! [A: $i,X: $i] :
% 1.71/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.71/1.30 => ! [Y: $i] :
% 1.71/1.30 ( ( in @ Y @ ( powerset @ A ) )
% 1.71/1.30 => ! [Xx: $i] :
% 1.71/1.30 ( ( in @ Xx @ A )
% 1.71/1.30 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 1.71/1.30 => ( ( in @ Xx @ Y )
% 1.71/1.30 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 1.71/1.30
% 1.71/1.30 thf(contraSubsetComplement,conjecture,
% 1.71/1.30 ( setminusI
% 1.71/1.30 => ( contrasubsetT
% 1.71/1.30 => ! [A: $i,X: $i] :
% 1.71/1.30 ( ( in @ X @ ( powerset @ A ) )
% 1.71/1.30 => ! [Y: $i] :
% 1.71/1.30 ( ( in @ Y @ ( powerset @ A ) )
% 1.71/1.30 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 1.71/1.30 => ! [Xx: $i] :
% 1.71/1.30 ( ( in @ Xx @ A )
% 1.71/1.30 => ( ( in @ Xx @ Y )
% 1.71/1.30 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 1.71/1.30 ------------------------
% 1.71/1.32 % (11892)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_11698 for (3000ds/2Mi)
% 1.71/1.32 % (11892)Instruction limit reached!
% 1.71/1.32 % (11892)------------------------------
% 1.71/1.32 % (11892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.32 % (11892)Termination reason: Unknown
% 1.71/1.32 % (11892)Termination phase: Saturation
% 1.71/1.32
% 1.71/1.32 % (11892)Memory used [KB]: 5500
% 1.71/1.32 % (11892)Time elapsed: 0.003 s
% 1.71/1.32 % (11892)Instructions burned: 4 (million)
% 1.71/1.32 % (11892)------------------------------
% 1.71/1.32 % (11892)------------------------------
% 1.71/1.32 % (11893)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_11698 for (3000ds/275Mi)
% 1.71/1.32 % (11894)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11698 for (3000ds/18Mi)
% 1.71/1.32 % (11888)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11698 for (3000ds/183Mi)
% 1.71/1.32 % (11889)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_11698 for (3000ds/4Mi)
% 1.71/1.32 % (11891)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11698 for (3000ds/2Mi)
% 1.71/1.33 % (11891)Instruction limit reached!
% 1.71/1.33 % (11891)------------------------------
% 1.71/1.33 % (11891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (11891)Termination reason: Unknown
% 1.71/1.33 % (11891)Termination phase: Property scanning
% 1.71/1.33
% 1.71/1.33 % (11891)Memory used [KB]: 1023
% 1.71/1.33 % (11891)Time elapsed: 0.003 s
% 1.71/1.33 % (11891)Instructions burned: 3 (million)
% 1.71/1.33 % (11891)------------------------------
% 1.71/1.33 % (11891)------------------------------
% 1.71/1.33 % (11889)Instruction limit reached!
% 1.71/1.33 % (11889)------------------------------
% 1.71/1.33 % (11889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (11889)Termination reason: Unknown
% 1.71/1.33 % (11889)Termination phase: Saturation
% 1.71/1.33
% 1.71/1.33 % (11889)Memory used [KB]: 5500
% 1.71/1.33 % (11889)Time elapsed: 0.005 s
% 1.71/1.33 % (11889)Instructions burned: 5 (million)
% 1.71/1.33 % (11889)------------------------------
% 1.71/1.33 % (11889)------------------------------
% 1.71/1.33 % (11893)First to succeed.
% 1.71/1.33 % (11895)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11698 for (2999ds/3Mi)
% 1.71/1.33 % (11895)Instruction limit reached!
% 1.71/1.33 % (11895)------------------------------
% 1.71/1.33 % (11895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (11895)Termination reason: Unknown
% 1.71/1.33 % (11895)Termination phase: Saturation
% 1.71/1.33
% 1.71/1.33 % (11895)Memory used [KB]: 5500
% 1.71/1.33 % (11895)Time elapsed: 0.003 s
% 1.71/1.33 % (11895)Instructions burned: 3 (million)
% 1.71/1.33 % (11895)------------------------------
% 1.71/1.33 % (11895)------------------------------
% 1.71/1.33 % (11888)Also succeeded, but the first one will report.
% 1.71/1.33 % (11893)Refutation found. Thanks to Tanya!
% 1.71/1.33 % SZS status Theorem for DTF2THF_11698
% 1.71/1.33 % SZS output start Proof for DTF2THF_11698
% 1.71/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.71/1.33 thf(func_def_1, type, powerset: $i > $i).
% 1.71/1.33 thf(func_def_2, type, subset: $i > $i > $o).
% 1.71/1.33 thf(func_def_3, type, setminus: $i > $i > $i).
% 1.71/1.33 thf(f76,plain,(
% 1.71/1.33 $false),
% 1.71/1.33 inference(subsumption_resolution,[status(thm)],[f75,f50])).
% 1.71/1.33 thf(f50,plain,(
% 1.71/1.33 ((in @ sK10 @ sK9) = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.33 thf(f33,plain,(
% 1.71/1.33 ((((in @ sK9 @ (powerset @ sK7)) = $true) & (((in @ sK10 @ (setminus @ sK7 @ sK8)) != $true) & ((in @ sK10 @ sK9) = $true) & ((in @ sK10 @ sK7) = $true)) & ((subset @ sK8 @ (setminus @ sK7 @ sK9)) = $true)) & ((in @ sK8 @ (powerset @ sK7)) = $true)) & (contrasubsetT = $true) & (setminusI = $true)),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f15,f32,f31,f30])).
% 1.71/1.33 thf(f30,plain,(
% 1.71/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ X1)) != $true) & ((in @ X3 @ X2) = $true) & ((in @ X3 @ X0) = $true)) & ((subset @ X1 @ (setminus @ X0 @ X2)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (((in @ X2 @ (powerset @ sK7)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK7 @ sK8)) != $true) & ((in @ X3 @ X2) = $true) & ($true = (in @ X3 @ sK7))) & ((subset @ sK8 @ (setminus @ sK7 @ X2)) = $true)) & ((in @ sK8 @ (powerset @ sK7)) = $true))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f31,plain,(
% 1.71/1.33 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK7)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK7 @ sK8)) != $true) & ((in @ X3 @ X2) = $true) & ($true = (in @ X3 @ sK7))) & ((subset @ sK8 @ (setminus @ sK7 @ X2)) = $true)) => (((in @ sK9 @ (powerset @ sK7)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK7 @ sK8)) != $true) & ((in @ X3 @ sK9) = $true) & ($true = (in @ X3 @ sK7))) & ((subset @ sK8 @ (setminus @ sK7 @ sK9)) = $true))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f32,plain,(
% 1.71/1.33 ? [X3 : $i] : (((in @ X3 @ (setminus @ sK7 @ sK8)) != $true) & ((in @ X3 @ sK9) = $true) & ($true = (in @ X3 @ sK7))) => (((in @ sK10 @ (setminus @ sK7 @ sK8)) != $true) & ((in @ sK10 @ sK9) = $true) & ((in @ sK10 @ sK7) = $true))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f15,plain,(
% 1.71/1.33 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ X0 @ X1)) != $true) & ((in @ X3 @ X2) = $true) & ((in @ X3 @ X0) = $true)) & ((subset @ X1 @ (setminus @ X0 @ X2)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (contrasubsetT = $true) & (setminusI = $true)),
% 1.71/1.33 inference(flattening,[status(thm)],[f14])).
% 1.71/1.33 thf(f14,plain,(
% 1.71/1.33 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((? [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ X1)) != $true) & ((in @ X3 @ X2) = $true)) & ((in @ X3 @ X0) = $true)) & ((subset @ X1 @ (setminus @ X0 @ X2)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (contrasubsetT = $true)) & (setminusI = $true)),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 1.71/1.33 thf(f11,plain,(
% 1.71/1.33 ~((setminusI = $true) => ((contrasubsetT = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => (((subset @ X1 @ (setminus @ X0 @ X2)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ X2) = $true) => ((in @ X3 @ (setminus @ X0 @ X1)) = $true))))))))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.71/1.33 thf(f10,plain,(
% 1.71/1.33 ~(setminusI => (contrasubsetT => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ (setminus @ X0 @ X1)))))))))),
% 1.71/1.33 inference(rectify,[status(thm)],[f4])).
% 1.71/1.33 thf(f4,negated_conjecture,(
% 1.71/1.33 ~(setminusI => (contrasubsetT => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X3 @ (setminus @ X0 @ X4)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X4) => (in @ X2 @ (setminus @ X0 @ X3)))))))))),
% 1.71/1.33 inference(negated_conjecture,[status(cth)],[f3])).
% 1.71/1.33 thf(f3,conjecture,(
% 1.71/1.33 setminusI => (contrasubsetT => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X3 @ (setminus @ X0 @ X4)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X4) => (in @ X2 @ (setminus @ X0 @ X3))))))))),
% 1.71/1.33 file('/export/starexec/sandbox/tmp/tmp.UPFCvlpbuE/DTF2THF_11698.p',contraSubsetComplement)).
% 1.71/1.33 thf(f75,plain,(
% 1.71/1.33 ((in @ sK10 @ sK9) != $true)),
% 1.71/1.33 inference(subsumption_resolution,[status(thm)],[f74,f49])).
% 1.71/1.33 thf(f49,plain,(
% 1.71/1.33 ((in @ sK10 @ sK7) = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.33 thf(f74,plain,(
% 1.71/1.33 ((in @ sK10 @ sK7) != $true) | ((in @ sK10 @ sK9) != $true)),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.71/1.33 thf(f73,plain,(
% 1.71/1.33 ((in @ sK10 @ sK9) != $true) | ((in @ sK10 @ sK7) != $true) | ($true != $true)),
% 1.71/1.33 inference(superposition,[status(thm)],[f72,f68])).
% 1.71/1.33 thf(f68,plain,(
% 1.71/1.33 ((in @ sK10 @ sK8) = $true)),
% 1.71/1.33 inference(subsumption_resolution,[status(thm)],[f67,f49])).
% 1.71/1.33 thf(f67,plain,(
% 1.71/1.33 ((in @ sK10 @ sK8) = $true) | ((in @ sK10 @ sK7) != $true)),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.71/1.33 thf(f66,plain,(
% 1.71/1.33 ($true != $true) | ((in @ sK10 @ sK8) = $true) | ((in @ sK10 @ sK7) != $true)),
% 1.71/1.33 inference(superposition,[status(thm)],[f51,f65])).
% 1.71/1.33 thf(f65,plain,(
% 1.71/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (setminus @ X1 @ X0)) = $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.71/1.33 thf(f53,plain,(
% 1.71/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ($true != $true) | ((in @ X2 @ (setminus @ X1 @ X0)) = $true) | ((in @ X2 @ X0) = $true)) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f37,f45])).
% 1.71/1.33 thf(f45,plain,(
% 1.71/1.33 (setminusI = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.33 thf(f37,plain,(
% 1.71/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ (setminus @ X1 @ X0)) = $true) | (setminusI != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f23])).
% 1.71/1.33 thf(f23,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ (setminus @ X1 @ X0)) = $true)) | (setminusI != $true)) & ((setminusI = $true) | (((in @ sK2 @ sK0) != $true) & ((in @ sK2 @ sK1) = $true) & ((in @ sK2 @ (setminus @ sK1 @ sK0)) != $true)))),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f22])).
% 1.71/1.33 thf(f22,plain,(
% 1.71/1.33 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) & ((in @ X5 @ X4) = $true) & ((in @ X5 @ (setminus @ X4 @ X3)) != $true)) => (((in @ sK2 @ sK0) != $true) & ((in @ sK2 @ sK1) = $true) & ((in @ sK2 @ (setminus @ sK1 @ sK0)) != $true))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f21,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ (setminus @ X1 @ X0)) = $true)) | (setminusI != $true)) & ((setminusI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) & ((in @ X5 @ X4) = $true) & ((in @ X5 @ (setminus @ X4 @ X3)) != $true)))),
% 1.71/1.33 inference(rectify,[status(thm)],[f20])).
% 1.71/1.33 thf(f20,plain,(
% 1.71/1.33 (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ (setminus @ X2 @ X1)) = $true)) | (setminusI != $true)) & ((setminusI = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X1) != $true) & ((in @ X0 @ X2) = $true) & ((in @ X0 @ (setminus @ X2 @ X1)) != $true)))),
% 1.71/1.33 inference(nnf_transformation,[status(thm)],[f17])).
% 1.71/1.33 thf(f17,plain,(
% 1.71/1.33 ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ (setminus @ X2 @ X1)) = $true)) <=> (setminusI = $true)),
% 1.71/1.33 inference(flattening,[status(thm)],[f16])).
% 1.71/1.33 thf(f16,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setminus @ X2 @ X1)) = $true) | ((in @ X0 @ X1) = $true)) | ((in @ X0 @ X2) != $true)) <=> (setminusI = $true)),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f13])).
% 1.71/1.33 thf(f13,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => (((in @ X0 @ X1) != $true) => ((in @ X0 @ (setminus @ X2 @ X1)) = $true))) <=> (setminusI = $true)),
% 1.71/1.33 inference(flattening,[status(thm)],[f7])).
% 1.71/1.33 thf(f7,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => (~((in @ X0 @ X1) = $true) => ((in @ X0 @ (setminus @ X2 @ X1)) = $true))) <=> (setminusI = $true)),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f6])).
% 1.71/1.33 thf(f6,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => (in @ X0 @ (setminus @ X2 @ X1)))) = setminusI)),
% 1.71/1.33 inference(rectify,[status(thm)],[f1])).
% 1.71/1.33 thf(f1,axiom,(
% 1.71/1.33 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 1.71/1.33 file('/export/starexec/sandbox/tmp/tmp.UPFCvlpbuE/DTF2THF_11698.p',setminusI)).
% 1.71/1.33 thf(f51,plain,(
% 1.71/1.33 ((in @ sK10 @ (setminus @ sK7 @ sK8)) != $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.33 thf(f72,plain,(
% 1.71/1.33 ( ! [X0 : $i] : (($true != (in @ X0 @ sK8)) | ((in @ X0 @ sK7) != $true) | ((in @ X0 @ sK9) != $true)) )),
% 1.71/1.33 inference(subsumption_resolution,[status(thm)],[f71,f47])).
% 1.71/1.33 thf(f47,plain,(
% 1.71/1.33 ((in @ sK8 @ (powerset @ sK7)) = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.33 thf(f71,plain,(
% 1.71/1.33 ( ! [X0 : $i] : (((in @ X0 @ sK9) != $true) | ((in @ X0 @ sK7) != $true) | ($true != (in @ X0 @ sK8)) | ((in @ sK8 @ (powerset @ sK7)) != $true)) )),
% 1.71/1.33 inference(subsumption_resolution,[status(thm)],[f70,f52])).
% 1.71/1.33 thf(f52,plain,(
% 1.71/1.33 ((in @ sK9 @ (powerset @ sK7)) = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.33 thf(f70,plain,(
% 1.71/1.33 ( ! [X0 : $i] : (((in @ X0 @ sK7) != $true) | ((in @ sK9 @ (powerset @ sK7)) != $true) | ((in @ X0 @ sK9) != $true) | ($true != (in @ X0 @ sK8)) | ((in @ sK8 @ (powerset @ sK7)) != $true)) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.71/1.33 thf(f69,plain,(
% 1.71/1.33 ( ! [X0 : $i] : (($true != $true) | ((in @ sK8 @ (powerset @ sK7)) != $true) | ($true != (in @ X0 @ sK8)) | ((in @ X0 @ sK9) != $true) | ((in @ X0 @ sK7) != $true) | ((in @ sK9 @ (powerset @ sK7)) != $true)) )),
% 1.71/1.33 inference(superposition,[status(thm)],[f64,f48])).
% 1.71/1.33 thf(f48,plain,(
% 1.71/1.33 ((subset @ sK8 @ (setminus @ sK7 @ sK9)) = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.33 thf(f64,plain,(
% 1.71/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ X1 @ (setminus @ X0 @ X2)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X3 @ X2) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X3 @ X0) != $true) | ($true != (in @ X3 @ X1))) )),
% 1.71/1.33 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.71/1.33 thf(f57,plain,(
% 1.71/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ($true != (in @ X3 @ X1)) | ((in @ X3 @ X0) != $true) | ($true != $true) | ((in @ X3 @ X2) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((subset @ X1 @ (setminus @ X0 @ X2)) != $true)) )),
% 1.71/1.33 inference(definition_unfolding,[status(thm)],[f44,f46])).
% 1.71/1.33 thf(f46,plain,(
% 1.71/1.33 (contrasubsetT = $true)),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.33 thf(f44,plain,(
% 1.71/1.33 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true) | ((subset @ X1 @ (setminus @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)) | ((in @ X1 @ (powerset @ X0)) != $true) | (contrasubsetT != $true)) )),
% 1.71/1.33 inference(cnf_transformation,[status(thm)],[f29])).
% 1.71/1.33 thf(f29,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true) | ((subset @ X1 @ (setminus @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (contrasubsetT != $true)) & ((contrasubsetT = $true) | ((((in @ sK5 @ (powerset @ sK3)) = $true) & (((in @ sK6 @ sK3) = $true) & ((in @ sK6 @ sK5) = $true) & ((subset @ sK4 @ (setminus @ sK3 @ sK5)) = $true) & ((in @ sK6 @ sK4) = $true))) & ((in @ sK4 @ (powerset @ sK3)) = $true)))),
% 1.71/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f25,f28,f27,f26])).
% 1.71/1.33 thf(f26,plain,(
% 1.71/1.33 ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ (powerset @ X4)) = $true) & ? [X7 : $i] : (($true = (in @ X7 @ X4)) & ($true = (in @ X7 @ X6)) & ($true = (subset @ X5 @ (setminus @ X4 @ X6))) & ((in @ X7 @ X5) = $true))) & ((in @ X5 @ (powerset @ X4)) = $true)) => (? [X6 : $i] : (((in @ X6 @ (powerset @ sK3)) = $true) & ? [X7 : $i] : (((in @ X7 @ sK3) = $true) & ($true = (in @ X7 @ X6)) & ((subset @ sK4 @ (setminus @ sK3 @ X6)) = $true) & ((in @ X7 @ sK4) = $true))) & ((in @ sK4 @ (powerset @ sK3)) = $true))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f27,plain,(
% 1.71/1.33 ? [X6 : $i] : (((in @ X6 @ (powerset @ sK3)) = $true) & ? [X7 : $i] : (((in @ X7 @ sK3) = $true) & ($true = (in @ X7 @ X6)) & ((subset @ sK4 @ (setminus @ sK3 @ X6)) = $true) & ((in @ X7 @ sK4) = $true))) => (((in @ sK5 @ (powerset @ sK3)) = $true) & ? [X7 : $i] : (((in @ X7 @ sK3) = $true) & ((in @ X7 @ sK5) = $true) & ((subset @ sK4 @ (setminus @ sK3 @ sK5)) = $true) & ((in @ X7 @ sK4) = $true)))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f28,plain,(
% 1.71/1.33 ? [X7 : $i] : (((in @ X7 @ sK3) = $true) & ((in @ X7 @ sK5) = $true) & ((subset @ sK4 @ (setminus @ sK3 @ sK5)) = $true) & ((in @ X7 @ sK4) = $true)) => (((in @ sK6 @ sK3) = $true) & ((in @ sK6 @ sK5) = $true) & ((subset @ sK4 @ (setminus @ sK3 @ sK5)) = $true) & ((in @ sK6 @ sK4) = $true))),
% 1.71/1.33 introduced(definition,[],[choice_axiom])).
% 1.71/1.33 thf(f25,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true) | ((subset @ X1 @ (setminus @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (contrasubsetT != $true)) & ((contrasubsetT = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ (powerset @ X4)) = $true) & ? [X7 : $i] : (($true = (in @ X7 @ X4)) & ($true = (in @ X7 @ X6)) & ($true = (subset @ X5 @ (setminus @ X4 @ X6))) & ((in @ X7 @ X5) = $true))) & ((in @ X5 @ (powerset @ X4)) = $true)))),
% 1.71/1.33 inference(rectify,[status(thm)],[f24])).
% 1.71/1.33 thf(f24,plain,(
% 1.71/1.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true) | ((subset @ X1 @ (setminus @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (contrasubsetT != $true)) & ((contrasubsetT = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) = $true) & ((subset @ X1 @ (setminus @ X0 @ X2)) = $true) & ($true = (in @ X3 @ X1)))) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 1.71/1.33 inference(nnf_transformation,[status(thm)],[f19])).
% 1.71/1.33 thf(f19,plain,(
% 1.71/1.33 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true) | ((subset @ X1 @ (setminus @ X0 @ X2)) != $true) | ($true != (in @ X3 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (contrasubsetT = $true)),
% 1.71/1.33 inference(flattening,[status(thm)],[f18])).
% 1.71/1.33 thf(f18,plain,(
% 1.71/1.33 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((($true != (in @ X3 @ X1)) | ((in @ X3 @ X2) != $true)) | ((subset @ X1 @ (setminus @ X0 @ X2)) != $true)) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (contrasubsetT = $true)),
% 1.71/1.33 inference(ennf_transformation,[status(thm)],[f12])).
% 1.71/1.33 thf(f12,plain,(
% 1.71/1.33 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((subset @ X1 @ (setminus @ X0 @ X2)) = $true) => (((in @ X3 @ X2) = $true) => ($true != (in @ X3 @ X1))))))) <=> (contrasubsetT = $true)),
% 1.71/1.33 inference(flattening,[status(thm)],[f9])).
% 1.71/1.33 thf(f9,plain,(
% 1.71/1.33 (contrasubsetT = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((subset @ X1 @ (setminus @ X0 @ X2)) = $true) => (((in @ X3 @ X2) = $true) => ~($true = (in @ X3 @ X1)))))))),
% 1.71/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.71/1.33 thf(f8,plain,(
% 1.71/1.33 (contrasubsetT = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((subset @ X1 @ (setminus @ X0 @ X2)) => ((in @ X3 @ X2) => ~(in @ X3 @ X1)))))))),
% 1.71/1.33 inference(rectify,[status(thm)],[f2])).
% 1.71/1.33 thf(f2,axiom,(
% 1.71/1.33 (contrasubsetT = ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((subset @ X3 @ (setminus @ X0 @ X4)) => ((in @ X2 @ X4) => ~(in @ X2 @ X3)))))))),
% 1.71/1.33 file('/export/starexec/sandbox/tmp/tmp.UPFCvlpbuE/DTF2THF_11698.p',contrasubsetT)).
% 1.71/1.33 % SZS output end Proof for DTF2THF_11698
% 1.71/1.33 % (11893)------------------------------
% 1.71/1.33 % (11893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (11893)Termination reason: Refutation
% 1.71/1.33
% 1.71/1.33 % (11893)Memory used [KB]: 5500
% 1.71/1.33 % (11893)Time elapsed: 0.009 s
% 1.71/1.33 % (11893)Instructions burned: 6 (million)
% 1.71/1.33 % (11893)------------------------------
% 1.71/1.33 % (11893)------------------------------
% 1.71/1.33 % (11887)Success in time 0.022 s
%------------------------------------------------------------------------------