%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU733^2 : 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 : n007.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 09:36:45 AM UTC 2026
% Result : Theorem 1.64s 1.31s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 926 ( 244 equ; 0 cnn)
% Maximal formula atoms : 12 ( 16 avg)
% Number of connectives : 1082 ( 109 ~; 78 |; 82 &; 750 @)
% ( 8 <=>; 55 =>; 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,
binintersect: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(f75,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f74,f43]) ).
thf(f43,plain,
( ( in @ sK6 @ ( powerset @ sK5 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( complementTnotintersectT = $true )
& ( setminusI = $true )
& ( ( in @ sK4 @ ( powerset @ sK5 ) )
= $true )
& ( ( in @ sK6 @ ( powerset @ sK5 ) )
= $true )
& ( $true
!= ( in @ sK7 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ sK6 ) ) ) )
& ( $true
= ( in @ sK7 @ sK5 ) )
& ( $true
= ( in @ sK7 @ ( setminus @ sK5 @ sK4 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f19,f28,f27,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) ) ) ) )
=> ( ( ( in @ sK4 @ ( powerset @ sK5 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK5 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ sK5 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK5 @ sK4 ) )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK5 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ sK5 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK5 @ sK4 ) )
= $true ) ) )
=> ( ( ( in @ sK6 @ ( powerset @ sK5 ) )
= $true )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ sK6 ) ) ) )
& ( ( in @ X3 @ sK5 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK5 @ sK4 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ sK6 ) ) ) )
& ( ( in @ X3 @ sK5 )
= $true )
& ( ( in @ X3 @ ( setminus @ sK5 @ sK4 ) )
= $true ) )
=> ( ( $true
!= ( in @ sK7 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ sK6 ) ) ) )
& ( $true
= ( in @ sK7 @ sK5 ) )
& ( $true
= ( in @ sK7 @ ( setminus @ sK5 @ sK4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( complementTnotintersectT = $true )
& ( setminusI = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( complementTnotintersectT = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( setminusI = $true )
=> ( ( complementTnotintersectT = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
=> ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( setminusI
=> ( complementTnotintersectT
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
=> ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( complementTnotintersectT
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ X3 ) )
=> ( in @ X2 @ ( setminus @ X0 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setminusI
=> ( complementTnotintersectT
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ X3 ) )
=> ( in @ X2 @ ( setminus @ X0 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sEjlSN3xKP/DTF2THF_11656.p',complementImpComplementIntersect) ).
thf(f74,plain,
( ( in @ sK6 @ ( powerset @ sK5 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( in @ sK6 @ ( powerset @ sK5 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f72,f65]) ).
thf(f65,plain,
( $true
= ( in @ sK7 @ ( binintersect @ sK4 @ sK6 ) ) ),
inference(subsumption_resolution,[status(thm)],[f64,f41]) ).
thf(f41,plain,
( $true
= ( in @ sK7 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f64,plain,
( ( $true
!= ( in @ sK7 @ sK5 ) )
| ( $true
= ( in @ sK7 @ ( binintersect @ sK4 @ sK6 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true
= ( in @ sK7 @ ( binintersect @ sK4 @ sK6 ) ) )
| ( $true
!= ( in @ sK7 @ sK5 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f42,f61]) ).
thf(f61,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( ( in @ X4 @ X3 )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( $true != $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f47,f45]) ).
thf(f45,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f47,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( setminusI = $true )
| ( ( ( in @ sK9 @ ( setminus @ sK10 @ sK8 ) )
!= $true )
& ( ( in @ sK9 @ sK10 )
= $true )
& ( $true
!= ( in @ sK9 @ sK8 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f31,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1 @ X0 ) ) )
=> ( ( ( in @ sK9 @ ( setminus @ sK10 @ sK8 ) )
!= $true )
& ( ( in @ sK9 @ sK10 )
= $true )
& ( $true
!= ( in @ sK9 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1 @ X0 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setminus @ X5 @ X3 ) ) )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X0 )
=> ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setminusI
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sEjlSN3xKP/DTF2THF_11656.p',setminusI) ).
thf(f42,plain,
( $true
!= ( in @ sK7 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ sK6 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f72,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK7 @ ( binintersect @ sK4 @ X0 ) ) )
| ( ( in @ X0 @ ( powerset @ sK5 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f71,f41]) ).
thf(f71,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK7 @ sK5 ) )
| ( $true
!= ( in @ sK7 @ ( binintersect @ sK4 @ X0 ) ) )
| ( ( in @ X0 @ ( powerset @ sK5 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f68,f44]) ).
thf(f44,plain,
( ( in @ sK4 @ ( powerset @ sK5 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f68,plain,
! [X0: $i] :
( ( ( in @ sK4 @ ( powerset @ sK5 ) )
!= $true )
| ( $true
!= ( in @ sK7 @ ( binintersect @ sK4 @ X0 ) ) )
| ( $true
!= ( in @ sK7 @ sK5 ) )
| ( ( in @ X0 @ ( powerset @ sK5 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
! [X0: $i] :
( ( ( in @ sK4 @ ( powerset @ sK5 ) )
!= $true )
| ( ( in @ X0 @ ( powerset @ sK5 ) )
!= $true )
| ( $true
!= ( in @ sK7 @ ( binintersect @ sK4 @ X0 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK7 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f62,f40]) ).
thf(f40,plain,
( $true
= ( in @ sK7 @ ( setminus @ sK5 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true != $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f39,f46]) ).
thf(f46,plain,
complementTnotintersectT = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( complementTnotintersectT != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( complementTnotintersectT != $true ) )
& ( ( complementTnotintersectT = $true )
| ( ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
= $true )
& ( ( in @ sK3 @ ( binintersect @ sK0 @ sK2 ) )
= $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f24,f23,f22]) ).
thf(f22,plain,
( ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) )
& ? [X7: $i] :
( ( ( in @ X7 @ X5 )
= $true )
& ( $true
= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
& ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
= $true ) ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) )
=> ( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ sK1 ) ) )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK1 ) )
& ( ( in @ X7 @ ( setminus @ sK1 @ sK0 ) )
= $true )
& ( ( in @ X7 @ ( binintersect @ sK0 @ X6 ) )
= $true ) ) )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ sK1 ) ) )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK1 ) )
& ( ( in @ X7 @ ( setminus @ sK1 @ sK0 ) )
= $true )
& ( ( in @ X7 @ ( binintersect @ sK0 @ X6 ) )
= $true ) ) )
=> ( ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK1 ) )
& ( ( in @ X7 @ ( setminus @ sK1 @ sK0 ) )
= $true )
& ( ( in @ X7 @ ( binintersect @ sK0 @ sK2 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK1 ) )
& ( ( in @ X7 @ ( setminus @ sK1 @ sK0 ) )
= $true )
& ( ( in @ X7 @ ( binintersect @ sK0 @ sK2 ) )
= $true ) )
=> ( ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK1 @ sK0 ) )
= $true )
& ( ( in @ sK3 @ ( binintersect @ sK0 @ sK2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( complementTnotintersectT != $true ) )
& ( ( complementTnotintersectT = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) )
& ? [X7: $i] :
( ( ( in @ X7 @ X5 )
= $true )
& ( $true
= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
& ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
= $true ) ) )
& ( ( in @ X4 @ ( powerset @ X5 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( complementTnotintersectT != $true ) )
& ( ( complementTnotintersectT = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
& ( $true
= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
<=> ( complementTnotintersectT = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( complementTnotintersectT = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( complementTnotintersectT = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) )
<=> ( complementTnotintersectT = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
=> ~ ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) ) )
= complementTnotintersectT ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X3: $i,X0: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ X3 ) )
=> ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ) ) ) )
= complementTnotintersectT ),
file('/export/starexec/sandbox2/tmp/tmp.sEjlSN3xKP/DTF2THF_11656.p',complementTnotintersectT) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU733^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n007.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:31:38 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEU733^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.19/0.46 % Version : Especial > Reduced > Especial.
% 0.19/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.19/0.46 % (! x:i.in x A -> in x (setminus A X) ->
% 0.19/0.46 % in x (setminus A (binintersect X Y)))))
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.46 % Source : [Bro08]
% 0.19/0.46 % Names : ZFC235l [Bro08]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % 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
% 0.19/0.46 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.19/0.46 % Number of atoms : 19 ( 2 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 7 ( 6 avg)
% 0.19/0.46 % Number of connectives : 56 ( 2 ~; 0 |; 0 &; 42 @)
% 0.19/0.46 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 15 ( 6 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : http://mathgate.info/detsetitem.php?id=295
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(in_type,type,
% 0.19/0.46 in: $i > $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(powerset_type,type,
% 0.19/0.46 powerset: $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(binintersect_type,type,
% 0.19/0.46 binintersect: $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(setminus_type,type,
% 0.19/0.46 setminus: $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(setminusI_type,type,
% 0.19/0.46 setminusI: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusI,definition,
% 0.19/0.46 ( setminusI
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( ~ ( in @ Xx @ B )
% 0.19/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(complementTnotintersectT_type,type,
% 0.19/0.46 complementTnotintersectT: $o ).
% 0.19/0.46
% 0.19/0.46 thf(complementTnotintersectT,definition,
% 0.19/0.46 ( complementTnotintersectT
% 0.19/0.46 = ( ! [A: $i,X: $i] :
% 0.19/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.46 => ! [Y: $i] :
% 0.19/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.46 => ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.19/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(complementImpComplementIntersect,conjecture,
% 0.19/0.46 ( setminusI
% 0.19/0.46 => ( complementTnotintersectT
% 0.19/0.46 => ! [A: $i,X: $i] :
% 0.19/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.46 => ! [Y: $i] :
% 0.19/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.46 => ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.19/0.46 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 12:31:39 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.sEjlSN3xKP/DTF2DTF11656.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(in_type,type,
% 1.47/1.28 in: $i > $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(powerset_type,type,
% 1.47/1.28 powerset: $i > $i ).
% 1.47/1.28
% 1.47/1.28 thf(binintersect_type,type,
% 1.47/1.28 binintersect: $i > $i > $i ).
% 1.47/1.28
% 1.47/1.28 thf(setminus_type,type,
% 1.47/1.28 setminus: $i > $i > $i ).
% 1.47/1.28
% 1.47/1.28 thf(setminusI_type,type,
% 1.47/1.28 setminusI: $o ).
% 1.47/1.28
% 1.47/1.28 thf(setminusI,definition,
% 1.47/1.28 ( setminusI
% 1.47/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.47/1.28 ( ( in @ Xx @ A )
% 1.47/1.28 => ( ~ ( in @ Xx @ B )
% 1.47/1.28 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(complementTnotintersectT_type,type,
% 1.47/1.28 complementTnotintersectT: $o ).
% 1.47/1.28
% 1.47/1.28 thf(complementTnotintersectT,definition,
% 1.47/1.28 ( complementTnotintersectT
% 1.47/1.28 = ( ! [A: $i,X: $i] :
% 1.47/1.28 ( ( in @ X @ ( powerset @ A ) )
% 1.47/1.28 => ! [Y: $i] :
% 1.47/1.28 ( ( in @ Y @ ( powerset @ A ) )
% 1.47/1.28 => ! [Xx: $i] :
% 1.47/1.28 ( ( in @ Xx @ A )
% 1.47/1.28 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 1.47/1.28 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(complementImpComplementIntersect,conjecture,
% 1.47/1.28 ( setminusI
% 1.47/1.28 => ( complementTnotintersectT
% 1.47/1.28 => ! [A: $i,X: $i] :
% 1.47/1.28 ( ( in @ X @ ( powerset @ A ) )
% 1.47/1.28 => ! [Y: $i] :
% 1.47/1.28 ( ( in @ Y @ ( powerset @ A ) )
% 1.47/1.28 => ! [Xx: $i] :
% 1.47/1.28 ( ( in @ Xx @ A )
% 1.47/1.28 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 1.47/1.28 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 1.47/1.28 ------------------------
% 1.64/1.30 % (11820)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11656 for (2999ds/18Mi)
% 1.64/1.30 % (11817)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11656 for (2999ds/2Mi)
% 1.64/1.30 % (11817)Instruction limit reached!
% 1.64/1.30 % (11817)------------------------------
% 1.64/1.30 % (11817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (11817)Termination reason: Unknown
% 1.64/1.30 % (11817)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (11817)Memory used [KB]: 1023
% 1.64/1.30 % (11817)Time elapsed: 0.002 s
% 1.64/1.30 % (11817)Instructions burned: 3 (million)
% 1.64/1.30 % (11817)------------------------------
% 1.64/1.30 % (11817)------------------------------
% 1.64/1.30 % (11820)Instruction limit reached!
% 1.64/1.30 % (11820)------------------------------
% 1.64/1.30 % (11820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (11820)Termination reason: Unknown
% 1.64/1.30 % (11820)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (11820)Memory used [KB]: 5628
% 1.64/1.30 % (11820)Time elapsed: 0.007 s
% 1.64/1.30 % (11820)Instructions burned: 18 (million)
% 1.64/1.30 % (11820)------------------------------
% 1.64/1.30 % (11820)------------------------------
% 1.64/1.30 % (11814)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11656 for (2999ds/183Mi)
% 1.64/1.30 % (11818)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_11656 for (2999ds/2Mi)
% 1.64/1.30 % (11816)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_11656 for (2999ds/27Mi)
% 1.64/1.30 % (11819)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_11656 for (2999ds/275Mi)
% 1.64/1.30 % (11815)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_11656 for (2999ds/4Mi)
% 1.64/1.31 % (11818)Instruction limit reached!
% 1.64/1.31 % (11818)------------------------------
% 1.64/1.31 % (11818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (11818)Termination reason: Unknown
% 1.64/1.31 % (11818)Termination phase: Property scanning
% 1.64/1.31
% 1.64/1.31 % (11818)Memory used [KB]: 895
% 1.64/1.31 % (11818)Time elapsed: 0.003 s
% 1.64/1.31 % (11818)Instructions burned: 2 (million)
% 1.64/1.31 % (11818)------------------------------
% 1.64/1.31 % (11818)------------------------------
% 1.64/1.31 % (11815)Instruction limit reached!
% 1.64/1.31 % (11815)------------------------------
% 1.64/1.31 % (11815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (11815)Termination reason: Unknown
% 1.64/1.31 % (11815)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (11815)Memory used [KB]: 5500
% 1.64/1.31 % (11815)Time elapsed: 0.004 s
% 1.64/1.31 % (11815)Instructions burned: 4 (million)
% 1.64/1.31 % (11815)------------------------------
% 1.64/1.31 % (11815)------------------------------
% 1.64/1.31 % (11821)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11656 for (2999ds/3Mi)
% 1.64/1.31 % (11819)First to succeed.
% 1.64/1.31 % (11821)Instruction limit reached!
% 1.64/1.31 % (11821)------------------------------
% 1.64/1.31 % (11821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (11821)Termination reason: Unknown
% 1.64/1.31 % (11821)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (11821)Memory used [KB]: 5500
% 1.64/1.31 % (11821)Time elapsed: 0.003 s
% 1.64/1.31 % (11821)Instructions burned: 4 (million)
% 1.64/1.31 % (11821)------------------------------
% 1.64/1.31 % (11821)------------------------------
% 1.64/1.31 % (11822)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_11656 for (2999ds/37Mi)
% 1.64/1.31 % (11814)Also succeeded, but the first one will report.
% 1.64/1.31 % (11819)Refutation found. Thanks to Tanya!
% 1.64/1.31 % SZS status Theorem for DTF2THF_11656
% 1.64/1.31 % SZS output start Proof for DTF2THF_11656
% 1.64/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.31 thf(func_def_1, type, powerset: $i > $i).
% 1.64/1.31 thf(func_def_2, type, binintersect: $i > $i > $i).
% 1.64/1.31 thf(func_def_3, type, setminus: $i > $i > $i).
% 1.64/1.31 thf(f75,plain,(
% 1.64/1.31 $false),
% 1.64/1.31 inference(subsumption_resolution,[status(thm)],[f74,f43])).
% 1.64/1.31 thf(f43,plain,(
% 1.64/1.31 ((in @ sK6 @ (powerset @ sK5)) = $true)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.31 thf(f29,plain,(
% 1.64/1.31 (complementTnotintersectT = $true) & (setminusI = $true) & (((in @ sK4 @ (powerset @ sK5)) = $true) & (((in @ sK6 @ (powerset @ sK5)) = $true) & (($true != (in @ sK7 @ (setminus @ sK5 @ (binintersect @ sK4 @ sK6)))) & ($true = (in @ sK7 @ sK5)) & ($true = (in @ sK7 @ (setminus @ sK5 @ sK4))))))),
% 1.64/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f19,f28,f27,f26])).
% 1.64/1.31 thf(f26,plain,(
% 1.64/1.31 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) & ((in @ X3 @ X1) = $true) & ($true = (in @ X3 @ (setminus @ X1 @ X0)))))) => (((in @ sK4 @ (powerset @ sK5)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ sK5)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK5 @ (binintersect @ sK4 @ X2))) != $true) & ((in @ X3 @ sK5) = $true) & ((in @ X3 @ (setminus @ sK5 @ sK4)) = $true))))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f27,plain,(
% 1.64/1.31 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK5)) = $true) & ? [X3 : $i] : (((in @ X3 @ (setminus @ sK5 @ (binintersect @ sK4 @ X2))) != $true) & ((in @ X3 @ sK5) = $true) & ((in @ X3 @ (setminus @ sK5 @ sK4)) = $true))) => (((in @ sK6 @ (powerset @ sK5)) = $true) & ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ sK5 @ (binintersect @ sK4 @ sK6)))) & ((in @ X3 @ sK5) = $true) & ((in @ X3 @ (setminus @ sK5 @ sK4)) = $true)))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f28,plain,(
% 1.64/1.31 ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ sK5 @ (binintersect @ sK4 @ sK6)))) & ((in @ X3 @ sK5) = $true) & ((in @ X3 @ (setminus @ sK5 @ sK4)) = $true)) => (($true != (in @ sK7 @ (setminus @ sK5 @ (binintersect @ sK4 @ sK6)))) & ($true = (in @ sK7 @ sK5)) & ($true = (in @ sK7 @ (setminus @ sK5 @ sK4))))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f19,plain,(
% 1.64/1.31 (complementTnotintersectT = $true) & (setminusI = $true) & ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (($true != (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) & ((in @ X3 @ X1) = $true) & ($true = (in @ X3 @ (setminus @ X1 @ X0))))))),
% 1.64/1.31 inference(flattening,[status(thm)],[f18])).
% 1.64/1.31 thf(f18,plain,(
% 1.64/1.31 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((($true != (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) & ($true = (in @ X3 @ (setminus @ X1 @ X0)))) & ((in @ X3 @ X1) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (complementTnotintersectT = $true)) & (setminusI = $true)),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f9])).
% 1.64/1.31 thf(f9,plain,(
% 1.64/1.31 ~((setminusI = $true) => ((complementTnotintersectT = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (($true = (in @ X3 @ (setminus @ X1 @ X0))) => ($true = (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))))))))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.64/1.31 thf(f8,plain,(
% 1.64/1.31 ~(setminusI => (complementTnotintersectT => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ X0)) => (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))))))))),
% 1.64/1.31 inference(rectify,[status(thm)],[f4])).
% 1.64/1.31 thf(f4,negated_conjecture,(
% 1.64/1.31 ~(setminusI => (complementTnotintersectT => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ X3)) => (in @ X2 @ (setminus @ X0 @ (binintersect @ X3 @ X4)))))))))),
% 1.64/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.31 thf(f3,conjecture,(
% 1.64/1.31 setminusI => (complementTnotintersectT => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ X3)) => (in @ X2 @ (setminus @ X0 @ (binintersect @ X3 @ X4))))))))),
% 1.64/1.31 file('/export/starexec/sandbox2/tmp/tmp.sEjlSN3xKP/DTF2THF_11656.p',complementImpComplementIntersect)).
% 1.64/1.31 thf(f74,plain,(
% 1.64/1.31 ((in @ sK6 @ (powerset @ sK5)) != $true)),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.64/1.31 thf(f73,plain,(
% 1.64/1.31 ((in @ sK6 @ (powerset @ sK5)) != $true) | ($true != $true)),
% 1.64/1.31 inference(superposition,[status(thm)],[f72,f65])).
% 1.64/1.31 thf(f65,plain,(
% 1.64/1.31 ($true = (in @ sK7 @ (binintersect @ sK4 @ sK6)))),
% 1.64/1.31 inference(subsumption_resolution,[status(thm)],[f64,f41])).
% 1.64/1.31 thf(f41,plain,(
% 1.64/1.31 ($true = (in @ sK7 @ sK5))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.31 thf(f64,plain,(
% 1.64/1.31 ($true != (in @ sK7 @ sK5)) | ($true = (in @ sK7 @ (binintersect @ sK4 @ sK6)))),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.64/1.31 thf(f63,plain,(
% 1.64/1.31 ($true = (in @ sK7 @ (binintersect @ sK4 @ sK6))) | ($true != (in @ sK7 @ sK5)) | ($true != $true)),
% 1.64/1.31 inference(superposition,[status(thm)],[f42,f61])).
% 1.64/1.31 thf(f61,plain,(
% 1.64/1.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ((in @ X4 @ X3) = $true) | ((in @ X4 @ X5) != $true)) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.64/1.31 thf(f60,plain,(
% 1.64/1.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ($true != $true) | ((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true)) )),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f47,f45])).
% 1.64/1.31 thf(f45,plain,(
% 1.64/1.31 (setminusI = $true)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.31 thf(f47,plain,(
% 1.64/1.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true) | (setminusI != $true)) )),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f33])).
% 1.64/1.32 thf(f33,plain,(
% 1.64/1.32 ((setminusI = $true) | (((in @ sK9 @ (setminus @ sK10 @ sK8)) != $true) & ((in @ sK9 @ sK10) = $true) & ($true != (in @ sK9 @ sK8)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true)) | (setminusI != $true))),
% 1.64/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f31,f32])).
% 1.64/1.32 thf(f32,plain,(
% 1.64/1.32 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) & ((in @ X1 @ X2) = $true) & ($true != (in @ X1 @ X0))) => (((in @ sK9 @ (setminus @ sK10 @ sK8)) != $true) & ((in @ sK9 @ sK10) = $true) & ($true != (in @ sK9 @ sK8)))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f31,plain,(
% 1.64/1.32 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) & ((in @ X1 @ X2) = $true) & ($true != (in @ X1 @ X0)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setminus @ X5 @ X3))) | ((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true)) | (setminusI != $true))),
% 1.64/1.32 inference(rectify,[status(thm)],[f30])).
% 1.64/1.32 thf(f30,plain,(
% 1.64/1.32 ((setminusI = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X2 @ (setminus @ X1 @ X0))) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) & (! [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) | (setminusI != $true))),
% 1.64/1.32 inference(nnf_transformation,[status(thm)],[f17])).
% 1.64/1.32 thf(f17,plain,(
% 1.64/1.32 (setminusI = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))),
% 1.64/1.32 inference(flattening,[status(thm)],[f16])).
% 1.64/1.32 thf(f16,plain,(
% 1.64/1.32 ! [X1 : $i,X0 : $i,X2 : $i] : ((($true = (in @ X2 @ (setminus @ X1 @ X0))) | ((in @ X2 @ X0) = $true)) | ((in @ X2 @ X1) != $true)) <=> (setminusI = $true)),
% 1.64/1.32 inference(ennf_transformation,[status(thm)],[f13])).
% 1.64/1.32 thf(f13,plain,(
% 1.64/1.32 ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) => (((in @ X2 @ X0) != $true) => ($true = (in @ X2 @ (setminus @ X1 @ X0))))) <=> (setminusI = $true)),
% 1.64/1.32 inference(flattening,[status(thm)],[f11])).
% 1.64/1.32 thf(f11,plain,(
% 1.64/1.32 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) => (~((in @ X2 @ X0) = $true) => ($true = (in @ X2 @ (setminus @ X1 @ X0)))))),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.32 thf(f10,plain,(
% 1.64/1.32 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (~(in @ X2 @ X0) => (in @ X2 @ (setminus @ X1 @ X0)))))),
% 1.64/1.32 inference(rectify,[status(thm)],[f1])).
% 1.64/1.32 thf(f1,axiom,(
% 1.64/1.32 (setminusI = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 1.64/1.32 file('/export/starexec/sandbox2/tmp/tmp.sEjlSN3xKP/DTF2THF_11656.p',setminusI)).
% 1.64/1.32 thf(f42,plain,(
% 1.64/1.32 ($true != (in @ sK7 @ (setminus @ sK5 @ (binintersect @ sK4 @ sK6))))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f72,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (($true != (in @ sK7 @ (binintersect @ sK4 @ X0))) | ((in @ X0 @ (powerset @ sK5)) != $true)) )),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f71,f41])).
% 1.64/1.32 thf(f71,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (($true != (in @ sK7 @ sK5)) | ($true != (in @ sK7 @ (binintersect @ sK4 @ X0))) | ((in @ X0 @ (powerset @ sK5)) != $true)) )),
% 1.64/1.32 inference(subsumption_resolution,[status(thm)],[f68,f44])).
% 1.64/1.32 thf(f44,plain,(
% 1.64/1.32 ((in @ sK4 @ (powerset @ sK5)) = $true)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f68,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((in @ sK4 @ (powerset @ sK5)) != $true) | ($true != (in @ sK7 @ (binintersect @ sK4 @ X0))) | ($true != (in @ sK7 @ sK5)) | ((in @ X0 @ (powerset @ sK5)) != $true)) )),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.64/1.32 thf(f67,plain,(
% 1.64/1.32 ( ! [X0 : $i] : (((in @ sK4 @ (powerset @ sK5)) != $true) | ((in @ X0 @ (powerset @ sK5)) != $true) | ($true != (in @ sK7 @ (binintersect @ sK4 @ X0))) | ($true != $true) | ($true != (in @ sK7 @ sK5))) )),
% 1.64/1.32 inference(superposition,[status(thm)],[f62,f40])).
% 1.64/1.32 thf(f40,plain,(
% 1.64/1.32 ($true = (in @ sK7 @ (setminus @ sK5 @ sK4)))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f62,plain,(
% 1.64/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X3 @ (setminus @ X1 @ X0))) | ($true != (in @ X2 @ (powerset @ X1))) | ((in @ X3 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | ($true != (in @ X3 @ (binintersect @ X0 @ X2)))) )),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.64/1.32 thf(f51,plain,(
% 1.64/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ($true != (in @ X3 @ (binintersect @ X0 @ X2))) | ($true != $true) | ((in @ X3 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | ($true != (in @ X3 @ (setminus @ X1 @ X0)))) )),
% 1.64/1.32 inference(definition_unfolding,[status(thm)],[f39,f46])).
% 1.64/1.32 thf(f46,plain,(
% 1.64/1.32 (complementTnotintersectT = $true)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.32 thf(f39,plain,(
% 1.64/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ((in @ X3 @ X1) != $true) | ($true != (in @ X3 @ (setminus @ X1 @ X0))) | ($true != (in @ X3 @ (binintersect @ X0 @ X2))) | ((in @ X0 @ (powerset @ X1)) != $true) | (complementTnotintersectT != $true)) )),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f25])).
% 1.64/1.32 thf(f25,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true != (in @ X3 @ (setminus @ X1 @ X0))) | ($true != (in @ X3 @ (binintersect @ X0 @ X2))))) | ((in @ X0 @ (powerset @ X1)) != $true)) | (complementTnotintersectT != $true)) & ((complementTnotintersectT = $true) | ((((in @ sK2 @ (powerset @ sK1)) = $true) & (((in @ sK3 @ sK1) = $true) & ((in @ sK3 @ (setminus @ sK1 @ sK0)) = $true) & ((in @ sK3 @ (binintersect @ sK0 @ sK2)) = $true))) & ((in @ sK0 @ (powerset @ sK1)) = $true)))),
% 1.64/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f24,f23,f22])).
% 1.64/1.32 thf(f22,plain,(
% 1.64/1.32 ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (($true = (in @ X6 @ (powerset @ X5))) & ? [X7 : $i] : (((in @ X7 @ X5) = $true) & ($true = (in @ X7 @ (setminus @ X5 @ X4))) & ((in @ X7 @ (binintersect @ X4 @ X6)) = $true))) & ((in @ X4 @ (powerset @ X5)) = $true)) => (? [X6 : $i] : (($true = (in @ X6 @ (powerset @ sK1))) & ? [X7 : $i] : (($true = (in @ X7 @ sK1)) & ((in @ X7 @ (setminus @ sK1 @ sK0)) = $true) & ((in @ X7 @ (binintersect @ sK0 @ X6)) = $true))) & ((in @ sK0 @ (powerset @ sK1)) = $true))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f23,plain,(
% 1.64/1.32 ? [X6 : $i] : (($true = (in @ X6 @ (powerset @ sK1))) & ? [X7 : $i] : (($true = (in @ X7 @ sK1)) & ((in @ X7 @ (setminus @ sK1 @ sK0)) = $true) & ((in @ X7 @ (binintersect @ sK0 @ X6)) = $true))) => (((in @ sK2 @ (powerset @ sK1)) = $true) & ? [X7 : $i] : (($true = (in @ X7 @ sK1)) & ((in @ X7 @ (setminus @ sK1 @ sK0)) = $true) & ((in @ X7 @ (binintersect @ sK0 @ sK2)) = $true)))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f24,plain,(
% 1.64/1.32 ? [X7 : $i] : (($true = (in @ X7 @ sK1)) & ((in @ X7 @ (setminus @ sK1 @ sK0)) = $true) & ((in @ X7 @ (binintersect @ sK0 @ sK2)) = $true)) => (((in @ sK3 @ sK1) = $true) & ((in @ sK3 @ (setminus @ sK1 @ sK0)) = $true) & ((in @ sK3 @ (binintersect @ sK0 @ sK2)) = $true))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f21,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true != (in @ X3 @ (setminus @ X1 @ X0))) | ($true != (in @ X3 @ (binintersect @ X0 @ X2))))) | ((in @ X0 @ (powerset @ X1)) != $true)) | (complementTnotintersectT != $true)) & ((complementTnotintersectT = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (($true = (in @ X6 @ (powerset @ X5))) & ? [X7 : $i] : (((in @ X7 @ X5) = $true) & ($true = (in @ X7 @ (setminus @ X5 @ X4))) & ((in @ X7 @ (binintersect @ X4 @ X6)) = $true))) & ((in @ X4 @ (powerset @ X5)) = $true)))),
% 1.64/1.32 inference(rectify,[status(thm)],[f20])).
% 1.64/1.32 thf(f20,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true != (in @ X3 @ (setminus @ X1 @ X0))) | ($true != (in @ X3 @ (binintersect @ X0 @ X2))))) | ((in @ X0 @ (powerset @ X1)) != $true)) | (complementTnotintersectT != $true)) & ((complementTnotintersectT = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ($true = (in @ X3 @ (setminus @ X1 @ X0))) & ($true = (in @ X3 @ (binintersect @ X0 @ X2))))) & ((in @ X0 @ (powerset @ X1)) = $true)))),
% 1.64/1.32 inference(nnf_transformation,[status(thm)],[f15])).
% 1.64/1.32 thf(f15,plain,(
% 1.64/1.32 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ($true != (in @ X3 @ (setminus @ X1 @ X0))) | ($true != (in @ X3 @ (binintersect @ X0 @ X2))))) | ((in @ X0 @ (powerset @ X1)) != $true)) <=> (complementTnotintersectT = $true)),
% 1.64/1.32 inference(flattening,[status(thm)],[f14])).
% 1.64/1.32 thf(f14,plain,(
% 1.64/1.32 (complementTnotintersectT = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((($true != (in @ X3 @ (binintersect @ X0 @ X2))) | ($true != (in @ X3 @ (setminus @ X1 @ X0)))) | ((in @ X3 @ X1) != $true)) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 1.64/1.32 inference(ennf_transformation,[status(thm)],[f12])).
% 1.64/1.32 thf(f12,plain,(
% 1.64/1.32 (complementTnotintersectT = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (($true = (in @ X3 @ (setminus @ X1 @ X0))) => ($true != (in @ X3 @ (binintersect @ X0 @ X2)))))))),
% 1.64/1.32 inference(flattening,[status(thm)],[f7])).
% 1.64/1.32 thf(f7,plain,(
% 1.64/1.32 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (($true = (in @ X3 @ (setminus @ X1 @ X0))) => ~($true = (in @ X3 @ (binintersect @ X0 @ X2))))))) <=> (complementTnotintersectT = $true)),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f6])).
% 1.64/1.32 thf(f6,plain,(
% 1.64/1.32 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ X0)) => ~(in @ X3 @ (binintersect @ X0 @ X2)))))) = complementTnotintersectT)),
% 1.64/1.32 inference(rectify,[status(thm)],[f2])).
% 1.64/1.32 thf(f2,axiom,(
% 1.64/1.32 (! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ X3)) => ~(in @ X2 @ (binintersect @ X3 @ X4)))))) = complementTnotintersectT)),
% 1.64/1.32 file('/export/starexec/sandbox2/tmp/tmp.sEjlSN3xKP/DTF2THF_11656.p',complementTnotintersectT)).
% 1.64/1.32 % SZS output end Proof for DTF2THF_11656
% 1.64/1.32 % (11819)------------------------------
% 1.64/1.32 % (11819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (11819)Termination reason: Refutation
% 1.64/1.32
% 1.64/1.32 % (11819)Memory used [KB]: 5500
% 1.64/1.32 % (11819)Time elapsed: 0.011 s
% 1.64/1.32 % (11819)Instructions burned: 6 (million)
% 1.64/1.32 % (11819)------------------------------
% 1.64/1.32 % (11819)------------------------------
% 1.64/1.32 % (11813)Success in time 0.025 s
%------------------------------------------------------------------------------