%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU759^2 : 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 : n009.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 09:36:58 AM UTC 2026
% Result : Theorem 1.55s 1.27s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 850 ( 246 equ; 0 cnn)
% Maximal formula atoms : 10 ( 13 avg)
% Number of connectives : 884 ( 97 ~; 79 |; 81 &; 570 @)
% ( 7 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 17 con; 0-2 aty)
% Number of variables : 186 ( 0 ^; 136 !; 50 ?; 186 :)
% 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_6,type,
binintersect: $i > $i > $i ).
thf(func_def_13,type,
sK3: $i > $i > $i ).
thf(f102,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f100,f52]) ).
thf(f52,plain,
( ( subset @ sK10 @ sK12 )
= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( binintersectEL = $true )
& ( subsetI1 = $true )
& ( $true
= ( in @ sK10 @ ( powerset @ sK9 ) ) )
& ( ( in @ sK12 @ ( powerset @ sK9 ) )
= $true )
& ( ( subset @ ( binintersect @ sK10 @ sK11 ) @ sK12 )
!= $true )
& ( ( subset @ sK10 @ sK12 )
= $true )
& ( ( in @ sK11 @ ( powerset @ sK9 ) )
= $true )
& ( subsetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f34,f37,f36,f35]) ).
thf(f35,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( subset @ X1 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK10 @ ( powerset @ sK9 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK9 ) )
= $true )
& ( $true
!= ( subset @ ( binintersect @ sK10 @ X2 ) @ X3 ) )
& ( ( subset @ sK10 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK9 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK9 ) )
= $true )
& ( $true
!= ( subset @ ( binintersect @ sK10 @ X2 ) @ X3 ) )
& ( ( subset @ sK10 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK9 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK9 ) )
= $true )
& ( $true
!= ( subset @ ( binintersect @ sK10 @ sK11 ) @ X3 ) )
& ( ( subset @ sK10 @ X3 )
= $true ) )
& ( ( in @ sK11 @ ( powerset @ sK9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK9 ) )
= $true )
& ( $true
!= ( subset @ ( binintersect @ sK10 @ sK11 ) @ X3 ) )
& ( ( subset @ sK10 @ X3 )
= $true ) )
=> ( ( ( in @ sK12 @ ( powerset @ sK9 ) )
= $true )
& ( ( subset @ ( binintersect @ sK10 @ sK11 ) @ sK12 )
!= $true )
& ( ( subset @ sK10 @ sK12 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ( binintersectEL = $true )
& ( subsetI1 = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( subset @ X1 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
& ( subsetE = $true ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( binintersectEL = $true )
& ( subsetI1 = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
& ( $true
!= ( subset @ ( binintersect @ X0 @ X2 ) @ X3 ) )
& ( ( subset @ X0 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) )
& ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( subset @ ( binintersect @ X0 @ X2 ) @ X3 ) )
& ( ( subset @ X0 @ X3 )
= $true )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binintersectEL = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( subsetI1 = $true )
=> ( ( subsetE = $true )
=> ( ( binintersectEL = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
=> ( ( ( subset @ X0 @ X3 )
= $true )
=> ( $true
= ( subset @ ( binintersect @ X0 @ X2 ) @ X3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( subsetI1
=> ( subsetE
=> ( binintersectEL
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ X3 )
=> ( subset @ ( binintersect @ X0 @ X2 ) @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( binintersectEL
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ( ( subset @ X3 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( subsetI1
=> ( subsetE
=> ( binintersectEL
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ( ( subset @ X3 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Tl5hrvA7SV/DTF2THF_29178.p',woz13rule1) ).
thf(f100,plain,
( ( subset @ sK10 @ sK12 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( ( subset @ sK10 @ sK12 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f53,f93]) ).
thf(f93,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ ( binintersect @ X0 @ X1 ) @ X2 )
= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X2 )
= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ ( binintersect @ X0 @ X1 ) @ X2 )
= $true )
| ( $true != $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X2 )
= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) ),
inference(superposition,[status(thm)],[f80,f77]) ).
thf(f77,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X0 )
= $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X0 )
= $true )
| ( $true != $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X2 )
= $true ) ),
inference(superposition,[status(thm)],[f72,f70]) ).
thf(f70,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( subset @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( $true != $true )
| ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f45,f56]) ).
thf(f56,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( ( in @ ( sK3 @ X1 @ X0 ) @ X0 )
!= $true )
& ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ( ( $true
!= ( subset @ sK5 @ sK4 ) )
& ! [X5: $i] :
( ( ( in @ X5 @ sK4 )
= $true )
| ( ( in @ X5 @ sK5 )
!= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f26,f28,f27]) ).
thf(f27,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( ( in @ ( sK3 @ X1 @ X0 ) @ X0 )
!= $true )
& ( ( in @ ( sK3 @ X1 @ X0 ) @ X1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ X4 )
!= $true ) ) )
=> ( ( $true
!= ( subset @ sK5 @ sK4 ) )
& ! [X5: $i] :
( ( ( in @ X5 @ sK4 )
= $true )
| ( ( in @ X5 @ sK5 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ X4 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
<=> ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( subsetI1 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Tl5hrvA7SV/DTF2THF_29178.p',subsetI1) ).
thf(f72,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true )
| ( $true
= ( in @ X4 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true )
| ( $true
= ( in @ X4 @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f47,f57]) ).
thf(f57,plain,
binintersectEL = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f47,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( binintersectEL = $true )
| ( ( ( in @ sK7 @ sK6 )
!= $true )
& ( ( in @ sK7 @ ( binintersect @ sK6 @ sK8 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true ) )
| ( binintersectEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f31,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
=> ( ( ( in @ sK7 @ sK6 )
!= $true )
& ( ( in @ sK7 @ ( binintersect @ sK6 @ sK8 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( ( in @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( binintersectEL = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Tl5hrvA7SV/DTF2THF_29178.p',binintersectEL) ).
thf(f80,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ X0 @ X1 ) @ X2 )
!= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( in @ ( sK3 @ X0 @ X1 ) @ X2 )
!= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f69,f71]) ).
thf(f71,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( subset @ X0 @ X2 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f42,f50]) ).
thf(f50,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( ( subset @ sK0 @ sK2 )
= $true )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK1 @ sK2 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f22,f23]) ).
thf(f23,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
& ( $true
= ( in @ X4 @ X3 ) )
& ( $true
!= ( in @ X4 @ X5 ) ) )
=> ( ( ( subset @ sK0 @ sK2 )
= $true )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK1 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
& ( $true
= ( in @ X4 @ X3 ) )
& ( $true
!= ( in @ X4 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.Tl5hrvA7SV/DTF2THF_29178.p',subsetE) ).
thf(f69,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK3 @ X1 @ X0 ) @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( in @ ( sK3 @ X1 @ X0 ) @ X0 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f46,f56]) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( in @ ( sK3 @ X1 @ X0 ) @ X0 )
!= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f53,plain,
( ( subset @ ( binintersect @ sK10 @ sK11 ) @ sK12 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU759^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:32:55 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU759^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Typed Set Theory - First Wizard of Oz Examples - WoZ1 Lemmas
% 0.18/0.45 % Version : Especial > Reduced > Especial.
% 0.18/0.45 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.18/0.45 % (! Z:i.in Z (powerset A) -> subset X Z ->
% 0.18/0.45 % subset (binintersect X Y) Z)))
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC261l [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.18/0.45 % Number of atoms : 22 ( 3 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 8 ( 5 avg)
% 0.18/0.45 % Number of connectives : 45 ( 0 ~; 0 |; 0 &; 33 @)
% 0.18/0.45 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 16 ( 5 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=320
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(powerset_type,type,
% 0.18/0.45 powerset: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(subset_type,type,
% 0.18/0.45 subset: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(subsetI1_type,type,
% 0.18/0.45 subsetI1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(subsetI1,definition,
% 0.18/0.45 ( subsetI1
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xx @ B ) )
% 0.29/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE_type,type,
% 0.29/0.45 subsetE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE,definition,
% 0.29/0.45 ( subsetE
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(binintersect_type,type,
% 0.29/0.45 binintersect: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(binintersectEL_type,type,
% 0.29/0.45 binintersectEL: $o ).
% 0.29/0.45
% 0.29/0.45 thf(binintersectEL,definition,
% 0.29/0.45 ( binintersectEL
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(woz13rule1,conjecture,
% 0.29/0.45 ( subsetI1
% 0.29/0.45 => ( subsetE
% 0.29/0.45 => ( binintersectEL
% 0.29/0.45 => ! [A: $i,X: $i] :
% 0.29/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.45 => ! [Y: $i] :
% 0.29/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.45 => ! [Z: $i] :
% 0.29/0.45 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.45 => ( ( subset @ X @ Z )
% 0.29/0.45 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.55/1.24 ---- Embedded in THF ---
% 1.55/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.24 %%% Generated on Tue Feb 24 12:32:55 EST 2026
% 1.55/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.24 %%% Logic specification used:
% 1.55/1.24 %%% thf(spec, logic, $$dhol).
% 1.55/1.24
% 1.55/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Tl5hrvA7SV/DTF2DTF29178.p
% See solution above
% 1.55/1.24 ------------------------
% 1.55/1.25 ---- Cleaned THF ---
% 1.55/1.25 thf(in_type,type,
% 1.55/1.25 in: $i > $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(powerset_type,type,
% 1.55/1.25 powerset: $i > $i ).
% 1.55/1.25
% 1.55/1.25 thf(subset_type,type,
% 1.55/1.25 subset: $i > $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(subsetI1_type,type,
% 1.55/1.25 subsetI1: $o ).
% 1.55/1.25
% 1.55/1.25 thf(subsetI1,definition,
% 1.55/1.25 ( subsetI1
% 1.55/1.25 = ( ! [A: $i,B: $i] :
% 1.55/1.25 ( ! [Xx: $i] :
% 1.55/1.25 ( ( in @ Xx @ A )
% 1.55/1.25 => ( in @ Xx @ B ) )
% 1.55/1.25 => ( subset @ A @ B ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(subsetE_type,type,
% 1.55/1.25 subsetE: $o ).
% 1.55/1.25
% 1.55/1.25 thf(subsetE,definition,
% 1.55/1.25 ( subsetE
% 1.55/1.25 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.55/1.25 ( ( subset @ A @ B )
% 1.55/1.25 => ( ( in @ Xx @ A )
% 1.55/1.25 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(binintersect_type,type,
% 1.55/1.25 binintersect: $i > $i > $i ).
% 1.55/1.25
% 1.55/1.25 thf(binintersectEL_type,type,
% 1.55/1.25 binintersectEL: $o ).
% 1.55/1.25
% 1.55/1.25 thf(binintersectEL,definition,
% 1.55/1.25 ( binintersectEL
% 1.55/1.25 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.55/1.25 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.55/1.25 => ( in @ Xx @ A ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(woz13rule1,conjecture,
% 1.55/1.25 ( subsetI1
% 1.55/1.25 => ( subsetE
% 1.55/1.25 => ( binintersectEL
% 1.55/1.25 => ! [A: $i,X: $i] :
% 1.55/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.55/1.25 => ! [Y: $i] :
% 1.55/1.25 ( ( in @ Y @ ( powerset @ A ) )
% 1.55/1.25 => ! [Z: $i] :
% 1.55/1.25 ( ( in @ Z @ ( powerset @ A ) )
% 1.55/1.25 => ( ( subset @ X @ Z )
% 1.55/1.25 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ).
% 1.55/1.25 ------------------------
% 1.55/1.27 % (29280)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_29178 for (3000ds/275Mi)
% 1.55/1.27 % (29279)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_29178 for (3000ds/2Mi)
% 1.55/1.27 % (29279)Instruction limit reached!
% 1.55/1.27 % (29279)------------------------------
% 1.55/1.27 % (29279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (29279)Termination reason: Unknown
% 1.55/1.27 % (29279)Termination phase: Saturation
% 1.55/1.27
% 1.55/1.27 % (29279)Memory used [KB]: 1023
% 1.55/1.27 % (29279)Time elapsed: 0.002 s
% 1.55/1.27 % (29279)Instructions burned: 3 (million)
% 1.55/1.27 % (29279)------------------------------
% 1.55/1.27 % (29279)------------------------------
% 1.55/1.27 % (29280)First to succeed.
% 1.55/1.27 % (29280)Refutation found. Thanks to Tanya!
% 1.55/1.27 % SZS status Theorem for DTF2THF_29178
% 1.55/1.27 % SZS output start Proof for DTF2THF_29178
% 1.55/1.27 thf(func_def_0, type, in: $i > $i > $o).
% 1.55/1.27 thf(func_def_1, type, powerset: $i > $i).
% 1.55/1.27 thf(func_def_2, type, subset: $i > $i > $o).
% 1.55/1.27 thf(func_def_6, type, binintersect: $i > $i > $i).
% 1.55/1.27 thf(func_def_13, type, sK3: $i > $i > $i).
% 1.55/1.27 thf(f102,plain,(
% 1.55/1.27 $false),
% 1.55/1.27 inference(subsumption_resolution,[status(thm)],[f100,f52])).
% 1.55/1.27 thf(f52,plain,(
% 1.55/1.27 ((subset @ sK10 @ sK12) = $true)),
% 1.55/1.27 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.27 thf(f38,plain,(
% 1.55/1.27 (binintersectEL = $true) & (subsetI1 = $true) & (($true = (in @ sK10 @ (powerset @ sK9))) & ((((in @ sK12 @ (powerset @ sK9)) = $true) & ((subset @ (binintersect @ sK10 @ sK11) @ sK12) != $true) & ((subset @ sK10 @ sK12) = $true)) & ((in @ sK11 @ (powerset @ sK9)) = $true))) & (subsetE = $true)),
% 1.55/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f34,f37,f36,f35])).
% 1.55/1.27 thf(f35,plain,(
% 1.55/1.27 ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((subset @ X1 @ X3) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))) => (($true = (in @ sK10 @ (powerset @ sK9))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ sK9)) = $true) & ($true != (subset @ (binintersect @ sK10 @ X2) @ X3)) & ((subset @ sK10 @ X3) = $true)) & ((in @ X2 @ (powerset @ sK9)) = $true)))),
% 1.55/1.27 introduced(definition,[],[choice_axiom])).
% 1.55/1.27 thf(f36,plain,(
% 1.55/1.27 ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ sK9)) = $true) & ($true != (subset @ (binintersect @ sK10 @ X2) @ X3)) & ((subset @ sK10 @ X3) = $true)) & ((in @ X2 @ (powerset @ sK9)) = $true)) => (? [X3 : $i] : (((in @ X3 @ (powerset @ sK9)) = $true) & ($true != (subset @ (binintersect @ sK10 @ sK11) @ X3)) & ((subset @ sK10 @ X3) = $true)) & ((in @ sK11 @ (powerset @ sK9)) = $true))),
% 1.55/1.27 introduced(definition,[],[choice_axiom])).
% 1.55/1.27 thf(f37,plain,(
% 1.55/1.27 ? [X3 : $i] : (((in @ X3 @ (powerset @ sK9)) = $true) & ($true != (subset @ (binintersect @ sK10 @ sK11) @ X3)) & ((subset @ sK10 @ X3) = $true)) => (((in @ sK12 @ (powerset @ sK9)) = $true) & ((subset @ (binintersect @ sK10 @ sK11) @ sK12) != $true) & ((subset @ sK10 @ sK12) = $true))),
% 1.55/1.27 introduced(definition,[],[choice_axiom])).
% 1.55/1.27 thf(f34,plain,(
% 1.55/1.27 (binintersectEL = $true) & (subsetI1 = $true) & ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((subset @ X1 @ X3) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))) & (subsetE = $true)),
% 1.55/1.27 inference(rectify,[status(thm)],[f16])).
% 1.55/1.27 thf(f16,plain,(
% 1.55/1.27 (binintersectEL = $true) & (subsetI1 = $true) & ? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ (powerset @ X1))) & ($true != (subset @ (binintersect @ X0 @ X2) @ X3)) & ((subset @ X0 @ X3) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true))) & (subsetE = $true)),
% 1.55/1.27 inference(flattening,[status(thm)],[f15])).
% 1.55/1.27 thf(f15,plain,(
% 1.55/1.27 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((($true != (subset @ (binintersect @ X0 @ X2) @ X3)) & ((subset @ X0 @ X3) = $true)) & ($true = (in @ X3 @ (powerset @ X1)))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (binintersectEL = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 1.55/1.27 inference(ennf_transformation,[status(thm)],[f8])).
% 1.55/1.27 thf(f8,plain,(
% 1.55/1.27 ~((subsetI1 = $true) => ((subsetE = $true) => ((binintersectEL = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ (powerset @ X1))) => (((subset @ X0 @ X3) = $true) => ($true = (subset @ (binintersect @ X0 @ X2) @ X3)))))))))),
% 1.55/1.27 inference(fool_elimination,[status(thm)],[f7])).
% 1.55/1.27 thf(f7,plain,(
% 1.55/1.27 ~(subsetI1 => (subsetE => (binintersectEL => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X0 @ X3) => (subset @ (binintersect @ X0 @ X2) @ X3))))))))),
% 1.55/1.27 inference(rectify,[status(thm)],[f5])).
% 1.55/1.27 thf(f5,negated_conjecture,(
% 1.55/1.27 ~(subsetI1 => (subsetE => (binintersectEL => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ((subset @ X3 @ X5) => (subset @ (binintersect @ X3 @ X4) @ X5))))))))),
% 1.55/1.27 inference(negated_conjecture,[status(cth)],[f4])).
% 1.55/1.27 thf(f4,conjecture,(
% 1.55/1.27 subsetI1 => (subsetE => (binintersectEL => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ((subset @ X3 @ X5) => (subset @ (binintersect @ X3 @ X4) @ X5)))))))),
% 1.55/1.27 file('/export/starexec/sandbox/tmp/tmp.Tl5hrvA7SV/DTF2THF_29178.p',woz13rule1)).
% 1.55/1.27 thf(f100,plain,(
% 1.55/1.27 ((subset @ sK10 @ sK12) != $true)),
% 1.55/1.27 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.55/1.27 thf(f99,plain,(
% 1.55/1.27 ((subset @ sK10 @ sK12) != $true) | ($true != $true)),
% 1.55/1.27 inference(superposition,[status(thm)],[f53,f93])).
% 1.55/1.27 thf(f93,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X2) = $true) | ((subset @ X0 @ X2) != $true)) )),
% 1.55/1.27 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.55/1.27 thf(f92,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((subset @ (binintersect @ X0 @ X1) @ X2) = $true) | ((subset @ X0 @ X2) != $true)) )),
% 1.55/1.27 inference(duplicate_literal_removal,[status(thm)],[f89])).
% 1.55/1.27 thf(f89,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X2) = $true) | ($true != $true) | ((subset @ (binintersect @ X0 @ X1) @ X2) = $true) | ((subset @ X0 @ X2) != $true)) )),
% 1.55/1.27 inference(superposition,[status(thm)],[f80,f77])).
% 1.55/1.27 thf(f77,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK3 @ (binintersect @ X0 @ X1) @ X2) @ X0) = $true) | ((subset @ (binintersect @ X0 @ X1) @ X2) = $true)) )),
% 1.55/1.27 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.55/1.27 thf(f76,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK3 @ (binintersect @ X0 @ X1) @ X2) @ X0) = $true) | ($true != $true) | ((subset @ (binintersect @ X0 @ X1) @ X2) = $true)) )),
% 1.55/1.27 inference(superposition,[status(thm)],[f72,f70])).
% 1.55/1.27 thf(f70,plain,(
% 1.55/1.27 ( ! [X0 : $i,X1 : $i] : (((in @ (sK3 @ X1 @ X0) @ X1) = $true) | ((subset @ X1 @ X0) = $true)) )),
% 1.55/1.27 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.55/1.27 thf(f63,plain,(
% 1.55/1.27 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ($true != $true) | ((in @ (sK3 @ X1 @ X0) @ X1) = $true)) )),
% 1.55/1.27 inference(definition_unfolding,[status(thm)],[f45,f56])).
% 1.55/1.27 thf(f56,plain,(
% 1.55/1.27 (subsetI1 = $true)),
% 1.55/1.27 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.27 thf(f45,plain,(
% 1.55/1.27 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ((in @ (sK3 @ X1 @ X0) @ X1) = $true) | (subsetI1 != $true)) )),
% 1.55/1.27 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.27 thf(f29,plain,(
% 1.55/1.27 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | (((in @ (sK3 @ X1 @ X0) @ X0) != $true) & ((in @ (sK3 @ X1 @ X0) @ X1) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != (subset @ sK5 @ sK4)) & ! [X5 : $i] : (((in @ X5 @ sK4) = $true) | ((in @ X5 @ sK5) != $true))))),
% 1.55/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f26,f28,f27])).
% 1.55/1.27 thf(f27,plain,(
% 1.55/1.27 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) => (((in @ (sK3 @ X1 @ X0) @ X0) != $true) & ((in @ (sK3 @ X1 @ X0) @ X1) = $true)))),
% 1.55/1.27 introduced(definition,[],[choice_axiom])).
% 1.55/1.27 thf(f28,plain,(
% 1.55/1.27 ? [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) != $true) & ! [X5 : $i] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true))) => (($true != (subset @ sK5 @ sK4)) & ! [X5 : $i] : (((in @ X5 @ sK4) = $true) | ((in @ X5 @ sK5) != $true)))),
% 1.55/1.27 introduced(definition,[],[choice_axiom])).
% 1.55/1.27 thf(f26,plain,(
% 1.55/1.27 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) != $true) & ! [X5 : $i] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true))))),
% 1.55/1.27 inference(rectify,[status(thm)],[f25])).
% 1.55/1.27 thf(f25,plain,(
% 1.55/1.27 (! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))))),
% 1.55/1.27 inference(nnf_transformation,[status(thm)],[f19])).
% 1.55/1.27 thf(f19,plain,(
% 1.55/1.27 ! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) <=> (subsetI1 = $true)),
% 1.55/1.27 inference(ennf_transformation,[status(thm)],[f12])).
% 1.55/1.27 thf(f12,plain,(
% 1.55/1.27 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true))),
% 1.55/1.27 inference(fool_elimination,[status(thm)],[f11])).
% 1.55/1.27 thf(f11,plain,(
% 1.55/1.27 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.55/1.27 inference(rectify,[status(thm)],[f1])).
% 1.55/1.27 thf(f1,axiom,(
% 1.55/1.27 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.55/1.27 file('/export/starexec/sandbox/tmp/tmp.Tl5hrvA7SV/DTF2THF_29178.p',subsetI1)).
% 1.55/1.27 thf(f72,plain,(
% 1.55/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (binintersect @ X3 @ X5)) != $true) | ($true = (in @ X4 @ X3))) )),
% 1.55/1.27 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.55/1.27 thf(f68,plain,(
% 1.55/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X4 @ (binintersect @ X3 @ X5)) != $true) | ($true = (in @ X4 @ X3))) )),
% 1.55/1.27 inference(definition_unfolding,[status(thm)],[f47,f57])).
% 1.55/1.27 thf(f57,plain,(
% 1.55/1.27 (binintersectEL = $true)),
% 1.55/1.27 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.27 thf(f47,plain,(
% 1.55/1.27 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ X3)) | ((in @ X4 @ (binintersect @ X3 @ X5)) != $true) | (binintersectEL != $true)) )),
% 1.55/1.27 inference(cnf_transformation,[status(thm)],[f33])).
% 1.55/1.27 thf(f33,plain,(
% 1.55/1.27 ((binintersectEL = $true) | (((in @ sK7 @ sK6) != $true) & ((in @ sK7 @ (binintersect @ sK6 @ sK8)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ X3)) | ((in @ X4 @ (binintersect @ X3 @ X5)) != $true)) | (binintersectEL != $true))),
% 1.55/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f31,f32])).
% 1.55/1.27 thf(f32,plain,(
% 1.55/1.27 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) != $true) & ($true = (in @ X1 @ (binintersect @ X0 @ X2)))) => (((in @ sK7 @ sK6) != $true) & ((in @ sK7 @ (binintersect @ sK6 @ sK8)) = $true))),
% 1.55/1.27 introduced(definition,[],[choice_axiom])).
% 1.55/1.27 thf(f31,plain,(
% 1.55/1.27 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) != $true) & ($true = (in @ X1 @ (binintersect @ X0 @ X2))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ X3)) | ((in @ X4 @ (binintersect @ X3 @ X5)) != $true)) | (binintersectEL != $true))),
% 1.55/1.27 inference(rectify,[status(thm)],[f30])).
% 1.55/1.27 thf(f30,plain,(
% 1.55/1.27 ((binintersectEL = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ (binintersect @ X0 @ X1)) = $true))) & (! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) | (binintersectEL != $true))),
% 1.55/1.27 inference(nnf_transformation,[status(thm)],[f20])).
% 1.55/1.27 thf(f20,plain,(
% 1.55/1.27 (binintersectEL = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true))),
% 1.55/1.27 inference(ennf_transformation,[status(thm)],[f10])).
% 1.55/1.27 thf(f10,plain,(
% 1.55/1.27 (binintersectEL = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) => ((in @ X2 @ X0) = $true))),
% 1.55/1.27 inference(fool_elimination,[status(thm)],[f9])).
% 1.55/1.27 thf(f9,plain,(
% 1.55/1.27 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.55/1.27 inference(rectify,[status(thm)],[f3])).
% 1.55/1.27 thf(f3,axiom,(
% 1.55/1.27 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 1.55/1.27 file('/export/starexec/sandbox/tmp/tmp.Tl5hrvA7SV/DTF2THF_29178.p',binintersectEL)).
% 1.55/1.27 thf(f80,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK3 @ X0 @ X1) @ X2) != $true) | ((subset @ X2 @ X1) != $true) | ((subset @ X0 @ X1) = $true)) )),
% 1.55/1.27 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.55/1.27 thf(f79,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK3 @ X0 @ X1) @ X2) != $true) | ((subset @ X2 @ X1) != $true) | ($true != $true)) )),
% 1.55/1.27 inference(superposition,[status(thm)],[f69,f71])).
% 1.55/1.27 thf(f71,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X2) = $true) | ((in @ X1 @ X0) != $true) | ((subset @ X0 @ X2) != $true)) )),
% 1.55/1.27 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.55/1.27 thf(f58,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) = $true) | ((subset @ X0 @ X2) != $true) | ($true != $true)) )),
% 1.55/1.27 inference(definition_unfolding,[status(thm)],[f42,f50])).
% 1.55/1.27 thf(f50,plain,(
% 1.55/1.27 (subsetE = $true)),
% 1.55/1.27 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.27 thf(f42,plain,(
% 1.55/1.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X0 @ X2) != $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) = $true) | (subsetE != $true)) )),
% 1.55/1.27 inference(cnf_transformation,[status(thm)],[f24])).
% 1.55/1.27 thf(f24,plain,(
% 1.55/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) != $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) = $true)) | (subsetE != $true)) & ((subsetE = $true) | (((subset @ sK0 @ sK2) = $true) & ((in @ sK1 @ sK0) = $true) & ((in @ sK1 @ sK2) != $true)))),
% 1.55/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f22,f23])).
% 1.55/1.27 thf(f23,plain,(
% 1.55/1.27 ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) & ($true = (in @ X4 @ X3)) & ($true != (in @ X4 @ X5))) => (((subset @ sK0 @ sK2) = $true) & ((in @ sK1 @ sK0) = $true) & ((in @ sK1 @ sK2) != $true))),
% 1.55/1.27 introduced(definition,[],[choice_axiom])).
% 1.55/1.27 thf(f22,plain,(
% 1.55/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) != $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) & ($true = (in @ X4 @ X3)) & ($true != (in @ X4 @ X5))))),
% 1.55/1.27 inference(rectify,[status(thm)],[f21])).
% 1.55/1.27 thf(f21,plain,(
% 1.55/1.27 (! [X1 : $i,X2 : $i,X0 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((subset @ X1 @ X0) = $true) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)))),
% 1.55/1.27 inference(nnf_transformation,[status(thm)],[f18])).
% 1.55/1.27 thf(f18,plain,(
% 1.55/1.27 ! [X1 : $i,X2 : $i,X0 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) <=> (subsetE = $true)),
% 1.55/1.27 inference(flattening,[status(thm)],[f17])).
% 1.55/1.27 thf(f17,plain,(
% 1.55/1.27 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) | ((subset @ X1 @ X0) != $true)) <=> (subsetE = $true)),
% 1.55/1.27 inference(ennf_transformation,[status(thm)],[f14])).
% 1.55/1.27 thf(f14,plain,(
% 1.55/1.27 ! [X1 : $i,X0 : $i,X2 : $i] : (((subset @ X1 @ X0) = $true) => (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true))) <=> (subsetE = $true)),
% 1.55/1.27 inference(fool_elimination,[status(thm)],[f13])).
% 1.55/1.27 thf(f13,plain,(
% 1.55/1.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = subsetE)),
% 1.55/1.27 inference(rectify,[status(thm)],[f2])).
% 1.55/1.27 thf(f2,axiom,(
% 1.55/1.27 (! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.55/1.27 file('/export/starexec/sandbox/tmp/tmp.Tl5hrvA7SV/DTF2THF_29178.p',subsetE)).
% 1.55/1.27 thf(f69,plain,(
% 1.55/1.27 ( ! [X0 : $i,X1 : $i] : (((in @ (sK3 @ X1 @ X0) @ X0) != $true) | ((subset @ X1 @ X0) = $true)) )),
% 1.55/1.27 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.55/1.27 thf(f62,plain,(
% 1.55/1.27 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ((in @ (sK3 @ X1 @ X0) @ X0) != $true) | ($true != $true)) )),
% 1.55/1.27 inference(definition_unfolding,[status(thm)],[f46,f56])).
% 1.55/1.27 thf(f46,plain,(
% 1.55/1.27 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ((in @ (sK3 @ X1 @ X0) @ X0) != $true) | (subsetI1 != $true)) )),
% 1.55/1.27 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.27 thf(f53,plain,(
% 1.55/1.27 ((subset @ (binintersect @ sK10 @ sK11) @ sK12) != $true)),
% 1.55/1.27 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.27 % SZS output end Proof for DTF2THF_29178
% 1.55/1.27 % (29280)------------------------------
% 1.55/1.27 % (29280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (29280)Termination reason: Refutation
% 1.55/1.27
% 1.55/1.27 % (29280)Memory used [KB]: 5628
% 1.55/1.27 % (29280)Time elapsed: 0.007 s
% 1.55/1.27 % (29280)Instructions burned: 11 (million)
% 1.55/1.27 % (29280)------------------------------
% 1.55/1.27 % (29280)------------------------------
% 1.55/1.27 % (29274)Success in time 0.003 s
%------------------------------------------------------------------------------