%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU593^2 : 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 : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:29 AM UTC 2026
% Result : Theorem 1.71s 1.37s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 92 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 1069 ( 341 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 1101 ( 157 ~; 139 |; 76 &; 662 @)
% ( 12 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 21 con; 0-2 aty)
% Number of variables : 231 ( 0 ^; 185 !; 46 ?; 231 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
binintersect: $i > $i > $i ).
thf(func_def_24,type,
sK9: $i > $i > $i ).
thf(f299,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f297,f61]) ).
thf(f61,plain,
( ( subset @ sK2 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( binintersectLsub = $true )
& ( subsetI1 = $true )
& ( setextsub = $true )
& ( ( binintersect @ sK2 @ sK3 )
!= sK2 )
& ( ( subset @ sK2 @ sK3 )
= $true )
& ( binintersectI = $true )
& ( subsetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f24,f36]) ).
thf(f36,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
=> ( ( ( binintersect @ sK2 @ sK3 )
!= sK2 )
& ( ( subset @ sK2 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( binintersectLsub = $true )
& ( subsetI1 = $true )
& ( setextsub = $true )
& ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
& ( binintersectI = $true )
& ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
& ( binintersectLsub = $true )
& ( binintersectI = $true )
& ( setextsub = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( ( subsetI1 = $true )
=> ( ( subsetE = $true )
=> ( ( setextsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectLsub = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectLsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectLsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( subsetI1
=> ( subsetE
=> ( setextsub
=> ( binintersectI
=> ( binintersectLsub
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',binintersectSubset2) ).
thf(f297,plain,
( ( subset @ sK2 @ sK3 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f282]) ).
thf(f282,plain,
( ( sK2 != sK2 )
| ( ( subset @ sK2 @ sK3 )
!= $true ) ),
inference(superposition,[status(thm)],[f62,f274]) ).
thf(f274,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f270,f100]) ).
thf(f100,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f75,f65]) ).
thf(f65,plain,
binintersectLsub = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f75,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ( ( subset @ ( binintersect @ sK11 @ sK10 ) @ sK11 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f48,f49]) ).
thf(f49,plain,
( ? [X2: $i,X3: $i] :
( ( subset @ ( binintersect @ X3 @ X2 ) @ X3 )
!= $true )
=> ( ( subset @ ( binintersect @ sK11 @ sK10 ) @ sK11 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f48,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X2: $i,X3: $i] :
( ( subset @ ( binintersect @ X3 @ X2 ) @ X3 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
<=> ( binintersectLsub = $true ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= binintersectLsub ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: $i,X0: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= binintersectLsub ),
file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',binintersectLsub) ).
thf(f270,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( binintersect @ X0 @ X1 )
= X0 )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f264]) ).
thf(f264,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true )
| ( ( binintersect @ X0 @ X1 )
= X0 ) ),
inference(superposition,[status(thm)],[f99,f260]) ).
thf(f260,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f259]) ).
thf(f259,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X0 @ ( binintersect @ X0 @ X1 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f254]) ).
thf(f254,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( subset @ X0 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f184,f101]) ).
thf(f101,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
= $true )
| ( ( subset @ X3 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
= $true )
| ( ( subset @ X3 @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f71,f64]) ).
thf(f64,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f71,plain,
! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( subsetI1 = $true )
| ( ( $true
!= ( subset @ sK7 @ sK8 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ sK7 )
!= $true )
| ( ( in @ X2 @ sK8 )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ( ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
= $true )
& ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
!= $true ) ) )
| ( subsetI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f43,f45,f44]) ).
thf(f44,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) )
=> ( ( $true
!= ( subset @ sK7 @ sK8 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ sK7 )
!= $true )
| ( ( in @ X2 @ sK8 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( $true
!= ( in @ X5 @ X4 ) ) )
=> ( ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
= $true )
& ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f43,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ? [X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( $true
!= ( in @ X5 @ X4 ) ) ) )
| ( subsetI1 != $true ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
| ( subsetI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,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.Nf5zMavudr/DTF2THF_8520.p',subsetI1) ).
thf(f184,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X0 )
!= $true )
| ( $true
!= ( subset @ X2 @ X1 ) )
| ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f183]) ).
thf(f183,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( subset @ X2 @ X1 ) )
| ( $true != $true )
| ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X0 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f178]) ).
thf(f178,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( $true
!= ( subset @ X2 @ X1 ) )
| ( $true != $true )
| ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f143,f101]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X3 ) )
| ( $true
!= ( subset @ X3 @ X1 ) )
| ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X0 )
!= $true )
| ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X0 )
!= $true )
| ( $true
!= ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X3 ) )
| ( $true
!= ( subset @ X3 @ X1 ) )
| ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f124,f102]) ).
thf(f102,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ X5 ) )
| ( ( in @ X3 @ X4 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
= ( in @ X3 @ X5 ) )
| ( ( subset @ X4 @ X5 )
!= $true )
| ( ( in @ X3 @ X4 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f66,f59]) ).
thf(f59,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f66,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( $true
= ( in @ X3 @ X5 ) )
| ( ( subset @ X4 @ X5 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( subsetE = $true )
| ( ( $true
= ( in @ sK4 @ sK5 ) )
& ( ( in @ sK4 @ sK6 )
!= $true )
& ( ( subset @ sK5 @ sK6 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( $true
= ( in @ X3 @ X5 ) )
| ( ( subset @ X4 @ X5 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f39,f40]) ).
thf(f40,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( subset @ X1 @ X2 ) ) )
=> ( ( $true
= ( in @ sK4 @ sK5 ) )
& ( ( in @ sK4 @ sK6 )
!= $true )
& ( ( subset @ sK5 @ sK6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( subset @ X1 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( $true
= ( in @ X3 @ X5 ) )
| ( ( subset @ X4 @ X5 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( subset @ X1 @ X2 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X1 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( $true
= ( in @ X0 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( subsetE
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',subsetE) ).
thf(f124,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X1 )
!= $true )
| ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X0 )
!= $true )
| ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f98,f103]) ).
thf(f103,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f79,f60]) ).
thf(f60,plain,
binintersectI = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f79,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( binintersectI != $true ) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ( ( ( in @ sK13 @ ( binintersect @ sK12 @ sK14 ) )
!= $true )
& ( $true
= ( in @ sK13 @ sK12 ) )
& ( $true
= ( in @ sK13 @ sK14 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f52,f53]) ).
thf(f53,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ X3 @ X5 ) ) )
& ( ( in @ X4 @ X3 )
= $true )
& ( $true
= ( in @ X4 @ X5 ) ) )
=> ( ( ( in @ sK13 @ ( binintersect @ sK12 @ sK14 ) )
!= $true )
& ( $true
= ( in @ sK13 @ sK12 ) )
& ( $true
= ( in @ sK13 @ sK14 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f52,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( binintersect @ X3 @ X5 ) ) )
& ( ( in @ X4 @ X3 )
= $true )
& ( $true
= ( in @ X4 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
!= $true )
& ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
<=> ( binintersectI = $true ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( binintersectI = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true ) ) )
<=> ( binintersectI = $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( binintersectI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( binintersectI
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',binintersectI) ).
thf(f98,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
!= $true )
| ( ( subset @ X3 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f70,f64]) ).
thf(f70,plain,
! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
!= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f99,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( subset @ X2 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( X2 = X3 )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( ( subset @ X2 @ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f55,f63]) ).
thf(f63,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f55,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 )
| ( setextsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( setextsub = $true )
| ( ( ( subset @ sK0 @ sK1 )
= $true )
& ( ( subset @ sK1 @ sK0 )
= $true )
& ( sK1 != sK0 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 ) )
| ( setextsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f33,f34]) ).
thf(f34,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 ) )
=> ( ( ( subset @ sK0 @ sK1 )
= $true )
& ( ( subset @ sK1 @ sK0 )
= $true )
& ( sK1 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 ) )
| ( setextsub != $true ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 ) )
| ( setextsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 ) ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( ( subset @ X0 @ X1 )
= $true )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( X0 = X1 ) ) )
= setextsub ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) )
= setextsub ),
file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',setextsub) ).
thf(f62,plain,
( ( binintersect @ sK2 @ sK3 )
!= sK2 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU593^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:27:57 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU593^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! B:i.subset A B -> binintersect A B = A)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC095l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 16 ( 6 unt; 9 typ; 6 def)
% 0.30/0.46 % Number of atoms : 32 ( 8 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 7 ( 4 avg)
% 0.30/0.46 % Number of connectives : 50 ( 0 ~; 0 |; 0 &; 36 @)
% 0.30/0.46 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 11 ( 2 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 10 ( 9 usr; 5 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 18 ( 3 ^; 15 !; 0 ?; 18 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=363
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(subset_type,type,
% 0.30/0.46 subset: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1_type,type,
% 0.30/0.46 subsetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1,definition,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE_type,type,
% 0.30/0.46 subsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE,definition,
% 0.30/0.46 ( subsetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextsub_type,type,
% 0.30/0.46 setextsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextsub,definition,
% 0.30/0.46 ( setextsub
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( subset @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersect_type,type,
% 0.30/0.46 binintersect: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binintersect,definition,
% 0.30/0.46 ( binintersect
% 0.30/0.46 = ( ^ [A: $i,B: $i] :
% 0.30/0.46 ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI_type,type,
% 0.30/0.46 binintersectI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI,definition,
% 0.30/0.46 ( binintersectI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectLsub_type,type,
% 0.30/0.46 binintersectLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectLsub,definition,
% 0.30/0.46 ( binintersectLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset2,conjecture,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 => ( subsetE
% 0.30/0.46 => ( setextsub
% 0.30/0.46 => ( binintersectI
% 0.30/0.46 => ( binintersectLsub
% 0.30/0.46 => ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = A ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.71/1.31 ---- Embedded in THF ---
% 1.71/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.31 %%% Generated on Tue Feb 24 12:27:57 EST 2026
% 1.71/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.31 %%% Logic specification used:
% 1.71/1.31 %%% thf(spec, logic, $$dhol).
% 1.71/1.31
% 1.71/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2DTF8520.p
% See solution above
% 1.71/1.31 ------------------------
% 1.71/1.32 ---- Cleaned THF ---
% 1.71/1.32 thf(in_type,type,
% 1.71/1.32 in: $i > $i > $o ).
% 1.71/1.32
% 1.71/1.32 thf(dsetconstr_type,type,
% 1.71/1.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.71/1.32
% 1.71/1.32 thf(subset_type,type,
% 1.71/1.32 subset: $i > $i > $o ).
% 1.71/1.32
% 1.71/1.32 thf(subsetI1_type,type,
% 1.71/1.32 subsetI1: $o ).
% 1.71/1.32
% 1.71/1.32 thf(subsetI1,definition,
% 1.71/1.32 ( subsetI1
% 1.71/1.32 = ( ! [A: $i,B: $i] :
% 1.71/1.32 ( ! [Xx: $i] :
% 1.71/1.32 ( ( in @ Xx @ A )
% 1.71/1.32 => ( in @ Xx @ B ) )
% 1.71/1.32 => ( subset @ A @ B ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(subsetE_type,type,
% 1.71/1.32 subsetE: $o ).
% 1.71/1.32
% 1.71/1.32 thf(subsetE,definition,
% 1.71/1.32 ( subsetE
% 1.71/1.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.71/1.32 ( ( subset @ A @ B )
% 1.71/1.32 => ( ( in @ Xx @ A )
% 1.71/1.32 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(setextsub_type,type,
% 1.71/1.32 setextsub: $o ).
% 1.71/1.32
% 1.71/1.32 thf(setextsub,definition,
% 1.71/1.32 ( setextsub
% 1.71/1.32 = ( ! [A: $i,B: $i] :
% 1.71/1.32 ( ( subset @ A @ B )
% 1.71/1.32 => ( ( subset @ B @ A )
% 1.71/1.32 => ( A = B ) ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(binintersect_type,type,
% 1.71/1.32 binintersect: $i > $i > $i ).
% 1.71/1.32
% 1.71/1.32 thf(binintersect,definition,
% 1.71/1.32 ( binintersect
% 1.71/1.32 = ( ^ [A: $i,B: $i] :
% 1.71/1.32 ( dsetconstr @ A
% 1.71/1.32 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(binintersectI_type,type,
% 1.71/1.32 binintersectI: $o ).
% 1.71/1.32
% 1.71/1.32 thf(binintersectI,definition,
% 1.71/1.32 ( binintersectI
% 1.71/1.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.71/1.32 ( ( in @ Xx @ A )
% 1.71/1.32 => ( ( in @ Xx @ B )
% 1.71/1.32 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(binintersectLsub_type,type,
% 1.71/1.32 binintersectLsub: $o ).
% 1.71/1.32
% 1.71/1.32 thf(binintersectLsub,definition,
% 1.71/1.32 ( binintersectLsub
% 1.71/1.32 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(binintersectSubset2,conjecture,
% 1.71/1.32 ( subsetI1
% 1.71/1.32 => ( subsetE
% 1.71/1.32 => ( setextsub
% 1.71/1.32 => ( binintersectI
% 1.71/1.32 => ( binintersectLsub
% 1.71/1.32 => ! [A: $i,B: $i] :
% 1.71/1.32 ( ( subset @ A @ B )
% 1.71/1.32 => ( ( binintersect @ A @ B )
% 1.71/1.32 = A ) ) ) ) ) ) ) ).
% 1.71/1.32 ------------------------
% 1.71/1.33 % (8713)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8520 for (2999ds/2Mi)
% 1.71/1.33 % (8713)Instruction limit reached!
% 1.71/1.33 % (8713)------------------------------
% 1.71/1.33 % (8713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.33 % (8713)Termination reason: Unknown
% 1.71/1.33 % (8713)Termination phase: Function definition elimination
% 1.71/1.33
% 1.71/1.33 % (8713)Memory used [KB]: 1023
% 1.71/1.33 % (8713)Time elapsed: 0.002 s
% 1.71/1.33 % (8713)Instructions burned: 3 (million)
% 1.71/1.33 % (8713)------------------------------
% 1.71/1.33 % (8713)------------------------------
% 1.71/1.33 % (8710)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8520 for (2999ds/183Mi)
% 1.71/1.34 % (8711)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_8520 for (2999ds/4Mi)
% 1.71/1.34 % (8715)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_8520 for (2999ds/275Mi)
% 1.71/1.34 % (8712)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_8520 for (2999ds/27Mi)
% 1.71/1.34 % (8716)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8520 for (2999ds/18Mi)
% 1.71/1.34 % (8717)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8520 for (2999ds/3Mi)
% 1.71/1.34 % (8711)Instruction limit reached!
% 1.71/1.34 % (8711)------------------------------
% 1.71/1.34 % (8711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (8711)Termination reason: Unknown
% 1.71/1.34 % (8711)Termination phase: Saturation
% 1.71/1.34
% 1.71/1.34 % (8711)Memory used [KB]: 5500
% 1.71/1.34 % (8711)Time elapsed: 0.005 s
% 1.71/1.34 % (8711)Instructions burned: 5 (million)
% 1.71/1.34 % (8711)------------------------------
% 1.71/1.34 % (8711)------------------------------
% 1.71/1.34 % (8717)Instruction limit reached!
% 1.71/1.34 % (8717)------------------------------
% 1.71/1.34 % (8717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (8717)Termination reason: Unknown
% 1.71/1.34 % (8717)Termination phase: Saturation
% 1.71/1.34
% 1.71/1.34 % (8717)Memory used [KB]: 1023
% 1.71/1.34 % (8717)Time elapsed: 0.002 s
% 1.71/1.34 % (8717)Instructions burned: 4 (million)
% 1.71/1.34 % (8717)------------------------------
% 1.71/1.34 % (8717)------------------------------
% 1.71/1.35 % (8714)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_8520 for (2999ds/2Mi)
% 1.71/1.35 % (8714)Instruction limit reached!
% 1.71/1.35 % (8714)------------------------------
% 1.71/1.35 % (8714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.35 % (8714)Termination reason: Unknown
% 1.71/1.35 % (8714)Termination phase: Property scanning
% 1.71/1.35
% 1.71/1.35 % (8714)Memory used [KB]: 1023
% 1.71/1.35 % (8714)Time elapsed: 0.004 s
% 1.71/1.35 % (8714)Instructions burned: 2 (million)
% 1.71/1.35 % (8714)------------------------------
% 1.71/1.35 % (8714)------------------------------
% 1.71/1.35 % (8716)Instruction limit reached!
% 1.71/1.35 % (8716)------------------------------
% 1.71/1.35 % (8716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.35 % (8716)Termination reason: Unknown
% 1.71/1.35 % (8716)Termination phase: Saturation
% 1.71/1.35
% 1.71/1.35 % (8716)Memory used [KB]: 5628
% 1.71/1.35 % (8716)Time elapsed: 0.014 s
% 1.71/1.35 % (8716)Instructions burned: 18 (million)
% 1.71/1.35 % (8716)------------------------------
% 1.71/1.35 % (8716)------------------------------
% 1.71/1.35 % (8719)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_8520 for (2999ds/15Mi)
% 1.71/1.36 % (8712)Instruction limit reached!
% 1.71/1.36 % (8712)------------------------------
% 1.71/1.36 % (8712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.36 % (8712)Termination reason: Unknown
% 1.71/1.36 % (8712)Termination phase: Saturation
% 1.71/1.36
% 1.71/1.36 % (8712)Memory used [KB]: 5628
% 1.71/1.36 % (8712)Time elapsed: 0.019 s
% 1.71/1.36 % (8712)Instructions burned: 27 (million)
% 1.71/1.36 % (8712)------------------------------
% 1.71/1.36 % (8712)------------------------------
% 1.71/1.36 % (8719)Instruction limit reached!
% 1.71/1.36 % (8719)------------------------------
% 1.71/1.36 % (8719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.36 % (8719)Termination reason: Unknown
% 1.71/1.36 % (8719)Termination phase: Saturation
% 1.71/1.36
% 1.71/1.36 % (8719)Memory used [KB]: 5628
% 1.71/1.36 % (8719)Time elapsed: 0.006 s
% 1.71/1.36 % (8719)Instructions burned: 15 (million)
% 1.71/1.36 % (8719)------------------------------
% 1.71/1.36 % (8719)------------------------------
% 1.71/1.36 % (8718)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_8520 for (2999ds/37Mi)
% 1.71/1.36 % (8715)First to succeed.
% 1.71/1.37 % (8720)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8520 for (2999ds/3Mi)
% 1.71/1.37 % (8715)Refutation found. Thanks to Tanya!
% 1.71/1.37 % SZS status Theorem for DTF2THF_8520
% 1.71/1.37 % SZS output start Proof for DTF2THF_8520
% 1.71/1.37 thf(func_def_0, type, in: $i > $i > $o).
% 1.71/1.37 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.71/1.37 thf(func_def_2, type, subset: $i > $i > $o).
% 1.71/1.37 thf(func_def_7, type, binintersect: $i > $i > $i).
% 1.71/1.37 thf(func_def_24, type, sK9: $i > $i > $i).
% 1.71/1.37 thf(f299,plain,(
% 1.71/1.37 $false),
% 1.71/1.37 inference(subsumption_resolution,[status(thm)],[f297,f61])).
% 1.71/1.37 thf(f61,plain,(
% 1.71/1.37 ((subset @ sK2 @ sK3) = $true)),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f37])).
% 1.71/1.37 thf(f37,plain,(
% 1.71/1.37 (binintersectLsub = $true) & (subsetI1 = $true) & (setextsub = $true) & (((binintersect @ sK2 @ sK3) != sK2) & ((subset @ sK2 @ sK3) = $true)) & (binintersectI = $true) & (subsetE = $true)),
% 1.71/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f24,f36])).
% 1.71/1.37 thf(f36,plain,(
% 1.71/1.37 ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X0) & ((subset @ X0 @ X1) = $true)) => (((binintersect @ sK2 @ sK3) != sK2) & ((subset @ sK2 @ sK3) = $true))),
% 1.71/1.37 introduced(definition,[],[choice_axiom])).
% 1.71/1.37 thf(f24,plain,(
% 1.71/1.37 (binintersectLsub = $true) & (subsetI1 = $true) & (setextsub = $true) & ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X0) & ((subset @ X0 @ X1) = $true)) & (binintersectI = $true) & (subsetE = $true)),
% 1.71/1.37 inference(flattening,[status(thm)],[f23])).
% 1.71/1.37 thf(f23,plain,(
% 1.71/1.37 ((((? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X0) & ((subset @ X0 @ X1) = $true)) & (binintersectLsub = $true)) & (binintersectI = $true)) & (setextsub = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 1.71/1.37 inference(ennf_transformation,[status(thm)],[f20])).
% 1.71/1.37 thf(f20,plain,(
% 1.71/1.37 ~((subsetI1 = $true) => ((subsetE = $true) => ((setextsub = $true) => ((binintersectI = $true) => ((binintersectLsub = $true) => ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => ((binintersect @ X0 @ X1) = X0)))))))),
% 1.71/1.37 inference(fool_elimination,[status(thm)],[f19])).
% 1.71/1.37 thf(f19,plain,(
% 1.71/1.37 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectLsub => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0)))))))),
% 1.71/1.37 inference(rectify,[status(thm)],[f8])).
% 1.71/1.37 thf(f8,negated_conjecture,(
% 1.71/1.37 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectLsub => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0)))))))),
% 1.71/1.37 inference(negated_conjecture,[status(cth)],[f7])).
% 1.71/1.37 thf(f7,conjecture,(
% 1.71/1.37 subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectLsub => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0))))))),
% 1.71/1.37 file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',binintersectSubset2)).
% 1.71/1.37 thf(f297,plain,(
% 1.71/1.37 ((subset @ sK2 @ sK3) != $true)),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f282])).
% 1.71/1.37 thf(f282,plain,(
% 1.71/1.37 (sK2 != sK2) | ((subset @ sK2 @ sK3) != $true)),
% 1.71/1.37 inference(superposition,[status(thm)],[f62,f274])).
% 1.71/1.37 thf(f274,plain,(
% 1.71/1.37 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ((subset @ X0 @ X1) != $true)) )),
% 1.71/1.37 inference(subsumption_resolution,[status(thm)],[f270,f100])).
% 1.71/1.37 thf(f100,plain,(
% 1.71/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X1) = $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.71/1.37 thf(f92,plain,(
% 1.71/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | ($true != $true)) )),
% 1.71/1.37 inference(definition_unfolding,[status(thm)],[f75,f65])).
% 1.71/1.37 thf(f65,plain,(
% 1.71/1.37 (binintersectLsub = $true)),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f37])).
% 1.71/1.37 thf(f75,plain,(
% 1.71/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) )),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f50])).
% 1.71/1.37 thf(f50,plain,(
% 1.71/1.37 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ((subset @ (binintersect @ sK11 @ sK10) @ sK11) != $true))),
% 1.71/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f48,f49])).
% 1.71/1.37 thf(f49,plain,(
% 1.71/1.37 ? [X2 : $i,X3 : $i] : ((subset @ (binintersect @ X3 @ X2) @ X3) != $true) => ((subset @ (binintersect @ sK11 @ sK10) @ sK11) != $true)),
% 1.71/1.37 introduced(definition,[],[choice_axiom])).
% 1.71/1.37 thf(f48,plain,(
% 1.71/1.37 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X2 : $i,X3 : $i] : ((subset @ (binintersect @ X3 @ X2) @ X3) != $true))),
% 1.71/1.37 inference(rectify,[status(thm)],[f47])).
% 1.71/1.37 thf(f47,plain,(
% 1.71/1.37 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) != $true))),
% 1.71/1.37 inference(nnf_transformation,[status(thm)],[f16])).
% 1.71/1.37 thf(f16,plain,(
% 1.71/1.37 ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) <=> (binintersectLsub = $true)),
% 1.71/1.37 inference(fool_elimination,[status(thm)],[f15])).
% 1.71/1.37 thf(f15,plain,(
% 1.71/1.37 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X1) = binintersectLsub)),
% 1.71/1.37 inference(rectify,[status(thm)],[f6])).
% 1.71/1.37 thf(f6,axiom,(
% 1.71/1.37 (! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0) = binintersectLsub)),
% 1.71/1.37 file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',binintersectLsub)).
% 1.71/1.37 thf(f270,plain,(
% 1.71/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((binintersect @ X0 @ X1) = X0) | ((subset @ (binintersect @ X0 @ X1) @ X0) != $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f264])).
% 1.71/1.37 thf(f264,plain,(
% 1.71/1.37 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((subset @ X0 @ X1) != $true) | ((subset @ (binintersect @ X0 @ X1) @ X0) != $true) | ((binintersect @ X0 @ X1) = X0)) )),
% 1.71/1.37 inference(superposition,[status(thm)],[f99,f260])).
% 1.71/1.37 thf(f260,plain,(
% 1.71/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X0 @ X1) != $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f259])).
% 1.71/1.37 thf(f259,plain,(
% 1.71/1.37 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((subset @ X0 @ X1) != $true) | ((subset @ X0 @ (binintersect @ X0 @ X1)) = $true)) )),
% 1.71/1.37 inference(duplicate_literal_removal,[status(thm)],[f254])).
% 1.71/1.37 thf(f254,plain,(
% 1.71/1.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X0 @ X1) != $true) | ($true != $true)) )),
% 1.71/1.37 inference(superposition,[status(thm)],[f184,f101])).
% 1.71/1.37 thf(f101,plain,(
% 1.71/1.37 ( ! [X3 : $i,X4 : $i] : (((in @ (sK9 @ X4 @ X3) @ X3) = $true) | ((subset @ X3 @ X4) = $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.71/1.37 thf(f90,plain,(
% 1.71/1.37 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ (sK9 @ X4 @ X3) @ X3) = $true) | ((subset @ X3 @ X4) = $true)) )),
% 1.71/1.37 inference(definition_unfolding,[status(thm)],[f71,f64])).
% 1.71/1.37 thf(f64,plain,(
% 1.71/1.37 (subsetI1 = $true)),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f37])).
% 1.71/1.37 thf(f71,plain,(
% 1.71/1.37 ( ! [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | ((in @ (sK9 @ X4 @ X3) @ X3) = $true) | (subsetI1 != $true)) )),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f46])).
% 1.71/1.37 thf(f46,plain,(
% 1.71/1.37 ((subsetI1 = $true) | (($true != (subset @ sK7 @ sK8)) & ! [X2 : $i] : (((in @ X2 @ sK7) != $true) | ((in @ X2 @ sK8) = $true)))) & (! [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | (((in @ (sK9 @ X4 @ X3) @ X3) = $true) & ((in @ (sK9 @ X4 @ X3) @ X4) != $true))) | (subsetI1 != $true))),
% 1.71/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f43,f45,f44])).
% 1.71/1.37 thf(f44,plain,(
% 1.71/1.37 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true))) => (($true != (subset @ sK7 @ sK8)) & ! [X2 : $i] : (((in @ X2 @ sK7) != $true) | ((in @ X2 @ sK8) = $true)))),
% 1.71/1.37 introduced(definition,[],[choice_axiom])).
% 1.71/1.37 thf(f45,plain,(
% 1.71/1.37 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X3) = $true) & ($true != (in @ X5 @ X4))) => (((in @ (sK9 @ X4 @ X3) @ X3) = $true) & ((in @ (sK9 @ X4 @ X3) @ X4) != $true)))),
% 1.71/1.37 introduced(definition,[],[choice_axiom])).
% 1.71/1.37 thf(f43,plain,(
% 1.71/1.37 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)))) & (! [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | ? [X5 : $i] : (((in @ X5 @ X3) = $true) & ($true != (in @ X5 @ X4)))) | (subsetI1 != $true))),
% 1.71/1.37 inference(rectify,[status(thm)],[f42])).
% 1.71/1.37 thf(f42,plain,(
% 1.71/1.37 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)))) & (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) | (subsetI1 != $true))),
% 1.71/1.37 inference(nnf_transformation,[status(thm)],[f25])).
% 1.71/1.37 thf(f25,plain,(
% 1.71/1.37 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)))),
% 1.71/1.37 inference(ennf_transformation,[status(thm)],[f22])).
% 1.71/1.37 thf(f22,plain,(
% 1.71/1.37 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true))),
% 1.71/1.37 inference(fool_elimination,[status(thm)],[f21])).
% 1.71/1.37 thf(f21,plain,(
% 1.71/1.37 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.71/1.37 inference(rectify,[status(thm)],[f1])).
% 1.71/1.37 thf(f1,axiom,(
% 1.71/1.37 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.71/1.37 file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',subsetI1)).
% 1.71/1.37 thf(f184,plain,(
% 1.71/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X0) != $true) | ($true != (subset @ X2 @ X1)) | ((subset @ X2 @ (binintersect @ X0 @ X1)) = $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f183])).
% 1.71/1.37 thf(f183,plain,(
% 1.71/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (subset @ X2 @ X1)) | ($true != $true) | ((subset @ X2 @ (binintersect @ X0 @ X1)) = $true) | ((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X0) != $true)) )),
% 1.71/1.37 inference(duplicate_literal_removal,[status(thm)],[f178])).
% 1.71/1.37 thf(f178,plain,(
% 1.71/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X2 @ (binintersect @ X0 @ X1)) = $true) | ($true != (subset @ X2 @ X1)) | ($true != $true) | ((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X0) != $true)) )),
% 1.71/1.37 inference(superposition,[status(thm)],[f143,f101])).
% 1.71/1.37 thf(f143,plain,(
% 1.71/1.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X3)) | ($true != (subset @ X3 @ X1)) | ((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X0) != $true) | ((subset @ X2 @ (binintersect @ X0 @ X1)) = $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.71/1.37 thf(f139,plain,(
% 1.71/1.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X0) != $true) | ($true != (in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X3)) | ($true != (subset @ X3 @ X1)) | ((subset @ X2 @ (binintersect @ X0 @ X1)) = $true) | ($true != $true)) )),
% 1.71/1.37 inference(superposition,[status(thm)],[f124,f102])).
% 1.71/1.37 thf(f102,plain,(
% 1.71/1.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ X5)) | ((in @ X3 @ X4) != $true) | ((subset @ X4 @ X5) != $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.71/1.37 thf(f87,plain,(
% 1.71/1.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true = (in @ X3 @ X5)) | ((subset @ X4 @ X5) != $true) | ((in @ X3 @ X4) != $true)) )),
% 1.71/1.37 inference(definition_unfolding,[status(thm)],[f66,f59])).
% 1.71/1.37 thf(f59,plain,(
% 1.71/1.37 (subsetE = $true)),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f37])).
% 1.71/1.37 thf(f66,plain,(
% 1.71/1.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) | ($true = (in @ X3 @ X5)) | ((subset @ X4 @ X5) != $true) | (subsetE != $true)) )),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.37 thf(f41,plain,(
% 1.71/1.37 ((subsetE = $true) | (($true = (in @ sK4 @ sK5)) & ((in @ sK4 @ sK6) != $true) & ((subset @ sK5 @ sK6) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) | ($true = (in @ X3 @ X5)) | ((subset @ X4 @ X5) != $true)) | (subsetE != $true))),
% 1.71/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f39,f40])).
% 1.71/1.37 thf(f40,plain,(
% 1.71/1.37 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) & ($true != (in @ X0 @ X2)) & ($true = (subset @ X1 @ X2))) => (($true = (in @ sK4 @ sK5)) & ((in @ sK4 @ sK6) != $true) & ((subset @ sK5 @ sK6) = $true))),
% 1.71/1.37 introduced(definition,[],[choice_axiom])).
% 1.71/1.37 thf(f39,plain,(
% 1.71/1.37 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) & ($true != (in @ X0 @ X2)) & ($true = (subset @ X1 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) | ($true = (in @ X3 @ X5)) | ((subset @ X4 @ X5) != $true)) | (subsetE != $true))),
% 1.71/1.37 inference(rectify,[status(thm)],[f38])).
% 1.71/1.37 thf(f38,plain,(
% 1.71/1.37 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) & ($true != (in @ X0 @ X2)) & ($true = (subset @ X1 @ X2)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) | ($true = (in @ X0 @ X2)) | ($true != (subset @ X1 @ X2))) | (subsetE != $true))),
% 1.71/1.37 inference(nnf_transformation,[status(thm)],[f31])).
% 1.71/1.37 thf(f31,plain,(
% 1.71/1.37 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) | ($true = (in @ X0 @ X2)) | ($true != (subset @ X1 @ X2)))),
% 1.71/1.37 inference(flattening,[status(thm)],[f30])).
% 1.71/1.37 thf(f30,plain,(
% 1.71/1.37 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) != $true)) | ($true != (subset @ X1 @ X2)))),
% 1.71/1.37 inference(ennf_transformation,[status(thm)],[f18])).
% 1.71/1.37 thf(f18,plain,(
% 1.71/1.37 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X1 @ X2)) => (((in @ X0 @ X1) = $true) => ($true = (in @ X0 @ X2))))),
% 1.71/1.37 inference(fool_elimination,[status(thm)],[f17])).
% 1.71/1.37 thf(f17,plain,(
% 1.71/1.37 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))))),
% 1.71/1.37 inference(rectify,[status(thm)],[f2])).
% 1.71/1.37 thf(f2,axiom,(
% 1.71/1.37 (subsetE = ! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.71/1.37 file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',subsetE)).
% 1.71/1.37 thf(f124,plain,(
% 1.71/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X1) != $true) | ((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X0) != $true) | ((subset @ X2 @ (binintersect @ X0 @ X1)) = $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.71/1.37 thf(f123,plain,(
% 1.71/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ (binintersect @ X0 @ X1)) = $true) | ((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X0) != $true) | ($true != $true) | ((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X1) != $true)) )),
% 1.71/1.37 inference(superposition,[status(thm)],[f98,f103])).
% 1.71/1.37 thf(f103,plain,(
% 1.71/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) != $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.71/1.37 thf(f94,plain,(
% 1.71/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) != $true) | ($true != $true) | ((in @ X1 @ (binintersect @ X0 @ X2)) = $true)) )),
% 1.71/1.37 inference(definition_unfolding,[status(thm)],[f79,f60])).
% 1.71/1.37 thf(f60,plain,(
% 1.71/1.37 (binintersectI = $true)),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f37])).
% 1.71/1.37 thf(f79,plain,(
% 1.71/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) != $true) | (binintersectI != $true)) )),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f54])).
% 1.71/1.37 thf(f54,plain,(
% 1.71/1.37 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | (((in @ sK13 @ (binintersect @ sK12 @ sK14)) != $true) & ($true = (in @ sK13 @ sK12)) & ($true = (in @ sK13 @ sK14))))),
% 1.71/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f52,f53])).
% 1.71/1.37 thf(f53,plain,(
% 1.71/1.37 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (binintersect @ X3 @ X5))) & ((in @ X4 @ X3) = $true) & ($true = (in @ X4 @ X5))) => (((in @ sK13 @ (binintersect @ sK12 @ sK14)) != $true) & ($true = (in @ sK13 @ sK12)) & ($true = (in @ sK13 @ sK14)))),
% 1.71/1.37 introduced(definition,[],[choice_axiom])).
% 1.71/1.37 thf(f52,plain,(
% 1.71/1.37 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (binintersect @ X3 @ X5))) & ((in @ X4 @ X3) = $true) & ($true = (in @ X4 @ X5))))),
% 1.71/1.37 inference(rectify,[status(thm)],[f51])).
% 1.71/1.37 thf(f51,plain,(
% 1.71/1.37 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) != $true) & ((in @ X1 @ X0) = $true) & ((in @ X1 @ X2) = $true)))),
% 1.71/1.37 inference(nnf_transformation,[status(thm)],[f29])).
% 1.71/1.37 thf(f29,plain,(
% 1.71/1.37 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ X2) != $true)) <=> (binintersectI = $true)),
% 1.71/1.37 inference(flattening,[status(thm)],[f28])).
% 1.71/1.37 thf(f28,plain,(
% 1.71/1.37 ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((in @ X1 @ X2) != $true)) | ((in @ X1 @ X0) != $true)) <=> (binintersectI = $true)),
% 1.71/1.37 inference(ennf_transformation,[status(thm)],[f13])).
% 1.71/1.37 thf(f13,plain,(
% 1.71/1.37 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) => (((in @ X1 @ X2) = $true) => ((in @ X1 @ (binintersect @ X0 @ X2)) = $true))) <=> (binintersectI = $true)),
% 1.71/1.37 inference(fool_elimination,[status(thm)],[f12])).
% 1.71/1.37 thf(f12,plain,(
% 1.71/1.37 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ X0 @ X2)))))),
% 1.71/1.37 inference(rectify,[status(thm)],[f5])).
% 1.71/1.37 thf(f5,axiom,(
% 1.71/1.37 (binintersectI = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 1.71/1.37 file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',binintersectI)).
% 1.71/1.37 thf(f98,plain,(
% 1.71/1.37 ( ! [X3 : $i,X4 : $i] : (((in @ (sK9 @ X4 @ X3) @ X4) != $true) | ((subset @ X3 @ X4) = $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.71/1.37 thf(f91,plain,(
% 1.71/1.37 ( ! [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | ((in @ (sK9 @ X4 @ X3) @ X4) != $true) | ($true != $true)) )),
% 1.71/1.37 inference(definition_unfolding,[status(thm)],[f70,f64])).
% 1.71/1.37 thf(f70,plain,(
% 1.71/1.37 ( ! [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | ((in @ (sK9 @ X4 @ X3) @ X4) != $true) | (subsetI1 != $true)) )),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f46])).
% 1.71/1.37 thf(f99,plain,(
% 1.71/1.37 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) != $true) | (X2 = X3) | ((subset @ X2 @ X3) != $true)) )),
% 1.71/1.37 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.71/1.37 thf(f83,plain,(
% 1.71/1.37 ( ! [X2 : $i,X3 : $i] : (($true != $true) | (X2 = X3) | ((subset @ X3 @ X2) != $true) | ((subset @ X2 @ X3) != $true)) )),
% 1.71/1.37 inference(definition_unfolding,[status(thm)],[f55,f63])).
% 1.71/1.37 thf(f63,plain,(
% 1.71/1.37 (setextsub = $true)),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f37])).
% 1.71/1.37 thf(f55,plain,(
% 1.71/1.37 ( ! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true) | (X2 = X3) | (setextsub != $true)) )),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f35])).
% 1.71/1.37 thf(f35,plain,(
% 1.71/1.37 ((setextsub = $true) | (((subset @ sK0 @ sK1) = $true) & ((subset @ sK1 @ sK0) = $true) & (sK1 != sK0))) & (! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true) | (X2 = X3)) | (setextsub != $true))),
% 1.71/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f33,f34])).
% 1.71/1.37 thf(f34,plain,(
% 1.71/1.37 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true) & (X0 != X1)) => (((subset @ sK0 @ sK1) = $true) & ((subset @ sK1 @ sK0) = $true) & (sK1 != sK0))),
% 1.71/1.37 introduced(definition,[],[choice_axiom])).
% 1.71/1.37 thf(f33,plain,(
% 1.71/1.37 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true) & (X0 != X1))) & (! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true) | (X2 = X3)) | (setextsub != $true))),
% 1.71/1.37 inference(rectify,[status(thm)],[f32])).
% 1.71/1.37 thf(f32,plain,(
% 1.71/1.37 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true) & (X0 != X1))) & (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((subset @ X1 @ X0) != $true) | (X0 = X1)) | (setextsub != $true))),
% 1.71/1.37 inference(nnf_transformation,[status(thm)],[f27])).
% 1.71/1.37 thf(f27,plain,(
% 1.71/1.37 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((subset @ X1 @ X0) != $true) | (X0 = X1))),
% 1.71/1.37 inference(flattening,[status(thm)],[f26])).
% 1.71/1.37 thf(f26,plain,(
% 1.71/1.37 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | ((subset @ X0 @ X1) != $true)) | ((subset @ X1 @ X0) != $true))),
% 1.71/1.37 inference(ennf_transformation,[status(thm)],[f11])).
% 1.71/1.37 thf(f11,plain,(
% 1.71/1.37 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => (((subset @ X0 @ X1) = $true) => (X0 = X1)))),
% 1.71/1.37 inference(fool_elimination,[status(thm)],[f10])).
% 1.71/1.37 thf(f10,plain,(
% 1.71/1.37 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))) = setextsub)),
% 1.71/1.37 inference(rectify,[status(thm)],[f3])).
% 1.71/1.37 thf(f3,axiom,(
% 1.71/1.37 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))) = setextsub)),
% 1.71/1.37 file('/export/starexec/sandbox/tmp/tmp.Nf5zMavudr/DTF2THF_8520.p',setextsub)).
% 1.71/1.37 thf(f62,plain,(
% 1.71/1.37 ((binintersect @ sK2 @ sK3) != sK2)),
% 1.71/1.37 inference(cnf_transformation,[status(thm)],[f37])).
% 1.71/1.37 % SZS output end Proof for DTF2THF_8520
% 1.71/1.37 % (8715)------------------------------
% 1.71/1.37 % (8715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.37 % (8715)Termination reason: Refutation
% 1.71/1.37
% 1.71/1.37 % (8715)Memory used [KB]: 5628
% 1.71/1.37 % (8715)Time elapsed: 0.027 s
% 1.71/1.37 % (8715)Instructions burned: 61 (million)
% 1.71/1.37 % (8715)------------------------------
% 1.71/1.37 % (8715)------------------------------
% 1.71/1.37 % (8709)Success in time 0.041 s
%------------------------------------------------------------------------------