%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU805^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 09:37:21 AM UTC 2026
% Result : Theorem 1.69s 1.33s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 77 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 811 ( 253 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 803 ( 130 ~; 105 |; 70 &; 456 @)
% ( 8 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 172 ( 0 ^; 116 !; 56 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_4,type,
nonempty: $i > $o ).
thf(func_def_6,type,
binintersect: $i > $i > $i ).
thf(func_def_16,type,
sK2: $i > $i ).
thf(func_def_19,type,
sK5: $i > $i > $i ).
thf(func_def_21,type,
sK7: $i > $i ).
thf(func_def_23,type,
sK9: $i > $i ).
thf(f117,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f88,f106,f116]) ).
thf(f116,plain,
~ spl10_2,
inference(avatar_contradiction_clause,[status(thm)],[f115]) ).
thf(f115,plain,
( $false
| ~ spl10_2 ),
inference(subsumption_resolution,[status(thm)],[f114,f46]) ).
thf(f46,plain,
( $true
= ( nonempty @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true
= ( nonempty @ sK0 ) )
& ! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( emptyset
!= ( binintersect @ X1 @ sK0 ) ) )
& ( disjointsetsI1 = $true )
& ( foundationAx = $true )
& ( nonemptyE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f23]) ).
thf(f23,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
& ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( emptyset
!= ( binintersect @ X1 @ X0 ) ) ) )
=> ( ( $true
= ( nonempty @ sK0 ) )
& ! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( emptyset
!= ( binintersect @ X1 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
& ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( emptyset
!= ( binintersect @ X1 @ X0 ) ) ) )
& ( disjointsetsI1 = $true )
& ( foundationAx = $true )
& ( nonemptyE1 = $true ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
& ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( emptyset
!= ( binintersect @ X1 @ X0 ) ) ) )
& ( disjointsetsI1 = $true )
& ( nonemptyE1 = $true )
& ( foundationAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ( foundationAx = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( disjointsetsI1 = $true )
=> ! [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
=> ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( emptyset
= ( binintersect @ X1 @ X0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
& ( in @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X3: $i] :
( ( emptyset
= ( binintersect @ X3 @ X0 ) )
& ( in @ X3 @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X3: $i] :
( ( emptyset
= ( binintersect @ X3 @ X0 ) )
& ( in @ X3 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8F5beL8ATw/DTF2THF_1422.p',foundation2) ).
thf(f114,plain,
( ( $true
!= ( nonempty @ sK0 ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $true
!= ( nonempty @ sK0 ) )
| ( $true != $true )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f87,f72]) ).
thf(f72,plain,
! [X2: $i] :
( ( ( in @ ( sK2 @ X2 ) @ X2 )
= $true )
| ( ( nonempty @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i] :
( ( ( nonempty @ X2 )
!= $true )
| ( ( in @ ( sK2 @ X2 ) @ X2 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f47,f42]) ).
thf(f42,plain,
nonemptyE1 = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f47,plain,
! [X2: $i] :
( ( ( nonempty @ X2 )
!= $true )
| ( ( in @ ( sK2 @ X2 ) @ X2 )
= $true )
| ( nonemptyE1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( nonemptyE1 = $true )
| ( ( ( nonempty @ sK1 )
= $true )
& ! [X1: $i] :
( ( in @ X1 @ sK1 )
!= $true ) ) )
& ( ! [X2: $i] :
( ( ( nonempty @ X2 )
!= $true )
| ( ( in @ ( sK2 @ X2 ) @ X2 )
= $true ) )
| ( nonemptyE1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f26,f28,f27]) ).
thf(f27,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) )
=> ( ( ( nonempty @ sK1 )
= $true )
& ! [X1: $i] :
( ( in @ X1 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
! [X2: $i] :
( ? [X3: $i] :
( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ ( sK2 @ X2 ) @ X2 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ( nonemptyE1 = $true )
| ? [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ! [X2: $i] :
( ( ( nonempty @ X2 )
!= $true )
| ? [X3: $i] :
( ( in @ X3 @ X2 )
= $true ) )
| ( nonemptyE1 != $true ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( nonemptyE1 = $true )
| ? [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ! [X0: $i] :
( ( ( nonempty @ X0 )
!= $true )
| ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) )
| ( nonemptyE1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( nonemptyE1 = $true )
<=> ! [X0: $i] :
( ( ( nonempty @ X0 )
!= $true )
| ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( nonemptyE1 = $true )
<=> ! [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
=> ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( nonemptyE1
= ( ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] : ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( nonemptyE1
= ( ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] : ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8F5beL8ATw/DTF2THF_1422.p',nonemptyE1) ).
thf(f87,plain,
( ! [X0: $i] :
( ( in @ X0 @ sK0 )
!= $true )
| ~ spl10_2 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f86,definition,
( spl10_2
<=> ! [X0: $i] :
( ( in @ X0 @ sK0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition]) ).
thf(f106,plain,
( spl10_2
| spl10_1 ),
inference(avatar_split_clause,[status(thm)],[f105,f82,f86]) ).
thf(f82,definition,
( spl10_1
<=> ( emptyset
= ( binintersect @ ( sK9 @ sK0 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition]) ).
thf(f105,plain,
( ! [X0: $i] :
( ( in @ X0 @ sK0 )
!= $true )
| spl10_1 ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK0 )
!= $true )
| ( emptyset != emptyset ) )
| spl10_1 ),
inference(superposition,[status(thm)],[f84,f103]) ).
thf(f103,plain,
! [X0: $i,X1: $i] :
( ( emptyset
= ( binintersect @ ( sK9 @ X0 ) @ X0 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( emptyset
= ( binintersect @ ( sK9 @ X0 ) @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f101]) ).
thf(f101,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( emptyset
= ( binintersect @ ( sK9 @ X0 ) @ X0 ) )
| ( emptyset
= ( binintersect @ ( sK9 @ X0 ) @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f97,f75]) ).
thf(f75,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK5 @ X4 @ X3 ) @ X3 )
= $true )
| ( emptyset
= ( binintersect @ X4 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( $true != $true )
| ( ( in @ ( sK5 @ X4 @ X3 ) @ X3 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f50,f44]) ).
thf(f44,plain,
disjointsetsI1 = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f50,plain,
! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( ( in @ ( sK5 @ X4 @ X3 ) @ X3 )
= $true )
| ( disjointsetsI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( disjointsetsI1 = $true )
| ( ( emptyset
!= ( binintersect @ sK4 @ sK3 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ sK4 )
!= $true )
| ( $true
!= ( in @ X2 @ sK3 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( ( ( in @ ( sK5 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK5 @ X4 @ X3 ) @ X3 )
= $true ) ) )
| ( disjointsetsI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f31,f33,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
=> ( ( emptyset
!= ( binintersect @ sK4 @ sK3 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ sK4 )
!= $true )
| ( $true
!= ( in @ X2 @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
= $true ) )
=> ( ( ( in @ ( sK5 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK5 @ X4 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( disjointsetsI1 = $true )
| ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
= $true ) ) )
| ( disjointsetsI1 != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( disjointsetsI1 = $true )
| ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( disjointsetsI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( disjointsetsI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( disjointsetsI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( emptyset
= ( binintersect @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X0 ) )
=> ( emptyset
= ( binintersect @ X1 @ X0 ) ) )
= disjointsetsI1 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $i,X0: $i] :
( ( ~ ? [X1: $i] :
( ( in @ X1 @ X0 )
& ( in @ X1 @ X2 ) )
=> ( emptyset
= ( binintersect @ X0 @ X2 ) ) )
= disjointsetsI1 ),
file('/export/starexec/sandbox2/tmp/tmp.8F5beL8ATw/DTF2THF_1422.p',disjointsetsI1) ).
thf(f97,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK5 @ ( sK9 @ X0 ) @ X1 ) @ X0 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( emptyset
= ( binintersect @ ( sK9 @ X0 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( sK5 @ ( sK9 @ X0 ) @ X1 ) @ X0 )
!= $true )
| ( emptyset
= ( binintersect @ ( sK9 @ X0 ) @ X1 ) )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f73,f74]) ).
thf(f74,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK5 @ X4 @ X3 ) @ X4 )
= $true )
| ( emptyset
= ( binintersect @ X4 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ ( sK5 @ X4 @ X3 ) @ X4 )
= $true )
| ( emptyset
= ( binintersect @ X4 @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f51,f44]) ).
thf(f51,plain,
! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( ( in @ ( sK5 @ X4 @ X3 ) @ X4 )
= $true )
| ( disjointsetsI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f73,plain,
! [X6: $i,X7: $i,X4: $i] :
( ( $true
!= ( in @ X6 @ ( sK9 @ X4 ) ) )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X6 @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X6: $i,X7: $i,X4: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( $true
!= ( in @ X6 @ ( sK9 @ X4 ) ) )
| ( $true != $true )
| ( ( in @ X7 @ X4 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f54,f43]) ).
thf(f43,plain,
foundationAx = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f54,plain,
! [X6: $i,X7: $i,X4: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( $true
!= ( in @ X6 @ ( sK9 @ X4 ) ) )
| ( ( in @ X7 @ X4 )
!= $true )
| ( foundationAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( foundationAx = $true )
| ( ! [X1: $i] :
( ( ( in @ X1 @ sK6 )
!= $true )
| ( ( ( in @ ( sK7 @ X1 ) @ sK6 )
= $true )
& ( $true
= ( in @ ( sK7 @ X1 ) @ X1 ) ) ) )
& ( $true
= ( in @ sK8 @ sK6 ) ) ) )
& ( ! [X4: $i] :
( ( ( ( in @ ( sK9 @ X4 ) @ X4 )
= $true )
& ! [X6: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( $true
!= ( in @ X6 @ ( sK9 @ X4 ) ) ) ) )
| ! [X7: $i] :
( ( in @ X7 @ X4 )
!= $true ) )
| ( foundationAx != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f36,f40,f39,f38,f37]) ).
thf(f37,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ? [X3: $i] :
( ( in @ X3 @ X0 )
= $true ) )
=> ( ! [X1: $i] :
( ( ( in @ X1 @ sK6 )
!= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ sK6 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ? [X3: $i] :
( ( in @ X3 @ sK6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
! [X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ sK6 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( ( in @ ( sK7 @ X1 ) @ sK6 )
= $true )
& ( $true
= ( in @ ( sK7 @ X1 ) @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ? [X3: $i] :
( ( in @ X3 @ sK6 )
= $true )
=> ( $true
= ( in @ sK8 @ sK6 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
! [X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ! [X6: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( ( in @ X6 @ X5 )
!= $true ) ) )
=> ( ( ( in @ ( sK9 @ X4 ) @ X4 )
= $true )
& ! [X6: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( $true
!= ( in @ X6 @ ( sK9 @ X4 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( ( foundationAx = $true )
| ? [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ? [X3: $i] :
( ( in @ X3 @ X0 )
= $true ) ) )
& ( ! [X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ! [X6: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
| ( ( in @ X6 @ X5 )
!= $true ) ) )
| ! [X7: $i] :
( ( in @ X7 @ X4 )
!= $true ) )
| ( foundationAx != $true ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( foundationAx = $true )
| ? [X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
| ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) )
| ( foundationAx != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( foundationAx = $true )
<=> ! [X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
| ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( foundationAx = $true )
<=> ! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
=> ? [X2: $i] :
( ~ ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( ? [X1: $i] : ( in @ X1 @ X0 )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X2 )
& ( in @ X3 @ X0 ) ) ) )
= foundationAx ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( ? [X1: $i] : ( in @ X1 @ X0 )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ? [X1: $i] :
( ( in @ X1 @ X2 )
& ( in @ X1 @ X0 ) ) ) )
= foundationAx ),
file('/export/starexec/sandbox2/tmp/tmp.8F5beL8ATw/DTF2THF_1422.p',foundationAx) ).
thf(f84,plain,
( ( emptyset
!= ( binintersect @ ( sK9 @ sK0 ) @ sK0 ) )
| spl10_1 ),
inference(avatar_component_clause,[status(thm)],[f82]) ).
thf(f88,plain,
( ~ spl10_1
| spl10_2 ),
inference(avatar_split_clause,[status(thm)],[f80,f86,f82]) ).
thf(f80,plain,
! [X0: $i] :
( ( emptyset
!= ( binintersect @ ( sK9 @ sK0 ) @ sK0 ) )
| ( ( in @ X0 @ sK0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK0 )
!= $true )
| ( $true != $true )
| ( emptyset
!= ( binintersect @ ( sK9 @ sK0 ) @ sK0 ) ) ),
inference(superposition,[status(thm)],[f45,f71]) ).
thf(f71,plain,
! [X7: $i,X4: $i] :
( ( ( in @ ( sK9 @ X4 ) @ X4 )
= $true )
| ( ( in @ X7 @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X7: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ ( sK9 @ X4 ) @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f55,f43]) ).
thf(f55,plain,
! [X7: $i,X4: $i] :
( ( ( in @ ( sK9 @ X4 ) @ X4 )
= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( foundationAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f45,plain,
! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( emptyset
!= ( binintersect @ X1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU805^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n019.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 12:34:39 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 : SEU805^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : The Foundation Axiom
% 0.18/0.45 % Version : Especial > Reduced > Especial.
% 0.18/0.45 % English : (! A:i.nonempty A -> (? X:i.in X A & binintersect X A = emptyset))
% 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 : ZFC307l [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 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 v4.0.0, 0.33 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 12 ( 4 unt; 7 typ; 4 def)
% 0.18/0.45 % Number of atoms : 24 ( 7 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 6 ( 4 avg)
% 0.18/0.45 % Number of connectives : 36 ( 3 ~; 0 |; 4 &; 22 @)
% 0.18/0.45 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 10 ( 3 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 12 ( 1 ^; 5 !; 6 ?; 12 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=429
% 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(emptyset_type,type,
% 0.18/0.45 emptyset: $i ).
% 0.18/0.45
% 0.18/0.45 thf(foundationAx_type,type,
% 0.18/0.45 foundationAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(foundationAx,definition,
% 0.18/0.45 ( foundationAx
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.45 => ? [B: $i] :
% 0.18/0.45 ( ( in @ B @ A )
% 0.18/0.45 & ~ ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonempty_type,type,
% 0.18/0.45 nonempty: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonempty,definition,
% 0.18/0.45 ( nonempty
% 0.18/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyE1_type,type,
% 0.18/0.45 nonemptyE1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyE1,definition,
% 0.18/0.45 ( nonemptyE1
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ( nonempty @ A )
% 0.18/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(binintersect_type,type,
% 0.18/0.45 binintersect: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(disjointsetsI1_type,type,
% 0.18/0.45 disjointsetsI1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(disjointsetsI1,definition,
% 0.18/0.45 ( disjointsetsI1
% 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 ) )
% 0.18/0.45 => ( ( binintersect @ A @ B )
% 0.18/0.45 = emptyset ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(foundation2,conjecture,
% 0.18/0.45 ( foundationAx
% 0.18/0.45 => ( nonemptyE1
% 0.18/0.45 => ( disjointsetsI1
% 0.18/0.45 => ! [A: $i] :
% 0.18/0.45 ( ( nonempty @ A )
% 0.18/0.45 => ? [X: $i] :
% 0.18/0.45 ( ( in @ X @ A )
% 0.18/0.45 & ( ( binintersect @ X @ A )
% 0.18/0.45 = emptyset ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.50/1.29 ---- Embedded in THF ---
% 1.50/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.29 %%% Generated on Tue Feb 24 12:34:40 EST 2026
% 1.50/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.29 %%% Logic specification used:
% 1.50/1.29 %%% thf(spec, logic, $$dhol).
% 1.50/1.29
% 1.50/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.8F5beL8ATw/DTF2DTF1422.p
% See solution above
% 1.50/1.29 ------------------------
% 1.69/1.30 ---- Cleaned THF ---
% 1.69/1.30 thf(in_type,type,
% 1.69/1.30 in: $i > $i > $o ).
% 1.69/1.30
% 1.69/1.30 thf(emptyset_type,type,
% 1.69/1.30 emptyset: $i ).
% 1.69/1.30
% 1.69/1.30 thf(foundationAx_type,type,
% 1.69/1.30 foundationAx: $o ).
% 1.69/1.30
% 1.69/1.30 thf(foundationAx,definition,
% 1.69/1.30 ( foundationAx
% 1.69/1.30 = ( ! [A: $i] :
% 1.69/1.30 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.69/1.30 => ? [B: $i] :
% 1.69/1.30 ( ( in @ B @ A )
% 1.69/1.30 & ~ ? [Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ B )
% 1.69/1.30 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(nonempty_type,type,
% 1.69/1.30 nonempty: $i > $o ).
% 1.69/1.30
% 1.69/1.30 thf(nonempty,definition,
% 1.69/1.30 ( nonempty
% 1.69/1.30 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(nonemptyE1_type,type,
% 1.69/1.30 nonemptyE1: $o ).
% 1.69/1.30
% 1.69/1.30 thf(nonemptyE1,definition,
% 1.69/1.30 ( nonemptyE1
% 1.69/1.30 = ( ! [A: $i] :
% 1.69/1.30 ( ( nonempty @ A )
% 1.69/1.30 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(binintersect_type,type,
% 1.69/1.30 binintersect: $i > $i > $i ).
% 1.69/1.30
% 1.69/1.30 thf(disjointsetsI1_type,type,
% 1.69/1.30 disjointsetsI1: $o ).
% 1.69/1.30
% 1.69/1.30 thf(disjointsetsI1,definition,
% 1.69/1.30 ( disjointsetsI1
% 1.69/1.30 = ( ! [A: $i,B: $i] :
% 1.69/1.30 ( ~ ? [Xx: $i] :
% 1.69/1.30 ( ( in @ Xx @ A )
% 1.69/1.30 & ( in @ Xx @ B ) )
% 1.69/1.30 => ( ( binintersect @ A @ B )
% 1.69/1.30 = emptyset ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(foundation2,conjecture,
% 1.69/1.30 ( foundationAx
% 1.69/1.30 => ( nonemptyE1
% 1.69/1.30 => ( disjointsetsI1
% 1.69/1.30 => ! [A: $i] :
% 1.69/1.30 ( ( nonempty @ A )
% 1.69/1.30 => ? [X: $i] :
% 1.69/1.30 ( ( in @ X @ A )
% 1.69/1.30 & ( ( binintersect @ X @ A )
% 1.69/1.30 = emptyset ) ) ) ) ) ) ).
% 1.69/1.30 ------------------------
% 1.69/1.32 % (1595)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_1422 for (2999ds/4Mi)
% 1.69/1.32 % (1599)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_1422 for (2999ds/275Mi)
% 1.69/1.32 % (1595)Instruction limit reached!
% 1.69/1.32 % (1595)------------------------------
% 1.69/1.32 % (1595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (1595)Termination reason: Unknown
% 1.69/1.32 % (1595)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (1595)Memory used [KB]: 5500
% 1.69/1.32 % (1595)Time elapsed: 0.003 s
% 1.69/1.32 % (1595)Instructions burned: 6 (million)
% 1.69/1.32 % (1595)------------------------------
% 1.69/1.32 % (1595)------------------------------
% 1.69/1.32 % (1597)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1422 for (2999ds/2Mi)
% 1.69/1.33 % (1600)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1422 for (2999ds/18Mi)
% 1.69/1.33 % (1594)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1422 for (2999ds/183Mi)
% 1.69/1.33 % (1597)Instruction limit reached!
% 1.69/1.33 % (1597)------------------------------
% 1.69/1.33 % (1597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (1597)Termination reason: Unknown
% 1.69/1.33 % (1597)Termination phase: Function definition elimination
% 1.69/1.33
% 1.69/1.33 % (1597)Memory used [KB]: 1023
% 1.69/1.33 % (1597)Time elapsed: 0.003 s
% 1.69/1.33 % (1597)Instructions burned: 2 (million)
% 1.69/1.33 % (1597)------------------------------
% 1.69/1.33 % (1597)------------------------------
% 1.69/1.33 % (1599)First to succeed.
% 1.69/1.33 % (1599)Refutation found. Thanks to Tanya!
% 1.69/1.33 % SZS status Theorem for DTF2THF_1422
% 1.69/1.33 % SZS output start Proof for DTF2THF_1422
% 1.69/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.33 thf(func_def_4, type, nonempty: $i > $o).
% 1.69/1.33 thf(func_def_6, type, binintersect: $i > $i > $i).
% 1.69/1.33 thf(func_def_16, type, sK2: $i > $i).
% 1.69/1.33 thf(func_def_19, type, sK5: $i > $i > $i).
% 1.69/1.33 thf(func_def_21, type, sK7: $i > $i).
% 1.69/1.33 thf(func_def_23, type, sK9: $i > $i).
% 1.69/1.33 thf(f117,plain,(
% 1.69/1.33 $false),
% 1.69/1.33 inference(avatar_sat_refutation,[status(thm)],[f88,f106,f116])).
% 1.69/1.33 thf(f116,plain,(
% 1.69/1.33 ~spl10_2),
% 1.69/1.33 inference(avatar_contradiction_clause,[status(thm)],[f115])).
% 1.69/1.33 thf(f115,plain,(
% 1.69/1.33 $false | ~spl10_2),
% 1.69/1.33 inference(subsumption_resolution,[status(thm)],[f114,f46])).
% 1.69/1.33 thf(f46,plain,(
% 1.69/1.33 ($true = (nonempty @ sK0))),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f24])).
% 1.69/1.33 thf(f24,plain,(
% 1.69/1.33 (($true = (nonempty @ sK0)) & ! [X1 : $i] : (($true != (in @ X1 @ sK0)) | (emptyset != (binintersect @ X1 @ sK0)))) & (disjointsetsI1 = $true) & (foundationAx = $true) & (nonemptyE1 = $true)),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f23])).
% 1.69/1.33 thf(f23,plain,(
% 1.69/1.33 ? [X0 : $i] : (((nonempty @ X0) = $true) & ! [X1 : $i] : (((in @ X1 @ X0) != $true) | (emptyset != (binintersect @ X1 @ X0)))) => (($true = (nonempty @ sK0)) & ! [X1 : $i] : (($true != (in @ X1 @ sK0)) | (emptyset != (binintersect @ X1 @ sK0))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f21,plain,(
% 1.69/1.33 ? [X0 : $i] : (((nonempty @ X0) = $true) & ! [X1 : $i] : (((in @ X1 @ X0) != $true) | (emptyset != (binintersect @ X1 @ X0)))) & (disjointsetsI1 = $true) & (foundationAx = $true) & (nonemptyE1 = $true)),
% 1.69/1.33 inference(flattening,[status(thm)],[f20])).
% 1.69/1.33 thf(f20,plain,(
% 1.69/1.33 ((? [X0 : $i] : (((nonempty @ X0) = $true) & ! [X1 : $i] : (((in @ X1 @ X0) != $true) | (emptyset != (binintersect @ X1 @ X0)))) & (disjointsetsI1 = $true)) & (nonemptyE1 = $true)) & (foundationAx = $true)),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f13])).
% 1.69/1.33 thf(f13,plain,(
% 1.69/1.33 ~((foundationAx = $true) => ((nonemptyE1 = $true) => ((disjointsetsI1 = $true) => ! [X0 : $i] : (((nonempty @ X0) = $true) => ? [X1 : $i] : (((in @ X1 @ X0) = $true) & (emptyset = (binintersect @ X1 @ X0)))))))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f12])).
% 1.69/1.33 thf(f12,plain,(
% 1.69/1.33 ~(foundationAx => (nonemptyE1 => (disjointsetsI1 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) & (in @ X1 @ X0))))))),
% 1.69/1.33 inference(rectify,[status(thm)],[f6])).
% 1.69/1.33 thf(f6,negated_conjecture,(
% 1.69/1.33 ~(foundationAx => (nonemptyE1 => (disjointsetsI1 => ! [X0 : $i] : ((nonempty @ X0) => ? [X3 : $i] : ((emptyset = (binintersect @ X3 @ X0)) & (in @ X3 @ X0))))))),
% 1.69/1.33 inference(negated_conjecture,[status(cth)],[f5])).
% 1.69/1.33 thf(f5,conjecture,(
% 1.69/1.33 foundationAx => (nonemptyE1 => (disjointsetsI1 => ! [X0 : $i] : ((nonempty @ X0) => ? [X3 : $i] : ((emptyset = (binintersect @ X3 @ X0)) & (in @ X3 @ X0)))))),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.8F5beL8ATw/DTF2THF_1422.p',foundation2)).
% 1.69/1.33 thf(f114,plain,(
% 1.69/1.33 ($true != (nonempty @ sK0)) | ~spl10_2),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.69/1.33 thf(f107,plain,(
% 1.69/1.33 ($true != (nonempty @ sK0)) | ($true != $true) | ~spl10_2),
% 1.69/1.33 inference(superposition,[status(thm)],[f87,f72])).
% 1.69/1.33 thf(f72,plain,(
% 1.69/1.33 ( ! [X2 : $i] : (((in @ (sK2 @ X2) @ X2) = $true) | ((nonempty @ X2) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.69/1.33 thf(f61,plain,(
% 1.69/1.33 ( ! [X2 : $i] : (((nonempty @ X2) != $true) | ((in @ (sK2 @ X2) @ X2) = $true) | ($true != $true)) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f47,f42])).
% 1.69/1.33 thf(f42,plain,(
% 1.69/1.33 (nonemptyE1 = $true)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f24])).
% 1.69/1.33 thf(f47,plain,(
% 1.69/1.33 ( ! [X2 : $i] : (((nonempty @ X2) != $true) | ((in @ (sK2 @ X2) @ X2) = $true) | (nonemptyE1 != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f29])).
% 1.69/1.33 thf(f29,plain,(
% 1.69/1.33 ((nonemptyE1 = $true) | (((nonempty @ sK1) = $true) & ! [X1 : $i] : ((in @ X1 @ sK1) != $true))) & (! [X2 : $i] : (((nonempty @ X2) != $true) | ((in @ (sK2 @ X2) @ X2) = $true)) | (nonemptyE1 != $true))),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f26,f28,f27])).
% 1.69/1.33 thf(f27,plain,(
% 1.69/1.33 ? [X0 : $i] : (((nonempty @ X0) = $true) & ! [X1 : $i] : ((in @ X1 @ X0) != $true)) => (((nonempty @ sK1) = $true) & ! [X1 : $i] : ((in @ X1 @ sK1) != $true))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f28,plain,(
% 1.69/1.33 ! [X2 : $i] : (? [X3 : $i] : ((in @ X3 @ X2) = $true) => ((in @ (sK2 @ X2) @ X2) = $true))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f26,plain,(
% 1.69/1.33 ((nonemptyE1 = $true) | ? [X0 : $i] : (((nonempty @ X0) = $true) & ! [X1 : $i] : ((in @ X1 @ X0) != $true))) & (! [X2 : $i] : (((nonempty @ X2) != $true) | ? [X3 : $i] : ((in @ X3 @ X2) = $true)) | (nonemptyE1 != $true))),
% 1.69/1.33 inference(rectify,[status(thm)],[f25])).
% 1.69/1.33 thf(f25,plain,(
% 1.69/1.33 ((nonemptyE1 = $true) | ? [X0 : $i] : (((nonempty @ X0) = $true) & ! [X1 : $i] : ((in @ X1 @ X0) != $true))) & (! [X0 : $i] : (((nonempty @ X0) != $true) | ? [X1 : $i] : ((in @ X1 @ X0) = $true)) | (nonemptyE1 != $true))),
% 1.69/1.33 inference(nnf_transformation,[status(thm)],[f19])).
% 1.69/1.33 thf(f19,plain,(
% 1.69/1.33 (nonemptyE1 = $true) <=> ! [X0 : $i] : (((nonempty @ X0) != $true) | ? [X1 : $i] : ((in @ X1 @ X0) = $true))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f9])).
% 1.69/1.33 thf(f9,plain,(
% 1.69/1.33 (nonemptyE1 = $true) <=> ! [X0 : $i] : (((nonempty @ X0) = $true) => ? [X1 : $i] : ((in @ X1 @ X0) = $true))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.69/1.33 thf(f8,plain,(
% 1.69/1.33 (nonemptyE1 = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)))),
% 1.69/1.33 inference(rectify,[status(thm)],[f3])).
% 1.69/1.33 thf(f3,axiom,(
% 1.69/1.33 (nonemptyE1 = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)))),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.8F5beL8ATw/DTF2THF_1422.p',nonemptyE1)).
% 1.69/1.33 thf(f87,plain,(
% 1.69/1.33 ( ! [X0 : $i] : (((in @ X0 @ sK0) != $true)) ) | ~spl10_2),
% 1.69/1.33 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.69/1.33 thf(f86,definition,(
% 1.69/1.33 spl10_2 <=> ! [X0 : $i] : ((in @ X0 @ sK0) != $true)),
% 1.69/1.33 introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition])).
% 1.69/1.33 thf(f106,plain,(
% 1.69/1.33 spl10_2 | spl10_1),
% 1.69/1.33 inference(avatar_split_clause,[status(thm)],[f105,f82,f86])).
% 1.69/1.33 thf(f82,definition,(
% 1.69/1.33 spl10_1 <=> (emptyset = (binintersect @ (sK9 @ sK0) @ sK0))),
% 1.69/1.33 introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition])).
% 1.69/1.33 thf(f105,plain,(
% 1.69/1.33 ( ! [X0 : $i] : (((in @ X0 @ sK0) != $true)) ) | spl10_1),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.69/1.33 thf(f104,plain,(
% 1.69/1.33 ( ! [X0 : $i] : (((in @ X0 @ sK0) != $true) | (emptyset != emptyset)) ) | spl10_1),
% 1.69/1.33 inference(superposition,[status(thm)],[f84,f103])).
% 1.69/1.33 thf(f103,plain,(
% 1.69/1.33 ( ! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ (sK9 @ X0) @ X0)) | ((in @ X1 @ X0) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.69/1.33 thf(f102,plain,(
% 1.69/1.33 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ X1 @ X0) != $true) | (emptyset = (binintersect @ (sK9 @ X0) @ X0))) )),
% 1.69/1.33 inference(duplicate_literal_removal,[status(thm)],[f101])).
% 1.69/1.33 thf(f101,plain,(
% 1.69/1.33 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | (emptyset = (binintersect @ (sK9 @ X0) @ X0)) | (emptyset = (binintersect @ (sK9 @ X0) @ X0)) | ($true != $true)) )),
% 1.69/1.33 inference(superposition,[status(thm)],[f97,f75])).
% 1.69/1.33 thf(f75,plain,(
% 1.69/1.33 ( ! [X3 : $i,X4 : $i] : (((in @ (sK5 @ X4 @ X3) @ X3) = $true) | (emptyset = (binintersect @ X4 @ X3))) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.69/1.33 thf(f65,plain,(
% 1.69/1.33 ( ! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | ($true != $true) | ((in @ (sK5 @ X4 @ X3) @ X3) = $true)) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f50,f44])).
% 1.69/1.33 thf(f44,plain,(
% 1.69/1.33 (disjointsetsI1 = $true)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f24])).
% 1.69/1.33 thf(f50,plain,(
% 1.69/1.33 ( ! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | ((in @ (sK5 @ X4 @ X3) @ X3) = $true) | (disjointsetsI1 != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 1.69/1.33 thf(f34,plain,(
% 1.69/1.33 ((disjointsetsI1 = $true) | ((emptyset != (binintersect @ sK4 @ sK3)) & ! [X2 : $i] : (((in @ X2 @ sK4) != $true) | ($true != (in @ X2 @ sK3))))) & (! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | (((in @ (sK5 @ X4 @ X3) @ X4) = $true) & ((in @ (sK5 @ X4 @ X3) @ X3) = $true))) | (disjointsetsI1 != $true))),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f31,f33,f32])).
% 1.69/1.33 thf(f32,plain,(
% 1.69/1.33 ? [X0 : $i,X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) != $true))) => ((emptyset != (binintersect @ sK4 @ sK3)) & ! [X2 : $i] : (((in @ X2 @ sK4) != $true) | ($true != (in @ X2 @ sK3))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f33,plain,(
% 1.69/1.33 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) = $true)) => (((in @ (sK5 @ X4 @ X3) @ X4) = $true) & ((in @ (sK5 @ X4 @ X3) @ X3) = $true)))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f31,plain,(
% 1.69/1.33 ((disjointsetsI1 = $true) | ? [X0 : $i,X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) != $true)))) & (! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | ? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) = $true))) | (disjointsetsI1 != $true))),
% 1.69/1.33 inference(rectify,[status(thm)],[f30])).
% 1.69/1.33 thf(f30,plain,(
% 1.69/1.33 ((disjointsetsI1 = $true) | ? [X0 : $i,X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) != $true)))) & (! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) = $true))) | (disjointsetsI1 != $true))),
% 1.69/1.33 inference(nnf_transformation,[status(thm)],[f22])).
% 1.69/1.33 thf(f22,plain,(
% 1.69/1.33 (disjointsetsI1 = $true) <=> ! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) = $true)))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f17])).
% 1.69/1.33 thf(f17,plain,(
% 1.69/1.33 (disjointsetsI1 = $true) <=> ! [X0 : $i,X1 : $i] : (~? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) = $true)) => (emptyset = (binintersect @ X1 @ X0)))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.33 thf(f16,plain,(
% 1.69/1.33 (! [X0 : $i,X1 : $i] : (~? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (emptyset = (binintersect @ X1 @ X0))) = disjointsetsI1)),
% 1.69/1.33 inference(rectify,[status(thm)],[f4])).
% 1.69/1.33 thf(f4,axiom,(
% 1.69/1.33 (! [X2 : $i,X0 : $i] : (~? [X1 : $i] : ((in @ X1 @ X0) & (in @ X1 @ X2)) => (emptyset = (binintersect @ X0 @ X2))) = disjointsetsI1)),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.8F5beL8ATw/DTF2THF_1422.p',disjointsetsI1)).
% 1.69/1.33 thf(f97,plain,(
% 1.69/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK5 @ (sK9 @ X0) @ X1) @ X0) != $true) | ((in @ X2 @ X0) != $true) | (emptyset = (binintersect @ (sK9 @ X0) @ X1))) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.69/1.33 thf(f95,plain,(
% 1.69/1.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK5 @ (sK9 @ X0) @ X1) @ X0) != $true) | (emptyset = (binintersect @ (sK9 @ X0) @ X1)) | ((in @ X2 @ X0) != $true)) )),
% 1.69/1.33 inference(superposition,[status(thm)],[f73,f74])).
% 1.69/1.33 thf(f74,plain,(
% 1.69/1.33 ( ! [X3 : $i,X4 : $i] : (((in @ (sK5 @ X4 @ X3) @ X4) = $true) | (emptyset = (binintersect @ X4 @ X3))) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.69/1.33 thf(f64,plain,(
% 1.69/1.33 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ (sK5 @ X4 @ X3) @ X4) = $true) | (emptyset = (binintersect @ X4 @ X3))) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f51,f44])).
% 1.69/1.33 thf(f51,plain,(
% 1.69/1.33 ( ! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | ((in @ (sK5 @ X4 @ X3) @ X4) = $true) | (disjointsetsI1 != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 1.69/1.33 thf(f73,plain,(
% 1.69/1.33 ( ! [X6 : $i,X7 : $i,X4 : $i] : (($true != (in @ X6 @ (sK9 @ X4))) | ((in @ X7 @ X4) != $true) | ((in @ X6 @ X4) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.69/1.33 thf(f70,plain,(
% 1.69/1.33 ( ! [X6 : $i,X7 : $i,X4 : $i] : (((in @ X6 @ X4) != $true) | ($true != (in @ X6 @ (sK9 @ X4))) | ($true != $true) | ((in @ X7 @ X4) != $true)) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f54,f43])).
% 1.69/1.33 thf(f43,plain,(
% 1.69/1.33 (foundationAx = $true)),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f24])).
% 1.69/1.33 thf(f54,plain,(
% 1.69/1.33 ( ! [X6 : $i,X7 : $i,X4 : $i] : (((in @ X6 @ X4) != $true) | ($true != (in @ X6 @ (sK9 @ X4))) | ((in @ X7 @ X4) != $true) | (foundationAx != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f41])).
% 1.69/1.33 thf(f41,plain,(
% 1.69/1.33 ((foundationAx = $true) | (! [X1 : $i] : (((in @ X1 @ sK6) != $true) | (((in @ (sK7 @ X1) @ sK6) = $true) & ($true = (in @ (sK7 @ X1) @ X1)))) & ($true = (in @ sK8 @ sK6)))) & (! [X4 : $i] : ((((in @ (sK9 @ X4) @ X4) = $true) & ! [X6 : $i] : (((in @ X6 @ X4) != $true) | ($true != (in @ X6 @ (sK9 @ X4))))) | ! [X7 : $i] : ((in @ X7 @ X4) != $true)) | (foundationAx != $true))),
% 1.69/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f36,f40,f39,f38,f37])).
% 1.69/1.33 thf(f37,plain,(
% 1.69/1.33 ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0) != $true) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) = $true))) & ? [X3 : $i] : ((in @ X3 @ X0) = $true)) => (! [X1 : $i] : (((in @ X1 @ sK6) != $true) | ? [X2 : $i] : (((in @ X2 @ sK6) = $true) & ((in @ X2 @ X1) = $true))) & ? [X3 : $i] : ((in @ X3 @ sK6) = $true))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f38,plain,(
% 1.69/1.33 ! [X1 : $i] : (? [X2 : $i] : (((in @ X2 @ sK6) = $true) & ((in @ X2 @ X1) = $true)) => (((in @ (sK7 @ X1) @ sK6) = $true) & ($true = (in @ (sK7 @ X1) @ X1))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f39,plain,(
% 1.69/1.33 ? [X3 : $i] : ((in @ X3 @ sK6) = $true) => ($true = (in @ sK8 @ sK6))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f40,plain,(
% 1.69/1.33 ! [X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ! [X6 : $i] : (((in @ X6 @ X4) != $true) | ((in @ X6 @ X5) != $true))) => (((in @ (sK9 @ X4) @ X4) = $true) & ! [X6 : $i] : (((in @ X6 @ X4) != $true) | ($true != (in @ X6 @ (sK9 @ X4))))))),
% 1.69/1.33 introduced(definition,[],[choice_axiom])).
% 1.69/1.33 thf(f36,plain,(
% 1.69/1.33 ((foundationAx = $true) | ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0) != $true) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) = $true))) & ? [X3 : $i] : ((in @ X3 @ X0) = $true))) & (! [X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ! [X6 : $i] : (((in @ X6 @ X4) != $true) | ((in @ X6 @ X5) != $true))) | ! [X7 : $i] : ((in @ X7 @ X4) != $true)) | (foundationAx != $true))),
% 1.69/1.33 inference(rectify,[status(thm)],[f35])).
% 1.69/1.33 thf(f35,plain,(
% 1.69/1.33 ((foundationAx = $true) | ? [X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) = $true))) & ? [X1 : $i] : ((in @ X1 @ X0) = $true))) & (! [X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true))) | ! [X1 : $i] : ((in @ X1 @ X0) != $true)) | (foundationAx != $true))),
% 1.69/1.33 inference(nnf_transformation,[status(thm)],[f18])).
% 1.69/1.33 thf(f18,plain,(
% 1.69/1.33 (foundationAx = $true) <=> ! [X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) != $true))) | ! [X1 : $i] : ((in @ X1 @ X0) != $true))),
% 1.69/1.33 inference(ennf_transformation,[status(thm)],[f15])).
% 1.69/1.33 thf(f15,plain,(
% 1.69/1.33 (foundationAx = $true) <=> ! [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) => ? [X2 : $i] : (~? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) = $true)) & ((in @ X2 @ X0) = $true)))),
% 1.69/1.33 inference(fool_elimination,[status(thm)],[f14])).
% 1.69/1.33 thf(f14,plain,(
% 1.69/1.33 (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : ((in @ X2 @ X0) & ~? [X3 : $i] : ((in @ X3 @ X2) & (in @ X3 @ X0)))) = foundationAx)),
% 1.69/1.33 inference(rectify,[status(thm)],[f1])).
% 1.69/1.33 thf(f1,axiom,(
% 1.69/1.33 (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : ((in @ X2 @ X0) & ~? [X1 : $i] : ((in @ X1 @ X2) & (in @ X1 @ X0)))) = foundationAx)),
% 1.69/1.33 file('/export/starexec/sandbox2/tmp/tmp.8F5beL8ATw/DTF2THF_1422.p',foundationAx)).
% 1.69/1.33 thf(f84,plain,(
% 1.69/1.33 (emptyset != (binintersect @ (sK9 @ sK0) @ sK0)) | spl10_1),
% 1.69/1.33 inference(avatar_component_clause,[status(thm)],[f82])).
% 1.69/1.33 thf(f88,plain,(
% 1.69/1.33 ~spl10_1 | spl10_2),
% 1.69/1.33 inference(avatar_split_clause,[status(thm)],[f80,f86,f82])).
% 1.69/1.33 thf(f80,plain,(
% 1.69/1.33 ( ! [X0 : $i] : ((emptyset != (binintersect @ (sK9 @ sK0) @ sK0)) | ((in @ X0 @ sK0) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.69/1.33 thf(f79,plain,(
% 1.69/1.33 ( ! [X0 : $i] : (((in @ X0 @ sK0) != $true) | ($true != $true) | (emptyset != (binintersect @ (sK9 @ sK0) @ sK0))) )),
% 1.69/1.33 inference(superposition,[status(thm)],[f45,f71])).
% 1.69/1.33 thf(f71,plain,(
% 1.69/1.33 ( ! [X7 : $i,X4 : $i] : (((in @ (sK9 @ X4) @ X4) = $true) | ((in @ X7 @ X4) != $true)) )),
% 1.69/1.33 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.69/1.33 thf(f69,plain,(
% 1.69/1.33 ( ! [X7 : $i,X4 : $i] : (($true != $true) | ((in @ X7 @ X4) != $true) | ((in @ (sK9 @ X4) @ X4) = $true)) )),
% 1.69/1.33 inference(definition_unfolding,[status(thm)],[f55,f43])).
% 1.69/1.33 thf(f55,plain,(
% 1.69/1.33 ( ! [X7 : $i,X4 : $i] : (((in @ (sK9 @ X4) @ X4) = $true) | ((in @ X7 @ X4) != $true) | (foundationAx != $true)) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f41])).
% 1.69/1.33 thf(f45,plain,(
% 1.69/1.33 ( ! [X1 : $i] : (($true != (in @ X1 @ sK0)) | (emptyset != (binintersect @ X1 @ sK0))) )),
% 1.69/1.33 inference(cnf_transformation,[status(thm)],[f24])).
% 1.69/1.33 % SZS output end Proof for DTF2THF_1422
% 1.69/1.33 % (1599)------------------------------
% 1.69/1.33 % (1599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (1599)Termination reason: Refutation
% 1.69/1.33
% 1.69/1.33 % (1599)Memory used [KB]: 5628
% 1.69/1.33 % (1599)Time elapsed: 0.009 s
% 1.69/1.33 % (1599)Instructions burned: 8 (million)
% 1.69/1.33 % (1599)------------------------------
% 1.69/1.33 % (1599)------------------------------
% 1.69/1.33 % (1593)Success in time 0.024 s
%------------------------------------------------------------------------------