%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU760^2 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:59 AM UTC 2026
% Result : Theorem 1.55s 1.26s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 848 ( 246 equ; 0 cnn)
% Maximal formula atoms : 10 ( 13 avg)
% Number of connectives : 884 ( 97 ~; 79 |; 81 &; 570 @)
% ( 7 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 17 con; 0-2 aty)
% Number of variables : 186 ( 0 ^; 136 !; 50 ?; 186 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
binintersect: $i > $i > $i ).
thf(func_def_19,type,
sK9: $i > $i > $i ).
thf(f102,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f101,f46]) ).
thf(f46,plain,
( ( subset @ sK5 @ sK6 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true )
& ( $true
!= ( subset @ ( binintersect @ sK4 @ sK5 ) @ sK6 ) )
& ( ( in @ sK6 @ ( powerset @ sK3 ) )
= $true )
& ( ( subset @ sK5 @ sK6 )
= $true )
& ( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true )
& ( subsetI1 = $true )
& ( subsetE = $true )
& ( binintersectER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f25,f28,f27,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X2 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
=> ( ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK4 @ X2 ) @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK3 ) ) )
& ( ( subset @ X2 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK3 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK4 @ X2 ) @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK3 ) ) )
& ( ( subset @ X2 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK3 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK4 @ sK5 ) @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK3 ) ) )
& ( ( subset @ sK5 @ X3 )
= $true ) )
& ( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ sK4 @ sK5 ) @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ ( powerset @ sK3 ) ) )
& ( ( subset @ sK5 @ X3 )
= $true ) )
=> ( ( $true
!= ( subset @ ( binintersect @ sK4 @ sK5 ) @ sK6 ) )
& ( ( in @ sK6 @ ( powerset @ sK3 ) )
= $true )
& ( ( subset @ sK5 @ sK6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ X1 @ X2 ) @ X3 )
!= $true )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X2 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
& ( subsetI1 = $true )
& ( subsetE = $true )
& ( binintersectER = $true ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ X0 @ X2 ) @ X3 )
!= $true )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X2 @ X3 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
& ( subsetI1 = $true )
& ( subsetE = $true )
& ( binintersectER = $true ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ ( binintersect @ X0 @ X2 ) @ X3 )
!= $true )
& ( ( subset @ X2 @ X3 )
= $true )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binintersectER = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( subsetI1 = $true )
=> ( ( subsetE = $true )
=> ( ( binintersectER = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ( ( ( subset @ X2 @ X3 )
= $true )
=> ( ( subset @ ( binintersect @ X0 @ X2 ) @ X3 )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( subsetI1
=> ( subsetE
=> ( binintersectER
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ X3 )
=> ( subset @ ( binintersect @ X0 @ X2 ) @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( binintersectER
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( subsetI1
=> ( subsetE
=> ( binintersectER
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ ( binintersect @ X3 @ X4 ) @ X5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a6laubwGw9/DTF2THF_31731.p',woz13rule2) ).
thf(f101,plain,
( ( subset @ sK5 @ sK6 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $true != $true )
| ( ( subset @ sK5 @ sK6 )
!= $true ) ),
inference(superposition,[status(thm)],[f48,f92]) ).
thf(f92,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X2 ) )
| ( ( subset @ X1 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X2 ) )
| ( ( subset @ X1 @ X2 )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X1 @ X2 )
!= $true )
| ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X2 ) )
| ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X2 ) ) ),
inference(superposition,[status(thm)],[f81,f77]) ).
thf(f77,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X1 )
= $true )
| ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK9 @ ( binintersect @ X0 @ X1 ) @ X2 ) @ X1 )
= $true )
| ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f70,f72]) ).
thf(f72,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( subset @ X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( subset @ X4 @ X3 )
= $true )
| ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f51,f44]) ).
thf(f44,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f51,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( subset @ X4 @ X3 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( subsetI1 = $true )
| ( ! [X2: $i] :
( ( ( in @ X2 @ sK8 )
!= $true )
| ( ( in @ X2 @ sK7 )
= $true ) )
& ( $true
!= ( subset @ sK8 @ sK7 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
!= $true ) )
| ( ( subset @ X4 @ X3 )
= $true ) )
| ( subsetI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f31,f33,f32]) ).
thf(f32,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( $true
!= ( subset @ X1 @ X0 ) ) )
=> ( ! [X2: $i] :
( ( ( in @ X2 @ sK8 )
!= $true )
| ( ( in @ X2 @ sK7 )
= $true ) )
& ( $true
!= ( subset @ sK8 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
!= $true ) )
=> ( ( ( in @ ( sK9 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( $true
!= ( subset @ X1 @ X0 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
!= $true ) )
| ( ( subset @ X4 @ X3 )
= $true ) )
| ( subsetI1 != $true ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( subsetI1 = $true )
| ? [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
& ( ( subset @ X0 @ X1 )
!= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( subsetI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( subsetI1 = $true )
<=> ! [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,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)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
file('/export/starexec/sandbox/tmp/tmp.a6laubwGw9/DTF2THF_31731.p',subsetI1) ).
thf(f70,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f41,f42]) ).
thf(f42,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f41,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ( ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ ( binintersect @ sK2 @ sK1 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f22,f23]) ).
thf(f23,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
& ( ( in @ X3 @ ( binintersect @ X5 @ X4 ) )
= $true ) )
=> ( ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ ( binintersect @ sK2 @ sK1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
& ( ( in @ X3 @ ( binintersect @ X5 @ X4 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
& ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
<=> ( binintersectER = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( binintersectER = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
=> ( ( in @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( binintersectER
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a6laubwGw9/DTF2THF_31731.p',binintersectER) ).
thf(f81,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK9 @ X0 @ X1 ) @ X2 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ ( sK9 @ X0 @ X1 ) @ X2 )
!= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f71,f69]) ).
thf(f69,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( $true != $true )
| ( ( in @ X2 @ X1 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f57,f43]) ).
thf(f43,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f57,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( ( in @ sK12 @ sK11 )
= $true )
& ( ( subset @ sK11 @ sK10 )
= $true )
& ( ( in @ sK12 @ sK10 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f36,f37]) ).
thf(f37,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( subset @ X4 @ X3 )
= $true )
& ( ( in @ X5 @ X3 )
!= $true ) )
=> ( ( ( in @ sK12 @ sK11 )
= $true )
& ( ( subset @ sK11 @ sK10 )
= $true )
& ( ( in @ sK12 @ sK10 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( subset @ X4 @ X3 )
= $true )
& ( ( in @ X5 @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( subset @ X1 @ X0 ) )
& ( ( in @ X2 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( subsetE
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a6laubwGw9/DTF2THF_31731.p',subsetE) ).
thf(f71,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( subset @ X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( subset @ X4 @ X3 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f50,f44]) ).
thf(f50,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK9 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( subset @ X4 @ X3 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f48,plain,
( $true
!= ( subset @ ( binintersect @ sK4 @ sK5 ) @ sK6 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU760^2 : 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 : n016.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 12:33:36 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
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU760^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Typed Set Theory - First Wizard of Oz Examples - WoZ1 Lemmas
% 0.20/0.46 % Version : Especial > Reduced > Especial.
% 0.20/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.20/0.46 % (! Z:i.in Z (powerset A) -> subset Y Z ->
% 0.20/0.46 % subset (binintersect X Y) Z)))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC262l [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.20/0.46 % Number of atoms : 22 ( 3 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 8 ( 5 avg)
% 0.20/0.46 % Number of connectives : 45 ( 0 ~; 0 |; 0 &; 33 @)
% 0.20/0.46 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 16 ( 5 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=321
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(powerset_type,type,
% 0.20/0.46 powerset: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(subset_type,type,
% 0.20/0.46 subset: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1_type,type,
% 0.20/0.46 subsetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1,definition,
% 0.20/0.46 ( subsetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE_type,type,
% 0.20/0.46 subsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE,definition,
% 0.20/0.46 ( subsetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersect_type,type,
% 0.20/0.46 binintersect: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER_type,type,
% 0.20/0.46 binintersectER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER,definition,
% 0.20/0.46 ( binintersectER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule2,conjecture,
% 0.20/0.46 ( subsetI1
% 0.20/0.46 => ( subsetE
% 0.20/0.46 => ( binintersectER
% 0.20/0.46 => ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ Y @ Z )
% 0.20/0.46 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.55/1.23 ---- Embedded in THF ---
% 1.55/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.23 %%% Generated on Tue Feb 24 12:33:37 EST 2026
% 1.55/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.23 %%% Logic specification used:
% 1.55/1.23 %%% thf(spec, logic, $$dhol).
% 1.55/1.23
% 1.55/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.a6laubwGw9/DTF2DTF31731.p
% See solution above
% 1.55/1.23 ------------------------
% 1.55/1.24 ---- Cleaned THF ---
% 1.55/1.25 thf(in_type,type,
% 1.55/1.25 in: $i > $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(powerset_type,type,
% 1.55/1.25 powerset: $i > $i ).
% 1.55/1.25
% 1.55/1.25 thf(subset_type,type,
% 1.55/1.25 subset: $i > $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(subsetI1_type,type,
% 1.55/1.25 subsetI1: $o ).
% 1.55/1.25
% 1.55/1.25 thf(subsetI1,definition,
% 1.55/1.25 ( subsetI1
% 1.55/1.25 = ( ! [A: $i,B: $i] :
% 1.55/1.25 ( ! [Xx: $i] :
% 1.55/1.25 ( ( in @ Xx @ A )
% 1.55/1.25 => ( in @ Xx @ B ) )
% 1.55/1.25 => ( subset @ A @ B ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(subsetE_type,type,
% 1.55/1.25 subsetE: $o ).
% 1.55/1.25
% 1.55/1.25 thf(subsetE,definition,
% 1.55/1.25 ( subsetE
% 1.55/1.25 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.55/1.25 ( ( subset @ A @ B )
% 1.55/1.25 => ( ( in @ Xx @ A )
% 1.55/1.25 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(binintersect_type,type,
% 1.55/1.25 binintersect: $i > $i > $i ).
% 1.55/1.25
% 1.55/1.25 thf(binintersectER_type,type,
% 1.55/1.25 binintersectER: $o ).
% 1.55/1.25
% 1.55/1.25 thf(binintersectER,definition,
% 1.55/1.25 ( binintersectER
% 1.55/1.25 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.55/1.25 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 1.55/1.25 => ( in @ Xx @ B ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(woz13rule2,conjecture,
% 1.55/1.25 ( subsetI1
% 1.55/1.25 => ( subsetE
% 1.55/1.25 => ( binintersectER
% 1.55/1.25 => ! [A: $i,X: $i] :
% 1.55/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.55/1.25 => ! [Y: $i] :
% 1.55/1.25 ( ( in @ Y @ ( powerset @ A ) )
% 1.55/1.25 => ! [Z: $i] :
% 1.55/1.25 ( ( in @ Z @ ( powerset @ A ) )
% 1.55/1.25 => ( ( subset @ Y @ Z )
% 1.55/1.25 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ).
% 1.55/1.25 ------------------------
% 1.55/1.26 % (31923)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31731 for (3000ds/2Mi)
% 1.55/1.26 % (31925)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_31731 for (3000ds/275Mi)
% 1.55/1.26 % (31920)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31731 for (3000ds/183Mi)
% 1.55/1.26 % (31923)Instruction limit reached!
% 1.55/1.26 % (31923)------------------------------
% 1.55/1.26 % (31923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (31923)Termination reason: Unknown
% 1.55/1.26 % (31923)Termination phase: Property scanning
% 1.55/1.26
% 1.55/1.26 % (31923)Memory used [KB]: 1023
% 1.55/1.26 % (31923)Time elapsed: 0.002 s
% 1.55/1.26 % (31923)Instructions burned: 3 (million)
% 1.55/1.26 % (31923)------------------------------
% 1.55/1.26 % (31923)------------------------------
% 1.55/1.26 % (31925)First to succeed.
% 1.55/1.26 % (31925)Refutation found. Thanks to Tanya!
% 1.55/1.26 % SZS status Theorem for DTF2THF_31731
% 1.55/1.26 % SZS output start Proof for DTF2THF_31731
% 1.55/1.26 thf(func_def_0, type, in: $i > $i > $o).
% 1.55/1.26 thf(func_def_1, type, powerset: $i > $i).
% 1.55/1.26 thf(func_def_2, type, subset: $i > $i > $o).
% 1.55/1.26 thf(func_def_6, type, binintersect: $i > $i > $i).
% 1.55/1.26 thf(func_def_19, type, sK9: $i > $i > $i).
% 1.55/1.26 thf(f102,plain,(
% 1.55/1.26 $false),
% 1.55/1.26 inference(subsumption_resolution,[status(thm)],[f101,f46])).
% 1.55/1.26 thf(f46,plain,(
% 1.55/1.26 ((subset @ sK5 @ sK6) = $true)),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.26 thf(f29,plain,(
% 1.55/1.26 (((in @ sK4 @ (powerset @ sK3)) = $true) & ((($true != (subset @ (binintersect @ sK4 @ sK5) @ sK6)) & ((in @ sK6 @ (powerset @ sK3)) = $true) & ((subset @ sK5 @ sK6) = $true)) & ((in @ sK5 @ (powerset @ sK3)) = $true))) & (subsetI1 = $true) & (subsetE = $true) & (binintersectER = $true)),
% 1.55/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f25,f28,f27,f26])).
% 1.55/1.26 thf(f26,plain,(
% 1.55/1.26 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ X2 @ X3) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))) => (((in @ sK4 @ (powerset @ sK3)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ sK4 @ X2) @ X3) != $true) & ($true = (in @ X3 @ (powerset @ sK3))) & ((subset @ X2 @ X3) = $true)) & ((in @ X2 @ (powerset @ sK3)) = $true)))),
% 1.55/1.26 introduced(definition,[],[choice_axiom])).
% 1.55/1.26 thf(f27,plain,(
% 1.55/1.26 ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ sK4 @ X2) @ X3) != $true) & ($true = (in @ X3 @ (powerset @ sK3))) & ((subset @ X2 @ X3) = $true)) & ((in @ X2 @ (powerset @ sK3)) = $true)) => (? [X3 : $i] : (((subset @ (binintersect @ sK4 @ sK5) @ X3) != $true) & ($true = (in @ X3 @ (powerset @ sK3))) & ((subset @ sK5 @ X3) = $true)) & ((in @ sK5 @ (powerset @ sK3)) = $true))),
% 1.55/1.26 introduced(definition,[],[choice_axiom])).
% 1.55/1.26 thf(f28,plain,(
% 1.55/1.26 ? [X3 : $i] : (((subset @ (binintersect @ sK4 @ sK5) @ X3) != $true) & ($true = (in @ X3 @ (powerset @ sK3))) & ((subset @ sK5 @ X3) = $true)) => (($true != (subset @ (binintersect @ sK4 @ sK5) @ sK6)) & ((in @ sK6 @ (powerset @ sK3)) = $true) & ((subset @ sK5 @ sK6) = $true))),
% 1.55/1.26 introduced(definition,[],[choice_axiom])).
% 1.55/1.26 thf(f25,plain,(
% 1.55/1.26 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ X2 @ X3) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))) & (subsetI1 = $true) & (subsetE = $true) & (binintersectER = $true)),
% 1.55/1.26 inference(rectify,[status(thm)],[f20])).
% 1.55/1.26 thf(f20,plain,(
% 1.55/1.26 ? [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (((subset @ (binintersect @ X0 @ X2) @ X3) != $true) & ((in @ X3 @ (powerset @ X1)) = $true) & ((subset @ X2 @ X3) = $true)) & ($true = (in @ X2 @ (powerset @ X1))))) & (subsetI1 = $true) & (subsetE = $true) & (binintersectER = $true)),
% 1.55/1.26 inference(flattening,[status(thm)],[f19])).
% 1.55/1.26 thf(f19,plain,(
% 1.55/1.26 ((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((subset @ (binintersect @ X0 @ X2) @ X3) != $true) & ((subset @ X2 @ X3) = $true)) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) & (binintersectER = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 1.55/1.26 inference(ennf_transformation,[status(thm)],[f14])).
% 1.55/1.26 thf(f14,plain,(
% 1.55/1.26 ~((subsetI1 = $true) => ((subsetE = $true) => ((binintersectER = $true) => ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) => (((subset @ X2 @ X3) = $true) => ((subset @ (binintersect @ X0 @ X2) @ X3) = $true))))))))),
% 1.55/1.26 inference(fool_elimination,[status(thm)],[f13])).
% 1.55/1.26 thf(f13,plain,(
% 1.55/1.26 ~(subsetI1 => (subsetE => (binintersectER => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X0 @ X2) @ X3))))))))),
% 1.55/1.26 inference(rectify,[status(thm)],[f5])).
% 1.55/1.26 thf(f5,negated_conjecture,(
% 1.55/1.26 ~(subsetI1 => (subsetE => (binintersectER => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ((subset @ X4 @ X5) => (subset @ (binintersect @ X3 @ X4) @ X5))))))))),
% 1.55/1.26 inference(negated_conjecture,[status(cth)],[f4])).
% 1.55/1.26 thf(f4,conjecture,(
% 1.55/1.26 subsetI1 => (subsetE => (binintersectER => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ((subset @ X4 @ X5) => (subset @ (binintersect @ X3 @ X4) @ X5)))))))),
% 1.55/1.26 file('/export/starexec/sandbox/tmp/tmp.a6laubwGw9/DTF2THF_31731.p',woz13rule2)).
% 1.55/1.26 thf(f101,plain,(
% 1.55/1.26 ((subset @ sK5 @ sK6) != $true)),
% 1.55/1.26 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.55/1.26 thf(f98,plain,(
% 1.55/1.26 ($true != $true) | ((subset @ sK5 @ sK6) != $true)),
% 1.55/1.26 inference(superposition,[status(thm)],[f48,f92])).
% 1.55/1.26 thf(f92,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ (binintersect @ X0 @ X1) @ X2)) | ((subset @ X1 @ X2) != $true)) )),
% 1.55/1.26 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.55/1.26 thf(f91,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ (binintersect @ X0 @ X1) @ X2)) | ((subset @ X1 @ X2) != $true) | ($true != $true)) )),
% 1.55/1.26 inference(duplicate_literal_removal,[status(thm)],[f89])).
% 1.55/1.26 thf(f89,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((subset @ X1 @ X2) != $true) | ($true = (subset @ (binintersect @ X0 @ X1) @ X2)) | ($true = (subset @ (binintersect @ X0 @ X1) @ X2))) )),
% 1.55/1.26 inference(superposition,[status(thm)],[f81,f77])).
% 1.55/1.26 thf(f77,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X1) = $true) | ($true = (subset @ (binintersect @ X0 @ X1) @ X2))) )),
% 1.55/1.26 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.55/1.26 thf(f74,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK9 @ (binintersect @ X0 @ X1) @ X2) @ X1) = $true) | ($true = (subset @ (binintersect @ X0 @ X1) @ X2)) | ($true != $true)) )),
% 1.55/1.26 inference(superposition,[status(thm)],[f70,f72])).
% 1.55/1.26 thf(f72,plain,(
% 1.55/1.26 ( ! [X3 : $i,X4 : $i] : (((in @ (sK9 @ X4 @ X3) @ X4) = $true) | ((subset @ X4 @ X3) = $true)) )),
% 1.55/1.26 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.55/1.26 thf(f63,plain,(
% 1.55/1.26 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((subset @ X4 @ X3) = $true) | ((in @ (sK9 @ X4 @ X3) @ X4) = $true)) )),
% 1.55/1.26 inference(definition_unfolding,[status(thm)],[f51,f44])).
% 1.55/1.26 thf(f44,plain,(
% 1.55/1.26 (subsetI1 = $true)),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.26 thf(f51,plain,(
% 1.55/1.26 ( ! [X3 : $i,X4 : $i] : (((in @ (sK9 @ X4 @ X3) @ X4) = $true) | ((subset @ X4 @ X3) = $true) | (subsetI1 != $true)) )),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f34])).
% 1.55/1.26 thf(f34,plain,(
% 1.55/1.26 ((subsetI1 = $true) | (! [X2 : $i] : (((in @ X2 @ sK8) != $true) | ((in @ X2 @ sK7) = $true)) & ($true != (subset @ sK8 @ sK7)))) & (! [X3 : $i,X4 : $i] : ((((in @ (sK9 @ X4 @ X3) @ X4) = $true) & ((in @ (sK9 @ X4 @ X3) @ X3) != $true)) | ((subset @ X4 @ X3) = $true)) | (subsetI1 != $true))),
% 1.55/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f31,f33,f32])).
% 1.55/1.26 thf(f32,plain,(
% 1.55/1.26 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ($true != (subset @ X1 @ X0))) => (! [X2 : $i] : (((in @ X2 @ sK8) != $true) | ((in @ X2 @ sK7) = $true)) & ($true != (subset @ sK8 @ sK7)))),
% 1.55/1.26 introduced(definition,[],[choice_axiom])).
% 1.55/1.26 thf(f33,plain,(
% 1.55/1.26 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) != $true)) => (((in @ (sK9 @ X4 @ X3) @ X4) = $true) & ((in @ (sK9 @ X4 @ X3) @ X3) != $true)))),
% 1.55/1.26 introduced(definition,[],[choice_axiom])).
% 1.55/1.26 thf(f31,plain,(
% 1.55/1.26 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ($true != (subset @ X1 @ X0)))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) != $true)) | ((subset @ X4 @ X3) = $true)) | (subsetI1 != $true))),
% 1.55/1.26 inference(rectify,[status(thm)],[f30])).
% 1.55/1.26 thf(f30,plain,(
% 1.55/1.26 ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)) & ((subset @ X0 @ X1) != $true))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) | ((subset @ X0 @ X1) = $true)) | (subsetI1 != $true))),
% 1.55/1.26 inference(nnf_transformation,[status(thm)],[f18])).
% 1.55/1.26 thf(f18,plain,(
% 1.55/1.26 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) | ((subset @ X0 @ X1) = $true))),
% 1.55/1.26 inference(ennf_transformation,[status(thm)],[f8])).
% 1.55/1.26 thf(f8,plain,(
% 1.55/1.26 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true))),
% 1.55/1.26 inference(fool_elimination,[status(thm)],[f7])).
% 1.55/1.26 thf(f7,plain,(
% 1.55/1.26 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.55/1.26 inference(rectify,[status(thm)],[f1])).
% 1.55/1.26 thf(f1,axiom,(
% 1.55/1.26 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 1.55/1.26 file('/export/starexec/sandbox/tmp/tmp.a6laubwGw9/DTF2THF_31731.p',subsetI1)).
% 1.55/1.26 thf(f70,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true)) )),
% 1.55/1.26 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.55/1.26 thf(f58,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) != $true) | ($true != $true) | ((in @ X0 @ X1) = $true)) )),
% 1.55/1.26 inference(definition_unfolding,[status(thm)],[f41,f42])).
% 1.55/1.26 thf(f42,plain,(
% 1.55/1.26 (binintersectER = $true)),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.26 thf(f41,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ (binintersect @ X2 @ X1)) != $true) | (binintersectER != $true)) )),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f24])).
% 1.55/1.26 thf(f24,plain,(
% 1.55/1.26 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ (binintersect @ X2 @ X1)) != $true)) | (binintersectER != $true)) & ((binintersectER = $true) | (((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ (binintersect @ sK2 @ sK1)) = $true)))),
% 1.55/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f22,f23])).
% 1.55/1.26 thf(f23,plain,(
% 1.55/1.26 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) & ((in @ X3 @ (binintersect @ X5 @ X4)) = $true)) => (((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ (binintersect @ sK2 @ sK1)) = $true))),
% 1.55/1.26 introduced(definition,[],[choice_axiom])).
% 1.55/1.26 thf(f22,plain,(
% 1.55/1.26 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ (binintersect @ X2 @ X1)) != $true)) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) & ((in @ X3 @ (binintersect @ X5 @ X4)) = $true)))),
% 1.55/1.26 inference(rectify,[status(thm)],[f21])).
% 1.55/1.26 thf(f21,plain,(
% 1.55/1.26 (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ X2) = $true) | ($true != (in @ X1 @ (binintersect @ X0 @ X2)))) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ X2) != $true) & ($true = (in @ X1 @ (binintersect @ X0 @ X2)))))),
% 1.55/1.26 inference(nnf_transformation,[status(thm)],[f15])).
% 1.55/1.26 thf(f15,plain,(
% 1.55/1.26 ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X1 @ X2) = $true) | ($true != (in @ X1 @ (binintersect @ X0 @ X2)))) <=> (binintersectER = $true)),
% 1.55/1.26 inference(ennf_transformation,[status(thm)],[f10])).
% 1.55/1.26 thf(f10,plain,(
% 1.55/1.26 (binintersectER = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X1 @ (binintersect @ X0 @ X2))) => ((in @ X1 @ X2) = $true))),
% 1.55/1.26 inference(fool_elimination,[status(thm)],[f9])).
% 1.55/1.26 thf(f9,plain,(
% 1.55/1.26 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X0 @ X2)) => (in @ X1 @ X2)))),
% 1.55/1.26 inference(rectify,[status(thm)],[f3])).
% 1.55/1.26 thf(f3,axiom,(
% 1.55/1.26 (binintersectER = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 1.55/1.26 file('/export/starexec/sandbox/tmp/tmp.a6laubwGw9/DTF2THF_31731.p',binintersectER)).
% 1.55/1.26 thf(f81,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK9 @ X0 @ X1) @ X2) != $true) | ((subset @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true)) )),
% 1.55/1.26 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.55/1.26 thf(f79,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK9 @ X0 @ X1) @ X2) != $true) | ((subset @ X2 @ X1) != $true) | ((subset @ X0 @ X1) = $true)) )),
% 1.55/1.26 inference(superposition,[status(thm)],[f71,f69])).
% 1.55/1.26 thf(f69,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true) | ($true != (subset @ X1 @ X0))) )),
% 1.55/1.26 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.55/1.26 thf(f65,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ($true != (subset @ X1 @ X0)) | ($true != $true) | ((in @ X2 @ X1) != $true)) )),
% 1.55/1.26 inference(definition_unfolding,[status(thm)],[f57,f43])).
% 1.55/1.26 thf(f43,plain,(
% 1.55/1.26 (subsetE = $true)),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.26 thf(f57,plain,(
% 1.55/1.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ($true != (subset @ X1 @ X0)) | ((in @ X2 @ X0) = $true) | (subsetE != $true)) )),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.26 thf(f38,plain,(
% 1.55/1.26 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (subset @ X1 @ X0)) | ((in @ X2 @ X0) = $true)) | (subsetE != $true)) & ((subsetE = $true) | (((in @ sK12 @ sK11) = $true) & ((subset @ sK11 @ sK10) = $true) & ((in @ sK12 @ sK10) != $true)))),
% 1.55/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f36,f37])).
% 1.55/1.26 thf(f37,plain,(
% 1.55/1.26 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) & ((subset @ X4 @ X3) = $true) & ((in @ X5 @ X3) != $true)) => (((in @ sK12 @ sK11) = $true) & ((subset @ sK11 @ sK10) = $true) & ((in @ sK12 @ sK10) != $true))),
% 1.55/1.26 introduced(definition,[],[choice_axiom])).
% 1.55/1.26 thf(f36,plain,(
% 1.55/1.26 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (subset @ X1 @ X0)) | ((in @ X2 @ X0) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) & ((subset @ X4 @ X3) = $true) & ((in @ X5 @ X3) != $true)))),
% 1.55/1.26 inference(rectify,[status(thm)],[f35])).
% 1.55/1.26 thf(f35,plain,(
% 1.55/1.26 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (subset @ X1 @ X0)) | ((in @ X2 @ X0) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ($true = (subset @ X1 @ X0)) & ((in @ X2 @ X0) != $true)))),
% 1.55/1.26 inference(nnf_transformation,[status(thm)],[f17])).
% 1.55/1.26 thf(f17,plain,(
% 1.55/1.26 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (subset @ X1 @ X0)) | ((in @ X2 @ X0) = $true)) <=> (subsetE = $true)),
% 1.55/1.26 inference(flattening,[status(thm)],[f16])).
% 1.55/1.26 thf(f16,plain,(
% 1.55/1.26 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) | ($true != (subset @ X1 @ X0)))),
% 1.55/1.26 inference(ennf_transformation,[status(thm)],[f12])).
% 1.55/1.26 thf(f12,plain,(
% 1.55/1.26 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) => (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)))),
% 1.55/1.26 inference(fool_elimination,[status(thm)],[f11])).
% 1.55/1.26 thf(f11,plain,(
% 1.55/1.26 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 1.55/1.26 inference(rectify,[status(thm)],[f2])).
% 1.55/1.26 thf(f2,axiom,(
% 1.55/1.26 (subsetE = ! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.55/1.26 file('/export/starexec/sandbox/tmp/tmp.a6laubwGw9/DTF2THF_31731.p',subsetE)).
% 1.55/1.26 thf(f71,plain,(
% 1.55/1.26 ( ! [X3 : $i,X4 : $i] : (((in @ (sK9 @ X4 @ X3) @ X3) != $true) | ((subset @ X4 @ X3) = $true)) )),
% 1.55/1.26 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.55/1.26 thf(f64,plain,(
% 1.55/1.26 ( ! [X3 : $i,X4 : $i] : (((in @ (sK9 @ X4 @ X3) @ X3) != $true) | ((subset @ X4 @ X3) = $true) | ($true != $true)) )),
% 1.55/1.26 inference(definition_unfolding,[status(thm)],[f50,f44])).
% 1.55/1.26 thf(f50,plain,(
% 1.55/1.26 ( ! [X3 : $i,X4 : $i] : (((in @ (sK9 @ X4 @ X3) @ X3) != $true) | ((subset @ X4 @ X3) = $true) | (subsetI1 != $true)) )),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f34])).
% 1.55/1.26 thf(f48,plain,(
% 1.55/1.26 ($true != (subset @ (binintersect @ sK4 @ sK5) @ sK6))),
% 1.55/1.26 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.26 % SZS output end Proof for DTF2THF_31731
% 1.55/1.26 % (31925)------------------------------
% 1.55/1.26 % (31925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (31925)Termination reason: Refutation
% 1.55/1.26
% 1.55/1.26 % (31925)Memory used [KB]: 5628
% 1.55/1.26 % (31925)Time elapsed: 0.006 s
% 1.55/1.26 % (31925)Instructions burned: 12 (million)
% 1.55/1.26 % (31925)------------------------------
% 1.55/1.26 % (31925)------------------------------
% 1.55/1.26 % (31919)Success in time 0.006 s
%------------------------------------------------------------------------------