%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU761^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:59 AM UTC 2026
% Result : Theorem 1.66s 1.39s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 1061 ( 293 equ; 0 cnn)
% Maximal formula atoms : 12 ( 14 avg)
% Number of connectives : 1049 ( 107 ~; 99 |; 96 &; 682 @)
% ( 8 <=>; 57 =>; 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 : 183 ( 0 ^; 133 !; 50 ?; 183 :)
% 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_20,type,
sK10: $i > $i > $i ).
thf(f346,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f335,f47]) ).
thf(f47,plain,
( ( subset @ sK3 @ ( binintersect @ sK5 @ sK6 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( subsetE = $true )
& ( subsetI1 = $true )
& ( binintersectI = $true )
& ( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ sK6 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ ( binintersect @ sK5 @ sK6 ) )
!= $true )
& ( ( subset @ sK3 @ sK5 )
= $true )
& ( ( subset @ sK3 @ sK6 )
= $true )
& ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f26,f29,f28,f27]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( $true
= ( subset @ X0 @ X2 ) )
& ( $true
= ( subset @ X0 @ X3 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
=> ( ( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( ( subset @ sK3 @ X2 )
= $true )
& ( ( subset @ sK3 @ X3 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK4 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( ( subset @ sK3 @ X2 )
= $true )
& ( ( subset @ sK3 @ X3 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK4 ) ) ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ ( binintersect @ sK5 @ X3 ) )
!= $true )
& ( ( subset @ sK3 @ sK5 )
= $true )
& ( ( subset @ sK3 @ X3 )
= $true ) )
& ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ ( binintersect @ sK5 @ X3 ) )
!= $true )
& ( ( subset @ sK3 @ sK5 )
= $true )
& ( ( subset @ sK3 @ X3 )
= $true ) )
=> ( ( ( in @ sK6 @ ( powerset @ sK4 ) )
= $true )
& ( ( subset @ sK3 @ ( binintersect @ sK5 @ sK6 ) )
!= $true )
& ( ( subset @ sK3 @ sK5 )
= $true )
& ( ( subset @ sK3 @ sK6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( subsetE = $true )
& ( subsetI1 = $true )
& ( binintersectI = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( $true
= ( subset @ X0 @ X2 ) )
& ( $true
= ( subset @ X0 @ X3 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( subsetE = $true )
& ( subsetI1 = $true )
& ( binintersectI = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( $true
!= ( subset @ X1 @ ( binintersect @ X2 @ X3 ) ) )
& ( $true
= ( subset @ X1 @ X2 ) )
& ( ( subset @ X1 @ X3 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( subset @ X1 @ ( binintersect @ X2 @ X3 ) ) )
& ( ( subset @ X1 @ X3 )
= $true )
& ( $true
= ( subset @ X1 @ X2 ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectI = $true )
& ( subsetE = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( subsetI1 = $true )
=> ( ( subsetE = $true )
=> ( ( binintersectI = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( ( subset @ X1 @ X3 )
= $true )
=> ( $true
= ( subset @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( subsetI1
=> ( subsetE
=> ( binintersectI
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X2 )
=> ( ( subset @ X1 @ X3 )
=> ( subset @ X1 @ ( binintersect @ X2 @ X3 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( subsetI1
=> ( subsetE
=> ( binintersectI
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ( ( subset @ X3 @ X4 )
=> ( ( subset @ X3 @ X5 )
=> ( subset @ X3 @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( subsetI1
=> ( subsetE
=> ( binintersectI
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ( ( subset @ X3 @ X4 )
=> ( ( subset @ X3 @ X5 )
=> ( subset @ X3 @ ( binintersect @ X4 @ X5 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.O4ok8h6Gzb/DTF2THF_28211.p',woz13rule3) ).
thf(f335,plain,
( ( subset @ sK3 @ ( binintersect @ sK5 @ sK6 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f334]) ).
thf(f334,plain,
( ( ( subset @ sK3 @ ( binintersect @ sK5 @ sK6 ) )
= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f329]) ).
thf(f329,plain,
( ( $true != $true )
| ( ( subset @ sK3 @ ( binintersect @ sK5 @ sK6 ) )
= $true )
| ( ( subset @ sK3 @ ( binintersect @ sK5 @ sK6 ) )
= $true ) ),
inference(superposition,[status(thm)],[f73,f260]) ).
thf(f260,plain,
! [X0: $i] :
( ( ( in @ ( sK10 @ sK3 @ X0 ) @ ( binintersect @ sK5 @ sK6 ) )
= $true )
| ( $true
= ( subset @ sK3 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f259]) ).
thf(f259,plain,
! [X0: $i] :
( ( $true
= ( subset @ sK3 @ X0 ) )
| ( $true != $true )
| ( ( in @ ( sK10 @ sK3 @ X0 ) @ ( binintersect @ sK5 @ sK6 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f254]) ).
thf(f254,plain,
! [X0: $i] :
( ( $true
= ( subset @ sK3 @ X0 ) )
| ( $true != $true )
| ( $true
= ( subset @ sK3 @ X0 ) )
| ( ( in @ ( sK10 @ sK3 @ X0 ) @ ( binintersect @ sK5 @ sK6 ) )
= $true ) ),
inference(superposition,[status(thm)],[f99,f96]) ).
thf(f96,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK10 @ sK3 @ X0 ) @ sK6 ) )
| ( $true
= ( subset @ sK3 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK10 @ sK3 @ X0 ) @ sK6 ) )
| ( $true
= ( subset @ sK3 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f83,f74]) ).
thf(f74,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ X1 @ X0 ) @ X1 )
= $true )
| ( $true
= ( subset @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( in @ ( sK10 @ X1 @ X0 ) @ X1 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f60,f51]) ).
thf(f51,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f60,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( in @ ( sK10 @ X1 @ X0 ) @ X1 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( ( in @ ( sK10 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ( ( $true
!= ( subset @ sK12 @ sK11 ) )
& ! [X5: $i] :
( ( ( in @ X5 @ sK12 )
!= $true )
| ( ( in @ X5 @ sK11 )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f36,f38,f37]) ).
thf(f37,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
=> ( ( ( in @ ( sK10 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ? [X3: $i,X4: $i] :
( ( $true
!= ( subset @ X4 @ X3 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( ( in @ X5 @ X3 )
= $true ) ) )
=> ( ( $true
!= ( subset @ sK12 @ sK11 ) )
& ! [X5: $i] :
( ( ( in @ X5 @ sK12 )
!= $true )
| ( ( in @ X5 @ sK11 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X3: $i,X4: $i] :
( ( $true
!= ( subset @ X4 @ X3 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( ( in @ X5 @ X3 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( $true
= ( subset @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetI1
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.O4ok8h6Gzb/DTF2THF_28211.p',subsetI1) ).
thf(f83,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK3 )
!= $true )
| ( ( in @ X0 @ sK6 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK6 )
= $true )
| ( ( in @ X0 @ sK3 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f75,f45]) ).
thf(f45,plain,
( ( subset @ sK3 @ sK6 )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f75,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( subset @ X0 @ X2 ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f43,f52]) ).
thf(f52,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f43,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X2 ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X0 @ X2 ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( $true
= ( subset @ sK0 @ sK2 ) )
& ( $true
!= ( in @ sK1 @ sK2 ) )
& ( $true
= ( in @ sK1 @ sK0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f24]) ).
thf(f24,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
& ( $true
!= ( in @ X4 @ X5 ) )
& ( ( in @ X4 @ X3 )
= $true ) )
=> ( ( $true
= ( subset @ sK0 @ sK2 ) )
& ( $true
!= ( in @ sK1 @ sK2 ) )
& ( $true
= ( in @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X0 @ X2 ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
& ( $true
!= ( in @ X4 @ X5 ) )
& ( ( in @ X4 @ X3 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.O4ok8h6Gzb/DTF2THF_28211.p',subsetE) ).
thf(f99,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK10 @ sK3 @ X0 ) @ X1 ) )
| ( $true
= ( subset @ sK3 @ X0 ) )
| ( ( in @ ( sK10 @ sK3 @ X0 ) @ ( binintersect @ sK5 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ sK3 @ X0 ) @ ( binintersect @ sK5 @ X1 ) )
= $true )
| ( $true
!= ( in @ ( sK10 @ sK3 @ X0 ) @ X1 ) )
| ( $true != $true )
| ( $true
= ( subset @ sK3 @ X0 ) ) ),
inference(superposition,[status(thm)],[f76,f94]) ).
thf(f94,plain,
! [X0: $i] :
( ( ( in @ ( sK10 @ sK3 @ X0 ) @ sK5 )
= $true )
| ( $true
= ( subset @ sK3 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
! [X0: $i] :
( ( ( in @ ( sK10 @ sK3 @ X0 ) @ sK5 )
= $true )
| ( $true
= ( subset @ sK3 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f82,f74]) ).
thf(f82,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK3 )
!= $true )
| ( ( in @ X0 @ sK5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ sK5 )
= $true )
| ( ( in @ X0 @ sK3 )
!= $true ) ),
inference(superposition,[status(thm)],[f75,f46]) ).
thf(f46,plain,
( ( subset @ sK3 @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f56,f50]) ).
thf(f50,plain,
binintersectI = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f56,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( binintersectI != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ( ( $true
!= ( in @ sK7 @ ( binintersect @ sK9 @ sK8 ) ) )
& ( ( in @ sK7 @ sK9 )
= $true )
& ( ( in @ sK7 @ sK8 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f32,f33]) ).
thf(f33,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
& ( ( in @ X3 @ X5 )
= $true )
& ( $true
= ( in @ X3 @ X4 ) ) )
=> ( ( $true
!= ( in @ sK7 @ ( binintersect @ sK9 @ sK8 ) ) )
& ( ( in @ sK7 @ sK9 )
= $true )
& ( ( in @ sK7 @ sK8 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
& ( ( in @ X3 @ X5 )
= $true )
& ( $true
= ( in @ X3 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( binintersectI = $true ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( binintersectI = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
= $true ) ) )
<=> ( binintersectI = $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) ) )
= binintersectI ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectI ),
file('/export/starexec/sandbox/tmp/tmp.O4ok8h6Gzb/DTF2THF_28211.p',binintersectI) ).
thf(f73,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true )
| ( $true
= ( subset @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f59,f51]) ).
thf(f59,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( in @ ( sK10 @ X1 @ X0 ) @ X0 )
!= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU761^2 : 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
% 0.17/0.34 % Computer : n028.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:33:12 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU761^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Typed Set Theory - First Wizard of Oz Examples - WoZ1 Lemmas
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.30/0.46 % (! Z:i.in Z (powerset A) -> subset X Y -> subset X Z ->
% 0.30/0.46 % subset X (binintersect Y Z))))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC263l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.30/0.46 % Number of atoms : 24 ( 3 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 9 ( 6 avg)
% 0.30/0.46 % Number of connectives : 51 ( 0 ~; 0 |; 0 &; 37 @)
% 0.30/0.46 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 16 ( 5 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=322
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(subset_type,type,
% 0.30/0.46 subset: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1_type,type,
% 0.30/0.46 subsetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1,definition,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE_type,type,
% 0.30/0.46 subsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE,definition,
% 0.30/0.46 ( subsetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersect_type,type,
% 0.30/0.46 binintersect: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI_type,type,
% 0.30/0.46 binintersectI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI,definition,
% 0.30/0.46 ( binintersectI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(woz13rule3,conjecture,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 => ( subsetE
% 0.30/0.46 => ( binintersectI
% 0.30/0.46 => ! [A: $i,X: $i] :
% 0.30/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.46 => ! [Y: $i] :
% 0.30/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.46 => ! [Z: $i] :
% 0.30/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.46 => ( ( subset @ X @ Y )
% 0.30/0.46 => ( ( subset @ X @ Z )
% 0.30/0.46 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.52/1.27 ---- Embedded in THF ---
% 1.52/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.27 %%% Generated on Tue Feb 24 12:33:12 EST 2026
% 1.52/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.27 %%% Logic specification used:
% 1.52/1.27 %%% thf(spec, logic, $$dhol).
% 1.52/1.27
% 1.52/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.O4ok8h6Gzb/DTF2DTF28211.p
% See solution above
% 1.52/1.27 ------------------------
% 1.52/1.28 ---- Cleaned THF ---
% 1.52/1.28 thf(in_type,type,
% 1.52/1.28 in: $i > $i > $o ).
% 1.52/1.28
% 1.52/1.28 thf(powerset_type,type,
% 1.52/1.28 powerset: $i > $i ).
% 1.52/1.28
% 1.52/1.28 thf(subset_type,type,
% 1.52/1.28 subset: $i > $i > $o ).
% 1.52/1.28
% 1.52/1.28 thf(subsetI1_type,type,
% 1.52/1.28 subsetI1: $o ).
% 1.52/1.28
% 1.52/1.28 thf(subsetI1,definition,
% 1.52/1.28 ( subsetI1
% 1.52/1.28 = ( ! [A: $i,B: $i] :
% 1.52/1.28 ( ! [Xx: $i] :
% 1.52/1.28 ( ( in @ Xx @ A )
% 1.52/1.28 => ( in @ Xx @ B ) )
% 1.52/1.28 => ( subset @ A @ B ) ) ) ) ).
% 1.52/1.28
% 1.52/1.28 thf(subsetE_type,type,
% 1.52/1.28 subsetE: $o ).
% 1.52/1.28
% 1.52/1.28 thf(subsetE,definition,
% 1.52/1.28 ( subsetE
% 1.52/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.52/1.28 ( ( subset @ A @ B )
% 1.52/1.28 => ( ( in @ Xx @ A )
% 1.52/1.28 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.52/1.28
% 1.52/1.28 thf(binintersect_type,type,
% 1.52/1.28 binintersect: $i > $i > $i ).
% 1.52/1.28
% 1.52/1.28 thf(binintersectI_type,type,
% 1.52/1.28 binintersectI: $o ).
% 1.52/1.28
% 1.52/1.28 thf(binintersectI,definition,
% 1.52/1.28 ( binintersectI
% 1.52/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.52/1.28 ( ( in @ Xx @ A )
% 1.52/1.28 => ( ( in @ Xx @ B )
% 1.52/1.28 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 1.52/1.28
% 1.52/1.28 thf(woz13rule3,conjecture,
% 1.52/1.28 ( subsetI1
% 1.52/1.28 => ( subsetE
% 1.52/1.28 => ( binintersectI
% 1.52/1.28 => ! [A: $i,X: $i] :
% 1.52/1.28 ( ( in @ X @ ( powerset @ A ) )
% 1.52/1.28 => ! [Y: $i] :
% 1.52/1.28 ( ( in @ Y @ ( powerset @ A ) )
% 1.52/1.28 => ! [Z: $i] :
% 1.52/1.28 ( ( in @ Z @ ( powerset @ A ) )
% 1.52/1.28 => ( ( subset @ X @ Y )
% 1.52/1.28 => ( ( subset @ X @ Z )
% 1.52/1.28 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 1.52/1.28 ------------------------
% 1.66/1.30 % (28400)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/27Mi)
% 1.66/1.30 % (28398)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/183Mi)
% 1.66/1.31 % (28399)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_28211 for (2999ds/4Mi)
% 1.66/1.31 % (28401)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/2Mi)
% 1.66/1.31 % (28402)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/2Mi)
% 1.66/1.31 % (28403)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_28211 for (2999ds/275Mi)
% 1.66/1.31 % (28404)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/18Mi)
% 1.66/1.31 % (28401)Instruction limit reached!
% 1.66/1.31 % (28401)------------------------------
% 1.66/1.31 % (28401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (28401)Termination reason: Unknown
% 1.66/1.31 % (28401)Termination phase: Property scanning
% 1.66/1.31
% 1.66/1.31 % (28401)Memory used [KB]: 895
% 1.66/1.31 % (28401)Time elapsed: 0.003 s
% 1.66/1.31 % (28401)Instructions burned: 2 (million)
% 1.66/1.31 % (28401)------------------------------
% 1.66/1.31 % (28401)------------------------------
% 1.66/1.31 % (28402)Instruction limit reached!
% 1.66/1.31 % (28402)------------------------------
% 1.66/1.31 % (28402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (28402)Termination reason: Unknown
% 1.66/1.31 % (28402)Termination phase: Property scanning
% 1.66/1.31
% 1.66/1.31 % (28402)Memory used [KB]: 895
% 1.66/1.31 % (28402)Time elapsed: 0.003 s
% 1.66/1.31 % (28402)Instructions burned: 2 (million)
% 1.66/1.31 % (28402)------------------------------
% 1.66/1.31 % (28402)------------------------------
% 1.66/1.31 % (28400)Instruction limit reached!
% 1.66/1.31 % (28400)------------------------------
% 1.66/1.31 % (28400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (28400)Termination reason: Unknown
% 1.66/1.31 % (28400)Termination phase: Saturation
% 1.66/1.31
% 1.66/1.31 % (28400)Memory used [KB]: 5628
% 1.66/1.31 % (28400)Time elapsed: 0.011 s
% 1.66/1.31 % (28400)Instructions burned: 29 (million)
% 1.66/1.31 % (28400)------------------------------
% 1.66/1.31 % (28400)------------------------------
% 1.66/1.31 % (28399)Instruction limit reached!
% 1.66/1.31 % (28399)------------------------------
% 1.66/1.31 % (28399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (28399)Termination reason: Unknown
% 1.66/1.31 % (28399)Termination phase: Saturation
% 1.66/1.31
% 1.66/1.31 % (28399)Memory used [KB]: 5500
% 1.66/1.31 % (28399)Time elapsed: 0.005 s
% 1.66/1.31 % (28399)Instructions burned: 5 (million)
% 1.66/1.31 % (28399)------------------------------
% 1.66/1.31 % (28399)------------------------------
% 1.66/1.32 % (28407)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/15Mi)
% 1.66/1.32 % (28404)Instruction limit reached!
% 1.66/1.32 % (28404)------------------------------
% 1.66/1.32 % (28404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (28404)Termination reason: Unknown
% 1.66/1.32 % (28404)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (28404)Memory used [KB]: 5628
% 1.66/1.32 % (28404)Time elapsed: 0.013 s
% 1.66/1.32 % (28404)Instructions burned: 18 (million)
% 1.66/1.32 % (28404)------------------------------
% 1.66/1.32 % (28404)------------------------------
% 1.66/1.32 % (28407)Instruction limit reached!
% 1.66/1.32 % (28407)------------------------------
% 1.66/1.32 % (28407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (28407)Termination reason: Unknown
% 1.66/1.32 % (28407)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (28407)Memory used [KB]: 5628
% 1.66/1.32 % (28407)Time elapsed: 0.007 s
% 1.66/1.32 % (28407)Instructions burned: 18 (million)
% 1.66/1.32 % (28407)------------------------------
% 1.66/1.32 % (28407)------------------------------
% 1.66/1.33 % (28405)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/3Mi)
% 1.66/1.33 % (28406)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/37Mi)
% 1.66/1.33 % (28408)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/3Mi)
% 1.66/1.33 % (28405)Instruction limit reached!
% 1.66/1.33 % (28405)------------------------------
% 1.66/1.33 % (28405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (28405)Termination reason: Unknown
% 1.66/1.33 % (28405)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (28405)Memory used [KB]: 5500
% 1.66/1.33 % (28405)Time elapsed: 0.004 s
% 1.66/1.33 % (28405)Instructions burned: 4 (million)
% 1.66/1.33 % (28405)------------------------------
% 1.66/1.33 % (28405)------------------------------
% 1.66/1.33 % (28408)Instruction limit reached!
% 1.66/1.33 % (28408)------------------------------
% 1.66/1.33 % (28408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (28408)Termination reason: Unknown
% 1.66/1.33 % (28408)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (28408)Memory used [KB]: 5500
% 1.66/1.33 % (28408)Time elapsed: 0.004 s
% 1.66/1.33 % (28408)Instructions burned: 4 (million)
% 1.66/1.33 % (28408)------------------------------
% 1.66/1.33 % (28408)------------------------------
% 1.66/1.33 % (28410)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/7Mi)
% 1.66/1.34 % (28410)Instruction limit reached!
% 1.66/1.34 % (28410)------------------------------
% 1.66/1.34 % (28410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (28410)Termination reason: Unknown
% 1.66/1.34 % (28410)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (28410)Memory used [KB]: 1023
% 1.66/1.34 % (28410)Time elapsed: 0.004 s
% 1.66/1.34 % (28410)Instructions burned: 9 (million)
% 1.66/1.34 % (28410)------------------------------
% 1.66/1.34 % (28410)------------------------------
% 1.66/1.34 % (28409)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/1041Mi)
% 1.66/1.34 % (28411)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/16Mi)
% 1.66/1.35 % (28413)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/3Mi)
% 1.66/1.35 % (28412)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/3Mi)
% 1.66/1.35 % (28406)Instruction limit reached!
% 1.66/1.35 % (28406)------------------------------
% 1.66/1.35 % (28406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (28406)Termination reason: Unknown
% 1.66/1.35 % (28406)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (28406)Memory used [KB]: 5756
% 1.66/1.35 % (28406)Time elapsed: 0.023 s
% 1.66/1.35 % (28406)Instructions burned: 38 (million)
% 1.66/1.35 % (28406)------------------------------
% 1.66/1.35 % (28406)------------------------------
% 1.66/1.35 % (28413)Instruction limit reached!
% 1.66/1.35 % (28413)------------------------------
% 1.66/1.35 % (28413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (28413)Termination reason: Unknown
% 1.66/1.35 % (28413)Termination phase: Property scanning
% 1.66/1.35
% 1.66/1.35 % (28413)Memory used [KB]: 1023
% 1.66/1.35 % (28413)Time elapsed: 0.002 s
% 1.66/1.35 % (28413)Instructions burned: 4 (million)
% 1.66/1.35 % (28413)------------------------------
% 1.66/1.35 % (28413)------------------------------
% 1.66/1.35 % (28412)Instruction limit reached!
% 1.66/1.35 % (28412)------------------------------
% 1.66/1.35 % (28412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (28412)Termination reason: Unknown
% 1.66/1.35 % (28412)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (28412)Memory used [KB]: 1023
% 1.66/1.35 % (28412)Time elapsed: 0.004 s
% 1.66/1.35 % (28412)Instructions burned: 4 (million)
% 1.66/1.35 % (28412)------------------------------
% 1.66/1.35 % (28412)------------------------------
% 1.66/1.36 % (28411)Instruction limit reached!
% 1.66/1.36 % (28411)------------------------------
% 1.66/1.36 % (28411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (28414)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/7Mi)
% 1.66/1.36 % (28411)Termination reason: Unknown
% 1.66/1.36 % (28411)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (28411)Memory used [KB]: 5884
% 1.66/1.36 % (28411)Time elapsed: 0.013 s
% 1.66/1.36 % (28411)Instructions burned: 17 (million)
% 1.66/1.36 % (28411)------------------------------
% 1.66/1.36 % (28411)------------------------------
% 1.66/1.36 % (28414)Refutation not found, incomplete strategy
% 1.66/1.36 % (28414)------------------------------
% 1.66/1.36 % (28414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (28414)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.36
% 1.66/1.36
% 1.66/1.36 % (28414)Memory used [KB]: 5500
% 1.66/1.36 % (28414)Time elapsed: 0.002 s
% 1.66/1.36 % (28414)Instructions burned: 4 (million)
% 1.66/1.36 % (28414)------------------------------
% 1.66/1.36 % (28414)------------------------------
% 1.66/1.36 % (28415)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/3Mi)
% 1.66/1.36 % (28416)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/4Mi)
% 1.66/1.36 % (28415)Instruction limit reached!
% 1.66/1.36 % (28415)------------------------------
% 1.66/1.36 % (28415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (28415)Termination reason: Unknown
% 1.66/1.36 % (28415)Termination phase: Property scanning
% 1.66/1.36
% 1.66/1.36 % (28415)Memory used [KB]: 1023
% 1.66/1.36 % (28415)Time elapsed: 0.002 s
% 1.66/1.36 % (28415)Instructions burned: 3 (million)
% 1.66/1.36 % (28415)------------------------------
% 1.66/1.36 % (28415)------------------------------
% 1.66/1.36 % (28398)Instruction limit reached!
% 1.66/1.36 % (28398)------------------------------
% 1.66/1.36 % (28398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (28398)Termination reason: Unknown
% 1.66/1.36 % (28398)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (28398)Memory used [KB]: 6396
% 1.66/1.36 % (28398)Time elapsed: 0.061 s
% 1.66/1.36 % (28398)Instructions burned: 183 (million)
% 1.66/1.36 % (28398)------------------------------
% 1.66/1.36 % (28398)------------------------------
% 1.66/1.36 % (28416)Instruction limit reached!
% 1.66/1.36 % (28416)------------------------------
% 1.66/1.36 % (28416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (28416)Termination reason: Unknown
% 1.66/1.36 % (28416)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (28416)Memory used [KB]: 5500
% 1.66/1.36 % (28416)Time elapsed: 0.003 s
% 1.66/1.36 % (28416)Instructions burned: 4 (million)
% 1.66/1.36 % (28416)------------------------------
% 1.66/1.36 % (28416)------------------------------
% 1.66/1.37 % (28418)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/710Mi)
% 1.66/1.37 % (28419)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/6Mi)
% 1.66/1.37 % (28420)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/902Mi)
% 1.66/1.37 % (28421)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/21Mi)
% 1.66/1.37 % (28419)Instruction limit reached!
% 1.66/1.37 % (28419)------------------------------
% 1.66/1.37 % (28419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (28419)Termination reason: Unknown
% 1.66/1.37 % (28419)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (28419)Memory used [KB]: 5500
% 1.66/1.37 % (28419)Time elapsed: 0.004 s
% 1.66/1.37 % (28419)Instructions burned: 6 (million)
% 1.66/1.37 % (28419)------------------------------
% 1.66/1.37 % (28419)------------------------------
% 1.66/1.37 % (28420)Refutation not found, incomplete strategy
% 1.66/1.37 % (28420)------------------------------
% 1.66/1.37 % (28420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (28420)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.37
% 1.66/1.37
% 1.66/1.37 % (28420)Memory used [KB]: 5500
% 1.66/1.37 % (28420)Time elapsed: 0.003 s
% 1.66/1.37 % (28420)Instructions burned: 4 (million)
% 1.66/1.37 % (28420)------------------------------
% 1.66/1.37 % (28420)------------------------------
% 1.66/1.37 % (28417)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/18Mi)
% 1.66/1.38 % (28421)Instruction limit reached!
% 1.66/1.38 % (28421)------------------------------
% 1.66/1.38 % (28421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (28421)Termination reason: Unknown
% 1.66/1.38 % (28421)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (28421)Memory used [KB]: 5628
% 1.66/1.38 % (28421)Time elapsed: 0.010 s
% 1.66/1.38 % (28421)Instructions burned: 23 (million)
% 1.66/1.38 % (28421)------------------------------
% 1.66/1.38 % (28421)------------------------------
% 1.66/1.38 % (28422)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/5Mi)
% 1.66/1.38 % (28423)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/6Mi)
% 1.66/1.38 % (28422)Instruction limit reached!
% 1.66/1.38 % (28422)------------------------------
% 1.66/1.38 % (28422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (28422)Termination reason: Unknown
% 1.66/1.38 % (28422)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (28422)Memory used [KB]: 5500
% 1.66/1.38 % (28422)Time elapsed: 0.004 s
% 1.66/1.38 % (28422)Instructions burned: 7 (million)
% 1.66/1.38 % (28422)------------------------------
% 1.66/1.38 % (28422)------------------------------
% 1.66/1.38 % (28423)Instruction limit reached!
% 1.66/1.38 % (28423)------------------------------
% 1.66/1.38 % (28423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (28423)Termination reason: Unknown
% 1.66/1.38 % (28423)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (28423)Memory used [KB]: 5500
% 1.66/1.38 % (28423)Time elapsed: 0.004 s
% 1.66/1.38 % (28423)Instructions burned: 8 (million)
% 1.66/1.38 % (28423)------------------------------
% 1.66/1.38 % (28423)------------------------------
% 1.66/1.38 % (28417)Instruction limit reached!
% 1.66/1.38 % (28417)------------------------------
% 1.66/1.38 % (28417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (28417)Termination reason: Unknown
% 1.66/1.38 % (28417)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (28417)Memory used [KB]: 5628
% 1.66/1.38 % (28417)Time elapsed: 0.013 s
% 1.66/1.38 % (28417)Instructions burned: 18 (million)
% 1.66/1.38 % (28417)------------------------------
% 1.66/1.38 % (28417)------------------------------
% 1.66/1.39 % (28418)First to succeed.
% 1.66/1.39 % (28424)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/377Mi)
% 1.66/1.39 % (28418)Refutation found. Thanks to Tanya!
% 1.66/1.39 % SZS status Theorem for DTF2THF_28211
% 1.66/1.39 % SZS output start Proof for DTF2THF_28211
% 1.66/1.39 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.39 thf(func_def_1, type, powerset: $i > $i).
% 1.66/1.39 thf(func_def_2, type, subset: $i > $i > $o).
% 1.66/1.39 thf(func_def_6, type, binintersect: $i > $i > $i).
% 1.66/1.39 thf(func_def_20, type, sK10: $i > $i > $i).
% 1.66/1.39 thf(f346,plain,(
% 1.66/1.39 $false),
% 1.66/1.39 inference(subsumption_resolution,[status(thm)],[f335,f47])).
% 1.66/1.39 thf(f47,plain,(
% 1.66/1.39 ((subset @ sK3 @ (binintersect @ sK5 @ sK6)) != $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f30])).
% 1.66/1.39 thf(f30,plain,(
% 1.66/1.39 (subsetE = $true) & (subsetI1 = $true) & (binintersectI = $true) & (((in @ sK3 @ (powerset @ sK4)) = $true) & ((((in @ sK6 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ (binintersect @ sK5 @ sK6)) != $true) & ((subset @ sK3 @ sK5) = $true) & ((subset @ sK3 @ sK6) = $true)) & ((in @ sK5 @ (powerset @ sK4)) = $true)))),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f26,f29,f28,f27])).
% 1.66/1.39 thf(f27,plain,(
% 1.66/1.39 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) & ((subset @ X0 @ (binintersect @ X2 @ X3)) != $true) & ($true = (subset @ X0 @ X2)) & ($true = (subset @ X0 @ X3))) & ($true = (in @ X2 @ (powerset @ X1))))) => (((in @ sK3 @ (powerset @ sK4)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ (binintersect @ X2 @ X3)) != $true) & ((subset @ sK3 @ X2) = $true) & ((subset @ sK3 @ X3) = $true)) & ($true = (in @ X2 @ (powerset @ sK4)))))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f28,plain,(
% 1.66/1.39 ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ (binintersect @ X2 @ X3)) != $true) & ((subset @ sK3 @ X2) = $true) & ((subset @ sK3 @ X3) = $true)) & ($true = (in @ X2 @ (powerset @ sK4)))) => (? [X3 : $i] : (((in @ X3 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ (binintersect @ sK5 @ X3)) != $true) & ((subset @ sK3 @ sK5) = $true) & ((subset @ sK3 @ X3) = $true)) & ((in @ sK5 @ (powerset @ sK4)) = $true))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f29,plain,(
% 1.66/1.39 ? [X3 : $i] : (((in @ X3 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ (binintersect @ sK5 @ X3)) != $true) & ((subset @ sK3 @ sK5) = $true) & ((subset @ sK3 @ X3) = $true)) => (((in @ sK6 @ (powerset @ sK4)) = $true) & ((subset @ sK3 @ (binintersect @ sK5 @ sK6)) != $true) & ((subset @ sK3 @ sK5) = $true) & ((subset @ sK3 @ sK6) = $true))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f26,plain,(
% 1.66/1.39 (subsetE = $true) & (subsetI1 = $true) & (binintersectI = $true) & ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) & ((subset @ X0 @ (binintersect @ X2 @ X3)) != $true) & ($true = (subset @ X0 @ X2)) & ($true = (subset @ X0 @ X3))) & ($true = (in @ X2 @ (powerset @ X1)))))),
% 1.66/1.39 inference(rectify,[status(thm)],[f20])).
% 1.66/1.39 thf(f20,plain,(
% 1.66/1.39 (subsetE = $true) & (subsetI1 = $true) & (binintersectI = $true) & ? [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) & ($true != (subset @ X1 @ (binintersect @ X2 @ X3))) & ($true = (subset @ X1 @ X2)) & ((subset @ X1 @ X3) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)))),
% 1.66/1.39 inference(flattening,[status(thm)],[f19])).
% 1.66/1.39 thf(f19,plain,(
% 1.66/1.39 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((($true != (subset @ X1 @ (binintersect @ X2 @ X3))) & ((subset @ X1 @ X3) = $true)) & ($true = (subset @ X1 @ X2))) & ((in @ X3 @ (powerset @ X0)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binintersectI = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 1.66/1.39 inference(ennf_transformation,[status(thm)],[f8])).
% 1.66/1.39 thf(f8,plain,(
% 1.66/1.39 ~((subsetI1 = $true) => ((subsetE = $true) => ((binintersectI = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) => (($true = (subset @ X1 @ X2)) => (((subset @ X1 @ X3) = $true) => ($true = (subset @ X1 @ (binintersect @ X2 @ X3)))))))))))),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.39 thf(f7,plain,(
% 1.66/1.39 ~(subsetI1 => (subsetE => (binintersectI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X2) => ((subset @ X1 @ X3) => (subset @ X1 @ (binintersect @ X2 @ X3))))))))))),
% 1.66/1.39 inference(rectify,[status(thm)],[f5])).
% 1.66/1.39 thf(f5,negated_conjecture,(
% 1.66/1.39 ~(subsetI1 => (subsetE => (binintersectI => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ((subset @ X3 @ X4) => ((subset @ X3 @ X5) => (subset @ X3 @ (binintersect @ X4 @ X5))))))))))),
% 1.66/1.39 inference(negated_conjecture,[status(cth)],[f4])).
% 1.66/1.39 thf(f4,conjecture,(
% 1.66/1.39 subsetI1 => (subsetE => (binintersectI => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ((subset @ X3 @ X4) => ((subset @ X3 @ X5) => (subset @ X3 @ (binintersect @ X4 @ X5)))))))))),
% 1.66/1.39 file('/export/starexec/sandbox/tmp/tmp.O4ok8h6Gzb/DTF2THF_28211.p',woz13rule3)).
% 1.66/1.39 thf(f335,plain,(
% 1.66/1.39 ((subset @ sK3 @ (binintersect @ sK5 @ sK6)) = $true)),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f334])).
% 1.66/1.39 thf(f334,plain,(
% 1.66/1.39 ((subset @ sK3 @ (binintersect @ sK5 @ sK6)) = $true) | ($true != $true)),
% 1.66/1.39 inference(duplicate_literal_removal,[status(thm)],[f329])).
% 1.66/1.39 thf(f329,plain,(
% 1.66/1.39 ($true != $true) | ((subset @ sK3 @ (binintersect @ sK5 @ sK6)) = $true) | ((subset @ sK3 @ (binintersect @ sK5 @ sK6)) = $true)),
% 1.66/1.39 inference(superposition,[status(thm)],[f73,f260])).
% 1.66/1.39 thf(f260,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (((in @ (sK10 @ sK3 @ X0) @ (binintersect @ sK5 @ sK6)) = $true) | ($true = (subset @ sK3 @ X0))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f259])).
% 1.66/1.39 thf(f259,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (($true = (subset @ sK3 @ X0)) | ($true != $true) | ((in @ (sK10 @ sK3 @ X0) @ (binintersect @ sK5 @ sK6)) = $true)) )),
% 1.66/1.39 inference(duplicate_literal_removal,[status(thm)],[f254])).
% 1.66/1.39 thf(f254,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (($true = (subset @ sK3 @ X0)) | ($true != $true) | ($true = (subset @ sK3 @ X0)) | ((in @ (sK10 @ sK3 @ X0) @ (binintersect @ sK5 @ sK6)) = $true)) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f99,f96])).
% 1.66/1.39 thf(f96,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (($true = (in @ (sK10 @ sK3 @ X0) @ sK6)) | ($true = (subset @ sK3 @ X0))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.66/1.39 thf(f95,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (($true = (in @ (sK10 @ sK3 @ X0) @ sK6)) | ($true = (subset @ sK3 @ X0)) | ($true != $true)) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f83,f74])).
% 1.66/1.39 thf(f74,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((in @ (sK10 @ X1 @ X0) @ X1) = $true) | ($true = (subset @ X1 @ X0))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.66/1.39 thf(f69,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ((in @ (sK10 @ X1 @ X0) @ X1) = $true) | ($true != $true)) )),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f60,f51])).
% 1.66/1.39 thf(f51,plain,(
% 1.66/1.39 (subsetI1 = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f30])).
% 1.66/1.39 thf(f60,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ((in @ (sK10 @ X1 @ X0) @ X1) = $true) | (subsetI1 != $true)) )),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f39])).
% 1.66/1.39 thf(f39,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | (((in @ (sK10 @ X1 @ X0) @ X1) = $true) & ((in @ (sK10 @ X1 @ X0) @ X0) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != (subset @ sK12 @ sK11)) & ! [X5 : $i] : (((in @ X5 @ sK12) != $true) | ((in @ X5 @ sK11) = $true))))),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f36,f38,f37])).
% 1.66/1.39 thf(f37,plain,(
% 1.66/1.39 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) => (((in @ (sK10 @ X1 @ X0) @ X1) = $true) & ((in @ (sK10 @ X1 @ X0) @ X0) != $true)))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f38,plain,(
% 1.66/1.39 ? [X3 : $i,X4 : $i] : (($true != (subset @ X4 @ X3)) & ! [X5 : $i] : (($true != (in @ X5 @ X4)) | ((in @ X5 @ X3) = $true))) => (($true != (subset @ sK12 @ sK11)) & ! [X5 : $i] : (((in @ X5 @ sK12) != $true) | ((in @ X5 @ sK11) = $true)))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f36,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (($true != (subset @ X4 @ X3)) & ! [X5 : $i] : (($true != (in @ X5 @ X4)) | ((in @ X5 @ X3) = $true))))),
% 1.66/1.39 inference(rectify,[status(thm)],[f35])).
% 1.66/1.39 thf(f35,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))))),
% 1.66/1.39 inference(nnf_transformation,[status(thm)],[f21])).
% 1.66/1.39 thf(f21,plain,(
% 1.66/1.39 ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) <=> (subsetI1 = $true)),
% 1.66/1.39 inference(ennf_transformation,[status(thm)],[f14])).
% 1.66/1.39 thf(f14,plain,(
% 1.66/1.39 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ($true = (subset @ X1 @ X0)))),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f13])).
% 1.66/1.39 thf(f13,plain,(
% 1.66/1.39 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 1.66/1.39 inference(rectify,[status(thm)],[f1])).
% 1.66/1.39 thf(f1,axiom,(
% 1.66/1.39 (subsetI1 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.66/1.39 file('/export/starexec/sandbox/tmp/tmp.O4ok8h6Gzb/DTF2THF_28211.p',subsetI1)).
% 1.66/1.39 thf(f83,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (((in @ X0 @ sK3) != $true) | ((in @ X0 @ sK6) = $true)) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.66/1.39 thf(f80,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (((in @ X0 @ sK6) = $true) | ((in @ X0 @ sK3) != $true) | ($true != $true)) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f75,f45])).
% 1.66/1.39 thf(f45,plain,(
% 1.66/1.39 ((subset @ sK3 @ sK6) = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f30])).
% 1.66/1.39 thf(f75,plain,(
% 1.66/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X2)) | ((in @ X1 @ X0) != $true) | ($true = (in @ X1 @ X2))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.66/1.39 thf(f61,plain,(
% 1.66/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (subset @ X0 @ X2)) | ($true = (in @ X1 @ X2)) | ((in @ X1 @ X0) != $true)) )),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f43,f52])).
% 1.66/1.39 thf(f52,plain,(
% 1.66/1.39 (subsetE = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f30])).
% 1.66/1.39 thf(f43,plain,(
% 1.66/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X2)) | ($true = (in @ X1 @ X2)) | ((in @ X1 @ X0) != $true) | (subsetE != $true)) )),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f25])).
% 1.66/1.39 thf(f25,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X0 @ X2)) | ($true = (in @ X1 @ X2)) | ((in @ X1 @ X0) != $true)) | (subsetE != $true)) & ((subsetE = $true) | (($true = (subset @ sK0 @ sK2)) & ($true != (in @ sK1 @ sK2)) & ($true = (in @ sK1 @ sK0))))),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f24])).
% 1.66/1.39 thf(f24,plain,(
% 1.66/1.39 ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) & ($true != (in @ X4 @ X5)) & ((in @ X4 @ X3) = $true)) => (($true = (subset @ sK0 @ sK2)) & ($true != (in @ sK1 @ sK2)) & ($true = (in @ sK1 @ sK0)))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f23,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X0 @ X2)) | ($true = (in @ X1 @ X2)) | ((in @ X1 @ X0) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) & ($true != (in @ X4 @ X5)) & ((in @ X4 @ X3) = $true)))),
% 1.66/1.39 inference(rectify,[status(thm)],[f22])).
% 1.66/1.39 thf(f22,plain,(
% 1.66/1.39 (! [X1 : $i,X0 : $i,X2 : $i] : (($true != (subset @ X1 @ X2)) | ((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (($true = (subset @ X1 @ X2)) & ((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true)))),
% 1.66/1.39 inference(nnf_transformation,[status(thm)],[f16])).
% 1.66/1.39 thf(f16,plain,(
% 1.66/1.39 ! [X1 : $i,X0 : $i,X2 : $i] : (($true != (subset @ X1 @ X2)) | ((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) <=> (subsetE = $true)),
% 1.66/1.39 inference(flattening,[status(thm)],[f15])).
% 1.66/1.39 thf(f15,plain,(
% 1.66/1.39 ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) | ($true != (subset @ X1 @ X2))) <=> (subsetE = $true)),
% 1.66/1.39 inference(ennf_transformation,[status(thm)],[f12])).
% 1.66/1.39 thf(f12,plain,(
% 1.66/1.39 ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) => (((in @ X0 @ X1) = $true) => ((in @ X0 @ X2) = $true))) <=> (subsetE = $true)),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f11])).
% 1.66/1.39 thf(f11,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = subsetE)),
% 1.66/1.39 inference(rectify,[status(thm)],[f2])).
% 1.66/1.39 thf(f2,axiom,(
% 1.66/1.39 (! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.66/1.39 file('/export/starexec/sandbox/tmp/tmp.O4ok8h6Gzb/DTF2THF_28211.p',subsetE)).
% 1.66/1.39 thf(f99,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK10 @ sK3 @ X0) @ X1)) | ($true = (subset @ sK3 @ X0)) | ((in @ (sK10 @ sK3 @ X0) @ (binintersect @ sK5 @ X1)) = $true)) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.66/1.39 thf(f98,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((in @ (sK10 @ sK3 @ X0) @ (binintersect @ sK5 @ X1)) = $true) | ($true != (in @ (sK10 @ sK3 @ X0) @ X1)) | ($true != $true) | ($true = (subset @ sK3 @ X0))) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f76,f94])).
% 1.66/1.39 thf(f94,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (((in @ (sK10 @ sK3 @ X0) @ sK5) = $true) | ($true = (subset @ sK3 @ X0))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.66/1.39 thf(f93,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (((in @ (sK10 @ sK3 @ X0) @ sK5) = $true) | ($true = (subset @ sK3 @ X0)) | ($true != $true)) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f82,f74])).
% 1.66/1.39 thf(f82,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (((in @ X0 @ sK3) != $true) | ((in @ X0 @ sK5) = $true)) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.66/1.39 thf(f81,plain,(
% 1.66/1.39 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ sK5) = $true) | ((in @ X0 @ sK3) != $true)) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f75,f46])).
% 1.66/1.39 thf(f46,plain,(
% 1.66/1.39 ((subset @ sK3 @ sK5) = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f30])).
% 1.66/1.39 thf(f76,plain,(
% 1.66/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) != $true) | ((in @ X0 @ (binintersect @ X2 @ X1)) = $true)) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.66/1.39 thf(f65,plain,(
% 1.66/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ($true != $true) | ((in @ X0 @ (binintersect @ X2 @ X1)) = $true) | ((in @ X0 @ X2) != $true)) )),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f56,f50])).
% 1.66/1.39 thf(f50,plain,(
% 1.66/1.39 (binintersectI = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f30])).
% 1.66/1.39 thf(f56,plain,(
% 1.66/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) = $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) != $true) | (binintersectI != $true)) )),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f34])).
% 1.66/1.39 thf(f34,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) = $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | (($true != (in @ sK7 @ (binintersect @ sK9 @ sK8))) & ((in @ sK7 @ sK9) = $true) & ((in @ sK7 @ sK8) = $true)))),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f32,f33])).
% 1.66/1.39 thf(f33,plain,(
% 1.66/1.39 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (binintersect @ X5 @ X4))) & ((in @ X3 @ X5) = $true) & ($true = (in @ X3 @ X4))) => (($true != (in @ sK7 @ (binintersect @ sK9 @ sK8))) & ((in @ sK7 @ sK9) = $true) & ((in @ sK7 @ sK8) = $true))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f32,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) = $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (binintersect @ X5 @ X4))) & ((in @ X3 @ X5) = $true) & ($true = (in @ X3 @ X4))))),
% 1.66/1.39 inference(rectify,[status(thm)],[f31])).
% 1.66/1.39 thf(f31,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) = $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) != $true) & ((in @ X0 @ X2) = $true) & ((in @ X0 @ X1) = $true)))),
% 1.66/1.39 inference(nnf_transformation,[status(thm)],[f18])).
% 1.66/1.39 thf(f18,plain,(
% 1.66/1.39 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binintersect @ X2 @ X1)) = $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) != $true)) <=> (binintersectI = $true)),
% 1.66/1.39 inference(flattening,[status(thm)],[f17])).
% 1.66/1.39 thf(f17,plain,(
% 1.66/1.39 ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1)) = $true) | ((in @ X0 @ X1) != $true)) | ((in @ X0 @ X2) != $true)) <=> (binintersectI = $true)),
% 1.66/1.39 inference(ennf_transformation,[status(thm)],[f10])).
% 1.66/1.39 thf(f10,plain,(
% 1.66/1.39 ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X2) = $true) => (((in @ X0 @ X1) = $true) => ((in @ X0 @ (binintersect @ X2 @ X1)) = $true))) <=> (binintersectI = $true)),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f9])).
% 1.66/1.39 thf(f9,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ (binintersect @ X2 @ X1)))) = binintersectI)),
% 1.66/1.39 inference(rectify,[status(thm)],[f3])).
% 1.66/1.39 thf(f3,axiom,(
% 1.66/1.39 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))) = binintersectI)),
% 1.66/1.39 file('/export/starexec/sandbox/tmp/tmp.O4ok8h6Gzb/DTF2THF_28211.p',binintersectI)).
% 1.66/1.39 thf(f73,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((in @ (sK10 @ X1 @ X0) @ X0) != $true) | ($true = (subset @ X1 @ X0))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.66/1.39 thf(f70,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ((in @ (sK10 @ X1 @ X0) @ X0) != $true) | ($true != $true)) )),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f59,f51])).
% 1.66/1.39 thf(f59,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ((in @ (sK10 @ X1 @ X0) @ X0) != $true) | (subsetI1 != $true)) )),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f39])).
% 1.66/1.39 % SZS output end Proof for DTF2THF_28211
% 1.66/1.39 % (28418)------------------------------
% 1.66/1.39 % (28418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (28418)Termination reason: Refutation
% 1.66/1.39
% 1.66/1.39 % (28418)Memory used [KB]: 5884
% 1.66/1.39 % (28418)Time elapsed: 0.023 s
% 1.66/1.39 % (28418)Instructions burned: 61 (million)
% 1.66/1.39 % (28418)------------------------------
% 1.66/1.39 % (28418)------------------------------
% 1.66/1.39 % (28397)Success in time 0.09 s
%------------------------------------------------------------------------------