%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU742^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 09:36:49 AM UTC 2026
% Result : Theorem 1.57s 1.28s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 91 ( 18 unt; 0 typ; 2 def)
% Number of atoms : 1756 ( 456 equ; 0 cnn)
% Maximal formula atoms : 14 ( 19 avg)
% Number of connectives : 2100 ( 223 ~; 188 |; 165 &;1432 @)
% ( 11 <=>; 81 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 25 con; 0-2 aty)
% Number of variables : 270 ( 0 ^; 175 !; 95 ?; 270 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
binintersect: $i > $i > $i ).
thf(f154,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f105,f129,f153]) ).
thf(f153,plain,
spl18_2,
inference(avatar_contradiction_clause,[status(thm)],[f152]) ).
thf(f152,plain,
( $false
| spl18_2 ),
inference(subsumption_resolution,[status(thm)],[f151,f71]) ).
thf(f71,plain,
( $true
= ( in @ sK15 @ ( powerset @ sK14 ) ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ( binintersectI = $true )
& ( inIntersectImpInUnion2 = $true )
& ( $true
= ( in @ sK15 @ ( powerset @ sK14 ) ) )
& ( ( in @ sK16 @ ( powerset @ sK14 ) )
= $true )
& ( $true
= ( in @ sK17 @ ( binintersect @ sK13 @ sK15 ) ) )
& ( $true
!= ( in @ sK17 @ ( binintersect @ ( binunion @ sK13 @ sK16 ) @ ( binunion @ sK15 @ sK16 ) ) ) )
& ( ( in @ sK17 @ sK14 )
= $true )
& ( ( in @ sK13 @ ( powerset @ sK14 ) )
= $true )
& ( inIntersectImpInUnion = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17])],[f41,f45,f44,f43,f42]) ).
thf(f42,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( $true
!= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
& ( $true
= ( in @ X4 @ X1 ) ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK14 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK14 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK13 @ X2 ) )
= $true )
& ( $true
!= ( in @ X4 @ ( binintersect @ ( binunion @ sK13 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
& ( ( in @ X4 @ sK14 )
= $true ) ) ) )
& ( ( in @ sK13 @ ( powerset @ sK14 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f43,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK14 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK14 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK13 @ X2 ) )
= $true )
& ( $true
!= ( in @ X4 @ ( binintersect @ ( binunion @ sK13 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
& ( ( in @ X4 @ sK14 )
= $true ) ) ) )
=> ( ( $true
= ( in @ sK15 @ ( powerset @ sK14 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK14 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK13 @ sK15 ) )
= $true )
& ( ( in @ X4 @ ( binintersect @ ( binunion @ sK13 @ X3 ) @ ( binunion @ sK15 @ X3 ) ) )
!= $true )
& ( ( in @ X4 @ sK14 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ sK14 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK13 @ sK15 ) )
= $true )
& ( ( in @ X4 @ ( binintersect @ ( binunion @ sK13 @ X3 ) @ ( binunion @ sK15 @ X3 ) ) )
!= $true )
& ( ( in @ X4 @ sK14 )
= $true ) ) )
=> ( ( ( in @ sK16 @ ( powerset @ sK14 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK13 @ sK15 ) )
= $true )
& ( ( in @ X4 @ ( binintersect @ ( binunion @ sK13 @ sK16 ) @ ( binunion @ sK15 @ sK16 ) ) )
!= $true )
& ( ( in @ X4 @ sK14 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK13 @ sK15 ) )
= $true )
& ( ( in @ X4 @ ( binintersect @ ( binunion @ sK13 @ sK16 ) @ ( binunion @ sK15 @ sK16 ) ) )
!= $true )
& ( ( in @ X4 @ sK14 )
= $true ) )
=> ( ( $true
= ( in @ sK17 @ ( binintersect @ sK13 @ sK15 ) ) )
& ( $true
!= ( in @ sK17 @ ( binintersect @ ( binunion @ sK13 @ sK16 ) @ ( binunion @ sK15 @ sK16 ) ) ) )
& ( ( in @ sK17 @ sK14 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( binintersectI = $true )
& ( inIntersectImpInUnion2 = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( $true
!= ( in @ X4 @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
& ( $true
= ( in @ X4 @ X1 ) ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( inIntersectImpInUnion = $true ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( binintersectI = $true )
& ( inIntersectImpInUnion2 = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) )
!= $true )
& ( $true
= ( in @ X4 @ X0 ) ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( inIntersectImpInUnion = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) )
!= $true )
& ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( $true
= ( in @ X4 @ X0 ) ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binintersectI = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( binintersectI = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ( ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
=> ( ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) )
= $true ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X2 @ ( binintersect @ ( binunion @ X3 @ X5 ) @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X2 @ ( binintersect @ ( binunion @ X3 @ X5 ) @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CtHZWL3RvT/DTF2THF_20595.p',inIntersectImpInIntersectUnions) ).
thf(f151,plain,
( ( $true
!= ( in @ sK15 @ ( powerset @ sK14 ) ) )
| spl18_2 ),
inference(subsumption_resolution,[status(thm)],[f150,f67]) ).
thf(f67,plain,
( ( in @ sK17 @ sK14 )
= $true ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f150,plain,
( ( ( in @ sK17 @ sK14 )
!= $true )
| ( $true
!= ( in @ sK15 @ ( powerset @ sK14 ) ) )
| spl18_2 ),
inference(subsumption_resolution,[status(thm)],[f149,f66]) ).
thf(f66,plain,
( ( in @ sK13 @ ( powerset @ sK14 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f149,plain,
( ( ( in @ sK13 @ ( powerset @ sK14 ) )
!= $true )
| ( $true
!= ( in @ sK15 @ ( powerset @ sK14 ) ) )
| ( ( in @ sK17 @ sK14 )
!= $true )
| spl18_2 ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
( ( $true
!= ( in @ sK15 @ ( powerset @ sK14 ) ) )
| ( ( in @ sK13 @ ( powerset @ sK14 ) )
!= $true )
| ( ( in @ sK17 @ sK14 )
!= $true )
| ( $true != $true )
| spl18_2 ),
inference(superposition,[status(thm)],[f146,f70]) ).
thf(f70,plain,
( ( in @ sK16 @ ( powerset @ sK14 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f146,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK16 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK15 @ ( powerset @ X0 ) ) )
| ( ( in @ sK13 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK17 @ X0 )
!= $true ) )
| spl18_2 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ! [X0: $i] :
( ( ( in @ sK17 @ X0 )
!= $true )
| ( $true
!= ( in @ sK16 @ ( powerset @ X0 ) ) )
| ( ( in @ sK13 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK15 @ ( powerset @ X0 ) ) )
| ( $true != $true ) )
| spl18_2 ),
inference(superposition,[status(thm)],[f133,f69]) ).
thf(f69,plain,
( $true
= ( in @ sK17 @ ( binintersect @ sK13 @ sK15 ) ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f133,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ sK17 @ ( binintersect @ X0 @ sK15 ) ) )
| ( ( in @ sK15 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ sK16 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ sK17 @ X1 )
!= $true ) )
| spl18_2 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ sK16 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ sK15 @ ( powerset @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( in @ sK17 @ X1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ sK17 @ ( binintersect @ X0 @ sK15 ) ) ) )
| spl18_2 ),
inference(superposition,[status(thm)],[f104,f92]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ X4 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f57,f72]) ).
thf(f72,plain,
inIntersectImpInUnion2 = $true,
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( inIntersectImpInUnion2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( inIntersectImpInUnion2 != $true ) )
& ( ( inIntersectImpInUnion2 = $true )
| ( ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
& ( ( in @ sK7 @ sK3 )
= $true )
& ( ( in @ sK7 @ ( binintersect @ sK4 @ sK5 ) )
= $true )
& ( ( in @ sK7 @ ( binunion @ sK5 @ sK6 ) )
!= $true )
& ( ( in @ sK6 @ ( powerset @ sK3 ) )
= $true )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f28,f32,f31,f30,f29]) ).
thf(f29,plain,
( ? [X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( powerset @ X5 ) ) )
& ? [X8: $i] :
( ? [X9: $i] :
( ( ( in @ X9 @ X5 )
= $true )
& ( $true
= ( in @ X9 @ ( binintersect @ X6 @ X7 ) ) )
& ( ( in @ X9 @ ( binunion @ X7 @ X8 ) )
!= $true ) )
& ( $true
= ( in @ X8 @ ( powerset @ X5 ) ) ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) )
=> ( ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( powerset @ sK3 ) ) )
& ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ sK3 ) )
& ( ( in @ X9 @ ( binintersect @ sK4 @ X7 ) )
= $true )
& ( ( in @ X9 @ ( binunion @ X7 @ X8 ) )
!= $true ) )
& ( ( in @ X8 @ ( powerset @ sK3 ) )
= $true ) ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( powerset @ sK3 ) ) )
& ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ sK3 ) )
& ( ( in @ X9 @ ( binintersect @ sK4 @ X7 ) )
= $true )
& ( ( in @ X9 @ ( binunion @ X7 @ X8 ) )
!= $true ) )
& ( ( in @ X8 @ ( powerset @ sK3 ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
& ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ sK3 ) )
& ( $true
= ( in @ X9 @ ( binintersect @ sK4 @ sK5 ) ) )
& ( ( in @ X9 @ ( binunion @ sK5 @ X8 ) )
!= $true ) )
& ( ( in @ X8 @ ( powerset @ sK3 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ sK3 ) )
& ( $true
= ( in @ X9 @ ( binintersect @ sK4 @ sK5 ) ) )
& ( ( in @ X9 @ ( binunion @ sK5 @ X8 ) )
!= $true ) )
& ( ( in @ X8 @ ( powerset @ sK3 ) )
= $true ) )
=> ( ? [X9: $i] :
( ( $true
= ( in @ X9 @ sK3 ) )
& ( $true
= ( in @ X9 @ ( binintersect @ sK4 @ sK5 ) ) )
& ( ( in @ X9 @ ( binunion @ sK5 @ sK6 ) )
!= $true ) )
& ( ( in @ sK6 @ ( powerset @ sK3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ sK3 ) )
& ( $true
= ( in @ X9 @ ( binintersect @ sK4 @ sK5 ) ) )
& ( ( in @ X9 @ ( binunion @ sK5 @ sK6 ) )
!= $true ) )
=> ( ( ( in @ sK7 @ sK3 )
= $true )
& ( ( in @ sK7 @ ( binintersect @ sK4 @ sK5 ) )
= $true )
& ( ( in @ sK7 @ ( binunion @ sK5 @ sK6 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( inIntersectImpInUnion2 != $true ) )
& ( ( inIntersectImpInUnion2 = $true )
| ? [X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ ( powerset @ X5 ) ) )
& ? [X8: $i] :
( ? [X9: $i] :
( ( ( in @ X9 @ X5 )
= $true )
& ( $true
= ( in @ X9 @ ( binintersect @ X6 @ X7 ) ) )
& ( ( in @ X9 @ ( binunion @ X7 @ X8 ) )
!= $true ) )
& ( $true
= ( in @ X8 @ ( powerset @ X5 ) ) ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( inIntersectImpInUnion2 != $true ) )
& ( ( inIntersectImpInUnion2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
& ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
!= $true ) )
& ( ( in @ X3 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) )
| ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( inIntersectImpInUnion2 = $true ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X4 @ X0 ) ) )
| ( ( in @ X3 @ ( powerset @ X0 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X0 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( inIntersectImpInUnion2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ( ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
= $true )
=> ( ( in @ X4 @ ( binunion @ X2 @ X3 ) )
= $true ) ) ) ) ) )
<=> ( inIntersectImpInUnion2 = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( inIntersectImpInUnion2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( inIntersectImpInUnion2
= ( ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CtHZWL3RvT/DTF2THF_20595.p',inIntersectImpInUnion2) ).
thf(f104,plain,
( ( ( in @ sK17 @ ( binunion @ sK15 @ sK16 ) )
!= $true )
| spl18_2 ),
inference(avatar_component_clause,[status(thm)],[f102]) ).
thf(f102,definition,
( spl18_2
<=> ( ( in @ sK17 @ ( binunion @ sK15 @ sK16 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl18_2])],[avatar_definition]) ).
thf(f129,plain,
spl18_1,
inference(avatar_contradiction_clause,[status(thm)],[f128]) ).
thf(f128,plain,
( $false
| spl18_1 ),
inference(subsumption_resolution,[status(thm)],[f127,f71]) ).
thf(f127,plain,
( ( $true
!= ( in @ sK15 @ ( powerset @ sK14 ) ) )
| spl18_1 ),
inference(subsumption_resolution,[status(thm)],[f126,f66]) ).
thf(f126,plain,
( ( ( in @ sK13 @ ( powerset @ sK14 ) )
!= $true )
| ( $true
!= ( in @ sK15 @ ( powerset @ sK14 ) ) )
| spl18_1 ),
inference(subsumption_resolution,[status(thm)],[f125,f67]) ).
thf(f125,plain,
( ( ( in @ sK17 @ sK14 )
!= $true )
| ( $true
!= ( in @ sK15 @ ( powerset @ sK14 ) ) )
| ( ( in @ sK13 @ ( powerset @ sK14 ) )
!= $true )
| spl18_1 ),
inference(trivial_inequality_removal,[status(thm)],[f124]) ).
thf(f124,plain,
( ( $true
!= ( in @ sK15 @ ( powerset @ sK14 ) ) )
| ( $true != $true )
| ( ( in @ sK13 @ ( powerset @ sK14 ) )
!= $true )
| ( ( in @ sK17 @ sK14 )
!= $true )
| spl18_1 ),
inference(superposition,[status(thm)],[f123,f70]) ).
thf(f123,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK16 @ ( powerset @ X0 ) ) )
| ( ( in @ sK17 @ X0 )
!= $true )
| ( $true
!= ( in @ sK15 @ ( powerset @ X0 ) ) )
| ( ( in @ sK13 @ ( powerset @ X0 ) )
!= $true ) )
| spl18_1 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ sK16 @ ( powerset @ X0 ) ) )
| ( ( in @ sK17 @ X0 )
!= $true )
| ( $true
!= ( in @ sK15 @ ( powerset @ X0 ) ) )
| ( ( in @ sK13 @ ( powerset @ X0 ) )
!= $true ) )
| spl18_1 ),
inference(superposition,[status(thm)],[f109,f69]) ).
thf(f109,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ sK17 @ ( binintersect @ sK13 @ X1 ) )
!= $true )
| ( ( in @ sK17 @ X0 )
!= $true )
| ( ( in @ sK13 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK16 @ ( powerset @ X0 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| spl18_1 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ sK13 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK17 @ X0 )
!= $true )
| ( $true
!= ( in @ sK16 @ ( powerset @ X0 ) ) )
| ( ( in @ sK17 @ ( binintersect @ sK13 @ X1 ) )
!= $true ) )
| spl18_1 ),
inference(superposition,[status(thm)],[f100,f94]) ).
thf(f94,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( $true
= ( in @ X9 @ ( binunion @ X5 @ X8 ) ) )
| ( ( in @ X8 @ ( powerset @ X6 ) )
!= $true )
| ( $true
!= ( in @ X7 @ ( powerset @ X6 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ X5 @ ( powerset @ X6 ) )
!= $true )
| ( $true
!= ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( $true
= ( in @ X9 @ ( binunion @ X5 @ X8 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( in @ X5 @ ( powerset @ X6 ) )
!= $true )
| ( ( in @ X8 @ ( powerset @ X6 ) )
!= $true )
| ( $true
!= ( in @ X7 @ ( powerset @ X6 ) ) )
| ( $true
!= ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f58,f65]) ).
thf(f65,plain,
inIntersectImpInUnion = $true,
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f58,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X6 ) )
!= $true )
| ( $true
!= ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
= ( in @ X9 @ ( binunion @ X5 @ X8 ) ) )
| ( ( in @ X8 @ ( powerset @ X6 ) )
!= $true )
| ( $true
!= ( in @ X7 @ ( powerset @ X6 ) ) )
| ( inIntersectImpInUnion != $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( inIntersectImpInUnion = $true )
| ( ( ( in @ sK8 @ ( powerset @ sK9 ) )
= $true )
& ( ( in @ sK12 @ ( binintersect @ sK8 @ sK10 ) )
= $true )
& ( $true
= ( in @ sK12 @ sK9 ) )
& ( ( in @ sK12 @ ( binunion @ sK8 @ sK11 ) )
!= $true )
& ( ( in @ sK11 @ ( powerset @ sK9 ) )
= $true )
& ( ( in @ sK10 @ ( powerset @ sK9 ) )
= $true ) ) )
& ( ! [X5: $i,X6: $i] :
( ( ( in @ X5 @ ( powerset @ X6 ) )
!= $true )
| ! [X7: $i] :
( ! [X8: $i] :
( ! [X9: $i] :
( ( $true
!= ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
= ( in @ X9 @ ( binunion @ X5 @ X8 ) ) ) )
| ( ( in @ X8 @ ( powerset @ X6 ) )
!= $true ) )
| ( $true
!= ( in @ X7 @ ( powerset @ X6 ) ) ) ) )
| ( inIntersectImpInUnion != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f35,f39,f38,f37,f36]) ).
thf(f36,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X4 @ X1 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
=> ( ( ( in @ sK8 @ ( powerset @ sK9 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ ( binintersect @ sK8 @ X2 ) ) )
& ( $true
= ( in @ X4 @ sK9 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ X3 ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK9 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK9 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ ( binintersect @ sK8 @ X2 ) ) )
& ( $true
= ( in @ X4 @ sK9 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ X3 ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK9 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK9 ) )
= $true ) )
=> ( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK8 @ sK10 ) )
= $true )
& ( $true
= ( in @ X4 @ sK9 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ X3 ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK9 ) )
= $true ) )
& ( ( in @ sK10 @ ( powerset @ sK9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK8 @ sK10 ) )
= $true )
& ( $true
= ( in @ X4 @ sK9 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ X3 ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK9 ) )
= $true ) )
=> ( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK8 @ sK10 ) )
= $true )
& ( $true
= ( in @ X4 @ sK9 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ sK11 ) ) ) )
& ( ( in @ sK11 @ ( powerset @ sK9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ sK8 @ sK10 ) )
= $true )
& ( $true
= ( in @ X4 @ sK9 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ sK8 @ sK11 ) ) ) )
=> ( ( ( in @ sK12 @ ( binintersect @ sK8 @ sK10 ) )
= $true )
& ( $true
= ( in @ sK12 @ sK9 ) )
& ( ( in @ sK12 @ ( binunion @ sK8 @ sK11 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ( ( inIntersectImpInUnion = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X4 @ X1 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) )
& ( ! [X5: $i,X6: $i] :
( ( ( in @ X5 @ ( powerset @ X6 ) )
!= $true )
| ! [X7: $i] :
( ! [X8: $i] :
( ! [X9: $i] :
( ( $true
!= ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
= ( in @ X9 @ ( binunion @ X5 @ X8 ) ) ) )
| ( ( in @ X8 @ ( powerset @ X6 ) )
!= $true ) )
| ( $true
!= ( in @ X7 @ ( powerset @ X6 ) ) ) ) )
| ( inIntersectImpInUnion != $true ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( inIntersectImpInUnion = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( $true
= ( in @ X4 @ X1 ) )
& ( $true
!= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X4 @ X1 ) )
| ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( inIntersectImpInUnion != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( inIntersectImpInUnion = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X4 @ X1 ) )
| ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) )
| ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( $true
!= ( in @ X4 @ X1 ) ) )
| ( ( in @ X3 @ ( powerset @ X1 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( inIntersectImpInUnion = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
= $true )
=> ( $true
= ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) ) ) ) ) )
<=> ( inIntersectImpInUnion = $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( inIntersectImpInUnion
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X4 @ ( binunion @ X0 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( inIntersectImpInUnion
= ( ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X2 @ ( binunion @ X3 @ X5 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CtHZWL3RvT/DTF2THF_20595.p',inIntersectImpInUnion) ).
thf(f100,plain,
( ( $true
!= ( in @ sK17 @ ( binunion @ sK13 @ sK16 ) ) )
| spl18_1 ),
inference(avatar_component_clause,[status(thm)],[f98]) ).
thf(f98,definition,
( spl18_1
<=> ( $true
= ( in @ sK17 @ ( binunion @ sK13 @ sK16 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl18_1])],[avatar_definition]) ).
thf(f105,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[status(thm)],[f96,f102,f98]) ).
thf(f96,plain,
( ( ( in @ sK17 @ ( binunion @ sK15 @ sK16 ) )
!= $true )
| ( $true
!= ( in @ sK17 @ ( binunion @ sK13 @ sK16 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $true
!= ( in @ sK17 @ ( binunion @ sK13 @ sK16 ) ) )
| ( $true != $true )
| ( ( in @ sK17 @ ( binunion @ sK15 @ sK16 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f68,f93]) ).
thf(f93,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f50,f73]) ).
thf(f73,plain,
binintersectI = $true,
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f50,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( binintersectI != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ( ( $true
!= ( in @ sK2 @ ( binintersect @ sK0 @ sK1 ) ) )
& ( ( in @ sK2 @ sK0 )
= $true )
& ( ( in @ sK2 @ sK1 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f25]) ).
thf(f25,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( in @ X5 @ X3 )
= $true )
& ( ( in @ X5 @ X4 )
= $true ) )
=> ( ( $true
!= ( in @ sK2 @ ( binintersect @ sK0 @ sK1 ) ) )
& ( ( in @ sK2 @ sK0 )
= $true )
& ( ( in @ sK2 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( in @ X5 @ X3 )
= $true )
& ( ( in @ X5 @ X4 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
!= $true )
& ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) )
<=> ( binintersectI = $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ( binintersectI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( binintersectI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
= binintersectI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectI ),
file('/export/starexec/sandbox2/tmp/tmp.CtHZWL3RvT/DTF2THF_20595.p',binintersectI) ).
thf(f68,plain,
( $true
!= ( in @ sK17 @ ( binintersect @ ( binunion @ sK13 @ sK16 ) @ ( binunion @ sK15 @ sK16 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU742^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.32 % Computer : n026.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue Feb 24 12:32:55 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.45 ---- Original DTF file ---
% 0.21/0.45 thf(spec,logic,$$dhol).
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 % File : SEU742^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.45 % Domain : Set Theory
% 0.21/0.45 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.21/0.45 % Version : Especial > Reduced > Especial.
% 0.21/0.45 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.21/0.45 % (! Z:i.in Z (powerset A) -> (! x:i.in x A ->
% 0.21/0.45 % in x (binintersect X Y) -> in x (binintersect (binunion X Z)
% 0.21/0.45 % (binunion Y Z))))))
% 0.21/0.45
% 0.21/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.45 % Source : [Bro08]
% 0.21/0.45 % Names : ZFC244l [Bro08]
% 0.21/0.45
% 0.21/0.45 % Status : Theorem
% 0.21/0.45 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 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 v3.7.0
% 0.21/0.45 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.21/0.45 % Number of atoms : 30 ( 3 equ; 0 cnn)
% 0.21/0.45 % Maximal formula atoms : 9 ( 7 avg)
% 0.21/0.45 % Number of connectives : 89 ( 0 ~; 0 |; 0 &; 69 @)
% 0.21/0.45 % ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% 0.21/0.45 % Maximal formula depth : 19 ( 6 avg)
% 0.21/0.45 % Number of types : 2 ( 0 usr)
% 0.21/0.45 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.21/0.45 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.21/0.45 % Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% 0.21/0.45 % SPC : TH0_THM_EQU_NAR
% 0.21/0.45
% 0.21/0.45 % Comments : http://mathgate.info/detsetitem.php?id=304
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 thf(in_type,type,
% 0.21/0.45 in: $i > $i > $o ).
% 0.21/0.45
% 0.21/0.45 thf(powerset_type,type,
% 0.21/0.45 powerset: $i > $i ).
% 0.21/0.45
% 0.21/0.45 thf(binunion_type,type,
% 0.21/0.45 binunion: $i > $i > $i ).
% 0.21/0.45
% 0.21/0.45 thf(binintersect_type,type,
% 0.21/0.45 binintersect: $i > $i > $i ).
% 0.21/0.45
% 0.21/0.45 thf(binintersectI_type,type,
% 0.21/0.45 binintersectI: $o ).
% 0.21/0.45
% 0.21/0.45 thf(binintersectI,definition,
% 0.21/0.45 ( binintersectI
% 0.21/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.45 ( ( in @ Xx @ A )
% 0.21/0.45 => ( ( in @ Xx @ B )
% 0.21/0.45 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(inIntersectImpInUnion_type,type,
% 0.21/0.45 inIntersectImpInUnion: $o ).
% 0.21/0.45
% 0.21/0.45 thf(inIntersectImpInUnion,definition,
% 0.21/0.45 ( inIntersectImpInUnion
% 0.21/0.45 = ( ! [A: $i,X: $i] :
% 0.21/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.45 => ! [Y: $i] :
% 0.21/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.45 => ! [Z: $i] :
% 0.21/0.45 ( ( in @ Z @ ( powerset @ A ) )
% 0.21/0.45 => ! [Xx: $i] :
% 0.21/0.45 ( ( in @ Xx @ A )
% 0.21/0.45 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.21/0.45 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(inIntersectImpInUnion2_type,type,
% 0.21/0.45 inIntersectImpInUnion2: $o ).
% 0.21/0.45
% 0.21/0.45 thf(inIntersectImpInUnion2,definition,
% 0.21/0.45 ( inIntersectImpInUnion2
% 0.21/0.45 = ( ! [A: $i,X: $i] :
% 0.21/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.45 => ! [Y: $i] :
% 0.21/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.45 => ! [Z: $i] :
% 0.21/0.45 ( ( in @ Z @ ( powerset @ A ) )
% 0.21/0.45 => ! [Xx: $i] :
% 0.21/0.45 ( ( in @ Xx @ A )
% 0.21/0.45 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.21/0.45 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(inIntersectImpInIntersectUnions,conjecture,
% 0.21/0.45 ( binintersectI
% 0.21/0.45 => ( inIntersectImpInUnion
% 0.21/0.45 => ( inIntersectImpInUnion2
% 0.21/0.45 => ! [A: $i,X: $i] :
% 0.21/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.45 => ! [Y: $i] :
% 0.21/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.45 => ! [Z: $i] :
% 0.21/0.45 ( ( in @ Z @ ( powerset @ A ) )
% 0.21/0.45 => ! [Xx: $i] :
% 0.21/0.45 ( ( in @ Xx @ A )
% 0.21/0.45 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.21/0.45 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 ------------------------
% 1.57/1.23 ---- Embedded in THF ---
% 1.57/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.23 %%% Generated on Tue Feb 24 12:32:56 EST 2026
% 1.57/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.23 %%% Logic specification used:
% 1.57/1.23 %%% thf(spec, logic, $$dhol).
% 1.57/1.23
% 1.57/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.CtHZWL3RvT/DTF2DTF20595.p
% See solution above
% 1.57/1.23 ------------------------
% 1.57/1.24 ---- Cleaned THF ---
% 1.57/1.24 thf(in_type,type,
% 1.57/1.24 in: $i > $i > $o ).
% 1.57/1.24
% 1.57/1.24 thf(powerset_type,type,
% 1.57/1.24 powerset: $i > $i ).
% 1.57/1.24
% 1.57/1.24 thf(binunion_type,type,
% 1.57/1.24 binunion: $i > $i > $i ).
% 1.57/1.24
% 1.57/1.24 thf(binintersect_type,type,
% 1.57/1.24 binintersect: $i > $i > $i ).
% 1.57/1.24
% 1.57/1.24 thf(binintersectI_type,type,
% 1.57/1.24 binintersectI: $o ).
% 1.57/1.24
% 1.57/1.24 thf(binintersectI,definition,
% 1.57/1.24 ( binintersectI
% 1.57/1.24 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.57/1.24 ( ( in @ Xx @ A )
% 1.57/1.24 => ( ( in @ Xx @ B )
% 1.57/1.24 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 1.57/1.24
% 1.57/1.24 thf(inIntersectImpInUnion_type,type,
% 1.57/1.24 inIntersectImpInUnion: $o ).
% 1.57/1.24
% 1.57/1.24 thf(inIntersectImpInUnion,definition,
% 1.57/1.24 ( inIntersectImpInUnion
% 1.57/1.24 = ( ! [A: $i,X: $i] :
% 1.57/1.24 ( ( in @ X @ ( powerset @ A ) )
% 1.57/1.24 => ! [Y: $i] :
% 1.57/1.24 ( ( in @ Y @ ( powerset @ A ) )
% 1.57/1.24 => ! [Z: $i] :
% 1.57/1.24 ( ( in @ Z @ ( powerset @ A ) )
% 1.57/1.24 => ! [Xx: $i] :
% 1.57/1.24 ( ( in @ Xx @ A )
% 1.57/1.24 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 1.57/1.24 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 1.57/1.24
% 1.57/1.24 thf(inIntersectImpInUnion2_type,type,
% 1.57/1.24 inIntersectImpInUnion2: $o ).
% 1.57/1.24
% 1.57/1.24 thf(inIntersectImpInUnion2,definition,
% 1.57/1.24 ( inIntersectImpInUnion2
% 1.57/1.24 = ( ! [A: $i,X: $i] :
% 1.57/1.24 ( ( in @ X @ ( powerset @ A ) )
% 1.57/1.24 => ! [Y: $i] :
% 1.57/1.24 ( ( in @ Y @ ( powerset @ A ) )
% 1.57/1.24 => ! [Z: $i] :
% 1.57/1.24 ( ( in @ Z @ ( powerset @ A ) )
% 1.57/1.24 => ! [Xx: $i] :
% 1.57/1.24 ( ( in @ Xx @ A )
% 1.57/1.24 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 1.57/1.24 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 1.57/1.24
% 1.57/1.24 thf(inIntersectImpInIntersectUnions,conjecture,
% 1.57/1.24 ( binintersectI
% 1.57/1.24 => ( inIntersectImpInUnion
% 1.57/1.24 => ( inIntersectImpInUnion2
% 1.57/1.24 => ! [A: $i,X: $i] :
% 1.57/1.24 ( ( in @ X @ ( powerset @ A ) )
% 1.57/1.24 => ! [Y: $i] :
% 1.57/1.24 ( ( in @ Y @ ( powerset @ A ) )
% 1.57/1.24 => ! [Z: $i] :
% 1.57/1.24 ( ( in @ Z @ ( powerset @ A ) )
% 1.57/1.24 => ! [Xx: $i] :
% 1.57/1.24 ( ( in @ Xx @ A )
% 1.57/1.24 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 1.57/1.24 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 1.57/1.24 ------------------------
% 1.57/1.25 % (20751)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_20595 for (2999ds/4Mi)
% 1.57/1.26 % (20751)Instruction limit reached!
% 1.57/1.26 % (20751)------------------------------
% 1.57/1.26 % (20751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (20751)Termination reason: Unknown
% 1.57/1.26 % (20751)Termination phase: Saturation
% 1.57/1.26
% 1.57/1.26 % (20751)Memory used [KB]: 5500
% 1.57/1.26 % (20751)Time elapsed: 0.003 s
% 1.57/1.26 % (20751)Instructions burned: 5 (million)
% 1.57/1.26 % (20751)------------------------------
% 1.57/1.26 % (20751)------------------------------
% 1.57/1.26 % (20753)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20595 for (2999ds/2Mi)
% 1.57/1.26 % (20750)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20595 for (2999ds/183Mi)
% 1.57/1.26 % (20753)Instruction limit reached!
% 1.57/1.26 % (20753)------------------------------
% 1.57/1.26 % (20753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (20753)Termination reason: Unknown
% 1.57/1.26 % (20753)Termination phase: Preprocessing 3
% 1.57/1.26
% 1.57/1.26 % (20753)Memory used [KB]: 1023
% 1.57/1.26 % (20753)Time elapsed: 0.004 s
% 1.57/1.26 % (20753)Instructions burned: 3 (million)
% 1.57/1.26 % (20753)------------------------------
% 1.57/1.26 % (20753)------------------------------
% 1.57/1.26 % (20752)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_20595 for (2999ds/27Mi)
% 1.57/1.26 % (20755)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_20595 for (2999ds/275Mi)
% 1.57/1.26 % (20756)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20595 for (2999ds/18Mi)
% 1.57/1.26 % (20754)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_20595 for (2999ds/2Mi)
% 1.57/1.26 % (20754)Instruction limit reached!
% 1.57/1.26 % (20754)------------------------------
% 1.57/1.26 % (20754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (20754)Termination reason: Unknown
% 1.57/1.26 % (20754)Termination phase: Property scanning
% 1.57/1.26
% 1.57/1.26 % (20754)Memory used [KB]: 1023
% 1.57/1.26 % (20754)Time elapsed: 0.003 s
% 1.57/1.26 % (20754)Instructions burned: 3 (million)
% 1.57/1.26 % (20754)------------------------------
% 1.57/1.26 % (20754)------------------------------
% 1.57/1.27 % (20758)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20595 for (2999ds/3Mi)
% 1.57/1.27 % (20758)Instruction limit reached!
% 1.57/1.27 % (20758)------------------------------
% 1.57/1.27 % (20758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.27 % (20758)Termination reason: Unknown
% 1.57/1.27 % (20758)Termination phase: Property scanning
% 1.57/1.27
% 1.57/1.27 % (20758)Memory used [KB]: 1023
% 1.57/1.27 % (20758)Time elapsed: 0.002 s
% 1.57/1.27 % (20758)Instructions burned: 4 (million)
% 1.57/1.27 % (20758)------------------------------
% 1.57/1.27 % (20758)------------------------------
% 1.57/1.27 % (20759)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_20595 for (2999ds/37Mi)
% 1.57/1.27 % (20755)First to succeed.
% 1.57/1.27 % (20756)Instruction limit reached!
% 1.57/1.27 % (20756)------------------------------
% 1.57/1.27 % (20756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.27 % (20756)Termination reason: Unknown
% 1.57/1.27 % (20756)Termination phase: Saturation
% 1.57/1.27
% 1.57/1.27 % (20756)Memory used [KB]: 5628
% 1.57/1.27 % (20756)Time elapsed: 0.014 s
% 1.57/1.27 % (20756)Instructions burned: 18 (million)
% 1.57/1.27 % (20756)------------------------------
% 1.57/1.27 % (20756)------------------------------
% 1.57/1.28 % (20761)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_20595 for (2999ds/3Mi)
% 1.57/1.28 % (20761)Instruction limit reached!
% 1.57/1.28 % (20761)------------------------------
% 1.57/1.28 % (20761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (20761)Termination reason: Unknown
% 1.57/1.28 % (20761)Termination phase: Preprocessing 3
% 1.57/1.28
% 1.57/1.28 % (20761)Memory used [KB]: 1023
% 1.57/1.28 % (20761)Time elapsed: 0.002 s
% 1.57/1.28 % (20761)Instructions burned: 3 (million)
% 1.57/1.28 % (20761)------------------------------
% 1.57/1.28 % (20761)------------------------------
% 1.57/1.28 % (20752)Instruction limit reached!
% 1.57/1.28 % (20752)------------------------------
% 1.57/1.28 % (20752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (20752)Termination reason: Unknown
% 1.57/1.28 % (20752)Termination phase: Saturation
% 1.57/1.28
% 1.57/1.28 % (20752)Memory used [KB]: 5628
% 1.57/1.28 % (20752)Time elapsed: 0.019 s
% 1.57/1.28 % (20752)Instructions burned: 27 (million)
% 1.57/1.28 % (20752)------------------------------
% 1.57/1.28 % (20752)------------------------------
% 1.57/1.28 % (20750)Also succeeded, but the first one will report.
% 1.57/1.28 % (20755)Refutation found. Thanks to Tanya!
% 1.57/1.28 % SZS status Theorem for DTF2THF_20595
% 1.57/1.28 % SZS output start Proof for DTF2THF_20595
% 1.57/1.28 thf(func_def_0, type, in: $i > $i > $o).
% 1.57/1.28 thf(func_def_1, type, powerset: $i > $i).
% 1.57/1.28 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.57/1.28 thf(func_def_3, type, binintersect: $i > $i > $i).
% 1.57/1.28 thf(f154,plain,(
% 1.57/1.28 $false),
% 1.57/1.28 inference(avatar_sat_refutation,[status(thm)],[f105,f129,f153])).
% 1.57/1.28 thf(f153,plain,(
% 1.57/1.28 spl18_2),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f152])).
% 1.57/1.28 thf(f152,plain,(
% 1.57/1.28 $false | spl18_2),
% 1.57/1.28 inference(subsumption_resolution,[status(thm)],[f151,f71])).
% 1.57/1.28 thf(f71,plain,(
% 1.57/1.28 ($true = (in @ sK15 @ (powerset @ sK14)))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f46])).
% 1.57/1.28 thf(f46,plain,(
% 1.57/1.28 (binintersectI = $true) & (inIntersectImpInUnion2 = $true) & ((($true = (in @ sK15 @ (powerset @ sK14))) & (((in @ sK16 @ (powerset @ sK14)) = $true) & (($true = (in @ sK17 @ (binintersect @ sK13 @ sK15))) & ($true != (in @ sK17 @ (binintersect @ (binunion @ sK13 @ sK16) @ (binunion @ sK15 @ sK16)))) & ((in @ sK17 @ sK14) = $true)))) & ((in @ sK13 @ (powerset @ sK14)) = $true)) & (inIntersectImpInUnion = $true)),
% 1.57/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17])],[f41,f45,f44,f43,f42])).
% 1.57/1.28 thf(f42,plain,(
% 1.57/1.28 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) & ? [X4 : $i] : (((in @ X4 @ (binintersect @ X0 @ X2)) = $true) & ($true != (in @ X4 @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) & ($true = (in @ X4 @ X1))))) & ($true = (in @ X0 @ (powerset @ X1)))) => (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK14))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ sK14)) = $true) & ? [X4 : $i] : (((in @ X4 @ (binintersect @ sK13 @ X2)) = $true) & ($true != (in @ X4 @ (binintersect @ (binunion @ sK13 @ X3) @ (binunion @ X2 @ X3)))) & ((in @ X4 @ sK14) = $true)))) & ((in @ sK13 @ (powerset @ sK14)) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f43,plain,(
% 1.57/1.28 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK14))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ sK14)) = $true) & ? [X4 : $i] : (((in @ X4 @ (binintersect @ sK13 @ X2)) = $true) & ($true != (in @ X4 @ (binintersect @ (binunion @ sK13 @ X3) @ (binunion @ X2 @ X3)))) & ((in @ X4 @ sK14) = $true)))) => (($true = (in @ sK15 @ (powerset @ sK14))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ sK14)) = $true) & ? [X4 : $i] : (((in @ X4 @ (binintersect @ sK13 @ sK15)) = $true) & ((in @ X4 @ (binintersect @ (binunion @ sK13 @ X3) @ (binunion @ sK15 @ X3))) != $true) & ((in @ X4 @ sK14) = $true))))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f44,plain,(
% 1.57/1.28 ? [X3 : $i] : (((in @ X3 @ (powerset @ sK14)) = $true) & ? [X4 : $i] : (((in @ X4 @ (binintersect @ sK13 @ sK15)) = $true) & ((in @ X4 @ (binintersect @ (binunion @ sK13 @ X3) @ (binunion @ sK15 @ X3))) != $true) & ((in @ X4 @ sK14) = $true))) => (((in @ sK16 @ (powerset @ sK14)) = $true) & ? [X4 : $i] : (((in @ X4 @ (binintersect @ sK13 @ sK15)) = $true) & ((in @ X4 @ (binintersect @ (binunion @ sK13 @ sK16) @ (binunion @ sK15 @ sK16))) != $true) & ((in @ X4 @ sK14) = $true)))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f45,plain,(
% 1.57/1.28 ? [X4 : $i] : (((in @ X4 @ (binintersect @ sK13 @ sK15)) = $true) & ((in @ X4 @ (binintersect @ (binunion @ sK13 @ sK16) @ (binunion @ sK15 @ sK16))) != $true) & ((in @ X4 @ sK14) = $true)) => (($true = (in @ sK17 @ (binintersect @ sK13 @ sK15))) & ($true != (in @ sK17 @ (binintersect @ (binunion @ sK13 @ sK16) @ (binunion @ sK15 @ sK16)))) & ((in @ sK17 @ sK14) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f41,plain,(
% 1.57/1.28 (binintersectI = $true) & (inIntersectImpInUnion2 = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) & ? [X4 : $i] : (((in @ X4 @ (binintersect @ X0 @ X2)) = $true) & ($true != (in @ X4 @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) & ($true = (in @ X4 @ X1))))) & ($true = (in @ X0 @ (powerset @ X1)))) & (inIntersectImpInUnion = $true)),
% 1.57/1.28 inference(rectify,[status(thm)],[f16])).
% 1.57/1.28 thf(f16,plain,(
% 1.57/1.28 (binintersectI = $true) & (inIntersectImpInUnion2 = $true) & ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) & ? [X4 : $i] : (((in @ X4 @ (binintersect @ X1 @ X2)) = $true) & ((in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))) != $true) & ($true = (in @ X4 @ X0))))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (inIntersectImpInUnion = $true)),
% 1.57/1.28 inference(flattening,[status(thm)],[f15])).
% 1.57/1.28 thf(f15,plain,(
% 1.57/1.28 ((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))) != $true) & ((in @ X4 @ (binintersect @ X1 @ X2)) = $true)) & ($true = (in @ X4 @ X0))) & ((in @ X3 @ (powerset @ X0)) = $true)) & ($true = (in @ X2 @ (powerset @ X0)))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binintersectI = $true)),
% 1.57/1.28 inference(ennf_transformation,[status(thm)],[f8])).
% 1.57/1.28 thf(f8,plain,(
% 1.57/1.28 ~((binintersectI = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) => ! [X4 : $i] : (($true = (in @ X4 @ X0)) => (((in @ X4 @ (binintersect @ X1 @ X2)) = $true) => ((in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))) = $true)))))))))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f7])).
% 1.57/1.28 thf(f7,plain,(
% 1.57/1.28 ~(binintersectI => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))))))))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f5])).
% 1.57/1.28 thf(f5,negated_conjecture,(
% 1.57/1.28 ~(binintersectI => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binintersect @ (binunion @ X3 @ X5) @ (binunion @ X4 @ X5)))))))))))),
% 1.57/1.28 inference(negated_conjecture,[status(cth)],[f4])).
% 1.57/1.28 thf(f4,conjecture,(
% 1.57/1.28 binintersectI => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binintersect @ (binunion @ X3 @ X5) @ (binunion @ X4 @ X5))))))))))),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.CtHZWL3RvT/DTF2THF_20595.p',inIntersectImpInIntersectUnions)).
% 1.57/1.28 thf(f151,plain,(
% 1.57/1.28 ($true != (in @ sK15 @ (powerset @ sK14))) | spl18_2),
% 1.57/1.28 inference(subsumption_resolution,[status(thm)],[f150,f67])).
% 1.57/1.28 thf(f67,plain,(
% 1.57/1.28 ((in @ sK17 @ sK14) = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f46])).
% 1.57/1.28 thf(f150,plain,(
% 1.57/1.28 ((in @ sK17 @ sK14) != $true) | ($true != (in @ sK15 @ (powerset @ sK14))) | spl18_2),
% 1.57/1.28 inference(subsumption_resolution,[status(thm)],[f149,f66])).
% 1.57/1.28 thf(f66,plain,(
% 1.57/1.28 ((in @ sK13 @ (powerset @ sK14)) = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f46])).
% 1.57/1.28 thf(f149,plain,(
% 1.57/1.28 ((in @ sK13 @ (powerset @ sK14)) != $true) | ($true != (in @ sK15 @ (powerset @ sK14))) | ((in @ sK17 @ sK14) != $true) | spl18_2),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.57/1.28 thf(f148,plain,(
% 1.57/1.28 ($true != (in @ sK15 @ (powerset @ sK14))) | ((in @ sK13 @ (powerset @ sK14)) != $true) | ((in @ sK17 @ sK14) != $true) | ($true != $true) | spl18_2),
% 1.57/1.28 inference(superposition,[status(thm)],[f146,f70])).
% 1.57/1.28 thf(f70,plain,(
% 1.57/1.28 ((in @ sK16 @ (powerset @ sK14)) = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f46])).
% 1.57/1.28 thf(f146,plain,(
% 1.57/1.28 ( ! [X0 : $i] : (($true != (in @ sK16 @ (powerset @ X0))) | ($true != (in @ sK15 @ (powerset @ X0))) | ((in @ sK13 @ (powerset @ X0)) != $true) | ((in @ sK17 @ X0) != $true)) ) | spl18_2),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.57/1.28 thf(f144,plain,(
% 1.57/1.28 ( ! [X0 : $i] : (((in @ sK17 @ X0) != $true) | ($true != (in @ sK16 @ (powerset @ X0))) | ((in @ sK13 @ (powerset @ X0)) != $true) | ($true != (in @ sK15 @ (powerset @ X0))) | ($true != $true)) ) | spl18_2),
% 1.57/1.28 inference(superposition,[status(thm)],[f133,f69])).
% 1.57/1.28 thf(f69,plain,(
% 1.57/1.28 ($true = (in @ sK17 @ (binintersect @ sK13 @ sK15)))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f46])).
% 1.57/1.28 thf(f133,plain,(
% 1.57/1.28 ( ! [X0 : $i,X1 : $i] : (($true != (in @ sK17 @ (binintersect @ X0 @ sK15))) | ((in @ sK15 @ (powerset @ X1)) != $true) | ((in @ sK16 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ sK17 @ X1) != $true)) ) | spl18_2),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.57/1.28 thf(f131,plain,(
% 1.57/1.28 ( ! [X0 : $i,X1 : $i] : (((in @ sK16 @ (powerset @ X1)) != $true) | ((in @ sK15 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ sK17 @ X1) != $true) | ($true != $true) | ($true != (in @ sK17 @ (binintersect @ X0 @ sK15)))) ) | spl18_2),
% 1.57/1.28 inference(superposition,[status(thm)],[f104,f92])).
% 1.57/1.28 thf(f92,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ X4 @ (binunion @ X2 @ X3)) = $true) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ (powerset @ X0)) != $true) | ($true != (in @ X2 @ (powerset @ X0))) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != (in @ X4 @ X0))) )),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.57/1.28 thf(f78,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X4 @ (binunion @ X2 @ X3)) = $true) | ($true != $true) | ($true != (in @ X4 @ X0)) | ((in @ X3 @ (powerset @ X0)) != $true) | ($true != (in @ X2 @ (powerset @ X0)))) )),
% 1.57/1.28 inference(definition_unfolding,[status(thm)],[f57,f72])).
% 1.57/1.28 thf(f72,plain,(
% 1.57/1.28 (inIntersectImpInUnion2 = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f46])).
% 1.57/1.28 thf(f57,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ X2 @ (powerset @ X0))) | ($true != (in @ X4 @ X0)) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X4 @ (binunion @ X2 @ X3)) = $true) | ((in @ X3 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | (inIntersectImpInUnion2 != $true)) )),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f33])).
% 1.57/1.28 thf(f33,plain,(
% 1.57/1.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X0))) | ! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X4 @ (binunion @ X2 @ X3)) = $true)) | ((in @ X3 @ (powerset @ X0)) != $true))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (inIntersectImpInUnion2 != $true)) & ((inIntersectImpInUnion2 = $true) | ((($true = (in @ sK5 @ (powerset @ sK3))) & ((((in @ sK7 @ sK3) = $true) & ((in @ sK7 @ (binintersect @ sK4 @ sK5)) = $true) & ((in @ sK7 @ (binunion @ sK5 @ sK6)) != $true)) & ((in @ sK6 @ (powerset @ sK3)) = $true))) & ($true = (in @ sK4 @ (powerset @ sK3)))))),
% 1.57/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f28,f32,f31,f30,f29])).
% 1.57/1.28 thf(f29,plain,(
% 1.57/1.28 ? [X5 : $i,X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ (powerset @ X5))) & ? [X8 : $i] : (? [X9 : $i] : (((in @ X9 @ X5) = $true) & ($true = (in @ X9 @ (binintersect @ X6 @ X7))) & ((in @ X9 @ (binunion @ X7 @ X8)) != $true)) & ($true = (in @ X8 @ (powerset @ X5))))) & ($true = (in @ X6 @ (powerset @ X5)))) => (? [X7 : $i] : (($true = (in @ X7 @ (powerset @ sK3))) & ? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ sK3)) & ((in @ X9 @ (binintersect @ sK4 @ X7)) = $true) & ((in @ X9 @ (binunion @ X7 @ X8)) != $true)) & ((in @ X8 @ (powerset @ sK3)) = $true))) & ($true = (in @ sK4 @ (powerset @ sK3))))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f30,plain,(
% 1.57/1.28 ? [X7 : $i] : (($true = (in @ X7 @ (powerset @ sK3))) & ? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ sK3)) & ((in @ X9 @ (binintersect @ sK4 @ X7)) = $true) & ((in @ X9 @ (binunion @ X7 @ X8)) != $true)) & ((in @ X8 @ (powerset @ sK3)) = $true))) => (($true = (in @ sK5 @ (powerset @ sK3))) & ? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ sK3)) & ($true = (in @ X9 @ (binintersect @ sK4 @ sK5))) & ((in @ X9 @ (binunion @ sK5 @ X8)) != $true)) & ((in @ X8 @ (powerset @ sK3)) = $true)))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f31,plain,(
% 1.57/1.28 ? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ sK3)) & ($true = (in @ X9 @ (binintersect @ sK4 @ sK5))) & ((in @ X9 @ (binunion @ sK5 @ X8)) != $true)) & ((in @ X8 @ (powerset @ sK3)) = $true)) => (? [X9 : $i] : (($true = (in @ X9 @ sK3)) & ($true = (in @ X9 @ (binintersect @ sK4 @ sK5))) & ((in @ X9 @ (binunion @ sK5 @ sK6)) != $true)) & ((in @ sK6 @ (powerset @ sK3)) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f32,plain,(
% 1.57/1.28 ? [X9 : $i] : (($true = (in @ X9 @ sK3)) & ($true = (in @ X9 @ (binintersect @ sK4 @ sK5))) & ((in @ X9 @ (binunion @ sK5 @ sK6)) != $true)) => (((in @ sK7 @ sK3) = $true) & ((in @ sK7 @ (binintersect @ sK4 @ sK5)) = $true) & ((in @ sK7 @ (binunion @ sK5 @ sK6)) != $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f28,plain,(
% 1.57/1.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X0))) | ! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X4 @ (binunion @ X2 @ X3)) = $true)) | ((in @ X3 @ (powerset @ X0)) != $true))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (inIntersectImpInUnion2 != $true)) & ((inIntersectImpInUnion2 = $true) | ? [X5 : $i,X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ (powerset @ X5))) & ? [X8 : $i] : (? [X9 : $i] : (((in @ X9 @ X5) = $true) & ($true = (in @ X9 @ (binintersect @ X6 @ X7))) & ((in @ X9 @ (binunion @ X7 @ X8)) != $true)) & ($true = (in @ X8 @ (powerset @ X5))))) & ($true = (in @ X6 @ (powerset @ X5)))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f27])).
% 1.57/1.28 thf(f27,plain,(
% 1.57/1.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X0))) | ! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X4 @ (binunion @ X2 @ X3)) = $true)) | ((in @ X3 @ (powerset @ X0)) != $true))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (inIntersectImpInUnion2 != $true)) & ((inIntersectImpInUnion2 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X0)) & ((in @ X4 @ (binintersect @ X1 @ X2)) = $true) & ((in @ X4 @ (binunion @ X2 @ X3)) != $true)) & ((in @ X3 @ (powerset @ X0)) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 1.57/1.28 inference(nnf_transformation,[status(thm)],[f18])).
% 1.57/1.28 thf(f18,plain,(
% 1.57/1.28 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ (powerset @ X0))) | ! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X4 @ (binunion @ X2 @ X3)) = $true)) | ((in @ X3 @ (powerset @ X0)) != $true))) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (inIntersectImpInUnion2 = $true)),
% 1.57/1.28 inference(flattening,[status(thm)],[f17])).
% 1.57/1.28 thf(f17,plain,(
% 1.57/1.28 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((((in @ X4 @ (binunion @ X2 @ X3)) = $true) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true)) | ($true != (in @ X4 @ X0))) | ((in @ X3 @ (powerset @ X0)) != $true)) | ($true != (in @ X2 @ (powerset @ X0)))) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (inIntersectImpInUnion2 = $true)),
% 1.57/1.28 inference(ennf_transformation,[status(thm)],[f14])).
% 1.57/1.28 thf(f14,plain,(
% 1.57/1.28 ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) => ! [X4 : $i] : (($true = (in @ X4 @ X0)) => (((in @ X4 @ (binintersect @ X1 @ X2)) = $true) => ((in @ X4 @ (binunion @ X2 @ X3)) = $true)))))) <=> (inIntersectImpInUnion2 = $true)),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f13])).
% 1.57/1.28 thf(f13,plain,(
% 1.57/1.28 (inIntersectImpInUnion2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binunion @ X2 @ X3))))))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f3])).
% 1.57/1.28 thf(f3,axiom,(
% 1.57/1.28 (inIntersectImpInUnion2 = ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binunion @ X4 @ X5))))))))),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.CtHZWL3RvT/DTF2THF_20595.p',inIntersectImpInUnion2)).
% 1.57/1.28 thf(f104,plain,(
% 1.57/1.28 ((in @ sK17 @ (binunion @ sK15 @ sK16)) != $true) | spl18_2),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f102])).
% 1.57/1.28 thf(f102,definition,(
% 1.57/1.28 spl18_2 <=> ((in @ sK17 @ (binunion @ sK15 @ sK16)) = $true)),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl18_2])],[avatar_definition])).
% 1.57/1.28 thf(f129,plain,(
% 1.57/1.28 spl18_1),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f128])).
% 1.57/1.28 thf(f128,plain,(
% 1.57/1.28 $false | spl18_1),
% 1.57/1.28 inference(subsumption_resolution,[status(thm)],[f127,f71])).
% 1.57/1.28 thf(f127,plain,(
% 1.57/1.28 ($true != (in @ sK15 @ (powerset @ sK14))) | spl18_1),
% 1.57/1.28 inference(subsumption_resolution,[status(thm)],[f126,f66])).
% 1.57/1.28 thf(f126,plain,(
% 1.57/1.28 ((in @ sK13 @ (powerset @ sK14)) != $true) | ($true != (in @ sK15 @ (powerset @ sK14))) | spl18_1),
% 1.57/1.28 inference(subsumption_resolution,[status(thm)],[f125,f67])).
% 1.57/1.28 thf(f125,plain,(
% 1.57/1.28 ((in @ sK17 @ sK14) != $true) | ($true != (in @ sK15 @ (powerset @ sK14))) | ((in @ sK13 @ (powerset @ sK14)) != $true) | spl18_1),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f124])).
% 1.57/1.28 thf(f124,plain,(
% 1.57/1.28 ($true != (in @ sK15 @ (powerset @ sK14))) | ($true != $true) | ((in @ sK13 @ (powerset @ sK14)) != $true) | ((in @ sK17 @ sK14) != $true) | spl18_1),
% 1.57/1.28 inference(superposition,[status(thm)],[f123,f70])).
% 1.57/1.28 thf(f123,plain,(
% 1.57/1.28 ( ! [X0 : $i] : (($true != (in @ sK16 @ (powerset @ X0))) | ((in @ sK17 @ X0) != $true) | ($true != (in @ sK15 @ (powerset @ X0))) | ((in @ sK13 @ (powerset @ X0)) != $true)) ) | spl18_1),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.57/1.28 thf(f120,plain,(
% 1.57/1.28 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ sK16 @ (powerset @ X0))) | ((in @ sK17 @ X0) != $true) | ($true != (in @ sK15 @ (powerset @ X0))) | ((in @ sK13 @ (powerset @ X0)) != $true)) ) | spl18_1),
% 1.57/1.28 inference(superposition,[status(thm)],[f109,f69])).
% 1.57/1.28 thf(f109,plain,(
% 1.57/1.28 ( ! [X0 : $i,X1 : $i] : (((in @ sK17 @ (binintersect @ sK13 @ X1)) != $true) | ((in @ sK17 @ X0) != $true) | ((in @ sK13 @ (powerset @ X0)) != $true) | ($true != (in @ sK16 @ (powerset @ X0))) | ((in @ X1 @ (powerset @ X0)) != $true)) ) | spl18_1),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.57/1.28 thf(f108,plain,(
% 1.57/1.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ sK13 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ sK17 @ X0) != $true) | ($true != (in @ sK16 @ (powerset @ X0))) | ((in @ sK17 @ (binintersect @ sK13 @ X1)) != $true)) ) | spl18_1),
% 1.57/1.28 inference(superposition,[status(thm)],[f100,f94])).
% 1.57/1.28 thf(f94,plain,(
% 1.57/1.28 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true = (in @ X9 @ (binunion @ X5 @ X8))) | ((in @ X8 @ (powerset @ X6)) != $true) | ($true != (in @ X7 @ (powerset @ X6))) | ($true != (in @ X9 @ X6)) | ((in @ X5 @ (powerset @ X6)) != $true) | ($true != (in @ X9 @ (binintersect @ X5 @ X7)))) )),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.57/1.28 thf(f91,plain,(
% 1.57/1.28 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true = (in @ X9 @ (binunion @ X5 @ X8))) | ($true != (in @ X9 @ X6)) | ((in @ X5 @ (powerset @ X6)) != $true) | ((in @ X8 @ (powerset @ X6)) != $true) | ($true != (in @ X7 @ (powerset @ X6))) | ($true != (in @ X9 @ (binintersect @ X5 @ X7))) | ($true != $true)) )),
% 1.57/1.28 inference(definition_unfolding,[status(thm)],[f58,f65])).
% 1.57/1.28 thf(f65,plain,(
% 1.57/1.28 (inIntersectImpInUnion = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f46])).
% 1.57/1.28 thf(f58,plain,(
% 1.57/1.28 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X6)) != $true) | ($true != (in @ X9 @ (binintersect @ X5 @ X7))) | ($true != (in @ X9 @ X6)) | ($true = (in @ X9 @ (binunion @ X5 @ X8))) | ((in @ X8 @ (powerset @ X6)) != $true) | ($true != (in @ X7 @ (powerset @ X6))) | (inIntersectImpInUnion != $true)) )),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f40])).
% 1.57/1.28 thf(f40,plain,(
% 1.57/1.28 ((inIntersectImpInUnion = $true) | (((in @ sK8 @ (powerset @ sK9)) = $true) & (((((in @ sK12 @ (binintersect @ sK8 @ sK10)) = $true) & ($true = (in @ sK12 @ sK9)) & ((in @ sK12 @ (binunion @ sK8 @ sK11)) != $true)) & ((in @ sK11 @ (powerset @ sK9)) = $true)) & ((in @ sK10 @ (powerset @ sK9)) = $true)))) & (! [X5 : $i,X6 : $i] : (((in @ X5 @ (powerset @ X6)) != $true) | ! [X7 : $i] : (! [X8 : $i] : (! [X9 : $i] : (($true != (in @ X9 @ (binintersect @ X5 @ X7))) | ($true != (in @ X9 @ X6)) | ($true = (in @ X9 @ (binunion @ X5 @ X8)))) | ((in @ X8 @ (powerset @ X6)) != $true)) | ($true != (in @ X7 @ (powerset @ X6))))) | (inIntersectImpInUnion != $true))),
% 1.57/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f35,f39,f38,f37,f36])).
% 1.57/1.28 thf(f36,plain,(
% 1.57/1.28 ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binintersect @ X0 @ X2)) = $true) & ($true = (in @ X4 @ X1)) & ($true != (in @ X4 @ (binunion @ X0 @ X3)))) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1))))) => (((in @ sK8 @ (powerset @ sK9)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ (binintersect @ sK8 @ X2))) & ($true = (in @ X4 @ sK9)) & ($true != (in @ X4 @ (binunion @ sK8 @ X3)))) & ((in @ X3 @ (powerset @ sK9)) = $true)) & ((in @ X2 @ (powerset @ sK9)) = $true)))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f37,plain,(
% 1.57/1.28 ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ (binintersect @ sK8 @ X2))) & ($true = (in @ X4 @ sK9)) & ($true != (in @ X4 @ (binunion @ sK8 @ X3)))) & ((in @ X3 @ (powerset @ sK9)) = $true)) & ((in @ X2 @ (powerset @ sK9)) = $true)) => (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binintersect @ sK8 @ sK10)) = $true) & ($true = (in @ X4 @ sK9)) & ($true != (in @ X4 @ (binunion @ sK8 @ X3)))) & ((in @ X3 @ (powerset @ sK9)) = $true)) & ((in @ sK10 @ (powerset @ sK9)) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f38,plain,(
% 1.57/1.28 ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binintersect @ sK8 @ sK10)) = $true) & ($true = (in @ X4 @ sK9)) & ($true != (in @ X4 @ (binunion @ sK8 @ X3)))) & ((in @ X3 @ (powerset @ sK9)) = $true)) => (? [X4 : $i] : (((in @ X4 @ (binintersect @ sK8 @ sK10)) = $true) & ($true = (in @ X4 @ sK9)) & ($true != (in @ X4 @ (binunion @ sK8 @ sK11)))) & ((in @ sK11 @ (powerset @ sK9)) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f39,plain,(
% 1.57/1.28 ? [X4 : $i] : (((in @ X4 @ (binintersect @ sK8 @ sK10)) = $true) & ($true = (in @ X4 @ sK9)) & ($true != (in @ X4 @ (binunion @ sK8 @ sK11)))) => (((in @ sK12 @ (binintersect @ sK8 @ sK10)) = $true) & ($true = (in @ sK12 @ sK9)) & ((in @ sK12 @ (binunion @ sK8 @ sK11)) != $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f35,plain,(
% 1.57/1.28 ((inIntersectImpInUnion = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binintersect @ X0 @ X2)) = $true) & ($true = (in @ X4 @ X1)) & ($true != (in @ X4 @ (binunion @ X0 @ X3)))) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))))) & (! [X5 : $i,X6 : $i] : (((in @ X5 @ (powerset @ X6)) != $true) | ! [X7 : $i] : (! [X8 : $i] : (! [X9 : $i] : (($true != (in @ X9 @ (binintersect @ X5 @ X7))) | ($true != (in @ X9 @ X6)) | ($true = (in @ X9 @ (binunion @ X5 @ X8)))) | ((in @ X8 @ (powerset @ X6)) != $true)) | ($true != (in @ X7 @ (powerset @ X6))))) | (inIntersectImpInUnion != $true))),
% 1.57/1.28 inference(rectify,[status(thm)],[f34])).
% 1.57/1.28 thf(f34,plain,(
% 1.57/1.28 ((inIntersectImpInUnion = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (binintersect @ X0 @ X2)) = $true) & ($true = (in @ X4 @ X1)) & ($true != (in @ X4 @ (binunion @ X0 @ X3)))) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))))) & (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ (binintersect @ X0 @ X2)) != $true) | ($true != (in @ X4 @ X1)) | ($true = (in @ X4 @ (binunion @ X0 @ X3)))) | ((in @ X3 @ (powerset @ X1)) != $true)) | ($true != (in @ X2 @ (powerset @ X1))))) | (inIntersectImpInUnion != $true))),
% 1.57/1.28 inference(nnf_transformation,[status(thm)],[f20])).
% 1.57/1.28 thf(f20,plain,(
% 1.57/1.28 (inIntersectImpInUnion = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ (binintersect @ X0 @ X2)) != $true) | ($true != (in @ X4 @ X1)) | ($true = (in @ X4 @ (binunion @ X0 @ X3)))) | ((in @ X3 @ (powerset @ X1)) != $true)) | ($true != (in @ X2 @ (powerset @ X1)))))),
% 1.57/1.28 inference(flattening,[status(thm)],[f19])).
% 1.57/1.28 thf(f19,plain,(
% 1.57/1.28 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((($true = (in @ X4 @ (binunion @ X0 @ X3))) | ((in @ X4 @ (binintersect @ X0 @ X2)) != $true)) | ($true != (in @ X4 @ X1))) | ((in @ X3 @ (powerset @ X1)) != $true)) | ($true != (in @ X2 @ (powerset @ X1)))) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (inIntersectImpInUnion = $true)),
% 1.57/1.28 inference(ennf_transformation,[status(thm)],[f10])).
% 1.57/1.28 thf(f10,plain,(
% 1.57/1.28 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) => ! [X4 : $i] : (($true = (in @ X4 @ X1)) => (((in @ X4 @ (binintersect @ X0 @ X2)) = $true) => ($true = (in @ X4 @ (binunion @ X0 @ X3)))))))) <=> (inIntersectImpInUnion = $true)),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f9])).
% 1.57/1.28 thf(f9,plain,(
% 1.57/1.28 (inIntersectImpInUnion = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ X4 @ (binintersect @ X0 @ X2)) => (in @ X4 @ (binunion @ X0 @ X3))))))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f2])).
% 1.57/1.28 thf(f2,axiom,(
% 1.57/1.28 (inIntersectImpInUnion = ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $i] : ((in @ X5 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binunion @ X3 @ X5))))))))),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.CtHZWL3RvT/DTF2THF_20595.p',inIntersectImpInUnion)).
% 1.57/1.28 thf(f100,plain,(
% 1.57/1.28 ($true != (in @ sK17 @ (binunion @ sK13 @ sK16))) | spl18_1),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f98])).
% 1.57/1.28 thf(f98,definition,(
% 1.57/1.28 spl18_1 <=> ($true = (in @ sK17 @ (binunion @ sK13 @ sK16)))),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl18_1])],[avatar_definition])).
% 1.57/1.28 thf(f105,plain,(
% 1.57/1.28 ~spl18_1 | ~spl18_2),
% 1.57/1.28 inference(avatar_split_clause,[status(thm)],[f96,f102,f98])).
% 1.57/1.28 thf(f96,plain,(
% 1.57/1.28 ((in @ sK17 @ (binunion @ sK15 @ sK16)) != $true) | ($true != (in @ sK17 @ (binunion @ sK13 @ sK16)))),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.57/1.28 thf(f95,plain,(
% 1.57/1.28 ($true != (in @ sK17 @ (binunion @ sK13 @ sK16))) | ($true != $true) | ((in @ sK17 @ (binunion @ sK15 @ sK16)) != $true)),
% 1.57/1.28 inference(superposition,[status(thm)],[f68,f93])).
% 1.57/1.28 thf(f93,plain,(
% 1.57/1.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) != $true)) )),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.57/1.28 thf(f74,plain,(
% 1.57/1.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ (binintersect @ X0 @ X1)) = $true)) )),
% 1.57/1.28 inference(definition_unfolding,[status(thm)],[f50,f73])).
% 1.57/1.28 thf(f73,plain,(
% 1.57/1.28 (binintersectI = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f46])).
% 1.57/1.28 thf(f50,plain,(
% 1.57/1.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) != $true) | (binintersectI != $true)) )),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f26])).
% 1.57/1.28 thf(f26,plain,(
% 1.57/1.28 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | (($true != (in @ sK2 @ (binintersect @ sK0 @ sK1))) & ((in @ sK2 @ sK0) = $true) & ((in @ sK2 @ sK1) = $true)))),
% 1.57/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f25])).
% 1.57/1.28 thf(f25,plain,(
% 1.57/1.28 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X3 @ X4)) != $true) & ((in @ X5 @ X3) = $true) & ((in @ X5 @ X4) = $true)) => (($true != (in @ sK2 @ (binintersect @ sK0 @ sK1))) & ((in @ sK2 @ sK0) = $true) & ((in @ sK2 @ sK1) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f24,plain,(
% 1.57/1.28 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X3 @ X4)) != $true) & ((in @ X5 @ X3) = $true) & ((in @ X5 @ X4) = $true)))),
% 1.57/1.28 inference(rectify,[status(thm)],[f23])).
% 1.57/1.28 thf(f23,plain,(
% 1.57/1.28 (! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ X2))) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) != $true) & ((in @ X1 @ X0) = $true) & ($true = (in @ X1 @ X2))))),
% 1.57/1.28 inference(nnf_transformation,[status(thm)],[f22])).
% 1.57/1.28 thf(f22,plain,(
% 1.57/1.28 ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ X2))) <=> (binintersectI = $true)),
% 1.57/1.28 inference(flattening,[status(thm)],[f21])).
% 1.57/1.28 thf(f21,plain,(
% 1.57/1.28 (binintersectI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ (binintersect @ X0 @ X2)) = $true) | ($true != (in @ X1 @ X2))) | ((in @ X1 @ X0) != $true))),
% 1.57/1.28 inference(ennf_transformation,[status(thm)],[f12])).
% 1.57/1.28 thf(f12,plain,(
% 1.57/1.28 (binintersectI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) => (($true = (in @ X1 @ X2)) => ((in @ X1 @ (binintersect @ X0 @ X2)) = $true)))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f11])).
% 1.57/1.28 thf(f11,plain,(
% 1.57/1.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ X0 @ X2)))) = binintersectI)),
% 1.57/1.28 inference(rectify,[status(thm)],[f1])).
% 1.57/1.28 thf(f1,axiom,(
% 1.57/1.28 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))) = binintersectI)),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.CtHZWL3RvT/DTF2THF_20595.p',binintersectI)).
% 1.57/1.28 thf(f68,plain,(
% 1.57/1.28 ($true != (in @ sK17 @ (binintersect @ (binunion @ sK13 @ sK16) @ (binunion @ sK15 @ sK16))))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f46])).
% 1.57/1.28 % SZS output end Proof for DTF2THF_20595
% 1.57/1.28 % (20755)------------------------------
% 1.57/1.28 % (20755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (20755)Termination reason: Refutation
% 1.57/1.28
% 1.57/1.28 % (20755)Memory used [KB]: 5628
% 1.57/1.28 % (20755)Time elapsed: 0.019 s
% 1.57/1.28 % (20755)Instructions burned: 17 (million)
% 1.57/1.28 % (20755)------------------------------
% 1.57/1.28 % (20755)------------------------------
% 1.57/1.28 % (20748)Success in time 0.033 s
%------------------------------------------------------------------------------