%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU600^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 : Thu Oct 9 02:43:59 PM UTC 2025
% Result : Theorem 0.60s 0.96s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 207
% Syntax : Number of formulae : 224 ( 36 unt; 0 typ; 10 def)
% Number of atoms : 615 ( 26 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1247 ( 129 ~; 112 |; 0 &; 725 @)
% ( 93 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 113 ( 111 usr; 108 con; 0-2 aty)
% Number of variables : 112 ( 2 ^; 110 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_binintersect,type,
binintersect: $i > $i > $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_binunion,type,
binunion: $i > $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ eigen__3 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( subset @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( sP2
=> ~ ( in @ eigen__4 @ eigen__0 ) )
=> ( ( ( in @ eigen__4 @ eigen__2 )
=> ~ ( in @ eigen__4 @ eigen__0 ) )
=> ~ ( in @ eigen__4 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__3 @ ( binintersect @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X2 @ X1 ) )
=> ( subset @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in @ eigen__4 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP2
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__3 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( in @ eigen__4 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ eigen__4 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ! [X1: $i] :
( ( in @ X1 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) )
=> ( subset @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( in @ eigen__4 @ eigen__2 )
=> ( in @ eigen__4 @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i,X3: $i,X4: $o] :
( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ( ( ( in @ X3 @ X1 )
=> X4 )
=> ( ( ( in @ X3 @ X2 )
=> X4 )
=> X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( in @ eigen__4 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP2
=> ( in @ eigen__4 @ ( binintersect @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP6
=> ( in @ eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( subset @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i,X3: $o] :
( ( in @ X2 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ X1 ) )
=> ( ( ( in @ X2 @ ( binintersect @ eigen__0 @ eigen__1 ) )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( in @ eigen__3 @ eigen__1 )
=> ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( in @ eigen__3 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> ( in @ eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( in @ eigen__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ eigen__0 @ eigen__1 ) )
=> ( in @ X2 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) )
=> ( in @ X2 @ X1 ) )
=> ( subset @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( in @ eigen__4 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> ( in @ eigen__4 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP12
=> ( ( sP6
=> ( sP12
=> sP3 ) )
=> ( ( ( in @ eigen__3 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> ( sP12
=> sP3 ) )
=> ( sP12
=> sP3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( in @ eigen__4 @ ( binintersect @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP17
=> ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP17
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( in @ eigen__3 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> ( in @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( in @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP12
=> ( sP20
=> ( sP25
=> sP28 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP25
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( in @ eigen__3 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> ( sP12
=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP12
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i,X2: $i,X3: $o] :
( ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) )
=> ( ( ( in @ X2 @ eigen__1 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ eigen__2 )
=> ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: $i] :
( ( subset @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) @ X1 )
=> ( ( subset @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP10
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( in @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $o] :
( sP12
=> ( ( sP6
=> X1 )
=> ( ( ( in @ eigen__3 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> X1 )
=> X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP11
=> ( ( sP26
=> ~ sP10 )
=> ~ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__2 )
=> ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( sP10
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP20
=> sP46 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ( sP6
=> sP49 )
=> ( sP48
=> sP49 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ eigen__0 @ X1 ) )
=> ( in @ X2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: $i] :
( ( in @ X1 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( ( in @ eigen__4 @ ( binintersect @ eigen__0 @ eigen__1 ) )
=> ( in @ eigen__4 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) ) )
=> ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( sP26
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( sP70
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ eigen__2 ) )
= ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( sP36
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( in @ eigen__4 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( sP6
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X1 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ eigen__0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( sP28
=> sP73 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( sP4
=> ( sP22
=> sP72 ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( sP48
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( sP22
=> sP72 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ! [X1: $i,X2: $o] :
( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( ( in @ X1 @ eigen__1 )
=> X2 )
=> ( ( ( in @ X1 @ eigen__2 )
=> X2 )
=> X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( sP6
=> ( in @ eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( in @ eigen__3 @ ( binintersect @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [X1: $i,X2: $o] :
( ( in @ X1 @ ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ eigen__2 ) ) )
=> ( ( ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__1 ) )
=> X2 )
=> ( ( ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__2 ) )
=> X2 )
=> X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ! [X1: $o] :
( sP39
=> ( ( sP2
=> X1 )
=> ( ( sP26
=> X1 )
=> X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( sP57
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( in @ eigen__4 @ ( binintersect @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(def_subsetI1,definition,
subsetI1 = sP60 ).
thf(def_setextsub,definition,
setextsub = sP76 ).
thf(def_binunionIL,definition,
binunionIL = sP8 ).
thf(def_binunionIR,definition,
binunionIR = sP44 ).
thf(def_binunionEcases,definition,
binunionEcases = sP16 ).
thf(def_binintersectI,definition,
binintersectI = sP88 ).
thf(def_binintersectEL,definition,
binintersectEL = sP68 ).
thf(def_binintersectER,definition,
binintersectER = sP1 ).
thf(bs114d,conjecture,
( sP60
=> ( sP76
=> ( sP8
=> ( sP44
=> ( sP16
=> ( sP88
=> ( sP68
=> ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP60
=> ( sP76
=> ( sP8
=> ( sP44
=> ( sP16
=> ( sP88
=> ( sP68
=> ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[bs114d]) ).
thf(h2,assumption,
sP60,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP76
=> ( sP8
=> ( sP44
=> ( sP16
=> ( sP88
=> ( sP68
=> ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP76,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP8
=> ( sP44
=> ( sP16
=> ( sP88
=> ( sP68
=> ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP8,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP44
=> ( sP16
=> ( sP88
=> ( sP68
=> ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP44,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP16
=> ( sP88
=> ( sP68
=> ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP16,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP88
=> ( sP68
=> ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP88,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP68
=> ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP68,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP1,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ! [X1: $i,X2: $i] :
( ( binintersect @ eigen__0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ eigen__0 @ X1 ) @ ( binintersect @ eigen__0 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ! [X1: $i] :
( ( binintersect @ eigen__0 @ ( binunion @ eigen__1 @ X1 ) )
= ( binunion @ ( binintersect @ eigen__0 @ eigen__1 ) @ ( binintersect @ eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP72,
introduced(assumption,[]) ).
thf(1,plain,
( sP70
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP11
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP77
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP29
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP41
| ~ sP87
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP65
| sP80 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP80
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP77
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP21
| sP86 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP86
| ~ sP6
| sP91 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP65
| sP50 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP50
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP55
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP53
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP56
| ~ sP10
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP15
| ~ sP26
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP55
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP47
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP62
| ~ sP10
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP19
| ~ sP2
| sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP16
| sP52 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP52
| sP85 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP85
| sP90 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP90
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP5
| ~ sP39
| sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP59
| ~ sP11
| sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP71
| ~ sP70
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP58
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP45
| ~ sP12
| sP63 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP63
| ~ sP20
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP46
| ~ sP25
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP44
| sP83 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP83
| sP61 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP61
| sP92 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP92
| ~ sP57
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP8
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP35
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP18
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP24
| ~ sP91
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP48
| sP87 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( sP75
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP44
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP27
| sP51 ),
inference(all_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP51
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP32
| ~ sP34
| sP74 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP8
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP30
| sP78 ),
inference(all_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP78
| sP67 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP67
| ~ sP93
| sP74 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP1
| sP77 ),
inference(all_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP77
| sP69 ),
inference(all_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP69
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP38
| ~ sP17
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP68
| sP65 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP65
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP43
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP40
| ~ sP17
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP88
| sP55 ),
inference(all_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP55
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP42
| sP79 ),
inference(all_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP79
| ~ sP28
| sP73 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP73
| ~ sP36
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP58
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP33
| ~ sP12
| sP64 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP64
| ~ sP75
| sP82 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP82
| ~ sP48
| sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP16
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP23
| sP89 ),
inference(all_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP89
| sP58 ),
inference(all_rule,[status(thm)],[]) ).
thf(70,plain,
( sP13
| ~ sP74 ),
inference(prop_rule,[status(thm)],[]) ).
thf(71,plain,
( sP13
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( sP49
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( sP49
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( sP37
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(75,plain,
( sP66
| ~ sP49 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(76,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP9
| ~ sP37
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( ~ sP31
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP14
| ~ sP66
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
( ~ sP60
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(81,plain,
( ~ sP60
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP76
| sP54 ),
inference(all_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP54
| sP81 ),
inference(all_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP81
| ~ sP4
| sP84 ),
inference(prop_rule,[status(thm)],[]) ).
thf(85,plain,
( ~ sP84
| ~ sP22
| sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(86,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,h2,h4,h6,h8,h10,h12,h14,h16,h20]) ).
thf(87,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__2)],[h19,86,h20]) ).
thf(88,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__1)],[h18,87,h19]) ).
thf(89,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__0)],[h17,88,h18]) ).
thf(90,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,89,h16,h17]) ).
thf(91,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,90,h14,h15]) ).
thf(92,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,91,h12,h13]) ).
thf(93,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,92,h10,h11]) ).
thf(94,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,93,h8,h9]) ).
thf(95,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,94,h6,h7]) ).
thf(96,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,95,h4,h5]) ).
thf(97,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,96,h2,h3]) ).
thf(98,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[97,h0]) ).
thf(0,theorem,
( sP60
=> ( sP76
=> ( sP8
=> ( sP44
=> ( sP16
=> ( sP88
=> ( sP68
=> ( sP1
=> ! [X1: $i,X2: $i,X3: $i] :
( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[97,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU600^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 21:59:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.60/0.96 % SZS status Theorem
% 0.60/0.96 % Mode: mode213
% 0.60/0.96 % Inferences: 401
% 0.60/0.96 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------