%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU794^2 : 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 : n024.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 02:50:08 PM UTC 2025
% Result : Theorem 194.92s 195.38s
% Output : Proof 194.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 129
% Syntax : Number of formulae : 148 ( 26 unt; 0 typ; 14 def)
% Number of atoms : 559 ( 164 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 870 ( 229 ~; 71 |; 0 &; 369 @)
% ( 59 <=>; 142 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 78 usr; 76 con; 0-2 aty)
% Number of variables : 184 ( 11 ^; 173 !; 0 ?; 184 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__25,type,
eigen__25: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__26,type,
eigen__26: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
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] :
~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__5 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__7 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__26,definition,
( eigen__26
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__9 )
=> ( in @ X1 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__26])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__8 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__25,definition,
( eigen__25
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__8 )
=> ( in @ X1 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__25])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__6 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__4 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in @ eigen__25 @ eigen__8 )
=> ( in @ eigen__25 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ eigen__25 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__4 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__6 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) )
=> ~ ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__6 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
= ( ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__25
!= ( eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__7 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) )
=> ~ ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__7 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $i] :
~ ! [X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( X1 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ eigen__26 @ eigen__9 )
= ( ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__26
!= ( eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( subset @ eigen__8 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( in @ eigen__26 @ eigen__9 )
=> ( in @ eigen__26 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__8 = eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__8 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) )
=> ( eigen__7 = eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__3 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__9 )
=> ( in @ X1 @ eigen__8 ) )
=> ( subset @ eigen__9 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__5 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP10
=> ( ( subset @ eigen__9 @ eigen__8 )
=> sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__9 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ eigen__9 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__25
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__7 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) )
=> ( eigen__6 = eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP17
=> ~ ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__5 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__9 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( subset @ eigen__9 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP24
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__6 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP17
=> ( eigen__4 = eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( in @ eigen__26 @ eigen__8 )
= ( ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__26
!= ( eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__8 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__7 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__6 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( in @ eigen__25 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( in @ eigen__26 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__8 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) )
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__8 )
=> ( in @ X1 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP35
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__8 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ( subset @ eigen__8 @ X1 )
=> ( ( subset @ X1 @ eigen__8 )
=> ( eigen__8 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__9 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__5 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__3 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) )
=> ( eigen__2 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X1 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__4 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ( eigen__7 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__26
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ~ ! [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( eigen__1 @ X4 ) ) ) ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( in @ eigen__26 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__8 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__9 )
=> ( in @ X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP45
=> ( eigen__3 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP32 = ( ~ sP20 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__2 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP31
=> ( eigen__5 = eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP45
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP54
=> ~ sP37 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__3 )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(def_exu,definition,
( exu
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ).
thf(def_subsetI1,definition,
subsetI1 = sP58 ).
thf(def_setextsub,definition,
setextsub = sP44 ).
thf(def_image1Ex,definition,
image1Ex = sP1 ).
thf(image1Ex1,conjecture,
( sP58
=> ( sP44
=> ( sP1
=> ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) )
=> ( X3 = X4 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP58
=> ( sP44
=> ( sP1
=> ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) )
=> ( X3 = X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[image1Ex1]) ).
thf(h2,assumption,
sP58,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP44
=> ( sP1
=> ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) )
=> ( X3 = X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP44,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP1
=> ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) )
=> ( X3 = X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) )
=> ( X3 = X4 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i > $i] :
~ ! [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( X1 @ X4 ) ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ( X4
!= ( X1 @ X5 ) ) ) ) )
=> ( X2 = X3 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP48,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP53
| sP32
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP6
| ~ sP3
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP9
| ~ sP33
| ~ sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP28
| sP49
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP50
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP41
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( sP11
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP11
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP51
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__26]) ).
thf(10,plain,
( ~ sP50
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP41
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( sP2
| ~ sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP2
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP35
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__25]) ).
thf(15,plain,
( ~ sP16
| ~ sP51
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP38
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP36
| ~ sP35
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP19
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP58
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP40
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP18
| ~ sP10
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP25
| ~ sP24
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP23
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP23
| sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP29
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(26,plain,
( ~ sP34
| ~ sP50
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP58
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP44
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP48
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( sP14
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP46
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(32,plain,
( ~ sP7
| ~ sP30
| ~ sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP48
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( sP21
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP26
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(36,plain,
( ~ sP5
| ~ sP31
| ~ sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP48
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( sP55
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( sP42
| ~ sP55 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(40,plain,
( ~ sP22
| ~ sP17
| ~ sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP48
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( sP27
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP4
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(44,plain,
( ~ sP56
| ~ sP45
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP48
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(46,plain,
( sP52
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( sP12
| ~ sP52 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(48,plain,
( ~ sP15
| ~ sP59
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP48
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(50,plain,
( sP43
| sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( sP37
| ~ sP43 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(52,plain,
( ~ sP48
| sP57 ),
inference(all_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP57
| ~ sP54
| ~ sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( sP39
| sP54 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(55,plain,
( ~ sP8
| ~ sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(57,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h8,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,h2,h4,h6,h9]) ).
thf(58,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h8,57,h9]) ).
thf(59,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h7,58,h8]) ).
thf(60,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,59,h6,h7]) ).
thf(61,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,60,h4,h5]) ).
thf(62,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,61,h2,h3]) ).
thf(63,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[62,h0]) ).
thf(0,theorem,
( sP58
=> ( sP44
=> ( sP1
=> ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) )
=> ( X3 = X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[62,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU794^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 21:04:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 194.92/195.38 % SZS status Theorem
% 194.92/195.38 % Mode: mode411
% 194.92/195.38 % Inferences: 1160
% 194.92/195.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------