%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV261^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 02:55:22 PM UTC 2025
% Result : Theorem 0.69s 0.88s
% Output : Proof 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 162
% Syntax : Number of formulae : 180 ( 23 unt; 0 typ; 12 def)
% Number of atoms : 678 ( 144 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 698 ( 301 ~; 96 |; 0 &; 98 @)
% ( 79 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 96 ( 94 usr; 87 con; 0-2 aty)
% Number of variables : 177 ( 126 ^; 51 !; 0 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__8,type,
eigen__8: a > $o ).
thf(ty_eigen__11,type,
eigen__11: a ).
thf(ty_eigen__7,type,
eigen__7: ( a > $o ) > $o ).
thf(ty_eigen__9,type,
eigen__9: a > $o ).
thf(ty_eigen__19,type,
eigen__19: a > $o ).
thf(ty_eigen__14,type,
eigen__14: a ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__6,type,
eigen__6: a > $o ).
thf(ty_eigen__10,type,
eigen__10: a > $o ).
thf(ty_eigen__13,type,
eigen__13: a ).
thf(ty_eigen__12,type,
eigen__12: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: a] :
~ ~ ( eigen__9 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: a > $o] :
~ ! [X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( ( X1
!= ( ^ [X4: a] : $false ) )
=> ( X1
= ( ^ [X4: a] : ~ $false ) ) )
=> ~ ( ( X2
!= ( ^ [X4: a] : $false ) )
=> ( X2
= ( ^ [X4: a] : ~ $false ) ) ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( ( X3
!= ( ^ [X4: a] : $false ) )
=> ( X3
= ( ^ [X4: a] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__0
@ ^ [X1: a] :
( ( eigen__10 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ( X1
= ( ^ [X2: a] : $false ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ~ ( ( ( eigen__6
!= ( ^ [X2: a] : $false ) )
=> ( eigen__6
= ( ^ [X2: a] : ~ $false ) ) )
=> ~ ( ( eigen__8
!= ( ^ [X2: a] : $false ) )
=> ( eigen__8
= ( ^ [X2: a] : ~ $false ) ) ) )
=> ( X1
!= ( ^ [X2: a] :
~ ( ( eigen__6 @ X2 )
=> ~ ( eigen__8 @ X2 ) ) ) ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: a] :
( ( eigen__9 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( ( eigen__6
!= ( ^ [X3: a] : $false ) )
=> ( eigen__6
= ( ^ [X3: a] : ~ $false ) ) )
=> ~ ( ( X1
!= ( ^ [X3: a] : $false ) )
=> ( X1
= ( ^ [X3: a] : ~ $false ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ( ( eigen__6 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : $false ) )
=> ( X2
= ( ^ [X3: a] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: a] :
~ ~ ( eigen__10 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a > $o] :
( ( eigen__7 @ X2 )
=> ( ( X2
!= ( ^ [X3: a] : $false ) )
=> ( X2
= ( ^ [X3: a] : ~ $false ) ) ) )
=> ( X1
!= ( ^ [X2: a] :
~ ! [X3: a > $o] :
( ( eigen__7 @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(h2,assumption,
! [X1: ( ( a > $o ) > $o ) > $o,X2: ( a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__2
@ ^ [X1: ( a > $o ) > $o] :
~ ! [X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( ( X3
!= ( ^ [X4: a] : $false ) )
=> ( X3
= ( ^ [X4: a] : ~ $false ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : $false ) )
=> ( X2
= ( ^ [X3: a] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ( eigen__7 @ X1 )
=> ~ ( X1 @ eigen__11 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( ( X3
!= ( ^ [X4: a] : $false ) )
=> ( X3
= ( ^ [X4: a] : ~ $false ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : $false ) )
=> ( X2
= ( ^ [X3: a] : ~ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__1
!= ( ^ [X1: a] : $false ) )
=> ( eigen__1
= ( ^ [X1: a] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( eigen__9 @ X1 )
= ( ~ ! [X2: a > $o] :
( ( eigen__7 @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ~ ( ~ ( ( ( eigen__6
!= ( ^ [X2: a] : $false ) )
=> ( eigen__6
= ( ^ [X2: a] : ~ $false ) ) )
=> ~ ( ( eigen__8
!= ( ^ [X2: a] : $false ) )
=> ( eigen__8
= ( ^ [X2: a] : ~ $false ) ) ) )
=> ( X1
!= ( ^ [X2: a] :
~ ( ( eigen__6 @ X2 )
=> ~ ( eigen__8 @ X2 ) ) ) ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__9
= ( ^ [X1: a] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__19
!= ( ^ [X1: a] : $false ) )
=> ( eigen__19
= ( ^ [X1: a] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__9 @ eigen__12 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__10
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__6 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__6 @ eigen__14 )
=> ~ ( eigen__8 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__9
= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ( eigen__7 @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__8 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > $o] :
( ( eigen__7 @ X1 )
=> ~ ( X1 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__10 @ eigen__14 )
= ( ~ sP11 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] :
( ( eigen__7 @ X1 )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( eigen__19 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__9
!= ( ^ [X1: a] : $false ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( eigen__9 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
~ ( eigen__8 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( ( X3
!= ( ^ [X4: a] : $false ) )
=> ( X3
= ( ^ [X4: a] : ~ $false ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : $false ) )
=> ( X2
= ( ^ [X3: a] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__6 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ( ( ( eigen__6
!= ( ^ [X1: a] : $false ) )
=> ( eigen__6
= ( ^ [X1: a] : ~ $false ) ) )
=> ~ ( ( eigen__8
!= ( ^ [X1: a] : $false ) )
=> ( eigen__8
= ( ^ [X1: a] : ~ $false ) ) ) )
=> ( eigen__10
!= ( ^ [X1: a] :
~ ( ( eigen__6 @ X1 )
=> ~ ( eigen__8 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__10
= ( ^ [X1: a] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a] :
( ( eigen__8 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP23 = ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a > $o] :
( ~ ( sP17
=> ( X1
!= ( ^ [X2: a] :
~ ! [X3: a > $o] :
( ( eigen__7 @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( ( eigen__6
!= ( ^ [X1: a] : $false ) )
=> ( eigen__6
= ( ^ [X1: a] : ~ $false ) ) )
=> ~ ( ( eigen__8
!= ( ^ [X1: a] : $false ) )
=> ( eigen__8
= ( ^ [X1: a] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__8 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a] :
~ ( eigen__10 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a] :
~ ( eigen__19 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( eigen__9
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( eigen__10 @ eigen__13 )
= ( ~ ( sP10
=> ~ sP14 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( eigen__6
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__9 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
( ( eigen__6 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: a > $o,X2: a > $o] :
( ~ ( ~ ( ( ~ sP35
=> ( eigen__6
= ( ^ [X3: a] : ~ $false ) ) )
=> ~ ( ( X1
!= ( ^ [X3: a] : $false ) )
=> ( X1
= ( ^ [X3: a] : ~ $false ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ( ( eigen__6 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : $false ) )
=> ( X2
= ( ^ [X3: a] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( eigen__19 @ eigen__12 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( ( X1
!= ( ^ [X2: a] : $false ) )
=> ( X1
= ( ^ [X2: a] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__19
= ( ^ [X1: a] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( eigen__6
= ( ^ [X1: a] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: a] :
~ ( eigen__6 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
= ( ~ ( ( eigen__6 @ X1 )
=> ~ ( eigen__8 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__19 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( eigen__9 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( eigen__7 @ eigen__19 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP46 = ( ~ sP15 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( eigen__1
= ( ^ [X1: a] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP17
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP10
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( eigen__19 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ( eigen__10 @ eigen__14 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( eigen__8
= ( ^ [X1: a] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP30 = ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP49
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ sP12
=> ( eigen__0
= ( ^ [X1: a] : ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ( eigen__8
!= ( ^ [X1: a] : $false ) )
=> sP54 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: a] :
~ ( eigen__9 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP47
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP47
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( ( X1
!= ( ^ [X4: a] : $false ) )
=> ( X1
= ( ^ [X4: a] : ~ $false ) ) )
=> ~ ( ( X2
!= ( ^ [X4: a] : $false ) )
=> ( X2
= ( ^ [X4: a] : ~ $false ) ) ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( ( X3
!= ( ^ [X4: a] : $false ) )
=> ( X3
= ( ^ [X4: a] : ~ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( eigen__19
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ~ sP1
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( ~ sP9
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( eigen__10
= ( ^ [X1: a] :
~ ( ( eigen__6 @ X1 )
=> ~ ( eigen__8 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP12
=> sP57 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: a > $o] :
( ( eigen__7 @ X1 )
=> ~ ( X1 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP47
=> ~ sP52 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ~ sP24
=> sP65 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ~ sP35
=> sP42 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ~ sP50
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( eigen__8
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( sP40
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( sP36 = ( ~ sP68 ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( eigen__10 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( eigen__10 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> $false ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(cINDISCRETE_TOPOLOGY_pme,conjecture,
~ sP64 ).
thf(h3,negated_conjecture,
sP64,
inference(assume_negation,[status(cth)],[cINDISCRETE_TOPOLOGY_pme]) ).
thf(1,plain,
( ~ sP39
| sP45
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP18
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP32
| ~ sP52 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP41
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP63
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP7
| sP63
| sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP61
| ~ sP47
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP60
| ~ sP47
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP17
| sP61 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP15
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP11
| ~ sP23
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP16
| sP77
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP27
| sP23
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP55
| sP30
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP44
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP37
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP26
| sP55 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( sP51
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP51
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP34
| ~ sP78
| ~ sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP44
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP43
| ~ sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP21
| ~ sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP48
| sP46
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP3
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( sP69
| sP52 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP69
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( sP68
| ~ sP69 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__19]) ).
thf(29,plain,
( ~ sP75
| ~ sP36
| ~ sP68 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP3
| sP75 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP54
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP73
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP58
| sP73
| sP54 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP42
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP35
| sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP71
| sP35
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( sP29
| sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP29
| sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP66
| sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP24
| sP66 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( sP24
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( sP53
| ~ sP77
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP76
| ~ sP53 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).
thf(44,plain,
( sP31
| sP78 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(45,plain,
( sP25
| ~ sP76 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP9
| ~ sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( sP65
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( sP65
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( sP70
| ~ sP65 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( sP70
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP13
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( sP50
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( sP50
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( sP8
| ~ sP46
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( sP20
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(56,plain,
( sP59
| sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(57,plain,
( sP5
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( sP33
| ~ sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( sP19
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( sP19
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( sP72
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( sP72
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( sP4
| ~ sP70 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__10]) ).
thf(64,plain,
( sP28
| ~ sP72 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9]) ).
thf(65,plain,
( sP38
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(66,plain,
( sP22
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__7]) ).
thf(67,plain,
( sP62
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(68,plain,
( sP2
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(69,plain,
( sP56
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(70,plain,
( sP56
| sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(71,plain,
~ sP79,
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( sP57
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( sP67
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( sP67
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(75,plain,
( sP6
| ~ sP56 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(76,plain,
( sP40
| ~ sP67 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(77,plain,
( ~ sP74
| ~ sP40
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( ~ sP1
| sP74
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP64
| sP1
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,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,h3]) ).
thf(81,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[80,h2]) ).
thf(82,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[81,h1]) ).
thf(83,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[82,h0]) ).
thf(0,theorem,
~ sP64,
inference(contra,[status(thm),contra(discharge,[h3])],[80,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV261^5 : TPTP v9.2.0. Released v4.0.0.
% 0.08/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 19:36:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.69/0.88 % SZS status Theorem
% 0.69/0.88 % Mode: cade22grackle2xfee4
% 0.69/0.88 % Steps: 7089
% 0.69/0.88 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------