%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO545^1 : TPTP v9.2.0. Released v5.2.0.
% 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 03:25:59 PM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 133
% Syntax : Number of formulae : 149 ( 25 unt; 0 typ; 5 def)
% Number of atoms : 752 ( 261 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 1013 ( 498 ~; 80 |; 0 &; 57 @)
% ( 60 <=>; 318 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 72 usr; 71 con; 0-2 aty)
% Number of variables : 110 ( 80 ^; 30 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__7,type,
eigen__7: $o ).
thf(ty_eps,type,
eps: ( $i > $o ) > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $o ).
thf(ty_eigen__5,type,
eigen__5: $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_f,type,
f: $o > $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= ( ~ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( eigen__0 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__0 != eigen__1 ) ) )
=> ~ ( ( f
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__0 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( eigen__0 != eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__7 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $o] :
( ( eigen__7 = X1 )
=> ( X1 = eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( f @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( f
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__2 != eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__6 = eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( f
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( f
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( f @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $o] :
( ( f @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ~ ( ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( eigen__3 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__3 != eigen__1 ) ) )
=> ~ ( sP10
=> ( eigen__3 != eigen__2 ) ) )
=> ~ ( sP11
=> ( eigen__3 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__7 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__6 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( eigen__1 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__1 != eigen__1 ) ) )
=> ~ ( sP10
=> ( eigen__1 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( f
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP12 = ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ~ ( ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( eigen__2 != eigen__0 ) )
=> ~ ( ( f
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__2 != eigen__1 ) ) )
=> ~ sP7 )
=> ~ ( sP11
=> ( eigen__2 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( f @ eigen__7 )
= ( ~ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> eigen__7 ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP10
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( sP22 = eigen__6 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP22 = eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( f @ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( f
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP27
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ sP18 )
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP27
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP17
=> ~ ( sP11
=> ( eigen__1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( f @ eigen__5 )
= eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $o] :
( ( f @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( eigen__1 != eigen__0 ) )
=> ~ ( sP27
=> ~ sP31 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( ( f
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP27
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP27
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X1 != eigen__3 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $o] :
( ( f @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP27
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X1 != eigen__3 ) ) ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( f @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $o] :
( ( f @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> eigen__6 ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP11
=> ( eigen__3 != eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP42 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ sP28
=> ~ ( sP11
=> ~ sP38 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP3
=> ~ ( sP27
=> ( eigen__0 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> $false ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ ( ( ( f
= ( ^ [X1: $o] : sP47 ) )
=> ( eigen__2 != eigen__0 ) )
=> ~ ( sP27
=> ( eigen__2 != eigen__1 ) ) )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ( f
= ( ^ [X1: $o] : sP47 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : sP47 ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP27
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f
= ( ^ [X2: $o] : sP47 ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP27
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X1 != eigen__3 ) ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> eigen__4 ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( f
= ( ^ [X1: $o] : sP47 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ sP2
=> ~ ( sP11
=> ( eigen__0 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( eigen__3 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP6 = sP47 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP27
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP11
=> ~ sP38 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( eigen__5 = sP51 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> eigen__5 ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(def_case,definition,
( case
= ( ^ [X1: $o > $o,X2: $i,X3: $i,X4: $i,X5: $i] :
( eps
@ ^ [X6: $i] :
( ~ ( ~ ( ( ( X1
= ( ^ [X7: $o] : sP47 ) )
=> ( X6 != X2 ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ X7 ) )
=> ( X6 != X3 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : X7 ) )
=> ( X6 != X4 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ sP47 ) )
=> ( X6 != X5 ) ) ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
!= X1 )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
= X2 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
= X3 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
= X4 ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
!= X1 )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
= X2 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
= X3 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
= X4 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP52
=> ( X4 != eigen__0 ) )
=> ~ ( sP27
=> ( X4 != X1 ) ) )
=> ~ ( sP10
=> ( X4 != X2 ) ) )
=> ~ ( sP11
=> ( X4 != X3 ) ) ) )
!= eigen__0 )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP52
=> ( X4 != eigen__0 ) )
=> ~ ( sP27
=> ( X4 != X1 ) ) )
=> ~ ( sP10
=> ( X4 != X2 ) ) )
=> ~ ( sP11
=> ( X4 != X3 ) ) ) )
= X1 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP52
=> ( X4 != eigen__0 ) )
=> ~ ( sP27
=> ( X4 != X1 ) ) )
=> ~ ( sP10
=> ( X4 != X2 ) ) )
=> ~ ( sP11
=> ( X4 != X3 ) ) ) )
= X2 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP52
=> ( X4 != eigen__0 ) )
=> ~ ( sP27
=> ( X4 != X1 ) ) )
=> ~ ( sP10
=> ( X4 != X2 ) ) )
=> ~ ( sP11
=> ( X4 != X3 ) ) ) )
= X3 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP52
=> ( X3 != eigen__0 ) )
=> ~ ( sP27
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X3 != X1 ) ) )
=> ~ ( sP11
=> ( X3 != X2 ) ) ) )
!= eigen__0 )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP52
=> ( X3 != eigen__0 ) )
=> ~ ( sP27
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X3 != X1 ) ) )
=> ~ ( sP11
=> ( X3 != X2 ) ) ) )
= eigen__1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP52
=> ( X3 != eigen__0 ) )
=> ~ ( sP27
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X3 != X1 ) ) )
=> ~ ( sP11
=> ( X3 != X2 ) ) ) )
= X1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP52
=> ( X3 != eigen__0 ) )
=> ~ ( sP27
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X3 != X1 ) ) )
=> ~ ( sP11
=> ( X3 != X2 ) ) ) )
= X2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ~ ( ~ ( ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP52
=> ( X2 != eigen__0 ) )
=> ~ ( sP27
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X2 != X1 ) ) ) )
!= eigen__0 )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP52
=> ( X2 != eigen__0 ) )
=> ~ ( sP27
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X2 != X1 ) ) ) )
= eigen__1 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP52
=> ( X2 != eigen__0 ) )
=> ~ ( sP27
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X2 != X1 ) ) ) )
= eigen__2 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP52
=> ( X2 != eigen__0 ) )
=> ~ ( sP27
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP10
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP11
=> ( X2 != X1 ) ) ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ sP50
=> sP36 )
=> sP1 )
=> sP38 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ sP50
=> sP36 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP38,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ sP50
=> sP36 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP50,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP36,
introduced(assumption,[]) ).
thf(1,plain,
( sP4
| ~ sP22
| ~ sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP15
| ~ sP22
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP25
| sP22
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP24
| ~ sP25
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( sP16
| ~ sP42
| ~ sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP44
| ~ sP42
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP59
| sP60
| sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP6
| sP26
| ~ sP9 ),
inference(mating_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP26
| sP12
| ~ sP4 ),
inference(mating_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP26
| sP39
| ~ sP15 ),
inference(mating_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP6
| sP12
| ~ sP16 ),
inference(mating_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP6
| sP39
| ~ sP44 ),
inference(mating_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP39
| sP12
| ~ sP59 ),
inference(mating_rule,[status(thm)],[]) ).
thf(16,plain,
~ sP47,
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP21
| ~ sP26
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP21
| sP26
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP37
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(20,plain,
( sP55
| sP6
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP13
| ~ sP55 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(22,plain,
( sP32
| ~ sP39
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP32
| sP39
| sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP33
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(25,plain,
( sP19
| ~ sP12
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
sP8,
inference(eq_sym,[status(thm)],[]) ).
thf(27,plain,
( sP40
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(28,plain,
( sP18
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP49
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( sP23
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP35
| ~ sP49
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( sP58
| sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP28
| sP35
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP45
| sP28
| ~ sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
sP54,
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP43
| ~ sP11
| ~ sP54 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( sP14
| sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
sP41,
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP7
| ~ sP10
| ~ sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP48
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( sP20
| ~ sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
sP31,
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP57
| ~ sP27
| ~ sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP34
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( sP17
| ~ sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP30
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( sP27
| ~ sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
sP56,
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( sP52
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( sP10
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP3
| ~ sP52
| ~ sP56 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( sP11
| ~ sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( sP46
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( sP2
| ~ sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( sP53
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP29
| ~ sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP29
| ~ sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP29
| ~ sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP29
| ~ sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ) ).
thf(60,plain,
( sP45
| sP29 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(61,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h4,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,h10,h11,h9,h7]) ).
thf(62,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,61,h10,h11]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,62,h8,h9]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,63,h6,h7]) ).
thf(65,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,64,h5]) ).
thf(66,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,65,h4]) ).
thf(67,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,66,h3]) ).
thf(68,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,67,h2]) ).
thf(69,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[68,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
!= X1 )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
= X2 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
= X3 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP52
=> ( X5 != X1 ) )
=> ~ ( sP27
=> ( X5 != X2 ) ) )
=> ~ ( sP10
=> ( X5 != X3 ) ) )
=> ~ ( sP11
=> ( X5 != X4 ) ) ) )
= X4 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[68,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO545^1 : TPTP v9.2.0. Released v5.2.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.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 : Thu Oct 9 00:35:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % Mode: mode213
% 0.20/0.41 % Inferences: 597
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------