%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL960^12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:02:57 PM UTC 2026
% Result : Theorem 67.27s 66.63s
% Output : Proof 67.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 135
% Syntax : Number of formulae : 148 ( 25 unt; 0 typ; 18 def)
% Number of atoms : 689 ( 19 equ; 0 cnn)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 1753 ( 251 ~; 76 |; 0 &; 983 @)
% ( 60 <=>; 378 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 85 usr; 84 con; 0-3 aty)
% ( 5 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 296 ( 31 ^; 265 !; 0 ?; 296 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(ty_eigen__44,type,
eigen__44: mworld ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__26,type,
eigen__26: mworld ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__11,type,
eigen__11: mworld ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__42,type,
eigen__42: mworld ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__43,type,
eigen__43: mworld ).
thf(ty_f,type,
f: $i > $i > mworld > $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] :
~ ( ( eiw_di @ X1 @ eigen__2 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X1 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( eiw_di @ X4 @ X2 )
=> ~ ! [X5: mworld] :
( ( mrel @ X2 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ~ ( ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X4 @ X8 ) )
=> ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X3 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( f @ X6 @ X6 @ X9 ) ) ) ) ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X3 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( f @ X6 @ X6 @ X9 ) ) ) )
=> ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X4 @ X8 ) ) ) ) ) ) ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( f @ X5 @ X3 @ X6 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__42,definition,
( eigen__42
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__2 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__42])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X2 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__2 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ X1 @ X5 ) )
=> ~ ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X3 @ X3 @ X6 ) ) ) ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ~ ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X3 @ X3 @ X6 ) ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ X1 @ X5 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__26,definition,
( eigen__26
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__11 @ X1 )
=> ( f @ eigen__4 @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__26])]) ).
thf(eigendef_eigen__43,definition,
( eigen__43
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__11 @ X1 )
=> ( f @ eigen__4 @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__43])]) ).
thf(eigendef_eigen__44,definition,
( eigen__44
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__11 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__44])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ eigen__2 )
=> ~ ! [X3: mworld] :
( ( mrel @ eigen__2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ~ ( ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X4 @ X2 @ X6 ) )
=> ~ ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X4 @ X1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X4 @ X4 @ X7 ) ) ) ) ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ~ ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X4 @ X1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X4 @ X4 @ X7 ) ) ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X4 @ X2 @ X6 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eiw_di @ eigen__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( mrel @ eigen__42 @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X2 @ X5 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eiw_di @ eigen__3 @ eigen__2 )
=> ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ X1 @ X5 ) )
=> ~ ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X3 @ X3 @ X6 ) ) ) ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ~ ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X3 @ X3 @ X6 ) ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ X1 @ X5 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ X1 @ X5 ) )
=> ~ ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X3 @ X3 @ X6 ) ) ) ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ~ ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( f @ X3 @ X3 @ X6 ) ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X3 @ X1 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mworld] :
( ( mrel @ eigen__11 @ X1 )
=> ( f @ eigen__4 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( mrel @ eigen__11 @ eigen__11 )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__11 @ X1 )
=> ( f @ eigen__4 @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ eigen__4 @ X4 ) )
=> ~ ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ eigen__3 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X2 @ X2 @ X5 ) ) ) ) ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ~ ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ eigen__3 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X2 @ X2 @ X5 ) ) ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ eigen__4 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( mrel @ eigen__2 @ eigen__11 )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__11 @ X1 )
=> ( f @ eigen__4 @ eigen__4 @ X1 ) )
=> ~ ( sP7
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__11 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__4 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: mworld] :
( ( mrel @ eigen__11 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( mrel @ eigen__2 @ eigen__43 )
=> ( f @ eigen__4 @ eigen__3 @ eigen__43 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( !! @ ( mrel @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( mrel @ eigen__2 @ eigen__2 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( f @ X1 @ eigen__3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__4 @ X2 ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ eigen__4 @ eigen__4 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( f @ eigen__4 @ eigen__3 @ eigen__43 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: mworld] :
( ( mrel @ eigen__42 @ X1 )
=> ( f @ eigen__4 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( mrel @ eigen__11 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP3
=> ( f @ eigen__4 @ eigen__4 @ eigen__26 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP2
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( f @ eigen__4 @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP7
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( mrel @ mactual @ eigen__1 )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X1 )
=> ~ ! [X4: mworld] :
( ( mrel @ X1 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ~ ( ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X5 @ X3 @ X7 ) )
=> ~ ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X5 @ X2 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X5 @ X5 @ X8 ) ) ) ) ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ~ ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X5 @ X2 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X5 @ X5 @ X8 ) ) ) )
=> ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X5 @ X3 @ X7 ) ) ) ) ) ) ) ) ) )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( !! @ ( mrel @ eigen__42 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( mrel @ eigen__1 @ eigen__2 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( mrel @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( mrel @ eigen__11 @ eigen__43 )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( f @ eigen__4 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP26
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ~ ( ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__4 @ X3 ) )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X1 @ X1 @ X4 ) ) ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X1 @ X1 @ X4 ) ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__4 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X1 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP2
=> ~ ( sP15
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ eigen__4 @ eigen__4 @ X3 ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__4 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X1 )
=> ~ ! [X4: mworld] :
( ( mrel @ X1 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ~ ( ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X5 @ X3 @ X7 ) )
=> ~ ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X5 @ X2 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X5 @ X5 @ X8 ) ) ) ) ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ~ ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X5 @ X2 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X5 @ X5 @ X8 ) ) ) )
=> ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( f @ X5 @ X3 @ X7 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( mrel @ eigen__2 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( mrel @ eigen__1 @ eigen__2 )
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( mrel @ eigen__11 @ eigen__26 )
=> ( f @ eigen__4 @ eigen__4 @ eigen__26 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( f @ X1 @ eigen__3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( f @ X2 @ eigen__3 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( !! @ ( mrel @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ eigen__4 @ eigen__4 @ X3 ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__4 @ eigen__4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: mworld] : ( !! @ ( mrel @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( mrel @ eigen__2 @ eigen__44 )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__44 @ X1 )
=> ( f @ eigen__4 @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP15
=> ~ sP39 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( f @ eigen__4 @ eigen__4 @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( eiw_di @ X4 @ X2 )
=> ~ ! [X5: mworld] :
( ( mrel @ X2 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ~ ( ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X4 @ X8 ) )
=> ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X3 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( f @ X6 @ X6 @ X9 ) ) ) ) ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X3 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( f @ X6 @ X6 @ X9 ) ) ) )
=> ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X4 @ X8 ) ) ) ) ) ) ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( f @ X5 @ X3 @ X6 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP2
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( mrel @ eigen__11 @ eigen__44 )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__44 @ X1 )
=> ( f @ eigen__4 @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( mrel @ eigen__2 @ eigen__42 )
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP32
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__11 @ X1 )
=> ( f @ eigen__4 @ eigen__4 @ X1 ) )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: mworld] :
( ( mrel @ eigen__11 @ X1 )
=> ( f @ eigen__4 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( mrel @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP33
=> ( ~ sP21
=> sP50 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( eiw_di @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP53
=> ~ sP37 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( mrel @ eigen__2 @ eigen__44 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( !! @ ( mrel @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ sP21
=> sP50 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: mworld] :
( ( mrel @ eigen__44 @ X1 )
=> ( f @ eigen__4 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( mrel @ eigen__2 @ eigen__43 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ~ ( ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__4 @ X3 ) )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X1 @ X1 @ X4 ) ) ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X1 @ X1 @ X4 ) ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__4 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ).
thf(def_mforall_di,definition,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(kalish256,conjecture,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( eiw_di @ X4 @ X2 )
=> ~ ! [X5: mworld] :
( ( mrel @ X2 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ~ ( ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X4 @ X8 ) )
=> ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X3 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( f @ X6 @ X6 @ X9 ) ) ) ) ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X3 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( f @ X6 @ X6 @ X9 ) ) ) )
=> ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X4 @ X8 ) ) ) ) ) ) ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( f @ X5 @ X3 @ X6 ) ) ) ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ sP44,
inference(assume_negation,[status(cth)],[kalish256]) ).
thf(1,plain,
( ~ sP24
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP38
| sP55 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP40
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP38
| sP59 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP13
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP17
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP19
| ~ sP3
| sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP38
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP38
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP56
| sP51 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP22
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP41
| ~ sP55
| ~ sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP28
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP12
| ~ sP59
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP35
| ~ sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP11
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP8
| ~ sP18
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP47
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP27
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP46
| sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP11
| ~ sP46 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__44]) ).
thf(22,plain,
( sP7
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__43]) ).
thf(23,plain,
( sP22
| ~ sP47 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__42]) ).
thf(24,plain,
( sP21
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP50
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__26]) ).
thf(26,plain,
( ~ sP40
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP10
| ~ sP33
| sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP49
| ~ sP50
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP39
| sP52 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP52
| ~ sP33
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP57
| sP21
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP21
| ~ sP7
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP42
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP42
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP36
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP20
| ~ sP2
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP60
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP31
| ~ sP2
| ~ sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP9
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP29
| ~ sP26
| sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( sP45
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP45
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP6
| ~ sP45 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(45,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP5
| ~ sP53
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP32
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP25
| ~ sP51
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP40
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP40
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP37
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP14
| ~ sP26
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( sP54
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( sP54
| sP53 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( sP30
| ~ sP54 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(56,plain,
( sP34
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( sP4
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(58,plain,
( sP48
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( sP48
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( sP23
| ~ sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( sP44
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(mrel_universal,axiom,
sP40 ).
thf(62,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,mrel_universal,h2]) ).
thf(63,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[62,h1]) ).
thf(64,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[63,h0]) ).
thf(0,theorem,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( eiw_di @ X4 @ X2 )
=> ~ ! [X5: mworld] :
( ( mrel @ X2 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ~ ( ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X4 @ X8 ) )
=> ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X3 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( f @ X6 @ X6 @ X9 ) ) ) ) ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X3 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( f @ X6 @ X6 @ X9 ) ) ) )
=> ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( f @ X6 @ X4 @ X8 ) ) ) ) ) ) ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( f @ X5 @ X3 @ X6 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[62,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL960^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.07/0.35 % Computer : n016.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 5 06:06:44 UTC 2026
% 0.07/0.35 % CPUTime :
% 67.27/66.63 % SZS status Theorem
% 67.27/66.63 % Mode: mode368
% 67.27/66.63 % Inferences: 35500
% 67.27/66.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------