TSTP Solution File: LCL960^12 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL960^12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n011.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 : 600s
% DateTime : Sun Jul 17 14:12:12 EDT 2022
% Result : Theorem 27.94s 28.19s
% Output : Proof 27.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 119
% Syntax : Number of formulae : 129 ( 22 unt; 10 typ; 15 def)
% Number of atoms : 585 ( 16 equ; 0 cnn)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 1510 ( 218 ~; 60 |; 0 &; 842 @)
% ( 48 <=>; 338 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 69 usr; 68 con; 0-3 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 271 ( 28 ^ 243 !; 0 ?; 271 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eigen__6,type,
eigen__6: mworld ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_mactual,type,
mactual: 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__1 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ 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__2 @ 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__2 @ 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__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 @ eigen__0 @ 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__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__1 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( 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__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__1 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X1 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( mrel @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( f @ eigen__3 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ 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,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( mrel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( mrel @ eigen__1 @ eigen__6 )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( f @ eigen__3 @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( !! @ ( mrel @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( mrel @ eigen__1 @ eigen__6 )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( f @ eigen__3 @ eigen__3 @ X1 ) )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( f @ eigen__3 @ eigen__2 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__3 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ~ ( ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__3 @ X3 ) )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__2 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X1 @ X1 @ X4 ) ) ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ( ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__2 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X1 @ X1 @ X4 ) ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ eigen__3 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP1
=> ( ~ ( sP2
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__3 @ X2 ) ) ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( f @ eigen__3 @ eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( f @ eigen__3 @ eigen__2 @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( mrel @ eigen__6 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ( f @ X1 @ eigen__2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP1
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__3 @ X2 ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__2 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ eigen__3 @ eigen__3 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( !! @ ( mrel @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP3
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ 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,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__2 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ eigen__3 @ eigen__3 @ X3 ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( f @ eigen__3 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( f @ eigen__3 @ eigen__3 @ X1 ) )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( mrel @ eigen__1 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ 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__2 @ 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__2 @ 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,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( eiw_di @ eigen__3 @ eigen__1 )
=> ~ ( sP14
=> ~ sP18 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( !! @ ( mrel @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP1
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP4
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ eigen__1 )
=> ~ ! [X3: mworld] :
( ( mrel @ eigen__1 @ 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,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( sP2
=> ~ sP15 )
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__3 @ eigen__3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP4
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X1 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ 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
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ eigen__3 @ X4 ) )
=> ~ ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ eigen__2 @ 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__2 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( f @ X2 @ X2 @ X5 ) ) ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ eigen__3 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( f @ X2 @ eigen__2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( eiw_di @ eigen__3 @ eigen__1 )
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: mworld] : ( !! @ ( mrel @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP1
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [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,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ 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,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ eigen__1 )
=> ~ ! [X3: mworld] :
( ( mrel @ eigen__1 @ 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,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP14
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( eiw_di @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP40
=> ~ sP32 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( eiw_di @ eigen__3 @ eigen__1 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP2
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( mrel @ mactual @ eigen__0 )
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( f @ eigen__3 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP11
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( eiw_di @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP40
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
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,
~ sP36,
inference(assume_negation,[status(cth)],[kalish256]) ).
thf(1,plain,
( ~ sP16
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP24
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP34
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP34
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP34
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP28
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP46
| ~ sP11
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP15
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP25
| ~ sP1
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP10
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP14
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP7
| ~ sP21
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP20
| ~ sP45
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP5
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP15
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(18,plain,
( ~ sP18
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP9
| ~ sP1
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP27
| sP43
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP43
| ~ sP2
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP39
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP39
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP31
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP13
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP8
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP23
| ~ sP47
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP12
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP42
| ~ sP47
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP33
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP33
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP22
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(33,plain,
( ~ sP32
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP35
| ~ sP1
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP38
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP48
| ~ sP40
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP41
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP41
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP30
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(40,plain,
( ~ sP3
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP26
| ~ sP4
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP29
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP37
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(44,plain,
( sP17
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP17
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP44
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP36
| ~ sP44 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(mrel_universal,axiom,
sP34 ).
thf(48,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,mrel_universal,h2]) ).
thf(49,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[48,h1]) ).
thf(50,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[49,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])],[48,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL960^12 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 17:14:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 27.94/28.19 % SZS status Theorem
% 27.94/28.19 % Mode: mode454
% 27.94/28.19 % Inferences: 5125
% 27.94/28.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------