TSTP Solution File: SYO069^4.001 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO069^4.001 : TPTP v8.1.2. 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 : Fri Sep 1 04:45:03 EDT 2023
% Result : Theorem 4.09s 4.25s
% Output : Proof 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 156
% Syntax : Number of formulae : 165 ( 30 unt; 11 typ; 23 def)
% Number of atoms : 682 ( 23 equ; 3 cnn)
% Maximal formula atoms : 42 ( 4 avg)
% Number of connectives : 1259 ( 132 ~; 78 |; 1 &; 646 @)
% ( 60 <=>; 342 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 95 ( 91 usr; 88 con; 0-2 aty)
% Number of variables : 240 ( 37 ^; 201 !; 2 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__16,type,
eigen__16: $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_a1,type,
a1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_a0,type,
a0: $i > $o ).
thf(ty_b1,type,
b1: $i > $o ).
thf(ty_b0,type,
b0: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_f,type,
f: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__2 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__15 @ X1 )
=> ( b0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(sP1,plain,
( sP1
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( irel @ eigen__2 @ eigen__16 )
=> ( b0 @ eigen__16 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( f @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( a0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( a0 @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> sP8 )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( f @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( irel @ eigen__2 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( irel @ eigen__3 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( irel @ eigen__2 @ eigen__3 )
=> ( a1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( a1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ( irel @ eigen__0 @ eigen__2 )
=> ~ ( irel @ eigen__2 @ eigen__3 ) )
=> ( irel @ eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( irel @ eigen__0 @ eigen__2 )
=> ~ ( irel @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( irel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( b1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( b0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( sP18
=> sP8 )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP17
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ~ ( sP17
=> ~ ( irel @ eigen__2 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( b0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) ) )
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( b0 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__2 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ~ ( sP10
=> ~ ( irel @ eigen__15 @ X1 ) )
=> ( irel @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP10
=> ~ ( irel @ eigen__15 @ eigen__16 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( irel @ eigen__2 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( irel @ eigen__0 @ eigen__3 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( irel @ eigen__15 @ eigen__16 )
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( irel @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( irel @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( sP25
=> sP4 )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP18
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( irel @ eigen__15 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( irel @ eigen__3 @ eigen__3 )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP37
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( irel @ eigen__3 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ~ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i] :
( ~ ( sP38
=> ~ ( irel @ eigen__3 @ X1 ) )
=> ( irel @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP11
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( irel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP43
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__3 @ X1 )
=> ( a0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP38
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP25
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ sP55
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ sP31
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( irel @ X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
( iand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
( ivalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(con,conjecture,
! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h2,assumption,
sP41,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP31
| ~ sP10
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP60
| sP31
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP30
| sP60 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP55
| ~ sP38
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP59
| sP55
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP29
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP51
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| ~ sP32
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP57
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP16
| ~ sP17
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP14
| sP16
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP29
| sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP24
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP2
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP56
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP54
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP36
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP36
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP26
| ~ sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).
thf(20,plain,
( sP19
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP52
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP52
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP18
| ~ sP52 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(24,plain,
( ~ sP46
| ~ sP48
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP8
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP43
| ~ sP18
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP21
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP7
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP9
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP34
| ~ sP37
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP47
| ~ sP37
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP44
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP25
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP35
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( sP6
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP20
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP22
| ~ sP40
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP1
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP1
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP12
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP12
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP50
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(43,plain,
( sP3
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP3
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP23
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP23
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP42
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(48,plain,
( ~ sP39
| ~ sP42
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( sP27
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( sP27
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP33
| ~ sP53
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP49
| ~ sP53
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP44
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP2
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP25
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP35
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( sP15
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( sP15
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( sP58
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( sP58
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP41
| ~ sP58
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(trans_axiom,axiom,
sP2 ).
thf(refl_axiom,axiom,
sP44 ).
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,h2,trans_axiom,refl_axiom]) ).
thf(63,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,62,h2]) ).
thf(64,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[63,h0]) ).
thf(0,theorem,
! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[63,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO069^4.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n003.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 : 300
% 0.12/0.33 % DateTime : Sat Aug 26 00:55:23 EDT 2023
% 0.12/0.33 % CPUTime :
% 4.09/4.25 % SZS status Theorem
% 4.09/4.25 % Mode: cade22grackle2xfee4
% 4.09/4.25 % Steps: 24792
% 4.09/4.25 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------