TSTP Solution File: SEV254^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV254^5 : 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 : n017.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 Aug 31 19:33:08 EDT 2023
% Result : Theorem 61.00s 61.22s
% Output : Proof 61.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 94
% Syntax : Number of formulae : 107 ( 17 unt; 7 typ; 7 def)
% Number of atoms : 301 ( 13 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 872 ( 189 ~; 54 |; 0 &; 393 @)
% ( 41 <=>; 195 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 91 ( 91 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 49 con; 0-2 aty)
% Number of variables : 214 ( 41 ^; 173 !; 0 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i > $o ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i > $o ).
thf(ty_eigen__29,type,
eigen__29: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
!= ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__2 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(h1,assumption,
! [X1: ( ( $i > $o ) > $i > $o ) > $o,X2: ( $i > $o ) > $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: ( $i > $o ) > $i > $o] :
~ ( ~ ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 ) ) )
=> ~ ( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
@ X2 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h2,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__2
@ ^ [X1: $i > $o] :
~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__2
@ ^ [X1: $i > $o] :
~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(eigendef_eigen__29,definition,
( eigen__29
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__5 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__29])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) ) )
=> ~ ( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ) )
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__5 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i] :
( ( eigen__5 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__0 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: $i] :
( ( eigen__5 @ X1 )
=> ( eigen__0 @ eigen__5 @ X1 ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP4
= ( ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__5 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__29 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__5 @ eigen__29 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__2 @ eigen__15 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( eigen__5 @ X1 )
=> ( eigen__0 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( eigen__5 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP10
=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP19
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP6
=> ~ ( eigen__2 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP6
=> ~ ( eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP12
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP3
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP14
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__4 ) )
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) ) )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 ) ) )
=> ~ ( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
@ X2 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__2 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP24
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(cTHM2C_pme,conjecture,
sP32 ).
thf(h3,negated_conjecture,
~ sP32,
inference(assume_negation,[status(cth)],[cTHM2C_pme]) ).
thf(1,plain,
( ~ sP29
| ~ sP14
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP17
| ~ sP10
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP25
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP25
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP33
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP15
| ~ sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__29]) ).
thf(8,plain,
( ~ sP20
| ~ sP19
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP2
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP22
| ~ sP6
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP7
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( sP13
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP13
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP27
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(15,plain,
( ~ sP16
| ~ sP37
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP34
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP5
| ~ sP15
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP35
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP18
| ~ sP27
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP35
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP28
| ~ sP3
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP39
| ~ sP24
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP14
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( sP8
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP8
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP41
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__5]) ).
thf(27,plain,
( ~ sP6
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( sP30
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP30
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP38
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(31,plain,
( ~ sP21
| ~ sP38
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP31
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP31
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP23
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP23
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP34
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__2]) ).
thf(37,plain,
( sP9
| ~ sP4
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP9
| sP4
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP40
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(40,plain,
( sP1
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP1
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP32
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(43,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,h3]) ).
thf(44,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[43,h2]) ).
thf(45,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[44,h1]) ).
thf(46,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[45,h0]) ).
thf(0,theorem,
sP32,
inference(contra,[status(thm),contra(discharge,[h3])],[43,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV254^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n017.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 Aug 24 01:27:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 61.00/61.22 % SZS status Theorem
% 61.00/61.22 % Mode: cade22grackle2x34cb
% 61.00/61.22 % Steps: 1027610
% 61.00/61.22 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------