TSTP Solution File: ALG294^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG294^5 : 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 : 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 : 300s
% DateTime : Wed Aug 30 16:33:53 EDT 2023
% Result : Theorem 0.74s 0.96s
% Output : Proof 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 107
% Syntax : Number of formulae : 133 ( 45 unt; 14 typ; 6 def)
% Number of atoms : 461 ( 227 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 2113 ( 623 ~; 40 |; 0 &; 910 @)
% ( 32 <=>; 508 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 112 ( 112 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 42 con; 0-2 aty)
% Number of variables : 497 ( 86 ^; 411 !; 0 ?; 497 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cR,type,
cR: a > a ).
thf(ty_cPHI,type,
cPHI: ( a > $o ) > a > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_cP,type,
cP: a > a > a ).
thf(ty_cZ,type,
cZ: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__18,type,
eigen__18: a ).
thf(ty_eigen__16,type,
eigen__16: a ).
thf(ty_cL,type,
cL: a > a ).
thf(ty_eigen__15,type,
eigen__15: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_cPSI,type,
cPSI: ( a > $o ) > a > $o ).
thf(ty_eigen__17,type,
eigen__17: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( cPSI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( cPHI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( ~ ( cPHI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 )
=> ( cPSI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0
= ( cP @ eigen__17 @ X1 ) )
=> ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__17 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0
= ( cP @ eigen__1 @ X1 ) )
=> ~ ( ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 )
=> ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0
= ( cP @ eigen__15 @ X1 ) )
=> ~ ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__15 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 = cZ ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__17 @ X1 ) )
=> ~ ( ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__17 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 )
=> ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__17 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0
= ( cP @ eigen__1 @ eigen__2 ) )
=> ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0
= ( cP @ eigen__15 @ eigen__16 ) )
=> ~ ( ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__15 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__16 )
=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__15 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__16 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0
= ( cP @ eigen__17 @ eigen__18 ) )
=> ~ ( ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__17 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__18 )
=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__17 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__18 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0
= ( cP @ eigen__1 @ eigen__2 ) )
=> ~ ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0
= ( cP @ eigen__17 @ eigen__18 ) )
=> ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__17 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__18 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0
= ( cP @ eigen__17 @ eigen__18 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__1 @ X1 ) )
=> ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 )
=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a,X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( ~ ( cPHI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 )
=> ( cPSI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__15 @ X1 ) )
=> ~ ( ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__15 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 )
=> ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__15 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP1
=> ~ ! [X1: a,X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( cPHI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__17 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__18 )
=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__17 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__18 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__15 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__16 )
=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__15 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__16 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0
= ( cP @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__17 @ X1 ) )
=> ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__17 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a,X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( cPHI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__1 @ X1 ) )
=> ~ ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a,X2: a] :
( ( eigen__0
= ( cP @ X1 @ X2 ) )
=> ~ ( cPSI
@ ^ [X3: a] :
! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( cL @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( cR @ X5 )
!= X3 ) ) )
@ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( ~ sP14
=> sP1 )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__15 @ X1 ) )
=> ~ ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__15 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP14
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0
= ( cP @ eigen__15 @ eigen__16 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP17
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP25
=> ~ ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__15 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__16 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ( eigen__0
= ( cP @ eigen__1 @ X1 ) )
=> ~ ( ~ ( cPHI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 )
=> ( cPSI
@ ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ( X3 @ eigen__1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( cL @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( cR @ X4 )
!= X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP1
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__17 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__18 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( cPSI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__15 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( cPHI
@ ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( cL @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( cR @ X3 )
!= X1 ) ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(cPU_X2310B_pme,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ( ( ^ [X1: a] :
( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) )
= ( ^ [X1: a] :
( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ( ( ^ [X1: a] :
( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) )
= ( ^ [X1: a] :
( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPU_X2310B_pme]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ( ^ [X1: a] :
( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) )
!= ( ^ [X1: a] :
( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ),
introduced(assumption,[]) ).
thf(h16,assumption,
( ( cL @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h17,assumption,
( ( cR @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ! [X1: a] :
( ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) )
= ( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP29 != sP22,
introduced(assumption,[]) ).
thf(h20,assumption,
sP29,
introduced(assumption,[]) ).
thf(h21,assumption,
sP22,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h25,assumption,
sP21,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h28,assumption,
sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| ~ sP17
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| ~ sP17
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP20
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP21
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP19
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP10
| sP32
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP26
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP26
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP28
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(11,plain,
( sP12
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(12,plain,
( ~ sP29
| sP1
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h27,h28,h26,h27,h24,h25,h20,h21,h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h20,h27,h28,h25]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h27,h24,h25,h20,h21,h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,13,h27,h28]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h20,h21,h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[h24,14,h26,h27]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h21,15,h24,h25]) ).
thf(h29,assumption,
sP12,
introduced(assumption,[]) ).
thf(17,plain,
( sP16
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP4
| ~ sP25
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP13
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP12
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP15
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP5
| ~ sP8
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP12
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( sP7
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP7
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP18
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).
thf(28,plain,
( sP19
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__17]) ).
thf(29,plain,
( ~ sP14
| sP1
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP24
| sP14
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP27
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP27
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP23
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).
thf(34,plain,
( sP21
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(35,plain,
( ~ sP22
| sP24
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h27,h29,h22,h23,h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,h27,h29,h23]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h27,h29])],[h22,36,h27,h29]) ).
thf(38,plain,
$false,
inference(tab_be,[status(thm),assumptions([h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_be(discharge,[h20,h21]),tab_be(discharge,[h22,h23])],[h19,16,37,h20,h21,h22,h23]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__0)],[h18,38,h19]) ).
thf(40,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_fe(discharge,[h18])],[h3,39,h18]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,40,h16,h17]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,41,h14,h15]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,42,h12,h13]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,43,h10,h11]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,44,h8,h9]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,45,h6,h7]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,46,h4,h5]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,47,h2,h3]) ).
thf(49,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[48,h0]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cL @ X3 ) ) ) )
=> ( X1 @ cZ ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPHI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ~ ! [X1: a > $o,X2: a] :
( ( cPSI @ X1 @ X2 )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X2 ) ) ) ) )
=> ( ( ^ [X1: a] :
( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 )
=> ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) )
= ( ^ [X1: a] :
( ~ ( ~ ( ( X1 != cZ )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPHI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) )
=> ( X1 = cZ ) )
=> ~ ! [X2: a,X3: a] :
( ( X1
= ( cP @ X2 @ X3 ) )
=> ~ ( cPSI
@ ^ [X4: a] :
! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( cL @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( cR @ X6 )
!= X4 ) ) )
@ X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[48,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG294^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n011.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 : Mon Aug 28 03:49:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.74/0.96 % SZS status Theorem
% 0.74/0.96 % Mode: cade22grackle2xfee4
% 0.74/0.96 % Steps: 13509
% 0.74/0.96 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------