TSTP Solution File: SEV123^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV123^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 : Tue Jul 19 18:04:57 EDT 2022
% Result : Theorem 3.36s 3.57s
% Output : Proof 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 98
% Syntax : Number of formulae : 115 ( 21 unt; 12 typ; 11 def)
% Number of atoms : 334 ( 38 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 1075 ( 264 ~; 48 |; 0 &; 483 @)
% ( 41 <=>; 239 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 247 ( 247 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 55 usr; 51 con; 0-2 aty)
% Number of variables : 299 ( 59 ^ 240 !; 0 ?; 299 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__7,type,
eigen__7: a > a > $o ).
thf(ty_eigen__1,type,
eigen__1: ( a > a > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: ( a > a > $o ) > $o ).
thf(ty_eigen__4,type,
eigen__4: a > a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__11,type,
eigen__11: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__8,type,
eigen__8: a > a > $o ).
thf(ty_eigen__9,type,
eigen__9: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__8 @ eigen__9 @ X1 )
=> ( eigen__4 @ eigen__9 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
~ ( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ~ ! [X6: a > a > $o] :
( ( eigen__1 @ X6 )
=> ( X5
!= ( ^ [X7: a,X8: a] :
! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X6 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ( eigen__0 @ X9 ) )
=> ( X9 @ X7 @ X8 ) ) ) ) )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__2 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ( eigen__1 @ X5 )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( ( a > a > $o ) > $o ) > $o,X2: ( a > a > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: ( a > a > $o ) > $o] :
~ ! [X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ~ ! [X8: a > a > $o] :
( ( X1 @ X8 )
=> ( X7
!= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ~ ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
=> ~ ( eigen__0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ( X1 @ X7 )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ! [X2: a > a > $o] :
( ~ ! [X3: a > a > $o] :
( ( eigen__1 @ X3 )
=> ( X2
!= ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( X3 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( eigen__0 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) ) ) )
=> ~ ( X2 @ eigen__5 @ X1 ) )
=> ( eigen__4 @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: ( a > a > $o ) > $o] :
~ ! [X2: ( a > a > $o ) > $o,X3: a,X4: a] :
( ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
( ~ ! [X9: a > a > $o] :
( ( X2 @ X9 )
=> ( X8
!= ( ^ [X10: a,X11: a] :
! [X12: a > a > $o] :
( ~ ( ! [X13: a,X14: a] :
( ( X9 @ X13 @ X14 )
=> ( X12 @ X13 @ X14 ) )
=> ~ ( X1 @ X12 ) )
=> ( X12 @ X10 @ X11 ) ) ) ) )
=> ~ ( X8 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
( ( X2 @ X8 )
=> ~ ( X8 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h2,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__2
@ ^ [X1: a > a > $o] :
~ ( ( eigen__1 @ X1 )
=> ( eigen__7
!= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ~ ! [X7: a > a > $o] :
( ( eigen__1 @ X7 )
=> ( X6
!= ( ^ [X8: a,X9: a] :
! [X10: a > a > $o] :
( ~ ( ! [X11: a,X12: a] :
( ( X7 @ X11 @ X12 )
=> ( X10 @ X11 @ X12 ) )
=> ~ ( eigen__0 @ X10 ) )
=> ( X10 @ X8 @ X9 ) ) ) ) )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ( eigen__1 @ X6 )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__2
@ ^ [X1: a > a > $o] :
~ ( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ( eigen__1 @ X4 )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__8 @ X1 @ X2 )
=> ( eigen__4 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__2
@ ^ [X1: a > a > $o] :
~ ( ~ ! [X2: a > a > $o] :
( ( eigen__1 @ X2 )
=> ( X1
!= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( eigen__0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ) )
=> ~ ( X1 @ eigen__5 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__1 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ( eigen__0 @ X7 ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ~ ! [X8: a > a > $o] :
( ( X1 @ X8 )
=> ( X7
!= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ~ ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
=> ~ ( eigen__0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ( X1 @ X7 )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > a > $o] :
( ~ ! [X2: a > a > $o] :
( ( eigen__1 @ X2 )
=> ( X1
!= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( eigen__0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ) )
=> ~ ( X1 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__8 @ eigen__9 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ( eigen__1 @ X4 )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__4 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP2
=> ( eigen__4 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ~ ! [X2: a > a > $o] :
( ~ ! [X3: a > a > $o] :
( ( eigen__1 @ X3 )
=> ( X2
!= ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( X3 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( eigen__0 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) ) ) )
=> ~ ( X2 @ eigen__5 @ X1 ) )
=> ( eigen__4 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__7 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__7 @ eigen__5 )
= ( ^ [X1: a] :
! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__8 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ~ ! [X5: a > a > $o] :
( ( eigen__1 @ X5 )
=> ( X4
!= ( ^ [X6: a,X7: a] :
! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( X5 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
=> ~ ( eigen__0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) ) ) )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__2 @ eigen__3 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__4 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__1 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ( eigen__0 @ X7 ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) )
=> ~ ( eigen__0 @ eigen__4 ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP8
= ( ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__8 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__5 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ! [X1: a > a > $o] :
( ( eigen__1 @ X1 )
=> ( eigen__7
!= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ) )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__4 @ eigen__9 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ~ ! [X2: a > a > $o] :
( ( eigen__1 @ X2 )
=> ~ ( X2 @ eigen__9 @ X1 ) )
=> ( eigen__4 @ eigen__9 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > a > $o] :
( ( eigen__1 @ X1 )
=> ( eigen__7
!= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__1 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ( eigen__0 @ X7 ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) )
=> ~ ( eigen__0 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__1 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ~ ! [X5: a > a > $o] :
( ( eigen__1 @ X5 )
=> ( X4
!= ( ^ [X6: a,X7: a] :
! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( X5 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
=> ~ ( eigen__0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) ) ) )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ! [X1: a,X2: a] :
( ( eigen__8 @ X1 @ X2 )
=> ( eigen__4 @ X1 @ X2 ) )
=> ~ ( eigen__0 @ eigen__4 ) )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP19
=> ( eigen__7
!= ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__8 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP19
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ! [X1: a,X2: a] :
( ( eigen__8 @ X1 @ X2 )
=> ( eigen__4 @ X1 @ X2 ) )
=> ~ ( eigen__0 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ( eigen__1 @ X3 )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) )
=> ~ ( eigen__0 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP3
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ( eigen__1 @ X3 )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__1 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ( eigen__0 @ X7 ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__7
= ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__8 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a,X2: a] :
( ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ~ ! [X7: a > a > $o] :
( ( eigen__1 @ X7 )
=> ( X6
!= ( ^ [X8: a,X9: a] :
! [X10: a > a > $o] :
( ~ ( ! [X11: a,X12: a] :
( ( X7 @ X11 @ X12 )
=> ( X10 @ X11 @ X12 ) )
=> ~ ( eigen__0 @ X10 ) )
=> ( X10 @ X8 @ X9 ) ) ) ) )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ( eigen__1 @ X6 )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: ( a > a > $o ) > $o,X2: ( a > a > $o ) > $o,X3: a,X4: a] :
( ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
( ~ ! [X9: a > a > $o] :
( ( X2 @ X9 )
=> ( X8
!= ( ^ [X10: a,X11: a] :
! [X12: a > a > $o] :
( ~ ( ! [X13: a,X14: a] :
( ( X9 @ X13 @ X14 )
=> ( X12 @ X13 @ X14 ) )
=> ~ ( X1 @ X12 ) )
=> ( X12 @ X10 @ X11 ) ) ) ) )
=> ~ ( X8 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
( ( X2 @ X8 )
=> ~ ( X8 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ! [X1: a > a > $o] :
( ( eigen__1 @ X1 )
=> ~ ( X1 @ eigen__9 @ eigen__11 ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a] :
( ( eigen__8 @ eigen__9 @ X1 )
=> ( eigen__4 @ eigen__9 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP25
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: a] :
( ( eigen__7 @ eigen__5 @ X1 )
= ( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__8 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ~ ! [X6: a > a > $o] :
( ( eigen__1 @ X6 )
=> ( X5
!= ( ^ [X7: a,X8: a] :
! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X6 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ( eigen__0 @ X9 ) )
=> ( X9 @ X7 @ X8 ) ) ) ) )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__2 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ( eigen__1 @ X5 )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: a] :
( ( eigen__7 @ X1 )
= ( ^ [X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__8 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a,X2: a] :
( ( eigen__8 @ X1 @ X2 )
=> ( eigen__4 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__8 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: a > a > $o] :
( ( eigen__1 @ X1 )
=> ~ ( X1 @ eigen__9 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(cTHM254_B_pme,conjecture,
sP31 ).
thf(h3,negated_conjecture,
~ sP31,
inference(assume_negation,[status(cth)],[cTHM254_B_pme]) ).
thf(1,plain,
( ~ sP41
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP23
| ~ sP19
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP27
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP16
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP32
| sP41
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP26
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP26
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP33
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(9,plain,
( sP39
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(10,plain,
( ~ sP40
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP21
| sP24
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP24
| ~ sP39
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP13
| ~ sP8
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP36
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP9
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP38
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP29
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP22
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP22
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP17
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__8]) ).
thf(21,plain,
( sP14
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP14
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP2
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__7]) ).
thf(24,plain,
( sP6
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP7
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(27,plain,
( sP28
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(28,plain,
( ~ sP20
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP12
| sP18
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP18
| ~ sP28
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP25
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP25
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP34
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP34
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP4
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__4]) ).
thf(36,plain,
( sP10
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP10
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP37
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(39,plain,
( sP30
| ~ sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(40,plain,
( sP1
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(41,plain,
( sP31
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(42,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,h3]) ).
thf(43,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[42,h2]) ).
thf(44,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[43,h1]) ).
thf(45,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[44,h0]) ).
thf(0,theorem,
sP31,
inference(contra,[status(thm),contra(discharge,[h3])],[42,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV123^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Tue Jun 28 16:21:26 EDT 2022
% 0.11/0.33 % CPUTime :
% 3.36/3.57 % SZS status Theorem
% 3.36/3.57 % Mode: mode506
% 3.36/3.57 % Inferences: 75841
% 3.36/3.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------