TSTP Solution File: SEV149^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV149^5 : 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 : n018.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 19:32:45 EDT 2023
% Result : Theorem 0.19s 0.73s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 126
% Syntax : Number of formulae : 146 ( 24 unt; 13 typ; 7 def)
% Number of atoms : 400 ( 7 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1615 ( 416 ~; 59 |; 0 &; 650 @)
% ( 51 <=>; 439 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 91 ( 91 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 65 usr; 59 con; 0-2 aty)
% Number of variables : 313 ( 7 ^; 306 !; 0 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__51,type,
eigen__51: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__17,type,
eigen__17: a > $o ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__50,type,
eigen__50: a > $o ).
thf(ty_eigen__16,type,
eigen__16: a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__50,definition,
( eigen__50
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__50])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__51,definition,
( eigen__51
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__51])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__1
@ ^ [X1: a] :
~ ( ~ ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: a] :
~ ( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__16 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__6 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__6 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( eigen__0 @ eigen__2 @ eigen__5 )
=> ( eigen__1 @ eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__50 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__17 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__17 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__17 @ X2 ) ) )
=> ( eigen__17 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( sP4
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) )
=> ( eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__1 @ eigen__2 @ eigen__5 )
=> ( eigen__17 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ( eigen__1 @ eigen__6 @ X1 )
=> ( eigen__51 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__17 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP4
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__16 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__16 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__16 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__0 @ eigen__2 @ eigen__5 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__51 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP2
=> ( eigen__1 @ eigen__6 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP17
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__1 @ eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP7
=> ( eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP8
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__1 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( eigen__4 @ eigen__6 )
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP18
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__16 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP9
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__50 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__50 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP2
=> ( eigen__50 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP14
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( eigen__50 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__0 @ eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__17 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__17 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__17 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ~ sP30
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ~ sP35
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP29
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X2 )
=> ( eigen__1 @ eigen__2 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ ( sP13
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__51 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__51 @ X2 ) ) )
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP13
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__51 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__51 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__17 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(cTHM251B_pme,conjecture,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ),
inference(assume_negation,[status(cth)],[cTHM251B_pme]) ).
thf(h3,assumption,
~ ! [X1: a > a > $o,X2: a,X3: a] :
( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( X1 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( X1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( eigen__0 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( eigen__0 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a,X2: a] :
( ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X3 )
=> ( eigen__1 @ eigen__2 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP47
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP47,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( sP31
=> ~ sP1 )
=> sP34 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP31
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP34,
introduced(assumption,[]) ).
thf(h12,assumption,
sP31,
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP46
| ~ sP29
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP49
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP36
| ~ sP2
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP35
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP48
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP48
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP44
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP44
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP20
| ~ sP48 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__51]) ).
thf(12,plain,
( sP17
| ~ sP44 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__50]) ).
thf(13,plain,
( sP24
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP24
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| ~ sP51
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP28
| sP8
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP6
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP12
| ~ sP25
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP50
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP42
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP19
| ~ sP41
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP33
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( sP18
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP10
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP10
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP32
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP32
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP3
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__17]) ).
thf(30,plain,
( sP37
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).
thf(31,plain,
( sP14
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP14
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP38
| ~ sP14
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP31
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP23
| sP2
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP30
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP30
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP43
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP43
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP45
| ~ sP43 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).
thf(41,plain,
( sP40
| ~ sP45 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(42,plain,
( ~ sP7
| sP41
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP26
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP26
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP4
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(46,plain,
( ~ sP16
| ~ sP4
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP11
| sP16
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP47
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h8,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,h7,h12,h13,h11]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,49,h12,h13]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,50,h10,h11]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__4)],[h8,51,h9]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,52,h7,h8]) ).
thf(54,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,53,h6]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,54,h5]) ).
thf(56,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,55,h4]) ).
thf(57,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,56,h3]) ).
thf(58,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[57,h1]) ).
thf(59,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[58,h0]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[57,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV149^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n018.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 : Thu Aug 24 03:46:27 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.73 % SZS status Theorem
% 0.19/0.73 % Mode: cade22grackle2xfee4
% 0.19/0.73 % Steps: 8188
% 0.19/0.73 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------