%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV031^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 Oct 9 02:54:58 PM UTC 2025
% Result : Theorem 0.54s 0.74s
% Output : Proof 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 106
% Syntax : Number of formulae : 123 ( 19 unt; 0 typ; 9 def)
% Number of atoms : 367 ( 9 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 994 ( 174 ~; 60 |; 0 &; 523 @)
% ( 50 <=>; 187 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 139 ( 139 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 63 usr; 56 con; 0-3 aty)
% Number of variables : 192 ( 9 ^; 183 !; 0 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__4,type,
eigen__4: a > b ).
thf(ty_eigen__7,type,
eigen__7: a > b ).
thf(ty_eigen__2,type,
eigen__2: a > b ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__10,type,
eigen__10: a ).
thf(ty_eigen__6,type,
eigen__6: a > b ).
thf(ty_eigen__8,type,
eigen__8: a > b ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__5,type,
eigen__5: a > b ).
thf(ty_eigen__9,type,
eigen__9: a ).
thf(ty_eigen__1,type,
eigen__1: a > ( a > b ) > ( a > b ) > $o ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__2 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( a > b ) > $o,X2: a > b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: a > b] :
~ ! [X2: a > b] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ eigen__4 @ X1 ) )
=> ~ ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X1 @ X2 ) ) )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ eigen__4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__4 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: a > b] :
~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__4 @ eigen__6 ) )
=> ~ ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__6 @ X1 ) ) )
=> ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__4 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a > b] :
~ ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: a > b] :
~ ! [X2: a > b,X3: a > b] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X2 ) )
=> ~ ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X2 @ X3 ) ) )
=> ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__7 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__1
@ ^ [X1: a > b] :
~ ( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__5 @ X1 ) )
=> ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X1 @ eigen__5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: a > b] :
~ ! [X2: a > b] :
( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X1 @ X2 ) )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ~ ( ~ ( ! [X2: a > b] : ( eigen__1 @ X1 @ X2 @ X2 )
=> ~ ! [X2: a > b,X3: a > b] :
( ( eigen__1 @ X1 @ X2 @ X3 )
=> ( eigen__1 @ X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: a > b,X3: a > b,X4: a > b] :
( ~ ( ( eigen__1 @ X1 @ X2 @ X3 )
=> ~ ( eigen__1 @ X1 @ X3 @ X4 ) )
=> ( eigen__1 @ X1 @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 @ eigen__9 @ eigen__7 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__2 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 @ eigen__3 @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: a > b] : ( eigen__1 @ eigen__9 @ X1 @ X1 )
=> ~ ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__9 @ X1 @ X2 )
=> ( eigen__1 @ eigen__9 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 @ eigen__10 )
=> ( eigen__1 @ eigen__10 @ eigen__4 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__10 )
=> ~ ( ~ ( ! [X1: a > b] : ( eigen__1 @ eigen__10 @ X1 @ X1 )
=> ~ ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__10 @ X1 @ X2 )
=> ( eigen__1 @ eigen__10 @ X2 @ X1 ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__10 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__10 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__10 @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP5
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__9 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__9 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__9 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 @ eigen__10 @ eigen__6 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a > b,X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a > b] :
( ( eigen__1 @ eigen__9 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__9 @ X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__4 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ( eigen__1 @ eigen__10 @ eigen__4 @ eigen__6 )
=> ~ sP9 )
=> ( eigen__1 @ eigen__10 @ eigen__4 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__1 @ eigen__10 @ eigen__4 @ eigen__6 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__1 @ eigen__9 @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__6 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > b,X2: a > b] :
( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X1 @ X2 ) )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__0 @ eigen__9 )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__7 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP15
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP20
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a > b] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__4 @ eigen__6 ) )
=> ~ ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__6 @ X1 ) ) )
=> ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a > b] :
( ~ ( ( eigen__1 @ eigen__10 @ eigen__4 @ eigen__6 )
=> ~ ( eigen__1 @ eigen__10 @ eigen__6 @ X1 ) )
=> ( eigen__1 @ eigen__10 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a > b,X2: a > b] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ eigen__4 @ X1 ) )
=> ~ ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X1 @ X2 ) ) )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__4 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__1 @ eigen__10 @ eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ ( ! [X1: a > b] : ( eigen__1 @ eigen__10 @ X1 @ X1 )
=> ~ ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__10 @ X1 @ X2 )
=> ( eigen__1 @ eigen__10 @ X2 @ X1 ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__10 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__10 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__10 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a > b] : ( eigen__1 @ eigen__3 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP27
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( eigen__0 @ eigen__10 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( eigen__0 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__5 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP10
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP33
=> ( eigen__1 @ eigen__10 @ eigen__4 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ sP35
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X2 ) )
=> ~ ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X2 @ X3 ) ) )
=> ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( sP30
=> ~ ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__3 @ X1 @ X2 )
=> ( eigen__1 @ eigen__3 @ X2 @ X1 ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__3 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__3 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__3 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__9 @ X1 @ X2 )
=> ( eigen__1 @ eigen__9 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP25
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: a > b] :
( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__5 @ X1 ) )
=> ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X1 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP25
=> ~ sP38 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ~ sP31
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP34
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__10 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__10 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__10 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: a > b,X2: a > b] :
( ~ ( ( eigen__1 @ eigen__10 @ eigen__4 @ X1 )
=> ~ ( eigen__1 @ eigen__10 @ X1 @ X2 ) )
=> ( eigen__1 @ eigen__10 @ eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X2 ) )
=> ~ ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X2 @ X3 ) ) )
=> ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__1 @ eigen__10 @ eigen__4 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP20
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP30
=> ~ ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__3 @ X1 @ X2 )
=> ( eigen__1 @ eigen__3 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(cTHM512_pme,conjecture,
! [X1: a > $o,X2: a > ( a > b ) > ( a > b ) > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( ~ ( ! [X4: a > b] : ( X2 @ X3 @ X4 @ X4 )
=> ~ ! [X4: a > b,X5: a > b] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) ) )
=> ~ ! [X4: a > b,X5: a > b,X6: a > b] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ~ ( ! [X3: a > b,X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 @ X3 @ X3 ) )
=> ~ ! [X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X3 @ X4 ) )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X4 @ X3 ) ) ) )
=> ~ ! [X3: a > b,X4: a > b,X5: a > b] :
( ~ ( ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X4 ) )
=> ~ ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X4 @ X5 ) ) )
=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X5 ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: a > $o,X2: a > ( a > b ) > ( a > b ) > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( ~ ( ! [X4: a > b] : ( X2 @ X3 @ X4 @ X4 )
=> ~ ! [X4: a > b,X5: a > b] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) ) )
=> ~ ! [X4: a > b,X5: a > b,X6: a > b] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ~ ( ! [X3: a > b,X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 @ X3 @ X3 ) )
=> ~ ! [X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X3 @ X4 ) )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X4 @ X3 ) ) ) )
=> ~ ! [X3: a > b,X4: a > b,X5: a > b] :
( ~ ( ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X4 ) )
=> ~ ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X4 @ X5 ) ) )
=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X5 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM512_pme]) ).
thf(h3,assumption,
~ ! [X1: a > ( a > b ) > ( a > b ) > $o] :
( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ~ ( ~ ( ! [X3: a > b] : ( X1 @ X2 @ X3 @ X3 )
=> ~ ! [X3: a > b,X4: a > b] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a > b,X4: a > b,X5: a > b] :
( ~ ( ( X1 @ X2 @ X3 @ X4 )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X2 @ X3 @ X5 ) ) ) )
=> ~ ( ~ ( ! [X2: a > b,X3: a] :
( ( eigen__0 @ X3 )
=> ( X1 @ X3 @ X2 @ X2 ) )
=> ~ ! [X2: a > b,X3: a > b] :
( ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( X1 @ X4 @ X2 @ X3 ) )
=> ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( X1 @ X4 @ X3 @ X2 ) ) ) )
=> ~ ! [X2: a > b,X3: a > b,X4: a > b] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ X2 @ X3 ) )
=> ~ ! [X5: a] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ X3 @ X4 ) ) )
=> ! [X5: a] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP1
=> ~ sP37 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
sP37,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP30
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP21
| ~ sP15
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP11
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP39
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP14
| ~ sP28
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP13
| sP14
| sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP24
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP46
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP45
| sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( sP50
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP38
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP42
| ~ sP25
| ~ sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP1
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( sP5
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP8
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP22
| ~ sP20
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP18
| ~ sP20
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP34
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP1
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( sP29
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP7
| ~ sP33
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP6
| ~ sP33
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP32
| ~ sP33
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP27
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP16
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( sP31
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( sP31
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP36
| ~ sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( sP36
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP12
| ~ sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(32,plain,
( sP43
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( sP43
| ~ sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP49
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP49
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP19
| ~ sP49 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(37,plain,
( sP44
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP44
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( sP23
| ~ sP43 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(40,plain,
( sP41
| ~ sP44 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).
thf(41,plain,
( sP26
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(42,plain,
( sP17
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(43,plain,
( sP47
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(44,plain,
( sP40
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( sP40
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP3
| ~ sP40 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(47,plain,
( sP10
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(48,plain,
( ~ sP35
| ~ sP10
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP37
| sP35
| ~ sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,h5,h6]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,50,h5,h6]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,51,h4]) ).
thf(53,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,52,h3]) ).
thf(54,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[53,h1]) ).
thf(55,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[54,h0]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > ( a > b ) > ( a > b ) > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( ~ ( ! [X4: a > b] : ( X2 @ X3 @ X4 @ X4 )
=> ~ ! [X4: a > b,X5: a > b] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) ) )
=> ~ ! [X4: a > b,X5: a > b,X6: a > b] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ~ ( ! [X3: a > b,X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 @ X3 @ X3 ) )
=> ~ ! [X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X3 @ X4 ) )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X4 @ X3 ) ) ) )
=> ~ ! [X3: a > b,X4: a > b,X5: a > b] :
( ~ ( ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X4 ) )
=> ~ ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X4 @ X5 ) ) )
=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X5 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[53,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV031^5 : TPTP v9.2.0. Released v4.0.0.
% 0.08/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 19:02:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.54/0.74 % SZS status Theorem
% 0.54/0.74 % Mode: cade22grackle2xfee4
% 0.54/0.74 % Steps: 2194
% 0.54/0.74 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------