%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL951^24 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:27:57 PM UTC 2026
% Result : Theorem 2.47s 7.06s
% Output : Proof 2.47s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(ty_in,type,
in: $i > $i > mworld > $o ).
thf(ty_singleton,type,
singleton: $i > $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__4,type,
eigen__4: mworld ).
thf(ty_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_empty_set,type,
empty_set: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_empty,type,
empty: $i > mworld > $o ).
thf(sP1,plain,
( sP1
<=> ( mrel @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mworld] : ( mrel @ mactual @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mworld] : ( mrel @ eigen__4 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( mrel @ eigen__4 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__4 )
=> ! [X2: mworld] :
( ( mrel @ eigen__4 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ X1 ) @ X4 ) ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X4 ) ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( in @ X4 @ eigen__1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( qmltpeq @ X4 @ X1 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( mrel @ mactual @ eigen__2 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X1 @ ( singleton @ X3 ) @ X6 ) ) )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X1 @ empty_set @ X6 ) ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( in @ X6 @ X1 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( qmltpeq @ X6 @ X3 @ X9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ eigen__3 ) @ X2 ) ) )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X2 ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( in @ X2 @ eigen__1 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ X2 @ eigen__3 @ X5 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( mrel @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( mrel @ eigen__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: mworld] : ( mrel @ eigen__2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ( eiw_di @ eigen__1 @ eigen__0 )
=> ~ sP8 )
=> ( eiw_di @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eiw_di @ eigen__3 @ eigen__4 )
=> ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ eigen__3 ) @ X3 ) ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X3 ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( in @ X3 @ eigen__1 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X3 @ eigen__3 @ X6 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( in @ X2 @ eigen__1 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ X2 @ eigen__3 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ eigen__3 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eiw_di @ eigen__3 @ eigen__2 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eiw_di @ eigen__1 @ eigen__0 )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eiw_di @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( mrel @ mactual @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eiw_di @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: mworld,X2: mworld,X3: $i] :
( ~ ( ( eiw_di @ X3 @ X1 )
=> ~ ( mrel @ X2 @ X1 ) )
=> ( eiw_di @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X2 ) ) )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eiw_di @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: mworld,X2: mworld] : ( mrel @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP17
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ X2 ) @ X5 ) ) )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X5 ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( in @ X5 @ eigen__1 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( qmltpeq @ X5 @ X2 @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__2 )
=> ~ ( mrel @ X1 @ eigen__2 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__0 )
=> ~ ( mrel @ X1 @ eigen__0 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ eigen__3 ) @ X3 ) ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X3 ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( in @ X3 @ eigen__1 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X3 @ eigen__3 @ X6 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__4 )
=> ! [X2: mworld] :
( ( mrel @ eigen__4 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ X1 ) @ X4 ) ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X4 ) ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( in @ X4 @ eigen__1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( qmltpeq @ X4 @ X1 @ X7 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eiw_di @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ X2 ) @ X5 ) ) )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X5 ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( in @ X5 @ eigen__1 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( qmltpeq @ X5 @ X2 @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__2 )
=> ~ sP9 )
=> ( eiw_di @ X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__0 )
=> ~ sP8 )
=> ( eiw_di @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X1 @ ( singleton @ X3 ) @ X6 ) ) )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X1 @ empty_set @ X6 ) ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( in @ X6 @ X1 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( qmltpeq @ X6 @ X3 @ X9 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( qmltpeq @ X2 @ ( singleton @ X4 ) @ X7 ) ) )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( qmltpeq @ X2 @ empty_set @ X7 ) ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ! [X7: $i] :
( ( eiw_di @ X7 @ X6 )
=> ! [X8: mworld] :
( ( mrel @ X6 @ X8 )
=> ( ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( in @ X7 @ X2 @ X9 ) )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ~ ! [X10: mworld] :
( ( mrel @ X9 @ X10 )
=> ( qmltpeq @ X7 @ X4 @ X10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ sP15
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP4
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( mrel @ X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
? [X3: mworld] :
( ( mrel @ X2 @ X3 )
& ( X1 @ X3 ) ) ) ) ).
thf(def_mforall_di,definition,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( eiw_di @ X3 @ X2 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X3: $i] :
( ( eiw_di @ X3 @ X2 )
& ( X1 @ X3 @ X2 ) ) ) ) ).
thf(t41_zfmisc_1,conjecture,
sP34 ).
thf(h0,negated_conjecture,
~ sP34,
inference(assume_negation,[status(cth)],[t41_zfmisc_1]) ).
thf(h1,assumption,
~ ( ( mrel @ mactual @ eigen__0 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X1 @ ( singleton @ X3 ) @ X6 ) ) )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X1 @ empty_set @ X6 ) ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( in @ X6 @ X1 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( qmltpeq @ X6 @ X3 @ X9 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
mrel @ mactual @ eigen__0,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X1 @ ( singleton @ X3 ) @ X6 ) ) )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X1 @ empty_set @ X6 ) ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( in @ X6 @ X1 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ~ ! [X9: mworld] :
( ( mrel @ X8 @ X9 )
=> ( qmltpeq @ X6 @ X3 @ X9 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP22
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ X2 ) @ X5 ) ) )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X5 ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( in @ X5 @ eigen__1 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( qmltpeq @ X5 @ X2 @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP22,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ X2 ) @ X5 ) ) )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X5 ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( in @ X5 @ eigen__1 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( qmltpeq @ X5 @ X2 @ X8 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( mrel @ eigen__0 @ eigen__2 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ X1 ) @ X4 ) ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X4 ) ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( in @ X4 @ eigen__1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( qmltpeq @ X4 @ X1 @ X7 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
mrel @ eigen__0 @ eigen__2,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ X1 ) @ X4 ) ) )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X4 ) ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( in @ X4 @ eigen__1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( qmltpeq @ X4 @ X1 @ X7 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP19
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ eigen__3 ) @ X3 ) ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X3 ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( in @ X3 @ eigen__1 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X3 @ eigen__3 @ X6 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP19,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ eigen__1 @ ( singleton @ eigen__3 ) @ X3 ) ) )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ eigen__1 @ empty_set @ X3 ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( in @ X3 @ eigen__1 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ X3 @ eigen__3 @ X6 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP1
=> sP7 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP1,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h16,assumption,
sP14,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(h18,assumption,
sP36,
introduced(assumption,[]) ).
thf(h19,assumption,
sP13,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ( eiw_di @ eigen__5 @ mactual )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( empty @ eigen__5 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
eiw_di @ eigen__5 @ mactual,
introduced(assumption,[]) ).
thf(h22,assumption,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( empty @ eigen__5 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ( eiw_di @ eigen__6 @ mactual )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( empty @ eigen__6 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
eiw_di @ eigen__6 @ mactual,
introduced(assumption,[]) ).
thf(h25,assumption,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( empty @ eigen__6 @ X1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP16
| ~ sP22
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP11
| sP16
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP32
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP26
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP20
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP5
| ~ sP1
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP30
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP24
| ~ sP17
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP33
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP6
| ~ sP18
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP15
| ~ sP19
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP35
| sP15
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP31
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP25
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP23
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP20
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP34
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP2
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP3
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP21
| ~ sP36
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP7
| ~ sP14
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP37
| ~ sP4
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP27
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP12
| ~ sP29
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP28
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP23
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP23
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(l45_zfmisc_1,axiom,
sP34 ).
thf(eiw_di_decr,axiom,
sP20 ).
thf(mrel_universal,axiom,
sP23 ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h25,h23,h21,h22,h20,h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,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,l45_zfmisc_1,h5,h11,h14,h16,h18,h19,eiw_di_decr,mrel_universal]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h20,h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,30,h24,h25]) ).
thf(rc1_xboole_0,axiom,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ( empty @ X1 @ X2 ) ) ) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__6)],[rc1_xboole_0,31,h23]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,32,h21,h22]) ).
thf(rc2_xboole_0,axiom,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( empty @ X1 @ X3 ) ) ) ) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[rc2_xboole_0,33,h20]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,34,h18,h19]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,35,h16,h17]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,36,h14,h15]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,37,h13]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,38,h11,h12]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,39,h10]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,40,h8,h9]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,41,h7]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,42,h5,h6]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,43,h4]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,44,h2,h3]) ).
thf(46,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,45,h1]) ).
thf(0,theorem,
sP34,
inference(contra,[status(thm),contra(discharge,[h0])],[46,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL951^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 06:12:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 2.47/7.06 % SZS status Theorem
% 2.47/7.06 % Mode: cade22grackle2xfee4
% 2.47/7.06 % Steps: 156160
% 2.47/7.06 % SZS output start Proof
% See solution above
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