TSTP Solution File: LCL958^18 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL958^18 : TPTP v8.1.2. Released v8.1.0.
% 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 08:06:05 EDT 2023
% Result : Theorem 1.57s 1.76s
% Output : Proof 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 103
% Syntax : Number of formulae : 116 ( 29 unt; 14 typ; 18 def)
% Number of atoms : 366 ( 18 equ; 1 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 748 ( 86 ~; 41 |; 3 &; 419 @)
% ( 39 <=>; 160 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 63 usr; 61 con; 0-2 aty)
% Number of variables : 149 ( 37 ^; 110 !; 2 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__25,type,
eigen__25: mworld ).
thf(ty_eigen__24,type,
eigen__24: $i ).
thf(ty_eigen__11,type,
eigen__11: mworld ).
thf(ty_eigen__23,type,
eigen__23: mworld ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__9,type,
eigen__9: mworld ).
thf(ty_eigen__7,type,
eigen__7: mworld ).
thf(ty_big_p,type,
big_p: $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_big_q,type,
big_q: $i > mworld > $o ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(h0,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__9 @ X1 )
=> ( big_p @ eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i] :
~ ~ ( eiw_di @ X1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__7 )
=> ! [X2: mworld] :
( ( mrel @ eigen__7 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__0 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__0 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__23,definition,
( eigen__23
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__8 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__8 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__23])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__7 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__0 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__0 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__8 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__25,definition,
( eigen__25
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__23 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__8 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__8 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__24 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__25])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__0 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__0 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__24,definition,
( eigen__24
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__23 )
=> ! [X2: mworld] :
( ( mrel @ eigen__23 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__8 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__8 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__24])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld] :
~ ! [X2: $i] :
~ ( eiw_di @ X2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__25 @ X1 )
=> ( big_p @ eigen__8 @ X1 ) )
=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__25 @ X1 )
=> ( big_q @ eigen__8 @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__25 @ X1 )
=> ( big_p @ eigen__24 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mworld] : ( mrel @ eigen__25 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eiw_di @ eigen__24 @ eigen__23 )
=> ! [X1: mworld] :
( ( mrel @ eigen__23 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__8 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__8 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__24 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( mrel @ mactual @ eigen__7 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__7 )
=> ! [X2: mworld] :
( ( mrel @ eigen__7 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__0 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__0 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__7 )
=> ~ ( mrel @ eigen__7 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( big_p @ eigen__8 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mworld] :
( ( mrel @ eigen__7 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__0 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__0 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__8 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eiw_di @ eigen__8 @ mactual )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__8 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__8 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__9 @ X1 )
=> ( big_p @ eigen__0 @ X1 ) )
=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__9 @ X1 )
=> ( big_q @ eigen__0 @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__9 @ X1 )
=> ( big_p @ eigen__8 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: mworld] : ( mrel @ eigen__7 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
~ ( eiw_di @ X1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( mrel @ eigen__7 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( mrel @ eigen__7 @ eigen__9 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( mrel @ mactual @ eigen__23 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__23 )
=> ! [X2: mworld] :
( ( mrel @ eigen__23 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__8 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__8 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: mworld] :
( ( mrel @ eigen__23 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__8 @ X2 ) )
=> ( ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_q @ eigen__8 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_p @ eigen__24 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__7 )
=> ! [X2: mworld] :
( ( mrel @ eigen__7 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__0 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__0 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__8 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__8 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( mrel @ eigen__23 @ eigen__25 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ! [X1: mworld] :
( ( mrel @ eigen__9 @ X1 )
=> ( big_q @ eigen__0 @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__9 @ X1 )
=> ( big_p @ eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eiw_di @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: mworld] :
( ( mrel @ eigen__9 @ X1 )
=> ( big_p @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eiw_di @ eigen__8 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP23
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: mworld,X2: mworld,X3: $i] :
( ~ ( ( eiw_di @ X3 @ X1 )
=> ~ ( mrel @ X1 @ X2 ) )
=> ( eiw_di @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( mrel @ eigen__25 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( mrel @ eigen__9 @ eigen__11 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: mworld,X2: mworld] : ( mrel @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP26
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eiw_di @ eigen__8 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP23
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__7 )
=> ~ sP13 )
=> ( eiw_di @ X1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: mworld] :
( ( mrel @ eigen__25 @ X1 )
=> ( big_p @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__23 )
=> ! [X2: mworld] :
( ( mrel @ eigen__23 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ eigen__8 @ X3 ) )
=> ( ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_q @ eigen__8 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_p @ X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ sP24
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( big_p @ X1 @ X5 ) )
=> ( ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( big_q @ X1 @ X5 ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( big_p @ X3 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ eigen__0 @ X4 ) )
=> ( ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_q @ eigen__0 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP21
=> ~ sP37 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
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(x2137,conjecture,
~ sP36 ).
thf(h2,negated_conjecture,
sP36,
inference(assume_negation,[status(cth)],[x2137]) ).
thf(1,plain,
( ~ sP3
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP28
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP29
| ~ sP26
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP33
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP2
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP19
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP16
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__25]) ).
thf(8,plain,
( sP4
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP34
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__24]) ).
thf(10,plain,
( sP15
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP18
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__23]) ).
thf(12,plain,
( ~ sP9
| ~ sP30
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP24
| ~ sP23
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP35
| sP24
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP36
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP32
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP6
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP11
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP28
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP25
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP27
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP22
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(23,plain,
( sP20
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP10
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP14
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP8
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(27,plain,
( sP31
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP31
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP17
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(30,plain,
( sP5
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP37
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(32,plain,
( ~ sP38
| ~ sP21
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP36
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( sP12
| sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(35,plain,
( ~ sP1
| ~ sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(eiw_di_cumul,axiom,
sP25 ).
thf(eiw_di_nonempty,axiom,
sP1 ).
thf(mrel_universal,axiom,
sP28 ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h2,eiw_di_cumul,eiw_di_nonempty,mrel_universal]) ).
thf(37,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[36,h1]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[37,h0]) ).
thf(0,theorem,
~ sP36,
inference(contra,[status(thm),contra(discharge,[h2])],[36,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL958^18 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 07:29:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.57/1.76 % SZS status Theorem
% 1.57/1.76 % Mode: cade22grackle2xfee4
% 1.57/1.76 % Steps: 11411
% 1.57/1.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------