TSTP Solution File: LCL959^24 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL959^24 : 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:06:06 EDT 2023
% Result : Theorem 24.59s 24.77s
% Output : Proof 24.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 120
% Syntax : Number of formulae : 141 ( 41 unt; 13 typ; 14 def)
% Number of atoms : 392 ( 14 equ; 1 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 822 ( 130 ~; 44 |; 3 &; 441 @)
% ( 40 <=>; 164 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 63 usr; 62 con; 0-2 aty)
% Number of variables : 170 ( 33 ^; 135 !; 2 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__19,type,
eigen__19: $i ).
thf(ty_eigen__23,type,
eigen__23: mworld ).
thf(ty_eigen__43,type,
eigen__43: mworld ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_eigen__15,type,
eigen__15: mworld ).
thf(ty_f,type,
f: $i > mworld > $o ).
thf(ty_eigen__9,type,
eigen__9: mworld ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(h0,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( f @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__23,definition,
( eigen__23
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__15 @ X1 )
=> ( f @ eigen__19 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__23])]) ).
thf(eigendef_eigen__43,definition,
( eigen__43
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__9 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__19 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__43])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__15 )
=> ! [X2: mworld] :
( ( mrel @ eigen__15 @ X2 )
=> ( f @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1,plain,
( sP1
<=> ( mrel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( mrel @ eigen__9 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mworld] :
( ( mrel @ eigen__9 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__19 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( mrel @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( f @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__15 )
=> ! [X2: mworld] :
( ( mrel @ eigen__15 @ X2 )
=> ( f @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eiw_di @ eigen__19 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( mrel @ eigen__9 @ eigen__2 )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( f @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mworld] : ( mrel @ eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mworld] :
( ( mrel @ eigen__15 @ X1 )
=> ( f @ eigen__19 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( mrel @ eigen__15 @ eigen__23 )
=> ( f @ eigen__19 @ eigen__23 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eiw_di @ eigen__19 @ eigen__15 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( f @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: mworld] : ( mrel @ eigen__43 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mworld,X2: mworld,X3: $i] :
( ~ ( ( eiw_di @ X3 @ X1 )
=> ~ ( mrel @ X2 @ X1 ) )
=> ( eiw_di @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( ( eiw_di @ eigen__19 @ eigen__15 )
=> ~ sP2 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP6
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eiw_di @ eigen__19 @ eigen__15 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( mrel @ eigen__9 @ eigen__43 )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__43 @ X1 )
=> ( f @ eigen__19 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( mrel @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__15 )
=> ~ sP2 )
=> ( eiw_di @ X1 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: mworld] : ( mrel @ eigen__2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( f @ eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: mworld] :
( ( mrel @ eigen__9 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: mworld] :
( ( mrel @ eigen__43 @ X1 )
=> ( f @ eigen__19 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( f @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__15 )
=> ~ ( mrel @ X1 @ eigen__15 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( mrel @ eigen__43 @ eigen__23 )
=> ( f @ eigen__19 @ eigen__23 ) ) ),
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
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__9 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__9 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( mrel @ eigen__43 @ eigen__23 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP1
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( f @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: mworld] : ( mrel @ eigen__9 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( f @ eigen__19 @ eigen__23 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( mrel @ eigen__9 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( f @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( mrel @ eigen__2 @ eigen__15 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( eiw_di @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP37
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( eiw_di @ eigen__19 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
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(kalish203,conjecture,
~ ( ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ X4 ) ) ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ X4 ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) ) ) ) ) ).
thf(h2,negated_conjecture,
( ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ X4 ) ) ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ X4 ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[kalish203]) ).
thf(h3,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ X4 ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ( mrel @ mactual @ eigen__9 )
=> ( sP23
=> ~ sP29 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
mrel @ mactual @ eigen__9,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP23
=> ~ sP29 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP23,
introduced(assumption,[]) ).
thf(h9,assumption,
sP29,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP28
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP27
| ~ sP30
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP24
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP18
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP3
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__43]) ).
thf(7,plain,
( ~ sP17
| ~ sP39
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP16
| ~ sP6
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP15
| sP17
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP29
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP20
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP26
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP10
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP14
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP32
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP9
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__23]) ).
thf(17,plain,
( sP11
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP11
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP5
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__19]) ).
thf(20,plain,
( sP36
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP25
| ~ sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(22,plain,
( ~ sP32
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP7
| ~ sP34
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP28
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP23
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(mrel_universal,axiom,
sP28 ).
thf(eiw_di_decr,axiom,
sP14 ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h7,h5,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,mrel_universal,eiw_di_decr,h8,h9]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,26,h8,h9]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,27,h6,h7]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__9)],[h3,28,h5]) ).
thf(h10,assumption,
~ ( ( mrel @ mactual @ eigen__0 )
=> ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ X3 ) ) ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
mrel @ mactual @ eigen__0,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ X3 ) ) ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( f @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP37
=> ~ sP22 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP37,
introduced(assumption,[]) ).
thf(h17,assumption,
sP22,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ( mrel @ eigen__0 @ eigen__2 )
=> ~ sP25 ),
introduced(assumption,[]) ).
thf(h19,assumption,
mrel @ eigen__0 @ eigen__2,
introduced(assumption,[]) ).
thf(h20,assumption,
sP25,
introduced(assumption,[]) ).
thf(30,plain,
( ~ sP38
| ~ sP37
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP12
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP8
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP21
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP31
| ~ sP1
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP4
| ~ sP19
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP28
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP28
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP22
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP25
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h20,h18,h16,h17,h15,h13,h14,h11,h12,h10,h4,h2,h1,h0])],[30,31,32,33,34,35,36,37,38,39,mrel_universal,h16,h17,h20]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h15,h13,h14,h11,h12,h10,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,40,h19,h20]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h13,h14,h11,h12,h10,h4,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__2)],[h14,41,h18]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h11,h12,h10,h4,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,42,h16,h17]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h11,h12,h10,h4,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__1)],[h13,43,h15]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,44,h13,h14]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,45,h11,h12]) ).
thf(47,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h4,46,h10]) ).
thf(48,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,29,47,h3,h4]) ).
thf(49,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[48,h1]) ).
thf(50,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[49,h0]) ).
thf(0,theorem,
~ ( ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ X4 ) ) ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( f @ X2 @ X4 ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( f @ X4 @ X5 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[48,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL959^24 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Aug 24 19:56:55 EDT 2023
% 0.11/0.33 % CPUTime :
% 24.59/24.77 % SZS status Theorem
% 24.59/24.77 % Mode: cade22grackle2x798d
% 24.59/24.77 % Steps: 49695
% 24.59/24.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------