TSTP Solution File: LCL956^18 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL956^18 : 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 : n028.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 0.19s 0.68s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 73
% Syntax : Number of formulae : 82 ( 22 unt; 10 typ; 14 def)
% Number of atoms : 257 ( 14 equ; 1 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 510 ( 74 ~; 31 |; 3 &; 264 @)
% ( 26 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 44 con; 0-2 aty)
% Number of variables : 107 ( 33 ^; 72 !; 2 ?; 107 :)
% 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: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_big_q,type,
big_q: $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_p,type,
p: mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(h0,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ mactual @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__0 )
=> ( ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( p @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__1 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( eiw_di @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ( ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( p @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( big_q @ eigen__4 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( mrel @ mactual @ eigen__0 )
=> ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ( ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( p @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ( ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( p @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP1
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( big_q @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( big_q @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( p @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( big_q @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eiw_di @ eigen__2 @ eigen__0 )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( big_q @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ( ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( p @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eiw_di @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP14
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( big_q @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( mrel @ mactual @ eigen__1 )
=> ( ~ sP17
=> ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ( sP14
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP17
=> ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ( sP14
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP15
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP16
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( big_q @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP5
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ( sP14
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__1 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
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(x2109,conjecture,
~ sP24 ).
thf(h2,negated_conjecture,
sP24,
inference(assume_negation,[status(cth)],[x2109]) ).
thf(1,plain,
( ~ sP10
| ~ sP15
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| ~ sP14
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP25
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP6
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP6
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP9
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(9,plain,
( sP17
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP17
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP20
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP20
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP7
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP7
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP21
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP21
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP22
| ~ sP16
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP13
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(19,plain,
( sP4
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP4
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP19
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP11
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(24,plain,
( sP5
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(25,plain,
( ~ sP24
| ~ sP5
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,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,h2]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[26,h1]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
~ sP24,
inference(contra,[status(thm),contra(discharge,[h2])],[26,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL956^18 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.17/0.33 % Computer : n028.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Fri Aug 25 00:06:05 EDT 2023
% 0.17/0.33 % CPUTime :
% 0.19/0.68 % SZS status Theorem
% 0.19/0.68 % Mode: cade22grackle2xfee4
% 0.19/0.68 % Steps: 2883
% 0.19/0.68 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------