TSTP Solution File: LCL957^6 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL957^6 : 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 : n011.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 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 79
% Syntax : Number of formulae : 91 ( 26 unt; 10 typ; 14 def)
% Number of atoms : 258 ( 14 equ; 1 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 554 ( 57 ~; 29 |; 2 &; 333 @)
% ( 27 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 47 con; 0-3 aty)
% Number of variables : 135 ( 31 ^; 102 !; 2 ?; 135 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__4,type,
eigen__4: mworld ).
thf(ty_eigen__6,type,
eigen__6: mworld ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_big_r,type,
big_r: $i > $i > mworld > $o ).
thf(ty_eigen__3,type,
eigen__3: mworld ).
thf(h0,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__0 @ X1 )
=> ( big_r @ eigen__1 @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__4 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_r @ eigen__1 @ eigen__1 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_r @ eigen__5 @ eigen__5 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__0 @ X1 )
=> ! [X2: $i,X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_r @ eigen__1 @ eigen__1 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_r @ X2 @ X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: $i] :
~ ! [X2: mworld] :
( ( mrel @ eigen__4 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_r @ eigen__1 @ eigen__1 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_r @ X1 @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ! [X3: $i,X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( big_r @ X1 @ X1 @ X5 ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( big_r @ X3 @ X3 @ X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ! [X2: $i,X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_r @ eigen__1 @ eigen__1 @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( big_r @ X2 @ X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( mrel @ eigen__0 @ eigen__3 )
=> ( big_r @ eigen__1 @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( mrel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( mrel @ eigen__6 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( mrel @ eigen__4 @ eigen__6 )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( big_r @ eigen__1 @ eigen__1 @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( big_r @ eigen__5 @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mworld] : ( mrel @ eigen__6 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( mrel @ eigen__0 @ eigen__4 )
=> ! [X1: $i,X2: mworld] :
( ( mrel @ eigen__4 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_r @ eigen__1 @ eigen__1 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_r @ X1 @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ! [X2: $i,X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_r @ X2 @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: mworld] :
( ( mrel @ eigen__6 @ X2 )
=> ( big_r @ X1 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( big_r @ eigen__1 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP4
=> ( ~ ! [X1: $i] :
~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_r @ X1 @ X1 @ X2 ) )
=> sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: mworld] :
( ( mrel @ eigen__4 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_r @ eigen__1 @ eigen__1 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( big_r @ X1 @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( big_r @ eigen__1 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( big_r @ eigen__1 @ eigen__1 @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( big_r @ eigen__5 @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: mworld] : ( mrel @ eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( mrel @ eigen__0 @ eigen__6 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( mrel @ eigen__0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_r @ X1 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_r @ X2 @ X2 @ X3 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ! [X3: $i,X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( big_r @ X3 @ X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: mworld,X2: mworld] : ( mrel @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP5
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_r @ eigen__1 @ eigen__1 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( big_r @ eigen__5 @ eigen__5 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP19
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( big_r @ eigen__1 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( big_r @ eigen__5 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
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] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(x2122,conjecture,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( big_r @ X3 @ X3 @ X4 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i,X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( big_r @ X4 @ X4 @ X5 ) ) ) ) )
=> ~ ! [X2: $i] :
~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i,X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( big_r @ X2 @ X2 @ X6 ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( big_r @ X4 @ X4 @ X6 ) ) ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( big_r @ X3 @ X3 @ X4 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i,X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( big_r @ X4 @ X4 @ X5 ) ) ) ) )
=> ~ ! [X2: $i] :
~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i,X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( big_r @ X2 @ X2 @ X6 ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( big_r @ X4 @ X4 @ X6 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[x2122]) ).
thf(h3,assumption,
~ ( ( mrel @ mactual @ eigen__0 )
=> ( sP20
=> ~ sP1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
mrel @ mactual @ eigen__0,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP20
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP20,
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP17
| ~ sP18
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP21
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP16
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP22
| ~ sP5
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP25
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP15
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP15
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP6
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP23
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(13,plain,
( sP13
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(14,plain,
( sP8
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP2
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(16,plain,
( sP3
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP14
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(18,plain,
( ~ sP1
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP19
| ~ sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP24
| sP19
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP12
| ~ sP4
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP16
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP21
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP20
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(mrel_universal,axiom,
sP21 ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,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,h6,h7,mrel_universal]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,25,h6,h7]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,26,h4,h5]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,27,h3]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[28,h1]) ).
thf(30,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[29,h0]) ).
thf(0,theorem,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( big_r @ X3 @ X3 @ X4 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ! [X4: $i,X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( big_r @ X4 @ X4 @ X5 ) ) ) ) )
=> ~ ! [X2: $i] :
~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i,X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( big_r @ X2 @ X2 @ X6 ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( big_r @ X4 @ X4 @ X6 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[28,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL957^6 : TPTP v8.1.2. Released v8.1.0.
% 0.10/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 23:27:37 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % Mode: cade22grackle2xfee4
% 0.20/0.46 % Steps: 549
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------