TSTP Solution File: SEU815^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU815^2 : TPTP v8.1.2. Released v3.7.0.
% 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 17:34:42 EDT 2023
% Result : Theorem 148.42s 148.81s
% Output : Proof 148.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 86
% Syntax : Number of formulae : 100 ( 25 unt; 7 typ; 7 def)
% Number of atoms : 276 ( 7 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 529 ( 46 ~; 34 |; 0 &; 305 @)
% ( 32 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 43 con; 0-2 aty)
% Number of variables : 107 ( 27 ^; 80 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ eigen__1 @ X1 )
=> ~ ( in @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__1 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in @ eigen__10 @ eigen__1 )
=> ( in @ eigen__10 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ eigen__8 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__8 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__8 )
=> ( subset @ X1 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o] :
( ! [X2: $i] :
( ( in @ eigen__1 @ X2 )
=> ( ( in @ X2 @ eigen__0 )
=> X1 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__8 )
=> ( subset @ X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ eigen__10 @ eigen__1 )
=> ( in @ eigen__10 @ ( setunion @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in @ eigen__10 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) )
=> ( subset @ eigen__1 @ ( setunion @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__10 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( in @ eigen__1 @ X1 )
=> ~ ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP10
=> ( ( in @ eigen__8 @ eigen__0 )
=> ( in @ eigen__10 @ ( setunion @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X3: $o] :
( ! [X4: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X4 @ X1 )
=> X3 ) )
=> X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( in @ eigen__1 @ eigen__8 )
=> ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ eigen__0 )
=> X2 ) )
=> X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( in @ eigen__1 @ eigen__8 )
=> ~ ( in @ eigen__8 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( subset @ eigen__1 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ eigen__0 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP1
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( in @ eigen__10 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( in @ eigen__10 @ X1 )
=> ( ( in @ X1 @ eigen__0 )
=> sP25 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( in @ eigen__1 @ eigen__8 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( in @ eigen__1 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( in @ eigen__8 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ X2 @ X1 ) )
=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP30
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(def_setunionI,definition,
( setunionI
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X2 @ X3 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X2 @ ( setunion @ X1 ) ) ) ) ) ) ).
thf(def_setunionE,definition,
( setunionE
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( setunion @ X1 ) )
@ ! [X3: $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X2 @ X4 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ X3 ) )
@ X3 ) ) ) ) ).
thf(def_subsetI1,definition,
( subsetI1
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) )
@ ( subset @ X1 @ X2 ) ) ) ) ).
thf(def_transitiveset,definition,
( transitiveset
= ( ^ [X1: $i] :
! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ X1 )
@ ( subset @ X2 @ X1 ) ) ) ) ).
thf(def_transitivesetOp2,definition,
( transitivesetOp2
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( transitiveset @ X1 )
@ ! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X2 @ X1 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X2 )
@ ( in @ X3 @ X1 ) ) ) ) ) ) ).
thf(setunionTransitive,conjecture,
( sP5
=> ( sP16
=> ( sP8
=> ( sP31
=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP5
=> ( sP16
=> ( sP8
=> ( sP31
=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setunionTransitive]) ).
thf(h2,assumption,
sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP16
=> ( sP8
=> ( sP31
=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP16,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP8
=> ( sP31
=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP8,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP31
=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP31,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP21
=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ( subset @ X1 @ ( setunion @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP21,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ( subset @ X1 @ ( setunion @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP1
=> sP22 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP1,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP32
| ~ sP30
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP15
| ~ sP10
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| ~ sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP26
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP28
| ~ sP29
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP23
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP17
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| ~ sP30
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP14
| ~ sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP31
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP21
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP9
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP9
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP27
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(16,plain,
( ~ sP11
| ~ sP27
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP20
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( sP19
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP19
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP13
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(21,plain,
( ~ sP6
| ~ sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP24
| ~ sP1
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP8
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP18
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP5
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP16
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h6,h7,h4,h5,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,h2,h4,h6,h8,h11,h14,h15]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,27,h14,h15]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__1)],[h12,28,h13]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,29,h11,h12]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h9,30,h10]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,31,h8,h9]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,32,h6,h7]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,33,h4,h5]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,34,h2,h3]) ).
thf(36,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[35,h0]) ).
thf(0,theorem,
( sP5
=> ( sP16
=> ( sP8
=> ( sP31
=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ( subset @ X2 @ ( setunion @ X1 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[35,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU815^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 22:09:42 EDT 2023
% 0.12/0.33 % CPUTime :
% 148.42/148.81 % SZS status Theorem
% 148.42/148.81 % Mode: cade22grackle2x01b3
% 148.42/148.81 % Steps: 32679
% 148.42/148.81 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------