TSTP Solution File: SEU815^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU815^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : 600s
% DateTime : Tue Jul 19 14:08:57 EDT 2022
% Result : Theorem 0.62s 0.94s
% Output : Proof 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 90
% Syntax : Number of formulae : 104 ( 25 unt; 7 typ; 7 def)
% Number of atoms : 289 ( 7 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 522 ( 51 ~; 37 |; 0 &; 282 @)
% ( 34 <=>; 118 =>; 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 : 49 ( 47 usr; 45 con; 0-2 aty)
% Number of variables : 80 ( 3 ^ 77 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $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__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ eigen__1 @ X1 )
=> ( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setunion @ X2 ) )
=> ! [X4: $o] :
( ! [X5: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ X5 @ X2 )
=> X4 ) )
=> X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__1 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( in @ eigen__3 @ eigen__1 )
=> ( in @ eigen__3 @ ( setunion @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__1 @ eigen__4 )
=> ( sP4
=> ( in @ eigen__3 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ eigen__1 @ eigen__4 )
=> ( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( in @ eigen__4 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__4 )
=> ( subset @ X1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [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,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( in @ eigen__4 @ eigen__0 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( in @ eigen__3 @ X1 )
=> ( ( in @ X1 @ eigen__0 )
=> ( in @ eigen__3 @ ( setunion @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [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,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__4 )
=> ( subset @ X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ! [X1: $i] :
( ( in @ eigen__1 @ X1 )
=> ( ( in @ X1 @ eigen__0 )
=> ~ sP9 ) )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( in @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP15
=> ( ( in @ eigen__4 @ eigen__0 )
=> ( in @ eigen__3 @ ( setunion @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( in @ eigen__1 @ eigen__4 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) )
=> ( subset @ eigen__1 @ ( setunion @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP4
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( in @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP1
=> ! [X1: $o] :
( ! [X2: $i] :
( ( in @ eigen__1 @ X2 )
=> ( ( in @ X2 @ eigen__0 )
=> X1 ) )
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( in @ eigen__4 @ eigen__0 )
=> ( in @ eigen__3 @ ( setunion @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( in @ eigen__4 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( subset @ eigen__1 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ eigen__4 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( in @ eigen__3 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $o] :
( ! [X2: $i] :
( ( in @ eigen__1 @ X2 )
=> ( ( in @ X2 @ eigen__0 )
=> X1 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ eigen__0 )
=> ( in @ X1 @ ( setunion @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [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,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( in @ eigen__1 @ X1 )
=> ( ( in @ X1 @ eigen__0 )
=> ~ sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP13
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(def_setunionI,definition,
setunionI = sP2 ).
thf(def_setunionE,definition,
setunionE = sP9 ).
thf(def_subsetI1,definition,
subsetI1 = sP6 ).
thf(def_transitiveset,definition,
( transitiveset
= ( ^ [X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( subset @ X2 @ X1 ) ) ) ) ).
thf(def_transitivesetOp2,definition,
( transitivesetOp2
= ( ! [X1: $i] :
( ( transitiveset @ X1 )
=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ) ) ) ).
thf(setunionTransitive,conjecture,
( sP2
=> ( sP9
=> ( sP6
=> ( sP32
=> ! [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,
~ ( sP2
=> ( sP9
=> ( sP6
=> ( sP32
=> ! [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,
sP2,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP9
=> ( sP6
=> ( sP32
=> ! [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,
sP9,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP6
=> ( sP32
=> ! [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,
sP6,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP32
=> ! [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,
sP32,
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,
~ ( sP22
=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ( subset @ X1 @ ( setunion @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP22,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ( subset @ X1 @ ( setunion @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP1
=> sP25 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP1,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP16
| ~ sP15
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP23
| ~ sP24
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP10
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP22
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| ~ sP24
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP32
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP34
| ~ sP13
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP26
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP5
| ~ sP20
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP19
| ~ sP4
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP31
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP17
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP17
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP2
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( sP3
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP3
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP33
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(20,plain,
( sP28
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(21,plain,
( ~ sP29
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP14
| ~ sP33
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP9
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP12
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP21
| ~ sP1
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP6
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP30
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP18
| ~ sP28
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,h2,h4,h6,h8,h11,h14,h15]) ).
thf(30,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])],[h13,29,h14,h15]) ).
thf(31,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)],[h12,30,h13]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,31,h11,h12]) ).
thf(33,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)],[h9,32,h10]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,33,h8,h9]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,34,h6,h7]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,35,h4,h5]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,36,h2,h3]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[37,h0]) ).
thf(0,theorem,
( sP2
=> ( sP9
=> ( sP6
=> ( sP32
=> ! [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])],[37,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU815^2 : TPTP v8.1.0. Released v3.7.0.
% 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.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 : 600
% 0.13/0.34 % DateTime : Mon Jun 20 07:22:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.62/0.94 % SZS status Theorem
% 0.62/0.94 % Mode: mode213
% 0.62/0.94 % Inferences: 467
% 0.62/0.94 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------