TSTP Solution File: LCL952^12 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL952^12 : 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 : n004.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 08:06:04 EDT 2023
% Result : Theorem 2.04s 2.24s
% Output : Proof 2.04s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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: mworld ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_empty,type,
empty: $i > mworld > $o ).
thf(ty_singleton,type,
singleton: $i > $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__4,type,
eigen__4: mworld ).
thf(ty_in,type,
in: $i > $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(ty_eigen__5,type,
eigen__5: mworld ).
thf(ty_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( mrel @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( qmltpeq @ ( set_intersection2 @ eigen__1 @ ( singleton @ eigen__3 ) ) @ ( singleton @ eigen__3 ) @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( in @ eigen__3 @ eigen__1 @ X2 ) ) ) ) ),
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 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ ( set_intersection2 @ X1 @ ( singleton @ X3 ) ) @ ( singleton @ X3 ) @ X5 ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( in @ X3 @ X1 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eiw_di @ eigen__1 @ eigen__0 )
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ ( set_intersection2 @ eigen__1 @ ( singleton @ X2 ) ) @ ( singleton @ X2 ) @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( in @ X2 @ eigen__1 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ( in @ eigen__3 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( mrel @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eiw_di @ eigen__3 @ eigen__2 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( mrel @ eigen__0 @ eigen__2 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( set_intersection2 @ eigen__1 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( in @ X1 @ eigen__1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( qmltpeq @ ( set_intersection2 @ X2 @ ( singleton @ X4 ) ) @ ( singleton @ X4 ) @ X6 ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( in @ X4 @ X2 @ X6 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in @ eigen__3 @ eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( qmltpeq @ ( set_intersection2 @ eigen__1 @ ( singleton @ X1 ) ) @ ( singleton @ X1 ) @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( in @ X1 @ eigen__1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( mrel @ mactual @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP6
=> ( ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ( qmltpeq @ ( set_intersection2 @ eigen__1 @ ( singleton @ eigen__3 ) ) @ ( singleton @ eigen__3 ) @ X1 ) )
=> sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ( qmltpeq @ ( set_intersection2 @ eigen__1 @ ( singleton @ eigen__3 ) ) @ ( singleton @ eigen__3 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( mrel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eiw_di @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP1
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( qmltpeq @ ( set_intersection2 @ eigen__1 @ ( singleton @ X2 ) ) @ ( singleton @ X2 ) @ X4 ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( in @ X2 @ eigen__1 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP14
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( qmltpeq @ ( set_intersection2 @ X1 @ ( singleton @ X3 ) ) @ ( singleton @ X3 ) @ X5 ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( in @ X3 @ X1 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eiw_di @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
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(t51_zfmisc_1,conjecture,
sP9 ).
thf(h0,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[t51_zfmisc_1]) ).
thf(h1,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
sP12,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h5,assumption,
sP21,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h8,assumption,
sP15,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h11,assumption,
sP16,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h14,assumption,
sP6,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h16,assumption,
sP14,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h19,assumption,
sP1,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ( eiw_di @ eigen__6 @ mactual )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( empty @ eigen__6 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
eiw_di @ eigen__6 @ mactual,
introduced(assumption,[]) ).
thf(h23,assumption,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( empty @ eigen__6 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( ( eiw_di @ eigen__7 @ mactual )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( empty @ eigen__7 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
eiw_di @ eigen__7 @ mactual,
introduced(assumption,[]) ).
thf(h26,assumption,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( empty @ eigen__7 @ X1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP15
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP18
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| ~ sP21
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP20
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| ~ sP12
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP13
| ~ sP6
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| ~ sP16
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP17
| ~ sP1
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP5
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP19
| ~ sP14
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(l30_zfmisc_1,axiom,
sP9 ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h25,h26,h24,h22,h23,h21,h19,h20,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,l30_zfmisc_1,h2,h5,h8,h11,h14,h16,h19,h20]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h22,h23,h21,h19,h20,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h25,h26])],[h24,14,h25,h26]) ).
thf(rc1_xboole_0,axiom,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ( empty @ X1 @ X2 ) ) ) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h23,h21,h19,h20,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__7)],[rc1_xboole_0,15,h24]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,16,h22,h23]) ).
thf(rc2_xboole_0,axiom,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( empty @ X1 @ X3 ) ) ) ) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__6)],[rc2_xboole_0,17,h21]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,18,h19,h20]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__5)],[h17,19,h18]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,20,h16,h17]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,21,h14,h15]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,22,h13]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,23,h11,h12]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,24,h10]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,25,h8,h9]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,26,h7]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,27,h5,h6]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,28,h4]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,29,h2,h3]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,30,h1]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h0])],[31,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL952^12 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : 300
% 0.13/0.34 % DateTime : Thu Aug 24 19:17:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 2.04/2.24 % SZS status Theorem
% 2.04/2.24 % Mode: cade22grackle2xfee4
% 2.04/2.24 % Steps: 87858
% 2.04/2.24 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------