TSTP Solution File: PHI004^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : PHI004^1 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 12:56:22 EDT 2023
% Result : Theorem 264.09s 264.35s
% Output : Proof 264.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_rel,type,
rel: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: mu ).
thf(ty_eigen__231,type,
eigen__231: mu > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__2,type,
eigen__2: mu > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: mu ).
thf(ty_positive,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( ( positive @ eigen__2 @ eigen__3 )
=> ( eigen__2 @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mu > $i > $o] :
( ( positive @ X1 @ eigen__3 )
=> ( X1 @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mu > $i > $o] :
( ( positive @ X1 @ eigen__0 )
=> ( X1 @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ( positive @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( positive
@ ^ [X1: mu,X2: $i] :
~ ( eigen__2 @ X1 @ X2 )
@ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( positive @ eigen__2 @ eigen__0 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mu > $i > $o] :
( ( positive
@ ^ [X2: mu,X3: $i] :
~ ( X1 @ X2 @ X3 )
@ eigen__0 )
= ( ~ ( positive @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( rel @ eigen__0 @ eigen__3 )
=> ( positive @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__2 @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( positive @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( positive @ eigen__231 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP11
=> ( eigen__231 @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__2 @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mu > $i > $o] :
( ( positive @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( rel @ eigen__0 @ X2 )
=> ( positive @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP5
= ( ~ ( positive @ eigen__2 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: mu > $i > $o] :
( ( positive
@ ^ [X3: mu,X4: $i] :
~ ( X2 @ X3 @ X4 )
@ X1 )
= ( ~ ( positive @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( rel @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( positive @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__231 @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP5
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: mu > $i > $o] :
( ( positive @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel @ X1 @ X3 )
=> ( positive @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(def_meq_ind,definition,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( ^ [X1: $i] : $false ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) )
| ( ( (~) @ ( X1 @ X3 ) )
& ( X2 @ X3 ) ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_indset,definition,
( mforall_indset
= ( ^ [X1: ( mu > $i > $o ) > $i > $o,X2: $i] :
! [X3: mu > $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
? [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_indset,definition,
( mexists_indset
= ( ^ [X1: ( mu > $i > $o ) > $i > $o,X2: $i] :
? [X3: mu > $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
? [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mbox_generic,definition,
( mbox_generic
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( (~) @ ( X1 @ X3 @ X4 ) )
| ( X2 @ X4 ) ) ) ) ).
thf(def_mdia_generic,definition,
( mdia_generic
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
? [X4: $i] :
( ( X1 @ X3 @ X4 )
& ( X2 @ X4 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( mbox_generic @ rel ) ) ).
thf(def_mdia,definition,
( mdia
= ( mdia_generic @ rel ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_god,definition,
( god
= ( ^ [X1: mu] :
( mforall_indset
@ ^ [X2: mu > $i > $o] : ( mimplies @ ( positive @ X2 ) @ ( X2 @ X1 ) ) ) ) ) ).
thf(def_essence,definition,
( essence
= ( ^ [X1: mu > $i > $o,X2: mu] :
( mand @ ( X1 @ X2 )
@ ( mforall_indset
@ ^ [X3: mu > $i > $o] :
( mimplies @ ( X3 @ X2 )
@ ( mbox
@ ( mforall_ind
@ ^ [X4: mu] : ( mimplies @ ( X1 @ X4 ) @ ( X3 @ X4 ) ) ) ) ) ) ) ) ) ).
thf(def_necessary_existence,definition,
( necessary_existence
= ( ^ [X1: mu] :
( mforall_indset
@ ^ [X2: mu > $i > $o] :
( mimplies @ ( essence @ X2 @ X1 )
@ ( mbox
@ ( mexists_ind
@ ^ [X3: mu] : ( X2 @ X3 ) ) ) ) ) ) ) ).
thf(thmT2,conjecture,
! [X1: $i,X2: mu] :
( ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) )
=> ~ ( ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) )
=> ~ ! [X3: mu > $i > $o] :
( ( X3 @ X2 @ X1 )
=> ! [X4: $i] :
( ( rel @ X1 @ X4 )
=> ! [X5: mu] :
( ! [X6: mu > $i > $o] :
( ( positive @ X6 @ X4 )
=> ( X6 @ X5 @ X4 ) )
=> ( X3 @ X5 @ X4 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: mu] :
( ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) )
=> ~ ( ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) )
=> ~ ! [X3: mu > $i > $o] :
( ( X3 @ X2 @ X1 )
=> ! [X4: $i] :
( ( rel @ X1 @ X4 )
=> ! [X5: mu] :
( ! [X6: mu > $i > $o] :
( ( positive @ X6 @ X4 )
=> ( X6 @ X5 @ X4 ) )
=> ( X3 @ X5 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thmT2]) ).
thf(h1,assumption,
~ ! [X1: mu] :
( ! [X2: mu > $i > $o] :
( ( positive @ X2 @ eigen__0 )
=> ( X2 @ X1 @ eigen__0 ) )
=> ~ ( ! [X2: mu > $i > $o] :
( ( positive @ X2 @ eigen__0 )
=> ( X2 @ X1 @ eigen__0 ) )
=> ~ ! [X2: mu > $i > $o] :
( ( X2 @ X1 @ eigen__0 )
=> ! [X3: $i] :
( ( rel @ eigen__0 @ X3 )
=> ! [X4: mu] :
( ! [X5: mu > $i > $o] :
( ( positive @ X5 @ X3 )
=> ( X5 @ X4 @ X3 ) )
=> ( X2 @ X4 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP3
=> ~ ( sP3
=> ~ ! [X1: mu > $i > $o] :
( ( X1 @ eigen__1 @ eigen__0 )
=> ! [X2: $i] :
( ( rel @ eigen__0 @ X2 )
=> ! [X3: mu] :
( ! [X4: mu > $i > $o] :
( ( positive @ X4 @ X2 )
=> ( X4 @ X3 @ X2 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
( sP3
=> ~ ! [X1: mu > $i > $o] :
( ( X1 @ eigen__1 @ eigen__0 )
=> ! [X2: $i] :
( ( rel @ eigen__0 @ X2 )
=> ! [X3: mu] :
( ! [X4: mu > $i > $o] :
( ( positive @ X4 @ X2 )
=> ( X4 @ X3 @ X2 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: mu > $i > $o] :
( ( X1 @ eigen__1 @ eigen__0 )
=> ! [X2: $i] :
( ( rel @ eigen__0 @ X2 )
=> ! [X3: mu] :
( ! [X4: mu > $i > $o] :
( ( positive @ X4 @ X2 )
=> ( X4 @ X3 @ X2 ) )
=> ( X1 @ X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h8,assumption,
sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| ~ sP11
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h3,h4,h2,h1,h0])],[1,2,h3,h8,h9]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,3,h8,h9]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__231)],[h5,4,h7]) ).
thf(h10,assumption,
~ ( sP13
=> ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ! [X2: mu] :
( ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) )
=> ( eigen__2 @ X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP13,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ! [X2: mu] :
( ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) )
=> ( eigen__2 @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP17
=> ! [X1: mu] :
( ! [X2: mu > $i > $o] :
( ( positive @ X2 @ eigen__3 )
=> ( X2 @ X1 @ eigen__3 ) )
=> ( eigen__2 @ X1 @ eigen__3 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP17,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: mu] :
( ! [X2: mu > $i > $o] :
( ( positive @ X2 @ eigen__3 )
=> ( X2 @ X1 @ eigen__3 ) )
=> ( eigen__2 @ X1 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP2
=> sP9 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP2,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(6,plain,
( ~ sP20
| ~ sP5
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP15
| sP5
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| ~ sP17
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP4
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| ~ sP18
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| ~ sP10
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP14
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP21
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(axA4,axiom,
sP21 ).
thf(axA1,axiom,
sP16 ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h11,h12,h10,h6,h3,h4,h2,h1,h0])],[6,7,8,9,10,11,12,13,14,15,16,17,h3,h11,h14,h17,h18,axA4,axA1]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h11,h12,h10,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,18,h17,h18]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__4)],[h15,19,h16]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,20,h14,h15]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__3)],[h12,21,h13]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,22,h11,h12]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__2)],[h6,23,h10]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,5,24,h5,h6]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,25,h3,h4]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,26,h2]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,27,h1]) ).
thf(0,theorem,
! [X1: $i,X2: mu] :
( ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) )
=> ~ ( ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) )
=> ~ ! [X3: mu > $i > $o] :
( ( X3 @ X2 @ X1 )
=> ! [X4: $i] :
( ( rel @ X1 @ X4 )
=> ! [X5: mu] :
( ! [X6: mu > $i > $o] :
( ( positive @ X6 @ X4 )
=> ( X6 @ X5 @ X4 ) )
=> ( X3 @ X5 @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[28,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PHI004^1 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 08:51:31 EDT 2023
% 0.19/0.34 % CPUTime :
% 264.09/264.35 % SZS status Theorem
% 264.09/264.35 % Mode: cade22grackle2x91f4
% 264.09/264.35 % Steps: 48222
% 264.09/264.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------