%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV214^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 Oct 9 02:55:17 PM UTC 2025
% Result : Theorem 80.90s 80.84s
% Output : Proof 80.90s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_iS,type,
iS: $tType ).
thf(ty_c0,type,
c0: iS ).
thf(ty_eigen__1,type,
eigen__1: iS ).
thf(ty_cP,type,
cP: iS > iS > iS ).
thf(ty_eigen__0,type,
eigen__0: iS ).
thf(sP1,plain,
( sP1
<=> ( c0
= ( cP @ eigen__0
@ @+[X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) )
!= ( c0 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( @+[X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) )
!= ( c0 = X1 ) ) )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: iS] :
( ( cP
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X2 @ X3 ) ) )
!= ( c0 = X2 ) )
@ X1 )
!= c0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cP
@ @+[X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) )
!= ( c0 = X1 ) )
@ eigen__1 )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( c0
= ( cP
@ @+[X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) )
!= ( c0 = X1 ) )
@ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cP @ eigen__0
@ @+[X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) )
!= ( c0 = X1 ) ) )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( c0
= ( @+[X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) )
!= ( c0 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( @+[X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) )
!= ( c0 = X1 ) ) )
= c0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( c0
= ( @+[X1: iS] :
( ( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) )
!= ( c0 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: iS] :
( ( cP @ eigen__0 @ X1 )
!= c0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cS_T_LR_LEM2_pme,conjecture,
( ~ ( ~ ( sP2
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X2: iS] : ( X1 @ X2 ) ) )
=> ~ ( ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) ) )
= ( ^ [X1: iS] : ( c0 = X1 ) ) )
=> ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) ) )
!= ( ^ [X1: iS] : ( c0 = X1 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( sP2
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X2: iS] : ( X1 @ X2 ) ) )
=> ~ ( ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) ) )
= ( ^ [X1: iS] : ( c0 = X1 ) ) )
=> ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) ) )
!= ( ^ [X1: iS] : ( c0 = X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cS_T_LR_LEM2_pme]) ).
thf(h1,assumption,
~ ( ~ ( sP2
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ( ~ ( ( X1
@ @+[X2: iS] :
~ ! [X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ~ ( X1
@ @+[X2: iS] :
~ ( ~ ( ( X1
@ @+[X3: iS] :
~ ! [X4: iS] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( cP @ X3 @ X4 ) ) ) )
=> ~ ( X1 @ X2 ) )
=> ( X1
@ ( cP
@ @+[X3: iS] :
~ ! [X4: iS] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( cP @ X3 @ X4 ) ) )
@ X2 ) ) ) ) )
=> ( X1
@ ( cP
@ @+[X2: iS] :
~ ! [X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) )
@ @+[X2: iS] :
~ ( ~ ( ( X1
@ @+[X3: iS] :
~ ! [X4: iS] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( cP @ X3 @ X4 ) ) ) )
=> ~ ( X1 @ X2 ) )
=> ( X1
@ ( cP
@ @+[X3: iS] :
~ ! [X4: iS] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( cP @ X3 @ X4 ) ) )
@ X2 ) ) ) ) ) ) )
=> ! [X2: iS] : ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ( ~ sP9
=> ~ ! [X1: iS] :
( c0
!= ( cP
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X2 @ X3 ) ) )
!= ( c0 = X2 ) )
@ X1 ) ) )
= sP10 )
=> ( ( ~ sP3
=> ~ ! [X1: iS] :
( c0
!= ( cP @ X1
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X3 @ X2 ) ) )
!= ( c0 = X2 ) ) ) ) )
!= sP8 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP2
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ( ~ ( ( X1
@ @+[X2: iS] :
~ ! [X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ~ ( X1
@ @+[X2: iS] :
~ ( ~ ( ( X1
@ @+[X3: iS] :
~ ! [X4: iS] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( cP @ X3 @ X4 ) ) ) )
=> ~ ( X1 @ X2 ) )
=> ( X1
@ ( cP
@ @+[X3: iS] :
~ ! [X4: iS] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( cP @ X3 @ X4 ) ) )
@ X2 ) ) ) ) )
=> ( X1
@ ( cP
@ @+[X2: iS] :
~ ! [X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) )
@ @+[X2: iS] :
~ ( ~ ( ( X1
@ @+[X3: iS] :
~ ! [X4: iS] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( cP @ X3 @ X4 ) ) ) )
=> ~ ( X1 @ X2 ) )
=> ( X1
@ ( cP
@ @+[X3: iS] :
~ ! [X4: iS] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( cP @ X3 @ X4 ) ) )
@ X2 ) ) ) ) ) ) )
=> ! [X2: iS] : ( X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
( ( ~ sP9
=> ~ ! [X1: iS] :
( c0
!= ( cP
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X2 @ X3 ) ) )
!= ( c0 = X2 ) )
@ X1 ) ) )
!= sP10 ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ( ~ sP3
=> ~ ! [X1: iS] :
( c0
!= ( cP @ X1
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X3 @ X2 ) ) )
!= ( c0 = X2 ) ) ) ) )
!= sP8 ),
introduced(assumption,[]) ).
thf(h9,assumption,
( ~ sP9
=> ~ ! [X1: iS] :
( c0
!= ( cP
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X2 @ X3 ) ) )
!= ( c0 = X2 ) )
@ X1 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP10,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ sP9
=> ~ ! [X1: iS] :
( c0
!= ( cP
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X2 @ X3 ) ) )
!= ( c0 = X2 ) )
@ X1 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h13,assumption,
sP9,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: iS] :
( c0
!= ( cP
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X2 @ X3 ) ) )
!= ( c0 = X2 ) )
@ X1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP10 ),
inference(symeq,[status(thm)],[]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h9,h10,h7,h5,h6,h3,h4,h1,h2,h0,h0])],[1,h13,h10]) ).
thf(h15,assumption,
sP6,
introduced(assumption,[]) ).
thf(3,plain,
( ~ sP4
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP6
| sP5 ),
inference(symeq,[status(thm)],[]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h14,h9,h10,h7,h5,h6,h3,h4,h1,h2,h0,h0])],[3,4,5,h5,h15]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h9,h10,h7,h5,h6,h3,h4,h1,h2,h0,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__1)],[h14,6,h15]) ).
thf(8,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h10,h7,h5,h6,h3,h4,h1,h2,h0,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[h9,2,7,h13,h14]) ).
thf(h16,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h17,assumption,
! [X1: iS] :
( c0
!= ( cP
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X2 @ X3 ) ) )
!= ( c0 = X2 ) )
@ X1 ) ),
introduced(assumption,[]) ).
thf(9,plain,
( ~ sP10
| sP9 ),
inference(symeq,[status(thm)],[]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h11,h12,h7,h5,h6,h3,h4,h1,h2,h0,h0])],[9,h16,h12]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h7,h5,h6,h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h16,h17])],[h11,10,h16,h17]) ).
thf(12,plain,
$false,
inference(tab_be,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0,h0]),tab_be(discharge,[h9,h10]),tab_be(discharge,[h11,h12])],[h7,8,11,h9,h10,h11,h12]) ).
thf(h18,assumption,
( ~ sP3
=> ~ ! [X1: iS] :
( c0
!= ( cP @ X1
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X3 @ X2 ) ) )
!= ( c0 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP8,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ~ sP3
=> ~ ! [X1: iS] :
( c0
!= ( cP @ X1
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X3 @ X2 ) ) )
!= ( c0 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h22,assumption,
sP3,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ! [X1: iS] :
( c0
!= ( cP @ X1
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X3 @ X2 ) ) )
!= ( c0 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(13,plain,
( ~ sP3
| sP8 ),
inference(symeq,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h18,h19,h8,h5,h6,h3,h4,h1,h2,h0,h0])],[13,h22,h19]) ).
thf(h24,assumption,
sP1,
introduced(assumption,[]) ).
thf(15,plain,
( ~ sP11
| ~ sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP1
| sP7 ),
inference(symeq,[status(thm)],[]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h23,h18,h19,h8,h5,h6,h3,h4,h1,h2,h0,h0])],[15,16,17,h5,h24]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h18,h19,h8,h5,h6,h3,h4,h1,h2,h0,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__0)],[h23,18,h24]) ).
thf(20,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h18,h19,h8,h5,h6,h3,h4,h1,h2,h0,h0]),tab_imp(discharge,[h22]),tab_imp(discharge,[h23])],[h18,14,19,h22,h23]) ).
thf(h25,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h26,assumption,
! [X1: iS] :
( c0
!= ( cP @ X1
@ @+[X2: iS] :
( ( ( X2 != c0 )
=> ~ ! [X3: iS] :
( c0
!= ( cP @ X3 @ X2 ) ) )
!= ( c0 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(21,plain,
( ~ sP8
| sP3 ),
inference(symeq,[status(thm)],[]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h25,h26,h20,h21,h8,h5,h6,h3,h4,h1,h2,h0,h0])],[21,h25,h21]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h8,h5,h6,h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h25,h26])],[h20,22,h25,h26]) ).
thf(24,plain,
$false,
inference(tab_be,[status(thm),assumptions([h8,h5,h6,h3,h4,h1,h2,h0,h0]),tab_be(discharge,[h18,h19]),tab_be(discharge,[h20,h21])],[h8,20,23,h18,h19,h20,h21]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h2,12,24,h7,h8]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h5,h6])],[h3,25,h5,h6]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0,h0]),tab_negimp(discharge,[h3,h4])],[h1,26,h3,h4]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0,h0]),tab_negimp(discharge,[h1,h2])],[h0,27,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( sP2
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X2: iS] : ( X1 @ X2 ) ) )
=> ~ ( ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X1 @ X2 ) ) ) )
= ( ^ [X1: iS] : ( c0 = X1 ) ) )
=> ( ( ^ [X1: iS] :
( ( X1 != c0 )
=> ~ ! [X2: iS] :
( c0
!= ( cP @ X2 @ X1 ) ) ) )
!= ( ^ [X1: iS] : ( c0 = X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[28,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV214^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n028.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 : Wed Oct 8 19:16:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 80.90/80.84 % SZS status Theorem
% 80.90/80.84 % Mode: cade22grackle2x4fb9
% 80.90/80.84 % Steps: 52
% 80.90/80.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------