%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU822^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : 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 Oct 9 02:52:27 PM UTC 2025
% Result : Theorem 0.14s 0.37s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_nonempty,type,
nonempty: $i > $o ).
thf(ty_transitiveset,type,
transitiveset: $i > $o ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ( in @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(def_stricttotalorderedByIn,definition,
( stricttotalorderedByIn
= ( ^ [X1: $i] :
~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) ) ) ) ).
thf(def_wellorderedByIn,definition,
( wellorderedByIn
= ( ^ [X1: $i] :
~ ( ( stricttotalorderedByIn @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) ) ) ).
thf(def_ordinal,definition,
( ordinal
= ( ^ [X1: $i] :
~ ( ( transitiveset @ X1 )
=> ~ ( wellorderedByIn @ X1 ) ) ) ) ).
thf(def_ordinalIrrefl,definition,
( ordinalIrrefl
= ( ! [X1: $i] :
( ( ordinal @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) ) ) ) ).
thf(ordinalIrrefl2,conjecture,
( ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ~ ( in @ X1 @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ~ ( in @ X1 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[ordinalIrrefl2]) ).
thf(h1,assumption,
! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ~ ( in @ X1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ( transitiveset @ eigen__0 )
=> ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ sP1 )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( nonempty @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ) )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( transitiveset @ eigen__0 )
=> ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ sP1 )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( nonempty @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
transitiveset @ eigen__0,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ sP1 )
=> ~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( nonempty @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( nonempty @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| ~ sP2
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h1,h2,h0])],[1,2,h11,h5]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h10,3,h12,h13]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h8,4,h10,h11]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,5,h8,h9]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h4,6,h6,h7]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,7,h4,h5]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,8,h3]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).
thf(0,theorem,
( ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ~ ( in @ X1 @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU822^2 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 22:02:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.37 % SZS status Theorem
% 0.14/0.37 % Mode: mode213
% 0.14/0.37 % Inferences: 3
% 0.14/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------