%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU809^2 : 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 : n023.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 02:51:23 PM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_omega,type,
omega: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__0 @ omega ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ ( setadjoin @ eigen__0 @ eigen__0 ) @ omega ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(def_omegaSAx,definition,
omegaSAx = sP2 ).
thf(omegaSclos,conjecture,
( sP2
=> sP2 ) ).
thf(h0,negated_conjecture,
~ ( sP2
=> sP2 ),
inference(assume_negation,[status(cth)],[omegaSclos]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h1,h2,h0])],[1,2,h1,h4,h5]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,3,h4,h5]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,4,h3]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,5,h1,h2]) ).
thf(0,theorem,
( sP2
=> sP2 ),
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU809^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n023.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 : Wed Oct 8 20:35:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 3
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------