%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU529^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 02:31:58 PM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( setadjoin @ eigen__0 @ emptyset )
= ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] : ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(def_setadjoinIL,definition,
setadjoinIL = sP5 ).
thf(eqinunit,conjecture,
( sP5
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP5
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(assume_negation,[status(cth)],[eqinunit]) ).
thf(h1,assumption,
sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( eigen__0 = X1 )
=> ( in @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP1
=> sP6 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( sP4
| sP3
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP6
| ~ sP4
| sP3 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
~ sP3,
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,h1,h5,h6]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,6,h5,h6]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,7,h4]) ).
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,
( sP5
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU529^2 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 21:10:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % Mode: cade22grackle2xfee4
% 0.20/0.41 % Steps: 35
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------