%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU746^2 : 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 : n018.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 02:35:51 PM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_binunion,type,
binunion: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $o ).
thf(sP1,plain,
( sP1
<=> ( ( in @ eigen__4 @ eigen__2 )
=> eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ~ sP2
=> ( in @ eigen__4 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in @ eigen__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP2
=> eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> eigen__3 ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ( ~ ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP2
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) )
=> ( ~ ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(def_binunionE,definition,
( binunionE
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
@ ( ( in @ X3 @ X1 )
| ( in @ X3 @ X2 ) ) ) ) ) ).
thf(binunionTE,conjecture,
( sP8
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X5 @ X2 )
=> X4 )
=> ( ( ( in @ X5 @ X3 )
=> X4 )
=> X4 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP8
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X5 @ X2 )
=> X4 )
=> ( ( ( in @ X5 @ X3 )
=> X4 )
=> X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[binunionTE]) ).
thf(h1,assumption,
sP8,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X5 @ X2 )
=> X4 )
=> ( ( ( in @ X5 @ X3 )
=> X4 )
=> X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ! [X3: $o,X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ X4 @ ( binunion @ X1 @ X2 ) )
=> ( ( ( in @ X4 @ X1 )
=> X3 )
=> ( ( ( in @ X4 @ X2 )
=> X3 )
=> X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $o,X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ X3 @ ( binunion @ eigen__1 @ X1 ) )
=> ( ( ( in @ X3 @ eigen__1 )
=> X2 )
=> ( ( ( in @ X3 @ X1 )
=> X2 )
=> X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
in @ eigen__1 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $o,X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ X3 @ ( binunion @ eigen__1 @ X1 ) )
=> ( ( ( in @ X3 @ eigen__1 )
=> X2 )
=> ( ( ( in @ X3 @ X1 )
=> X2 )
=> X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( ( in @ X2 @ eigen__1 )
=> X1 )
=> ( ( ( in @ X2 @ eigen__2 )
=> X1 )
=> X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
in @ eigen__2 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( ( in @ X2 @ eigen__1 )
=> X1 )
=> ( ( ( in @ X2 @ eigen__2 )
=> X1 )
=> X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( ( in @ X1 @ eigen__1 )
=> sP7 )
=> ( ( ( in @ X1 @ eigen__2 )
=> sP7 )
=> sP7 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ( in @ eigen__4 @ eigen__0 )
=> ( sP10
=> ( sP6
=> ( sP1
=> sP7 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
in @ eigen__4 @ eigen__0,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP10
=> ( sP6
=> ( sP1
=> sP7 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP10,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP6
=> ( sP1
=> sP7 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP6,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP1
=> sP7 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP2
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| ~ sP10
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP11
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP6
| ~ sP2
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP1
| ~ sP4
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,7,h1,h14,h16,h18,h19]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,8,h18,h19]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,9,h16,h17]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,10,h14,h15]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,11,h12,h13]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__4)],[h10,12,h11]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,13,h10]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,14,h8,h9]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,15,h7]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,16,h5,h6]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,17,h4]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,18,h3]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,19,h1,h2]) ).
thf(0,theorem,
( sP8
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X5 @ X2 )
=> X4 )
=> ( ( ( in @ X5 @ X3 )
=> X4 )
=> X4 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU746^2 : 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 : n018.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 21:29:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % Mode: cade22grackle2xfee4
% 0.21/0.43 % Steps: 164
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------