%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU540^2 : 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 : n012.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 02:32:02 PM UTC 2025
% Result : Theorem 20.26s 20.47s
% Output : Proof 20.26s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $o ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(sP1,plain,
( sP1
<=> eigen__0 ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [X1: $i] : sP1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( powerset @ emptyset ) )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ ( powerset @ emptyset ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ emptyset ) )
=> ( in @ X1 @ ( powerset @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ emptyset @ ( powerset @ emptyset ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ emptyset @ ( powerset @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( in @ X2 @ ( powerset @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [X1: $i] : sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ emptyset ) )
=> ( sP1
=> ( in @ X1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : sP1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(def_dsetconstrI,definition,
( dsetconstrI
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ).
thf(def_prop2set,definition,
( prop2set
= ( ^ [X1: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X1 ) ) ) ).
thf(def_powersetI,definition,
( powersetI
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X2 )
@ ( in @ X3 @ X1 ) )
@ ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ).
thf(prop2setI,conjecture,
( sP9
=> ( sP7
=> ! [X1: $o] :
( X1
=> ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X1 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP9
=> ( sP7
=> ! [X1: $o] :
( X1
=> ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[prop2setI]) ).
thf(h1,assumption,
sP9,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP7
=> ! [X1: $o] :
( X1
=> ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP7,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $o] :
( X1
=> ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP5
| ~ sP6
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP3
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,h1,h3,h6,h7]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,8,h6,h7]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,9,h5]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,10,h3,h4]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,11,h1,h2]) ).
thf(0,theorem,
( sP9
=> ( sP7
=> ! [X1: $o] :
( X1
=> ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU540^2 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 21:32:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 20.26/20.47 % SZS status Theorem
% 20.26/20.47 % Mode: cade22grackle2x798d
% 20.26/20.47 % Steps: 134
% 20.26/20.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------