%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU505^2 : 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 : n009.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 02:31:49 PM UTC 2025
% Result : Theorem 0.46s 0.63s
% Output : Proof 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 33
% Syntax : Number of formulae : 43 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 119 ( 16 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 20 ~; 15 |; 0 &; 88 @)
% ( 13 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 18 con; 0-2 aty)
% Number of variables : 35 ( 3 ^; 32 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
( ( in @ X1 @ eigen__0 )
!= ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ( in @ eigen__2 @ eigen__0 )
= ( in @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( in @ eigen__2 @ eigen__1 )
=> ( in @ eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
= ( in @ X2 @ X1 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP5
=> ( in @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
= ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( in @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP7
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
= ( in @ X3 @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_setextAx,definition,
( setextAx
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ( in @ X3 @ X1 )
<=> ( in @ X3 @ X2 ) )
@ ( X1 = X2 ) ) ) ) ).
thf(setext,conjecture,
( sP12
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP12
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ),
inference(assume_negation,[status(cth)],[setext]) ).
thf(h2,assumption,
sP12,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ eigen__0 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP8
=> ( sP2
=> sP10 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP8,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP2
=> sP10 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP2,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP9
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP6
| ~ sP5
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP8
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( sP1
| ~ sP5
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP1
| sP5
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP7
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(8,plain,
( ~ sP11
| ~ sP7
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP4
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP12
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h2,h6,h8,h9]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,11,h8,h9]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,12,h6,h7]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,13,h5]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,14,h4]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,15,h2,h3]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[16,h0]) ).
thf(0,theorem,
( sP12
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[16,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU505^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 21:29:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.46/0.63 % SZS status Theorem
% 0.46/0.63 % Mode: cade22grackle2xfee4
% 0.46/0.63 % Steps: 5484
% 0.46/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------