%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU560^2 : 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 02:32:10 PM UTC 2025
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(def_subset,definition,
( subset
= ( ^ [X1: $i,X2: $i] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) ) ) ) ).
thf(def_subsetI1,definition,
( subsetI1
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) )
@ ( subset @ X1 @ X2 ) ) ) ) ).
thf(eqimpsubset2,conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[eqimpsubset2]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ( eigen__0 = X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP3
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP1
=> sP4 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP2
| ~ sP3
| sP5 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
~ sP5,
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP1
| sP4
| ~ sP2
| sP5 ),
inference(mating_rule,[status(thm)],[]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,h3,h6,h7]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,4,h6,h7]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,5,h5]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,6,h3,h4]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,7,h2]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,8,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SEU560^2 : TPTP v9.2.0. Released v3.7.0.
% 0.14/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 21:54:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % Mode: cade22grackle2xfee4
% 0.22/0.41 % Steps: 14
% 0.22/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------