%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU548^2 : TPTP v9.2.0. Bugfixed v4.0.0.
% 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 02:32:05 PM UTC 2025
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__3,type,
eigen__3: $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(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ eigen__0 ) ),
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__3 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> $false ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(def_inCongP,definition,
( inCongP
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( X1 = X2 )
@ ! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X3 = X4 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X3 @ X1 )
@ ( in @ X4 @ X2 ) ) ) ) ) ) ).
thf(in__Cong,conjecture,
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[in__Cong]) ).
thf(h1,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( eigen__0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ eigen__0 )
= ( in @ X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP7
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ eigen__0 )
= ( in @ X2 @ eigen__1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP7,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ eigen__0 )
= ( in @ X2 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( sP1
= ( in @ X1 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP5
=> ( sP1 = sP6 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP5,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1 != sP6,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
sP6,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP6
| ~ sP7
| ~ sP5 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h5,h6,h4,h3,h1,h2,h0])],[1,h5,h9,h11,h12]) ).
thf(3,plain,
( ~ sP7
| sP2
| ~ sP7
| sP4 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP5
| sP3
| ~ sP5
| sP4 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
~ sP4,
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP6
| sP1
| ~ sP2
| ~ sP3 ),
inference(mating_rule,[status(thm)],[]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h9,h10,h8,h7,h5,h6,h4,h3,h1,h2,h0])],[3,4,5,6,h5,h9,h13,h14]) ).
thf(8,plain,
$false,
inference(tab_be,[status(thm),assumptions([h9,h10,h8,h7,h5,h6,h4,h3,h1,h2,h0]),tab_be(discharge,[h11,h12]),tab_be(discharge,[h13,h14])],[h10,2,7,h11,h12,h13,h14]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,8,h9,h10]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,9,h8]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,10,h7]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,11,h5,h6]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,12,h4]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,13,h3]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,14,h1,h2]) ).
thf(0,theorem,
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X4 @ X2 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU548^2 : TPTP v9.2.0. Bugfixed v4.0.0.
% 0.07/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n018.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 21:08:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % Mode: cade22grackle2xfee4
% 0.21/0.45 % Steps: 640
% 0.21/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------