%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO351^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 03:23:16 PM UTC 2025
% Result : Theorem 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
~ ( eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ^ [X1: a] : $false )
= 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
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(cE6EXT_pme,conjecture,
( ( ^ [X1: a > $o] :
! [X2: a] :
~ ( X1 @ X2 ) )
= ( ^ [X1: a > $o] :
( ( ^ [X2: a] : $false )
= X1 ) ) ) ).
thf(h0,negated_conjecture,
( ( ^ [X1: a > $o] :
! [X2: a] :
~ ( X1 @ X2 ) )
!= ( ^ [X1: a > $o] :
( ( ^ [X2: a] : $false )
= X1 ) ) ),
inference(assume_negation,[status(cth)],[cE6EXT_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o] :
( ( ! [X2: a] :
~ ( X1 @ X2 ) )
= ( ( ^ [X2: a] : $false )
= X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP1 != sP2,
introduced(assumption,[]) ).
thf(h3,assumption,
sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
sP2,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a] :
( $false
= ( eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h7,h3,h4,h2,h1,h0])],[1,h3,h8]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,2,h8]) ).
thf(4,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_fe(discharge,[h7])],[h4,3,h7]) ).
thf(h9,assumption,
sP4,
introduced(assumption,[]) ).
thf(5,plain,
( ~ sP1
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP2
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h5,h6,h2,h1,h0])],[5,6,h9,h6]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h5,7,h9]) ).
thf(9,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,4,8,h3,h4,h5,h6]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,9,h2]) ).
thf(11,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,10,h1]) ).
thf(0,theorem,
( ( ^ [X1: a > $o] :
! [X2: a] :
~ ( X1 @ X2 ) )
= ( ^ [X1: a > $o] :
( ( ^ [X2: a] : $false )
= X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SYO351^5 : TPTP v9.2.0. Released v4.0.0.
% 0.09/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Oct 9 01:31:08 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % Mode: cade22grackle2xfee4
% 0.23/0.42 % Steps: 12
% 0.23/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------