%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET063^5 : 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 : n015.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 02:23:36 PM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% 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(sP1,plain,
( sP1
<=> ! [X1: a] :
~ ( eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(cBOOL_PROP_30_pme,conjecture,
! [X1: a > $o] :
( ! [X2: a] :
~ ( X1 @ X2 )
=> ( X1
= ( ^ [X2: a] : $false ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o] :
( ! [X2: a] :
~ ( X1 @ X2 )
=> ( X1
= ( ^ [X2: a] : $false ) ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_30_pme]) ).
thf(h1,assumption,
~ ( sP1
=> ( eigen__0
= ( ^ [X1: a] : $false ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
( eigen__0
!= ( ^ [X1: a] : $false ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ( eigen__0 @ X1 )
= $false ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| ~ sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h4,h2,h3,h1,h0])],[1,h2,h5]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,2,h5]) ).
thf(4,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h3,h1,h0]),tab_fe(discharge,[h4])],[h3,3,h4]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,4,h2,h3]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,5,h1]) ).
thf(0,theorem,
! [X1: a > $o] :
( ! [X2: a] :
~ ( X1 @ X2 )
=> ( X1
= ( ^ [X2: a] : $false ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET063^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n015.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 14:53:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % Mode: cade22grackle2xfee4
% 0.20/0.40 % Steps: 4
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------