%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:26:56 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cX,type,
cX: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_cY,type,
cY: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ cX ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cX = cY ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o] :
( ( X1 @ cY )
=> ( X1 @ cX ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ cY ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(cTHM76A,conjecture,
( sP3
=> ! [X1: $i > $o] :
( ( X1 @ cX )
=> ( X1 @ cY ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP3
=> ! [X1: $i > $o] :
( ( X1 @ cX )
=> ( X1 @ cY ) ) ),
inference(assume_negation,[status(cth)],[cTHM76A]) ).
thf(h1,assumption,
sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $o] :
( ( X1 @ cX )
=> ( X1 @ cY ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP1
=> sP4 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP1
| sP4
| ~ sP2 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h1,h2,h0])],[1,2,h1,h4,h5]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,3,h4,h5]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,4,h3]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,5,h1,h2]) ).
thf(0,theorem,
( sP3
=> ! [X1: $i > $o] :
( ( X1 @ cX )
=> ( X1 @ cY ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.03 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.36 % Computer : n031.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 6 00:16:55 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % Mode: cade22grackle2xfee4
% 0.13/0.38 % Steps: 701
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------