%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU809^2 : 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 : n014.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 02:39:45 PM UTC 2025
% Result : Theorem 0.15s 0.39s
% Output : Proof 0.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(def_omegaSAx,definition,
( omegaSAx
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( in @ X1 @ omega )
@ ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ) ) ).
thf(omegaSclos,conjecture,
~ sP1 ).
thf(h0,negated_conjecture,
sP1,
inference(assume_negation,[status(cth)],[omegaSclos]) ).
thf(1,plain,
~ sP1,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,h0]) ).
thf(0,theorem,
~ sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU809^2 : TPTP v9.2.0. Released v3.7.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 8 20:35:08 EDT 2025
% 0.15/0.35 % CPUTime :
% 0.15/0.39 % SZS status Theorem
% 0.15/0.39 % Mode: cade22grackle2xfee4
% 0.15/0.39 % Steps: 1
% 0.15/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------