%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV405^5 : 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 : n006.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 02:55:51 PM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cA,type,
cA: $o ).
thf(sP1,plain,
( sP1
<=> ( ( ~ $false ) = cA ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
= cA ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> cA ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(cCOMP1,conjecture,
~ sP3 ).
thf(h0,negated_conjecture,
sP3,
inference(assume_negation,[status(cth)],[cCOMP1]) ).
thf(1,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
~ sP2,
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP1
| sP2
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP3
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,h0]) ).
thf(0,theorem,
~ sP3,
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV405^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n006.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 19:38:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: cade22grackle2xfee4
% 0.12/0.37 % Steps: 19
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------