%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP219^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 : Sat Feb 28 09:29:49 AM UTC 2026
% Result : Theorem 0.38s 1.02s
% Output : Proof 0.38s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_assn,type,
assn: $tType ).
thf(ty_p,type,
p: assn ).
thf(ty_bot_bot_assn,type,
bot_bot_assn: assn ).
thf(ty_entails,type,
entails: assn > assn > $o ).
thf(ty_q,type,
q: assn ).
thf(sP1,plain,
( sP1
<=> ( entails @ p @ bot_bot_assn ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: assn] : ( entails @ bot_bot_assn @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: assn] :
( sP1
=> ( ( entails @ bot_bot_assn @ X1 )
=> ( entails @ p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( entails @ bot_bot_assn @ q ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: assn,X2: assn,X3: assn] :
( ( entails @ X1 @ X2 )
=> ( ( entails @ X2 @ X3 )
=> ( entails @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: assn,X2: assn] :
( ( entails @ p @ X1 )
=> ( ( entails @ X1 @ X2 )
=> ( entails @ p @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP1
=> ( sP4
=> ( entails @ p @ q ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( entails @ p @ q ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP4
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(conj_0,conjecture,
sP8 ).
thf(h0,negated_conjecture,
~ sP8,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP9
| ~ sP4
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| ~ sP1
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_7_ent__false,axiom,
sP2 ).
thf(fact_5_ent__trans,axiom,
sP5 ).
thf(fact_1__092_060open_062P_A_092_060Longrightarrow_062_092_060_094sub_062A_Afalse_092_060close_062,axiom,
sP1 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,h0,fact_7_ent__false,fact_5_ent__trans,fact_1__092_060open_062P_A_092_060Longrightarrow_062_092_060_094sub_062A_Afalse_092_060close_062]) ).
thf(0,theorem,
sP8,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP219^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.34 % Computer : n010.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Feb 26 06:25:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.38/1.02 % SZS status Theorem
% 0.38/1.02 % Mode: cade22sinegrackle2x6978
% 0.38/1.02 % Steps: 11272
% 0.38/1.02 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------