%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP055^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n009.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 01:44:55 PM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_list_c1059388851t_unit,type,
list_c1059388851t_unit: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_na,type,
na: nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_m,type,
m: nat ).
thf(ty_fe,type,
fe: nat > list_c1059388851t_unit ).
thf(ty_prefix1615116500t_unit,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(sP1,plain,
( sP1
<=> ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ord_less_nat @ m @ na ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(conj_0,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
m = na,
introduced(assumption,[]) ).
thf(h2,assumption,
sP2,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(fact_0__092_060open_062m_A_060_An_092_060close_062,axiom,
sP2 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h1,h0])],[fact_0__092_060open_062m_A_060_An_092_060close_062,h3]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h4,h1,h0])],[h4,h0]) ).
thf(fact_2_IA_I1_J,axiom,
( sP2
=> sP1 ) ).
thf(3,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_2_IA_I1_J,1,2,h3,h4]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h2,h0])],[h2,h3]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h4,h2,h0])],[h4,h0]) ).
thf(6,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_2_IA_I1_J,4,5,h3,h4]) ).
thf(fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062,axiom,
( ( m != na )
=> sP2 ) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062,3,6,h1,h2]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP055^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 18:17:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % Mode: cade22sinegrackle2x6978
% 0.21/0.43 % Steps: 0
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------