%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SCT171^1 : TPTP v9.2.0. Released v5.3.0.
% 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 : Thu Oct 9 02:19:44 PM UTC 2025
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_arrow_1092341143e_indi,type,
arrow_1092341143e_indi: $tType ).
thf(ty_produc1832616231le_alt,type,
produc1832616231le_alt: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_arrow_1346734812le_alt,type,
arrow_1346734812le_alt: $tType ).
thf(ty_e,type,
e: arrow_1346734812le_alt ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_f,type,
f: ( arrow_1092341143e_indi > produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
thf(ty_member545531028le_alt,type,
member545531028le_alt: produc1832616231le_alt > ( produc1832616231le_alt > $o ) > $o ).
thf(ty_if_Pro399136856_alt_o,type,
if_Pro399136856_alt_o: $o > ( produc1832616231le_alt > $o ) > ( produc1832616231le_alt > $o ) > produc1832616231le_alt > $o ).
thf(ty_h,type,
h: arrow_1092341143e_indi > nat ).
thf(ty_arrow_452340254_above,type,
arrow_452340254_above: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(ty_arrow_1717184938_mkbot,type,
arrow_1717184938_mkbot: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(ty_n,type,
n: nat ).
thf(ty_lab,type,
lab: produc1832616231le_alt > $o ).
thf(ty_lba,type,
lba: produc1832616231le_alt > $o ).
thf(ty_c,type,
c: arrow_1346734812le_alt ).
thf(ty_p,type,
p: arrow_1092341143e_indi > produc1832616231le_alt > $o ).
thf(ty_arrow_1865892024_mktop,type,
arrow_1865892024_mktop: ( produc1832616231le_alt > $o ) > arrow_1346734812le_alt > produc1832616231le_alt > $o ).
thf(ty_a,type,
a: arrow_1346734812le_alt ).
thf(ty_d,type,
d: arrow_1346734812le_alt ).
thf(ty_produc990411159le_alt,type,
produc990411159le_alt: arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt ).
thf(ty_b,type,
b: arrow_1346734812le_alt ).
thf(sP1,plain,
( sP1
<=> ( member545531028le_alt @ ( produc990411159le_alt @ c @ d ) @ ( f @ p ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( member545531028le_alt @ ( produc990411159le_alt @ e @ d )
@ ( f
@ ^ [X1: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ X1 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ X1 )
= n )
@ ( arrow_452340254_above @ ( p @ X1 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ X1 ) @ e ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( member545531028le_alt @ ( produc990411159le_alt @ c @ d )
@ ( f
@ ^ [X1: arrow_1092341143e_indi] :
( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ ( arrow_1865892024_mktop @ ( p @ X1 ) @ e )
@ ( if_Pro399136856_alt_o
@ ( ( h @ X1 )
= n )
@ ( arrow_452340254_above @ ( p @ X1 ) @ c @ e )
@ ( arrow_1717184938_mkbot @ ( p @ X1 ) @ e ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(conj_0,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
( member545531028le_alt @ ( produc990411159le_alt @ b @ a )
@ ( f
@ ^ [X1: arrow_1092341143e_indi] : ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ lab @ lba ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( member545531028le_alt @ ( produc990411159le_alt @ b @ a )
@ ( f
@ ^ [X1: arrow_1092341143e_indi] : ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ lab @ lba ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
sP3,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h6,h1,h2,h0])],[h5,h0]) ).
thf(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
sP3 ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h8,h1,h2,h0])],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,h8]) ).
thf(fact_14_PW,axiom,
sP1 = sP3 ).
thf(3,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h1,h2,h0]),tab_bq(discharge,[h5,h6]),tab_bq(discharge,[h7,h8])],[fact_14_PW,1,2,h5,h6,h7,h8]) ).
thf(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
sP2 ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h6,h3,h4,h0])],[fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,h3]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h8,h3,h4,h0])],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,h8]) ).
thf(6,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h3,h4,h0]),tab_bq(discharge,[h5,h6]),tab_bq(discharge,[h7,h8])],[fact_14_PW,4,5,h5,h6,h7,h8]) ).
thf(fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
( sP2
= ( member545531028le_alt @ ( produc990411159le_alt @ b @ a )
@ ( f
@ ^ [X1: arrow_1092341143e_indi] : ( if_Pro399136856_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ lab @ lba ) ) ) ) ).
thf(7,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h0]),tab_bq(discharge,[h1,h2]),tab_bq(discharge,[h3,h4])],[fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,3,6,h1,h2,h3,h4]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT171^1 : TPTP v9.2.0. Released v5.3.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 17:27:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % Mode: cade22sinegrackle2x6978
% 0.20/0.44 % Steps: 0
% 0.20/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------