%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT171^3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:21:50 AM UTC 2026
% Result : Theorem 7.53s 1.46s
% Output : Refutation 7.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 213 ( 25 equ; 0 cnn)
% Maximal formula atoms : 15 ( 8 avg)
% Number of connectives : 372 ( 10 ~; 4 |; 0 &; 355 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 690 ( 687 usr; 14 con; 0-6 aty)
% Number of variables : 12 ( 0 sgn 0 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
arrow_1389031998le_alt: $tType ).
thf(type_def_6,type,
arrow_1196572341e_indi: $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
product_unit: $tType ).
thf(type_def_9,type,
produc1572197287le_alt: $tType ).
thf(type_def_10,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
all: ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_1,type,
arrow_1955289568le_IIA: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_2,type,
arrow_1982173296le_Lin: ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_3,type,
arrow_1647925946e_Prof: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_4,type,
arrow_556571452_above: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(func_def_5,type,
arrow_1865170000_below: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(func_def_6,type,
arrow_968343245ctator: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_7,type,
arrow_1821416136_mkbot: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(func_def_8,type,
arrow_1970123222_mktop: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(func_def_9,type,
arrow_1282657667nimity: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_10,type,
big_co387207925at_nat: ( nat > nat ) > ( nat > $o ) > nat ).
thf(func_def_11,type,
finite2011930979e_indi: ( arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_12,type,
finite_card_nat: ( nat > $o ) > nat ).
thf(func_def_13,type,
finite1949902593t_unit: ( product_unit > $o ) > nat ).
thf(func_def_14,type,
finite431949602e_indi: ( arrow_1196572341e_indi > $o ) > $o ).
thf(func_def_15,type,
finite_finite_nat: ( nat > $o ) > $o ).
thf(func_def_16,type,
inj_on1505595958di_nat: ( arrow_1196572341e_indi > nat ) > ( arrow_1196572341e_indi > $o ) > $o ).
thf(func_def_17,type,
inj_on_nat_nat: ( nat > nat ) > ( nat > $o ) > $o ).
thf(func_def_18,type,
pi_Arr1865419731lt_o_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_19,type,
pi_Arr470535441e_indi: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ).
thf(func_def_20,type,
pi_Arr2096782767t_unit: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit ) > $o ).
thf(func_def_21,type,
pi_Arr1196397536_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_22,type,
pi_Arr1709554855lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_23,type,
pi_Arr272777533e_indi: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ).
thf(func_def_24,type,
pi_Arr509685723t_unit: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit ) > $o ).
thf(func_def_25,type,
pi_Pro386796690lt_o_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > $o > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_26,type,
pi_Pro2039443474e_indi: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ) > ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ).
thf(func_def_27,type,
pi_Pro30504752t_unit: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > product_unit > $o ) > ( ( produc1572197287le_alt > $o ) > product_unit ) > $o ).
thf(func_def_28,type,
pi_o_A1994447367_alt_o: ( $o > $o ) > ( $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_29,type,
pi_o_A1479825007_alt_o: ( $o > $o ) > ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( $o > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_30,type,
pi_o_P1417870404_alt_o: ( $o > $o ) > ( $o > ( produc1572197287le_alt > $o ) > $o ) > ( $o > produc1572197287le_alt > $o ) > $o ).
thf(func_def_31,type,
pi_o_nat: ( $o > $o ) > ( $o > nat > $o ) > ( $o > nat ) > $o ).
thf(func_def_32,type,
pi_o_P728361163le_alt: ( $o > $o ) > ( $o > produc1572197287le_alt > $o ) > ( $o > produc1572197287le_alt ) > $o ).
thf(func_def_33,type,
pi_Arr583278353_alt_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_34,type,
pi_Arr456308197_alt_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_35,type,
pi_Arr1309696186_alt_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_36,type,
pi_Arr778514268di_nat: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > nat > $o ) > ( arrow_1196572341e_indi > nat ) > $o ).
thf(func_def_37,type,
pi_Arr1762714837le_alt: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt ) > $o ).
thf(func_def_38,type,
pi_nat_o: ( nat > $o ) > ( nat > $o > $o ) > ( nat > $o ) > $o ).
thf(func_def_39,type,
pi_nat986275508e_indi: ( nat > $o ) > ( nat > arrow_1196572341e_indi > $o ) > ( nat > arrow_1196572341e_indi ) > $o ).
thf(func_def_40,type,
pi_nat_Product_unit: ( nat > $o ) > ( nat > product_unit > $o ) > ( nat > product_unit ) > $o ).
thf(func_def_41,type,
pi_Pro443817391_alt_o: ( product_unit > $o ) > ( product_unit > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_42,type,
pi_Pro1959068871_alt_o: ( product_unit > $o ) > ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_43,type,
pi_Pro29851292_alt_o: ( product_unit > $o ) > ( product_unit > ( produc1572197287le_alt > $o ) > $o ) > ( product_unit > produc1572197287le_alt > $o ) > $o ).
thf(func_def_44,type,
pi_Product_unit_nat: ( product_unit > $o ) > ( product_unit > nat > $o ) > ( product_unit > nat ) > $o ).
thf(func_def_45,type,
pi_Pro772884595le_alt: ( product_unit > $o ) > ( product_unit > produc1572197287le_alt > $o ) > ( product_unit > produc1572197287le_alt ) > $o ).
thf(func_def_46,type,
pi_Pro418549519_alt_o: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_47,type,
pi_Pro1246947541e_indi: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > arrow_1196572341e_indi > $o ) > ( produc1572197287le_alt > arrow_1196572341e_indi ) > $o ).
thf(func_def_48,type,
pi_Pro926528371t_unit: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > product_unit > $o ) > ( produc1572197287le_alt > product_unit ) > $o ).
thf(func_def_49,type,
one_one_nat: nat ).
thf(func_def_50,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_51,type,
times_times_nat: nat > nat > nat ).
thf(func_def_52,type,
zero_zero_nat: nat ).
thf(func_def_53,type,
bool_size: $o > nat ).
thf(func_def_54,type,
hilber1125280539di_nat: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > nat ) > nat > arrow_1196572341e_indi ).
thf(func_def_55,type,
hilber195283148at_nat: ( nat > $o ) > ( nat > nat ) > nat > nat ).
thf(func_def_56,type,
if_Pro278423000_alt_o: $o > ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(func_def_57,type,
semila848761471_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_58,type,
suc: nat > nat ).
thf(func_def_59,type,
nat_case_o: $o > ( nat > $o ) > nat > $o ).
thf(func_def_60,type,
nat_size: nat > nat ).
thf(func_def_61,type,
size_size_nat: nat > nat ).
thf(func_def_62,type,
ord_le1382328578lt_o_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_63,type,
ord_le914873172lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_64,type,
ord_le874404799lt_o_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_65,type,
ord_le1339521307_alt_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > $o ).
thf(func_def_66,type,
ord_le1991507760indi_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > $o ) > $o ).
thf(func_def_67,type,
ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_68,type,
ord_le232288914unit_o: ( product_unit > $o ) > ( product_unit > $o ) > $o ).
thf(func_def_69,type,
ord_le1852932542_alt_o: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_70,type,
ord_less_o: $o > $o > $o ).
thf(func_def_71,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_72,type,
ord_le1805007862lt_o_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_73,type,
ord_le602483040lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_74,type,
ord_le1027220427lt_o_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_75,type,
ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_76,type,
ord_le1463467535_alt_o: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > $o ).
thf(func_def_77,type,
ord_le1423491573_alt_o: ( arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > $o ) > $o ).
thf(func_def_78,type,
ord_le865407012indi_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > $o ) > $o ).
thf(func_def_79,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_80,type,
ord_le1511552390unit_o: ( product_unit > $o ) > ( product_unit > $o ) > $o ).
thf(func_def_81,type,
ord_le962286258_alt_o: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_82,type,
ord_less_eq_o: $o > $o > $o ).
thf(func_def_83,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_84,type,
top_to1492351398lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_85,type,
top_to732317616lt_o_o: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_86,type,
top_to1806834203lt_o_o: ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_87,type,
top_top_o_o: $o > $o ).
thf(func_def_88,type,
top_to1627321279_alt_o: arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_89,type,
top_to54564308indi_o: arrow_1196572341e_indi > $o ).
thf(func_def_90,type,
top_top_nat_o: nat > $o ).
thf(func_def_91,type,
top_to1984820022unit_o: product_unit > $o ).
thf(func_def_92,type,
top_to558618722_alt_o: produc1572197287le_alt > $o ).
thf(func_def_93,type,
top_top_o: $o ).
thf(func_def_94,type,
produc897867031le_alt: arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt ).
thf(func_def_95,type,
ord_at238088361st_nat: nat > nat > nat > $o ).
thf(func_def_96,type,
ord_at4362885an_nat: nat > nat > nat > $o ).
thf(func_def_97,type,
ord_atLeast_nat: nat > nat > $o ).
thf(func_def_98,type,
ord_gr375877188st_nat: nat > nat > nat > $o ).
thf(func_def_99,type,
ord_gr660468384an_nat: nat > nat > nat > $o ).
thf(func_def_100,type,
ord_greaterThan_nat: nat > nat > $o ).
thf(func_def_101,type,
collec670126350_alt_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_102,type,
collec979749928_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_103,type,
collec958969213_alt_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_104,type,
collec1936859488e_indi: ( arrow_1196572341e_indi > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_105,type,
collect_nat: ( nat > $o ) > nat > $o ).
thf(func_def_106,type,
collect_Product_unit: ( product_unit > $o ) > product_unit > $o ).
thf(func_def_107,type,
collec940901970le_alt: ( produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(func_def_108,type,
image_1011045538di_nat: ( arrow_1196572341e_indi > nat ) > ( arrow_1196572341e_indi > $o ) > nat > $o ).
thf(func_def_109,type,
image_nat_nat: ( nat > nat ) > ( nat > $o ) > nat > $o ).
thf(func_def_110,type,
member1346253567lt_o_o: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ) > $o ).
thf(func_def_111,type,
member1539010427e_indi: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ) > $o ).
thf(func_def_112,type,
member1043380889t_unit: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit ) > ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit ) > $o ) > $o ).
thf(func_def_113,type,
member1425217232_alt_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_114,type,
member1696373143lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ) > $o ).
thf(func_def_115,type,
member1186582243e_indi: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ) > $o ).
thf(func_def_116,type,
member1537523201t_unit: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit ) > $o ) > $o ).
thf(func_def_117,type,
member1925470338lt_o_o: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( ( produc1572197287le_alt > $o ) > $o ) > $o ) > $o ).
thf(func_def_118,type,
member1830244024e_indi: ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > ( ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > $o ) > $o ).
thf(func_def_119,type,
member1092867670t_unit: ( ( produc1572197287le_alt > $o ) > product_unit ) > ( ( ( produc1572197287le_alt > $o ) > product_unit ) > $o ) > $o ).
thf(func_def_120,type,
member161783341_alt_o: ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_121,type,
member984757343_alt_o: ( $o > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( $o > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_122,type,
member1495989556_alt_o: ( $o > produc1572197287le_alt > $o ) > ( ( $o > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_123,type,
member_o_nat: ( $o > nat ) > ( ( $o > nat ) > $o ) > $o ).
thf(func_def_124,type,
member1158049649le_alt: ( $o > produc1572197287le_alt ) > ( ( $o > produc1572197287le_alt ) > $o ) > $o ).
thf(func_def_125,type,
member1521294075_alt_o: ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_126,type,
member2071265553_alt_o: ( arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_127,type,
member822980838_alt_o: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_128,type,
member1842285448di_nat: ( arrow_1196572341e_indi > nat ) > ( ( arrow_1196572341e_indi > nat ) > $o ) > $o ).
thf(func_def_129,type,
member232085823le_alt: ( arrow_1196572341e_indi > produc1572197287le_alt ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt ) > $o ) > $o ).
thf(func_def_130,type,
member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_131,type,
member1113138010e_indi: ( nat > arrow_1196572341e_indi ) > ( ( nat > arrow_1196572341e_indi ) > $o ) > $o ).
thf(func_def_132,type,
member616671224t_unit: ( nat > product_unit ) > ( ( nat > product_unit ) > $o ) > $o ).
thf(func_def_133,type,
member1888392857_alt_o: ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > ( ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_134,type,
member2021528307_alt_o: ( product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_135,type,
member1295651272_alt_o: ( product_unit > produc1572197287le_alt > $o ) > ( ( product_unit > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_136,type,
member1827227242it_nat: ( product_unit > nat ) > ( ( product_unit > nat ) > $o ) > $o ).
thf(func_def_137,type,
member1161214429le_alt: ( product_unit > produc1572197287le_alt ) > ( ( product_unit > produc1572197287le_alt ) > $o ) > $o ).
thf(func_def_138,type,
member1241905979_alt_o: ( produc1572197287le_alt > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > $o ).
thf(func_def_139,type,
member1074431551e_indi: ( produc1572197287le_alt > arrow_1196572341e_indi ) > ( ( produc1572197287le_alt > arrow_1196572341e_indi ) > $o ) > $o ).
thf(func_def_140,type,
member44534621t_unit: ( produc1572197287le_alt > product_unit ) > ( ( produc1572197287le_alt > product_unit ) > $o ) > $o ).
thf(func_def_141,type,
member_o: $o > ( $o > $o ) > $o ).
thf(func_def_142,type,
member1818997282e_indi: arrow_1196572341e_indi > ( arrow_1196572341e_indi > $o ) > $o ).
thf(func_def_143,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(func_def_144,type,
member_Product_unit: product_unit > ( product_unit > $o ) > $o ).
thf(func_def_145,type,
member285112084le_alt: produc1572197287le_alt > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_146,type,
f: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(func_def_147,type,
lab: produc1572197287le_alt > $o ).
thf(func_def_148,type,
lba: produc1572197287le_alt > $o ).
thf(func_def_149,type,
p: arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_150,type,
a: arrow_1389031998le_alt ).
thf(func_def_151,type,
b: arrow_1389031998le_alt ).
thf(func_def_152,type,
c: arrow_1389031998le_alt ).
thf(func_def_153,type,
d: arrow_1389031998le_alt ).
thf(func_def_154,type,
e: arrow_1389031998le_alt ).
thf(func_def_155,type,
h: arrow_1196572341e_indi > nat ).
thf(func_def_156,type,
n: nat ).
thf(func_def_158,type,
vAND: $o > $o > $o ).
thf(func_def_161,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_162,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_163,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_164,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_165,type,
sP0: arrow_1196572341e_indi > $o ).
thf(func_def_166,type,
sP1: arrow_1196572341e_indi > $o ).
thf(func_def_167,type,
sP2: arrow_1196572341e_indi > $o ).
thf(func_def_168,type,
sP3: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_169,type,
sP4: arrow_1196572341e_indi > $o ).
thf(func_def_170,type,
sP5: arrow_1196572341e_indi > $o ).
thf(func_def_171,type,
sP6: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_172,type,
sK7: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_173,type,
sK8: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_174,type,
sK9: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_175,type,
sK10: arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_176,type,
sK11: arrow_1389031998le_alt > arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_177,type,
sK12: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_178,type,
sK13: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_179,type,
sK14: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_180,type,
sK15: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_181,type,
sK16: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_182,type,
sK17: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_183,type,
sK18: arrow_1389031998le_alt > arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_184,type,
sK19: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_185,type,
sK20: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_186,type,
sK21: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_187,type,
sK22: arrow_1389031998le_alt > arrow_1389031998le_alt > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_188,type,
sK23: arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_189,type,
sK24: produc1572197287le_alt > $o ).
thf(func_def_190,type,
sK25: produc1572197287le_alt > $o ).
thf(func_def_191,type,
sK26: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_192,type,
sK27: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_193,type,
sK28: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_194,type,
sK29: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > arrow_1389031998le_alt ).
thf(func_def_195,type,
sK30: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > arrow_1389031998le_alt ).
thf(func_def_196,type,
sK31: arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(func_def_197,type,
sK32: nat ).
thf(func_def_198,type,
sK33: nat ).
thf(func_def_199,type,
sK34: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > produc1572197287le_alt > $o ).
thf(func_def_200,type,
sK35: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(func_def_201,type,
sK36: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_202,type,
sK37: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > produc1572197287le_alt ).
thf(func_def_203,type,
sK38: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > $o ) > arrow_1196572341e_indi ).
thf(func_def_204,type,
sK39: ( product_unit > $o ) > ( product_unit > $o ) > product_unit ).
thf(func_def_205,type,
sK40: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_206,type,
sK41: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_207,type,
sK42: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > nat ) > arrow_1196572341e_indi ).
thf(func_def_208,type,
sK43: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > nat ) > arrow_1196572341e_indi ).
thf(func_def_209,type,
sK44: ( nat > $o ) > ( nat > nat ) > nat ).
thf(func_def_210,type,
sK45: ( nat > $o ) > ( nat > nat ) > nat ).
thf(func_def_211,type,
sK46: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > arrow_1196572341e_indi > $o ) > ( produc1572197287le_alt > arrow_1196572341e_indi ) > produc1572197287le_alt ).
thf(func_def_212,type,
sK47: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > product_unit > $o ) > ( produc1572197287le_alt > product_unit ) > produc1572197287le_alt ).
thf(func_def_213,type,
sK48: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_214,type,
sK49: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_215,type,
sK50: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_216,type,
sK51: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(func_def_217,type,
sK52: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(func_def_218,type,
sK53: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(func_def_219,type,
sK54: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi > $o ) > ( ( produc1572197287le_alt > $o ) > arrow_1196572341e_indi ) > produc1572197287le_alt > $o ).
thf(func_def_220,type,
sK55: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > $o > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > produc1572197287le_alt > $o ).
thf(func_def_221,type,
sK56: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > product_unit > $o ) > ( ( produc1572197287le_alt > $o ) > product_unit ) > produc1572197287le_alt > $o ).
thf(func_def_222,type,
sK57: ( nat > $o ) > ( nat > arrow_1196572341e_indi > $o ) > ( nat > arrow_1196572341e_indi ) > nat ).
thf(func_def_223,type,
sK58: ( nat > $o ) > ( nat > $o > $o ) > ( nat > $o ) > nat ).
thf(func_def_224,type,
sK59: ( nat > $o ) > ( nat > product_unit > $o ) > ( nat > product_unit ) > nat ).
thf(func_def_225,type,
sK60: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt ) > arrow_1196572341e_indi ).
thf(func_def_226,type,
sK61: ( $o > $o ) > ( $o > produc1572197287le_alt > $o ) > ( $o > produc1572197287le_alt ) > $o ).
thf(func_def_227,type,
sK62: ( product_unit > $o ) > ( product_unit > produc1572197287le_alt > $o ) > ( product_unit > produc1572197287le_alt ) > product_unit ).
thf(func_def_228,type,
sK63: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_229,type,
sK64: ( $o > $o ) > ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( $o > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_230,type,
sK65: ( product_unit > $o ) > ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( product_unit > arrow_1196572341e_indi > produc1572197287le_alt > $o ) > product_unit ).
thf(func_def_231,type,
sK66: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_232,type,
sK67: ( $o > $o ) > ( $o > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( $o > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_233,type,
sK68: ( product_unit > $o ) > ( product_unit > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( product_unit > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > product_unit ).
thf(func_def_234,type,
sK69: ( $o > $o ) > ( $o > ( produc1572197287le_alt > $o ) > $o ) > ( $o > produc1572197287le_alt > $o ) > $o ).
thf(func_def_235,type,
sK70: ( product_unit > $o ) > ( product_unit > ( produc1572197287le_alt > $o ) > $o ) > ( product_unit > produc1572197287le_alt > $o ) > product_unit ).
thf(func_def_236,type,
sK71: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > nat > $o ) > ( arrow_1196572341e_indi > nat ) > arrow_1196572341e_indi ).
thf(func_def_237,type,
sK72: ( $o > $o ) > ( $o > nat > $o ) > ( $o > nat ) > $o ).
thf(func_def_238,type,
sK73: ( product_unit > $o ) > ( product_unit > nat > $o ) > ( product_unit > nat ) > product_unit ).
thf(func_def_239,type,
sK74: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o > $o ) > ( produc1572197287le_alt > $o ) > produc1572197287le_alt ).
thf(func_def_240,type,
sK75: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_241,type,
sK76: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > arrow_1196572341e_indi ).
thf(func_def_242,type,
sK77: ( arrow_1196572341e_indi > nat ) > ( nat > arrow_1196572341e_indi ) > nat ).
thf(func_def_243,type,
sK78: ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_244,type,
sK79: ( arrow_1196572341e_indi > nat ) > arrow_1196572341e_indi ).
thf(func_def_245,type,
sK80: ( arrow_1196572341e_indi > nat ) > arrow_1196572341e_indi ).
thf(func_def_246,type,
sK81: ( nat > nat ) > nat ).
thf(func_def_247,type,
sK82: ( nat > nat ) > nat ).
thf(func_def_248,type,
sK83: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_249,type,
sK84: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_250,type,
sK85: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_251,type,
sK86: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_252,type,
sK87: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_253,type,
sK88: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_254,type,
sK89: ( nat > nat > $o ) > nat ).
thf(func_def_255,type,
sK90: ( nat > nat > $o ) > nat ).
thf(func_def_256,type,
sK91: ( nat > product_unit > $o ) > nat ).
thf(func_def_257,type,
sK92: ( nat > product_unit > $o ) > nat ).
thf(func_def_258,type,
sK93: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_259,type,
sK94: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_260,type,
sK95: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_261,type,
sK96: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_262,type,
sK97: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_263,type,
sK98: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_264,type,
sK99: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_265,type,
sK100: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_266,type,
sK101: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_267,type,
sK102: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_268,type,
sK103: ( nat > $o ) > nat ).
thf(func_def_269,type,
sK104: ( nat > $o ) > nat ).
thf(func_def_270,type,
sK105: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_271,type,
sK106: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_272,type,
sK107: ( ( nat > $o ) > nat ) > nat > $o ).
thf(func_def_273,type,
sK108: ( ( nat > $o ) > nat ) > nat > $o ).
thf(func_def_274,type,
sK109: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_275,type,
sK110: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_276,type,
sK111: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_277,type,
sK112: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_278,type,
sK113: ( nat > nat > $o ) > nat ).
thf(func_def_279,type,
sK114: ( nat > nat > $o ) > nat ).
thf(func_def_280,type,
sK115: ( nat > product_unit > $o ) > nat ).
thf(func_def_281,type,
sK116: ( nat > product_unit > $o ) > nat ).
thf(func_def_282,type,
sK117: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_283,type,
sK118: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_284,type,
sK119: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_285,type,
sK120: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_286,type,
sK121: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_287,type,
sK122: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_288,type,
sK123: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_289,type,
sK124: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_290,type,
sK125: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_291,type,
sK126: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_292,type,
sK127: ( nat > $o ) > nat ).
thf(func_def_293,type,
sK128: ( nat > $o ) > nat ).
thf(func_def_294,type,
sK129: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_295,type,
sK130: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_296,type,
sK131: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_297,type,
sK132: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_298,type,
sK133: ( ( nat > $o ) > product_unit > $o ) > nat > $o ).
thf(func_def_299,type,
sK134: ( ( nat > $o ) > product_unit > $o ) > nat > $o ).
thf(func_def_300,type,
sK135: ( ( nat > $o ) > arrow_1196572341e_indi > $o ) > nat > $o ).
thf(func_def_301,type,
sK136: ( ( nat > $o ) > arrow_1196572341e_indi > $o ) > nat > $o ).
thf(func_def_302,type,
sK137: ( ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_303,type,
sK138: ( ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_304,type,
sK139: ( ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_305,type,
sK140: ( ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_306,type,
sK141: ( ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_307,type,
sK142: ( ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_308,type,
sK143: ( ( nat > $o ) > produc1572197287le_alt > $o ) > nat > $o ).
thf(func_def_309,type,
sK144: ( ( nat > $o ) > produc1572197287le_alt > $o ) > nat > $o ).
thf(func_def_310,type,
sK145: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_311,type,
sK146: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_312,type,
sK147: ( ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ).
thf(func_def_313,type,
sK148: ( ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ).
thf(func_def_314,type,
sK149: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_315,type,
sK150: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_316,type,
sK151: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_317,type,
sK152: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_318,type,
sK153: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_319,type,
sK154: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_320,type,
sK155: ( ( produc1572197287le_alt > $o ) > nat > $o ) > produc1572197287le_alt > $o ).
thf(func_def_321,type,
sK156: ( ( produc1572197287le_alt > $o ) > nat > $o ) > produc1572197287le_alt > $o ).
thf(func_def_322,type,
sK157: ( $o > nat > $o ) > $o ).
thf(func_def_323,type,
sK158: ( $o > nat > $o ) > $o ).
thf(func_def_324,type,
sK159: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_325,type,
sK160: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_326,type,
sK161: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_327,type,
sK162: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_328,type,
sK163: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_329,type,
sK164: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_330,type,
sK165: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_331,type,
sK166: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_332,type,
sK167: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_333,type,
sK168: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_334,type,
sK169: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_335,type,
sK170: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_336,type,
sK171: ( ( produc1572197287le_alt > $o ) > nat ) > produc1572197287le_alt > $o ).
thf(func_def_337,type,
sK172: ( ( produc1572197287le_alt > $o ) > nat ) > produc1572197287le_alt > $o ).
thf(func_def_338,type,
sK173: ( $o > nat ) > $o ).
thf(func_def_339,type,
sK174: ( $o > nat ) > $o ).
thf(func_def_340,type,
sK175: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_341,type,
sK176: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_342,type,
sK177: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_343,type,
sK178: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_344,type,
sK179: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_345,type,
sK180: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_346,type,
sK181: ( ( produc1572197287le_alt > $o ) > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > produc1572197287le_alt > $o ).
thf(func_def_347,type,
sK182: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ).
thf(func_def_348,type,
sK183: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(func_def_349,type,
sK184: ( produc1572197287le_alt > $o ) > ( produc1572197287le_alt > $o ) > produc1572197287le_alt ).
thf(func_def_350,type,
sK185: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > $o ) > arrow_1196572341e_indi ).
thf(func_def_351,type,
sK186: ( product_unit > $o ) > ( product_unit > $o ) > product_unit ).
thf(func_def_352,type,
sK187: ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > arrow_1389031998le_alt ).
thf(func_def_353,type,
sK188: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_354,type,
sK189: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_355,type,
sK190: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_356,type,
sK191: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_357,type,
sK192: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_358,type,
sK193: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_359,type,
sK194: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_360,type,
sK195: ( nat > nat > $o ) > nat ).
thf(func_def_361,type,
sK196: ( nat > nat > $o ) > nat ).
thf(func_def_362,type,
sK197: ( nat > product_unit > $o ) > nat ).
thf(func_def_363,type,
sK198: ( nat > product_unit > $o ) > nat ).
thf(func_def_364,type,
sK199: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_365,type,
sK200: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_366,type,
sK201: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_367,type,
sK202: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_368,type,
sK203: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_369,type,
sK204: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_370,type,
sK205: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_371,type,
sK206: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_372,type,
sK207: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_373,type,
sK208: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_374,type,
sK209: ( nat > $o ) > nat ).
thf(func_def_375,type,
sK210: ( nat > $o ) > nat ).
thf(func_def_376,type,
sK211: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_377,type,
sK212: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_378,type,
sK213: ( ( nat > $o ) > nat ) > nat > $o ).
thf(func_def_379,type,
sK214: ( ( nat > $o ) > nat ) > nat > $o ).
thf(func_def_380,type,
sK215: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_381,type,
sK216: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_382,type,
sK217: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_383,type,
sK218: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_384,type,
sK219: ( nat > nat > $o ) > nat ).
thf(func_def_385,type,
sK220: ( nat > nat > $o ) > nat ).
thf(func_def_386,type,
sK221: ( nat > product_unit > $o ) > nat ).
thf(func_def_387,type,
sK222: ( nat > product_unit > $o ) > nat ).
thf(func_def_388,type,
sK223: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_389,type,
sK224: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_390,type,
sK225: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_391,type,
sK226: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_392,type,
sK227: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_393,type,
sK228: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_394,type,
sK229: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_395,type,
sK230: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_396,type,
sK231: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_397,type,
sK232: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_398,type,
sK233: ( nat > $o ) > nat ).
thf(func_def_399,type,
sK234: ( nat > $o ) > nat ).
thf(func_def_400,type,
sK235: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_401,type,
sK236: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_402,type,
sK237: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_403,type,
sK238: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_404,type,
sK239: ( ( nat > $o ) > product_unit > $o ) > nat > $o ).
thf(func_def_405,type,
sK240: ( ( nat > $o ) > product_unit > $o ) > nat > $o ).
thf(func_def_406,type,
sK241: ( ( nat > $o ) > arrow_1196572341e_indi > $o ) > nat > $o ).
thf(func_def_407,type,
sK242: ( ( nat > $o ) > arrow_1196572341e_indi > $o ) > nat > $o ).
thf(func_def_408,type,
sK243: ( ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_409,type,
sK244: ( ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_410,type,
sK245: ( ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_411,type,
sK246: ( ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_412,type,
sK247: ( ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_413,type,
sK248: ( ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_414,type,
sK249: ( ( nat > $o ) > produc1572197287le_alt > $o ) > nat > $o ).
thf(func_def_415,type,
sK250: ( ( nat > $o ) > produc1572197287le_alt > $o ) > nat > $o ).
thf(func_def_416,type,
sK251: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_417,type,
sK252: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_418,type,
sK253: ( ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ).
thf(func_def_419,type,
sK254: ( ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ).
thf(func_def_420,type,
sK255: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_421,type,
sK256: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_422,type,
sK257: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_423,type,
sK258: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_424,type,
sK259: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_425,type,
sK260: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_426,type,
sK261: ( ( produc1572197287le_alt > $o ) > nat > $o ) > produc1572197287le_alt > $o ).
thf(func_def_427,type,
sK262: ( ( produc1572197287le_alt > $o ) > nat > $o ) > produc1572197287le_alt > $o ).
thf(func_def_428,type,
sK263: ( $o > nat > $o ) > $o ).
thf(func_def_429,type,
sK264: ( $o > nat > $o ) > $o ).
thf(func_def_430,type,
sK265: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_431,type,
sK266: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_432,type,
sK267: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_433,type,
sK268: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_434,type,
sK269: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_435,type,
sK270: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_436,type,
sK271: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_437,type,
sK272: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_438,type,
sK273: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_439,type,
sK274: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_440,type,
sK275: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_441,type,
sK276: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_442,type,
sK277: ( ( produc1572197287le_alt > $o ) > nat ) > produc1572197287le_alt > $o ).
thf(func_def_443,type,
sK278: ( ( produc1572197287le_alt > $o ) > nat ) > produc1572197287le_alt > $o ).
thf(func_def_444,type,
sK279: ( $o > nat ) > $o ).
thf(func_def_445,type,
sK280: ( $o > nat ) > $o ).
thf(func_def_446,type,
sK281: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_447,type,
sK282: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_448,type,
sK283: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_449,type,
sK284: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_450,type,
sK285: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_451,type,
sK286: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_452,type,
sK287: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_453,type,
sK288: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_454,type,
sK289: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_455,type,
sK290: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_456,type,
sK291: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_457,type,
sK292: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_458,type,
sK293: ( nat > nat > $o ) > nat ).
thf(func_def_459,type,
sK294: ( nat > nat > $o ) > nat ).
thf(func_def_460,type,
sK295: ( nat > product_unit > $o ) > nat ).
thf(func_def_461,type,
sK296: ( nat > product_unit > $o ) > nat ).
thf(func_def_462,type,
sK297: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_463,type,
sK298: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_464,type,
sK299: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_465,type,
sK300: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_466,type,
sK301: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_467,type,
sK302: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_468,type,
sK303: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_469,type,
sK304: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_470,type,
sK305: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_471,type,
sK306: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_472,type,
sK307: ( nat > $o ) > nat ).
thf(func_def_473,type,
sK308: ( nat > $o ) > nat ).
thf(func_def_474,type,
sK309: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_475,type,
sK310: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_476,type,
sK311: ( ( nat > $o ) > nat ) > nat > $o ).
thf(func_def_477,type,
sK312: ( ( nat > $o ) > nat ) > nat > $o ).
thf(func_def_478,type,
sK313: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_479,type,
sK314: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_480,type,
sK315: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_481,type,
sK316: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_482,type,
sK317: ( nat > nat > $o ) > nat ).
thf(func_def_483,type,
sK318: ( nat > nat > $o ) > nat ).
thf(func_def_484,type,
sK319: ( nat > product_unit > $o ) > nat ).
thf(func_def_485,type,
sK320: ( nat > product_unit > $o ) > nat ).
thf(func_def_486,type,
sK321: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_487,type,
sK322: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_488,type,
sK323: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_489,type,
sK324: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_490,type,
sK325: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_491,type,
sK326: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_492,type,
sK327: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_493,type,
sK328: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_494,type,
sK329: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_495,type,
sK330: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_496,type,
sK331: ( nat > $o ) > nat ).
thf(func_def_497,type,
sK332: ( nat > $o ) > nat ).
thf(func_def_498,type,
sK333: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_499,type,
sK334: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_500,type,
sK335: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_501,type,
sK336: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_502,type,
sK337: ( ( nat > $o ) > product_unit > $o ) > nat > $o ).
thf(func_def_503,type,
sK338: ( ( nat > $o ) > product_unit > $o ) > nat > $o ).
thf(func_def_504,type,
sK339: ( ( nat > $o ) > arrow_1196572341e_indi > $o ) > nat > $o ).
thf(func_def_505,type,
sK340: ( ( nat > $o ) > arrow_1196572341e_indi > $o ) > nat > $o ).
thf(func_def_506,type,
sK341: ( ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_507,type,
sK342: ( ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_508,type,
sK343: ( ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_509,type,
sK344: ( ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_510,type,
sK345: ( ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_511,type,
sK346: ( ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_512,type,
sK347: ( ( nat > $o ) > produc1572197287le_alt > $o ) > nat > $o ).
thf(func_def_513,type,
sK348: ( ( nat > $o ) > produc1572197287le_alt > $o ) > nat > $o ).
thf(func_def_514,type,
sK349: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_515,type,
sK350: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_516,type,
sK351: ( ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ).
thf(func_def_517,type,
sK352: ( ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ).
thf(func_def_518,type,
sK353: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_519,type,
sK354: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_520,type,
sK355: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_521,type,
sK356: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_522,type,
sK357: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_523,type,
sK358: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_524,type,
sK359: ( ( produc1572197287le_alt > $o ) > nat > $o ) > produc1572197287le_alt > $o ).
thf(func_def_525,type,
sK360: ( ( produc1572197287le_alt > $o ) > nat > $o ) > produc1572197287le_alt > $o ).
thf(func_def_526,type,
sK361: ( $o > nat > $o ) > $o ).
thf(func_def_527,type,
sK362: ( $o > nat > $o ) > $o ).
thf(func_def_528,type,
sK363: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_529,type,
sK364: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_530,type,
sK365: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_531,type,
sK366: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_532,type,
sK367: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_533,type,
sK368: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_534,type,
sK369: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_535,type,
sK370: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_536,type,
sK371: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_537,type,
sK372: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_538,type,
sK373: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_539,type,
sK374: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_540,type,
sK375: ( ( produc1572197287le_alt > $o ) > nat ) > produc1572197287le_alt > $o ).
thf(func_def_541,type,
sK376: ( ( produc1572197287le_alt > $o ) > nat ) > produc1572197287le_alt > $o ).
thf(func_def_542,type,
sK377: ( $o > nat ) > $o ).
thf(func_def_543,type,
sK378: ( $o > nat ) > $o ).
thf(func_def_544,type,
sK379: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_545,type,
sK380: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_546,type,
sK381: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_547,type,
sK382: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_548,type,
sK383: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_549,type,
sK384: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_550,type,
sK385: ( nat > nat > $o ) > nat ).
thf(func_def_551,type,
sK386: ( nat > nat > $o ) > nat ).
thf(func_def_552,type,
sK387: ( nat > product_unit > $o ) > nat ).
thf(func_def_553,type,
sK388: ( nat > product_unit > $o ) > nat ).
thf(func_def_554,type,
sK389: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_555,type,
sK390: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_556,type,
sK391: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_557,type,
sK392: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_558,type,
sK393: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_559,type,
sK394: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_560,type,
sK395: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_561,type,
sK396: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_562,type,
sK397: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_563,type,
sK398: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_564,type,
sK399: ( nat > $o ) > nat ).
thf(func_def_565,type,
sK400: ( nat > $o ) > nat ).
thf(func_def_566,type,
sK401: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_567,type,
sK402: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_568,type,
sK403: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_569,type,
sK404: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_570,type,
sK405: ( ( nat > $o ) > product_unit > $o ) > nat > $o ).
thf(func_def_571,type,
sK406: ( ( nat > $o ) > product_unit > $o ) > nat > $o ).
thf(func_def_572,type,
sK407: ( ( nat > $o ) > arrow_1196572341e_indi > $o ) > nat > $o ).
thf(func_def_573,type,
sK408: ( ( nat > $o ) > arrow_1196572341e_indi > $o ) > nat > $o ).
thf(func_def_574,type,
sK409: ( ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_575,type,
sK410: ( ( nat > $o ) > ( produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_576,type,
sK411: ( ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_577,type,
sK412: ( ( nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_578,type,
sK413: ( ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_579,type,
sK414: ( ( nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ).
thf(func_def_580,type,
sK415: ( ( nat > $o ) > produc1572197287le_alt > $o ) > nat > $o ).
thf(func_def_581,type,
sK416: ( ( nat > $o ) > produc1572197287le_alt > $o ) > nat > $o ).
thf(func_def_582,type,
sK417: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_583,type,
sK418: ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_584,type,
sK419: ( ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ).
thf(func_def_585,type,
sK420: ( ( nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ).
thf(func_def_586,type,
sK421: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_587,type,
sK422: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_588,type,
sK423: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_589,type,
sK424: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_590,type,
sK425: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_591,type,
sK426: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_592,type,
sK427: ( ( produc1572197287le_alt > $o ) > nat > $o ) > produc1572197287le_alt > $o ).
thf(func_def_593,type,
sK428: ( ( produc1572197287le_alt > $o ) > nat > $o ) > produc1572197287le_alt > $o ).
thf(func_def_594,type,
sK429: ( $o > nat > $o ) > $o ).
thf(func_def_595,type,
sK430: ( $o > nat > $o ) > $o ).
thf(func_def_596,type,
sK431: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_597,type,
sK432: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_598,type,
sK433: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_599,type,
sK434: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_600,type,
sK435: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_601,type,
sK436: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_602,type,
sK437: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_603,type,
sK438: ( ( ( produc1572197287le_alt > $o ) > $o ) > nat ) > ( produc1572197287le_alt > $o ) > $o ).
thf(func_def_604,type,
sK439: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_605,type,
sK440: ( ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ).
thf(func_def_606,type,
sK441: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_607,type,
sK442: ( ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(func_def_608,type,
sK443: ( ( produc1572197287le_alt > $o ) > nat ) > produc1572197287le_alt > $o ).
thf(func_def_609,type,
sK444: ( ( produc1572197287le_alt > $o ) > nat ) > produc1572197287le_alt > $o ).
thf(func_def_610,type,
sK445: ( $o > nat ) > $o ).
thf(func_def_611,type,
sK446: ( $o > nat ) > $o ).
thf(func_def_612,type,
sK447: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_613,type,
sK448: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_614,type,
sK449: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_615,type,
sK450: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_616,type,
sK451: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_617,type,
sK452: ( ( arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ) > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ).
thf(func_def_618,type,
sK453: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_619,type,
sK454: ( ( nat > $o ) > nat > $o ) > nat > $o ).
thf(func_def_620,type,
sK455: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_621,type,
sK456: ( ( product_unit > $o ) > nat > $o ) > product_unit > $o ).
thf(func_def_622,type,
sK457: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_623,type,
sK458: ( ( arrow_1196572341e_indi > $o ) > nat > $o ) > arrow_1196572341e_indi > $o ).
thf(func_def_624,type,
sK459: ( nat > nat > $o ) > nat ).
thf(func_def_625,type,
sK460: ( nat > nat > $o ) > nat ).
thf(func_def_626,type,
sK461: ( nat > product_unit > $o ) > nat ).
thf(func_def_627,type,
sK462: ( nat > product_unit > $o ) > nat ).
thf(func_def_628,type,
sK463: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_629,type,
sK464: ( nat > arrow_1196572341e_indi > $o ) > nat ).
thf(func_def_630,type,
sK465: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_631,type,
sK466: ( nat > ( produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_632,type,
sK467: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_633,type,
sK468: ( nat > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_634,type,
sK469: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_635,type,
sK470: ( nat > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > nat ).
thf(func_def_636,type,
sK471: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_637,type,
sK472: ( nat > produc1572197287le_alt > $o ) > nat ).
thf(func_def_638,type,
sK473: ( nat > $o ) > nat ).
thf(func_def_639,type,
sK474: ( nat > $o ) > nat ).
thf(func_def_640,type,
sK475: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_641,type,
sK476: ( nat > arrow_1389031998le_alt > arrow_1389031998le_alt > $o ) > nat ).
thf(func_def_642,type,
sK477: ( ( nat > $o ) > nat ) > nat > $o ).
thf(func_def_643,type,
sK478: ( ( nat > $o ) > nat ) > nat > $o ).
thf(func_def_644,type,
sK479: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_645,type,
sK480: ( ( product_unit > $o ) > nat ) > product_unit > $o ).
thf(func_def_646,type,
sK481: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_647,type,
sK482: ( ( arrow_1196572341e_indi > $o ) > nat ) > arrow_1196572341e_indi > $o ).
thf(func_def_648,type,
sK483: nat > nat > nat ).
thf(func_def_649,type,
sK484: ( nat > nat ) > nat ).
thf(func_def_650,type,
sK485: ( nat > nat ) > nat ).
thf(func_def_651,type,
sK486: ( nat > nat ) > nat ).
thf(func_def_652,type,
sK487: ( nat > nat ) > nat ).
thf(func_def_653,type,
sK488: produc1572197287le_alt > $o ).
thf(func_def_654,type,
sK489: nat > ( nat > $o ) > nat ).
thf(func_def_655,type,
sK490: ( nat > $o ) > nat ).
thf(func_def_656,type,
sK491: nat > ( nat > $o ) > nat ).
thf(func_def_657,type,
sK492: ( nat > $o ) > nat ).
thf(func_def_658,type,
sK493: ( nat > nat ) > nat ).
thf(func_def_659,type,
sK494: ( nat > $o ) > nat > nat ).
thf(func_def_660,type,
sK495: ( nat > $o ) > nat > nat ).
thf(func_def_661,type,
sK496: ( nat > $o ) > nat > nat ).
thf(func_def_662,type,
sK497: nat > nat > nat ).
thf(func_def_663,type,
sK498: nat > nat ).
thf(func_def_664,type,
sK499: nat > nat > nat ).
thf(func_def_665,type,
sK500: nat > nat > nat ).
thf(func_def_666,type,
sK501: nat > ( nat > $o ) > nat ).
thf(func_def_667,type,
sK502: nat > nat > nat ).
thf(func_def_668,type,
sK503: nat > nat ).
thf(func_def_669,type,
sK504: nat > nat ).
thf(func_def_670,type,
sK505: nat > nat > nat ).
thf(func_def_671,type,
sK506: nat > nat > nat ).
thf(func_def_672,type,
sK507: nat > nat ).
thf(func_def_673,type,
sK508: nat > nat ).
thf(func_def_674,type,
sK509: ( nat > $o ) > nat ).
thf(func_def_675,type,
sK510: ( nat > $o ) > nat ).
thf(func_def_676,type,
sK511: arrow_1196572341e_indi > nat ).
thf(func_def_677,type,
sK512: nat > ( nat > $o ) > nat ).
thf(func_def_678,type,
sK513: nat > ( nat > $o ) > nat ).
thf(func_def_679,type,
sK514: nat > ( nat > $o ) > nat ).
thf(func_def_680,type,
sK515: nat > ( nat > $o ) > nat ).
thf(func_def_681,type,
sK516: ( nat > nat ) > nat ).
thf(func_def_682,type,
sK517: ( nat > nat ) > nat ).
thf(func_def_683,type,
sK518: nat > ( nat > $o ) > nat ).
thf(func_def_684,type,
sK519: nat > ( nat > $o ) > nat ).
thf(func_def_685,type,
sK520: nat > ( nat > $o ) > nat ).
thf(func_def_686,type,
sK521: nat > ( nat > $o ) > nat ).
thf(func_def_687,type,
vNOT: $o > $o ).
thf(f14,axiom,
( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_556571452_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ X0 ) @ e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(f15,axiom,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_556571452_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ X0 ) @ e ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).
thf(f1204,conjecture,
member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f1205,negated_conjecture,
~ ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) ),
inference(negated_conjecture,[status(cth)],[f1204]) ).
thf(f1230,plain,
( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_556571452_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ X0 ) @ e ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f1231,plain,
( $true
= ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_556571452_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(fool_elimination,[],[f1230]) ).
thf(f1232,plain,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [X0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ X0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ X0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ X0 )
= n )
@ ( arrow_556571452_above @ ( p @ X0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ X0 ) @ e ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f1233,plain,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) )
= ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_556571452_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(fool_elimination,[],[f1232]) ).
thf(f3451,plain,
~ ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) ),
inference(rectify,[],[f1205]) ).
thf(f3452,plain,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) )
!= $true ),
inference(fool_elimination,[],[f3451]) ).
thf(f3585,plain,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) )
!= $true ),
inference(flattening,[],[f3452]) ).
thf(f5678,plain,
( $true
= ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_556571452_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(cnf_transformation,[],[f1231]) ).
thf(f5679,plain,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) )
= ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_556571452_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ),
inference(cnf_transformation,[],[f1233]) ).
thf(f7474,plain,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) )
!= $true ),
inference(cnf_transformation,[],[f3585]) ).
thf(f8005,plain,
( ( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d ) @ ( f @ p ) )
= $true )
| ( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_556571452_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ Y0 ) @ e ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f5679]) ).
thf(f8260,definition,
( spl522_39
<=> ( $true
= ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_556571452_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl522_39])],[avatar_definition]) ).
thf(f8262,plain,
( ( $true
= ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_556571452_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ Y0 ) @ e ) ) ) ) ) )
| ~ spl522_39 ),
inference(avatar_component_clause,[],[f8260]) ).
thf(f8268,plain,
( ( member285112084le_alt @ ( produc897867031le_alt @ c @ d )
@ ( f
@ ^ [Y0: arrow_1196572341e_indi] :
( if_Pro278423000_alt_o @ ( ord_less_nat @ ( h @ Y0 ) @ n ) @ ( arrow_1970123222_mktop @ ( p @ Y0 ) @ e )
@ ( if_Pro278423000_alt_o
@ ( ( h @ Y0 )
= n )
@ ( arrow_556571452_above @ ( p @ Y0 ) @ c @ e )
@ ( arrow_1821416136_mkbot @ ( p @ Y0 ) @ e ) ) ) ) )
= $false ),
inference(forward_subsumption_resolution,[],[f8005,f7474]) ).
thf(f8269,plain,
spl522_39,
inference(avatar_split_clause,[],[f5678,f8260]) ).
thf(f8345,plain,
( ( $true = $false )
| ~ spl522_39 ),
inference(forward_demodulation,[],[f8262,f8268]) ).
thf(f8346,plain,
( $false
| ~ spl522_39 ),
inference(trivial_inequality_removal,[],[f8345]) ).
thf(f8347,plain,
~ spl522_39,
inference(avatar_contradiction_clause,[],[f8346]) ).
cnf(s46,plain,
spl522_39,
inference(sat_conversion,[],[f8269]) ).
cnf(s52,plain,
~ spl522_39,
inference(sat_conversion,[],[f8347]) ).
cnf(s53,plain,
$false,
inference(rat,[],[s46,s52]) ).
thf(f8348,plain,
$false,
inference(avatar_sat_refutation,[],[s53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT171^3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:34:33 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.53/1.46 % (766083)Will run a generic schedule for satisfiability detection.
% 7.53/1.46 % (766089)% WARNING: option uhcvi not known.
% 7.53/1.46 % (766092)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2337077307:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 7.53/1.46 % (766089)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=921747827:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 7.53/1.46 % (766090)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1107838824:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 7.53/1.46 % (766088)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2837803466_2999 on theBenchmark for (2999ds/0Mi)
% 7.53/1.46 % (766093)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1478510160:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 7.53/1.46 % (766091)dis+10_1_sil=32000:sp=arity:random_seed=3083637671:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 7.53/1.46 % (766094)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1708151345:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 7.53/1.46 % (766092)Instruction limit reached!
% 7.53/1.46 % (766092)------------------------------
% 7.53/1.46 % (766092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766092)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766092)Termination reason: Instruction limit
% 7.53/1.46 % (766092)Termination phase: Property scanning
% 7.53/1.46 % (766092)Time elapsed: 0.025 s
% 7.53/1.46 % (766092)Peak memory usage: 13 MB
% 7.53/1.46 % (766092)Instructions burned: 120 (million)
% 7.53/1.46 % (766102)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2185766660:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 7.53/1.46 % (766093)Instruction limit reached!
% 7.53/1.46 % (766093)------------------------------
% 7.53/1.46 % (766093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766093)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766093)Termination reason: Instruction limit
% 7.53/1.46 % (766093)Termination phase: Property scanning
% 7.53/1.46 % (766093)Time elapsed: 0.056 s
% 7.53/1.46 % (766093)Peak memory usage: 13 MB
% 7.53/1.46 % (766093)Instructions burned: 132 (million)
% 7.53/1.46 % (766089)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.53/1.46 % (766091)Instruction limit reached!
% 7.53/1.46 % (766091)------------------------------
% 7.53/1.46 % (766091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766091)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766091)Termination reason: Instruction limit
% 7.53/1.46 % (766091)Termination phase: Initialization
% 7.53/1.46 % (766091)Time elapsed: 0.078 s
% 7.53/1.46 % (766091)Peak memory usage: 12 MB
% 7.53/1.46 % (766091)Instructions burned: 103 (million)
% 7.53/1.46 % (766104)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3704389765:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 7.53/1.46 % (766105)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1912853490:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 7.53/1.46 % Exception at run slice level
% 7.53/1.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.53/1.46 % (766108)ott-21_1_sil=16000:fs=off:random_seed=2174212169:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 7.53/1.46 % (766094)Instruction limit reached!
% 7.53/1.46 % (766094)------------------------------
% 7.53/1.46 % (766094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766094)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766094)Termination reason: Instruction limit
% 7.53/1.46 % (766094)Termination phase: Property scanning
% 7.53/1.46 % (766094)Time elapsed: 0.123 s
% 7.53/1.46 % (766094)Peak memory usage: 13 MB
% 7.53/1.46 % (766094)Instructions burned: 160 (million)
% 7.53/1.46 % (766110)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1646602030:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 7.53/1.46 % (766089)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.53/1.46 % Exception at run slice level
% 7.53/1.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.53/1.46 % (766112)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2984850327:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 7.53/1.46 % (766104)Instruction limit reached!
% 7.53/1.46 % (766104)------------------------------
% 7.53/1.46 % (766104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766104)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766104)Termination reason: Instruction limit
% 7.53/1.46 % (766104)Termination phase: Property scanning
% 7.53/1.46 % (766104)Time elapsed: 0.100 s
% 7.53/1.46 % (766104)Peak memory usage: 12 MB
% 7.53/1.46 % (766104)Instructions burned: 132 (million)
% 7.53/1.46 % (766114)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3592568211:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 7.53/1.46 % (766105)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.53/1.46 % (766108)Instruction limit reached!
% 7.53/1.46 % (766108)------------------------------
% 7.53/1.46 % (766108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766108)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766108)Termination reason: Instruction limit
% 7.53/1.46 % (766108)Termination phase: Naming
% 7.53/1.46 % (766108)Time elapsed: 0.104 s
% 7.53/1.46 % (766108)Peak memory usage: 14 MB
% 7.53/1.46 % (766108)Instructions burned: 181 (million)
% 7.53/1.46 % (766116)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=972448473:i=889:ins=1_2996 on theBenchmark for (2996ds/889Mi)
% 7.53/1.46 % Exception at run slice level
% 7.53/1.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.53/1.46 % (766118)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=4090192748:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2995 on theBenchmark for (2995ds/692Mi)
% 7.53/1.46 % (766105)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.53/1.46 % (766110)Instruction limit reached!
% 7.53/1.46 % (766110)------------------------------
% 7.53/1.46 % (766110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766110)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766110)Termination reason: Instruction limit
% 7.53/1.46 % (766110)Termination phase: Saturation
% 7.53/1.46 % (766110)Time elapsed: 0.252 s
% 7.53/1.46 % (766110)Peak memory usage: 17 MB
% 7.53/1.46 % (766110)Instructions burned: 477 (million)
% 7.53/1.46 % (766120)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=174321325:i=879:kws=inv_precedence:fsr=off_2995 on theBenchmark for (2995ds/879Mi)
% 7.53/1.46 % (766118)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.53/1.46 % Exception at run slice level
% 7.53/1.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.53/1.46 % (766114)Instruction limit reached!
% 7.53/1.46 % (766114)------------------------------
% 7.53/1.46 % (766114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766114)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766114)Termination reason: Instruction limit
% 7.53/1.46 % (766114)Termination phase: Saturation
% 7.53/1.46 % (766114)Time elapsed: 0.284 s
% 7.53/1.46 % (766114)Peak memory usage: 21 MB
% 7.53/1.46 % (766114)Instructions burned: 1181 (million)
% 7.53/1.46 % (766122)fmb+10_1_sil=64000:random_seed=862480176:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 7.53/1.46 % (766123)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=134877386:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 7.53/1.46 % (766120)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.53/1.46 % Exception at run slice level
% 7.53/1.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.53/1.46 % (766105)Instruction limit reached!
% 7.53/1.46 % (766105)------------------------------
% 7.53/1.46 % (766105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766105)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766105)Termination reason: Instruction limit
% 7.53/1.46 % (766105)Termination phase: Saturation
% 7.53/1.46 % (766105)Time elapsed: 0.504 s
% 7.53/1.46 % (766105)Peak memory usage: 18 MB
% 7.53/1.46 % (766105)Instructions burned: 684 (million)
% 7.53/1.46 % (766128)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2811595736:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 7.53/1.46 % (766127)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3861691090:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 7.53/1.46 % (766122)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.53/1.46 % (766128)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.53/1.46 % Exception at run slice level
% 7.53/1.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.53/1.46 % (766118)Instruction limit reached!
% 7.53/1.46 % (766118)------------------------------
% 7.53/1.46 % (766118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766118)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766118)Termination reason: Instruction limit
% 7.53/1.46 % (766118)Termination phase: Saturation
% 7.53/1.46 % (766118)Time elapsed: 0.313 s
% 7.53/1.46 % (766118)Peak memory usage: 20 MB
% 7.53/1.46 % (766118)Instructions burned: 692 (million)
% 7.53/1.46 % (766131)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1258297302:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 7.53/1.46 % (766132)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2962501661:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 7.53/1.46 % (766120)Instruction limit reached!
% 7.53/1.46 % (766120)------------------------------
% 7.53/1.46 % (766120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.46 % (766120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.46 % (766120)CaDiCaL version: 2.1.3
% 7.53/1.46 % (766120)Termination reason: Instruction limit
% 7.53/1.46 % (766120)Termination phase: Saturation
% 7.53/1.46 % (766120)Time elapsed: 0.389 s
% 7.53/1.46 % (766120)Peak memory usage: 21 MB
% 7.53/1.46 % (766120)Instructions burned: 880 (million)
% 7.53/1.46 % (766135)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=368632538:fmbsr=2.30978:i=2174_2991 on theBenchmark for (2991ds/2174Mi)
% 7.53/1.46 % Exception at run slice level
% 7.53/1.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.53/1.46 % (766137)ott-2_1_sil=16000:newcnf=on:random_seed=2852733836:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2990 on theBenchmark for (2990ds/869Mi)
% 7.53/1.46 % Exception at run slice level
% 7.53/1.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.53/1.46 % (766131)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.53/1.46 % (766137)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.53/1.46 % (766139)ott+10_1_sil=32000:tgt=ground:random_seed=418790047:i=5114:av=off_2989 on theBenchmark for (2989ds/5114Mi)
% 7.53/1.46 % Exception at run slice level
% 7.53/1.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.53/1.46 % (766131)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.53/1.46 % (766141)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2167425292:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 7.53/1.46 % (766137) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-766083-766137"...
% 7.53/1.46 % (766137)...printing done.
% 7.53/1.46 % (766137)Refutation found. Thanks to Tanya!
% 7.53/1.46 % SZS status Theorem for theBenchmark
% 7.53/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 7.53/1.47 % (766137)------------------------------
% 7.53/1.47 % (766137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.47 % (766137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.47 % (766137)CaDiCaL version: 2.1.3
% 7.53/1.47 % (766137)Termination reason: Refutation
% 7.53/1.47 % (766137)Time elapsed: 0.282 s
% 7.53/1.47 % (766137)Peak memory usage: 19 MB
% 7.53/1.47 % (766137)Instructions burned: 658 (million)
% 7.53/1.47 % (766083)Success in time 1.249 s
% 7.53/1.47 % Vampire exiting
%------------------------------------------------------------------------------