%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP178^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 08:11:00 AM UTC 2026
% Result : Theorem 7.29s 1.45s
% Output : Refutation 7.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 102 ( 37 unt; 0 typ; 5 def)
% Number of atoms : 396 ( 128 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 2643 ( 85 ~; 80 |; 21 &;2416 @)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 42 ( 41 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 473 ( 468 usr; 26 con; 0-6 aty)
% ( 10 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 122 ( 0 sgn 94 !; 2 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr2123625671_a_nat: $tType ).
thf(type_def_6,type,
produc116665063_a_nat: $tType ).
thf(type_def_7,type,
set_Pr924198087_a_nat: $tType ).
thf(type_def_8,type,
produc398057191_a_nat: $tType ).
thf(type_def_9,type,
set_Pr1173424071_b_nat: $tType ).
thf(type_def_10,type,
set_Pr1839611079term_b: $tType ).
thf(type_def_11,type,
produc446386919_b_nat: $tType ).
thf(type_def_12,type,
produc1116408039term_b: $tType ).
thf(type_def_13,type,
set_Pr1987088711_a_nat: $tType ).
thf(type_def_14,type,
set_Pr665622551at_nat: $tType ).
thf(type_def_15,type,
produc1871334759_a_nat: $tType ).
thf(type_def_16,type,
produc1391440311at_nat: $tType ).
thf(type_def_17,type,
set_Pr551076371_b_nat: $tType ).
thf(type_def_18,type,
set_Pr1647387645at_nat: $tType ).
thf(type_def_19,type,
set_Pr1490359111at_nat: $tType ).
thf(type_def_20,type,
set_Pr1163220871term_b: $tType ).
thf(type_def_21,type,
set_Pr2041158302at_nat: $tType ).
thf(type_def_22,type,
produc1235635379_b_nat: $tType ).
thf(type_def_23,type,
produc842455143at_nat: $tType ).
thf(type_def_24,type,
produc1478835367term_b: $tType ).
thf(type_def_25,type,
set_la1083530965_a_nat: $tType ).
thf(type_def_26,type,
labele935650037_a_nat: $tType ).
thf(type_def_27,type,
labele1835409643at_nat: $tType ).
thf(type_def_28,type,
set_Pr9961929at_nat: $tType ).
thf(type_def_29,type,
allego510293162tant_a: $tType ).
thf(type_def_30,type,
allego1565409692at_nat: $tType ).
thf(type_def_31,type,
set_la1976028319_b_nat: $tType ).
thf(type_def_32,type,
set_St761939237tant_a: $tType ).
thf(type_def_33,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_34,type,
set_al1193902458term_b: $tType ).
thf(type_def_35,type,
labeled_graph_b_nat: $tType ).
thf(type_def_36,type,
set_Product_prod_b_b: $tType ).
thf(type_def_37,type,
standard_Constant_a: $tType ).
thf(type_def_38,type,
product_prod_nat_nat: $tType ).
thf(type_def_39,type,
allegorical_term_b: $tType ).
thf(type_def_40,type,
set_nat: $tType ).
thf(type_def_41,type,
itself_nat: $tType ).
thf(type_def_42,type,
set_b: $tType ).
thf(type_def_43,type,
set_a: $tType ).
thf(type_def_44,type,
nat: $tType ).
thf(type_def_45,type,
b: $tType ).
thf(type_def_46,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_1,type,
finite1242387294at_nat: set_Pr1647387645at_nat > $o ).
thf(func_def_2,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_3,type,
finite48957584at_nat: set_Pr1490359111at_nat > $o ).
thf(func_def_4,type,
finite1987068434at_nat: set_Pr9961929at_nat > $o ).
thf(func_def_5,type,
finite1015599120od_b_b: set_Product_prod_b_b > $o ).
thf(func_def_6,type,
finite_finite_b: set_b > $o ).
thf(func_def_7,type,
allego745587551tant_a: allego510293162tant_a > allego510293162tant_a > allego510293162tant_a ).
thf(func_def_8,type,
allego266765201at_nat: allego1565409692at_nat > allego1565409692at_nat > allego1565409692at_nat ).
thf(func_def_9,type,
allegorical_A_Int_b: allegorical_term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_10,type,
semantics_b_nat: labeled_graph_b_nat > allegorical_term_b > set_Pr1986765409at_nat ).
thf(func_def_11,type,
graph_2130075512at_nat: labele935650037_a_nat > labele935650037_a_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_12,type,
graph_2111906684at_nat: labele1835409643at_nat > labele1835409643at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_13,type,
graph_529870330at_nat: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_14,type,
graph_union_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_15,type,
labeled_LG_b_nat: set_Pr9961929at_nat > set_nat > labeled_graph_b_nat ).
thf(func_def_16,type,
labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat ).
thf(func_def_17,type,
labele2032268018at_nat: labele1835409643at_nat > set_Pr1490359111at_nat ).
thf(func_def_18,type,
labeled_edges_b_nat: labeled_graph_b_nat > set_Pr9961929at_nat ).
thf(func_def_19,type,
labele1810595089_a_nat: labele935650037_a_nat > set_nat ).
thf(func_def_20,type,
labele560327297at_nat: labele1835409643at_nat > set_nat ).
thf(func_def_21,type,
labele460410879_b_nat: labeled_graph_b_nat > set_nat ).
thf(func_def_22,type,
restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_23,type,
restri321299017at_nat: labele1835409643at_nat > labele1835409643at_nat ).
thf(func_def_24,type,
restrict_b_nat: labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_25,type,
unival1191217828term_b: set_Pr1163220871term_b > $o ).
thf(func_def_26,type,
unival1637751524_a_nat: set_Pr1987088711_a_nat > $o ).
thf(func_def_27,type,
unival857119480_b_nat: set_Pr551076371_b_nat > $o ).
thf(func_def_28,type,
univalent_nat_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_29,type,
unival633212949at_nat: set_Pr2041158302at_nat > $o ).
thf(func_def_30,type,
unival989235430at_nat: set_Pr9961929at_nat > $o ).
thf(func_def_31,type,
bot_bo1024461546_nat_o: produc1871334759_a_nat > $o ).
thf(func_def_32,type,
bot_bot_nat: nat ).
thf(func_def_33,type,
bot_bot_set_nat: set_nat ).
thf(func_def_34,type,
bot_bo1836341171_a_nat: set_Pr1987088711_a_nat ).
thf(func_def_35,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(func_def_36,type,
bot_bo1626616373at_nat: set_Pr9961929at_nat ).
thf(func_def_37,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_38,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_39,type,
ord_le138473255term_b: set_Pr1163220871term_b > set_Pr1163220871term_b > $o ).
thf(func_def_40,type,
ord_le1718765799_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > $o ).
thf(func_def_41,type,
ord_le13035955_b_nat: set_Pr551076371_b_nat > set_Pr551076371_b_nat > $o ).
thf(func_def_42,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_43,type,
ord_le910748009at_nat: set_Pr9961929at_nat > set_Pr9961929at_nat > $o ).
thf(func_def_44,type,
produc1990145943term_b: allegorical_term_b > allegorical_term_b > produc1478835367term_b ).
thf(func_def_45,type,
produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat ).
thf(func_def_46,type,
produc590202991at_nat: labele1835409643at_nat > labele1835409643at_nat > produc1391440311at_nat ).
thf(func_def_47,type,
produc951298923_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat ).
thf(func_def_48,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_49,type,
produc859843415term_b: produc1478835367term_b > produc1478835367term_b > produc1116408039term_b ).
thf(func_def_50,type,
produc1677124439_a_nat: produc1871334759_a_nat > produc1871334759_a_nat > produc398057191_a_nat ).
thf(func_def_51,type,
produc1754969175_b_nat: produc1235635379_b_nat > produc1235635379_b_nat > produc446386919_b_nat ).
thf(func_def_52,type,
produc1168807639at_nat: product_prod_nat_nat > product_prod_nat_nat > produc842455143at_nat ).
thf(func_def_53,type,
produc170611543_a_nat: produc398057191_a_nat > produc398057191_a_nat > produc116665063_a_nat ).
thf(func_def_54,type,
produc854192515term_b: produc1478835367term_b > allegorical_term_b ).
thf(func_def_55,type,
produc719117507_a_nat: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_56,type,
produc1995789403at_nat: produc1391440311at_nat > labele1835409643at_nat ).
thf(func_def_57,type,
produc1542243159_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_58,type,
product_fst_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_59,type,
produc1049080131_a_nat: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_60,type,
produc1223098053term_b: produc1478835367term_b > allegorical_term_b ).
thf(func_def_61,type,
produc880161797_a_nat: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_62,type,
produc1564126365at_nat: produc1391440311at_nat > labele1835409643at_nat ).
thf(func_def_63,type,
produc194497945_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_64,type,
product_snd_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_65,type,
produc1022852229_a_nat: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_66,type,
domain859272460term_b: set_Pr1163220871term_b > set_al1193902458term_b ).
thf(func_def_67,type,
domain1068567884_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat ).
thf(func_def_68,type,
domain767519072_b_nat: set_Pr551076371_b_nat > set_la1976028319_b_nat ).
thf(func_def_69,type,
domain_nat_nat: set_Pr1986765409at_nat > set_nat ).
thf(func_def_70,type,
domain1101989710at_nat: set_Pr9961929at_nat > set_b ).
thf(func_def_71,type,
id_on_1536886967term_b: set_al1193902458term_b > set_Pr1163220871term_b ).
thf(func_def_72,type,
id_on_689842066_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_73,type,
id_on_583275916_b_nat: set_la1976028319_b_nat > set_Pr551076371_b_nat ).
thf(func_def_74,type,
id_on_nat: set_nat > set_Pr1986765409at_nat ).
thf(func_def_75,type,
id_on_1664915780term_b: set_Pr1163220871term_b > set_Pr1839611079term_b ).
thf(func_def_76,type,
id_on_1651096324_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat ).
thf(func_def_77,type,
id_on_138931664_b_nat: set_Pr551076371_b_nat > set_Pr1173424071_b_nat ).
thf(func_def_78,type,
id_on_2144791838at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat ).
thf(func_def_79,type,
id_on_1395957380_a_nat: set_Pr924198087_a_nat > set_Pr2123625671_a_nat ).
thf(func_def_80,type,
image_329221075term_b: set_Pr1163220871term_b > set_al1193902458term_b > set_al1193902458term_b ).
thf(func_def_81,type,
image_1971191571_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).
thf(func_def_82,type,
image_1183964583_b_nat: set_Pr551076371_b_nat > set_la1976028319_b_nat > set_la1976028319_b_nat ).
thf(func_def_83,type,
image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat ).
thf(func_def_84,type,
image_1168831379_a_nat: set_Pr924198087_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_85,type,
image_1356842150at_nat: set_Pr2041158302at_nat > set_Pr9961929at_nat > set_nat ).
thf(func_def_86,type,
image_2112855445at_nat: set_Pr9961929at_nat > set_b > set_Pr1986765409at_nat ).
thf(func_def_87,type,
relcom1955155673term_b: set_Pr1163220871term_b > set_Pr1163220871term_b > set_Pr1163220871term_b ).
thf(func_def_88,type,
relcom1338300020_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_89,type,
relcom1426860350_b_nat: set_Pr551076371_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat ).
thf(func_def_90,type,
relcomp_nat_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_91,type,
relcom195261566at_nat: set_Pr9961929at_nat > set_Pr1490359111at_nat > set_Pr9961929at_nat ).
thf(func_def_92,type,
relcom14055552at_nat: set_Product_prod_b_b > set_Pr9961929at_nat > set_Pr9961929at_nat ).
thf(func_def_93,type,
inv_translation: set_nat > $o ).
thf(func_def_94,type,
transl1275713022tant_a: allego510293162tant_a > labele935650037_a_nat ).
thf(func_def_95,type,
transl490985778at_nat: allego1565409692at_nat > labele1835409643at_nat ).
thf(func_def_96,type,
translation_b: allegorical_term_b > labeled_graph_b_nat ).
thf(func_def_97,type,
agree_on_b_nat_nat: labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_98,type,
chain_b_nat: ( nat > labeled_graph_b_nat ) > $o ).
thf(func_def_99,type,
chain_sup_b_nat: ( nat > labeled_graph_b_nat ) > labeled_graph_b_nat ).
thf(func_def_100,type,
conseq1730780375at_nat: set_Pr551076371_b_nat > labeled_graph_b_nat > $o ).
thf(func_def_101,type,
extensible_b_nat_nat: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_102,type,
fair_chain_b_nat_nat: set_Pr551076371_b_nat > ( nat > labeled_graph_b_nat ) > $o ).
thf(func_def_103,type,
fin_ma971967913at_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o ).
thf(func_def_104,type,
maintained_b_nat_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o ).
thf(func_def_105,type,
set_of1384085797_a_nat: set_Pr1987088711_a_nat > $o ).
thf(func_def_106,type,
set_of195930477at_nat: set_Pr665622551at_nat > $o ).
thf(func_def_107,type,
set_of41538795_b_nat: set_Pr551076371_b_nat > $o ).
thf(func_def_108,type,
weak_u2026406106at_nat: itself_nat > produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_109,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_110,type,
collec135640594term_b: ( produc1478835367term_b > $o ) > set_Pr1163220871term_b ).
thf(func_def_111,type,
collec357096914_a_nat: ( produc1871334759_a_nat > $o ) > set_Pr1987088711_a_nat ).
thf(func_def_112,type,
collec1615000990_b_nat: ( produc1235635379_b_nat > $o ) > set_Pr551076371_b_nat ).
thf(func_def_113,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_114,type,
collec1701899602_a_nat: ( produc398057191_a_nat > $o ) > set_Pr924198087_a_nat ).
thf(func_def_115,type,
standa1897115818ules_a: set_a > set_Pr1987088711_a_nat ).
thf(func_def_116,type,
standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat ).
thf(func_def_117,type,
standa1410829644tant_a: produc1871334759_a_nat ).
thf(func_def_118,type,
standa214789732at_nat: produc1391440311at_nat ).
thf(func_def_119,type,
standa879863266rule_b: produc1235635379_b_nat ).
thf(func_def_120,type,
standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_121,type,
standa2131591247at_nat: product_prod_nat_nat > produc1391440311at_nat ).
thf(func_def_122,type,
standa1329480013rule_b: b > produc1235635379_b_nat ).
thf(func_def_123,type,
standa305748545tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_124,type,
standa153097263at_nat: product_prod_nat_nat > produc1391440311at_nat ).
thf(func_def_125,type,
standa1360217389rule_b: b > produc1235635379_b_nat ).
thf(func_def_126,type,
member93680451term_b: allegorical_term_b > set_al1193902458term_b > $o ).
thf(func_def_127,type,
member964390942_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > $o ).
thf(func_def_128,type,
member1483953152_b_nat: labeled_graph_b_nat > set_la1976028319_b_nat > $o ).
thf(func_def_129,type,
member_nat: nat > set_nat > $o ).
thf(func_def_130,type,
member516522448term_b: produc1478835367term_b > set_Pr1163220871term_b > $o ).
thf(func_def_131,type,
member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).
thf(func_def_132,type,
member1129678944at_nat: produc1391440311at_nat > set_Pr665622551at_nat > $o ).
thf(func_def_133,type,
member963855452_b_nat: produc1235635379_b_nat > set_Pr551076371_b_nat > $o ).
thf(func_def_134,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_135,type,
member1449757456term_b: produc1116408039term_b > set_Pr1839611079term_b > $o ).
thf(func_def_136,type,
member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).
thf(func_def_137,type,
member889223696_b_nat: produc446386919_b_nat > set_Pr1173424071_b_nat > $o ).
thf(func_def_138,type,
member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_139,type,
member829905680_a_nat: produc116665063_a_nat > set_Pr2123625671_a_nat > $o ).
thf(func_def_140,type,
c: set_a ).
thf(func_def_141,type,
u: allegorical_term_b ).
thf(func_def_142,type,
v: allegorical_term_b ).
thf(func_def_143,type,
x: produc1871334759_a_nat ).
thf(func_def_147,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_148,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_149,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_150,type,
vAND: $o > $o > $o ).
thf(func_def_151,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_152,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_153,type,
vIMP: $o > $o > $o ).
thf(func_def_154,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_155,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_156,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_157,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_158,type,
vNOT: $o > $o ).
thf(func_def_159,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_160,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_161,type,
sP0: produc1235635379_b_nat > labeled_graph_b_nat > $o ).
thf(func_def_162,type,
sP1: produc1871334759_a_nat > $o ).
thf(func_def_163,type,
sP2: produc1235635379_b_nat > $o ).
thf(func_def_164,type,
sP3: produc1871334759_a_nat > $o ).
thf(func_def_165,type,
sP4: produc1235635379_b_nat > $o ).
thf(func_def_166,type,
sP5: produc1871334759_a_nat > $o ).
thf(func_def_167,type,
sP6: set_Pr551076371_b_nat > labeled_graph_b_nat > $o ).
thf(func_def_168,type,
sP7: set_Pr551076371_b_nat > ( nat > labeled_graph_b_nat ) > $o ).
thf(func_def_169,type,
sP8: nat > set_nat > $o ).
thf(func_def_170,type,
sP9: nat > set_nat > $o ).
thf(func_def_171,type,
sP10: ( nat > nat > $o ) > $o ).
thf(func_def_172,type,
sP11: nat > nat > nat > $o ).
thf(func_def_173,type,
sP12: nat > nat > nat > $o ).
thf(func_def_174,type,
sP13: nat > nat > nat > $o ).
thf(func_def_175,type,
sP14: nat > nat > nat > $o ).
thf(func_def_176,type,
sP15: nat > nat > nat > $o ).
thf(func_def_177,type,
sP16: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > $o ).
thf(func_def_178,type,
sP17: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > ( labele935650037_a_nat > labele935650037_a_nat > $o ) > $o ).
thf(func_def_179,type,
sP18: set_Pr551076371_b_nat > set_Pr551076371_b_nat > ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > $o ).
thf(func_def_180,type,
sP19: set_Pr1163220871term_b > set_Pr1163220871term_b > ( allegorical_term_b > allegorical_term_b > $o ) > $o ).
thf(func_def_181,type,
sP20: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > $o ).
thf(func_def_182,type,
sP21: produc1235635379_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat > $o ).
thf(func_def_183,type,
sP22: produc1478835367term_b > set_Pr1163220871term_b > set_Pr1163220871term_b > $o ).
thf(func_def_184,type,
sP23: ( nat > $o ) > nat > $o ).
thf(func_def_185,type,
sK24: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_186,type,
sK25: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_187,type,
sK26: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_188,type,
sK27: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_189,type,
sK28: ( produc1871334759_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_190,type,
sK29: ( produc1871334759_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_191,type,
sK30: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_192,type,
sK31: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_193,type,
sK32: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_194,type,
sK33: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_195,type,
sK34: product_prod_nat_nat > nat ).
thf(func_def_196,type,
sK35: product_prod_nat_nat > nat ).
thf(func_def_197,type,
sK36: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_198,type,
sK37: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_199,type,
sK38: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_200,type,
sK39: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_201,type,
sK40: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_202,type,
sK41: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_203,type,
sK42: produc1478835367term_b > allegorical_term_b ).
thf(func_def_204,type,
sK43: produc1478835367term_b > allegorical_term_b ).
thf(func_def_205,type,
sK44: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_206,type,
sK45: ( produc398057191_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_207,type,
sK46: ( produc398057191_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_208,type,
sK47: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_209,type,
sK48: produc398057191_a_nat > labele935650037_a_nat ).
thf(func_def_210,type,
sK49: produc398057191_a_nat > labele935650037_a_nat ).
thf(func_def_211,type,
sK50: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_212,type,
sK51: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_213,type,
sK52: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_214,type,
sK53: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_215,type,
sK54: ( produc1871334759_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_216,type,
sK55: ( produc1871334759_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_217,type,
sK56: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_218,type,
sK57: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_219,type,
sK58: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_220,type,
sK59: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_221,type,
sK60: product_prod_nat_nat > nat ).
thf(func_def_222,type,
sK61: product_prod_nat_nat > nat ).
thf(func_def_223,type,
sK62: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_224,type,
sK63: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_225,type,
sK64: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_226,type,
sK65: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_227,type,
sK66: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_228,type,
sK67: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_229,type,
sK68: produc1478835367term_b > allegorical_term_b ).
thf(func_def_230,type,
sK69: produc1478835367term_b > allegorical_term_b ).
thf(func_def_231,type,
sK70: ( produc1871334759_a_nat > $o ) > ( produc1871334759_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_232,type,
sK71: produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_233,type,
sK72: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_234,type,
sK73: ( allegorical_term_b > allegorical_term_b > $o ) > allegorical_term_b ).
thf(func_def_235,type,
sK74: ( allegorical_term_b > allegorical_term_b > $o ) > allegorical_term_b ).
thf(func_def_236,type,
sK75: ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_237,type,
sK76: ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_238,type,
sK77: set_Pr1987088711_a_nat > produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_239,type,
sK78: set_la1083530965_a_nat > produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_240,type,
sK79: set_nat > product_prod_nat_nat > nat ).
thf(func_def_241,type,
sK80: set_la1976028319_b_nat > produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_242,type,
sK81: set_al1193902458term_b > produc1478835367term_b > allegorical_term_b ).
thf(func_def_243,type,
sK82: set_Pr1986765409at_nat > produc1235635379_b_nat > ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_244,type,
sK83: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_245,type,
sK84: set_Pr551076371_b_nat > labeled_graph_b_nat > produc1235635379_b_nat ).
thf(func_def_246,type,
sK85: set_Pr551076371_b_nat > produc1235635379_b_nat ).
thf(func_def_247,type,
sK86: set_Pr551076371_b_nat > ( nat > labeled_graph_b_nat ) > produc1235635379_b_nat ).
thf(func_def_248,type,
sK87: set_Pr551076371_b_nat > ( nat > labeled_graph_b_nat ) > set_Pr1986765409at_nat ).
thf(func_def_249,type,
sK88: set_Pr551076371_b_nat > ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_250,type,
sK89: set_Pr1986765409at_nat > set_nat > set_Pr9961929at_nat > ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_251,type,
sK90: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_252,type,
sK91: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_253,type,
sK92: set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_254,type,
sK93: set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_255,type,
sK94: set_Pr1163220871term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_256,type,
sK95: set_Pr1163220871term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_257,type,
sK96: nat > set_nat > nat ).
thf(func_def_258,type,
sK97: nat > set_nat > nat ).
thf(func_def_259,type,
sK98: set_Pr1986765409at_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_260,type,
sK99: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_261,type,
sK100: ( nat > nat > $o ) > nat ).
thf(func_def_262,type,
sK101: ( nat > nat > $o ) > nat ).
thf(func_def_263,type,
sK102: ( nat > nat > $o ) > nat ).
thf(func_def_264,type,
sK103: ( nat > nat > $o ) > nat ).
thf(func_def_265,type,
sK104: ( nat > nat ) > nat ).
thf(func_def_266,type,
sK105: ( nat > nat ) > nat ).
thf(func_def_267,type,
sK106: ( nat > nat ) > nat ).
thf(func_def_268,type,
sK107: ( nat > nat ) > nat ).
thf(func_def_269,type,
sK108: ( nat > nat ) > nat ).
thf(func_def_270,type,
sK109: ( nat > nat ) > nat ).
thf(func_def_271,type,
sK110: ( nat > nat ) > nat ).
thf(func_def_272,type,
sK111: ( nat > nat ) > nat ).
thf(func_def_273,type,
sK112: set_Pr1986765409at_nat > labeled_graph_b_nat > produc1235635379_b_nat > set_Pr1986765409at_nat ).
thf(func_def_274,type,
sK113: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_275,type,
sK114: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_276,type,
sK115: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_277,type,
sK116: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > ( labele935650037_a_nat > labele935650037_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_278,type,
sK117: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > ( labele935650037_a_nat > labele935650037_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_279,type,
sK118: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > ( labele935650037_a_nat > labele935650037_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_280,type,
sK119: set_Pr551076371_b_nat > set_Pr551076371_b_nat > ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_281,type,
sK120: set_Pr551076371_b_nat > set_Pr551076371_b_nat > ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_282,type,
sK121: set_Pr551076371_b_nat > set_Pr551076371_b_nat > ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_283,type,
sK122: set_Pr1163220871term_b > set_Pr1163220871term_b > ( allegorical_term_b > allegorical_term_b > $o ) > allegorical_term_b ).
thf(func_def_284,type,
sK123: set_Pr1163220871term_b > set_Pr1163220871term_b > ( allegorical_term_b > allegorical_term_b > $o ) > allegorical_term_b ).
thf(func_def_285,type,
sK124: set_Pr1163220871term_b > set_Pr1163220871term_b > ( allegorical_term_b > allegorical_term_b > $o ) > allegorical_term_b ).
thf(func_def_286,type,
sK125: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_287,type,
sK126: set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_288,type,
sK127: set_Pr1163220871term_b > set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_289,type,
sK128: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_290,type,
sK129: set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_291,type,
sK130: set_Pr1163220871term_b > set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_292,type,
sK131: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_293,type,
sK132: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_294,type,
sK133: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_295,type,
sK134: produc1235635379_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_296,type,
sK135: produc1235635379_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_297,type,
sK136: produc1235635379_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_298,type,
sK137: produc1478835367term_b > set_Pr1163220871term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_299,type,
sK138: produc1478835367term_b > set_Pr1163220871term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_300,type,
sK139: produc1478835367term_b > set_Pr1163220871term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_301,type,
sK140: set_nat > nat ).
thf(func_def_302,type,
sK141: set_nat > nat ).
thf(func_def_303,type,
sK142: ( nat > $o ) > nat > nat ).
thf(func_def_304,type,
sK143: ( nat > $o ) > nat ).
thf(func_def_305,type,
sK144: set_Pr1986765409at_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_306,type,
sK145: set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_307,type,
sK146: set_Pr1986765409at_nat > set_nat > ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_308,type,
sK147: set_Pr2041158302at_nat > set_Pr9961929at_nat > ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_309,type,
sK148: ( labele935650037_a_nat > $o ) > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_310,type,
sK149: ( labele935650037_a_nat > $o ) > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_311,type,
sK150: ( labeled_graph_b_nat > $o ) > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_312,type,
sK151: ( labeled_graph_b_nat > $o ) > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_313,type,
sK152: ( allegorical_term_b > $o ) > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_314,type,
sK153: ( allegorical_term_b > $o ) > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_315,type,
sK154: set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_316,type,
sK155: set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_317,type,
sK156: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_318,type,
sK157: set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_319,type,
sK158: set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_320,type,
sK159: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_321,type,
sK160: nat > nat ).
thf(func_def_322,type,
sK161: set_Pr1163220871term_b > allegorical_term_b > set_al1193902458term_b > allegorical_term_b ).
thf(func_def_323,type,
sK162: set_Pr551076371_b_nat > labeled_graph_b_nat > set_la1976028319_b_nat > labeled_graph_b_nat ).
thf(func_def_324,type,
sK163: set_Pr1987088711_a_nat > labele935650037_a_nat > set_la1083530965_a_nat > labele935650037_a_nat ).
thf(func_def_325,type,
sK164: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_326,type,
sK165: set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_327,type,
sK166: set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_328,type,
sK167: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_329,type,
sK168: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_330,type,
sK169: set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_331,type,
sK170: set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_332,type,
sK171: set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_333,type,
sK172: set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_334,type,
sK173: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_335,type,
sK174: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_336,type,
sK175: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_337,type,
sK176: nat > set_nat > nat ).
thf(func_def_338,type,
sK177: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_339,type,
sK178: set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_340,type,
sK179: set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_341,type,
sK180: set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_342,type,
sK181: set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_343,type,
sK182: set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_344,type,
sK183: set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_345,type,
sK184: set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_346,type,
sK185: set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_347,type,
sK186: set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_348,type,
sK187: set_Pr1986765409at_nat > labeled_graph_b_nat > produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_349,type,
sK188: produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_350,type,
sK189: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_351,type,
sK190: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_352,type,
sK191: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_353,type,
sK192: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_354,type,
sK193: nat > set_nat > nat ).
thf(func_def_355,type,
sK194: nat > set_nat > nat ).
thf(func_def_356,type,
sK195: nat > set_nat > nat ).
thf(func_def_357,type,
sK196: nat > set_nat > nat ).
thf(func_def_358,type,
sK197: nat ).
thf(func_def_359,type,
sK198: nat ).
thf(func_def_360,type,
sK199: allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_361,type,
sK200: allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_362,type,
sK201: allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_363,type,
sK202: labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_364,type,
sK203: labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_365,type,
sK204: labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_366,type,
sK205: labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_367,type,
sK206: labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_368,type,
sK207: labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_369,type,
sK208: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_370,type,
sK209: set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_371,type,
sK210: labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_372,type,
sK211: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_373,type,
sK212: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_374,type,
sK213: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_375,type,
sK214: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_376,type,
sK215: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_377,type,
sK216: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_378,type,
sK217: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_379,type,
sK218: set_nat > nat ).
thf(func_def_380,type,
sK219: nat > set_nat > nat ).
thf(func_def_381,type,
sK220: set_nat > nat ).
thf(func_def_382,type,
sK221: set_nat > nat > nat ).
thf(func_def_383,type,
sK222: set_nat > nat ).
thf(func_def_384,type,
sK223: set_nat > nat > nat ).
thf(func_def_385,type,
sK224: nat > set_nat > nat ).
thf(func_def_386,type,
sK225: nat > set_nat > nat ).
thf(func_def_387,type,
sK226: set_nat > set_Pr1986765409at_nat > set_Pr9961929at_nat > set_Pr9961929at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_388,type,
sK227: produc1478835367term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_389,type,
sK228: produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_390,type,
sK229: produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_391,type,
sK230: produc1478835367term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_392,type,
sK231: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_393,type,
sK232: set_nat > nat > nat ).
thf(func_def_394,type,
sK233: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_395,type,
sK234: allegorical_term_b > set_Pr1986765409at_nat > labeled_graph_b_nat > allegorical_term_b > set_Pr1986765409at_nat ).
thf(func_def_396,type,
sK235: allegorical_term_b > labeled_graph_b_nat > allegorical_term_b > set_Pr1986765409at_nat ).
thf(func_def_397,type,
sK236: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_398,type,
sK237: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_399,type,
sK238: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_400,type,
sK239: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_401,type,
sK240: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_402,type,
sK241: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_403,type,
sK242: allegorical_term_b > set_Pr1986765409at_nat > labeled_graph_b_nat > allegorical_term_b > set_Pr1986765409at_nat ).
thf(func_def_404,type,
sK243: allegorical_term_b > labeled_graph_b_nat > allegorical_term_b > set_Pr1986765409at_nat ).
thf(func_def_405,type,
sK244: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_406,type,
sK245: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_407,type,
sK246: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_408,type,
sK247: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_409,type,
sK248: set_Pr1986765409at_nat > ( nat > labeled_graph_b_nat ) > produc1235635379_b_nat > nat ).
thf(func_def_410,type,
sK249: set_Pr1986765409at_nat > ( nat > labeled_graph_b_nat ) > produc1235635379_b_nat > set_Pr1986765409at_nat ).
thf(func_def_411,type,
sK250: set_Pr1986765409at_nat > ( nat > labeled_graph_b_nat ) > produc1235635379_b_nat > nat ).
thf(func_def_412,type,
sK251: set_Pr1986765409at_nat > ( nat > labeled_graph_b_nat ) > produc1235635379_b_nat > set_Pr1986765409at_nat ).
thf(func_def_413,type,
sK252: labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_414,type,
sK253: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_415,type,
sK254: labeled_graph_b_nat > produc1235635379_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_416,type,
sK255: labeled_graph_b_nat > produc1235635379_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_417,type,
sK256: set_Pr551076371_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_418,type,
sK257: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_419,type,
sK258: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_420,type,
sK259: produc1871334759_a_nat > nat ).
thf(func_def_421,type,
sK260: ( nat > labeled_graph_b_nat ) > produc1235635379_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_422,type,
sK261: ( nat > labeled_graph_b_nat ) > set_Pr551076371_b_nat > nat ).
thf(func_def_423,type,
sK262: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_424,type,
sK263: ( nat > labeled_graph_b_nat ) > set_Pr551076371_b_nat > set_Pr1986765409at_nat ).
thf(func_def_425,type,
sK264: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_426,type,
sK265: ( nat > labeled_graph_b_nat ) > set_Pr551076371_b_nat > produc1235635379_b_nat ).
thf(func_def_427,type,
sK266: ( nat > labeled_graph_b_nat ) > set_Pr551076371_b_nat > set_Pr1986765409at_nat ).
thf(func_def_428,type,
sK267: ( nat > labeled_graph_b_nat ) > nat ).
thf(func_def_429,type,
sK268: ( nat > labeled_graph_b_nat ) > set_Pr551076371_b_nat > produc1235635379_b_nat ).
thf(func_def_430,type,
sK269: set_Pr551076371_b_nat > produc1235635379_b_nat ).
thf(func_def_431,type,
sK270: nat > set_Pr551076371_b_nat > nat ).
thf(func_def_432,type,
sK271: set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_433,type,
sK272: nat > set_Pr1987088711_a_nat > nat ).
thf(func_def_434,type,
sK273: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_435,type,
sK274: set_Pr551076371_b_nat > produc1235635379_b_nat ).
thf(func_def_436,type,
sK275: nat > set_Pr551076371_b_nat > nat ).
thf(func_def_437,type,
sK276: produc1235635379_b_nat > nat ).
thf(func_def_438,type,
sK277: set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_439,type,
sK278: nat > set_Pr1987088711_a_nat > nat ).
thf(func_def_440,type,
sK279: produc1871334759_a_nat > nat ).
thf(func_def_441,type,
sK280: set_Pr551076371_b_nat > produc1235635379_b_nat ).
thf(func_def_442,type,
sK281: nat > set_Pr551076371_b_nat > nat ).
thf(func_def_443,type,
sK282: produc1235635379_b_nat > nat ).
thf(func_def_444,type,
sK283: set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_445,type,
sK284: nat > set_Pr1987088711_a_nat > nat ).
thf(func_def_446,type,
sK285: produc1871334759_a_nat > nat ).
thf(func_def_447,type,
sK286: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_448,type,
sK287: labeled_graph_b_nat > nat > nat ).
thf(func_def_449,type,
sK288: produc1235635379_b_nat > labeled_graph_b_nat > nat ).
thf(func_def_450,type,
sK289: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_451,type,
sK290: b > nat ).
thf(func_def_452,type,
sK291: standard_Constant_a > nat ).
thf(func_def_453,type,
sK292: product_prod_nat_nat > nat ).
thf(func_def_454,type,
sK293: allegorical_term_b > nat ).
thf(func_def_455,type,
sK294: allego510293162tant_a > nat ).
thf(func_def_456,type,
sK295: b > nat ).
thf(func_def_457,type,
sK296: standard_Constant_a > nat ).
thf(func_def_458,type,
sK297: product_prod_nat_nat > nat ).
thf(func_def_459,type,
sK298: nat ).
thf(func_def_460,type,
sK299: nat ).
thf(func_def_461,type,
sK300: nat ).
thf(func_def_462,type,
sK301: allegorical_term_b > allegorical_term_b > nat ).
thf(func_def_463,type,
sK302: allego510293162tant_a > allego510293162tant_a > nat ).
thf(func_def_464,type,
sK303: allego1565409692at_nat > allego1565409692at_nat > nat ).
thf(f4,axiom,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_graph__rule__translation) ).
thf(f13,axiom,
! [X0: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_verts__in__translation__finite_I2_J) ).
thf(f21,axiom,
! [X0: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_verts__in__translation__finite_I1_J) ).
thf(f181,axiom,
! [X0: produc1478835367term_b,X1: allegorical_term_b,X2: allegorical_term_b] :
( ( X0
= ( produc1990145943term_b @ X1 @ X2 ) )
=> ( ( produc1223098053term_b @ X0 )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_sndI) ).
thf(f182,axiom,
! [X0: produc1235635379_b_nat,X1: labeled_graph_b_nat,X2: labeled_graph_b_nat] :
( ( X0
= ( produc951298923_b_nat @ X1 @ X2 ) )
=> ( ( produc194497945_b_nat @ X0 )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_sndI) ).
thf(f187,axiom,
! [X0: produc1235635379_b_nat,X1: labeled_graph_b_nat,X2: labeled_graph_b_nat] :
( ( X0
= ( produc951298923_b_nat @ X1 @ X2 ) )
=> ( ( produc1542243159_b_nat @ X0 )
= X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_fstI) ).
thf(f188,axiom,
! [X0: produc1478835367term_b,X1: allegorical_term_b,X2: allegorical_term_b] :
( ( X0
= ( produc1990145943term_b @ X1 @ X2 ) )
=> ( ( produc854192515term_b @ X0 )
= X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_fstI) ).
thf(f263,axiom,
( finite_finite_nat
= ( ^ [X0: set_nat] :
? [X1: nat] :
! [X2: nat] :
( ( member_nat @ X2 @ X0 )
=> ( ord_less_eq_nat @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_finite__nat__set__iff__bounded__le) ).
thf(f356,conjecture,
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f357,negated_conjecture,
~ ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f364,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f365,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
= $true )
& ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
= $true )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) ) )
= $true ) ),
inference(fool_elimination,[],[f364]) ).
thf(f378,plain,
! [X0: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) ),
inference(rectify,[],[f13]) ).
thf(f379,plain,
! [X0: allegorical_term_b] :
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f378]) ).
thf(f394,plain,
! [X0: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) ),
inference(rectify,[],[f21]) ).
thf(f395,plain,
! [X0: allegorical_term_b] :
( ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f394]) ).
thf(f696,plain,
( finite_finite_nat
= ( ^ [X0: set_nat] :
? [X1: nat] :
! [X2: nat] :
( ( member_nat @ X2 @ X0 )
=> ( ord_less_eq_nat @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f263]) ).
thf(f697,plain,
( finite_finite_nat
= ( ^ [Y0: set_nat] :
( ?? @ nat
@ ^ [Y1: nat] :
( !! @ nat
@ ^ [Y2: nat] :
( ( member_nat @ Y2 @ Y0 )
=> ( ord_less_eq_nat @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f696]) ).
thf(f872,plain,
~ ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f357]) ).
thf(f873,plain,
~ ( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
= $true )
& ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
= $true )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
= $true ) ),
inference(fool_elimination,[],[f872]) ).
thf(f1012,plain,
! [X0: produc1478835367term_b,X1: allegorical_term_b,X2: allegorical_term_b] :
( ( ( produc1223098053term_b @ X0 )
= X2 )
| ( ( produc1990145943term_b @ X1 @ X2 )
!= X0 ) ),
inference(ennf_transformation,[],[f181]) ).
thf(f1013,plain,
! [X0: produc1235635379_b_nat,X1: labeled_graph_b_nat,X2: labeled_graph_b_nat] :
( ( ( produc194497945_b_nat @ X0 )
= X2 )
| ( ( produc951298923_b_nat @ X1 @ X2 )
!= X0 ) ),
inference(ennf_transformation,[],[f182]) ).
thf(f1018,plain,
! [X0: produc1235635379_b_nat,X1: labeled_graph_b_nat,X2: labeled_graph_b_nat] :
( ( ( produc1542243159_b_nat @ X0 )
= X1 )
| ( ( produc951298923_b_nat @ X1 @ X2 )
!= X0 ) ),
inference(ennf_transformation,[],[f187]) ).
thf(f1019,plain,
! [X0: produc1478835367term_b,X1: allegorical_term_b,X2: allegorical_term_b] :
( ( ( produc854192515term_b @ X0 )
= X1 )
| ( ( produc1990145943term_b @ X1 @ X2 )
!= X0 ) ),
inference(ennf_transformation,[],[f188]) ).
thf(f1217,plain,
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(ennf_transformation,[],[f873]) ).
thf(f1398,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f365]) ).
thf(f1399,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f365]) ).
thf(f1410,plain,
! [X0: allegorical_term_b] :
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(cnf_transformation,[],[f379]) ).
thf(f1436,plain,
! [X0: allegorical_term_b] :
( ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(cnf_transformation,[],[f395]) ).
thf(f1641,plain,
! [X2: allegorical_term_b,X0: produc1478835367term_b,X1: allegorical_term_b] :
( ( ( produc1223098053term_b @ X0 )
= X2 )
| ( ( produc1990145943term_b @ X1 @ X2 )
!= X0 ) ),
inference(cnf_transformation,[],[f1012]) ).
thf(f1642,plain,
! [X2: labeled_graph_b_nat,X0: produc1235635379_b_nat,X1: labeled_graph_b_nat] :
( ( ( produc194497945_b_nat @ X0 )
= X2 )
| ( ( produc951298923_b_nat @ X1 @ X2 )
!= X0 ) ),
inference(cnf_transformation,[],[f1013]) ).
thf(f1650,plain,
! [X2: labeled_graph_b_nat,X0: produc1235635379_b_nat,X1: labeled_graph_b_nat] :
( ( ( produc1542243159_b_nat @ X0 )
= X1 )
| ( ( produc951298923_b_nat @ X1 @ X2 )
!= X0 ) ),
inference(cnf_transformation,[],[f1018]) ).
thf(f1651,plain,
! [X2: allegorical_term_b,X0: produc1478835367term_b,X1: allegorical_term_b] :
( ( ( produc854192515term_b @ X0 )
= X1 )
| ( ( produc1990145943term_b @ X1 @ X2 )
!= X0 ) ),
inference(cnf_transformation,[],[f1019]) ).
thf(f1759,plain,
( finite_finite_nat
= ( ^ [Y0: set_nat] :
( ?? @ nat
@ ^ [Y1: nat] :
( !! @ nat
@ ^ [Y2: nat] :
( ( member_nat @ Y2 @ Y0 )
=> ( ord_less_eq_nat @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f697]) ).
thf(f1889,plain,
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(cnf_transformation,[],[f1217]) ).
thf(f1909,plain,
! [X0: allegorical_term_b] :
( $true
= ( ^ [Y0: set_nat] :
( ?? @ nat
@ ^ [Y1: nat] :
( !! @ nat
@ ^ [Y2: nat] :
( ( member_nat @ Y2 @ Y0 )
=> ( ord_less_eq_nat @ Y2 @ Y1 ) ) ) )
@ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) ) ),
inference(definition_unfolding,[],[f1436,f1759]) ).
thf(f1979,plain,
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( $true
!= ( ^ [Y0: set_nat] :
( ?? @ nat
@ ^ [Y1: nat] :
( !! @ nat
@ ^ [Y2: nat] :
( ( member_nat @ Y2 @ Y0 )
=> ( ord_less_eq_nat @ Y2 @ Y1 ) ) ) )
@ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(definition_unfolding,[],[f1889,f1759]) ).
thf(f1997,plain,
! [X2: allegorical_term_b,X1: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ X1 @ X2 ) )
= X2 ),
inference(equality_resolution,[],[f1641]) ).
thf(f1998,plain,
! [X2: labeled_graph_b_nat,X1: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X1 @ X2 ) )
= X2 ),
inference(equality_resolution,[],[f1642]) ).
thf(f1999,plain,
! [X2: labeled_graph_b_nat,X1: labeled_graph_b_nat] :
( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X1 @ X2 ) )
= X1 ),
inference(equality_resolution,[],[f1650]) ).
thf(f2000,plain,
! [X2: allegorical_term_b,X1: allegorical_term_b] :
( ( produc854192515term_b @ ( produc1990145943term_b @ X1 @ X2 ) )
= X1 ),
inference(equality_resolution,[],[f1651]) ).
thf(f2013,plain,
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( $true
!= ( ?? @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( member_nat @ Y1 @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
=> ( ord_less_eq_nat @ Y1 @ Y0 ) ) ) ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f1979]) ).
thf(f2014,plain,
! [X1: nat] :
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( $false
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( member_nat @ Y1 @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
=> ( ord_less_eq_nat @ Y1 @ Y0 ) ) )
@ X1 ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(pi_proxy_clausification,[],[f2013]) ).
thf(f2015,plain,
! [X1: nat] :
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( $false
= ( !! @ nat
@ ^ [Y0: nat] :
( ( member_nat @ Y0 @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
=> ( ord_less_eq_nat @ Y0 @ X1 ) ) ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f2014]) ).
thf(f2016,plain,
! [X1: nat] :
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( $false
= ( ^ [Y0: nat] :
( ( member_nat @ Y0 @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
=> ( ord_less_eq_nat @ Y0 @ X1 ) )
@ ( sK160 @ X1 ) ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(sigma_proxy_clausification,[],[f2015]) ).
thf(f2017,plain,
! [X1: nat] :
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( $false
= ( ( member_nat @ ( sK160 @ X1 ) @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
=> ( ord_less_eq_nat @ ( sK160 @ X1 ) @ X1 ) ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f2016]) ).
thf(f2018,plain,
! [X1: nat] :
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( $false
= ( ord_less_eq_nat @ ( sK160 @ X1 ) @ X1 ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(imp_proxy_clausification,[],[f2017]) ).
thf(f2019,plain,
! [X1: nat] :
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( $true
= ( member_nat @ ( sK160 @ X1 ) @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(imp_proxy_clausification,[],[f2017]) ).
thf(f3174,plain,
! [X0: allegorical_term_b] :
( $true
= ( ?? @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( member_nat @ Y1 @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
=> ( ord_less_eq_nat @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1909]) ).
thf(f3175,plain,
! [X0: allegorical_term_b] :
( $true
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( member_nat @ Y1 @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
=> ( ord_less_eq_nat @ Y1 @ Y0 ) ) )
@ ( sK293 @ X0 ) ) ),
inference(sigma_proxy_clausification,[],[f3174]) ).
thf(f3176,plain,
! [X0: allegorical_term_b] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( member_nat @ Y0 @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
=> ( ord_less_eq_nat @ Y0 @ ( sK293 @ X0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3175]) ).
thf(f3177,plain,
! [X0: allegorical_term_b,X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( member_nat @ Y0 @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
=> ( ord_less_eq_nat @ Y0 @ ( sK293 @ X0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f3176]) ).
thf(f3178,plain,
! [X0: allegorical_term_b,X1: nat] :
( $true
= ( ( member_nat @ X1 @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
=> ( ord_less_eq_nat @ X1 @ ( sK293 @ X0 ) ) ) ),
inference(beta-eta_normalization,[],[f3177]) ).
thf(f3179,plain,
! [X0: allegorical_term_b,X1: nat] :
( ( $false
= ( member_nat @ X1 @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) ) )
| ( $true
= ( ord_less_eq_nat @ X1 @ ( sK293 @ X0 ) ) ) ),
inference(imp_proxy_clausification,[],[f3178]) ).
thf(f3257,definition,
( spl304_1
<=> ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl304_1])],[avatar_definition]) ).
thf(f3259,plain,
( ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true )
| spl304_1 ),
inference(avatar_component_clause,[],[f3257]) ).
thf(f3261,definition,
( spl304_2
<=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_2])],[avatar_definition]) ).
thf(f3263,plain,
( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| spl304_2 ),
inference(avatar_component_clause,[],[f3261]) ).
thf(f3265,definition,
( spl304_3
<=> ! [X1: nat] :
( $true
= ( member_nat @ ( sK160 @ X1 ) @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_3])],[avatar_definition]) ).
thf(f3266,plain,
( ! [X1: nat] :
( $true
= ( member_nat @ ( sK160 @ X1 ) @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
| ~ spl304_3 ),
inference(avatar_component_clause,[],[f3265]) ).
thf(f3268,definition,
( spl304_4
<=> ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl304_4])],[avatar_definition]) ).
thf(f3270,plain,
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| spl304_4 ),
inference(avatar_component_clause,[],[f3268]) ).
thf(f3271,plain,
( ~ spl304_1
| ~ spl304_2
| spl304_3
| ~ spl304_4 ),
inference(avatar_split_clause,[],[f2019,f3268,f3265,f3261,f3257]) ).
thf(f3273,definition,
( spl304_5
<=> ! [X1: nat] :
( $false
= ( ord_less_eq_nat @ ( sK160 @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl304_5])],[avatar_definition]) ).
thf(f3274,plain,
( ! [X1: nat] :
( $false
= ( ord_less_eq_nat @ ( sK160 @ X1 ) @ X1 ) )
| ~ spl304_5 ),
inference(avatar_component_clause,[],[f3273]) ).
thf(f3275,plain,
( ~ spl304_1
| ~ spl304_2
| spl304_5
| ~ spl304_4 ),
inference(avatar_split_clause,[],[f2018,f3268,f3273,f3261,f3257]) ).
thf(f3322,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( $true
= ( graph_529870330at_nat @ ( translation_b @ X0 ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) ) ) ),
inference(forward_demodulation,[],[f1398,f1999]) ).
thf(f3323,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) )
= ( restrict_b_nat @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ),
inference(forward_demodulation,[],[f1399,f1998]) ).
thf(f3349,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( $true
= ( graph_529870330at_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) ) ) ),
inference(forward_demodulation,[],[f3322,f1998]) ).
thf(f3365,plain,
( ( $true
!= ( graph_529870330at_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| spl304_1 ),
inference(forward_demodulation,[],[f3259,f1999]) ).
thf(f3366,plain,
( ( $true
!= ( graph_529870330at_nat @ ( translation_b @ u ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ u ) ) ) ) )
| spl304_1 ),
inference(forward_demodulation,[],[f3365,f2000]) ).
thf(f3367,plain,
( ( $true
!= ( graph_529870330at_nat @ ( translation_b @ u ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ u ) ) ) ) )
| spl304_1 ),
inference(forward_demodulation,[],[f3366,f1998]) ).
thf(f3368,plain,
( ( $true
!= ( graph_529870330at_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ u ) ) ) ) )
| spl304_1 ),
inference(forward_demodulation,[],[f3367,f1997]) ).
thf(f3369,plain,
( ( $true != $true )
| spl304_1 ),
inference(forward_demodulation,[],[f3368,f3349]) ).
thf(f3370,plain,
( $false
| spl304_1 ),
inference(trivial_inequality_removal,[],[f3369]) ).
thf(f3371,plain,
spl304_1,
inference(avatar_contradiction_clause,[],[f3370]) ).
thf(f3373,plain,
( ( ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) )
!= ( restrict_b_nat @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
| spl304_2 ),
inference(forward_demodulation,[],[f3263,f1998]) ).
thf(f3375,plain,
( ( ( translation_b @ ( allegorical_A_Int_b @ u @ v ) )
!= ( restrict_b_nat @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
| spl304_2 ),
inference(forward_demodulation,[],[f3373,f1997]) ).
thf(f3377,plain,
( ( ( translation_b @ ( allegorical_A_Int_b @ u @ v ) )
!= ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) )
| spl304_2 ),
inference(forward_demodulation,[],[f3375,f3323]) ).
thf(f3378,plain,
( $false
| spl304_2 ),
inference(trivial_inequality_removal,[],[f3377]) ).
thf(f3379,plain,
spl304_2,
inference(avatar_contradiction_clause,[],[f3378]) ).
thf(f3382,plain,
( ( $true
!= ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
| spl304_4 ),
inference(forward_demodulation,[],[f3270,f1998]) ).
thf(f3384,plain,
( ( $true != $true )
| spl304_4 ),
inference(forward_demodulation,[],[f3382,f1410]) ).
thf(f3385,plain,
( $false
| spl304_4 ),
inference(trivial_inequality_removal,[],[f3384]) ).
thf(f3386,plain,
spl304_4,
inference(avatar_contradiction_clause,[],[f3385]) ).
thf(f3387,plain,
( ! [X1: nat] :
( $true
= ( member_nat @ ( sK160 @ X1 ) @ ( labele460410879_b_nat @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
| ~ spl304_3 ),
inference(forward_demodulation,[],[f3266,f1998]) ).
thf(f3389,plain,
( ! [X1: nat] :
( $true
= ( member_nat @ ( sK160 @ X1 ) @ ( labele460410879_b_nat @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
| ~ spl304_3 ),
inference(forward_demodulation,[],[f3387,f1997]) ).
thf(f3855,plain,
( ! [X0: nat] :
( ( $true = $false )
| ( $true
= ( ord_less_eq_nat @ ( sK160 @ X0 ) @ ( sK293 @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
| ~ spl304_3 ),
inference(constrained_superposition,[],[f3389,f3179]) ).
thf(f3856,plain,
( ! [X0: nat] :
( $true
= ( ord_less_eq_nat @ ( sK160 @ X0 ) @ ( sK293 @ ( allegorical_A_Int_b @ u @ v ) ) ) )
| ~ spl304_3 ),
inference(trivial_inequality_removal,[],[f3855]) ).
thf(f3863,plain,
( ( $true = $false )
| ~ spl304_3
| ~ spl304_5 ),
inference(constrained_superposition,[],[f3856,f3274]) ).
thf(f3879,plain,
( $false
| ~ spl304_3
| ~ spl304_5 ),
inference(trivial_inequality_removal,[],[f3863]) ).
thf(f3880,plain,
( ~ spl304_3
| ~ spl304_5 ),
inference(avatar_contradiction_clause,[],[f3879]) ).
cnf(s2,plain,
( ~ spl304_1
| ~ spl304_2
| spl304_3
| ~ spl304_4 ),
inference(sat_conversion,[],[f3271]) ).
cnf(s4,plain,
( ~ spl304_1
| ~ spl304_2
| ~ spl304_4
| spl304_5 ),
inference(sat_conversion,[],[f3275]) ).
cnf(s576,plain,
spl304_1,
inference(sat_conversion,[],[f3371]) ).
cnf(s577,plain,
spl304_2,
inference(sat_conversion,[],[f3379]) ).
cnf(s578,plain,
spl304_4,
inference(sat_conversion,[],[f3386]) ).
cnf(s668,plain,
( ~ spl304_3
| ~ spl304_5 ),
inference(sat_conversion,[],[f3880]) ).
cnf(s673,plain,
spl304_5,
inference(rat,[],[s4,s578,s577,s576]) ).
cnf(s674,plain,
~ spl304_3,
inference(rat,[],[s668,s673]) ).
cnf(s675,plain,
$false,
inference(rat,[],[s2,s578,s674,s577,s576]) ).
thf(f3881,plain,
$false,
inference(avatar_sat_refutation,[],[s675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP178^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 20:08:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 5.46/1.07 % (1788196)Will run a generic schedule for satisfiability detection.
% 5.46/1.07 % (1788230)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2259639029:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.46/1.07 % (1788226)% WARNING: option uhcvi not known.
% 5.46/1.07 % (1788225)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3136641185_2999 on theBenchmark for (2999ds/0Mi)
% 5.46/1.07 % (1788226)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4123039310:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.46/1.07 % (1788227)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2127376235:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.46/1.07 % (1788228)dis+10_1_sil=32000:sp=arity:random_seed=2170063629:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.46/1.07 % (1788229)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1665307502:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.46/1.07 % (1788231)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=424333681:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.46/1.07 % (1788226)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.46/1.07 % (1788229)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.46/1.07 % (1788230)Instruction limit reached!
% 5.46/1.07 % (1788230)------------------------------
% 5.46/1.07 % (1788230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.07 % (1788230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.07 % (1788230)CaDiCaL version: 2.1.3
% 5.46/1.07 % (1788230)Termination reason: Instruction limit
% 5.46/1.07 % (1788230)Termination phase: Saturation
% 5.46/1.07 % (1788230)Time elapsed: 0.031 s
% 5.46/1.07 % (1788230)Peak memory usage: 13 MB
% 5.46/1.07 % (1788230)Instructions burned: 134 (million)
% 5.46/1.07 % (1788253)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3656848660:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.46/1.07 % (1788228)Instruction limit reached!
% 5.46/1.07 % (1788228)------------------------------
% 5.46/1.07 % (1788228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.07 % (1788228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.07 % (1788228)CaDiCaL version: 2.1.3
% 5.46/1.07 % (1788228)Termination reason: Instruction limit
% 5.46/1.07 % (1788228)Termination phase: Property scanning
% 5.46/1.07 % (1788228)Time elapsed: 0.043 s
% 5.46/1.07 % (1788228)Peak memory usage: 11 MB
% 5.46/1.07 % (1788228)Instructions burned: 103 (million)
% 5.46/1.07 % (1788229)Instruction limit reached!
% 5.46/1.07 % (1788229)------------------------------
% 5.46/1.07 % (1788229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.07 % (1788229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.07 % (1788229)CaDiCaL version: 2.1.3
% 5.46/1.07 % (1788229)Termination reason: Instruction limit
% 5.46/1.07 % (1788229)Termination phase: Property scanning
% 5.46/1.07 % (1788229)Time elapsed: 0.048 s
% 5.46/1.07 % (1788229)Peak memory usage: 11 MB
% 5.46/1.07 % (1788229)Instructions burned: 116 (million)
% 5.46/1.07 % Exception at run slice level
% 5.46/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.46/1.07 % (1788226)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.46/1.07 % Exception at run slice level
% 5.46/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.46/1.07 % (1788265)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=591669480:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 5.46/1.07 % (1788266)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=3257556915:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.46/1.07 % (1788231)Instruction limit reached!
% 5.46/1.07 % (1788231)------------------------------
% 5.46/1.07 % (1788231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.07 % (1788231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.07 % (1788231)CaDiCaL version: 2.1.3
% 5.46/1.07 % (1788231)Termination reason: Instruction limit
% 7.29/1.45 % (1788231)Termination phase: Saturation
% 7.29/1.45 % (1788231)Time elapsed: 0.068 s
% 7.29/1.45 % (1788231)Peak memory usage: 13 MB
% 7.29/1.45 % (1788231)Instructions burned: 160 (million)
% 7.29/1.45 % (1788271)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2883056326:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 7.29/1.45 % (1788269)ott-21_1_sil=16000:fs=off:random_seed=1387574341:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 7.29/1.45 % (1788276)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=926837853:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 7.29/1.45 % (1788266)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.29/1.45 % (1788265)Instruction limit reached!
% 7.29/1.45 % (1788265)------------------------------
% 7.29/1.45 % (1788265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788265)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788265)Termination reason: Instruction limit
% 7.29/1.45 % (1788265)Termination phase: Saturation
% 7.29/1.45 % (1788265)Time elapsed: 0.055 s
% 7.29/1.45 % (1788265)Peak memory usage: 13 MB
% 7.29/1.45 % (1788265)Instructions burned: 133 (million)
% 7.29/1.45 % (1788266)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.29/1.45 % (1788296)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3006306675:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 7.29/1.45 % Exception at run slice level
% 7.29/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.29/1.45 % (1788269)Instruction limit reached!
% 7.29/1.45 % (1788269)------------------------------
% 7.29/1.45 % (1788269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788269)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788269)Termination reason: Instruction limit
% 7.29/1.45 % (1788269)Termination phase: Saturation
% 7.29/1.45 % (1788269)Time elapsed: 0.075 s
% 7.29/1.45 % (1788269)Peak memory usage: 13 MB
% 7.29/1.45 % (1788269)Instructions burned: 180 (million)
% 7.29/1.45 % (1788307)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2517579510:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 7.29/1.45 % (1788315)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=4027363840:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 7.29/1.45 % (1788315)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.29/1.45 % (1788271)Instruction limit reached!
% 7.29/1.45 % (1788271)------------------------------
% 7.29/1.45 % (1788271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788271)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788271)Termination reason: Instruction limit
% 7.29/1.45 % (1788271)Termination phase: Saturation
% 7.29/1.45 % (1788271)Time elapsed: 0.126 s
% 7.29/1.45 % (1788271)Peak memory usage: 15 MB
% 7.29/1.45 % (1788271)Instructions burned: 478 (million)
% 7.29/1.45 % (1788342)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2984417147:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 7.29/1.45 % Exception at run slice level
% 7.29/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.29/1.45 % (1788342)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.29/1.45 % (1788344)fmb+10_1_sil=64000:random_seed=1798417790:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 7.29/1.45 % (1788344)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.29/1.45 % Exception at run slice level
% 7.29/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.29/1.45 % (1788346)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=635978853:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 7.29/1.45 % Exception at run slice level
% 7.29/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.29/1.45 % (1788266)Instruction limit reached!
% 7.29/1.45 % (1788266)------------------------------
% 7.29/1.45 % (1788266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788266)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788266)Termination reason: Instruction limit
% 7.29/1.45 % (1788266)Termination phase: Saturation
% 7.29/1.45 % (1788266)Time elapsed: 0.308 s
% 7.29/1.45 % (1788266)Peak memory usage: 17 MB
% 7.29/1.45 % (1788266)Instructions burned: 686 (million)
% 7.29/1.45 % (1788348)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3318365397:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 7.29/1.45 % (1788349)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3865385454:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 7.29/1.45 % (1788349)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.29/1.45 % (1788342)Instruction limit reached!
% 7.29/1.45 % (1788342)------------------------------
% 7.29/1.45 % (1788342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788342)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788342)Termination reason: Instruction limit
% 7.29/1.45 % (1788342)Termination phase: Saturation
% 7.29/1.45 % (1788342)Time elapsed: 0.218 s
% 7.29/1.45 % (1788342)Peak memory usage: 21 MB
% 7.29/1.45 % (1788342)Instructions burned: 880 (million)
% 7.29/1.45 % Exception at run slice level
% 7.29/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.29/1.45 % (1788352)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2458898586:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 7.29/1.45 % (1788353)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1082953631:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 7.29/1.45 % (1788352)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.29/1.45 % (1788352)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.29/1.45 % (1788315)Instruction limit reached!
% 7.29/1.45 % (1788315)------------------------------
% 7.29/1.45 % (1788315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788315)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788315)Termination reason: Instruction limit
% 7.29/1.45 % (1788315)Termination phase: Saturation
% 7.29/1.45 % (1788315)Time elapsed: 0.328 s
% 7.29/1.45 % (1788315)Peak memory usage: 19 MB
% 7.29/1.45 % (1788315)Instructions burned: 693 (million)
% 7.29/1.45 % Exception at run slice level
% 7.29/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.29/1.45 % (1788356)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=788492327:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 7.29/1.45 % (1788357)ott-2_1_sil=16000:newcnf=on:random_seed=3939448791:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 7.29/1.45 % (1788357)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.29/1.45 % Exception at run slice level
% 7.29/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.29/1.45 % (1788360)ott+10_1_sil=32000:tgt=ground:random_seed=1241621632:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 7.29/1.45 % (1788296)Instruction limit reached!
% 7.29/1.45 % (1788296)------------------------------
% 7.29/1.45 % (1788296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788296)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788296)Termination reason: Instruction limit
% 7.29/1.45 % (1788296)Termination phase: Saturation
% 7.29/1.45 % (1788296)Time elapsed: 0.552 s
% 7.29/1.45 % (1788296)Peak memory usage: 22 MB
% 7.29/1.45 % (1788296)Instructions burned: 1180 (million)
% 7.29/1.45 % (1788362)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1785406312:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 7.29/1.45 % Exception at run slice level
% 7.29/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.29/1.45 % (1788364)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3024944821:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 7.29/1.45 % (1788352)Instruction limit reached!
% 7.29/1.45 % (1788352)------------------------------
% 7.29/1.45 % (1788352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788352)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788352)Termination reason: Instruction limit
% 7.29/1.45 % (1788352)Termination phase: Saturation
% 7.29/1.45 % (1788352)Time elapsed: 0.367 s
% 7.29/1.45 % (1788352)Peak memory usage: 19 MB
% 7.29/1.45 % (1788352)Instructions burned: 1477 (million)
% 7.29/1.45 % (1788366)dis+21_1_sil=32000:sas=cadical:random_seed=1621940904:i=3773:amm=off_2991 on theBenchmark for (2991ds/3773Mi)
% 7.29/1.45 % (1788364)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.29/1.45 % (1788357)Instruction limit reached!
% 7.29/1.45 % (1788357)------------------------------
% 7.29/1.45 % (1788357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788357)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788357)Termination reason: Instruction limit
% 7.29/1.45 % (1788357)Termination phase: Saturation
% 7.29/1.45 % (1788357)Time elapsed: 0.395 s
% 7.29/1.45 % (1788357)Peak memory usage: 19 MB
% 7.29/1.45 % (1788357)Instructions burned: 869 (million)
% 7.29/1.45 % (1788368)ott+11_1_sil=16000:gs=on:random_seed=3383509291:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2990 on theBenchmark for (2990ds/2251Mi)
% 7.29/1.45 % (1788368)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.29/1.45 % (1788368) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1788196-1788368"...
% 7.29/1.45 % (1788368)...printing done.
% 7.29/1.45 % (1788368)Refutation found. Thanks to Tanya!
% 7.29/1.45 % SZS status Theorem for theBenchmark
% 7.29/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 7.29/1.45 % (1788368)------------------------------
% 7.29/1.45 % (1788368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.29/1.45 % (1788368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.29/1.45 % (1788368)CaDiCaL version: 2.1.3
% 7.29/1.45 % (1788368)Termination reason: Refutation
% 7.29/1.45 % (1788368)Time elapsed: 0.199 s
% 7.29/1.45 % (1788368)Peak memory usage: 18 MB
% 7.29/1.45 % (1788368)Instructions burned: 409 (million)
% 7.29/1.45 % (1788196)Success in time 1.208 s
% 7.29/1.45 % Vampire exiting
%------------------------------------------------------------------------------