%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP178^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:08:41 AM UTC 2026
% Result : Theorem 0.55s 0.39s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 79 ( 38 unt; 0 typ; 6 def)
% Number of atoms : 211 ( 65 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1464 ( 40 ~; 37 |; 21 &;1360 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 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 : 331 ( 328 usr; 20 con; 0-6 aty)
% Number of variables : 52 ( 0 sgn 46 !; 0 ?; 52 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_148,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_149,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_150,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_151,type,
vAND: $o > $o > $o ).
thf(func_def_152,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_153,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_154,type,
vIMP: $o > $o > $o ).
thf(func_def_155,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_156,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_157,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_158,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_159,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_160,type,
sP0: nat > nat > nat > $o ).
thf(func_def_161,type,
sP1: nat > nat > nat > $o ).
thf(func_def_162,type,
sK2: set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_163,type,
sK3: set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_164,type,
sK4: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_165,type,
sK5: ( nat > labeled_graph_b_nat ) > set_Pr1986765409at_nat > set_nat > nat ).
thf(func_def_166,type,
sK6: labeled_graph_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_167,type,
sK7: labeled_graph_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_168,type,
sK8: labeled_graph_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_169,type,
sK9: produc398057191_a_nat > labele935650037_a_nat ).
thf(func_def_170,type,
sK10: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_171,type,
sK11: produc398057191_a_nat > labele935650037_a_nat ).
thf(func_def_172,type,
sK12: produc398057191_a_nat > set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_173,type,
sK13: labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_174,type,
sK14: product_prod_nat_nat > nat ).
thf(func_def_175,type,
sK15: product_prod_nat_nat > nat ).
thf(func_def_176,type,
sK16: ( allegorical_term_b > $o ) > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_177,type,
sK17: ( allegorical_term_b > $o ) > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_178,type,
sK18: ( nat > nat ) > nat ).
thf(func_def_179,type,
sK19: ( nat > nat ) > nat ).
thf(func_def_180,type,
sK20: ( nat > nat ) > nat ).
thf(func_def_181,type,
sK21: ( nat > nat ) > nat ).
thf(func_def_182,type,
sK22: ( nat > $o ) > nat > nat ).
thf(func_def_183,type,
sK23: ( nat > $o ) > nat ).
thf(func_def_184,type,
sK24: nat > set_nat > nat ).
thf(func_def_185,type,
sK25: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_186,type,
sK26: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_187,type,
sK27: set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_188,type,
sK28: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_189,type,
sK29: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_190,type,
sK30: set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_191,type,
sK31: set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_192,type,
sK32: produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_193,type,
sK33: ( nat > nat ) > nat ).
thf(func_def_194,type,
sK34: ( nat > nat ) > nat ).
thf(func_def_195,type,
sK35: set_Pr1163220871term_b > produc1478835367term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_196,type,
sK36: set_Pr1163220871term_b > produc1478835367term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_197,type,
sK37: set_Pr1163220871term_b > produc1478835367term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_198,type,
sK38: set_Pr551076371_b_nat > labeled_graph_b_nat > set_la1976028319_b_nat > labeled_graph_b_nat ).
thf(func_def_199,type,
sK39: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_200,type,
sK40: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_201,type,
sK41: labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_202,type,
sK42: labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_203,type,
sK43: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_204,type,
sK44: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_205,type,
sK45: set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_206,type,
sK46: ( nat > labeled_graph_b_nat ) > set_Pr9961929at_nat > set_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_207,type,
sK47: labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_208,type,
sK48: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_209,type,
sK49: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_210,type,
sK50: allegorical_term_b > produc1478835367term_b > allegorical_term_b ).
thf(func_def_211,type,
sK51: set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_212,type,
sK52: set_Pr1987088711_a_nat > labele935650037_a_nat > set_la1083530965_a_nat > labele935650037_a_nat ).
thf(func_def_213,type,
sK53: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_214,type,
sK54: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_215,type,
sK55: labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_216,type,
sK56: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_217,type,
sK57: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_218,type,
sK58: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_219,type,
sK59: ( produc1871334759_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_220,type,
sK60: ( produc1871334759_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_221,type,
sK61: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_222,type,
sK62: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_223,type,
sK63: ( nat > nat > $o ) > nat ).
thf(func_def_224,type,
sK64: ( nat > nat > $o ) > nat ).
thf(func_def_225,type,
sK65: ( nat > nat > $o ) > nat ).
thf(func_def_226,type,
sK66: ( nat > nat > $o ) > nat ).
thf(func_def_227,type,
sK67: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > produc1871334759_a_nat ).
thf(func_def_228,type,
sK68: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_229,type,
sK69: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_230,type,
sK70: ( produc1871334759_a_nat > $o ) > ( produc1871334759_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_231,type,
sK71: ( nat > nat ) > nat ).
thf(func_def_232,type,
sK72: ( nat > nat ) > nat ).
thf(func_def_233,type,
sK73: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_234,type,
sK74: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_235,type,
sK75: set_al1193902458term_b > produc1478835367term_b > allegorical_term_b ).
thf(func_def_236,type,
sK76: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_237,type,
sK77: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_238,type,
sK78: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_239,type,
sK79: allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_240,type,
sK80: ( allegorical_term_b > allegorical_term_b > $o ) > allegorical_term_b ).
thf(func_def_241,type,
sK81: ( allegorical_term_b > allegorical_term_b > $o ) > allegorical_term_b ).
thf(func_def_242,type,
sK82: ( nat > labeled_graph_b_nat ) > set_Pr551076371_b_nat > produc1235635379_b_nat ).
thf(func_def_243,type,
sK83: ( nat > labeled_graph_b_nat ) > set_Pr551076371_b_nat > nat ).
thf(func_def_244,type,
sK84: ( nat > labeled_graph_b_nat ) > set_Pr551076371_b_nat > set_Pr1986765409at_nat ).
thf(func_def_245,type,
sK85: set_Pr551076371_b_nat > set_Pr551076371_b_nat > produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_246,type,
sK86: set_Pr551076371_b_nat > set_Pr551076371_b_nat > produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_247,type,
sK87: set_Pr551076371_b_nat > set_Pr551076371_b_nat > produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_248,type,
sK88: labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_249,type,
sK89: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_250,type,
sK90: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_251,type,
sK91: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_252,type,
sK92: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_253,type,
sK93: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_254,type,
sK94: set_nat > nat ).
thf(func_def_255,type,
sK95: produc1478835367term_b > allegorical_term_b ).
thf(func_def_256,type,
sK96: produc1478835367term_b > allegorical_term_b ).
thf(func_def_257,type,
sK97: produc1235635379_b_nat > ( nat > labeled_graph_b_nat ) > set_Pr1986765409at_nat > nat ).
thf(func_def_258,type,
sK98: product_prod_nat_nat > set_nat > nat ).
thf(func_def_259,type,
sK99: labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_260,type,
sK100: set_Pr551076371_b_nat > produc1235635379_b_nat ).
thf(func_def_261,type,
sK101: set_Pr551076371_b_nat > labeled_graph_b_nat > produc1235635379_b_nat ).
thf(func_def_262,type,
sK102: produc1478835367term_b > allegorical_term_b ).
thf(func_def_263,type,
sK103: produc1478835367term_b > allegorical_term_b ).
thf(func_def_264,type,
sK104: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_265,type,
sK105: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_266,type,
sK106: set_Pr1163220871term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_267,type,
sK107: set_Pr1163220871term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_268,type,
sK108: set_Pr2041158302at_nat > ( nat > labeled_graph_b_nat ) > set_Pr9961929at_nat > nat ).
thf(func_def_269,type,
sK109: labeled_graph_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_270,type,
sK110: produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_271,type,
sK111: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_272,type,
sK112: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat ).
thf(func_def_273,type,
sK113: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_274,type,
sK114: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_275,type,
sK115: set_nat > nat ).
thf(func_def_276,type,
sK116: produc1871334759_a_nat > set_la1083530965_a_nat > labele935650037_a_nat ).
thf(func_def_277,type,
sK117: labeled_graph_b_nat > produc1235635379_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_278,type,
sK118: set_Pr551076371_b_nat > labeled_graph_b_nat > set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_279,type,
sK119: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_280,type,
sK120: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_281,type,
sK121: set_nat > nat > nat ).
thf(func_def_282,type,
sK122: ( labele935650037_a_nat > $o ) > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_283,type,
sK123: ( labele935650037_a_nat > $o ) > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_284,type,
sK124: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat ).
thf(func_def_285,type,
sK125: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_286,type,
sK126: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_287,type,
sK127: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat > set_Pr1986765409at_nat > labeled_graph_b_nat ).
thf(func_def_288,type,
sK128: ( produc1871334759_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_289,type,
sK129: ( produc1871334759_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_290,type,
sK130: set_Pr551076371_b_nat > set_Pr551076371_b_nat > ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_291,type,
sK131: set_Pr551076371_b_nat > set_Pr551076371_b_nat > ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_292,type,
sK132: set_Pr551076371_b_nat > set_Pr551076371_b_nat > ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_293,type,
sK133: ( produc398057191_a_nat > $o ) > produc1871334759_a_nat ).
thf(func_def_294,type,
sK134: ( produc398057191_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_295,type,
sK135: ( produc398057191_a_nat > $o ) > labele935650037_a_nat ).
thf(func_def_296,type,
sK136: set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_297,type,
sK137: set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_298,type,
sK138: set_Pr1987088711_a_nat > labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_299,type,
sK139: set_Pr1987088711_a_nat > labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_300,type,
sK140: set_Pr1987088711_a_nat > labele935650037_a_nat > set_Pr1987088711_a_nat > labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_301,type,
sK141: set_Pr551076371_b_nat > ( labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_302,type,
sK142: set_Pr551076371_b_nat > ( labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_303,type,
sK143: labeled_graph_b_nat > produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_304,type,
sK144: allegorical_term_b > produc1478835367term_b > allegorical_term_b ).
thf(func_def_305,type,
sK145: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_306,type,
sK146: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_307,type,
sK147: product_prod_nat_nat > nat ).
thf(func_def_308,type,
sK148: product_prod_nat_nat > nat ).
thf(func_def_309,type,
sK149: allegorical_term_b > set_al1193902458term_b > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_310,type,
sK150: set_la1976028319_b_nat > produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_311,type,
sK151: set_Pr1987088711_a_nat > ( labele935650037_a_nat > labele935650037_a_nat > $o ) > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_312,type,
sK152: set_Pr1987088711_a_nat > ( labele935650037_a_nat > labele935650037_a_nat > $o ) > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_313,type,
sK153: set_Pr1987088711_a_nat > ( labele935650037_a_nat > labele935650037_a_nat > $o ) > set_Pr1987088711_a_nat > labele935650037_a_nat ).
thf(func_def_314,type,
sK154: set_Pr551076371_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_315,type,
sK155: set_Pr1163220871term_b > allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_316,type,
sK156: set_Pr1163220871term_b > allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_317,type,
sK157: set_Pr1163220871term_b > allegorical_term_b > set_Pr1163220871term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_318,type,
sK158: ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_319,type,
sK159: ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_320,type,
sK160: set_Pr1163220871term_b > ( allegorical_term_b > allegorical_term_b > $o ) > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_321,type,
sK161: set_Pr1163220871term_b > ( allegorical_term_b > allegorical_term_b > $o ) > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_322,type,
sK162: set_Pr1163220871term_b > ( allegorical_term_b > allegorical_term_b > $o ) > set_Pr1163220871term_b > allegorical_term_b ).
thf(func_def_323,type,
vNOT: $o > $o ).
thf(f4,axiom,
! [X1: allegorical_term_b,X0: 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 ) ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( 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 ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_20_verts__in__translation__finite_I1_J) ).
thf(f31,axiom,
( ( ^ [X0: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ X0 ) ) )
= translation_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_translation__graph) ).
thf(f76,axiom,
! [X1: labeled_graph_b_nat,X0: labeled_graph_b_nat] :
( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X0 @ X1 ) )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_fst__conv) ).
thf(f77,axiom,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( produc854192515term_b @ ( produc1990145943term_b @ X0 @ X1 ) )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_fst__conv) ).
thf(f86,axiom,
! [X1: allegorical_term_b,X0: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ X0 @ X1 ) )
= X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_snd__conv) ).
thf(f87,axiom,
! [X1: labeled_graph_b_nat,X0: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X0 @ X1 ) )
= X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_snd__conv) ).
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 ) ) ) ) ) ) ) )
& ( 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 ) ) ) ) ) ) ) ) )
& ( ( 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 ) ) ) ) ) ) ) )
& ( 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 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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 ) ) ) ) ) ) ) )
& ( 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 ) ) ) ) ) ) ) ) )
& ( ( 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 ) ) ) ) ) ) ) )
& ( 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 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f367,plain,
( translation_b
= ( ^ [Y0: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ Y0 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f407,plain,
! [X0: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) ),
inference(rectify,[],[f21]) ).
thf(f408,plain,
! [X0: allegorical_term_b] :
( ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f407]) ).
thf(f423,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 ) ) ) ) ) ) ) )
& ( 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 ) ) ) ) ) ) ) ) )
& ( ( 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 ) ) ) ) ) ) ) )
& ( 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 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f357]) ).
thf(f424,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 ) ) ) ) ) ) ) )
& ( ( 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 )
& ( ( 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 )
& ( ( 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 ) ),
inference(fool_elimination,[],[f423]) ).
thf(f606,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f607,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) )
& ( $true
= ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) )
& ( $true
= ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) ) )
& ( $true
= ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f606]) ).
thf(f857,plain,
! [X0: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) ),
inference(rectify,[],[f13]) ).
thf(f858,plain,
! [X0: allegorical_term_b] :
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f857]) ).
thf(f901,plain,
! [X1: labeled_graph_b_nat,X0: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X1 @ X0 ) )
= X0 ),
inference(rectify,[],[f87]) ).
thf(f917,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ X1 @ X0 ) )
= X0 ),
inference(rectify,[],[f86]) ).
thf(f1269,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 )
| ( ( 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 ) ) ) ) ) ) ) )
| ( ( 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 ) ),
inference(ennf_transformation,[],[f424]) ).
thf(f1425,plain,
! [X0: labeled_graph_b_nat,X1: labeled_graph_b_nat] :
( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X1 @ X0 ) )
= X1 ),
inference(rectify,[],[f76]) ).
thf(f1588,plain,
! [X0: labeled_graph_b_nat,X1: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X0 @ X1 ) )
= X1 ),
inference(rectify,[],[f901]) ).
thf(f1679,plain,
( translation_b
= ( ^ [Y0: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f367]) ).
thf(f1706,plain,
! [X0: allegorical_term_b] :
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(cnf_transformation,[],[f858]) ).
thf(f1716,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( produc854192515term_b @ ( produc1990145943term_b @ X0 @ X1 ) )
= X0 ),
inference(cnf_transformation,[],[f77]) ).
thf(f1741,plain,
( ( ( 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 )
| ( ( 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 )
| ( ( 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 )
| ( ( 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 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f1269]) ).
thf(f1795,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ X1 @ X0 ) )
= X0 ),
inference(cnf_transformation,[],[f917]) ).
thf(f1837,plain,
! [X0: allegorical_term_b] :
( ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(cnf_transformation,[],[f408]) ).
thf(f1859,plain,
! [X0: labeled_graph_b_nat,X1: labeled_graph_b_nat] :
( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X1 @ X0 ) )
= X1 ),
inference(cnf_transformation,[],[f1425]) ).
thf(f1931,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( $true
= ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f607]) ).
thf(f2103,plain,
! [X0: labeled_graph_b_nat,X1: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X0 @ X1 ) )
= X1 ),
inference(cnf_transformation,[],[f1588]) ).
thf(f2455,definition,
( spl163_26
<=> ( ( 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,[spl163_26])],[avatar_definition]) ).
thf(f2457,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 )
| spl163_26 ),
inference(avatar_component_clause,[],[f2455]) ).
thf(f2459,definition,
( spl163_27
<=> ( ( 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,[spl163_27])],[avatar_definition]) ).
thf(f2461,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 ) ) ) ) ) ) ) )
| spl163_27 ),
inference(avatar_component_clause,[],[f2459]) ).
thf(f2463,definition,
( spl163_28
<=> ( ( 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,[spl163_28])],[avatar_definition]) ).
thf(f2465,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 )
| spl163_28 ),
inference(avatar_component_clause,[],[f2463]) ).
thf(f2467,definition,
( spl163_29
<=> ( ( 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 ) ),
introduced(definition,[new_symbols(definition,[spl163_29])],[avatar_definition]) ).
thf(f2469,plain,
( ( ( 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 )
| spl163_29 ),
inference(avatar_component_clause,[],[f2467]) ).
thf(f2470,plain,
( ~ spl163_26
| ~ spl163_27
| ~ spl163_28
| ~ spl163_29 ),
inference(avatar_split_clause,[],[f1741,f2467,f2463,f2459,f2455]) ).
thf(f2537,definition,
( spl163_43
<=> ( translation_b
= ( ^ [Y0: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl163_43])],[avatar_definition]) ).
thf(f2539,plain,
( ( translation_b
= ( ^ [Y0: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ Y0 ) ) ) )
| ~ spl163_43 ),
inference(avatar_component_clause,[],[f2537]) ).
thf(f2540,plain,
spl163_43,
inference(avatar_split_clause,[],[f1679,f2537]) ).
thf(f2570,plain,
( ( $true
!= ( 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 ) ) ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ) )
| spl163_26 ),
inference(superposition,[],[f2457,f2103]) ).
thf(f2571,plain,
( ( $true
!= ( graph_529870330at_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 ) ) ) ) ) ) ) )
| spl163_26 ),
inference(forward_demodulation,[],[f2570,f1859]) ).
thf(f2572,plain,
( ( ( 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 ) ) ) )
!= $true )
| spl163_26 ),
inference(forward_demodulation,[],[f2571,f1716]) ).
thf(f2573,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 ) ) ) ) )
| spl163_26 ),
inference(forward_demodulation,[],[f2572,f1795]) ).
thf(f2575,definition,
( spl163_48
<=> ( $true
= ( graph_529870330at_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ u ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl163_48])],[avatar_definition]) ).
thf(f2577,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 ) ) ) ) )
| spl163_48 ),
inference(avatar_component_clause,[],[f2575]) ).
thf(f2578,plain,
( ~ spl163_48
| spl163_26 ),
inference(avatar_split_clause,[],[f2573,f2455,f2575]) ).
thf(f2597,plain,
( ! [X1: allegorical_term_b] :
( ( translation_b @ X1 )
= ( ^ [Y0: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ Y0 ) )
@ X1 ) )
| ~ spl163_43 ),
inference(argument_congruence,[],[f2539]) ).
thf(f2598,plain,
( ! [X1: allegorical_term_b] :
( ( translation_b @ X1 )
= ( restrict_b_nat @ ( translation_b @ X1 ) ) )
| ~ spl163_43 ),
inference(beta-eta_normalization,[],[f2597]) ).
thf(f3191,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( $true
= ( graph_529870330at_nat @ ( translation_b @ X1 ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ X1 ) ) ) ) ),
inference(forward_demodulation,[],[f1931,f1859]) ).
thf(f3192,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( $true
= ( graph_529870330at_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ X1 ) ) ) ) ),
inference(forward_demodulation,[],[f3191,f2103]) ).
thf(f3198,plain,
( ( $true != $true )
| spl163_48 ),
inference(superposition,[],[f2577,f3192]) ).
thf(f3207,plain,
( $false
| spl163_48 ),
inference(trivial_inequality_removal,[],[f3198]) ).
thf(f3208,plain,
spl163_48,
inference(avatar_contradiction_clause,[],[f3207]) ).
thf(f3218,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 ) ) ) ) ) )
| spl163_27 ),
inference(forward_demodulation,[],[f2461,f2103]) ).
thf(f3224,plain,
( $false
| spl163_27
| ~ spl163_43 ),
inference(forward_subsumption_resolution,[],[f3218,f2598]) ).
thf(f3225,plain,
( spl163_27
| ~ spl163_43 ),
inference(avatar_contradiction_clause,[],[f3224]) ).
thf(f3230,plain,
( ( $true
!= ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
| spl163_28 ),
inference(forward_demodulation,[],[f2465,f2103]) ).
thf(f3235,plain,
( $false
| spl163_28 ),
inference(forward_subsumption_resolution,[],[f3230,f1706]) ).
thf(f3236,plain,
spl163_28,
inference(avatar_contradiction_clause,[],[f3235]) ).
thf(f3239,plain,
( ( $true
!= ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
| spl163_29 ),
inference(forward_demodulation,[],[f2469,f2103]) ).
thf(f3241,plain,
( $false
| spl163_29 ),
inference(forward_subsumption_resolution,[],[f3239,f1837]) ).
thf(f3242,plain,
spl163_29,
inference(avatar_contradiction_clause,[],[f3241]) ).
cnf(s29,plain,
( ~ spl163_26
| ~ spl163_27
| ~ spl163_28
| ~ spl163_29 ),
inference(sat_conversion,[],[f2470]) ).
cnf(s44,plain,
spl163_43,
inference(sat_conversion,[],[f2540]) ).
cnf(s49,plain,
( spl163_26
| ~ spl163_48 ),
inference(sat_conversion,[],[f2578]) ).
cnf(s79,plain,
spl163_48,
inference(sat_conversion,[],[f3208]) ).
cnf(s83,plain,
( spl163_27
| ~ spl163_43 ),
inference(sat_conversion,[],[f3225]) ).
cnf(s84,plain,
spl163_28,
inference(sat_conversion,[],[f3236]) ).
cnf(s85,plain,
spl163_29,
inference(sat_conversion,[],[f3242]) ).
cnf(s86,plain,
spl163_26,
inference(rat,[],[s49,s79]) ).
cnf(s89,plain,
spl163_27,
inference(rat,[],[s83,s44]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s29,s85,s84,s89,s86]) ).
thf(f3243,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 20:05:45 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.39 % (3149180)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.55/0.39 % (3149215)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=169094520:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.55/0.39 % (3149218)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.55/0.39 % (3149218)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.55/0.39 % (3149212)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=687896935:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.55/0.39 % (3149213)lrs+10_16_si=on:nwc=1.5:random_seed=3364730686:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.55/0.39 % (3149214)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1977304971:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.55/0.39 % (3149217)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3061167528:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.55/0.39 % (3149216)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=646604054:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.55/0.39 % (3149218)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=411278016:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.55/0.39 % (3149214)Instruction limit reached!
% 0.55/0.39 % (3149214)------------------------------
% 0.55/0.39 % (3149214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149214)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149214)Termination reason: Instruction limit
% 0.55/0.39 % (3149214)Termination phase: shuffling
% 0.55/0.39 % (3149214)Time elapsed: 0.002 s
% 0.55/0.39 % (3149214)Peak memory usage: 10 MB
% 0.55/0.39 % (3149214)Instructions burned: 3 (million)
% 0.55/0.39 % (3149213)Instruction limit reached!
% 0.55/0.39 % (3149213)------------------------------
% 0.55/0.39 % (3149213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149213)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149213)Termination reason: Instruction limit
% 0.55/0.39 % (3149213)Termination phase: shuffling
% 0.55/0.39 % (3149213)Time elapsed: 0.009 s
% 0.55/0.39 % (3149213)Peak memory usage: 10 MB
% 0.55/0.39 % (3149213)Instructions burned: 20 (million)
% 0.55/0.39 % (3149216)Instruction limit reached!
% 0.55/0.39 % (3149216)------------------------------
% 0.55/0.39 % (3149216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149216)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149216)Termination reason: Instruction limit
% 0.55/0.39 % (3149216)Termination phase: Property scanning
% 0.55/0.39 % (3149216)Time elapsed: 0.013 s
% 0.55/0.39 % (3149216)Peak memory usage: 11 MB
% 0.55/0.39 % (3149216)Instructions burned: 30 (million)
% 0.55/0.39 % (3149230)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=50653833:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.55/0.39 % (3149230)Instruction limit reached!
% 0.55/0.39 % (3149230)------------------------------
% 0.55/0.39 % (3149230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149230)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149230)Termination reason: Instruction limit
% 0.55/0.39 % (3149230)Termination phase: shuffling
% 0.55/0.39 % (3149230)Time elapsed: 0.002 s
% 0.55/0.39 % (3149230)Peak memory usage: 10 MB
% 0.55/0.39 % (3149230)Instructions burned: 3 (million)
% 0.55/0.39 % (3149231)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=674632157:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.55/0.39 % (3149232)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.55/0.39 % (3149231)Instruction limit reached!
% 0.55/0.39 % (3149231)------------------------------
% 0.55/0.39 % (3149231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149232)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1353813291:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.55/0.39 % (3149231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149231)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149231)Termination reason: Instruction limit
% 0.55/0.39 % (3149231)Termination phase: shuffling
% 0.55/0.39 % (3149231)Time elapsed: 0.004 s
% 0.55/0.39 % (3149231)Peak memory usage: 10 MB
% 0.55/0.39 % (3149231)Instructions burned: 7 (million)
% 0.55/0.39 % (3149217)Instruction limit reached!
% 0.55/0.39 % (3149217)------------------------------
% 0.55/0.39 % (3149217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149217)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149217)Termination reason: Instruction limit
% 0.55/0.39 % (3149217)Termination phase: Preprocessing 3
% 0.55/0.39 % (3149217)Time elapsed: 0.035 s
% 0.55/0.39 % (3149217)Peak memory usage: 12 MB
% 0.55/0.39 % (3149217)Instructions burned: 75 (million)
% 0.55/0.39 % (3149232)Instruction limit reached!
% 0.55/0.39 % (3149232)------------------------------
% 0.55/0.39 % (3149232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149232)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149232)Termination reason: Instruction limit
% 0.55/0.39 % (3149232)Termination phase: shuffling
% 0.55/0.39 % (3149232)Time elapsed: 0.005 s
% 0.55/0.39 % (3149232)Peak memory usage: 10 MB
% 0.55/0.39 % (3149232)Instructions burned: 9 (million)
% 0.55/0.39 % (3149212)Instruction limit reached!
% 0.55/0.39 % (3149212)------------------------------
% 0.55/0.39 % (3149212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149212)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149212)Termination reason: Instruction limit
% 0.55/0.39 % (3149212)Termination phase: Property scanning
% 0.55/0.39 % (3149212)Time elapsed: 0.040 s
% 0.55/0.39 % (3149212)Peak memory usage: 12 MB
% 0.55/0.39 % (3149212)Instructions burned: 88 (million)
% 0.55/0.39 % (3149234)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=589903594:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.55/0.39 % (3149237)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.55/0.39 % (3149237)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.55/0.39 % (3149234)Instruction limit reached!
% 0.55/0.39 % (3149234)------------------------------
% 0.55/0.39 % (3149234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149234)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149234)Termination reason: Instruction limit
% 0.55/0.39 % (3149234)Termination phase: shuffling
% 0.55/0.39 % (3149234)Time elapsed: 0.006 s
% 0.55/0.39 % (3149234)Peak memory usage: 10 MB
% 0.55/0.39 % (3149234)Instructions burned: 13 (million)
% 0.55/0.39 % (3149237)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2944988683:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.55/0.39 % (3149238)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2777961797:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.55/0.39 % (3149240)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.55/0.39 % (3149239)lrs+10_1_si=on:cs=on:random_seed=1778954180:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.55/0.39 % (3149240)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2045340852:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.55/0.39 % (3149240)Instruction limit reached!
% 0.55/0.39 % (3149240)------------------------------
% 0.55/0.39 % (3149240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149240)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149240)Termination reason: Instruction limit
% 0.55/0.39 % (3149240)Termination phase: shuffling
% 0.55/0.39 % (3149240)Time elapsed: 0.002 s
% 0.55/0.39 % (3149240)Peak memory usage: 10 MB
% 0.55/0.39 % (3149240)Instructions burned: 3 (million)
% 0.55/0.39 % (3149239)Instruction limit reached!
% 0.55/0.39 % (3149239)------------------------------
% 0.55/0.39 % (3149239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149239)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149239)Termination reason: Instruction limit
% 0.55/0.39 % (3149239)Termination phase: shuffling
% 0.55/0.39 % (3149239)Time elapsed: 0.004 s
% 0.55/0.39 % (3149239)Peak memory usage: 10 MB
% 0.55/0.39 % (3149239)Instructions burned: 8 (million)
% 0.55/0.39 % (3149215) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3149180-3149215"...
% 0.55/0.39 % (3149237)Instruction limit reached!
% 0.55/0.39 % (3149237)------------------------------
% 0.55/0.39 % (3149237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.39 % (3149237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.39 % (3149237)CaDiCaL version: 2.1.3
% 0.55/0.39 % (3149237)Termination reason: Instruction limit
% 0.55/0.39 % (3149237)Termination phase: shuffling
% 0.55/0.39 % (3149237)Time elapsed: 0.013 s
% 0.55/0.39 % (3149237)Peak memory usage: 11 MB
% 0.55/0.39 % (3149237)Instructions burned: 28 (million)
% 0.55/0.39 % (3149242)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1553619254:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.55/0.39 % (3149215)...printing done.
% 0.55/0.39 % (3149215)Refutation found. Thanks to Tanya!
% 0.55/0.39 % SZS status Theorem for theBenchmark
% 0.55/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.55/0.40 % (3149215)------------------------------
% 0.55/0.40 % (3149215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (3149215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (3149215)CaDiCaL version: 2.1.3
% 0.55/0.40 % (3149215)Termination reason: Refutation
% 0.55/0.40 % (3149215)Time elapsed: 0.077 s
% 0.55/0.40 % (3149215)Peak memory usage: 16 MB
% 0.55/0.40 % (3149215)Instructions burned: 278 (million)
% 0.55/0.40 % (3149180)Success in time 0.127 s
% 0.55/0.40 % Vampire exiting
%------------------------------------------------------------------------------