%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP179^1 : 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 : n007.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 7.45s 1.37s
% Output : Refutation 7.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 118 ( 57 unt; 0 typ; 7 def)
% Number of atoms : 423 ( 170 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1890 ( 105 ~; 107 |; 25 &;1628 @)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 55 ( 54 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 313 ( 309 usr; 39 con; 0-4 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 79 ( 0 sgn 59 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1355257963at_nat: $tType ).
thf(type_def_6,type,
set_Pr1429673827um_a_b: $tType ).
thf(type_def_7,type,
set_Pr2065572323um_a_b: $tType ).
thf(type_def_8,type,
set_Pr1558970842um_a_b: $tType ).
thf(type_def_9,type,
set_Pr1121389018um_a_b: $tType ).
thf(type_def_10,type,
produc1733247354um_a_b: $tType ).
thf(type_def_11,type,
produc1681803642um_a_b: $tType ).
thf(type_def_12,type,
produc1871334759_a_nat: $tType ).
thf(type_def_13,type,
labele498606060at_nat: $tType ).
thf(type_def_14,type,
set_Pr304595758um_a_b: $tType ).
thf(type_def_15,type,
set_Pr409224873um_a_b: $tType ).
thf(type_def_16,type,
set_Pr45173959um_a_b: $tType ).
thf(type_def_17,type,
set_Pr689416536at_nat: $tType ).
thf(type_def_18,type,
set_Pr1134469976at_nat: $tType ).
thf(type_def_19,type,
labele1191284958um_a_b: $tType ).
thf(type_def_20,type,
produc1963079155um_a_b: $tType ).
thf(type_def_21,type,
produc1918750183um_a_b: $tType ).
thf(type_def_22,type,
set_Pr55236280um_a_b: $tType ).
thf(type_def_23,type,
set_Pr326391507um_a_b: $tType ).
thf(type_def_24,type,
set_Pr386468381um_a_b: $tType ).
thf(type_def_25,type,
labele261019144um_a_b: $tType ).
thf(type_def_26,type,
produc1003469085um_a_b: $tType ).
thf(type_def_27,type,
produc1546082365um_a_b: $tType ).
thf(type_def_28,type,
set_Pr1783309276um_a_b: $tType ).
thf(type_def_29,type,
set_Pr507214050_b_nat: $tType ).
thf(type_def_30,type,
set_Pr653770722um_a_b: $tType ).
thf(type_def_31,type,
set_Pr1155046920um_a_b: $tType ).
thf(type_def_32,type,
set_Pr1647387645at_nat: $tType ).
thf(type_def_33,type,
produc323101606um_a_b: $tType ).
thf(type_def_34,type,
produc585753260um_a_b: $tType ).
thf(type_def_35,type,
produc1032616263at_nat: $tType ).
thf(type_def_36,type,
set_Pr1994339542um_a_b: $tType ).
thf(type_def_37,type,
set_Pr1902304780_b_nat: $tType ).
thf(type_def_38,type,
set_Pr195945996um_a_b: $tType ).
thf(type_def_39,type,
set_Pr1618094130um_a_b: $tType ).
thf(type_def_40,type,
labele431970251um_a_b: $tType ).
thf(type_def_41,type,
produc1394389750um_a_b: $tType ).
thf(type_def_42,type,
produc1798470614um_a_b: $tType ).
thf(type_def_43,type,
produc204140796um_a_b: $tType ).
thf(type_def_44,type,
set_Pr1916610317um_a_b: $tType ).
thf(type_def_45,type,
labele935650037_a_nat: $tType ).
thf(type_def_46,type,
produc1548871597um_a_b: $tType ).
thf(type_def_47,type,
set_Pr375490359_b_nat: $tType ).
thf(type_def_48,type,
set_Pr1174980151um_a_b: $tType ).
thf(type_def_49,type,
produc1978941143_b_nat: $tType ).
thf(type_def_50,type,
produc1124793815um_a_b: $tType ).
thf(type_def_51,type,
set_St761939237tant_a: $tType ).
thf(type_def_52,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_53,type,
standard_Constant_a: $tType ).
thf(type_def_54,type,
product_prod_nat_nat: $tType ).
thf(type_def_55,type,
set_Sum_sum_a_b: $tType ).
thf(type_def_56,type,
sum_sum_a_b: $tType ).
thf(type_def_57,type,
set_nat: $tType ).
thf(type_def_58,type,
nat: $tType ).
thf(type_def_59,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
zero_zero_nat: nat ).
thf(func_def_1,type,
standard_S_Bot_a: standard_Constant_a ).
thf(func_def_2,type,
standard_S_Idt_a: standard_Constant_a ).
thf(func_def_3,type,
getRel1465196352um_a_b: standard_Constant_a > labele431970251um_a_b > set_Pr1916610317um_a_b ).
thf(func_def_4,type,
edge_p170421892tant_a: set_Pr1986765409at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o ).
thf(func_def_5,type,
edge_p1382426714tant_a: set_Pr1174980151um_a_b > set_Pr1647387645at_nat > set_Pr409224873um_a_b > $o ).
thf(func_def_6,type,
edge_p749155930tant_a: set_Pr375490359_b_nat > set_Pr409224873um_a_b > set_Pr1647387645at_nat > $o ).
thf(func_def_7,type,
edge_p1871801392tant_a: set_Pr1916610317um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o ).
thf(func_def_8,type,
graph_2130075512at_nat: labele935650037_a_nat > labele935650037_a_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_9,type,
graph_1452133198um_a_b: labele935650037_a_nat > labele431970251um_a_b > set_Pr1174980151um_a_b > $o ).
thf(func_def_10,type,
graph_149544303at_nat: labele498606060at_nat > labele935650037_a_nat > set_Pr689416536at_nat > $o ).
thf(func_def_11,type,
graph_166346565um_a_b: labele498606060at_nat > labele431970251um_a_b > set_Pr304595758um_a_b > $o ).
thf(func_def_12,type,
graph_1203757137_b_nat: labele261019144um_a_b > labele935650037_a_nat > set_Pr1902304780_b_nat > $o ).
thf(func_def_13,type,
graph_502887975um_a_b: labele261019144um_a_b > labele431970251um_a_b > set_Pr653770722um_a_b > $o ).
thf(func_def_14,type,
graph_1815313447_b_nat: labele1191284958um_a_b > labele935650037_a_nat > set_Pr507214050_b_nat > $o ).
thf(func_def_15,type,
graph_1763806717um_a_b: labele1191284958um_a_b > labele431970251um_a_b > set_Pr55236280um_a_b > $o ).
thf(func_def_16,type,
graph_165730638_b_nat: labele431970251um_a_b > labele935650037_a_nat > set_Pr375490359_b_nat > $o ).
thf(func_def_17,type,
graph_611893540um_a_b: labele431970251um_a_b > labele431970251um_a_b > set_Pr1916610317um_a_b > $o ).
thf(func_def_18,type,
labele16114835_a_nat: set_Pr1647387645at_nat > set_nat > labele935650037_a_nat ).
thf(func_def_19,type,
labele1813985418at_nat: set_Pr1355257963at_nat > set_Pr1647387645at_nat > labele498606060at_nat ).
thf(func_def_20,type,
labele2034032468um_a_b: set_Pr2065572323um_a_b > set_Pr1174980151um_a_b > labele261019144um_a_b ).
thf(func_def_21,type,
labele989994um_a_b: set_Pr1429673827um_a_b > set_Pr1916610317um_a_b > labele1191284958um_a_b ).
thf(func_def_22,type,
labele1729654377um_a_b: set_Pr409224873um_a_b > set_Sum_sum_a_b > labele431970251um_a_b ).
thf(func_def_23,type,
labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat ).
thf(func_def_24,type,
labele1939049654um_a_b: labele431970251um_a_b > set_Pr409224873um_a_b ).
thf(func_def_25,type,
labele1810595089_a_nat: labele935650037_a_nat > set_nat ).
thf(func_def_26,type,
labele577278695um_a_b: labele431970251um_a_b > set_Sum_sum_a_b ).
thf(func_def_27,type,
restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_28,type,
restri1162247455um_a_b: labele431970251um_a_b > labele431970251um_a_b ).
thf(func_def_29,type,
unival860567212at_nat: set_Pr1647387645at_nat > $o ).
thf(func_def_30,type,
unival1487587672um_a_b: set_Pr409224873um_a_b > $o ).
thf(func_def_31,type,
unival2092813468um_a_b: set_Pr1174980151um_a_b > $o ).
thf(func_def_32,type,
unival118648434um_a_b: set_Pr1916610317um_a_b > $o ).
thf(func_def_33,type,
bot_bot_nat: nat ).
thf(func_def_34,type,
bot_bo1160111033tant_a: set_St761939237tant_a ).
thf(func_def_35,type,
bot_bot_set_nat: set_nat ).
thf(func_def_36,type,
bot_bo810816657at_nat: set_Pr1647387645at_nat ).
thf(func_def_37,type,
bot_bo1524397311at_nat: set_Pr1355257963at_nat ).
thf(func_def_38,type,
bot_bo1208513655um_a_b: set_Pr2065572323um_a_b ).
thf(func_def_39,type,
bot_bo1262778871um_a_b: set_Pr1429673827um_a_b ).
thf(func_def_40,type,
bot_bo1262634813um_a_b: set_Pr409224873um_a_b ).
thf(func_def_41,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(func_def_42,type,
bot_bo575978147um_a_b: set_Pr1174980151um_a_b ).
thf(func_def_43,type,
bot_bo1582968772at_nat: set_Pr689416536at_nat ).
thf(func_def_44,type,
bot_bo627753370um_a_b: set_Pr304595758um_a_b ).
thf(func_def_45,type,
bot_bo949957280_b_nat: set_Pr1902304780_b_nat ).
thf(func_def_46,type,
bot_bo1892785270um_a_b: set_Pr653770722um_a_b ).
thf(func_def_47,type,
bot_bo1746228598_b_nat: set_Pr507214050_b_nat ).
thf(func_def_48,type,
bot_bo1217542988um_a_b: set_Pr55236280um_a_b ).
thf(func_def_49,type,
bot_bo1923972003_b_nat: set_Pr375490359_b_nat ).
thf(func_def_50,type,
bot_bo225809273um_a_b: set_Pr1916610317um_a_b ).
thf(func_def_51,type,
bot_bo1491243248um_a_b: set_Sum_sum_a_b ).
thf(func_def_52,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_53,type,
ord_le1739761029tant_a: set_St761939237tant_a > set_St761939237tant_a > $o ).
thf(func_def_54,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_55,type,
ord_le1909159005at_nat: set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o ).
thf(func_def_56,type,
ord_le615126793um_a_b: set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o ).
thf(func_def_57,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_58,type,
ord_le823954903um_a_b: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > $o ).
thf(func_def_59,type,
ord_le1059794605um_a_b: set_Pr1916610317um_a_b > set_Pr1916610317um_a_b > $o ).
thf(func_def_60,type,
ord_le192794300um_a_b: set_Sum_sum_a_b > set_Sum_sum_a_b > $o ).
thf(func_def_61,type,
produc407553657at_nat: standard_Constant_a > product_prod_nat_nat > produc1032616263at_nat ).
thf(func_def_62,type,
produc414524239um_a_b: standard_Constant_a > produc1124793815um_a_b > produc1003469085um_a_b ).
thf(func_def_63,type,
produc1697725733um_a_b: standard_Constant_a > produc1548871597um_a_b > produc1963079155um_a_b ).
thf(func_def_64,type,
produc584843310um_a_b: standard_Constant_a > sum_sum_a_b > produc1394389750um_a_b ).
thf(func_def_65,type,
produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat ).
thf(func_def_66,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_67,type,
produc1346373166um_a_b: nat > produc1124793815um_a_b > produc204140796um_a_b ).
thf(func_def_68,type,
produc1808556047um_a_b: nat > sum_sum_a_b > produc1124793815um_a_b ).
thf(func_def_69,type,
produc522766386um_a_b: produc1963079155um_a_b > sum_sum_a_b > produc1681803642um_a_b ).
thf(func_def_70,type,
produc335036333um_a_b: product_prod_nat_nat > produc1124793815um_a_b > produc1546082365um_a_b ).
thf(func_def_71,type,
produc1872245072um_a_b: product_prod_nat_nat > sum_sum_a_b > produc1798470614um_a_b ).
thf(func_def_72,type,
produc27163479um_a_b: produc1124793815um_a_b > produc1124793815um_a_b > produc1918750183um_a_b ).
thf(func_def_73,type,
produc831476262um_a_b: produc1124793815um_a_b > sum_sum_a_b > produc585753260um_a_b ).
thf(func_def_74,type,
produc522153487_b_nat: sum_sum_a_b > nat > produc1978941143_b_nat ).
thf(func_def_75,type,
produc230853810um_a_b: sum_sum_a_b > produc1963079155um_a_b > produc1733247354um_a_b ).
thf(func_def_76,type,
produc1637282520um_a_b: sum_sum_a_b > produc1124793815um_a_b > produc323101606um_a_b ).
thf(func_def_77,type,
produc176426981um_a_b: sum_sum_a_b > sum_sum_a_b > produc1548871597um_a_b ).
thf(func_def_78,type,
domain1060562500at_nat: set_Pr1647387645at_nat > set_St761939237tant_a ).
thf(func_def_79,type,
domain1362581744um_a_b: set_Pr409224873um_a_b > set_St761939237tant_a ).
thf(func_def_80,type,
domain_nat_nat: set_Pr1986765409at_nat > set_nat ).
thf(func_def_81,type,
domain1368163076um_a_b: set_Pr1174980151um_a_b > set_nat ).
thf(func_def_82,type,
domain2069673178um_a_b: set_Pr1916610317um_a_b > set_Sum_sum_a_b ).
thf(func_def_83,type,
id_on_Sum_sum_a_b: set_Sum_sum_a_b > set_Pr1916610317um_a_b ).
thf(func_def_84,type,
image_127502653at_nat: set_Pr1647387645at_nat > set_St761939237tant_a > set_Pr1986765409at_nat ).
thf(func_def_85,type,
image_1179143699um_a_b: set_Pr326391507um_a_b > set_St761939237tant_a > set_Pr1174980151um_a_b ).
thf(func_def_86,type,
image_2023280617um_a_b: set_Pr409224873um_a_b > set_St761939237tant_a > set_Pr1916610317um_a_b ).
thf(func_def_87,type,
image_2129435242um_a_b: set_Pr1994339542um_a_b > set_St761939237tant_a > set_Sum_sum_a_b ).
thf(func_def_88,type,
image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat ).
thf(func_def_89,type,
image_489788268at_nat: set_Pr1134469976at_nat > set_nat > set_Pr1647387645at_nat ).
thf(func_def_90,type,
image_1228479730um_a_b: set_Pr1618094130um_a_b > set_nat > set_Pr1174980151um_a_b ).
thf(func_def_91,type,
image_166667464um_a_b: set_Pr1155046920um_a_b > set_nat > set_Pr1916610317um_a_b ).
thf(func_def_92,type,
image_256773707um_a_b: set_Pr1174980151um_a_b > set_nat > set_Sum_sum_a_b ).
thf(func_def_93,type,
image_452296684at_nat: set_Pr689416536at_nat > set_Pr1647387645at_nat > set_nat ).
thf(func_def_94,type,
image_1774897262um_a_b: set_Pr1121389018um_a_b > set_Pr409224873um_a_b > set_Sum_sum_a_b ).
thf(func_def_95,type,
image_320480233um_a_b: set_Pr386468381um_a_b > set_Pr1986765409at_nat > set_Pr1174980151um_a_b ).
thf(func_def_96,type,
image_1754351636um_a_b: set_Pr195945996um_a_b > set_Pr1986765409at_nat > set_Sum_sum_a_b ).
thf(func_def_97,type,
image_128716052_b_nat: set_Pr1902304780_b_nat > set_Pr1174980151um_a_b > set_nat ).
thf(func_def_98,type,
image_1464989587um_a_b: set_Pr45173959um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b ).
thf(func_def_99,type,
image_869585130um_a_b: set_Pr653770722um_a_b > set_Pr1174980151um_a_b > set_Sum_sum_a_b ).
thf(func_def_100,type,
image_1117854795_b_nat: set_Pr375490359_b_nat > set_Sum_sum_a_b > set_nat ).
thf(func_def_101,type,
image_1482984686um_a_b: set_Pr1558970842um_a_b > set_Sum_sum_a_b > set_Pr409224873um_a_b ).
thf(func_def_102,type,
image_1675391388um_a_b: set_Pr1783309276um_a_b > set_Sum_sum_a_b > set_Pr1174980151um_a_b ).
thf(func_def_103,type,
image_1918588449um_a_b: set_Pr1916610317um_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b ).
thf(func_def_104,type,
mainta522127984um_a_b: produc1871334759_a_nat > labele431970251um_a_b > $o ).
thf(func_def_105,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_106,type,
collec52779676at_nat: ( produc1032616263at_nat > $o ) > set_Pr1647387645at_nat ).
thf(func_def_107,type,
collec1254333256um_a_b: ( produc1963079155um_a_b > $o ) > set_Pr409224873um_a_b ).
thf(func_def_108,type,
collec492052930um_a_b: ( produc1124793815um_a_b > $o ) > set_Pr1174980151um_a_b ).
thf(func_def_109,type,
collec1769032088um_a_b: ( produc1548871597um_a_b > $o ) > set_Pr1916610317um_a_b ).
thf(func_def_110,type,
collect_Sum_sum_a_b: ( sum_sum_a_b > $o ) > set_Sum_sum_a_b ).
thf(func_def_111,type,
insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).
thf(func_def_112,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_113,type,
insert1625259895at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat ).
thf(func_def_114,type,
insert323157027um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b ).
thf(func_def_115,type,
insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_116,type,
insert983991207um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b ).
thf(func_def_117,type,
insert1435405693um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > set_Pr1916610317um_a_b ).
thf(func_def_118,type,
insert_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b ).
thf(func_def_119,type,
standa1343274079tant_a: standard_Constant_a > standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_120,type,
standa1410829644tant_a: produc1871334759_a_nat ).
thf(func_def_121,type,
standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_122,type,
standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_123,type,
standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_124,type,
member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).
thf(func_def_125,type,
member_nat: nat > set_nat > $o ).
thf(func_def_126,type,
member1696759390at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > $o ).
thf(func_def_127,type,
member1502344244um_a_b: produc1003469085um_a_b > set_Pr326391507um_a_b > $o ).
thf(func_def_128,type,
member1998628618um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > $o ).
thf(func_def_129,type,
member1641046175um_a_b: produc1394389750um_a_b > set_Pr1994339542um_a_b > $o ).
thf(func_def_130,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_131,type,
member1139034387um_a_b: produc204140796um_a_b > set_Pr1618094130um_a_b > $o ).
thf(func_def_132,type,
member1294585472um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > $o ).
thf(func_def_133,type,
member1590479267um_a_b: produc1681803642um_a_b > set_Pr1121389018um_a_b > $o ).
thf(func_def_134,type,
member834135910um_a_b: produc1546082365um_a_b > set_Pr386468381um_a_b > $o ).
thf(func_def_135,type,
member585880557um_a_b: produc1798470614um_a_b > set_Pr195945996um_a_b > $o ).
thf(func_def_136,type,
member429827856um_a_b: produc1918750183um_a_b > set_Pr45173959um_a_b > $o ).
thf(func_def_137,type,
member748122307um_a_b: produc585753260um_a_b > set_Pr653770722um_a_b > $o ).
thf(func_def_138,type,
member1249152_b_nat: produc1978941143_b_nat > set_Pr375490359_b_nat > $o ).
thf(func_def_139,type,
member1641922979um_a_b: produc1733247354um_a_b > set_Pr1558970842um_a_b > $o ).
thf(func_def_140,type,
member485470653um_a_b: produc323101606um_a_b > set_Pr1783309276um_a_b > $o ).
thf(func_def_141,type,
member947389014um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > $o ).
thf(func_def_142,type,
member_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > $o ).
thf(func_def_143,type,
g: labele431970251um_a_b ).
thf(func_def_144,type,
f: set_Pr1174980151um_a_b ).
thf(func_def_145,type,
l: standard_Constant_a ).
thf(func_def_146,type,
v: sum_sum_a_b ).
thf(func_def_150,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_154,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_155,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_156,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_157,type,
vNOT: $o > $o ).
thf(func_def_158,type,
vOR: $o > $o > $o ).
thf(func_def_159,type,
vIMP: $o > $o > $o ).
thf(func_def_160,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_161,type,
sK0: sum_sum_a_b ).
thf(func_def_162,type,
sK1: labele935650037_a_nat > set_Pr1647387645at_nat ).
thf(func_def_163,type,
sK2: labele935650037_a_nat > set_nat ).
thf(func_def_164,type,
sK3: labele431970251um_a_b > set_Pr409224873um_a_b ).
thf(func_def_165,type,
sK4: labele431970251um_a_b > set_Sum_sum_a_b ).
thf(func_def_166,type,
sK5: ( labele935650037_a_nat > $o ) > set_Pr1647387645at_nat ).
thf(func_def_167,type,
sK6: ( labele935650037_a_nat > $o ) > set_nat ).
thf(func_def_168,type,
sK7: ( labele431970251um_a_b > $o ) > set_Pr409224873um_a_b ).
thf(func_def_169,type,
sK8: ( labele431970251um_a_b > $o ) > set_Sum_sum_a_b ).
thf(func_def_170,type,
sK9: set_nat > set_Pr1986765409at_nat > nat > nat ).
thf(func_def_171,type,
sK10: set_nat > set_Pr1174980151um_a_b > sum_sum_a_b > nat ).
thf(func_def_172,type,
sK11: set_St761939237tant_a > set_Pr1647387645at_nat > product_prod_nat_nat > standard_Constant_a ).
thf(func_def_173,type,
sK12: set_Sum_sum_a_b > set_Pr1916610317um_a_b > sum_sum_a_b > sum_sum_a_b ).
thf(func_def_174,type,
sK13: set_Pr1174980151um_a_b > set_Pr653770722um_a_b > sum_sum_a_b > produc1124793815um_a_b ).
thf(func_def_175,type,
sK14: set_Sum_sum_a_b > set_Pr1783309276um_a_b > produc1124793815um_a_b > sum_sum_a_b ).
thf(func_def_176,type,
sK15: set_St761939237tant_a > set_Pr409224873um_a_b > produc1548871597um_a_b > standard_Constant_a ).
thf(func_def_177,type,
sK16: set_Pr1174980151um_a_b > set_Pr45173959um_a_b > produc1124793815um_a_b > produc1124793815um_a_b ).
thf(func_def_178,type,
sK17: set_Pr409224873um_a_b > set_Pr1121389018um_a_b > sum_sum_a_b > produc1963079155um_a_b ).
thf(func_def_179,type,
sK18: set_Sum_sum_a_b > set_Pr1558970842um_a_b > produc1963079155um_a_b > sum_sum_a_b ).
thf(func_def_180,type,
sK19: ( standard_Constant_a > $o ) > set_Pr1647387645at_nat > standard_Constant_a ).
thf(func_def_181,type,
sK20: ( standard_Constant_a > $o ) > set_Pr1647387645at_nat > product_prod_nat_nat ).
thf(func_def_182,type,
sK21: ( nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_183,type,
sK22: ( nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_184,type,
sK23: ( nat > $o ) > set_Pr1174980151um_a_b > nat ).
thf(func_def_185,type,
sK24: ( nat > $o ) > set_Pr1174980151um_a_b > sum_sum_a_b ).
thf(func_def_186,type,
sK25: ( standard_Constant_a > $o ) > set_Pr409224873um_a_b > standard_Constant_a ).
thf(func_def_187,type,
sK26: ( standard_Constant_a > $o ) > set_Pr409224873um_a_b > produc1548871597um_a_b ).
thf(func_def_188,type,
sK27: ( sum_sum_a_b > $o ) > set_Pr1916610317um_a_b > sum_sum_a_b ).
thf(func_def_189,type,
sK28: ( sum_sum_a_b > $o ) > set_Pr1916610317um_a_b > sum_sum_a_b ).
thf(func_def_190,type,
sK29: set_Pr1647387645at_nat > standard_Constant_a > product_prod_nat_nat ).
thf(func_def_191,type,
sK30: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_192,type,
sK31: set_Pr1174980151um_a_b > nat > sum_sum_a_b ).
thf(func_def_193,type,
sK32: set_Pr409224873um_a_b > standard_Constant_a > produc1548871597um_a_b ).
thf(func_def_194,type,
sK33: set_Pr1916610317um_a_b > sum_sum_a_b > sum_sum_a_b ).
thf(func_def_195,type,
sK34: set_Pr1647387645at_nat > standard_Constant_a > product_prod_nat_nat ).
thf(func_def_196,type,
sK35: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_197,type,
sK36: set_Pr1174980151um_a_b > nat > sum_sum_a_b ).
thf(func_def_198,type,
sK37: set_Pr409224873um_a_b > standard_Constant_a > produc1548871597um_a_b ).
thf(func_def_199,type,
sK38: set_Pr1916610317um_a_b > sum_sum_a_b > sum_sum_a_b ).
thf(func_def_200,type,
sK39: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_201,type,
sK40: set_Pr409224873um_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_202,type,
sK41: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_203,type,
sK42: set_Pr1647387645at_nat > set_Pr1647387645at_nat > standard_Constant_a ).
thf(func_def_204,type,
sK43: set_Pr1647387645at_nat > set_Pr1647387645at_nat > product_prod_nat_nat ).
thf(func_def_205,type,
sK44: set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_206,type,
sK45: set_Pr1986765409at_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_207,type,
sK46: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > nat ).
thf(func_def_208,type,
sK47: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > sum_sum_a_b ).
thf(func_def_209,type,
sK48: set_Pr409224873um_a_b > set_Pr409224873um_a_b > standard_Constant_a ).
thf(func_def_210,type,
sK49: set_Pr409224873um_a_b > set_Pr409224873um_a_b > produc1548871597um_a_b ).
thf(func_def_211,type,
sK50: set_Pr1916610317um_a_b > set_Pr1916610317um_a_b > sum_sum_a_b ).
thf(func_def_212,type,
sK51: set_Pr1916610317um_a_b > set_Pr1916610317um_a_b > sum_sum_a_b ).
thf(func_def_213,type,
sK52: set_Pr1647387645at_nat > produc1032616263at_nat ).
thf(func_def_214,type,
sK53: set_nat > nat ).
thf(func_def_215,type,
sK54: set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_216,type,
sK55: set_Pr1916610317um_a_b > produc1548871597um_a_b ).
thf(func_def_217,type,
sK56: set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_218,type,
sK57: set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_219,type,
sK58: ( sum_sum_a_b > $o ) > ( sum_sum_a_b > $o ) > sum_sum_a_b ).
thf(func_def_220,type,
sK59: ( nat > $o ) > nat ).
thf(func_def_221,type,
sK60: nat > ( nat > $o ) > nat ).
thf(func_def_222,type,
sK61: sum_sum_a_b ).
thf(func_def_223,type,
sK62: ( sum_sum_a_b > $o ) > ( sum_sum_a_b > $o ) > sum_sum_a_b ).
thf(func_def_224,type,
sK63: ( sum_sum_a_b > $o ) > ( sum_sum_a_b > $o ) > sum_sum_a_b ).
thf(func_def_225,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_226,type,
sK64: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_227,type,
sK65: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_228,type,
sK66: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_229,type,
sK67: set_Pr409224873um_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_230,type,
sK68: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_231,type,
sK69: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_232,type,
sK70: set_Pr409224873um_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_233,type,
sK71: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_234,type,
sK72: set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_235,type,
sK73: set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_236,type,
sK74: set_Pr1916610317um_a_b > produc1548871597um_a_b ).
thf(func_def_237,type,
sK75: set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_238,type,
sK76: set_nat > nat ).
thf(func_def_239,type,
sK77: set_Pr1647387645at_nat > produc1032616263at_nat ).
thf(func_def_240,type,
sK78: labele431970251um_a_b > produc1963079155um_a_b ).
thf(func_def_241,type,
sK79: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_242,type,
sK80: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_243,type,
sK81: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_244,type,
sK82: ( sum_sum_a_b > $o ) > sum_sum_a_b ).
thf(func_def_245,type,
sK83: ( produc1963079155um_a_b > $o ) > produc1963079155um_a_b ).
thf(func_def_246,type,
sK84: ( produc1548871597um_a_b > $o ) > produc1548871597um_a_b ).
thf(func_def_247,type,
sK85: ( produc1124793815um_a_b > $o ) > produc1124793815um_a_b ).
thf(func_def_248,type,
sK86: ( nat > $o ) > nat ).
thf(func_def_249,type,
sK87: ( produc1032616263at_nat > $o ) > produc1032616263at_nat ).
thf(func_def_250,type,
sK88: ( sum_sum_a_b > $o ) > sum_sum_a_b ).
thf(func_def_251,type,
sK89: ( produc1963079155um_a_b > $o ) > produc1963079155um_a_b ).
thf(func_def_252,type,
sK90: ( produc1548871597um_a_b > $o ) > produc1548871597um_a_b ).
thf(func_def_253,type,
sK91: ( produc1124793815um_a_b > $o ) > produc1124793815um_a_b ).
thf(func_def_254,type,
sK92: ( nat > $o ) > nat ).
thf(func_def_255,type,
sK93: ( produc1032616263at_nat > $o ) > produc1032616263at_nat ).
thf(func_def_256,type,
sK94: set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_257,type,
sK95: set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_258,type,
sK96: set_Pr1916610317um_a_b > produc1548871597um_a_b ).
thf(func_def_259,type,
sK97: set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_260,type,
sK98: set_nat > nat ).
thf(func_def_261,type,
sK99: set_Pr1647387645at_nat > produc1032616263at_nat ).
thf(func_def_262,type,
sK100: set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_263,type,
sK101: set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_264,type,
sK102: set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_265,type,
sK103: set_Sum_sum_a_b > sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_266,type,
sK104: set_Sum_sum_a_b > sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_267,type,
sK105: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_268,type,
sK106: set_Pr409224873um_a_b > produc1963079155um_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_269,type,
sK107: set_Pr409224873um_a_b > produc1963079155um_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_270,type,
sK108: set_Pr409224873um_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_271,type,
sK109: set_Pr1174980151um_a_b > produc1124793815um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_272,type,
sK110: set_Pr1174980151um_a_b > produc1124793815um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_273,type,
sK111: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_274,type,
sK112: sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_275,type,
sK113: produc1963079155um_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_276,type,
sK114: produc1124793815um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_277,type,
sK115: set_Sum_sum_a_b > sum_sum_a_b > sum_sum_a_b ).
thf(func_def_278,type,
sK116: set_Pr409224873um_a_b > produc1963079155um_a_b > produc1963079155um_a_b ).
thf(func_def_279,type,
sK117: set_Pr1174980151um_a_b > produc1124793815um_a_b > produc1124793815um_a_b ).
thf(func_def_280,type,
sK118: set_Pr409224873um_a_b > set_Pr409224873um_a_b > produc1963079155um_a_b ).
thf(func_def_281,type,
sK119: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_282,type,
sK120: set_Pr1916610317um_a_b > sum_sum_a_b > sum_sum_a_b ).
thf(func_def_283,type,
sK121: set_Pr409224873um_a_b > standard_Constant_a > produc1548871597um_a_b ).
thf(func_def_284,type,
sK122: set_Pr1174980151um_a_b > nat > sum_sum_a_b ).
thf(func_def_285,type,
sK123: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_286,type,
sK124: set_Pr1647387645at_nat > standard_Constant_a > product_prod_nat_nat ).
thf(func_def_287,type,
sK125: set_Pr1916610317um_a_b > sum_sum_a_b > sum_sum_a_b ).
thf(func_def_288,type,
sK126: set_Pr1916610317um_a_b > sum_sum_a_b > sum_sum_a_b ).
thf(func_def_289,type,
sK127: set_Pr409224873um_a_b > standard_Constant_a > produc1548871597um_a_b ).
thf(func_def_290,type,
sK128: set_Pr409224873um_a_b > standard_Constant_a > standard_Constant_a ).
thf(func_def_291,type,
sK129: set_Pr1174980151um_a_b > nat > sum_sum_a_b ).
thf(func_def_292,type,
sK130: set_Pr1174980151um_a_b > nat > nat ).
thf(func_def_293,type,
sK131: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_294,type,
sK132: set_Pr1986765409at_nat > nat > nat ).
thf(func_def_295,type,
sK133: set_Pr1647387645at_nat > standard_Constant_a > product_prod_nat_nat ).
thf(func_def_296,type,
sK134: set_Pr1647387645at_nat > standard_Constant_a > standard_Constant_a ).
thf(func_def_297,type,
sK135: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_298,type,
sK136: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > produc1124793815um_a_b ).
thf(func_def_299,type,
sK137: set_Pr1916610317um_a_b > sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).
thf(func_def_300,type,
sK138: set_Pr409224873um_a_b > produc1548871597um_a_b > set_St761939237tant_a > standard_Constant_a ).
thf(func_def_301,type,
sK139: set_Pr1174980151um_a_b > sum_sum_a_b > set_nat > nat ).
thf(func_def_302,type,
sK140: set_Pr1986765409at_nat > nat > set_nat > nat ).
thf(func_def_303,type,
sK141: set_Pr1647387645at_nat > product_prod_nat_nat > set_St761939237tant_a > standard_Constant_a ).
thf(f1,axiom,
( g
= ( restri1162247455um_a_b @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_g) ).
thf(f3,axiom,
edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062) ).
thf(f4,axiom,
ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_r) ).
thf(f5,axiom,
( f
= ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_f) ).
thf(f6,axiom,
( ( domain1368163076um_a_b @ f )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_d) ).
thf(f8,axiom,
! [X0: standard_Constant_a,X1: nat,X2: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X0 @ ( product_Pair_nat_nat @ X1 @ X2 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X0 @ ( product_Pair_nat_nat @ X1 @ X2 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_graph__single) ).
thf(f10,axiom,
unival2092813468um_a_b @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_u) ).
thf(f41,axiom,
! [X0: set_Pr1647387645at_nat,X1: set_nat,X2: set_Pr1647387645at_nat,X3: set_nat] :
( ( ( ( labele16114835_a_nat @ X0 @ X1 )
= ( labele16114835_a_nat @ X2 @ X3 ) )
= ( X1 = X3 ) )
& ( X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_labeled__graph_Oinject) ).
thf(f136,axiom,
! [X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X0 @ X1 ) )
= X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_labeled__graph_Osel_I2_J) ).
thf(f138,axiom,
! [X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X0 @ X1 ) )
= X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_labeled__graph_Osel_I1_J) ).
thf(f253,axiom,
! [X0: nat,X1: set_nat] :
( ( insert_nat @ X0 @ ( insert_nat @ X0 @ X1 ) )
= ( insert_nat @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_insert__absorb2) ).
thf(f312,axiom,
( ord_le192794300um_a_b
= ( ^ [X0: set_Sum_sum_a_b,X1: set_Sum_sum_a_b] :
! [X2: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ X2 @ X0 )
=> ( member_Sum_sum_a_b @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_subset__eq) ).
thf(f343,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_bot__nat__def) ).
thf(f353,conjecture,
( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) )
& ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
& ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
& ( g
= ( restri1162247455um_a_b @ g ) )
& ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
& ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f354,negated_conjecture,
~ ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) )
& ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
& ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
& ( g
= ( restri1162247455um_a_b @ g ) )
& ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
& ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f353]) ).
thf(f357,plain,
edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
inference(rectify,[],[f3]) ).
thf(f358,plain,
( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) )
= $true ),
inference(fool_elimination,[],[f357]) ).
thf(f359,plain,
ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
inference(rectify,[],[f4]) ).
thf(f360,plain,
( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ) )
= $true ),
inference(fool_elimination,[],[f359]) ).
thf(f363,plain,
unival2092813468um_a_b @ f,
inference(rectify,[],[f10]) ).
thf(f364,plain,
( ( unival2092813468um_a_b @ f )
= $true ),
inference(fool_elimination,[],[f363]) ).
thf(f365,plain,
! [X0: set_Pr1647387645at_nat,X1: set_nat,X2: set_Pr1647387645at_nat,X3: set_nat] :
( ( ( labele16114835_a_nat @ X0 @ X1 )
= ( labele16114835_a_nat @ X2 @ X3 ) )
= ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f813,plain,
( ord_le192794300um_a_b
= ( ^ [X0: set_Sum_sum_a_b,X1: set_Sum_sum_a_b] :
! [X2: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ X2 @ X0 )
=> ( member_Sum_sum_a_b @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f312]) ).
thf(f814,plain,
( ord_le192794300um_a_b
= ( ^ [Y0: set_Sum_sum_a_b,Y1: set_Sum_sum_a_b] :
( !! @ sum_sum_a_b
@ ^ [Y2: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ Y2 @ Y0 )
=> ( member_Sum_sum_a_b @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f813]) ).
thf(f887,plain,
~ ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) )
& ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
& ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
& ( g
= ( restri1162247455um_a_b @ g ) )
& ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
& ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(rectify,[],[f354]) ).
thf(f888,plain,
~ ( ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) )
= $true )
& ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
= $true )
& ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
= $true )
& ( g
= ( restri1162247455um_a_b @ g ) )
& ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
& ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(fool_elimination,[],[f887]) ).
thf(f1120,plain,
( ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) )
!= $true )
| ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
!= $true )
| ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
!= $true )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
| ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(ennf_transformation,[],[f888]) ).
thf(f1168,plain,
( g
= ( restri1162247455um_a_b @ g ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f1170,plain,
( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) )
= $true ),
inference(cnf_transformation,[],[f358]) ).
thf(f1171,plain,
( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ) )
= $true ),
inference(cnf_transformation,[],[f360]) ).
thf(f1172,plain,
( ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b )
= f ),
inference(cnf_transformation,[],[f5]) ).
thf(f1173,plain,
( ( insert_nat @ zero_zero_nat @ bot_bot_set_nat )
= ( domain1368163076um_a_b @ f ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f1175,plain,
! [X2: nat,X0: standard_Constant_a,X1: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X0 @ ( product_Pair_nat_nat @ X1 @ X2 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X0 @ ( product_Pair_nat_nat @ X1 @ X2 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f1177,plain,
( ( unival2092813468um_a_b @ f )
= $true ),
inference(cnf_transformation,[],[f364]) ).
thf(f1208,plain,
! [X2: set_Pr1647387645at_nat,X3: set_nat,X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( ( labele16114835_a_nat @ X0 @ X1 )
= ( labele16114835_a_nat @ X2 @ X3 ) )
= ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(cnf_transformation,[],[f365]) ).
thf(f1318,plain,
! [X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X0 @ X1 ) )
= X1 ),
inference(cnf_transformation,[],[f136]) ).
thf(f1320,plain,
! [X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X0 @ X1 ) )
= X0 ),
inference(cnf_transformation,[],[f138]) ).
thf(f1446,plain,
! [X0: nat,X1: set_nat] :
( ( insert_nat @ X0 @ X1 )
= ( insert_nat @ X0 @ ( insert_nat @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f253]) ).
thf(f1511,plain,
( ord_le192794300um_a_b
= ( ^ [Y0: set_Sum_sum_a_b,Y1: set_Sum_sum_a_b] :
( !! @ sum_sum_a_b
@ ^ [Y2: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ Y2 @ Y0 )
=> ( member_Sum_sum_a_b @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f814]) ).
thf(f1546,plain,
zero_zero_nat = bot_bot_nat,
inference(cnf_transformation,[],[f343]) ).
thf(f1556,plain,
( ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) )
!= $true )
| ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
!= $true )
| ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
!= $true )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
| ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(cnf_transformation,[],[f1120]) ).
thf(f1560,plain,
( $true
= ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) ) ),
inference(definition_unfolding,[],[f1170,f1546,f1546,f1546]) ).
thf(f1561,plain,
( $true
= ( ^ [Y0: set_Sum_sum_a_b,Y1: set_Sum_sum_a_b] :
( !! @ sum_sum_a_b
@ ^ [Y2: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ Y2 @ Y0 )
=> ( member_Sum_sum_a_b @ Y2 @ Y1 ) ) )
@ ( image_256773707um_a_b @ f @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
@ ( labele577278695um_a_b @ g ) ) ),
inference(definition_unfolding,[],[f1171,f1511,f1546]) ).
thf(f1562,plain,
( f
= ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ),
inference(definition_unfolding,[],[f1172,f1546]) ).
thf(f1563,plain,
( ( domain1368163076um_a_b @ f )
= ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ),
inference(definition_unfolding,[],[f1173,f1546]) ).
thf(f1627,plain,
( ( $true
!= ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) )
| ( $true
!= ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| ( $true
!= ( ^ [Y0: set_Sum_sum_a_b,Y1: set_Sum_sum_a_b] :
( !! @ sum_sum_a_b
@ ^ [Y2: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ Y2 @ Y0 )
=> ( member_Sum_sum_a_b @ Y2 @ Y1 ) ) )
@ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
@ ( labele577278695um_a_b @ g ) ) )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(definition_unfolding,[],[f1556,f1546,f1546,f1546,f1546,f1546,f1511,f1546,f1546,f1546,f1546,f1546,f1546,f1546,f1546,f1546,f1546,f1546,f1546,f1546,f1546]) ).
thf(f1647,plain,
( ( $true
!= ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) )
| ( $true
!= ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| ( $true
!= ( !! @ sum_sum_a_b
@ ^ [Y0: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ Y0 @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) ) )
=> ( member_Sum_sum_a_b @ Y0 @ ( labele577278695um_a_b @ g ) ) ) ) )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(beta-eta_normalization,[],[f1627]) ).
thf(f1648,plain,
( ( $true
!= ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) )
| ( $true
!= ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| ( $false
= ( ^ [Y0: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ Y0 @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) ) )
=> ( member_Sum_sum_a_b @ Y0 @ ( labele577278695um_a_b @ g ) ) )
@ sK61 ) )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(sigma_proxy_clausification,[],[f1647]) ).
thf(f1649,plain,
( ( $true
!= ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) )
| ( $true
!= ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| ( $false
= ( ( member_Sum_sum_a_b @ sK61 @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) ) )
=> ( member_Sum_sum_a_b @ sK61 @ ( labele577278695um_a_b @ g ) ) ) )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(beta-eta_normalization,[],[f1648]) ).
thf(f1650,plain,
( ( $true
!= ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) )
| ( $true
!= ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| ( $false
= ( member_Sum_sum_a_b @ sK61 @ ( labele577278695um_a_b @ g ) ) )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(imp_proxy_clausification,[],[f1649]) ).
thf(f1651,plain,
( ( $true
!= ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) )
| ( $true
!= ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| ( $true
= ( member_Sum_sum_a_b @ sK61 @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) ) ) )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
inference(imp_proxy_clausification,[],[f1649]) ).
thf(f2799,plain,
! [X2: set_Pr1647387645at_nat,X3: set_nat,X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( $true
= ( ( labele16114835_a_nat @ X0 @ X1 )
= ( labele16114835_a_nat @ X2 @ X3 ) ) )
| ( ( ( X0 = X2 )
& ( X1 = X3 ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f1208]) ).
thf(f2806,plain,
! [X2: set_Pr1647387645at_nat,X3: set_nat,X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( ( labele16114835_a_nat @ X0 @ X1 )
= ( labele16114835_a_nat @ X2 @ X3 ) )
| ( ( ( X0 = X2 )
& ( X1 = X3 ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f2799]) ).
thf(f2807,plain,
! [X2: set_Pr1647387645at_nat,X3: set_nat,X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( ( labele16114835_a_nat @ X0 @ X1 )
= ( labele16114835_a_nat @ X2 @ X3 ) )
| ( ( X1 = X3 )
= $false )
| ( ( X0 = X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f2806]) ).
thf(f2808,plain,
! [X2: set_Pr1647387645at_nat,X3: set_nat,X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( ( labele16114835_a_nat @ X0 @ X1 )
= ( labele16114835_a_nat @ X2 @ X3 ) )
| ( X1 != X3 )
| ( ( X0 = X2 )
= $false ) ),
inference(equality_proxy_clausification,[],[f2807]) ).
thf(f2809,plain,
! [X2: set_Pr1647387645at_nat,X3: set_nat,X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( ( labele16114835_a_nat @ X0 @ X1 )
= ( labele16114835_a_nat @ X2 @ X3 ) )
| ( X1 != X3 )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[],[f2808]) ).
thf(f2830,plain,
( $true
= ( !! @ sum_sum_a_b
@ ^ [Y0: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ Y0 @ ( image_256773707um_a_b @ f @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
=> ( member_Sum_sum_a_b @ Y0 @ ( labele577278695um_a_b @ g ) ) ) ) ),
inference(beta-eta_normalization,[],[f1561]) ).
thf(f2831,plain,
! [X1: sum_sum_a_b] :
( $true
= ( ^ [Y0: sum_sum_a_b] :
( ( member_Sum_sum_a_b @ Y0 @ ( image_256773707um_a_b @ f @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
=> ( member_Sum_sum_a_b @ Y0 @ ( labele577278695um_a_b @ g ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f2830]) ).
thf(f2832,plain,
! [X1: sum_sum_a_b] :
( $true
= ( ( member_Sum_sum_a_b @ X1 @ ( image_256773707um_a_b @ f @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
=> ( member_Sum_sum_a_b @ X1 @ ( labele577278695um_a_b @ g ) ) ) ),
inference(beta-eta_normalization,[],[f2831]) ).
thf(f2833,plain,
! [X1: sum_sum_a_b] :
( ( $false
= ( member_Sum_sum_a_b @ X1 @ ( image_256773707um_a_b @ f @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| ( $true
= ( member_Sum_sum_a_b @ X1 @ ( labele577278695um_a_b @ g ) ) ) ),
inference(imp_proxy_clausification,[],[f2832]) ).
thf(f2835,definition,
( spl142_1
<=> ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
introduced(definition,[new_symbols(definition,[spl142_1])],[avatar_definition]) ).
thf(f2837,plain,
( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| spl142_1 ),
inference(avatar_component_clause,[],[f2835]) ).
thf(f2839,definition,
( spl142_2
<=> ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl142_2])],[avatar_definition]) ).
thf(f2841,plain,
( ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| spl142_2 ),
inference(avatar_component_clause,[],[f2839]) ).
thf(f2843,definition,
( spl142_3
<=> ( g
= ( restri1162247455um_a_b @ g ) ) ),
introduced(definition,[new_symbols(definition,[spl142_3])],[avatar_definition]) ).
thf(f2847,definition,
( spl142_4
<=> ( $true
= ( member_Sum_sum_a_b @ sK61 @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl142_4])],[avatar_definition]) ).
thf(f2849,plain,
( ( $true
= ( member_Sum_sum_a_b @ sK61 @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) ) ) )
| ~ spl142_4 ),
inference(avatar_component_clause,[],[f2847]) ).
thf(f2851,definition,
( spl142_5
<=> ( $true
= ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
introduced(definition,[new_symbols(definition,[spl142_5])],[avatar_definition]) ).
thf(f2853,plain,
( ( $true
!= ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| spl142_5 ),
inference(avatar_component_clause,[],[f2851]) ).
thf(f2855,definition,
( spl142_6
<=> ( $true
= ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ) ),
introduced(definition,[new_symbols(definition,[spl142_6])],[avatar_definition]) ).
thf(f2857,plain,
( ( $true
!= ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) )
| spl142_6 ),
inference(avatar_component_clause,[],[f2855]) ).
thf(f2858,plain,
( ~ spl142_1
| ~ spl142_2
| ~ spl142_3
| spl142_4
| ~ spl142_5
| ~ spl142_6 ),
inference(avatar_split_clause,[],[f1651,f2855,f2851,f2847,f2843,f2839,f2835]) ).
thf(f2860,definition,
( spl142_7
<=> ( $false
= ( member_Sum_sum_a_b @ sK61 @ ( labele577278695um_a_b @ g ) ) ) ),
introduced(definition,[new_symbols(definition,[spl142_7])],[avatar_definition]) ).
thf(f2862,plain,
( ( $false
= ( member_Sum_sum_a_b @ sK61 @ ( labele577278695um_a_b @ g ) ) )
| ~ spl142_7 ),
inference(avatar_component_clause,[],[f2860]) ).
thf(f2863,plain,
( ~ spl142_1
| ~ spl142_2
| ~ spl142_3
| spl142_7
| ~ spl142_5
| ~ spl142_6 ),
inference(avatar_split_clause,[],[f1650,f2855,f2851,f2860,f2843,f2839,f2835]) ).
thf(f2864,plain,
spl142_3,
inference(avatar_split_clause,[],[f1168,f2843]) ).
thf(f2894,plain,
( ( ( insert_nat @ bot_bot_nat @ bot_bot_set_nat )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ bot_bot_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| spl142_1 ),
inference(constrained_superposition,[],[f2837,f1318]) ).
thf(f2946,plain,
( ( ( domain1368163076um_a_b @ f )
!= ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) )
| spl142_1 ),
inference(constrained_superposition,[],[f2894,f1562]) ).
thf(f2951,plain,
( $false
| spl142_1 ),
inference(forward_subsumption_resolution,[],[f2946,f1563]) ).
thf(f2952,plain,
spl142_1,
inference(avatar_contradiction_clause,[],[f2951]) ).
thf(f2954,plain,
( ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( domain1368163076um_a_b @ f ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( domain1368163076um_a_b @ f ) ) ) )
| spl142_2 ),
inference(forward_demodulation,[],[f2841,f1563]) ).
thf(f3005,plain,
( ( domain1368163076um_a_b @ f )
= ( insert_nat @ bot_bot_nat @ ( domain1368163076um_a_b @ f ) ) ),
inference(constrained_superposition,[],[f1446,f1563]) ).
thf(f5250,plain,
! [X1: sum_sum_a_b] :
( ( $false
= ( member_Sum_sum_a_b @ X1 @ ( image_256773707um_a_b @ f @ ( domain1368163076um_a_b @ f ) ) ) )
| ( $true
= ( member_Sum_sum_a_b @ X1 @ ( labele577278695um_a_b @ g ) ) ) ),
inference(forward_demodulation,[],[f2833,f1563]) ).
thf(f8932,plain,
( $true
= ( edge_p1382426714tant_a @ f @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) ) ),
inference(forward_demodulation,[],[f1560,f1562]) ).
thf(f15217,plain,
( ! [X0: set_Pr1647387645at_nat,X1: set_nat] :
( ( ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat )
!= X0 )
| ( ( domain1368163076um_a_b @ f )
!= X1 )
| ( ( labele16114835_a_nat @ X0 @ X1 )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ X0 @ X1 ) ) ) )
| spl142_2 ),
inference(constrained_superposition,[],[f2954,f2809]) ).
thf(f15237,plain,
( ! [X0: set_nat] :
( ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ X0 )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ X0 ) ) )
| ( ( domain1368163076um_a_b @ f )
!= X0 ) )
| spl142_2 ),
inference(equality_resolution,[],[f15217]) ).
thf(f15240,plain,
( ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
!= ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| ( ( domain1368163076um_a_b @ f )
!= ( insert_nat @ bot_bot_nat @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
| spl142_2 ),
inference(constrained_superposition,[],[f15237,f1175]) ).
thf(f15241,plain,
( ( ( domain1368163076um_a_b @ f )
!= ( insert_nat @ bot_bot_nat @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) )
| spl142_2 ),
inference(trivial_inequality_removal,[],[f15240]) ).
thf(f15242,plain,
( ( ( domain1368163076um_a_b @ f )
!= ( insert_nat @ bot_bot_nat @ ( domain1368163076um_a_b @ f ) ) )
| spl142_2 ),
inference(forward_demodulation,[],[f15241,f1563]) ).
thf(f15243,plain,
( $false
| spl142_2 ),
inference(forward_subsumption_resolution,[],[f15242,f3005]) ).
thf(f15244,plain,
spl142_2,
inference(avatar_contradiction_clause,[],[f15243]) ).
thf(f15246,plain,
( ( ( unival2092813468um_a_b @ f )
!= $true )
| spl142_5 ),
inference(forward_demodulation,[],[f2853,f1562]) ).
thf(f15247,plain,
( $false
| spl142_5 ),
inference(forward_subsumption_resolution,[],[f15246,f1177]) ).
thf(f15248,plain,
spl142_5,
inference(avatar_contradiction_clause,[],[f15247]) ).
thf(f15250,plain,
( ( $true
!= ( edge_p1382426714tant_a @ f @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) )
| spl142_6 ),
inference(forward_demodulation,[],[f2857,f1562]) ).
thf(f15251,plain,
( ( $true
!= ( edge_p1382426714tant_a @ f @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) ) )
| spl142_6 ),
inference(forward_demodulation,[],[f15250,f1320]) ).
thf(f15252,plain,
( $false
| spl142_6 ),
inference(forward_subsumption_resolution,[],[f15251,f8932]) ).
thf(f15253,plain,
spl142_6,
inference(avatar_contradiction_clause,[],[f15252]) ).
thf(f15254,plain,
( ( $true
= ( member_Sum_sum_a_b @ sK61 @ ( image_256773707um_a_b @ f @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ bot_bot_nat @ bot_bot_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) ) ) )
| ~ spl142_4 ),
inference(forward_demodulation,[],[f2849,f1562]) ).
thf(f15256,plain,
( ( $true
= ( member_Sum_sum_a_b @ sK61 @ ( image_256773707um_a_b @ f @ ( insert_nat @ bot_bot_nat @ bot_bot_set_nat ) ) ) )
| ~ spl142_4 ),
inference(forward_demodulation,[],[f15254,f1318]) ).
thf(f15258,plain,
( ( $true
= ( member_Sum_sum_a_b @ sK61 @ ( image_256773707um_a_b @ f @ ( domain1368163076um_a_b @ f ) ) ) )
| ~ spl142_4 ),
inference(forward_demodulation,[],[f15256,f1563]) ).
thf(f15369,plain,
( ( $true = $false )
| ( $true
= ( member_Sum_sum_a_b @ sK61 @ ( labele577278695um_a_b @ g ) ) )
| ~ spl142_4 ),
inference(constrained_superposition,[],[f15258,f5250]) ).
thf(f15408,plain,
( ( $true
= ( member_Sum_sum_a_b @ sK61 @ ( labele577278695um_a_b @ g ) ) )
| ~ spl142_4 ),
inference(trivial_inequality_removal,[],[f15369]) ).
thf(f15412,plain,
( ( $true = $false )
| ~ spl142_4
| ~ spl142_7 ),
inference(forward_demodulation,[],[f15408,f2862]) ).
thf(f15413,plain,
( $false
| ~ spl142_4
| ~ spl142_7 ),
inference(trivial_inequality_removal,[],[f15412]) ).
thf(f15414,plain,
( ~ spl142_4
| ~ spl142_7 ),
inference(avatar_contradiction_clause,[],[f15413]) ).
cnf(s1,plain,
( ~ spl142_1
| ~ spl142_2
| ~ spl142_3
| spl142_4
| ~ spl142_5
| ~ spl142_6 ),
inference(sat_conversion,[],[f2858]) ).
cnf(s2,plain,
( ~ spl142_1
| ~ spl142_2
| ~ spl142_3
| ~ spl142_5
| ~ spl142_6
| spl142_7 ),
inference(sat_conversion,[],[f2863]) ).
cnf(s3,plain,
spl142_3,
inference(sat_conversion,[],[f2864]) ).
cnf(s5,plain,
spl142_1,
inference(sat_conversion,[],[f2952]) ).
cnf(s243,plain,
spl142_2,
inference(sat_conversion,[],[f15244]) ).
cnf(s244,plain,
spl142_5,
inference(sat_conversion,[],[f15248]) ).
cnf(s245,plain,
spl142_6,
inference(sat_conversion,[],[f15253]) ).
cnf(s250,plain,
( ~ spl142_4
| ~ spl142_7 ),
inference(sat_conversion,[],[f15414]) ).
cnf(s259,plain,
spl142_7,
inference(rat,[],[s2,s245,s244,s3,s243,s5]) ).
cnf(s260,plain,
~ spl142_4,
inference(rat,[],[s250,s259]) ).
cnf(s261,plain,
$false,
inference(rat,[],[s1,s245,s244,s260,s3,s243,s5]) ).
thf(f15415,plain,
$false,
inference(avatar_sat_refutation,[],[s261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP179^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n007.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 20:04:56 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.77/1.25 % (3864504)Will run a generic schedule for satisfiability detection.
% 6.77/1.25 % (3864511)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1059120822:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.77/1.25 % (3864510)% WARNING: option uhcvi not known.
% 6.77/1.25 % (3864510)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=397195147:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.77/1.25 % (3864509)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2168535507_2999 on theBenchmark for (2999ds/0Mi)
% 6.77/1.25 % (3864512)dis+10_1_sil=32000:sp=arity:random_seed=3486317434:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.77/1.25 % (3864513)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3394103128:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.77/1.25 % (3864514)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=903796251:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.77/1.25 % (3864515)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3601086429:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.77/1.25 % (3864510)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.77/1.25 % (3864513)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.77/1.25 % (3864510)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.77/1.25 % (3864512)Instruction limit reached!
% 6.77/1.25 % (3864512)------------------------------
% 6.77/1.25 % (3864512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.25 % (3864512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.25 % (3864512)CaDiCaL version: 2.1.3
% 6.77/1.25 % (3864512)Termination reason: Instruction limit
% 6.77/1.25 % (3864512)Termination phase: Saturation
% 6.77/1.25 % (3864512)Time elapsed: 0.044 s
% 6.77/1.25 % (3864512)Peak memory usage: 13 MB
% 6.77/1.25 % (3864512)Instructions burned: 103 (million)
% 6.77/1.25 % Exception at run slice level
% 6.77/1.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.25 % (3864513)Instruction limit reached!
% 6.77/1.25 % (3864513)------------------------------
% 6.77/1.25 % (3864513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.25 % (3864513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.25 % (3864513)CaDiCaL version: 2.1.3
% 6.77/1.25 % (3864513)Termination reason: Instruction limit
% 6.77/1.25 % (3864513)Termination phase: Saturation
% 6.77/1.25 % (3864513)Time elapsed: 0.050 s
% 6.77/1.25 % (3864513)Peak memory usage: 13 MB
% 6.77/1.25 % (3864513)Instructions burned: 117 (million)
% 6.77/1.25 % (3864514)Instruction limit reached!
% 6.77/1.25 % (3864514)------------------------------
% 6.77/1.25 % (3864514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.25 % (3864514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.25 % (3864514)CaDiCaL version: 2.1.3
% 6.77/1.25 % (3864514)Termination reason: Instruction limit
% 6.77/1.25 % (3864514)Termination phase: Saturation
% 6.77/1.25 % (3864514)Time elapsed: 0.057 s
% 6.77/1.25 % (3864514)Peak memory usage: 13 MB
% 6.77/1.25 % (3864514)Instructions burned: 132 (million)
% 6.77/1.25 % (3864524)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3423966897:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 6.77/1.25 % (3864525)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=2191034126:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.77/1.25 % (3864523)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1414635416:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 6.77/1.25 % (3864527)ott-21_1_sil=16000:fs=off:random_seed=1564917222:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.77/1.25 % (3864515)Instruction limit reached!
% 6.77/1.25 % (3864515)------------------------------
% 6.77/1.25 % (3864515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.25 % (3864515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.25 % (3864515)CaDiCaL version: 2.1.3
% 6.77/1.25 % (3864515)Termination reason: Instruction limit
% 7.45/1.37 % (3864515)Termination phase: Saturation
% 7.45/1.37 % (3864515)Time elapsed: 0.078 s
% 7.45/1.37 % (3864515)Peak memory usage: 14 MB
% 7.45/1.37 % (3864515)Instructions burned: 160 (million)
% 7.45/1.37 % (3864525)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.45/1.37 % (3864525)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.45/1.37 % (3864531)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3951100285:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 7.45/1.37 % (3864524)Instruction limit reached!
% 7.45/1.37 % (3864524)------------------------------
% 7.45/1.37 % (3864524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.37 % (3864524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.37 % (3864524)CaDiCaL version: 2.1.3
% 7.45/1.37 % (3864524)Termination reason: Instruction limit
% 7.45/1.37 % (3864524)Termination phase: Saturation
% 7.45/1.37 % (3864524)Time elapsed: 0.060 s
% 7.45/1.37 % (3864524)Peak memory usage: 13 MB
% 7.45/1.37 % (3864524)Instructions burned: 131 (million)
% 7.45/1.37 % Exception at run slice level
% 7.45/1.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.37 % (3864533)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2251877645:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 7.45/1.37 % (3864534)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3158760704:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 7.45/1.37 % (3864527)Instruction limit reached!
% 7.45/1.37 % (3864527)------------------------------
% 7.45/1.37 % (3864527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.37 % (3864527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.37 % (3864527)CaDiCaL version: 2.1.3
% 7.45/1.37 % (3864527)Termination reason: Instruction limit
% 7.45/1.37 % (3864527)Termination phase: Saturation
% 7.45/1.37 % (3864527)Time elapsed: 0.079 s
% 7.45/1.37 % (3864527)Peak memory usage: 14 MB
% 7.45/1.37 % (3864527)Instructions burned: 182 (million)
% 7.45/1.37 % Exception at run slice level
% 7.45/1.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.37 % (3864537)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=741380256:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 7.45/1.37 % (3864538)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=2999718217: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)
% 7.45/1.37 % (3864538)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.45/1.37 % Exception at run slice level
% 7.45/1.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.37 % (3864541)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3722273913:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 7.45/1.37 % (3864541)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.45/1.37 % (3864531)Instruction limit reached!
% 7.45/1.37 % (3864531)------------------------------
% 7.45/1.37 % (3864531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.37 % (3864531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.37 % (3864531)CaDiCaL version: 2.1.3
% 7.45/1.37 % (3864531)Termination reason: Instruction limit
% 7.45/1.37 % (3864531)Termination phase: Saturation
% 7.45/1.37 % (3864531)Time elapsed: 0.254 s
% 7.45/1.37 % (3864531)Peak memory usage: 15 MB
% 7.45/1.37 % (3864531)Instructions burned: 478 (million)
% 7.45/1.37 % (3864543)fmb+10_1_sil=64000:random_seed=3028260657:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 7.45/1.37 % (3864525)Instruction limit reached!
% 7.45/1.37 % (3864525)------------------------------
% 7.45/1.37 % (3864525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.37 % (3864525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.37 % (3864525)CaDiCaL version: 2.1.3
% 7.45/1.37 % (3864525)Termination reason: Instruction limit
% 7.45/1.37 % (3864525)Termination phase: Saturation
% 7.45/1.37 % (3864525)Time elapsed: 0.325 s
% 7.45/1.37 % (3864525)Peak memory usage: 17 MB
% 7.45/1.37 % (3864525)Instructions burned: 691 (million)
% 7.45/1.37 % (3864543)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.45/1.37 % Exception at run slice level
% 7.45/1.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.37 % (3864545)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=323658498:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 7.45/1.37 % (3864547)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1715719106:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 7.45/1.37 % Exception at run slice level
% 7.45/1.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.37 % Exception at run slice level
% 7.45/1.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.37 % (3864549)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3989924198:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 7.45/1.37 % (3864549)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.45/1.37 % (3864551)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1604603296:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 7.45/1.37 % (3864551)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.45/1.37 % (3864538)Instruction limit reached!
% 7.45/1.37 % (3864538)------------------------------
% 7.45/1.37 % (3864538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.37 % (3864538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.37 % (3864538)CaDiCaL version: 2.1.3
% 7.45/1.37 % (3864538)Termination reason: Instruction limit
% 7.45/1.37 % (3864538)Termination phase: Saturation
% 7.45/1.37 % (3864538)Time elapsed: 0.316 s
% 7.45/1.37 % (3864538)Peak memory usage: 17 MB
% 7.45/1.37 % (3864538)Instructions burned: 693 (million)
% 7.45/1.37 % (3864551)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.45/1.37 % (3864553)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3150469409:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 7.45/1.37 % Exception at run slice level
% 7.45/1.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.37 % (3864555)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3707727594:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 7.45/1.37 % Exception at run slice level
% 7.45/1.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.37 % (3864557)ott-2_1_sil=16000:newcnf=on:random_seed=1402097718:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 7.45/1.37 % (3864557)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.45/1.37 % (3864541)Instruction limit reached!
% 7.45/1.37 % (3864541)------------------------------
% 7.45/1.37 % (3864541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.37 % (3864541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.37 % (3864541)CaDiCaL version: 2.1.3
% 7.45/1.37 % (3864541)Termination reason: Instruction limit
% 7.45/1.37 % (3864541)Termination phase: Saturation
% 7.45/1.37 % (3864541)Time elapsed: 0.433 s
% 7.45/1.37 % (3864541)Peak memory usage: 19 MB
% 7.45/1.37 % (3864541)Instructions burned: 881 (million)
% 7.45/1.37 % (3864559)ott+10_1_sil=32000:tgt=ground:random_seed=3301003957:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 7.45/1.37 % (3864534)Instruction limit reached!
% 7.45/1.37 % (3864534)------------------------------
% 7.45/1.37 % (3864534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.37 % (3864534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.37 % (3864534)CaDiCaL version: 2.1.3
% 7.45/1.37 % (3864534)Termination reason: Instruction limit
% 7.45/1.37 % (3864534)Termination phase: Saturation
% 7.45/1.37 % (3864534)Time elapsed: 0.768 s
% 7.45/1.37 % (3864534)Peak memory usage: 23 MB
% 7.45/1.37 % (3864534)Instructions burned: 1181 (million)
% 7.45/1.37 % (3864561)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=4104034474:i=54282_2990 on theBenchmark for (2990ds/54282Mi)
% 7.45/1.37 % Exception at run slice level
% 7.45/1.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.45/1.37 % (3864563)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=145414159:i=3512:aac=none_2989 on theBenchmark for (2989ds/3512Mi)
% 7.45/1.37 % (3864563)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.45/1.37 % (3864557)Instruction limit reached!
% 7.45/1.37 % (3864557)------------------------------
% 7.45/1.37 % (3864557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.37 % (3864557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.37 % (3864557)CaDiCaL version: 2.1.3
% 7.45/1.37 % (3864557)Termination reason: Instruction limit
% 7.45/1.37 % (3864557)Termination phase: Saturation
% 7.45/1.37 % (3864557)Time elapsed: 0.401 s
% 7.45/1.37 % (3864557)Peak memory usage: 20 MB
% 7.45/1.37 % (3864557)Instructions burned: 870 (million)
% 7.45/1.37 % (3864565)dis+21_1_sil=32000:sas=cadical:random_seed=1284725752:i=3773:amm=off_2988 on theBenchmark for (2988ds/3773Mi)
% 7.45/1.37 % (3864510) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3864504-3864510"...
% 7.45/1.37 % (3864510)...printing done.
% 7.45/1.37 % (3864510)Refutation found. Thanks to Tanya!
% 7.45/1.37 % SZS status Theorem for theBenchmark
% 7.45/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 7.45/1.37 % (3864510)------------------------------
% 7.45/1.37 % (3864510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.37 % (3864510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.37 % (3864510)CaDiCaL version: 2.1.3
% 7.45/1.37 % (3864510)Termination reason: Refutation
% 7.45/1.37 % (3864510)Time elapsed: 1.088 s
% 7.45/1.37 % (3864510)Peak memory usage: 28 MB
% 7.45/1.37 % (3864510)Instructions burned: 2286 (million)
% 7.45/1.37 % (3864504)Success in time 1.154 s
% 7.45/1.37 % Vampire exiting
%------------------------------------------------------------------------------