%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP093^1 : 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 : n013.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 08:10:40 AM UTC 2026
% Result : Theorem 0.83s 0.40s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 26 unt; 0 typ; 2 def)
% Number of atoms : 198 ( 59 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 289 ( 50 ~; 38 |; 0 &; 193 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 32 ( 31 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 410 ( 407 usr; 10 con; 0-4 aty)
% Number of variables : 105 ( 46 sgn 30 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1295299783od_a_a: $tType ).
thf(type_def_6,type,
pair_p1593840546t_unit: $tType ).
thf(type_def_7,type,
pair_p2041852168t_unit: $tType ).
thf(type_def_8,type,
set_Pr1490359111at_nat: $tType ).
thf(type_def_9,type,
pair_p1765063010t_unit: $tType ).
thf(type_def_10,type,
set_se958357159od_a_a: $tType ).
thf(type_def_11,type,
set_Pr1948701895od_a_a: $tType ).
thf(type_def_12,type,
pair_p1914262621t_unit: $tType ).
thf(type_def_13,type,
set_Pr1746169692at_nat: $tType ).
thf(type_def_14,type,
produc1572603623od_a_a: $tType ).
thf(type_def_15,type,
pair_p125712459t_unit: $tType ).
thf(type_def_16,type,
set_Pr7688842at_nat: $tType ).
thf(type_def_17,type,
set_Pr894832732_a_nat: $tType ).
thf(type_def_18,type,
set_Pr339609346od_a_a: $tType ).
thf(type_def_19,type,
set_Pr681306928od_a_a: $tType ).
thf(type_def_20,type,
set_Pr1689873822_a_a_a: $tType ).
thf(type_def_21,type,
set_se1612935105at_nat: $tType ).
thf(type_def_22,type,
set_se1596668135od_a_a: $tType ).
thf(type_def_23,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_24,type,
set_Pr548851891_a_nat: $tType ).
thf(type_def_25,type,
set_Pr967348953_nat_a: $tType ).
thf(type_def_26,type,
set_Product_prod_a_a: $tType ).
thf(type_def_27,type,
product_prod_nat_nat: $tType ).
thf(type_def_28,type,
set_set_nat: $tType ).
thf(type_def_29,type,
product_prod_a_a: $tType ).
thf(type_def_30,type,
set_set_a: $tType ).
thf(type_def_31,type,
set_nat: $tType ).
thf(type_def_32,type,
product_unit: $tType ).
thf(type_def_33,type,
set_a: $tType ).
thf(type_def_34,type,
nat: $tType ).
thf(type_def_35,type,
a: $tType ).
thf(type_def_36,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
finite_Fpow_nat: set_nat > set_set_nat ).
thf(func_def_1,type,
finite361944167at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat ).
thf(func_def_2,type,
finite702915405od_a_a: set_Pr1948701895od_a_a > set_se958357159od_a_a ).
thf(func_def_3,type,
finite351630733od_a_a: set_Product_prod_a_a > set_se1596668135od_a_a ).
thf(func_def_4,type,
finite_Fpow_a: set_a > set_set_a ).
thf(func_def_5,type,
finite_card_a: set_a > nat ).
thf(func_def_6,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_7,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_8,type,
finite277291581at_nat: set_Pr1746169692at_nat > $o ).
thf(func_def_9,type,
finite1297454819od_a_a: set_Pr339609346od_a_a > $o ).
thf(func_def_10,type,
finite1808550458_nat_a: set_Pr967348953_nat_a > $o ).
thf(func_def_11,type,
finite48957584at_nat: set_Pr1490359111at_nat > $o ).
thf(func_def_12,type,
finite256329232od_a_a: set_Pr1295299783od_a_a > $o ).
thf(func_def_13,type,
finite1837575485_a_nat: set_Pr894832732_a_nat > $o ).
thf(func_def_14,type,
finite1664988688od_a_a: set_Pr1948701895od_a_a > $o ).
thf(func_def_15,type,
finite1919032935_a_a_a: set_Pr1689873822_a_a_a > $o ).
thf(func_def_16,type,
finite1743148308_a_nat: set_Pr548851891_a_nat > $o ).
thf(func_def_17,type,
finite942416723at_nat: set_Pr7688842at_nat > $o ).
thf(func_def_18,type,
finite676513017od_a_a: set_Pr681306928od_a_a > $o ).
thf(func_def_19,type,
finite179568208od_a_a: set_Product_prod_a_a > $o ).
thf(func_def_20,type,
finite2012248349et_nat: set_set_nat > $o ).
thf(func_def_21,type,
finite1457549322at_nat: set_se1612935105at_nat > $o ).
thf(func_def_22,type,
finite323969008od_a_a: set_se958357159od_a_a > $o ).
thf(func_def_23,type,
finite1145471536od_a_a: set_se1596668135od_a_a > $o ).
thf(func_def_24,type,
finite_finite_set_a: set_set_a > $o ).
thf(func_def_25,type,
finite_finite_a: set_a > $o ).
thf(func_def_26,type,
bot_bot_set_nat: set_nat ).
thf(func_def_27,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(func_def_28,type,
bot_bo2131659635od_a_a: set_Product_prod_a_a ).
thf(func_def_29,type,
bot_bot_set_a: set_a ).
thf(func_def_30,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_31,type,
ord_le1347718902_a_a_o: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > $o ).
thf(func_def_32,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_33,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_34,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_35,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_36,type,
ord_le2084554594od_a_a: set_Pr339609346od_a_a > set_Pr339609346od_a_a > $o ).
thf(func_def_37,type,
ord_le344568633_nat_a: set_Pr967348953_nat_a > set_Pr967348953_nat_a > $o ).
thf(func_def_38,type,
ord_le492294332_a_nat: set_Pr894832732_a_nat > set_Pr894832732_a_nat > $o ).
thf(func_def_39,type,
ord_le456379495od_a_a: set_Pr1948701895od_a_a > set_Pr1948701895od_a_a > $o ).
thf(func_def_40,type,
ord_le677315902_a_a_a: set_Pr1689873822_a_a_a > set_Pr1689873822_a_a_a > $o ).
thf(func_def_41,type,
ord_le2073555219_a_nat: set_Pr548851891_a_nat > set_Pr548851891_a_nat > $o ).
thf(func_def_42,type,
ord_le1816232656od_a_a: set_Pr681306928od_a_a > set_Pr681306928od_a_a > $o ).
thf(func_def_43,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_44,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_45,type,
pair_p128415500ph_nat: pair_p1914262621t_unit > $o ).
thf(func_def_46,type,
pair_p752841413at_nat: pair_p2041852168t_unit > $o ).
thf(func_def_47,type,
pair_p159207083od_a_a: pair_p1593840546t_unit > $o ).
thf(func_def_48,type,
pair_p374947051od_a_a: pair_p1765063010t_unit > $o ).
thf(func_def_49,type,
pair_p1802376898raph_a: pair_p125712459t_unit > $o ).
thf(func_def_50,type,
pair_p1027063983ms_nat: pair_p1914262621t_unit > $o ).
thf(func_def_51,type,
pair_p56914274at_nat: pair_p2041852168t_unit > $o ).
thf(func_def_52,type,
pair_p1906342088od_a_a: pair_p1593840546t_unit > $o ).
thf(func_def_53,type,
pair_p504738056od_a_a: pair_p1765063010t_unit > $o ).
thf(func_def_54,type,
pair_p1864019935ioms_a: pair_p125712459t_unit > $o ).
thf(func_def_55,type,
pair_p69470259t_unit: pair_p1914262621t_unit > product_unit ).
thf(func_def_56,type,
pair_p1984658862t_unit: pair_p1765063010t_unit > product_unit ).
thf(func_def_57,type,
pair_p1896222615t_unit: pair_p125712459t_unit > product_unit ).
thf(func_def_58,type,
pair_p1167410509t_unit: set_nat > set_Pr1986765409at_nat > product_unit > pair_p1914262621t_unit ).
thf(func_def_59,type,
pair_p398687508t_unit: set_Product_prod_a_a > set_Pr1948701895od_a_a > product_unit > pair_p1765063010t_unit ).
thf(func_def_60,type,
pair_p1621517565t_unit: set_a > set_Product_prod_a_a > product_unit > pair_p125712459t_unit ).
thf(func_def_61,type,
pair_p715279805t_unit: pair_p1914262621t_unit > set_Pr1986765409at_nat ).
thf(func_def_62,type,
pair_p806300874t_unit: pair_p2041852168t_unit > set_Pr1490359111at_nat ).
thf(func_def_63,type,
pair_p1559300324t_unit: pair_p1593840546t_unit > set_Pr1295299783od_a_a ).
thf(func_def_64,type,
pair_p1783210148t_unit: pair_p1765063010t_unit > set_Pr1948701895od_a_a ).
thf(func_def_65,type,
pair_p133601421t_unit: pair_p125712459t_unit > set_Product_prod_a_a ).
thf(func_def_66,type,
pair_p1677060310t_unit: pair_p1914262621t_unit > set_nat ).
thf(func_def_67,type,
pair_p210955889t_unit: pair_p2041852168t_unit > set_Pr1986765409at_nat ).
thf(func_def_68,type,
pair_p1652294923t_unit: pair_p1593840546t_unit > set_Pr1948701895od_a_a ).
thf(func_def_69,type,
pair_p447552203t_unit: pair_p1765063010t_unit > set_Product_prod_a_a ).
thf(func_def_70,type,
pair_p1047056820t_unit: pair_p125712459t_unit > set_a ).
thf(func_def_71,type,
pair_p1515597646ph_nat: pair_p1914262621t_unit > $o ).
thf(func_def_72,type,
pair_p646030121od_a_a: pair_p1765063010t_unit > $o ).
thf(func_def_73,type,
pair_p68905728raph_a: pair_p125712459t_unit > $o ).
thf(func_def_74,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(func_def_75,type,
produc45129834at_nat: set_nat > ( nat > set_nat ) > set_Pr1986765409at_nat ).
thf(func_def_76,type,
produc894163943at_nat: set_nat > ( nat > set_Pr1986765409at_nat ) > set_Pr1746169692at_nat ).
thf(func_def_77,type,
produc1182842125od_a_a: set_nat > ( nat > set_Product_prod_a_a ) > set_Pr339609346od_a_a ).
thf(func_def_78,type,
product_Sigma_nat_a: set_nat > ( nat > set_a ) > set_Pr967348953_nat_a ).
thf(func_def_79,type,
produc931712687_a_nat: set_Product_prod_a_a > ( product_prod_a_a > set_nat ) > set_Pr894832732_a_nat ).
thf(func_def_80,type,
produc304751368od_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_Product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(func_def_81,type,
produc1282482655_a_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_a ) > set_Pr1689873822_a_a_a ).
thf(func_def_82,type,
product_Sigma_a_nat: set_a > ( a > set_nat ) > set_Pr548851891_a_nat ).
thf(func_def_83,type,
produc292491723at_nat: set_a > ( a > set_Pr1986765409at_nat ) > set_Pr7688842at_nat ).
thf(func_def_84,type,
produc520147185od_a_a: set_a > ( a > set_Product_prod_a_a ) > set_Pr681306928od_a_a ).
thf(func_def_85,type,
product_Sigma_a_a: set_a > ( a > set_a ) > set_Product_prod_a_a ).
thf(func_def_86,type,
produc1833107820_a_a_o: ( a > a > $o ) > product_prod_a_a > $o ).
thf(func_def_87,type,
product_product_a_a: set_a > set_a > set_Product_prod_a_a ).
thf(func_def_88,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_89,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_90,type,
collec1635618130od_a_a: ( produc1572603623od_a_a > $o ) > set_Pr1948701895od_a_a ).
thf(func_def_91,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(func_def_92,type,
collect_set_nat: ( set_nat > $o ) > set_set_nat ).
thf(func_def_93,type,
collec1606769740at_nat: ( set_Pr1986765409at_nat > $o ) > set_se1612935105at_nat ).
thf(func_def_94,type,
collec453062450od_a_a: ( set_Pr1948701895od_a_a > $o ) > set_se958357159od_a_a ).
thf(func_def_95,type,
collec183727474od_a_a: ( set_Product_prod_a_a > $o ) > set_se1596668135od_a_a ).
thf(func_def_96,type,
collect_set_a: ( set_a > $o ) > set_set_a ).
thf(func_def_97,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_98,type,
member_nat: nat > set_nat > $o ).
thf(func_def_99,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_100,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_101,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_102,type,
member1838126896od_a_a: set_Product_prod_a_a > set_se1596668135od_a_a > $o ).
thf(func_def_103,type,
member_set_a: set_a > set_set_a > $o ).
thf(func_def_104,type,
member_a: a > set_a > $o ).
thf(func_def_105,type,
g: pair_p125712459t_unit ).
thf(func_def_106,type,
n: nat ).
thf(func_def_108,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_111,type,
vAND: $o > $o > $o ).
thf(func_def_112,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_113,type,
vOR: $o > $o > $o ).
thf(func_def_114,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_115,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_116,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_117,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_118,type,
vIMP: $o > $o > $o ).
thf(func_def_119,type,
vNOT: $o > $o ).
thf(func_def_120,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_121,type,
sP0: nat > nat > nat > $o ).
thf(func_def_122,type,
sP1: nat > nat > nat > $o ).
thf(func_def_123,type,
sP2: nat > nat > nat > $o ).
thf(func_def_124,type,
sK3: set_Product_prod_a_a > set_se1596668135od_a_a > set_Product_prod_a_a ).
thf(func_def_125,type,
sK4: nat > set_nat > nat ).
thf(func_def_126,type,
sK5: set_nat > set_set_nat > set_nat ).
thf(func_def_127,type,
sK6: set_a > set_set_a > set_a ).
thf(func_def_128,type,
sK7: ( a > set_nat ) > set_a > a ).
thf(func_def_129,type,
sK8: ( nat > set_a ) > set_nat > nat ).
thf(func_def_130,type,
sK9: ( nat > set_nat ) > set_nat > nat ).
thf(func_def_131,type,
sK10: ( a > set_a ) > set_a > a ).
thf(func_def_132,type,
sK11: ( product_prod_a_a > set_a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_133,type,
sK12: ( product_prod_a_a > set_nat ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_134,type,
sK13: ( a > set_Product_prod_a_a ) > set_a > a ).
thf(func_def_135,type,
sK14: ( a > set_Pr1986765409at_nat ) > set_a > a ).
thf(func_def_136,type,
sK15: ( nat > set_Product_prod_a_a ) > set_nat > nat ).
thf(func_def_137,type,
sK16: ( nat > set_Pr1986765409at_nat ) > set_nat > nat ).
thf(func_def_138,type,
sK17: ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_139,type,
sK18: ( a > $o ) > a ).
thf(func_def_140,type,
sK19: ( nat > $o ) > nat ).
thf(func_def_141,type,
sK20: ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_142,type,
sK21: ( produc1572603623od_a_a > $o ) > produc1572603623od_a_a ).
thf(func_def_143,type,
sK22: ( a > a > $o ) > set_a > set_a > a ).
thf(func_def_144,type,
sK23: ( a > a > $o ) > set_a > set_a > a ).
thf(func_def_145,type,
sK24: ( a > nat > $o ) > set_nat > set_a > nat ).
thf(func_def_146,type,
sK25: ( a > nat > $o ) > set_nat > set_a > a ).
thf(func_def_147,type,
sK26: ( nat > a > $o ) > set_a > set_nat > a ).
thf(func_def_148,type,
sK27: ( nat > a > $o ) > set_a > set_nat > nat ).
thf(func_def_149,type,
sK28: ( nat > nat > $o ) > set_nat > set_nat > nat ).
thf(func_def_150,type,
sK29: ( nat > nat > $o ) > set_nat > set_nat > nat ).
thf(func_def_151,type,
sK30: ( product_prod_a_a > a > $o ) > set_a > set_Product_prod_a_a > a ).
thf(func_def_152,type,
sK31: ( product_prod_a_a > a > $o ) > set_a > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_153,type,
sK32: ( product_prod_a_a > nat > $o ) > set_nat > set_Product_prod_a_a > nat ).
thf(func_def_154,type,
sK33: ( product_prod_a_a > nat > $o ) > set_nat > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_155,type,
sK34: ( a > product_prod_a_a > $o ) > set_Product_prod_a_a > set_a > product_prod_a_a ).
thf(func_def_156,type,
sK35: ( a > product_prod_a_a > $o ) > set_Product_prod_a_a > set_a > a ).
thf(func_def_157,type,
sK36: ( a > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_a > product_prod_nat_nat ).
thf(func_def_158,type,
sK37: ( a > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_a > a ).
thf(func_def_159,type,
sK38: ( nat > product_prod_a_a > $o ) > set_Product_prod_a_a > set_nat > product_prod_a_a ).
thf(func_def_160,type,
sK39: ( nat > product_prod_a_a > $o ) > set_Product_prod_a_a > set_nat > nat ).
thf(func_def_161,type,
sK40: ( nat > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_nat > product_prod_nat_nat ).
thf(func_def_162,type,
sK41: ( nat > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_nat > nat ).
thf(func_def_163,type,
sK42: set_Product_prod_a_a > set_se1596668135od_a_a > set_Product_prod_a_a ).
thf(func_def_164,type,
sK43: nat > set_nat > nat ).
thf(func_def_165,type,
sK44: set_nat > set_set_nat > set_nat ).
thf(func_def_166,type,
sK45: set_a > set_set_a > set_a ).
thf(func_def_167,type,
sK46: ( product_prod_a_a > set_Product_prod_a_a ) > ( product_prod_a_a > set_Product_prod_a_a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_168,type,
sK47: ( product_prod_a_a > set_nat ) > ( product_prod_a_a > set_nat ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_169,type,
sK48: ( product_prod_a_a > set_a ) > ( product_prod_a_a > set_a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_170,type,
sK49: ( nat > set_Product_prod_a_a ) > ( nat > set_Product_prod_a_a ) > set_nat > nat ).
thf(func_def_171,type,
sK50: ( nat > set_nat ) > ( nat > set_nat ) > set_nat > nat ).
thf(func_def_172,type,
sK51: ( nat > set_a ) > ( nat > set_a ) > set_nat > nat ).
thf(func_def_173,type,
sK52: ( a > set_Product_prod_a_a ) > ( a > set_Product_prod_a_a ) > set_a > a ).
thf(func_def_174,type,
sK53: ( a > set_nat ) > ( a > set_nat ) > set_a > a ).
thf(func_def_175,type,
sK54: ( a > set_a ) > ( a > set_a ) > set_a > a ).
thf(func_def_176,type,
sK55: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_177,type,
sK56: set_nat > set_nat > nat ).
thf(func_def_178,type,
sK57: set_a > set_a > a ).
thf(func_def_179,type,
sK58: ( a > set_a ) > ( a > set_a ) > set_a > a ).
thf(func_def_180,type,
sK59: ( nat > nat > $o ) > nat ).
thf(func_def_181,type,
sK60: ( nat > nat > $o ) > nat ).
thf(func_def_182,type,
sK61: ( nat > nat > $o ) > nat ).
thf(func_def_183,type,
sK62: ( nat > nat > $o ) > nat ).
thf(func_def_184,type,
sK63: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_185,type,
sK64: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_186,type,
sK65: ( nat > nat ) > nat ).
thf(func_def_187,type,
sK66: ( nat > nat ) > nat ).
thf(func_def_188,type,
sK67: ( nat > set_nat ) > nat ).
thf(func_def_189,type,
sK68: ( nat > set_nat ) > nat ).
thf(func_def_190,type,
sK69: ( nat > set_a ) > nat ).
thf(func_def_191,type,
sK70: ( nat > set_a ) > nat ).
thf(func_def_192,type,
sK71: ( set_nat > nat ) > set_nat ).
thf(func_def_193,type,
sK72: ( set_nat > nat ) > set_nat ).
thf(func_def_194,type,
sK73: ( set_a > nat ) > set_a ).
thf(func_def_195,type,
sK74: ( set_a > nat ) > set_a ).
thf(func_def_196,type,
sK75: ( set_nat > set_nat ) > set_nat ).
thf(func_def_197,type,
sK76: ( set_nat > set_nat ) > set_nat ).
thf(func_def_198,type,
sK77: ( set_nat > set_a ) > set_nat ).
thf(func_def_199,type,
sK78: ( set_nat > set_a ) > set_nat ).
thf(func_def_200,type,
sK79: ( set_a > set_nat ) > set_a ).
thf(func_def_201,type,
sK80: ( set_a > set_nat ) > set_a ).
thf(func_def_202,type,
sK81: ( set_a > set_a ) > set_a ).
thf(func_def_203,type,
sK82: ( set_a > set_a ) > set_a ).
thf(func_def_204,type,
sK83: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_205,type,
sK84: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_206,type,
sK85: ( nat > nat ) > nat ).
thf(func_def_207,type,
sK86: ( nat > nat ) > nat ).
thf(func_def_208,type,
sK87: ( nat > set_nat ) > nat ).
thf(func_def_209,type,
sK88: ( nat > set_nat ) > nat ).
thf(func_def_210,type,
sK89: ( nat > set_a ) > nat ).
thf(func_def_211,type,
sK90: ( nat > set_a ) > nat ).
thf(func_def_212,type,
sK91: ( set_nat > nat ) > set_nat ).
thf(func_def_213,type,
sK92: ( set_nat > nat ) > set_nat ).
thf(func_def_214,type,
sK93: ( set_a > nat ) > set_a ).
thf(func_def_215,type,
sK94: ( set_a > nat ) > set_a ).
thf(func_def_216,type,
sK95: ( set_nat > set_nat ) > set_nat ).
thf(func_def_217,type,
sK96: ( set_nat > set_nat ) > set_nat ).
thf(func_def_218,type,
sK97: ( set_nat > set_a ) > set_nat ).
thf(func_def_219,type,
sK98: ( set_nat > set_a ) > set_nat ).
thf(func_def_220,type,
sK99: ( set_a > set_nat ) > set_a ).
thf(func_def_221,type,
sK100: ( set_a > set_nat ) > set_a ).
thf(func_def_222,type,
sK101: ( set_a > set_a ) > set_a ).
thf(func_def_223,type,
sK102: ( set_a > set_a ) > set_a ).
thf(func_def_224,type,
sK103: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_225,type,
sK104: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_226,type,
sK105: ( nat > nat ) > nat ).
thf(func_def_227,type,
sK106: ( nat > nat ) > nat ).
thf(func_def_228,type,
sK107: ( nat > set_nat ) > nat ).
thf(func_def_229,type,
sK108: ( nat > set_nat ) > nat ).
thf(func_def_230,type,
sK109: ( nat > set_a ) > nat ).
thf(func_def_231,type,
sK110: ( nat > set_a ) > nat ).
thf(func_def_232,type,
sK111: ( set_nat > nat ) > set_nat ).
thf(func_def_233,type,
sK112: ( set_nat > nat ) > set_nat ).
thf(func_def_234,type,
sK113: ( set_a > nat ) > set_a ).
thf(func_def_235,type,
sK114: ( set_a > nat ) > set_a ).
thf(func_def_236,type,
sK115: ( set_nat > set_nat ) > set_nat ).
thf(func_def_237,type,
sK116: ( set_nat > set_nat ) > set_nat ).
thf(func_def_238,type,
sK117: ( set_nat > set_a ) > set_nat ).
thf(func_def_239,type,
sK118: ( set_nat > set_a ) > set_nat ).
thf(func_def_240,type,
sK119: ( set_a > set_nat ) > set_a ).
thf(func_def_241,type,
sK120: ( set_a > set_nat ) > set_a ).
thf(func_def_242,type,
sK121: ( set_a > set_a ) > set_a ).
thf(func_def_243,type,
sK122: ( set_a > set_a ) > set_a ).
thf(func_def_244,type,
sK123: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_245,type,
sK124: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_246,type,
sK125: ( nat > nat ) > nat ).
thf(func_def_247,type,
sK126: ( nat > nat ) > nat ).
thf(func_def_248,type,
sK127: ( set_nat > nat ) > set_nat ).
thf(func_def_249,type,
sK128: ( set_nat > nat ) > set_nat ).
thf(func_def_250,type,
sK129: ( set_a > nat ) > set_a ).
thf(func_def_251,type,
sK130: ( set_a > nat ) > set_a ).
thf(func_def_252,type,
sK131: ( nat > set_nat ) > nat ).
thf(func_def_253,type,
sK132: ( nat > set_nat ) > nat ).
thf(func_def_254,type,
sK133: ( nat > set_a ) > nat ).
thf(func_def_255,type,
sK134: ( nat > set_a ) > nat ).
thf(func_def_256,type,
sK135: ( set_nat > set_nat ) > set_nat ).
thf(func_def_257,type,
sK136: ( set_nat > set_nat ) > set_nat ).
thf(func_def_258,type,
sK137: ( set_a > set_nat ) > set_a ).
thf(func_def_259,type,
sK138: ( set_a > set_nat ) > set_a ).
thf(func_def_260,type,
sK139: ( set_nat > set_a ) > set_nat ).
thf(func_def_261,type,
sK140: ( set_nat > set_a ) > set_nat ).
thf(func_def_262,type,
sK141: ( set_a > set_a ) > set_a ).
thf(func_def_263,type,
sK142: ( set_a > set_a ) > set_a ).
thf(func_def_264,type,
sK143: ( nat > set_Product_prod_a_a ) > nat ).
thf(func_def_265,type,
sK144: ( nat > set_Product_prod_a_a ) > nat ).
thf(func_def_266,type,
sK145: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_267,type,
sK146: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_268,type,
sK147: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_269,type,
sK148: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_270,type,
sK149: ( nat > $o ) > ( nat > $o ) > set_nat > nat ).
thf(func_def_271,type,
sK150: ( a > $o ) > ( a > $o ) > set_a > a ).
thf(func_def_272,type,
sK151: ( nat > $o ) > nat ).
thf(func_def_273,type,
sK152: nat > ( nat > $o ) > nat ).
thf(func_def_274,type,
sK153: ( nat > nat ) > nat ).
thf(func_def_275,type,
sK154: nat > ( nat > nat ) > nat ).
thf(func_def_276,type,
sK155: set_nat > nat ).
thf(func_def_277,type,
sK156: set_nat > nat > nat ).
thf(func_def_278,type,
sK157: nat > set_nat > nat ).
thf(func_def_279,type,
sK158: set_nat > nat ).
thf(func_def_280,type,
sK159: nat > nat ).
thf(func_def_281,type,
sK160: ( nat > $o ) > nat ).
thf(func_def_282,type,
sK161: ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_283,type,
sK162: ( nat > $o ) > nat ).
thf(func_def_284,type,
sK163: ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_285,type,
sK164: set_nat > nat ).
thf(func_def_286,type,
sK165: set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_287,type,
sK166: set_nat > nat ).
thf(func_def_288,type,
sK167: set_nat > nat > nat ).
thf(func_def_289,type,
sK168: set_nat > nat ).
thf(func_def_290,type,
sK169: set_nat > nat > nat ).
thf(func_def_291,type,
sK170: set_nat > nat ).
thf(func_def_292,type,
sK171: set_nat > nat > nat ).
thf(func_def_293,type,
sK172: set_nat > nat ).
thf(func_def_294,type,
sK173: set_nat > nat ).
thf(func_def_295,type,
sK174: set_nat > nat > nat ).
thf(func_def_296,type,
sK175: nat > set_nat > nat ).
thf(func_def_297,type,
sK176: set_nat > nat ).
thf(func_def_298,type,
sK177: set_nat > nat > nat ).
thf(func_def_299,type,
sK178: set_nat > nat ).
thf(func_def_300,type,
sK179: set_nat > nat > nat ).
thf(func_def_301,type,
sK180: pair_p1914262621t_unit > nat ).
thf(func_def_302,type,
sK181: nat > pair_p1914262621t_unit > nat ).
thf(func_def_303,type,
sK182: nat > pair_p1914262621t_unit > nat ).
thf(func_def_304,type,
sK183: set_a > ( a > $o ) > a ).
thf(func_def_305,type,
sK184: set_nat > ( nat > $o ) > nat ).
thf(func_def_306,type,
sK185: set_Product_prod_a_a > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_307,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_308,type,
sK186: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_309,type,
sK187: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_310,type,
sK188: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_311,type,
sK189: set_nat > nat ).
thf(func_def_312,type,
sK190: set_nat > nat ).
thf(func_def_313,type,
sK191: set_nat > nat ).
thf(func_def_314,type,
sK192: set_nat > nat ).
thf(func_def_315,type,
sK193: set_nat > nat ).
thf(func_def_316,type,
sK194: set_nat > nat ).
thf(func_def_317,type,
sK195: set_nat > nat ).
thf(func_def_318,type,
sK196: set_nat > nat > nat ).
thf(func_def_319,type,
sK197: set_nat > nat > nat ).
thf(func_def_320,type,
sK198: set_nat > nat > nat ).
thf(func_def_321,type,
sK199: pair_p1914262621t_unit > nat ).
thf(func_def_322,type,
sK200: nat > pair_p1914262621t_unit > nat ).
thf(func_def_323,type,
sK201: set_nat > nat > nat ).
thf(func_def_324,type,
sK202: set_nat > nat > nat ).
thf(func_def_325,type,
sK203: set_nat > nat > nat ).
thf(func_def_326,type,
sK204: set_nat > nat > nat ).
thf(func_def_327,type,
sK205: nat > set_nat > nat ).
thf(func_def_328,type,
sK206: set_nat > nat > nat ).
thf(func_def_329,type,
sK207: set_nat > nat > nat ).
thf(func_def_330,type,
sK208: set_nat > nat ).
thf(func_def_331,type,
sK209: set_nat > nat ).
thf(func_def_332,type,
sK210: set_nat > nat ).
thf(func_def_333,type,
sK211: nat > set_Pr1986765409at_nat > set_nat > ( nat > product_prod_nat_nat > $o ) > nat ).
thf(func_def_334,type,
sK212: set_nat > nat ).
thf(func_def_335,type,
sK213: set_Pr1986765409at_nat > set_nat > ( nat > product_prod_nat_nat > $o ) > nat > nat ).
thf(func_def_336,type,
sK214: set_nat > nat ).
thf(func_def_337,type,
sK215: set_nat > nat ).
thf(func_def_338,type,
sK216: set_nat > nat ).
thf(func_def_339,type,
sK217: nat > set_Product_prod_a_a > set_nat > ( nat > product_prod_a_a > $o ) > nat ).
thf(func_def_340,type,
sK218: set_nat > nat ).
thf(func_def_341,type,
sK219: set_Product_prod_a_a > set_nat > ( nat > product_prod_a_a > $o ) > nat > nat ).
thf(func_def_342,type,
sK220: nat > set_nat > nat ).
thf(func_def_343,type,
sK221: set_nat > nat > nat ).
thf(func_def_344,type,
sK222: nat > set_nat > nat ).
thf(func_def_345,type,
sK223: set_nat > nat > nat ).
thf(func_def_346,type,
sK224: set_nat > nat ).
thf(func_def_347,type,
sK225: nat > set_nat > nat ).
thf(func_def_348,type,
sK226: set_nat > nat ).
thf(func_def_349,type,
sK227: set_nat > nat > nat ).
thf(func_def_350,type,
sK228: set_nat > nat ).
thf(func_def_351,type,
sK229: nat > set_nat > set_nat > ( nat > nat > $o ) > nat ).
thf(func_def_352,type,
sK230: set_nat > nat > nat ).
thf(func_def_353,type,
sK231: set_nat > nat ).
thf(func_def_354,type,
sK232: set_nat > set_nat > ( nat > nat > $o ) > nat > nat ).
thf(func_def_355,type,
sK233: nat > set_nat > nat ).
thf(func_def_356,type,
sK234: set_nat > nat ).
thf(func_def_357,type,
sK235: set_nat > nat ).
thf(func_def_358,type,
sK236: set_nat > nat ).
thf(func_def_359,type,
sK237: nat > set_a > set_nat > ( nat > a > $o ) > nat ).
thf(func_def_360,type,
sK238: set_nat > nat ).
thf(func_def_361,type,
sK239: set_a > set_nat > ( nat > a > $o ) > nat > nat ).
thf(func_def_362,type,
sK240: nat > set_nat > nat ).
thf(func_def_363,type,
sK241: set_nat > nat > nat ).
thf(func_def_364,type,
sK242: nat > set_nat > nat ).
thf(func_def_365,type,
sK243: set_nat > nat > nat ).
thf(func_def_366,type,
sK244: ( nat > $o ) > nat ).
thf(func_def_367,type,
sK245: pair_p1914262621t_unit > nat ).
thf(func_def_368,type,
sK246: nat > pair_p1914262621t_unit > nat ).
thf(func_def_369,type,
sK247: nat > pair_p1914262621t_unit > nat ).
thf(func_def_370,type,
sK248: set_nat > nat > nat ).
thf(func_def_371,type,
sK249: set_nat > nat > nat ).
thf(func_def_372,type,
sK250: set_nat > nat > nat ).
thf(func_def_373,type,
sK251: set_nat > nat > nat ).
thf(func_def_374,type,
sK252: ( product_prod_a_a > set_nat ) > set_Product_prod_a_a > nat > nat ).
thf(func_def_375,type,
sK253: set_nat > nat > nat ).
thf(func_def_376,type,
sK254: ( nat > set_nat ) > set_nat > nat > nat ).
thf(func_def_377,type,
sK255: nat > set_nat > nat ).
thf(func_def_378,type,
sK256: set_nat > nat > nat ).
thf(func_def_379,type,
sK257: set_nat > nat > nat ).
thf(func_def_380,type,
sK258: ( a > set_nat ) > set_a > nat > nat ).
thf(func_def_381,type,
sK259: nat > set_nat > nat ).
thf(func_def_382,type,
sK260: ( nat > $o ) > nat ).
thf(func_def_383,type,
sK261: ( nat > $o ) > ( nat > $o ) > nat > nat ).
thf(func_def_384,type,
sK262: ( nat > $o ) > nat ).
thf(func_def_385,type,
sK263: ( nat > $o ) > ( nat > $o ) > nat > nat ).
thf(func_def_386,type,
sK264: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_387,type,
sK265: ( nat > $o ) > nat > nat ).
thf(func_def_388,type,
sK266: nat > ( nat > $o ) > nat ).
thf(func_def_389,type,
sK267: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_390,type,
sK268: ( nat > $o ) > nat > nat ).
thf(func_def_391,type,
sK269: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_392,type,
sK270: ( nat > $o ) > nat > nat ).
thf(func_def_393,type,
sK271: set_nat > nat > nat ).
thf(func_def_394,type,
sK272: set_nat > nat > nat ).
thf(func_def_395,type,
sK273: set_nat > nat > nat ).
thf(func_def_396,type,
sK274: set_nat > nat ).
thf(func_def_397,type,
sK275: set_nat > nat > nat ).
thf(func_def_398,type,
sK276: set_nat > nat ).
thf(func_def_399,type,
sK277: set_nat > nat > nat ).
thf(func_def_400,type,
sK278: set_nat > nat ).
thf(func_def_401,type,
sK279: set_nat > nat > nat ).
thf(func_def_402,type,
sK280: nat > pair_p1914262621t_unit > nat ).
thf(func_def_403,type,
sK281: pair_p1914262621t_unit > nat ).
thf(func_def_404,type,
sK282: nat > pair_p1914262621t_unit > nat ).
thf(func_def_406,type,
sK284: pair_p125712459t_unit > product_prod_a_a ).
thf(func_def_407,type,
sK285: ( a > set_a ) > product_prod_a_a ).
thf(f1,axiom,
( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [X0: a] : ( pair_p1047056820t_unit @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062) ).
thf(f2,axiom,
( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [X0: a] : ( pair_p1047056820t_unit @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062) ).
thf(f28,axiom,
! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ X0 )
=> ( ( ord_le1824328871od_a_a @ X1 @ X0 )
=> ( finite179568208od_a_a @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rev__finite__subset) ).
thf(f142,axiom,
( ord_le1824328871od_a_a
= ( ^ [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [X2: product_prod_a_a] : ( member449909584od_a_a @ X2 @ X0 )
@ ^ [X2: product_prod_a_a] : ( member449909584od_a_a @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_less__eq__set__def) ).
thf(f355,conjecture,
finite179568208od_a_a @ ( pair_p133601421t_unit @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f356,negated_conjecture,
~ ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f357,plain,
( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [X0: a] : ( pair_p1047056820t_unit @ g ) ) ),
inference(rectify,[],[f1]) ).
thf(f358,plain,
( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) )
= $true ),
inference(fool_elimination,[],[f357]) ).
thf(f359,plain,
( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [X0: a] : ( pair_p1047056820t_unit @ g ) ) ),
inference(rectify,[],[f2]) ).
thf(f360,plain,
( $true
= ( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) ) ),
inference(fool_elimination,[],[f359]) ).
thf(f411,plain,
! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ X0 )
=> ( ( ord_le1824328871od_a_a @ X1 @ X0 )
=> ( finite179568208od_a_a @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f412,plain,
! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( ( finite179568208od_a_a @ X0 )
= $true )
=> ( ( ( ord_le1824328871od_a_a @ X1 @ X0 )
= $true )
=> ( ( finite179568208od_a_a @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f411]) ).
thf(f633,plain,
( ord_le1824328871od_a_a
= ( ^ [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [X2: product_prod_a_a] : ( member449909584od_a_a @ X2 @ X0 )
@ ^ [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f142]) ).
thf(f634,plain,
( ord_le1824328871od_a_a
= ( ^ [Y0: set_Product_prod_a_a,Y1: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [Y2: product_prod_a_a] : ( member449909584od_a_a @ Y2 @ Y0 )
@ ^ [Y2: product_prod_a_a] : ( member449909584od_a_a @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f633]) ).
thf(f1032,plain,
~ ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ),
inference(rectify,[],[f356]) ).
thf(f1033,plain,
( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
!= $true ),
inference(fool_elimination,[],[f1032]) ).
thf(f1071,plain,
( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
!= $true ),
inference(flattening,[],[f1033]) ).
thf(f1109,plain,
! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( ( finite179568208od_a_a @ X1 )
= $true )
| ( ( ord_le1824328871od_a_a @ X1 @ X0 )
!= $true )
| ( ( finite179568208od_a_a @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f412]) ).
thf(f1110,plain,
! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( ( finite179568208od_a_a @ X1 )
= $true )
| ( ( ord_le1824328871od_a_a @ X1 @ X0 )
!= $true )
| ( ( finite179568208od_a_a @ X0 )
!= $true ) ),
inference(flattening,[],[f1109]) ).
thf(f1610,plain,
( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) )
= $true ),
inference(cnf_transformation,[],[f358]) ).
thf(f1611,plain,
( $true
= ( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) ) ),
inference(cnf_transformation,[],[f360]) ).
thf(f1637,plain,
! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( ( finite179568208od_a_a @ X1 )
= $true )
| ( ( ord_le1824328871od_a_a @ X1 @ X0 )
!= $true )
| ( ( finite179568208od_a_a @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f1110]) ).
thf(f1825,plain,
( ord_le1824328871od_a_a
= ( ^ [Y0: set_Product_prod_a_a,Y1: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [Y2: product_prod_a_a] : ( member449909584od_a_a @ Y2 @ Y0 )
@ ^ [Y2: product_prod_a_a] : ( member449909584od_a_a @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f634]) ).
thf(f2111,plain,
( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
!= $true ),
inference(cnf_transformation,[],[f1071]) ).
thf(f2121,plain,
( $true
= ( ^ [Y0: set_Product_prod_a_a,Y1: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [Y2: product_prod_a_a] : ( member449909584od_a_a @ Y2 @ Y0 )
@ ^ [Y2: product_prod_a_a] : ( member449909584od_a_a @ Y2 @ Y1 ) )
@ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) ) ),
inference(definition_unfolding,[],[f1611,f1825]) ).
thf(f2136,plain,
! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( ( finite179568208od_a_a @ X1 )
= $true )
| ( $true
!= ( ^ [Y0: set_Product_prod_a_a,Y1: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [Y2: product_prod_a_a] : ( member449909584od_a_a @ Y2 @ Y0 )
@ ^ [Y2: product_prod_a_a] : ( member449909584od_a_a @ Y2 @ Y1 ) )
@ X1
@ X0 ) )
| ( ( finite179568208od_a_a @ X0 )
!= $true ) ),
inference(definition_unfolding,[],[f1637,f1825]) ).
thf(f3885,plain,
! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( $true
!= ( ord_le1347718902_a_a_o
@ ^ [Y0: product_prod_a_a] : ( member449909584od_a_a @ Y0 @ X1 )
@ ^ [Y0: product_prod_a_a] : ( member449909584od_a_a @ Y0 @ X0 ) ) )
| ( ( finite179568208od_a_a @ X1 )
= $true )
| ( ( finite179568208od_a_a @ X0 )
!= $true ) ),
inference(beta-eta_normalization,[],[f2136]) ).
thf(f3951,plain,
( $true
= ( ord_le1347718902_a_a_o
@ ^ [Y0: product_prod_a_a] : ( member449909584od_a_a @ Y0 @ ( pair_p133601421t_unit @ g ) )
@ ^ [Y0: product_prod_a_a] :
( member449909584od_a_a @ Y0
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y1: a] : ( pair_p1047056820t_unit @ g ) ) ) ) ),
inference(beta-eta_normalization,[],[f2121]) ).
thf(f3980,plain,
! [X2: a > set_a,X0: pair_p125712459t_unit,X1: set_a] :
( ( $true != $true )
| ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ X0 ) )
= $true )
| ( $true
!= ( finite179568208od_a_a @ ( product_Sigma_a_a @ X1 @ X2 ) ) )
| ( ( ^ [Y0: product_prod_a_a] : g )
!= ( ^ [Y0: product_prod_a_a] : X0 ) )
| ( ( ^ [Y0: product_prod_a_a,Y1: a] : ( pair_p1047056820t_unit @ g ) )
!= ( ^ [Y0: product_prod_a_a] : X2 ) )
| ( ( ^ [Y0: product_prod_a_a] : X1 )
!= ( ^ [Y0: product_prod_a_a] : ( pair_p1047056820t_unit @ g ) ) ) ),
inference(constrained_superposition,[],[f3885,f3951]) ).
thf(f3981,plain,
! [X2: a > set_a,X0: pair_p125712459t_unit,X1: set_a] :
( ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ X0 ) )
= $true )
| ( $true
!= ( finite179568208od_a_a @ ( product_Sigma_a_a @ X1 @ X2 ) ) )
| ( ( ^ [Y0: product_prod_a_a] : g )
!= ( ^ [Y0: product_prod_a_a] : X0 ) )
| ( ( ^ [Y0: product_prod_a_a,Y1: a] : ( pair_p1047056820t_unit @ g ) )
!= ( ^ [Y0: product_prod_a_a] : X2 ) )
| ( ( ^ [Y0: product_prod_a_a] : X1 )
!= ( ^ [Y0: product_prod_a_a] : ( pair_p1047056820t_unit @ g ) ) ) ),
inference(trivial_inequality_removal,[],[f3980]) ).
thf(f3985,definition,
( spl283_1
<=> ! [X2: a > set_a,X1: set_a] :
( ( $true
!= ( finite179568208od_a_a @ ( product_Sigma_a_a @ X1 @ X2 ) ) )
| ( ( ^ [Y0: product_prod_a_a] : X1 )
!= ( ^ [Y0: product_prod_a_a] : ( pair_p1047056820t_unit @ g ) ) )
| ( ( ^ [Y0: product_prod_a_a,Y1: a] : ( pair_p1047056820t_unit @ g ) )
!= ( ^ [Y0: product_prod_a_a] : X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl283_1])],[avatar_definition]) ).
thf(f3986,plain,
( ! [X2: a > set_a,X1: set_a] :
( ( ( ^ [Y0: product_prod_a_a,Y1: a] : ( pair_p1047056820t_unit @ g ) )
!= ( ^ [Y0: product_prod_a_a] : X2 ) )
| ( ( ^ [Y0: product_prod_a_a] : X1 )
!= ( ^ [Y0: product_prod_a_a] : ( pair_p1047056820t_unit @ g ) ) )
| ( $true
!= ( finite179568208od_a_a @ ( product_Sigma_a_a @ X1 @ X2 ) ) ) )
| ~ spl283_1 ),
inference(avatar_component_clause,[],[f3985]) ).
thf(f3988,definition,
( spl283_2
<=> ! [X0: pair_p125712459t_unit] :
( ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ X0 ) )
= $true )
| ( ( ^ [Y0: product_prod_a_a] : g )
!= ( ^ [Y0: product_prod_a_a] : X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl283_2])],[avatar_definition]) ).
thf(f3989,plain,
( ! [X0: pair_p125712459t_unit] :
( ( ( ^ [Y0: product_prod_a_a] : g )
!= ( ^ [Y0: product_prod_a_a] : X0 ) )
| ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ X0 ) )
= $true ) )
| ~ spl283_2 ),
inference(avatar_component_clause,[],[f3988]) ).
thf(f3990,plain,
( spl283_1
| spl283_2 ),
inference(avatar_split_clause,[],[f3981,f3988,f3985]) ).
thf(f3997,plain,
( ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
= $true )
| ~ spl283_2 ),
inference(equality_resolution,[],[f3989]) ).
thf(f3999,plain,
( $false
| ~ spl283_2 ),
inference(forward_subsumption_resolution,[],[f3997,f2111]) ).
thf(f4000,plain,
~ spl283_2,
inference(avatar_contradiction_clause,[],[f3999]) ).
thf(f4002,plain,
( ! [X0: set_a] :
( ( ( ^ [Y0: product_prod_a_a] : ( pair_p1047056820t_unit @ g ) )
!= ( ^ [Y0: product_prod_a_a] : X0 ) )
| ( $true
!= ( finite179568208od_a_a
@ ( product_Sigma_a_a @ X0
@ ^ [Y0: a] :
( pair_p1047056820t_unit
@ ( ^ [Y1: a] : g
@ Y0 ) ) ) ) ) )
| ~ spl283_1 ),
inference(equality_resolution,[],[f3986]) ).
thf(f4003,plain,
( ! [X0: set_a] :
( ( $true
!= ( finite179568208od_a_a
@ ( product_Sigma_a_a @ X0
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) ) )
| ( ( ^ [Y0: product_prod_a_a] : ( pair_p1047056820t_unit @ g ) )
!= ( ^ [Y0: product_prod_a_a] : X0 ) ) )
| ~ spl283_1 ),
inference(beta-eta_normalization,[],[f4002]) ).
thf(f4012,plain,
( ( $true != $true )
| ( ( ^ [Y0: product_prod_a_a] : ( pair_p1047056820t_unit @ g ) )
!= ( ^ [Y0: product_prod_a_a] : ( pair_p1047056820t_unit @ g ) ) )
| ~ spl283_1 ),
inference(constrained_superposition,[],[f4003,f1610]) ).
thf(f4013,plain,
( $false
| ~ spl283_1 ),
inference(trivial_inequality_removal,[],[f4012]) ).
thf(f4014,plain,
~ spl283_1,
inference(avatar_contradiction_clause,[],[f4013]) ).
cnf(s1,plain,
( spl283_1
| spl283_2 ),
inference(sat_conversion,[],[f3990]) ).
cnf(s4,plain,
~ spl283_2,
inference(sat_conversion,[],[f4000]) ).
cnf(s5,plain,
~ spl283_1,
inference(sat_conversion,[],[f4014]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s4,s5]) ).
thf(f4016,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP093^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n013.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 19:52:06 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 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
% 0.83/0.40 % (2576652)Will run a generic schedule for satisfiability detection.
% 0.83/0.40 % (2576660)dis+10_1_sil=32000:sp=arity:random_seed=2341219688:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.83/0.40 % (2576658)% WARNING: option uhcvi not known.
% 0.83/0.40 % (2576657)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1095281988_2999 on theBenchmark for (2999ds/0Mi)
% 0.83/0.40 % (2576658)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2407964832:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.83/0.40 % (2576659)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3585695077:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.83/0.40 % (2576661)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3852547580:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.83/0.40 % (2576662)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3909390509:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.83/0.40 % (2576663)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=489946540:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.83/0.40 % (2576660)Instruction limit reached!
% 0.83/0.40 % (2576660)------------------------------
% 0.83/0.40 % (2576660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (2576660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (2576660)CaDiCaL version: 2.1.3
% 0.83/0.40 % (2576660)Termination reason: Instruction limit
% 0.83/0.40 % (2576660)Termination phase: Property scanning
% 0.83/0.40 % (2576660)Time elapsed: 0.023 s
% 0.83/0.40 % (2576660)Peak memory usage: 12 MB
% 0.83/0.40 % (2576660)Instructions burned: 104 (million)
% 0.83/0.40 % (2576658)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.83/0.40 % (2576661)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.83/0.40 % (2576671)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2593962003:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.83/0.40 % (2576661)Instruction limit reached!
% 0.83/0.40 % (2576661)------------------------------
% 0.83/0.40 % (2576661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (2576661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (2576661)CaDiCaL version: 2.1.3
% 0.83/0.40 % (2576661)Termination reason: Instruction limit
% 0.83/0.40 % (2576661)Termination phase: Property scanning
% 0.83/0.40 % (2576661)Time elapsed: 0.050 s
% 0.83/0.40 % (2576661)Peak memory usage: 11 MB
% 0.83/0.40 % (2576661)Instructions burned: 116 (million)
% 0.83/0.40 % Exception at run slice level
% 0.83/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.83/0.40 % (2576662)Instruction limit reached!
% 0.83/0.40 % (2576662)------------------------------
% 0.83/0.40 % (2576662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (2576662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (2576662)CaDiCaL version: 2.1.3
% 0.83/0.40 % (2576662)Termination reason: Instruction limit
% 0.83/0.40 % (2576662)Termination phase: Property scanning
% 0.83/0.40 % (2576662)Time elapsed: 0.055 s
% 0.83/0.40 % (2576662)Peak memory usage: 12 MB
% 0.83/0.40 % (2576662)Instructions burned: 131 (million)
% 0.83/0.40 % (2576658)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.83/0.40 % Exception at run slice level
% 0.83/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.83/0.40 % (2576674)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=39810505:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.83/0.40 % (2576673)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2095334642:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.83/0.40 % (2576663)Instruction limit reached!
% 0.83/0.40 % (2576663)------------------------------
% 0.83/0.40 % (2576663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (2576663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (2576663)CaDiCaL version: 2.1.3
% 0.83/0.40 % (2576663)Termination reason: Instruction limit
% 0.83/0.40 % (2576663)Termination phase: Saturation
% 0.83/0.40 % (2576663)Time elapsed: 0.068 s
% 0.83/0.40 % (2576663)Peak memory usage: 13 MB
% 0.83/0.40 % (2576663)Instructions burned: 161 (million)
% 0.83/0.40 % (2576674)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.83/0.40 % (2576676)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2832102742:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.83/0.40 % (2576675)ott-21_1_sil=16000:fs=off:random_seed=2249482936:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.83/0.40 % (2576674)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.83/0.40 % (2576679)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1147824338:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.83/0.40 % (2576674) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2576652-2576674"...
% 0.83/0.40 % (2576674)...printing done.
% 0.83/0.40 % (2576674)Refutation found. Thanks to Tanya!
% 0.83/0.40 % SZS status Theorem for theBenchmark
% 0.83/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.83/0.40 % (2576674)------------------------------
% 0.83/0.40 % (2576674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (2576674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (2576674)CaDiCaL version: 2.1.3
% 0.83/0.40 % (2576674)Termination reason: Refutation
% 0.83/0.40 % (2576674)Time elapsed: 0.053 s
% 0.83/0.40 % (2576674)Peak memory usage: 16 MB
% 0.83/0.40 % (2576674)Instructions burned: 228 (million)
% 0.83/0.40 % (2576652)Success in time 0.185 s
% 0.83/0.40 % Vampire exiting
%------------------------------------------------------------------------------