%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP093^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:08:18 AM UTC 2026
% Result : Theorem 0.52s 0.43s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 23 unt; 0 typ; 3 def)
% Number of atoms : 135 ( 31 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 190 ( 30 ~; 23 |; 0 &; 128 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 32 ( 31 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 292 ( 289 usr; 11 con; 0-4 aty)
% Number of variables : 26 ( 14 sgn 12 !; 0 ?; 26 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_109,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_110,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_111,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_112,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_115,type,
vNOT: $o > $o ).
thf(func_def_116,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_117,type,
vIMP: $o > $o > $o ).
thf(func_def_118,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_119,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_120,type,
vOR: $o > $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,
sK2: set_a > ( a > set_nat ) > a ).
thf(func_def_124,type,
sK3: ( product_prod_a_a > set_a ) > set_Product_prod_a_a > ( product_prod_a_a > set_a ) > product_prod_a_a ).
thf(func_def_125,type,
sK4: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_126,type,
sK5: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_127,type,
sK6: ( set_nat > set_nat ) > set_nat ).
thf(func_def_128,type,
sK7: ( set_nat > set_nat ) > set_nat ).
thf(func_def_129,type,
sK8: set_nat > nat ).
thf(func_def_130,type,
sK9: nat > set_nat > nat ).
thf(func_def_131,type,
sK10: ( nat > set_Pr1986765409at_nat ) > set_nat > nat ).
thf(func_def_132,type,
sK11: ( a > set_a ) > ( a > set_a ) > set_a > a ).
thf(func_def_133,type,
sK12: ( set_a > set_a ) > set_a ).
thf(func_def_134,type,
sK13: ( set_a > set_a ) > set_a ).
thf(func_def_135,type,
sK14: ( nat > nat ) > nat ).
thf(func_def_136,type,
sK15: ( a > $o ) > a ).
thf(func_def_137,type,
sK16: ( nat > $o ) > nat ).
thf(func_def_138,type,
sK17: ( set_nat > set_nat ) > set_nat ).
thf(func_def_139,type,
sK18: ( set_nat > set_nat ) > set_nat ).
thf(func_def_140,type,
sK19: ( nat > set_a ) > set_nat > ( nat > set_a ) > nat ).
thf(func_def_141,type,
sK20: ( product_prod_a_a > set_a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_142,type,
sK21: ( nat > nat ) > nat ).
thf(func_def_143,type,
sK22: ( nat > nat ) > nat ).
thf(func_def_144,type,
sK23: ( nat > set_a ) > nat ).
thf(func_def_145,type,
sK24: ( nat > set_a ) > nat ).
thf(func_def_146,type,
sK25: ( a > set_nat ) > ( a > set_nat ) > set_a > a ).
thf(func_def_147,type,
sK26: ( set_a > nat ) > set_a ).
thf(func_def_148,type,
sK27: ( set_a > nat ) > set_a ).
thf(func_def_149,type,
sK28: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_150,type,
sK29: ( produc1572603623od_a_a > $o ) > produc1572603623od_a_a ).
thf(func_def_151,type,
sK30: ( set_nat > set_nat ) > set_nat ).
thf(func_def_152,type,
sK31: ( set_nat > set_nat ) > set_nat ).
thf(func_def_153,type,
sK32: ( nat > set_a ) > nat ).
thf(func_def_154,type,
sK33: ( nat > set_a ) > nat ).
thf(func_def_155,type,
sK34: set_nat > ( a > nat > $o ) > set_a > a ).
thf(func_def_156,type,
sK35: set_nat > ( a > nat > $o ) > set_a > nat ).
thf(func_def_157,type,
sK36: ( nat > nat ) > nat ).
thf(func_def_158,type,
sK37: ( nat > nat ) > nat ).
thf(func_def_159,type,
sK38: ( nat > $o ) > nat ).
thf(func_def_160,type,
sK39: set_set_nat > set_nat > set_nat ).
thf(func_def_161,type,
sK40: set_a > set_a > a ).
thf(func_def_162,type,
sK41: set_a > set_set_a > set_a ).
thf(func_def_163,type,
sK42: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_164,type,
sK43: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_165,type,
sK44: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_166,type,
sK45: ( nat > set_a ) > nat ).
thf(func_def_167,type,
sK46: ( nat > set_a ) > nat ).
thf(func_def_168,type,
sK47: ( a > set_Pr1986765409at_nat ) > set_a > a ).
thf(func_def_169,type,
sK48: ( set_nat > nat ) > set_nat ).
thf(func_def_170,type,
sK49: ( set_nat > nat ) > set_nat ).
thf(func_def_171,type,
sK50: ( set_a > nat ) > set_a ).
thf(func_def_172,type,
sK51: ( set_a > nat ) > set_a ).
thf(func_def_173,type,
sK52: ( set_a > set_a ) > set_a ).
thf(func_def_174,type,
sK53: ( set_a > set_a ) > set_a ).
thf(func_def_175,type,
sK54: ( nat > set_nat ) > nat ).
thf(func_def_176,type,
sK55: ( nat > set_nat ) > nat ).
thf(func_def_177,type,
sK56: set_a > set_set_a > set_a ).
thf(func_def_178,type,
sK57: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_179,type,
sK58: nat > set_nat > nat ).
thf(func_def_180,type,
sK59: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_181,type,
sK60: ( nat > set_a ) > nat ).
thf(func_def_182,type,
sK61: ( nat > set_a ) > nat ).
thf(func_def_183,type,
sK62: ( nat > $o ) > nat ).
thf(func_def_184,type,
sK63: ( nat > $o ) > nat > nat ).
thf(func_def_185,type,
sK64: ( set_a > nat ) > set_a ).
thf(func_def_186,type,
sK65: ( set_a > nat ) > set_a ).
thf(func_def_187,type,
sK66: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_188,type,
sK67: ( a > set_a ) > ( a > set_a ) > set_a > a ).
thf(func_def_189,type,
sK68: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_190,type,
sK69: ( set_Product_prod_a_a > nat ) > set_Product_prod_a_a ).
thf(func_def_191,type,
sK70: set_a > ( a > a > $o ) > set_a > a ).
thf(func_def_192,type,
sK71: set_a > ( a > a > $o ) > set_a > a ).
thf(func_def_193,type,
sK72: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_194,type,
sK73: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_195,type,
sK74: ( nat > set_nat ) > nat ).
thf(func_def_196,type,
sK75: ( nat > set_nat ) > nat ).
thf(func_def_197,type,
sK76: ( set_a > set_nat ) > set_a ).
thf(func_def_198,type,
sK77: ( set_a > set_nat ) > set_a ).
thf(func_def_199,type,
sK78: ( nat > nat > $o ) > nat ).
thf(func_def_200,type,
sK79: ( nat > nat > $o ) > nat ).
thf(func_def_201,type,
sK80: ( nat > nat > $o ) > nat ).
thf(func_def_202,type,
sK81: ( nat > nat > $o ) > nat ).
thf(func_def_203,type,
sK82: set_a > ( a > product_prod_a_a > $o ) > set_Product_prod_a_a > a ).
thf(func_def_204,type,
sK83: set_a > ( a > product_prod_a_a > $o ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_205,type,
sK84: ( product_prod_a_a > nat > $o ) > set_Product_prod_a_a > set_nat > product_prod_a_a ).
thf(func_def_206,type,
sK85: ( product_prod_a_a > nat > $o ) > set_Product_prod_a_a > set_nat > nat ).
thf(func_def_207,type,
sK86: ( nat > nat ) > nat ).
thf(func_def_208,type,
sK87: ( nat > nat ) > nat ).
thf(func_def_209,type,
sK88: ( nat > a > $o ) > set_nat > set_a > a ).
thf(func_def_210,type,
sK89: ( nat > a > $o ) > set_nat > set_a > nat ).
thf(func_def_211,type,
sK90: set_nat > nat > nat ).
thf(func_def_212,type,
sK91: set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_213,type,
sK92: set_nat > nat ).
thf(func_def_214,type,
sK93: ( product_prod_a_a > $o ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_215,type,
sK94: ( nat > set_nat ) > nat ).
thf(func_def_216,type,
sK95: ( nat > set_nat ) > nat ).
thf(func_def_217,type,
sK96: ( a > $o ) > ( a > $o ) > set_a > a ).
thf(func_def_218,type,
sK97: ( nat > $o ) > ( nat > $o ) > set_nat > nat ).
thf(func_def_219,type,
sK98: ( set_a > set_nat ) > set_a ).
thf(func_def_220,type,
sK99: ( set_a > set_nat ) > set_a ).
thf(func_def_221,type,
sK100: ( nat > $o ) > nat ).
thf(func_def_222,type,
sK101: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_223,type,
sK102: ( product_prod_a_a > set_nat ) > ( product_prod_a_a > set_nat ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_224,type,
sK103: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_225,type,
sK104: ( set_nat > set_nat ) > set_nat ).
thf(func_def_226,type,
sK105: ( set_nat > set_nat ) > set_nat ).
thf(func_def_227,type,
sK106: ( set_nat > set_a ) > set_nat ).
thf(func_def_228,type,
sK107: ( set_nat > set_a ) > set_nat ).
thf(func_def_229,type,
sK108: set_set_nat > set_nat > set_nat ).
thf(func_def_230,type,
sK109: ( nat > set_a ) > set_nat > nat ).
thf(func_def_231,type,
sK110: ( set_nat > nat ) > set_nat ).
thf(func_def_232,type,
sK111: ( set_nat > nat ) > set_nat ).
thf(func_def_233,type,
sK112: ( nat > $o ) > set_nat > nat ).
thf(func_def_234,type,
sK113: ( nat > set_nat ) > set_nat > nat ).
thf(func_def_235,type,
sK114: ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_236,type,
sK115: ( a > set_Product_prod_a_a ) > set_a > ( a > set_Product_prod_a_a ) > a ).
thf(func_def_237,type,
sK116: set_nat > set_nat > nat ).
thf(func_def_238,type,
sK117: set_Product_prod_a_a > set_se1596668135od_a_a > set_Product_prod_a_a ).
thf(func_def_239,type,
sK118: ( set_a > set_a ) > set_a ).
thf(func_def_240,type,
sK119: ( set_a > set_a ) > set_a ).
thf(func_def_241,type,
sK120: ( a > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_a > a ).
thf(func_def_242,type,
sK121: ( a > product_prod_nat_nat > $o ) > set_Pr1986765409at_nat > set_a > product_prod_nat_nat ).
thf(func_def_243,type,
sK122: ( product_prod_a_a > set_Product_prod_a_a ) > set_Product_prod_a_a > ( product_prod_a_a > set_Product_prod_a_a ) > product_prod_a_a ).
thf(func_def_244,type,
sK123: ( set_nat > nat ) > set_nat ).
thf(func_def_245,type,
sK124: ( set_nat > nat ) > set_nat ).
thf(func_def_246,type,
sK125: set_Product_prod_a_a > set_se1596668135od_a_a > set_Product_prod_a_a ).
thf(func_def_247,type,
sK126: ( set_nat > set_a ) > set_nat ).
thf(func_def_248,type,
sK127: ( set_nat > set_a ) > set_nat ).
thf(func_def_249,type,
sK128: ( set_nat > nat ) > set_nat ).
thf(func_def_250,type,
sK129: ( set_nat > nat ) > set_nat ).
thf(func_def_251,type,
sK130: set_Pr1986765409at_nat > set_nat > ( nat > product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_252,type,
sK131: set_Pr1986765409at_nat > set_nat > ( nat > product_prod_nat_nat > $o ) > nat ).
thf(func_def_253,type,
sK132: ( set_nat > set_a ) > set_nat ).
thf(func_def_254,type,
sK133: ( set_nat > set_a ) > set_nat ).
thf(func_def_255,type,
sK134: ( set_nat > set_a ) > set_nat ).
thf(func_def_256,type,
sK135: ( set_nat > set_a ) > set_nat ).
thf(func_def_257,type,
sK136: ( nat > set_nat ) > nat ).
thf(func_def_258,type,
sK137: ( nat > set_nat ) > nat ).
thf(func_def_259,type,
sK138: ( nat > set_Product_prod_a_a ) > set_nat > nat ).
thf(func_def_260,type,
sK139: set_a > ( a > set_Product_prod_a_a ) > a ).
thf(func_def_261,type,
sK140: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_262,type,
sK141: set_a > ( a > $o ) > a ).
thf(func_def_263,type,
sK142: set_nat > ( nat > set_Product_prod_a_a ) > ( nat > set_Product_prod_a_a ) > nat ).
thf(func_def_264,type,
sK143: ( nat > product_prod_a_a > $o ) > set_Product_prod_a_a > set_nat > nat ).
thf(func_def_265,type,
sK144: ( nat > product_prod_a_a > $o ) > set_Product_prod_a_a > set_nat > product_prod_a_a ).
thf(func_def_266,type,
sK145: ( set_a > nat ) > set_a ).
thf(func_def_267,type,
sK146: ( set_a > nat ) > set_a ).
thf(func_def_268,type,
sK147: ( nat > nat ) > nat ).
thf(func_def_269,type,
sK148: ( nat > nat ) > nat ).
thf(func_def_270,type,
sK149: ( nat > set_Product_prod_a_a ) > nat ).
thf(func_def_271,type,
sK150: ( nat > set_Product_prod_a_a ) > nat ).
thf(func_def_272,type,
sK151: ( a > set_a ) > set_a > a ).
thf(func_def_273,type,
sK152: ( set_a > set_nat ) > set_a ).
thf(func_def_274,type,
sK153: ( set_a > set_nat ) > set_a ).
thf(func_def_275,type,
sK154: ( set_a > set_a ) > set_a ).
thf(func_def_276,type,
sK155: ( set_a > set_a ) > set_a ).
thf(func_def_277,type,
sK156: ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_278,type,
sK157: set_nat > set_nat > ( nat > nat > $o ) > nat ).
thf(func_def_279,type,
sK158: set_nat > set_nat > ( nat > nat > $o ) > nat ).
thf(func_def_280,type,
sK159: ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_281,type,
sK160: ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_282,type,
sK161: set_nat > ( nat > set_nat ) > ( nat > set_nat ) > nat ).
thf(func_def_283,type,
sK162: ( product_prod_a_a > set_nat ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_284,type,
sK163: ( set_a > set_nat ) > set_a ).
thf(func_def_285,type,
sK164: ( set_a > set_nat ) > set_a ).
thf(func_def_286,type,
sK165: set_Product_prod_a_a > ( product_prod_a_a > a > $o ) > set_a > product_prod_a_a ).
thf(func_def_287,type,
sK166: set_Product_prod_a_a > ( product_prod_a_a > a > $o ) > set_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_27_rev__finite__subset) ).
thf(f355,conjecture,
finite179568208od_a_a @ ( pair_p133601421t_unit @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f356,negated_conjecture,
~ ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f440,plain,
( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [X0: a] : ( pair_p1047056820t_unit @ g ) ) ),
inference(rectify,[],[f1]) ).
thf(f441,plain,
( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) )
= $true ),
inference(fool_elimination,[],[f440]) ).
thf(f450,plain,
~ ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ),
inference(rectify,[],[f356]) ).
thf(f451,plain,
( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
!= $true ),
inference(fool_elimination,[],[f450]) ).
thf(f634,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(f635,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,[],[f634]) ).
thf(f788,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(f789,plain,
! [X1: set_Product_prod_a_a,X0: 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,[],[f788]) ).
thf(f1041,plain,
( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
!= $true ),
inference(flattening,[],[f451]) ).
thf(f1491,plain,
! [X1: set_Product_prod_a_a,X0: 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,[],[f789]) ).
thf(f1492,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(flattening,[],[f1491]) ).
thf(f1878,plain,
! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ X1 @ X0 )
!= $true )
| ( ( finite179568208od_a_a @ X1 )
= $true )
| ( ( finite179568208od_a_a @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f1492]) ).
thf(f1991,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,[],[f635]) ).
thf(f2029,plain,
( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
!= $true ),
inference(cnf_transformation,[],[f1041]) ).
thf(f2183,plain,
( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) )
= $true ),
inference(cnf_transformation,[],[f441]) ).
thf(f2665,definition,
( spl167_14
<=> ( $true
= ( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl167_14])],[avatar_definition]) ).
thf(f2667,plain,
( ( $true
= ( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) ) )
| ~ spl167_14 ),
inference(avatar_component_clause,[],[f2665]) ).
thf(f2668,plain,
spl167_14,
inference(avatar_split_clause,[],[f1991,f2665]) ).
thf(f2680,definition,
( spl167_17
<=> ( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl167_17])],[avatar_definition]) ).
thf(f2682,plain,
( ( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) )
= $true )
| ~ spl167_17 ),
inference(avatar_component_clause,[],[f2680]) ).
thf(f2683,plain,
spl167_17,
inference(avatar_split_clause,[],[f2183,f2680]) ).
thf(f2735,definition,
( spl167_28
<=> ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl167_28])],[avatar_definition]) ).
thf(f2737,plain,
( ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
!= $true )
| spl167_28 ),
inference(avatar_component_clause,[],[f2735]) ).
thf(f2738,plain,
~ spl167_28,
inference(avatar_split_clause,[],[f2029,f2735]) ).
thf(f2882,plain,
( ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
= $true )
| ( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) )
!= $true )
| ( $true != $true )
| ~ spl167_14 ),
inference(superposition,[],[f1878,f2667]) ).
thf(f2883,plain,
( ( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Y0: a] : ( pair_p1047056820t_unit @ g ) ) )
!= $true )
| ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
= $true )
| ~ spl167_14 ),
inference(trivial_inequality_removal,[],[f2882]) ).
thf(f2884,plain,
( ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) )
= $true )
| ~ spl167_14
| ~ spl167_17 ),
inference(forward_subsumption_resolution,[],[f2883,f2682]) ).
thf(f2885,plain,
( $false
| ~ spl167_14
| ~ spl167_17
| spl167_28 ),
inference(forward_subsumption_resolution,[],[f2884,f2737]) ).
thf(f2886,plain,
( ~ spl167_14
| ~ spl167_17
| spl167_28 ),
inference(avatar_contradiction_clause,[],[f2885]) ).
cnf(s16,plain,
spl167_14,
inference(sat_conversion,[],[f2668]) ).
cnf(s19,plain,
spl167_17,
inference(sat_conversion,[],[f2683]) ).
cnf(s31,plain,
~ spl167_28,
inference(sat_conversion,[],[f2738]) ).
cnf(s49,plain,
( ~ spl167_14
| ~ spl167_17
| spl167_28 ),
inference(sat_conversion,[],[f2886]) ).
cnf(s51,plain,
~ spl167_14,
inference(rat,[],[s49,s31,s19]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s16,s51]) ).
thf(f2887,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP093^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:52:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.21/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.41 % (2576916)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.52/0.41 % (2576928)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3299101155:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.52/0.41 % (2576931)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.52/0.41 % (2576931)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.52/0.41 % (2576924)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2359377199:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.52/0.41 % (2576928)Instruction limit reached!
% 0.52/0.41 % (2576928)------------------------------
% 0.52/0.41 % (2576928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.41 % (2576929)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3925140706:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.52/0.41 % (2576928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.41 % (2576928)CaDiCaL version: 2.1.3
% 0.52/0.41 % (2576928)Termination reason: Instruction limit
% 0.52/0.41 % (2576928)Termination phase: Property scanning
% 0.52/0.41 % (2576928)Time elapsed: 0.007 s
% 0.52/0.41 % (2576928)Peak memory usage: 11 MB
% 0.52/0.41 % (2576928)Instructions burned: 28 (million)
% 0.52/0.41 % (2576926)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1231488139:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.52/0.41 % (2576927)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4042820432:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.52/0.41 % (2576931)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3628504164:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.52/0.41 % (2576925)lrs+10_16_si=on:nwc=1.5:random_seed=384794634:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.52/0.41 % (2576926)Instruction limit reached!
% 0.52/0.41 % (2576926)------------------------------
% 0.52/0.41 % (2576926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.41 % (2576926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.41 % (2576926)CaDiCaL version: 2.1.3
% 0.52/0.41 % (2576926)Termination reason: Instruction limit
% 0.52/0.41 % (2576926)Termination phase: shuffling
% 0.52/0.41 % (2576926)Time elapsed: 0.004 s
% 0.52/0.41 % (2576926)Peak memory usage: 10 MB
% 0.52/0.41 % (2576926)Instructions burned: 8 (million)
% 0.52/0.41 % (2576941)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3300440645:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.52/0.41 % (2576925)Instruction limit reached!
% 0.52/0.41 % (2576925)------------------------------
% 0.52/0.41 % (2576925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.41 % (2576925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.41 % (2576941)Instruction limit reached!
% 0.52/0.41 % (2576941)------------------------------
% 0.52/0.41 % (2576941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.41 % (2576941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.41 % (2576925)CaDiCaL version: 2.1.3
% 0.52/0.41 % (2576925)Termination reason: Instruction limit
% 0.52/0.41 % (2576925)Termination phase: shuffling
% 0.52/0.41 % (2576925)Time elapsed: 0.011 s
% 0.52/0.41 % (2576941)CaDiCaL version: 2.1.3
% 0.52/0.41 % (2576941)Termination reason: Instruction limit
% 0.52/0.41 % (2576941)Termination phase: shuffling
% 0.52/0.41 % (2576941)Time elapsed: 0.001 s
% 0.52/0.41 % (2576925)Peak memory usage: 10 MB
% 0.52/0.41 % (2576941)Peak memory usage: 10 MB
% 0.52/0.41 % (2576941)Instructions burned: 3 (million)
% 0.52/0.41 % (2576925)Instructions burned: 20 (million)
% 0.52/0.41 % (2576948)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.42 % (2576948)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=882053029:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.52/0.42 % (2576944)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=83958314:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.52/0.42 % (2576948)Instruction limit reached!
% 0.52/0.42 % (2576948)------------------------------
% 0.52/0.42 % (2576948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576948)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576948)Termination reason: Instruction limit
% 0.52/0.42 % (2576948)Termination phase: shuffling
% 0.52/0.42 % (2576948)Time elapsed: 0.004 s
% 0.52/0.42 % (2576948)Peak memory usage: 10 MB
% 0.52/0.42 % (2576948)Instructions burned: 15 (million)
% 0.52/0.42 % (2576944)Instruction limit reached!
% 0.52/0.42 % (2576944)------------------------------
% 0.52/0.42 % (2576944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576944)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576944)Termination reason: Instruction limit
% 0.52/0.42 % (2576944)Termination phase: shuffling
% 0.52/0.42 % (2576944)Time elapsed: 0.004 s
% 0.52/0.42 % (2576944)Peak memory usage: 10 MB
% 0.52/0.42 % (2576944)Instructions burned: 6 (million)
% 0.52/0.42 % (2576929)Instruction limit reached!
% 0.52/0.42 % (2576929)------------------------------
% 0.52/0.42 % (2576929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576929)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576929)Termination reason: Instruction limit
% 0.52/0.42 % (2576929)Termination phase: Property scanning
% 0.52/0.42 % (2576929)Time elapsed: 0.037 s
% 0.52/0.42 % (2576929)Peak memory usage: 12 MB
% 0.52/0.42 % (2576929)Instructions burned: 77 (million)
% 0.52/0.42 % (2576950)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2732104150:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.52/0.42 % (2576924)Instruction limit reached!
% 0.52/0.42 % (2576924)------------------------------
% 0.52/0.42 % (2576924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576924)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576924)Termination reason: Instruction limit
% 0.52/0.42 % (2576924)Termination phase: Property scanning
% 0.52/0.42 % (2576924)Time elapsed: 0.041 s
% 0.52/0.42 % (2576924)Peak memory usage: 12 MB
% 0.52/0.42 % (2576924)Instructions burned: 88 (million)
% 0.52/0.42 % (2576964)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3710683502:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.52/0.42 % (2576950)Instruction limit reached!
% 0.52/0.42 % (2576950)------------------------------
% 0.52/0.42 % (2576950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576950)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576950)Termination reason: Instruction limit
% 0.52/0.42 % (2576950)Termination phase: shuffling
% 0.52/0.42 % (2576950)Time elapsed: 0.006 s
% 0.52/0.42 % (2576950)Peak memory usage: 10 MB
% 0.52/0.42 % (2576950)Instructions burned: 13 (million)
% 0.52/0.42 % (2576963)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.52/0.42 % (2576963)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.42 % (2576963)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=425430362:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.52/0.42 % (2576971)lrs+10_1_si=on:cs=on:random_seed=79366795:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.52/0.42 % (2576976)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.52/0.42 % (2576971)Instruction limit reached!
% 0.52/0.42 % (2576971)------------------------------
% 0.52/0.42 % (2576971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576971)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576971)Termination reason: Instruction limit
% 0.52/0.42 % (2576971)Termination phase: shuffling
% 0.52/0.42 % (2576971)Time elapsed: 0.004 s
% 0.52/0.42 % (2576971)Peak memory usage: 10 MB
% 0.52/0.42 % (2576971)Instructions burned: 8 (million)
% 0.52/0.42 % (2576976)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3070522063:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.52/0.42 % (2576964)Instruction limit reached!
% 0.52/0.42 % (2576964)------------------------------
% 0.52/0.42 % (2576964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576964)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576964)Termination reason: Instruction limit
% 0.52/0.42 % (2576964)Termination phase: Property scanning
% 0.52/0.42 % (2576964)Time elapsed: 0.020 s
% 0.52/0.42 % (2576964)Peak memory usage: 11 MB
% 0.52/0.42 % (2576964)Instructions burned: 88 (million)
% 0.52/0.42 % (2576976)Instruction limit reached!
% 0.52/0.42 % (2576976)------------------------------
% 0.52/0.42 % (2576976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576976)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576976)Termination reason: Instruction limit
% 0.52/0.42 % (2576976)Termination phase: shuffling
% 0.52/0.42 % (2576976)Time elapsed: 0.002 s
% 0.52/0.42 % (2576976)Peak memory usage: 10 MB
% 0.52/0.42 % (2576976)Instructions burned: 3 (million)
% 0.52/0.42 % (2576979)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3697165622:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.52/0.42 % (2576963)Instruction limit reached!
% 0.52/0.42 % (2576963)------------------------------
% 0.52/0.42 % (2576963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576963)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576963)Termination reason: Instruction limit
% 0.52/0.42 % (2576963)Termination phase: shuffling
% 0.52/0.42 % (2576963)Time elapsed: 0.013 s
% 0.52/0.42 % (2576963)Peak memory usage: 10 MB
% 0.52/0.42 % (2576963)Instructions burned: 29 (million)
% 0.52/0.42 % (2576931)Instruction limit reached!
% 0.52/0.42 % (2576931)------------------------------
% 0.52/0.42 % (2576931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576931)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576931)Termination reason: Instruction limit
% 0.52/0.42 % (2576931)Termination phase: Saturation
% 0.52/0.42 % (2576931)Time elapsed: 0.070 s
% 0.52/0.42 % (2576931)Peak memory usage: 14 MB
% 0.52/0.42 % (2576931)Instructions burned: 158 (million)
% 0.52/0.42 % (2576994)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2543067399:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.52/0.42 % (2576994)Instruction limit reached!
% 0.52/0.42 % (2576994)------------------------------
% 0.52/0.42 % (2576994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576994)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576994)Termination reason: Instruction limit
% 0.52/0.42 % (2576994)Termination phase: shuffling
% 0.52/0.42 % (2576994)Time elapsed: 0.006 s
% 0.52/0.42 % (2576994)Peak memory usage: 10 MB
% 0.52/0.42 % (2576994)Instructions burned: 25 (million)
% 0.52/0.42 % (2576993)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1043699055:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.52/0.42 % (2576979)Instruction limit reached!
% 0.52/0.42 % (2576979)------------------------------
% 0.52/0.42 % (2576979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.42 % (2576979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.42 % (2576979)CaDiCaL version: 2.1.3
% 0.52/0.42 % (2576979)Termination reason: Instruction limit
% 0.52/0.42 % (2576979)Termination phase: Property scanning
% 0.52/0.42 % (2576979)Time elapsed: 0.017 s
% 0.52/0.42 % (2576979)Peak memory usage: 11 MB
% 0.52/0.42 % (2576979)Instructions burned: 38 (million)
% 0.52/0.42 % (2576996)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2654725667:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.52/0.42 % (2576999)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2017744257:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.52/0.42 % (2576927) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2576916-2576927"...
% 0.52/0.42 % (2577005)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2505108980:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.52/0.43 % (2577000)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2005333005:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.52/0.43 % (2577005)Instruction limit reached!
% 0.52/0.43 % (2577005)------------------------------
% 0.52/0.43 % (2577005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.43 % (2577005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.43 % (2577005)CaDiCaL version: 2.1.3
% 0.52/0.43 % (2577005)Termination reason: Instruction limit
% 0.52/0.43 % (2577005)Termination phase: shuffling
% 0.52/0.43 % (2577005)Time elapsed: 0.001 s
% 0.52/0.43 % (2577005)Peak memory usage: 10 MB
% 0.52/0.43 % (2577005)Instructions burned: 3 (million)
% 0.52/0.43 % (2576996)Instruction limit reached!
% 0.52/0.43 % (2576996)------------------------------
% 0.52/0.43 % (2576996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.43 % (2576996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.43 % (2576996)CaDiCaL version: 2.1.3
% 0.52/0.43 % (2576996)Termination reason: Instruction limit
% 0.52/0.43 % (2576996)Termination phase: shuffling
% 0.52/0.43 % (2576996)Time elapsed: 0.008 s
% 0.52/0.43 % (2576996)Peak memory usage: 11 MB
% 0.52/0.43 % (2576996)Instructions burned: 15 (million)
% 0.52/0.43 % (2576927)...printing done.
% 0.52/0.43 % (2576927)Refutation found. Thanks to Tanya!
% 0.52/0.43 % SZS status Theorem for theBenchmark
% 0.52/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.52/0.43 % (2576927)------------------------------
% 0.52/0.43 % (2576927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.43 % (2576927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.43 % (2576927)CaDiCaL version: 2.1.3
% 0.52/0.43 % (2576927)Termination reason: Refutation
% 0.52/0.43 % (2576927)Time elapsed: 0.091 s
% 0.52/0.43 % (2576927)Peak memory usage: 15 MB
% 0.52/0.43 % (2576927)Instructions burned: 189 (million)
% 0.52/0.43 % (2576916)Success in time 0.136 s
% 0.52/0.43 % Vampire exiting
%------------------------------------------------------------------------------