%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP154^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:35 AM UTC 2026
% Result : Theorem 0.57s 0.39s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 49 ( 10 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 131 ( 10 ~; 7 |; 1 &; 112 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 25 ( 24 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 225 ( 222 usr; 15 con; 0-4 aty)
% Number of variables : 4 ( 0 sgn 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1295299783od_a_a: $tType ).
thf(type_def_6,type,
produc1990712039od_a_a: $tType ).
thf(type_def_7,type,
produc398359056_set_a: $tType ).
thf(type_def_8,type,
produc1299534078_set_a: $tType ).
thf(type_def_9,type,
set_Pr1948701895od_a_a: $tType ).
thf(type_def_10,type,
produc304417648_set_a: $tType ).
thf(type_def_11,type,
produc270245360od_a_a: $tType ).
thf(type_def_12,type,
produc386552094_set_a: $tType ).
thf(type_def_13,type,
produc1472671646_set_a: $tType ).
thf(type_def_14,type,
produc1572603623od_a_a: $tType ).
thf(type_def_15,type,
produc376942416od_a_a: $tType ).
thf(type_def_16,type,
produc275558334_set_a: $tType ).
thf(type_def_17,type,
produc407913767_set_a: $tType ).
thf(type_def_18,type,
set_Pr2045688071_set_a: $tType ).
thf(type_def_19,type,
produc1083127431_set_a: $tType ).
thf(type_def_20,type,
produc522143687_set_a: $tType ).
thf(type_def_21,type,
set_se1596668135od_a_a: $tType ).
thf(type_def_22,type,
produc1691597095_set_a: $tType ).
thf(type_def_23,type,
set_Product_prod_a_a: $tType ).
thf(type_def_24,type,
set_set_set_a: $tType ).
thf(type_def_25,type,
product_prod_a_a: $tType ).
thf(type_def_26,type,
set_set_a: $tType ).
thf(type_def_27,type,
set_a: $tType ).
thf(type_def_28,type,
a: $tType ).
thf(type_def_29,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
bNF_Ca850758276_set_a: set_Product_prod_a_a > ( a > set_a ) > $o ).
thf(func_def_1,type,
finite283787856_set_a: set_Pr2045688071_set_a > $o ).
thf(func_def_2,type,
finite179568208od_a_a: set_Product_prod_a_a > $o ).
thf(func_def_3,type,
finite1145471536od_a_a: set_se1596668135od_a_a > $o ).
thf(func_def_4,type,
finite1606323175_set_a: set_set_set_a > $o ).
thf(func_def_5,type,
finite_finite_set_a: set_set_a > $o ).
thf(func_def_6,type,
finite_finite_a: set_a > $o ).
thf(func_def_7,type,
inf_in920712437od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(func_def_8,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(func_def_9,type,
sup_su615935707od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(func_def_10,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(func_def_11,type,
lattic1600076923_set_a: set_set_a > set_a ).
thf(func_def_12,type,
lattic501550101_set_a: set_set_a > set_a ).
thf(func_def_13,type,
order_491428350od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(func_def_14,type,
order_359341630od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(func_def_15,type,
order_816746613_set_a: set_set_a > set_Pr2045688071_set_a > $o ).
thf(func_def_16,type,
order_preorder_on_a: set_a > set_Product_prod_a_a > $o ).
thf(func_def_17,type,
order_under_a: set_Product_prod_a_a > a > set_a ).
thf(func_def_18,type,
bot_bo1293121322_a_a_o: product_prod_a_a > $o ).
thf(func_def_19,type,
bot_bot_a_o: a > $o ).
thf(func_def_20,type,
bot_bo1519632275_set_a: produc1691597095_set_a ).
thf(func_def_21,type,
bot_bo1116205875od_a_a: set_Pr1948701895od_a_a ).
thf(func_def_22,type,
bot_bo671027059_set_a: set_Pr2045688071_set_a ).
thf(func_def_23,type,
bot_bo2131659635od_a_a: set_Product_prod_a_a ).
thf(func_def_24,type,
bot_bo1424703315od_a_a: set_se1596668135od_a_a ).
thf(func_def_25,type,
bot_bo1264989578_set_a: set_set_set_a ).
thf(func_def_26,type,
bot_bot_set_set_a: set_set_a ).
thf(func_def_27,type,
bot_bot_set_a: set_a ).
thf(func_def_28,type,
ord_le2039441566_set_a: produc1299534078_set_a > produc1299534078_set_a > $o ).
thf(func_def_29,type,
ord_le1729087294_set_a: produc1472671646_set_a > produc1472671646_set_a > $o ).
thf(func_def_30,type,
ord_le642967742_set_a: produc386552094_set_a > produc386552094_set_a > $o ).
thf(func_def_31,type,
ord_le2095302494_set_a: produc275558334_set_a > produc275558334_set_a > $o ).
thf(func_def_32,type,
ord_le1138266544_set_a: produc398359056_set_a > produc398359056_set_a > $o ).
thf(func_def_33,type,
ord_le526661008od_a_a: produc270245360od_a_a > produc270245360od_a_a > $o ).
thf(func_def_34,type,
ord_le723713223_set_a: produc407913767_set_a > produc407913767_set_a > $o ).
thf(func_def_35,type,
ord_le1201700711_set_a: produc522143687_set_a > produc522143687_set_a > $o ).
thf(func_def_36,type,
ord_le560833296_set_a: produc304417648_set_a > produc304417648_set_a > $o ).
thf(func_def_37,type,
ord_le49202928od_a_a: produc376942416od_a_a > produc376942416od_a_a > $o ).
thf(func_def_38,type,
ord_le1762684455_set_a: produc1083127431_set_a > produc1083127431_set_a > $o ).
thf(func_def_39,type,
ord_le486764743_set_a: produc1691597095_set_a > produc1691597095_set_a > $o ).
thf(func_def_40,type,
ord_le456379495od_a_a: set_Pr1948701895od_a_a > set_Pr1948701895od_a_a > $o ).
thf(func_def_41,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_42,type,
ord_le318720350_set_a: set_set_a > set_set_a > $o ).
thf(func_def_43,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_44,type,
order_Greatest_set_a: ( set_a > $o ) > set_a ).
thf(func_def_45,type,
prefer1867335523od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > set_Pr1948701895od_a_a ).
thf(func_def_46,type,
prefer74720675od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(func_def_47,type,
prefer270414042_set_a: set_a > set_set_a > set_Pr2045688071_set_a > set_set_a ).
thf(func_def_48,type,
prefer436369274d_as_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(func_def_49,type,
prefer55414563od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > set_Pr1948701895od_a_a ).
thf(func_def_50,type,
prefer477097315od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(func_def_51,type,
prefer1203288218_set_a: set_a > set_set_a > set_Pr2045688071_set_a > set_set_a ).
thf(func_def_52,type,
prefer161218362good_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(func_def_53,type,
prefer926864306od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > set_Pr1948701895od_a_a ).
thf(func_def_54,type,
prefer1498087410od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(func_def_55,type,
prefer1671525929_set_a: set_a > set_set_a > set_Pr2045688071_set_a > set_set_a ).
thf(func_def_56,type,
prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(func_def_57,type,
prefer1409946857od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(func_def_58,type,
prefer1338892073od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(func_def_59,type,
prefer1710114912_set_a: set_set_a > set_Pr2045688071_set_a > $o ).
thf(func_def_60,type,
prefer1292084992ence_a: set_a > set_Product_prod_a_a > $o ).
thf(func_def_61,type,
prefer1828051771od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(func_def_62,type,
prefer697821563od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(func_def_63,type,
prefer484977842_set_a: set_set_a > set_Pr2045688071_set_a > $o ).
thf(func_def_64,type,
prefer719835986ence_a: set_a > set_Product_prod_a_a > $o ).
thf(func_def_65,type,
prefer580340847ioms_a: set_a > set_Product_prod_a_a > $o ).
thf(func_def_66,type,
produc1935643479od_a_a: produc1572603623od_a_a > produc1572603623od_a_a > produc1990712039od_a_a ).
thf(func_def_67,type,
produc759028718_set_a: produc1691597095_set_a > set_set_a > produc1299534078_set_a ).
thf(func_def_68,type,
produc1719072398_set_a: produc1691597095_set_a > set_a > produc1472671646_set_a ).
thf(func_def_69,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(func_def_70,type,
produc1599887374_set_a: set_Product_prod_a_a > set_set_a > produc386552094_set_a ).
thf(func_def_71,type,
produc194376366_set_a: set_Product_prod_a_a > set_a > produc275558334_set_a ).
thf(func_def_72,type,
produc760262016_set_a: set_set_a > produc1691597095_set_a > produc398359056_set_a ).
thf(func_def_73,type,
produc1618062688od_a_a: set_set_a > set_Product_prod_a_a > produc270245360od_a_a ).
thf(func_def_74,type,
produc2102896407_set_a: set_set_a > set_set_a > produc407913767_set_a ).
thf(func_def_75,type,
produc32105911_set_a: set_set_a > set_a > produc522143687_set_a ).
thf(func_def_76,type,
produc272677600_set_a: set_a > produc1691597095_set_a > produc304417648_set_a ).
thf(func_def_77,type,
produc1397177024od_a_a: set_a > set_Product_prod_a_a > produc376942416od_a_a ).
thf(func_def_78,type,
produc1560024183_set_a: set_a > set_set_a > produc1083127431_set_a ).
thf(func_def_79,type,
produc1928581911_set_a: set_a > set_a > produc1691597095_set_a ).
thf(func_def_80,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(func_def_81,type,
id_on_1182990020od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a ).
thf(func_def_82,type,
id_on_a: set_a > set_Product_prod_a_a ).
thf(func_def_83,type,
refl_o1298442278od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(func_def_84,type,
refl_on_a: set_a > set_Product_prod_a_a > $o ).
thf(func_def_85,type,
total_1490170027od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(func_def_86,type,
total_on_a: set_a > set_Product_prod_a_a > $o ).
thf(func_def_87,type,
trans_a: set_Product_prod_a_a > $o ).
thf(func_def_88,type,
collec1635618130od_a_a: ( produc1572603623od_a_a > $o ) > set_Pr1948701895od_a_a ).
thf(func_def_89,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(func_def_90,type,
collect_set_a: ( set_a > $o ) > set_set_a ).
thf(func_def_91,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_92,type,
is_empty_a: set_a > $o ).
thf(func_def_93,type,
member1899387664od_a_a: produc1990712039od_a_a > set_Pr1295299783od_a_a > $o ).
thf(func_def_94,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(func_def_95,type,
member593450832_set_a: produc1691597095_set_a > set_Pr2045688071_set_a > $o ).
thf(func_def_96,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_97,type,
member1838126896od_a_a: set_Product_prod_a_a > set_se1596668135od_a_a > $o ).
thf(func_def_98,type,
member_set_set_a: set_set_a > set_set_set_a > $o ).
thf(func_def_99,type,
member_set_a: set_a > set_set_a > $o ).
thf(func_def_100,type,
member_a: a > set_a > $o ).
thf(func_def_101,type,
carrier: set_a ).
thf(func_def_102,type,
relation: set_Product_prod_a_a ).
thf(func_def_103,type,
x: a ).
thf(func_def_104,type,
y: a ).
thf(func_def_106,type,
vAND: $o > $o > $o ).
thf(func_def_107,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_108,type,
vIMP: $o > $o > $o ).
thf(func_def_109,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_110,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_111,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_112,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_113,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_116,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_117,type,
vNOT: $o > $o ).
thf(func_def_118,type,
vOR: $o > $o > $o ).
thf(func_def_119,type,
sK0: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_120,type,
sK1: ( set_a > set_a ) > set_a ).
thf(func_def_121,type,
sK2: ( set_a > set_a ) > set_a ).
thf(func_def_122,type,
sK3: set_Product_prod_a_a > set_a > a ).
thf(func_def_123,type,
sK4: set_Product_prod_a_a > set_a > a ).
thf(func_def_124,type,
sK5: set_Product_prod_a_a > set_a > a ).
thf(func_def_125,type,
sK6: set_Product_prod_a_a > set_a > a ).
thf(func_def_126,type,
sK7: set_a > product_prod_a_a > a ).
thf(func_def_127,type,
sK8: set_Pr2045688071_set_a > set_set_a > set_a ).
thf(func_def_128,type,
sK9: set_Pr2045688071_set_a > set_set_a > set_a ).
thf(func_def_129,type,
sK10: set_Pr2045688071_set_a > set_set_a > set_a ).
thf(func_def_130,type,
sK11: set_Pr2045688071_set_a > set_set_a > set_a ).
thf(func_def_131,type,
sK12: set_Product_prod_a_a > a ).
thf(func_def_132,type,
sK13: set_Product_prod_a_a > a ).
thf(func_def_133,type,
sK14: set_Product_prod_a_a > a ).
thf(func_def_134,type,
sK15: set_Pr1948701895od_a_a > produc1572603623od_a_a ).
thf(func_def_135,type,
sK16: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_136,type,
sK17: ( product_prod_a_a > $o ) > set_Product_prod_a_a > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_137,type,
sK18: set_Pr2045688071_set_a > produc1691597095_set_a ).
thf(func_def_138,type,
sK19: set_a > a ).
thf(func_def_139,type,
sK20: ( a > $o ) > a ).
thf(func_def_140,type,
sK21: ( product_prod_a_a > $o ) > a ).
thf(func_def_141,type,
sK22: ( product_prod_a_a > $o ) > a ).
thf(func_def_142,type,
sK23: set_set_a > set_a ).
thf(func_def_143,type,
sK24: ( set_a > $o ) > set_a ).
thf(func_def_144,type,
sK25: set_set_set_a > set_set_a ).
thf(func_def_145,type,
sK26: ( a > $o ) > a ).
thf(func_def_146,type,
sK27: set_Pr2045688071_set_a > produc1691597095_set_a ).
thf(func_def_147,type,
sK28: set_a > set_set_a > set_a ).
thf(func_def_148,type,
sK29: ( set_a > $o ) > ( set_a > $o ) > set_a ).
thf(func_def_149,type,
sK30: set_a > ( set_a > $o ) > set_a ).
thf(func_def_150,type,
sK31: set_set_a > set_a ).
thf(func_def_151,type,
sK32: ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_152,type,
sK33: set_a > ( a > $o ) > ( a > $o ) > a ).
thf(func_def_153,type,
sK34: set_se1596668135od_a_a > set_Product_prod_a_a ).
thf(func_def_154,type,
sK35: set_a > a ).
thf(func_def_155,type,
sK36: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_156,type,
sK37: set_se1596668135od_a_a > set_Product_prod_a_a ).
thf(func_def_157,type,
sK38: set_a > ( a > a > $o ) > a ).
thf(func_def_158,type,
sK39: ( a > a > $o ) > a ).
thf(func_def_159,type,
sK40: ( a > a > $o ) > a ).
thf(func_def_160,type,
sK41: ( a > a > $o ) > a ).
thf(func_def_161,type,
sK42: ( a > a > $o ) > a ).
thf(func_def_162,type,
sK43: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_163,type,
sK44: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_164,type,
sK45: ( product_prod_a_a > $o ) > a ).
thf(func_def_165,type,
sK46: ( product_prod_a_a > $o ) > a ).
thf(func_def_166,type,
sK47: set_set_a > set_set_a > set_a ).
thf(func_def_167,type,
sK48: set_Pr1948701895od_a_a > produc1572603623od_a_a ).
thf(func_def_168,type,
sK49: set_set_a > set_a ).
thf(func_def_169,type,
sK50: set_a > a ).
thf(func_def_170,type,
sK51: ( set_a > $o ) > ( set_a > $o ) > set_a ).
thf(func_def_171,type,
sK52: set_Pr1948701895od_a_a > set_Pr1948701895od_a_a > produc1572603623od_a_a ).
thf(func_def_172,type,
sK53: ( set_a > $o ) > set_a ).
thf(func_def_173,type,
sK54: ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_174,type,
sK55: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > produc1572603623od_a_a ).
thf(func_def_175,type,
sK56: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > produc1572603623od_a_a ).
thf(func_def_176,type,
sK57: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > produc1572603623od_a_a ).
thf(func_def_177,type,
sK58: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > produc1572603623od_a_a ).
thf(func_def_178,type,
sK59: set_Pr1948701895od_a_a > produc1572603623od_a_a ).
thf(func_def_179,type,
sK60: ( product_prod_a_a > product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_180,type,
sK61: ( product_prod_a_a > product_prod_a_a > $o ) > set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_181,type,
sK62: ( product_prod_a_a > product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_182,type,
sK63: ( product_prod_a_a > product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_183,type,
sK64: ( product_prod_a_a > product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_184,type,
sK65: set_set_a > set_a > set_a ).
thf(func_def_185,type,
sK66: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_186,type,
sK67: set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_187,type,
sK68: set_a > set_set_a > set_a ).
thf(func_def_188,type,
sK69: set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_189,type,
sK70: set_a > set_a > a ).
thf(func_def_190,type,
sK71: set_set_a > set_a > set_a ).
thf(func_def_191,type,
sK72: set_Product_prod_a_a > produc1572603623od_a_a > product_prod_a_a ).
thf(func_def_192,type,
sK73: set_set_a > set_a ).
thf(func_def_193,type,
sK74: set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_194,type,
sK75: set_Product_prod_a_a > set_Pr1948701895od_a_a > product_prod_a_a ).
thf(func_def_195,type,
sK76: set_Product_prod_a_a > set_Pr1948701895od_a_a > product_prod_a_a ).
thf(func_def_196,type,
sK77: set_set_set_a > set_set_a ).
thf(func_def_197,type,
sK78: set_set_a > set_a > set_a ).
thf(func_def_198,type,
sK79: set_a > ( set_a > $o ) > set_a ).
thf(func_def_199,type,
sK80: ( set_a > set_a ) > set_a ).
thf(func_def_200,type,
sK81: ( set_a > set_a ) > set_a ).
thf(func_def_201,type,
sK82: ( set_a > set_a ) > set_a ).
thf(func_def_202,type,
sK83: ( set_a > set_a ) > set_a ).
thf(func_def_203,type,
sK84: product_prod_a_a > a ).
thf(func_def_204,type,
sK85: product_prod_a_a > a ).
thf(func_def_205,type,
sK86: set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_206,type,
sK87: set_Product_prod_a_a > set_Pr1948701895od_a_a > product_prod_a_a ).
thf(func_def_207,type,
sK88: set_Product_prod_a_a > set_Pr1948701895od_a_a > product_prod_a_a ).
thf(func_def_208,type,
sK89: set_Product_prod_a_a > set_Pr1948701895od_a_a > product_prod_a_a ).
thf(func_def_209,type,
sK90: set_Product_prod_a_a > set_Pr1948701895od_a_a > product_prod_a_a ).
thf(func_def_210,type,
sK91: set_set_a > set_a ).
thf(func_def_211,type,
sK92: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_212,type,
sK93: ( set_a > $o ) > ( set_a > $o ) > set_a ).
thf(func_def_213,type,
sK94: ( set_a > set_a ) > set_a ).
thf(func_def_214,type,
sK95: ( set_a > set_a ) > set_a ).
thf(func_def_215,type,
sK96: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(func_def_216,type,
sK97: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(func_def_217,type,
sK98: set_a > set_Product_prod_a_a > a ).
thf(func_def_218,type,
sK99: set_a > set_Product_prod_a_a > a ).
thf(func_def_219,type,
sK100: set_a > set_set_a > set_a ).
thf(func_def_220,type,
sK101: product_prod_a_a > a ).
thf(func_def_221,type,
sK102: product_prod_a_a > a ).
thf(func_def_222,type,
sK103: set_a > a ).
thf(f196,axiom,
! [X0: set_a] : ( ord_less_eq_set_a @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_subset__refl) ).
thf(f355,conjecture,
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f356,negated_conjecture,
~ ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f641,plain,
~ ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
inference(rectify,[],[f356]) ).
thf(f642,plain,
~ ( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
= $true ) ),
inference(fool_elimination,[],[f641]) ).
thf(f649,plain,
! [X0: set_a] : ( ord_less_eq_set_a @ X0 @ X0 ),
inference(rectify,[],[f196]) ).
thf(f650,plain,
! [X0: set_a] :
( ( ord_less_eq_set_a @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f649]) ).
thf(f1476,plain,
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
!= $true )
& ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
!= $true ) ),
inference(ennf_transformation,[],[f642]) ).
thf(f1936,plain,
! [X0: set_a] :
( ( ord_less_eq_set_a @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f650]) ).
thf(f2222,plain,
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
!= $true ),
inference(cnf_transformation,[],[f1476]) ).
thf(f2543,definition,
( spl104_12
<=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl104_12])],[avatar_definition]) ).
thf(f2545,plain,
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
!= $true )
| spl104_12 ),
inference(avatar_component_clause,[],[f2543]) ).
thf(f2546,plain,
~ spl104_12,
inference(avatar_split_clause,[],[f2222,f2543]) ).
thf(f2710,plain,
( ( $true != $true )
| spl104_12 ),
inference(superposition,[],[f2545,f1936]) ).
thf(f2711,plain,
( $false
| spl104_12 ),
inference(trivial_inequality_removal,[],[f2710]) ).
thf(f2712,plain,
spl104_12,
inference(avatar_contradiction_clause,[],[f2711]) ).
cnf(s14,plain,
~ spl104_12,
inference(sat_conversion,[],[f2546]) ).
cnf(s55,plain,
spl104_12,
inference(sat_conversion,[],[f2712]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s14,s55]) ).
thf(f2713,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP154^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:02:15 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.22/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.39 % (3142523)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.39 % (3142540)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=1113974900: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)
% 0.22/0.39 % (3142543)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.39 % (3142543)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
% 0.22/0.39 % (3142537)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3804078386:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.39 % (3142538)lrs+10_16_si=on:nwc=1.5:random_seed=1017730706:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.39 % (3142539)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=587556855:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.39 % (3142541)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3582157265:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.39 % (3142542)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=590413605:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.39 % (3142543)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=4226794885:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.39 % (3142539)Instruction limit reached!
% 0.22/0.39 % (3142539)------------------------------
% 0.22/0.39 % (3142539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (3142539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (3142539)CaDiCaL version: 2.1.3
% 0.22/0.39 % (3142539)Termination reason: Instruction limit
% 0.22/0.39 % (3142539)Termination phase: shuffling
% 0.22/0.39 % (3142539)Time elapsed: 0.003 s
% 0.22/0.39 % (3142539)Peak memory usage: 10 MB
% 0.22/0.39 % (3142539)Instructions burned: 4 (million)
% 0.22/0.39 % (3142538)Instruction limit reached!
% 0.22/0.39 % (3142538)------------------------------
% 0.22/0.39 % (3142538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (3142538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (3142538)CaDiCaL version: 2.1.3
% 0.22/0.39 % (3142538)Termination reason: Instruction limit
% 0.22/0.39 % (3142538)Termination phase: shuffling
% 0.22/0.39 % (3142538)Time elapsed: 0.009 s
% 0.22/0.39 % (3142538)Peak memory usage: 10 MB
% 0.22/0.39 % (3142538)Instructions burned: 19 (million)
% 0.22/0.39 % (3142541)Instruction limit reached!
% 0.22/0.39 % (3142541)------------------------------
% 0.22/0.39 % (3142541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (3142541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (3142541)CaDiCaL version: 2.1.3
% 0.57/0.39 % (3142541)Termination reason: Instruction limit
% 0.57/0.39 % (3142541)Termination phase: shuffling
% 0.57/0.39 % (3142541)Time elapsed: 0.013 s
% 0.57/0.39 % (3142541)Peak memory usage: 10 MB
% 0.57/0.39 % (3142541)Instructions burned: 30 (million)
% 0.57/0.39 % (3142551)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2106869949:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.57/0.39 % (3142551)Instruction limit reached!
% 0.57/0.39 % (3142551)------------------------------
% 0.57/0.39 % (3142551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.39 % (3142551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.39 % (3142551)CaDiCaL version: 2.1.3
% 0.57/0.39 % (3142551)Termination reason: Instruction limit
% 0.57/0.39 % (3142551)Termination phase: shuffling
% 0.57/0.39 % (3142551)Time elapsed: 0.004 s
% 0.57/0.39 % (3142551)Peak memory usage: 10 MB
% 0.57/0.39 % (3142551)Instructions burned: 7 (million)
% 0.57/0.39 % (3142552)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=327433514:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.57/0.39 % (3142552)Instruction limit reached!
% 0.57/0.39 % (3142552)------------------------------
% 0.57/0.39 % (3142552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.39 % (3142552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.39 % (3142552)CaDiCaL version: 2.1.3
% 0.57/0.39 % (3142552)Termination reason: Instruction limit
% 0.57/0.39 % (3142552)Termination phase: shuffling
% 0.57/0.39 % (3142552)Time elapsed: 0.003 s
% 0.57/0.39 % (3142552)Peak memory usage: 10 MB
% 0.57/0.39 % (3142552)Instructions burned: 5 (million)
% 0.57/0.39 % (3142553)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.57/0.39 % (3142542)Instruction limit reached!
% 0.57/0.39 % (3142542)------------------------------
% 0.57/0.39 % (3142542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.39 % (3142542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.39 % (3142542)CaDiCaL version: 2.1.3
% 0.57/0.39 % (3142542)Termination reason: Instruction limit
% 0.57/0.39 % (3142542)Termination phase: Clausification
% 0.57/0.39 % (3142542)Time elapsed: 0.035 s
% 0.57/0.39 % (3142542)Peak memory usage: 12 MB
% 0.57/0.39 % (3142542)Instructions burned: 76 (million)
% 0.57/0.39 % (3142540) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3142523-3142540"...
% 0.57/0.39 % (3142553)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4131039383:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.57/0.39 % (3142537)Instruction limit reached!
% 0.57/0.39 % (3142537)------------------------------
% 0.57/0.39 % (3142537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.39 % (3142537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.39 % (3142537)CaDiCaL version: 2.1.3
% 0.57/0.39 % (3142537)Termination reason: Instruction limit
% 0.57/0.39 % (3142537)Termination phase: Property scanning
% 0.57/0.39 % (3142537)Time elapsed: 0.039 s
% 0.57/0.39 % (3142537)Peak memory usage: 12 MB
% 0.57/0.39 % (3142537)Instructions burned: 87 (million)
% 0.57/0.39 % (3142540)...printing done.
% 0.57/0.39 % (3142540)Refutation found. Thanks to Tanya!
% 0.57/0.39 % SZS status Theorem for theBenchmark
% 0.57/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.57/0.39 % (3142540)------------------------------
% 0.57/0.39 % (3142540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.39 % (3142540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.39 % (3142540)CaDiCaL version: 2.1.3
% 0.57/0.39 % (3142540)Termination reason: Refutation
% 0.57/0.39 % (3142540)Time elapsed: 0.045 s
% 0.57/0.39 % (3142540)Peak memory usage: 15 MB
% 0.57/0.39 % (3142540)Instructions burned: 181 (million)
% 0.57/0.39 % (3142523)Success in time 0.091 s
% 0.57/0.39 % Vampire exiting
%------------------------------------------------------------------------------