TSTP Solution File: ITP176^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP176^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:54:58 EDT 2024
% Result : Theorem 0.16s 0.41s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 283
% Syntax : Number of formulae : 291 ( 10 unt; 281 typ; 0 def)
% Number of atoms : 174 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 17 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &; 0 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 30 ( 29 usr)
% Number of type conns : 464 ( 463 >; 1 *; 0 +; 0 <<)
% Number of symbols : 226 ( 224 usr; 12 con; 0-6 aty)
% Number of variables : 21 ( 6 ^ 0 !; 0 ?; 21 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr2109276827od_b_b: $tType ).
thf(type_def_6,type,
set_Product_prod_b_b: $tType ).
thf(type_def_7,type,
produc1213276845od_b_b: $tType ).
thf(type_def_8,type,
b: $tType ).
thf(type_def_9,type,
set_b: $tType ).
thf(type_def_10,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_11,type,
set_Pr2007082183od_b_b: $tType ).
thf(type_def_12,type,
product_prod_b_b: $tType ).
thf(type_def_13,type,
set_Pr1324126435od_b_b: $tType ).
thf(type_def_14,type,
standard_Constant_a: $tType ).
thf(type_def_15,type,
labele1159362096nt_a_b: $tType ).
thf(type_def_16,type,
labele1835558936od_b_b: $tType ).
thf(type_def_17,type,
set_Pr357419743_b_b_b: $tType ).
thf(type_def_18,type,
set_Pr1021918435od_b_b: $tType ).
thf(type_def_19,type,
set_St761939237tant_a: $tType ).
thf(type_def_20,type,
produc970027067od_b_b: $tType ).
thf(type_def_21,type,
produc1990339951od_b_b: $tType ).
thf(type_def_22,type,
produc276146823_b_b_b: $tType ).
thf(type_def_23,type,
produc1367125253tant_a: $tType ).
thf(type_def_24,type,
produc1052326083od_b_b: $tType ).
thf(type_def_25,type,
produc1168037607od_b_b: $tType ).
thf(type_def_26,type,
produc2112523263_b_b_b: $tType ).
thf(type_def_27,type,
produc1605346267od_b_b: $tType ).
thf(type_def_28,type,
produc255402447od_b_b: $tType ).
thf(type_def_29,type,
set_Pr2134561957od_b_b: $tType ).
thf(type_def_30,type,
set_Pr1906739389_b_b_b: $tType ).
thf(type_def_31,type,
set_Pr1071216121od_b_b: $tType ).
thf(type_def_32,type,
set_Pr2060523537od_b_b: $tType ).
thf(type_def_33,type,
set_Pr621705391od_b_b: $tType ).
thf(type_def_34,type,
set_Pr306736955tant_a: $tType ).
thf(func_def_0,type,
set_Pr2109276827od_b_b: $tType ).
thf(func_def_1,type,
produc970027067od_b_b: $tType ).
thf(func_def_2,type,
set_Pr1071216121od_b_b: $tType ).
thf(func_def_3,type,
set_Pr2134561957od_b_b: $tType ).
thf(func_def_4,type,
set_Pr1021918435od_b_b: $tType ).
thf(func_def_5,type,
produc1052326083od_b_b: $tType ).
thf(func_def_6,type,
produc1990339951od_b_b: $tType ).
thf(func_def_7,type,
set_Pr2060523537od_b_b: $tType ).
thf(func_def_8,type,
set_Pr1906739389_b_b_b: $tType ).
thf(func_def_9,type,
produc1605346267od_b_b: $tType ).
thf(func_def_10,type,
produc276146823_b_b_b: $tType ).
thf(func_def_11,type,
set_Pr306736955tant_a: $tType ).
thf(func_def_12,type,
set_Pr1324126435od_b_b: $tType ).
thf(func_def_13,type,
labele1835558936od_b_b: $tType ).
thf(func_def_14,type,
set_Pr2007082183od_b_b: $tType ).
thf(func_def_15,type,
produc1367125253tant_a: $tType ).
thf(func_def_16,type,
produc1213276845od_b_b: $tType ).
thf(func_def_17,type,
produc1168037607od_b_b: $tType ).
thf(func_def_18,type,
labele1159362096nt_a_b: $tType ).
thf(func_def_19,type,
set_Pr621705391od_b_b: $tType ).
thf(func_def_20,type,
set_Pr357419743_b_b_b: $tType ).
thf(func_def_21,type,
produc255402447od_b_b: $tType ).
thf(func_def_22,type,
produc2112523263_b_b_b: $tType ).
thf(func_def_23,type,
set_St761939237tant_a: $tType ).
thf(func_def_24,type,
set_Product_prod_b_b: $tType ).
thf(func_def_25,type,
standard_Constant_a: $tType ).
thf(func_def_26,type,
product_prod_b_b: $tType ).
thf(func_def_27,type,
set_b: $tType ).
thf(func_def_28,type,
b: $tType ).
thf(func_def_29,type,
equiv_1629197578_set_b: set_Pr2109276827od_b_b > set_Product_prod_b_b > ( produc1213276845od_b_b > b > set_b ) > $o ).
thf(func_def_30,type,
equiv_1036235914_set_b: set_Pr2007082183od_b_b > set_Product_prod_b_b > ( product_prod_b_b > b > set_b ) > $o ).
thf(func_def_31,type,
equiv_167626658_set_b: set_Product_prod_b_b > set_Product_prod_b_b > ( b > b > set_b ) > $o ).
thf(func_def_32,type,
equiv_1821124534_set_b: set_Product_prod_b_b > ( b > set_b ) > $o ).
thf(func_def_33,type,
equiv_2048442231od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).
thf(func_def_34,type,
equiv_1125628061od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).
thf(func_def_35,type,
equiv_equiv_b: set_b > set_Product_prod_b_b > $o ).
thf(func_def_36,type,
equiv_proj_b_b: set_Product_prod_b_b > b > set_b ).
thf(func_def_37,type,
hilber46179633od_b_b: ( produc1213276845od_b_b > $o ) > produc1213276845od_b_b ).
thf(func_def_38,type,
hilber620807523od_b_b: ( product_prod_b_b > $o ) > product_prod_b_b ).
thf(func_def_39,type,
hilbert_Eps_b: ( b > $o ) > b ).
thf(func_def_40,type,
if_b: $o > b > b > b ).
thf(func_def_41,type,
standard_S_Idt_a: standard_Constant_a ).
thf(func_def_42,type,
getRel904497637nt_a_b: standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b ).
thf(func_def_43,type,
graph_792023598_b_b_b: labele1835558936od_b_b > labele1159362096nt_a_b > set_Pr357419743_b_b_b > $o ).
thf(func_def_44,type,
graph_222606102_a_b_b: labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o ).
thf(func_def_45,type,
labele170595300od_b_b: set_Pr1021918435od_b_b > set_Product_prod_b_b > labele1835558936od_b_b ).
thf(func_def_46,type,
labele1230159100nt_a_b: set_Pr1324126435od_b_b > set_b > labele1159362096nt_a_b ).
thf(func_def_47,type,
labele377702064od_b_b: ( set_Pr1324126435od_b_b > set_b > set_Pr1324126435od_b_b ) > labele1159362096nt_a_b > set_Pr1324126435od_b_b ).
thf(func_def_48,type,
labele1287464530_set_b: ( set_Pr1324126435od_b_b > set_b > set_b ) > labele1159362096nt_a_b > set_b ).
thf(func_def_49,type,
labele1741081071nt_a_b: labele1159362096nt_a_b > set_Pr1324126435od_b_b ).
thf(func_def_50,type,
labele1424214014nt_a_b: labele1159362096nt_a_b > set_b ).
thf(func_def_51,type,
restri446606278nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b ).
thf(func_def_52,type,
order_609163036od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).
thf(func_def_53,type,
order_653178932r_on_b: set_b > set_Product_prod_b_b > $o ).
thf(func_def_54,type,
bot_bo1734638456_b_b_o: standard_Constant_a > product_prod_b_b > $o ).
thf(func_def_55,type,
bot_bo1167600078_b_b_o: produc1213276845od_b_b > $o ).
thf(func_def_56,type,
bot_bo1302443370_b_b_o: product_prod_b_b > $o ).
thf(func_def_57,type,
bot_bot_b_b_o: b > b > $o ).
thf(func_def_58,type,
bot_bot_b_o: b > $o ).
thf(func_def_59,type,
bot_bo1160111033tant_a: set_St761939237tant_a ).
thf(func_def_60,type,
bot_bo1964903287od_b_b: set_Pr1021918435od_b_b ).
thf(func_def_61,type,
bot_bo1664927607od_b_b: set_Pr1324126435od_b_b ).
thf(func_def_62,type,
bot_bo1174586163od_b_b: set_Pr2007082183od_b_b ).
thf(func_def_63,type,
bot_bo1124087115_b_b_b: set_Pr357419743_b_b_b ).
thf(func_def_64,type,
bot_bo1343651123od_b_b: set_Product_prod_b_b ).
thf(func_def_65,type,
bot_bot_set_b: set_b ).
thf(func_def_66,type,
ord_le123089219od_b_b: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o ).
thf(func_def_67,type,
ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).
thf(func_def_68,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(func_def_69,type,
produc1432590431od_b_b: standard_Constant_a > product_prod_b_b > produc1213276845od_b_b ).
thf(func_def_70,type,
produc449289715od_b_b: produc1213276845od_b_b > produc1213276845od_b_b > produc970027067od_b_b ).
thf(func_def_71,type,
produc1597690145od_b_b: produc1213276845od_b_b > product_prod_b_b > produc1990339951od_b_b ).
thf(func_def_72,type,
produc1580777273_b_b_b: produc1213276845od_b_b > b > produc276146823_b_b_b ).
thf(func_def_73,type,
produc1977323903tant_a: product_prod_b_b > standard_Constant_a > produc1367125253tant_a ).
thf(func_def_74,type,
produc732676669od_b_b: product_prod_b_b > produc1213276845od_b_b > produc1052326083od_b_b ).
thf(func_def_75,type,
produc546497367od_b_b: product_prod_b_b > product_prod_b_b > produc1168037607od_b_b ).
thf(func_def_76,type,
produc1001682799_b_b_b: product_prod_b_b > b > produc2112523263_b_b_b ).
thf(func_def_77,type,
produc800495189od_b_b: b > produc1213276845od_b_b > produc1605346267od_b_b ).
thf(func_def_78,type,
produc1257047359od_b_b: b > product_prod_b_b > produc255402447od_b_b ).
thf(func_def_79,type,
product_Pair_b_b: b > b > product_prod_b_b ).
thf(func_def_80,type,
image_1916422435od_b_b: set_Pr1324126435od_b_b > set_St761939237tant_a > set_Product_prod_b_b ).
thf(func_def_81,type,
image_763305007od_b_b: set_Pr2109276827od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_82,type,
image_1397930469od_b_b: set_Pr2134561957od_b_b > set_Pr1324126435od_b_b > set_Product_prod_b_b ).
thf(func_def_83,type,
image_1764625405_b_b_b: set_Pr1906739389_b_b_b > set_Pr1324126435od_b_b > set_b ).
thf(func_def_84,type,
image_532916993od_b_b: set_Pr1071216121od_b_b > set_Product_prod_b_b > set_Pr1324126435od_b_b ).
thf(func_def_85,type,
image_1928024979od_b_b: set_Pr2007082183od_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
thf(func_def_86,type,
image_921732011_b_b_b: set_Pr357419743_b_b_b > set_Product_prod_b_b > set_b ).
thf(func_def_87,type,
image_984343321od_b_b: set_Pr2060523537od_b_b > set_b > set_Pr1324126435od_b_b ).
thf(func_def_88,type,
image_1177096571od_b_b: set_Pr621705391od_b_b > set_b > set_Product_prod_b_b ).
thf(func_def_89,type,
image_b_b: set_Product_prod_b_b > set_b > set_b ).
thf(func_def_90,type,
conver1398856763od_b_b: set_Pr1324126435od_b_b > set_Pr306736955tant_a ).
thf(func_def_91,type,
conver1943590235tant_a: set_Pr306736955tant_a > set_Pr1324126435od_b_b ).
thf(func_def_92,type,
converse_b_b: set_Product_prod_b_b > set_Product_prod_b_b ).
thf(func_def_93,type,
refl_o1921098222od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).
thf(func_def_94,type,
refl_o2134473190od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).
thf(func_def_95,type,
refl_on_b: set_b > set_Product_prod_b_b > $o ).
thf(func_def_96,type,
total_771970601od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).
thf(func_def_97,type,
total_178717291od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).
thf(func_def_98,type,
total_on_b: set_b > set_Product_prod_b_b > $o ).
thf(func_def_99,type,
collec279084418od_b_b: ( produc1213276845od_b_b > $o ) > set_Pr1324126435od_b_b ).
thf(func_def_100,type,
collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).
thf(func_def_101,type,
collect_b: ( b > $o ) > set_b ).
thf(func_def_102,type,
insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).
thf(func_def_103,type,
insert2037698781od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_104,type,
insert1098249399od_b_b: produc1168037607od_b_b > set_Pr2007082183od_b_b > set_Pr2007082183od_b_b ).
thf(func_def_105,type,
insert1952693431od_b_b: product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
thf(func_def_106,type,
insert_b: b > set_b > set_b ).
thf(func_def_107,type,
is_sin1465183929od_b_b: set_Pr1324126435od_b_b > $o ).
thf(func_def_108,type,
is_sin1713057243od_b_b: set_Product_prod_b_b > $o ).
thf(func_def_109,type,
is_singleton_b: set_b > $o ).
thf(func_def_110,type,
the_el329196508od_b_b: set_Product_prod_b_b > product_prod_b_b ).
thf(func_def_111,type,
the_elem_b: set_b > b ).
thf(func_def_112,type,
member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).
thf(func_def_113,type,
member1516365892od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > $o ).
thf(func_def_114,type,
member1086024932od_b_b: produc970027067od_b_b > set_Pr2109276827od_b_b > $o ).
thf(func_def_115,type,
member942707974od_b_b: produc1990339951od_b_b > set_Pr2134561957od_b_b > $o ).
thf(func_def_116,type,
member1417789726_b_b_b: produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o ).
thf(func_def_117,type,
member1670214300tant_a: produc1367125253tant_a > set_Pr306736955tant_a > $o ).
thf(func_def_118,type,
member4694106od_b_b: produc1052326083od_b_b > set_Pr1071216121od_b_b > $o ).
thf(func_def_119,type,
member1652792080od_b_b: produc1168037607od_b_b > set_Pr2007082183od_b_b > $o ).
thf(func_def_120,type,
member351494440_b_b_b: produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o ).
thf(func_def_121,type,
member599505522od_b_b: produc1605346267od_b_b > set_Pr2060523537od_b_b > $o ).
thf(func_def_122,type,
member641857272od_b_b: produc255402447od_b_b > set_Pr621705391od_b_b > $o ).
thf(func_def_123,type,
member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
thf(func_def_124,type,
member_b: b > set_b > $o ).
thf(func_def_125,type,
g: labele1159362096nt_a_b ).
thf(func_def_126,type,
p: b > b > $o ).
thf(func_def_127,type,
f: b > b ).
thf(func_def_128,type,
x: b ).
thf(func_def_129,type,
y: b ).
thf(func_def_133,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_134,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_135,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_136,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_137,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_138,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_139,type,
vIMP: $o > $o > $o ).
thf(func_def_140,type,
vNOT: $o > $o ).
thf(func_def_141,type,
vOR: $o > $o > $o ).
thf(func_def_142,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_143,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_144,type,
vAND: $o > $o > $o ).
thf(func_def_145,type,
sP0: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).
thf(func_def_146,type,
sP1: set_b > set_Product_prod_b_b > $o ).
thf(func_def_147,type,
sP2: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).
thf(func_def_148,type,
sK3: set_Pr1324126435od_b_b > produc1213276845od_b_b ).
thf(func_def_149,type,
sK4: set_Pr1324126435od_b_b > produc1213276845od_b_b ).
thf(func_def_150,type,
sK5: set_Product_prod_b_b > product_prod_b_b ).
thf(func_def_151,type,
sK6: set_Product_prod_b_b > product_prod_b_b ).
thf(func_def_152,type,
sK7: set_b > b ).
thf(func_def_153,type,
sK8: set_b > b ).
thf(func_def_154,type,
sK9: set_Pr1324126435od_b_b > produc1213276845od_b_b ).
thf(func_def_155,type,
sK10: set_b > b ).
thf(func_def_156,type,
sK11: set_Product_prod_b_b > product_prod_b_b ).
thf(func_def_157,type,
sK12: set_b > b ).
thf(func_def_158,type,
sK13: set_Product_prod_b_b > product_prod_b_b ).
thf(func_def_159,type,
sK14: produc1213276845od_b_b > standard_Constant_a ).
thf(func_def_160,type,
sK15: produc1213276845od_b_b > product_prod_b_b ).
thf(func_def_161,type,
sK16: product_prod_b_b > b ).
thf(func_def_162,type,
sK17: product_prod_b_b > b ).
thf(func_def_163,type,
sK18: produc1213276845od_b_b > standard_Constant_a ).
thf(func_def_164,type,
sK19: produc1213276845od_b_b > b ).
thf(func_def_165,type,
sK20: produc1213276845od_b_b > b ).
thf(func_def_166,type,
sK21: produc1213276845od_b_b > standard_Constant_a ).
thf(func_def_167,type,
sK22: produc1213276845od_b_b > product_prod_b_b ).
thf(func_def_168,type,
sK23: product_prod_b_b > b ).
thf(func_def_169,type,
sK24: product_prod_b_b > b ).
thf(func_def_170,type,
sK25: ( b > $o ) > ( b > $o ) > b ).
thf(func_def_171,type,
sK26: ( b > $o ) > ( b > $o ) > b ).
thf(func_def_172,type,
sK27: ( b > $o ) > ( b > $o ) > b ).
thf(func_def_173,type,
sK28: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b ).
thf(func_def_174,type,
sK29: set_b > set_b > b ).
thf(func_def_175,type,
sK30: set_Product_prod_b_b > set_Product_prod_b_b > product_prod_b_b ).
thf(func_def_176,type,
sK31: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > produc1213276845od_b_b ).
thf(func_def_177,type,
sK32: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > produc1213276845od_b_b ).
thf(func_def_178,type,
sK33: set_b > set_Product_prod_b_b > b ).
thf(func_def_179,type,
sK34: set_b > set_Product_prod_b_b > b ).
thf(func_def_180,type,
sK35: set_Product_prod_b_b > set_Pr2007082183od_b_b > product_prod_b_b ).
thf(func_def_181,type,
sK36: set_Product_prod_b_b > set_Pr2007082183od_b_b > product_prod_b_b ).
thf(func_def_182,type,
sK37: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > standard_Constant_a ).
thf(func_def_183,type,
sK38: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > product_prod_b_b ).
thf(func_def_184,type,
sK39: ( b > set_b ) > set_Product_prod_b_b > b ).
thf(func_def_185,type,
sK40: ( b > set_b ) > set_Product_prod_b_b > b ).
thf(func_def_186,type,
sK41: set_Product_prod_b_b > set_Product_prod_b_b > b ).
thf(func_def_187,type,
sK42: set_Product_prod_b_b > set_Product_prod_b_b > b ).
thf(func_def_188,type,
sK43: ( produc1213276845od_b_b > $o ) > standard_Constant_a ).
thf(func_def_189,type,
sK44: ( produc1213276845od_b_b > $o ) > product_prod_b_b ).
thf(func_def_190,type,
sK45: ( produc1213276845od_b_b > $o ) > standard_Constant_a ).
thf(func_def_191,type,
sK46: ( produc1213276845od_b_b > $o ) > product_prod_b_b ).
thf(func_def_192,type,
sK47: ( product_prod_b_b > $o ) > b ).
thf(func_def_193,type,
sK48: ( product_prod_b_b > $o ) > b ).
thf(func_def_194,type,
sK49: ( product_prod_b_b > $o ) > b ).
thf(func_def_195,type,
sK50: ( product_prod_b_b > $o ) > b ).
thf(func_def_196,type,
sK51: ( produc1213276845od_b_b > $o ) > standard_Constant_a ).
thf(func_def_197,type,
sK52: ( produc1213276845od_b_b > $o ) > b ).
thf(func_def_198,type,
sK53: ( produc1213276845od_b_b > $o ) > b ).
thf(func_def_199,type,
sK54: b > ( b > $o ) > b ).
thf(func_def_200,type,
sK55: ( b > $o ) > ( b > $o ) > b ).
thf(func_def_201,type,
sK56: b > ( b > $o ) > b ).
thf(func_def_202,type,
sK57: set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_203,type,
sK58: set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_204,type,
sK59: set_b > b > set_b ).
thf(func_def_205,type,
sK60: set_b > b > set_b ).
thf(func_def_206,type,
sK61: set_Product_prod_b_b > product_prod_b_b > set_Product_prod_b_b ).
thf(func_def_207,type,
sK62: set_Product_prod_b_b > product_prod_b_b > set_Product_prod_b_b ).
thf(func_def_208,type,
sK63: set_Pr1324126435od_b_b > produc1367125253tant_a > standard_Constant_a ).
thf(func_def_209,type,
sK64: set_Pr1324126435od_b_b > produc1367125253tant_a > product_prod_b_b ).
thf(func_def_210,type,
sK65: set_Pr306736955tant_a > produc1213276845od_b_b > product_prod_b_b ).
thf(func_def_211,type,
sK66: set_Pr306736955tant_a > produc1213276845od_b_b > standard_Constant_a ).
thf(func_def_212,type,
sK67: set_Product_prod_b_b > product_prod_b_b > b ).
thf(func_def_213,type,
sK68: set_Product_prod_b_b > product_prod_b_b > b ).
thf(func_def_214,type,
sK69: ( produc1213276845od_b_b > $o ) > ( produc1213276845od_b_b > $o ) > set_Pr1324126435od_b_b > produc1213276845od_b_b ).
thf(func_def_215,type,
sK70: ( b > $o ) > ( b > $o ) > set_b > b ).
thf(func_def_216,type,
sK71: ( product_prod_b_b > $o ) > ( product_prod_b_b > $o ) > set_Product_prod_b_b > product_prod_b_b ).
thf(func_def_217,type,
sK72: ( b > $o ) > ( b > $o ) > b ).
thf(func_def_218,type,
sK73: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > produc1213276845od_b_b > produc1213276845od_b_b ).
thf(func_def_219,type,
sK74: set_b > set_Pr2060523537od_b_b > produc1213276845od_b_b > b ).
thf(func_def_220,type,
sK75: set_Product_prod_b_b > set_Pr1071216121od_b_b > produc1213276845od_b_b > product_prod_b_b ).
thf(func_def_221,type,
sK76: set_Pr1324126435od_b_b > set_Pr1906739389_b_b_b > b > produc1213276845od_b_b ).
thf(func_def_222,type,
sK77: set_b > set_Product_prod_b_b > b > b ).
thf(func_def_223,type,
sK78: set_Product_prod_b_b > set_Pr357419743_b_b_b > b > product_prod_b_b ).
thf(func_def_224,type,
sK79: set_St761939237tant_a > set_Pr1324126435od_b_b > product_prod_b_b > standard_Constant_a ).
thf(func_def_225,type,
sK80: set_Pr1324126435od_b_b > set_Pr2134561957od_b_b > product_prod_b_b > produc1213276845od_b_b ).
thf(func_def_226,type,
sK81: set_b > set_Pr621705391od_b_b > product_prod_b_b > b ).
thf(func_def_227,type,
sK82: set_Product_prod_b_b > set_Pr2007082183od_b_b > product_prod_b_b > product_prod_b_b ).
thf(func_def_228,type,
sK83: ( product_prod_b_b > standard_Constant_a > $o ) > set_Pr1324126435od_b_b > standard_Constant_a ).
thf(func_def_229,type,
sK84: ( product_prod_b_b > standard_Constant_a > $o ) > set_Pr1324126435od_b_b > product_prod_b_b ).
thf(func_def_230,type,
sK85: ( standard_Constant_a > product_prod_b_b > $o ) > set_Pr306736955tant_a > product_prod_b_b ).
thf(func_def_231,type,
sK86: ( standard_Constant_a > product_prod_b_b > $o ) > set_Pr306736955tant_a > standard_Constant_a ).
thf(func_def_232,type,
sK87: ( b > b > $o ) > set_Product_prod_b_b > b ).
thf(func_def_233,type,
sK88: ( b > b > $o ) > set_Product_prod_b_b > b ).
thf(func_def_234,type,
sK89: set_Product_prod_b_b > product_prod_b_b > set_Product_prod_b_b > product_prod_b_b > set_Product_prod_b_b ).
thf(func_def_235,type,
sK90: set_b > b > set_b > b > set_b ).
thf(func_def_236,type,
sK91: set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b > produc1213276845od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_237,type,
sK92: b > b > set_Product_prod_b_b > b ).
thf(func_def_238,type,
sK93: product_prod_b_b > standard_Constant_a > set_Pr306736955tant_a > standard_Constant_a ).
thf(func_def_239,type,
sK94: standard_Constant_a > product_prod_b_b > set_Pr1324126435od_b_b > product_prod_b_b ).
thf(func_def_240,type,
sK95: set_Pr1324126435od_b_b > set_St761939237tant_a > product_prod_b_b > standard_Constant_a ).
thf(func_def_241,type,
sK96: set_Product_prod_b_b > set_b > b > b ).
thf(func_def_242,type,
sK97: ( b > $o ) > ( b > $o ) > b ).
thf(func_def_243,type,
sK98: ( b > $o ) > b ).
thf(func_def_244,type,
sK99: set_Product_prod_b_b > product_prod_b_b ).
thf(func_def_245,type,
sK100: set_b > b ).
thf(func_def_246,type,
sK101: set_Pr1324126435od_b_b > produc1213276845od_b_b ).
thf(func_def_247,type,
sK102: set_Product_prod_b_b > product_prod_b_b ).
thf(func_def_248,type,
sK103: set_b > b ).
thf(func_def_249,type,
sK104: set_Pr1324126435od_b_b > produc1213276845od_b_b ).
thf(func_def_250,type,
sK105: ( b > $o ) > b ).
thf(func_def_251,type,
sK106: ( b > $o ) > b ).
thf(func_def_252,type,
sK107: ( product_prod_b_b > $o ) > product_prod_b_b ).
thf(func_def_253,type,
sK108: ( product_prod_b_b > $o ) > product_prod_b_b ).
thf(f2460,plain,
$false,
inference(trivial_inequality_removal,[],[f2459]) ).
thf(f2459,plain,
vAPP(sTfun(b,$o),b,hilbert_Eps_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)))) != vAPP(sTfun(b,$o),b,hilbert_Eps_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)))),
inference(backward_demodulation,[],[f1454,f1459]) ).
thf(f1459,plain,
vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)) = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,y),bot_bot_set_b)),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)) = vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,y),bot_bot_set_b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062) ).
thf(f1454,plain,
vAPP(sTfun(b,$o),b,hilbert_Eps_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)))) != vAPP(sTfun(b,$o),b,hilbert_Eps_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,y),bot_bot_set_b)))),
inference(cnf_transformation,[],[f967]) ).
thf(f967,plain,
vAPP(sTfun(b,$o),b,hilbert_Eps_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)))) != vAPP(sTfun(b,$o),b,hilbert_Eps_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,y),bot_bot_set_b)))),
inference(flattening,[],[f364]) ).
thf(f364,plain,
vAPP(sTfun(b,$o),b,hilbert_Eps_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)))) != vAPP(sTfun(b,$o),b,hilbert_Eps_b,vAPP(set_b,sTfun(b,$o),vAPP(sTfun(b,sTfun(set_b,$o)),sTfun(set_b,sTfun(b,$o)),cCOMB,member_b),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,y),bot_bot_set_b)))),
inference(fool_elimination,[],[f363]) ).
thf(f363,plain,
( vAPP(sTfun(b,$o),b,hilbert_Eps_b,
^ [X0: b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X0),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)))) != vAPP(sTfun(b,$o),b,hilbert_Eps_b,
^ [X1: b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X1),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,y),bot_bot_set_b)))) ),
inference(rectify,[],[f360]) ).
thf(f360,negated_conjecture,
( vAPP(sTfun(b,$o),b,hilbert_Eps_b,
^ [X2: b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)))) != vAPP(sTfun(b,$o),b,hilbert_Eps_b,
^ [X2: b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,y),bot_bot_set_b)))) ),
inference(negated_conjecture,[],[f359]) ).
thf(f359,conjecture,
( vAPP(sTfun(b,$o),b,hilbert_Eps_b,
^ [X2: b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,x),bot_bot_set_b)))) = vAPP(sTfun(b,$o),b,hilbert_Eps_b,
^ [X2: b] : vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,X2),vAPP(set_b,set_b,vAPP(set_Product_prod_b_b,sTfun(set_b,set_b),image_b_b,vAPP(labele1159362096nt_a_b,set_Product_prod_b_b,vAPP(standard_Constant_a,sTfun(labele1159362096nt_a_b,set_Product_prod_b_b),getRel904497637nt_a_b,standard_S_Idt_a),g)),vAPP(set_b,set_b,vAPP(b,sTfun(set_b,set_b),insert_b,y),bot_bot_set_b)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ITP176^1 : TPTP v8.2.0. Released v7.5.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n023.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat May 18 16:26:53 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.31 % (21105)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.35 % (21108)WARNING: value z3 for option sas not known
% 0.16/0.35 % (21108)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.35 % (21107)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.35 % (21106)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.35 % (21112)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.35 % (21110)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.35 % (21109)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.35 % (21111)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.39 % (21112)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.40 % Exception at run slice level
% 0.16/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.40 % Exception at run slice level
% 0.16/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.40 % Exception at run slice level
% 0.16/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.41 % (21111)First to succeed.
% 0.16/0.41 % (21111)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21105"
% 0.16/0.41 % (21111)Refutation found. Thanks to Tanya!
% 0.16/0.41 % SZS status Theorem for theBenchmark
% 0.16/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.41 % (21111)------------------------------
% 0.16/0.41 % (21111)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.41 % (21111)Termination reason: Refutation
% 0.16/0.41
% 0.16/0.41 % (21111)Memory used [KB]: 2110
% 0.16/0.41 % (21111)Time elapsed: 0.061 s
% 0.16/0.41 % (21111)Instructions burned: 148 (million)
% 0.16/0.41 % (21105)Success in time 0.095 s
%------------------------------------------------------------------------------