%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP112^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:44 AM UTC 2026
% Result : Theorem 2.38s 0.64s
% Output : Refutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 187 ( 8 ~; 3 |; 0 &; 173 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 507 ( 504 usr; 8 con; 0-4 aty)
% Number of variables : 44 ( 29 ^; 15 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
filter2049122004_ereal: $tType ).
thf(type_def_6,type,
set_Extended_ereal: $tType ).
thf(type_def_7,type,
filter_real: $tType ).
thf(type_def_8,type,
filter_nat: $tType ).
thf(type_def_9,type,
filter_int: $tType ).
thf(type_def_10,type,
set_real: $tType ).
thf(type_def_11,type,
filter_a: $tType ).
thf(type_def_12,type,
extended_ereal: $tType ).
thf(type_def_13,type,
real: $tType ).
thf(type_def_14,type,
nat: $tType ).
thf(type_def_15,type,
int: $tType ).
thf(type_def_16,type,
a: $tType ).
thf(type_def_17,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
extend1289208545_ereal: extended_ereal ).
thf(func_def_1,type,
extended_ereal2: real > extended_ereal ).
thf(func_def_2,type,
at_bot_real: filter_real ).
thf(func_def_3,type,
at_top_nat: filter_nat ).
thf(func_def_4,type,
at_top_real: filter_real ).
thf(func_def_5,type,
filter1531173832_ereal: ( nat > extended_ereal ) > filter2049122004_ereal > filter_nat > $o ).
thf(func_def_6,type,
filterlim_nat_int: ( nat > int ) > filter_int > filter_nat > $o ).
thf(func_def_7,type,
filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
thf(func_def_8,type,
filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
thf(func_def_9,type,
filterlim_nat_a: ( nat > a ) > filter_a > filter_nat > $o ).
thf(func_def_10,type,
filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
thf(func_def_11,type,
comp_E1308517939al_nat: ( extended_ereal > extended_ereal ) > ( nat > extended_ereal ) > nat > extended_ereal ).
thf(func_def_12,type,
comp_E489644891real_a: ( extended_ereal > extended_ereal ) > ( a > extended_ereal ) > a > extended_ereal ).
thf(func_def_13,type,
comp_E1436437929nt_nat: ( extended_ereal > int ) > ( nat > extended_ereal ) > nat > int ).
thf(func_def_14,type,
comp_E1523169101at_nat: ( extended_ereal > nat ) > ( nat > extended_ereal ) > nat > nat ).
thf(func_def_15,type,
comp_E1477338153al_nat: ( extended_ereal > real ) > ( nat > extended_ereal ) > nat > real ).
thf(func_def_16,type,
comp_n1096781355al_nat: ( nat > extended_ereal ) > ( nat > nat ) > nat > extended_ereal ).
thf(func_def_17,type,
comp_nat_a_nat: ( nat > a ) > ( nat > nat ) > nat > a ).
thf(func_def_18,type,
comp_r1410008527al_nat: ( real > extended_ereal ) > ( nat > real ) > nat > extended_ereal ).
thf(func_def_19,type,
comp_real_int_nat: ( real > int ) > ( nat > real ) > nat > int ).
thf(func_def_20,type,
comp_real_nat_nat: ( real > nat ) > ( nat > real ) > nat > nat ).
thf(func_def_21,type,
comp_a1112243075al_nat: ( a > extended_ereal ) > ( nat > a ) > nat > extended_ereal ).
thf(func_def_22,type,
comp_a780206603real_a: ( a > extended_ereal ) > ( a > a ) > a > extended_ereal ).
thf(func_def_23,type,
comp_a_int_nat: ( a > int ) > ( nat > a ) > nat > int ).
thf(func_def_24,type,
comp_a_nat_nat: ( a > nat ) > ( nat > a ) > nat > nat ).
thf(func_def_25,type,
comp_a_real_nat: ( a > real ) > ( nat > a ) > nat > real ).
thf(func_def_26,type,
comp_a_a_nat: ( a > a ) > ( nat > a ) > nat > a ).
thf(func_def_27,type,
plus_p2118002693_ereal: extended_ereal > extended_ereal > extended_ereal ).
thf(func_def_28,type,
plus_plus_int: int > int > int ).
thf(func_def_29,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_30,type,
plus_plus_real: real > real > real ).
thf(func_def_31,type,
uminus1208298309_ereal: extended_ereal > extended_ereal ).
thf(func_def_32,type,
uminus_uminus_int: int > int ).
thf(func_def_33,type,
uminus_uminus_real: real > real ).
thf(func_def_34,type,
uniq_Extended_ereal: ( extended_ereal > $o ) > $o ).
thf(func_def_35,type,
uniq_real: ( real > $o ) > $o ).
thf(func_def_36,type,
uniq_a: ( a > $o ) > $o ).
thf(func_def_37,type,
liminf1045857232_ereal: filter_nat > ( nat > extended_ereal ) > extended_ereal ).
thf(func_def_38,type,
lower_1087098792_ereal: extended_ereal > ( extended_ereal > extended_ereal ) > $o ).
thf(func_def_39,type,
lower_48196818al_int: extended_ereal > ( extended_ereal > int ) > $o ).
thf(func_def_40,type,
lower_1558406774al_nat: extended_ereal > ( extended_ereal > nat ) > $o ).
thf(func_def_41,type,
lower_1165973074l_real: extended_ereal > ( extended_ereal > real ) > $o ).
thf(func_def_42,type,
lower_551915512_ereal: real > ( real > extended_ereal ) > $o ).
thf(func_def_43,type,
lower_153911426al_int: real > ( real > int ) > $o ).
thf(func_def_44,type,
lower_1664121382al_nat: real > ( real > nat ) > $o ).
thf(func_def_45,type,
lower_191460856_ereal: a > ( a > extended_ereal ) > $o ).
thf(func_def_46,type,
lower_956963458_a_int: a > ( a > int ) > $o ).
thf(func_def_47,type,
lower_319689766_a_nat: a > ( a > nat ) > $o ).
thf(func_def_48,type,
lower_231615490a_real: a > ( a > real ) > $o ).
thf(func_def_49,type,
lower_1071158961_ereal: extended_ereal > ( extended_ereal > extended_ereal ) > $o ).
thf(func_def_50,type,
lower_637387785al_int: extended_ereal > ( extended_ereal > int ) > $o ).
thf(func_def_51,type,
lower_114093al_nat: extended_ereal > ( extended_ereal > nat ) > $o ).
thf(func_def_52,type,
lower_737640969l_real: extended_ereal > ( extended_ereal > real ) > $o ).
thf(func_def_53,type,
lower_1075504779al_int: real > ( real > int ) > $o ).
thf(func_def_54,type,
lower_438231087al_nat: real > ( real > nat ) > $o ).
thf(func_def_55,type,
lower_534855297_ereal: a > ( a > extended_ereal ) > $o ).
thf(func_def_56,type,
lower_1672990777_a_int: a > ( a > int ) > $o ).
thf(func_def_57,type,
lower_1035717085_a_nat: a > ( a > nat ) > $o ).
thf(func_def_58,type,
lower_755922489a_real: a > ( a > real ) > $o ).
thf(func_def_59,type,
semiri2019852685at_int: nat > int ).
thf(func_def_60,type,
semiri2110766477t_real: nat > real ).
thf(func_def_61,type,
ord_le824540014_ereal: extended_ereal > extended_ereal > $o ).
thf(func_def_62,type,
ord_le1745708096er_nat: filter_nat > filter_nat > $o ).
thf(func_def_63,type,
ord_le132810396r_real: filter_real > filter_real > $o ).
thf(func_def_64,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_65,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_66,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_67,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_68,type,
topolo1069469409_ereal: ( nat > extended_ereal ) > $o ).
thf(func_def_69,type,
topolo411883481eq_int: ( nat > int ) > $o ).
thf(func_def_70,type,
topolo1922093437eq_nat: ( nat > nat ) > $o ).
thf(func_def_71,type,
topolo144289241q_real: ( nat > real ) > $o ).
thf(func_def_72,type,
topolo2140997059_ereal: extended_ereal > filter2049122004_ereal ).
thf(func_def_73,type,
topolo54776183ds_int: int > filter_int ).
thf(func_def_74,type,
topolo1564986139ds_nat: nat > filter_nat ).
thf(func_def_75,type,
topolo1664202871s_real: real > filter_real ).
thf(func_def_76,type,
topolo705128563nhds_a: a > filter_a ).
thf(func_def_77,type,
member1900190071_ereal: extended_ereal > set_Extended_ereal > $o ).
thf(func_def_78,type,
member_real: real > set_real > $o ).
thf(func_def_79,type,
a2: extended_ereal ).
thf(func_def_80,type,
f: a > extended_ereal ).
thf(func_def_81,type,
x0: a ).
thf(func_def_82,type,
x: nat > a ).
thf(func_def_86,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_87,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_88,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_89,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_90,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_91,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_92,type,
vIMP: $o > $o > $o ).
thf(func_def_93,type,
vAND: $o > $o > $o ).
thf(func_def_94,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_95,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_96,type,
vOR: $o > $o > $o ).
thf(func_def_97,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_98,type,
vNOT: $o > $o ).
thf(func_def_99,type,
sP0: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_100,type,
sP1: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_101,type,
sP2: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_102,type,
sP3: nat > nat > nat > $o ).
thf(func_def_103,type,
sP4: nat > nat > nat > $o ).
thf(func_def_104,type,
sP5: nat > nat > nat > $o ).
thf(func_def_105,type,
sP6: real > real > real > $o ).
thf(func_def_106,type,
sP7: real > real > real > $o ).
thf(func_def_107,type,
sP8: real > real > real > $o ).
thf(func_def_108,type,
sP9: int > int > int > $o ).
thf(func_def_109,type,
sP10: int > int > int > $o ).
thf(func_def_110,type,
sP11: int > int > int > $o ).
thf(func_def_111,type,
sP12: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_112,type,
sP13: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_113,type,
sP14: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_114,type,
sP15: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_115,type,
sP16: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_116,type,
sP17: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_117,type,
sP18: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_118,type,
sP19: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_119,type,
sP20: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_120,type,
sP21: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_121,type,
sP22: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_122,type,
sP23: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_123,type,
sP24: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_124,type,
sP25: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_125,type,
sP26: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_126,type,
sP27: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_127,type,
sP28: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_128,type,
sP29: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_129,type,
sP30: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_130,type,
sP31: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_131,type,
sP32: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_132,type,
sP33: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_133,type,
sP34: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_134,type,
sP35: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_135,type,
sP36: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_136,type,
sP37: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_137,type,
sP38: extended_ereal > extended_ereal > $o ).
thf(func_def_138,type,
sP39: extended_ereal > extended_ereal > $o ).
thf(func_def_139,type,
sP40: extended_ereal > extended_ereal > $o ).
thf(func_def_140,type,
sP41: extended_ereal > extended_ereal > $o ).
thf(func_def_141,type,
sP42: extended_ereal > extended_ereal > $o ).
thf(func_def_142,type,
sP43: extended_ereal > extended_ereal > $o ).
thf(func_def_143,type,
sP44: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_144,type,
sP45: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_145,type,
sP46: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_146,type,
sP47: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_147,type,
sK48: ( nat > extended_ereal ) > ( nat > real ) > ( real > extended_ereal ) > nat ).
thf(func_def_148,type,
sK49: ( nat > extended_ereal ) > ( nat > a ) > ( a > extended_ereal ) > nat ).
thf(func_def_149,type,
sK50: set_Extended_ereal > extended_ereal ).
thf(func_def_150,type,
sK51: extended_ereal > set_Extended_ereal > extended_ereal ).
thf(func_def_151,type,
sK52: set_Extended_ereal > extended_ereal ).
thf(func_def_152,type,
sK53: extended_ereal > set_Extended_ereal > extended_ereal ).
thf(func_def_153,type,
sK54: ( nat > nat ) > ( nat > nat ) > nat > nat ).
thf(func_def_154,type,
sK55: ( nat > int ) > ( nat > int ) > nat > nat ).
thf(func_def_155,type,
sK56: ( nat > extended_ereal ) > ( nat > extended_ereal ) > nat > nat ).
thf(func_def_156,type,
sK57: ( nat > real ) > ( nat > real ) > nat > nat ).
thf(func_def_157,type,
sK58: nat > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_158,type,
sK59: nat > ( nat > int ) > ( nat > int ) > nat ).
thf(func_def_159,type,
sK60: nat > ( nat > extended_ereal ) > ( nat > extended_ereal ) > nat ).
thf(func_def_160,type,
sK61: nat > ( nat > real ) > ( nat > real ) > nat ).
thf(func_def_161,type,
sK62: ( real > $o ) > ( real > $o ) > real ).
thf(func_def_162,type,
sK63: nat > nat > ( nat > nat ) > nat ).
thf(func_def_163,type,
sK64: int > nat > ( nat > int ) > nat ).
thf(func_def_164,type,
sK65: extended_ereal > nat > ( nat > extended_ereal ) > nat ).
thf(func_def_165,type,
sK66: real > nat > ( nat > real ) > nat ).
thf(func_def_166,type,
sK67: nat > nat > ( nat > nat ) > nat ).
thf(func_def_167,type,
sK68: int > nat > ( nat > int ) > nat ).
thf(func_def_168,type,
sK69: extended_ereal > nat > ( nat > extended_ereal ) > nat ).
thf(func_def_169,type,
sK70: real > nat > ( nat > real ) > nat ).
thf(func_def_170,type,
sK71: nat > nat > ( nat > nat ) > nat ).
thf(func_def_171,type,
sK72: nat > int > ( nat > int ) > nat ).
thf(func_def_172,type,
sK73: nat > extended_ereal > ( nat > extended_ereal ) > nat ).
thf(func_def_173,type,
sK74: nat > real > ( nat > real ) > nat ).
thf(func_def_174,type,
sK75: nat > nat > ( nat > nat ) > nat ).
thf(func_def_175,type,
sK76: nat > int > ( nat > int ) > nat ).
thf(func_def_176,type,
sK77: nat > extended_ereal > ( nat > extended_ereal ) > nat ).
thf(func_def_177,type,
sK78: nat > real > ( nat > real ) > nat ).
thf(func_def_178,type,
sK79: ( nat > extended_ereal ) > extended_ereal ).
thf(func_def_179,type,
sK80: ( nat > extended_ereal ) > nat ).
thf(func_def_180,type,
sK81: ( nat > extended_ereal ) > nat ).
thf(func_def_181,type,
sK82: ( nat > extended_ereal ) > extended_ereal ).
thf(func_def_182,type,
sK83: ( nat > extended_ereal ) > nat ).
thf(func_def_183,type,
sK84: ( nat > extended_ereal ) > nat ).
thf(func_def_184,type,
sK85: ( nat > extended_ereal ) > nat ).
thf(func_def_185,type,
sK86: ( nat > extended_ereal ) > nat ).
thf(func_def_186,type,
sK87: ( nat > nat ) > nat ).
thf(func_def_187,type,
sK88: ( nat > nat ) > nat ).
thf(func_def_188,type,
sK89: ( nat > real ) > nat ).
thf(func_def_189,type,
sK90: ( nat > real ) > nat ).
thf(func_def_190,type,
sK91: ( nat > int ) > nat ).
thf(func_def_191,type,
sK92: ( nat > int ) > nat ).
thf(func_def_192,type,
sK93: ( nat > extended_ereal ) > nat ).
thf(func_def_193,type,
sK94: ( nat > extended_ereal ) > nat ).
thf(func_def_194,type,
sK95: ( nat > nat ) > nat ).
thf(func_def_195,type,
sK96: ( nat > nat ) > nat ).
thf(func_def_196,type,
sK97: ( nat > real ) > nat ).
thf(func_def_197,type,
sK98: ( nat > real ) > nat ).
thf(func_def_198,type,
sK99: ( nat > int ) > nat ).
thf(func_def_199,type,
sK100: ( nat > int ) > nat ).
thf(func_def_200,type,
sK101: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_201,type,
sK102: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_202,type,
sK103: ( nat > extended_ereal ) > nat ).
thf(func_def_203,type,
sK104: ( nat > extended_ereal ) > nat ).
thf(func_def_204,type,
sK105: ( real > extended_ereal ) > real ).
thf(func_def_205,type,
sK106: ( real > extended_ereal ) > real ).
thf(func_def_206,type,
sK107: ( int > extended_ereal ) > int ).
thf(func_def_207,type,
sK108: ( int > extended_ereal ) > int ).
thf(func_def_208,type,
sK109: ( extended_ereal > nat ) > extended_ereal ).
thf(func_def_209,type,
sK110: ( extended_ereal > nat ) > extended_ereal ).
thf(func_def_210,type,
sK111: ( nat > nat ) > nat ).
thf(func_def_211,type,
sK112: ( nat > nat ) > nat ).
thf(func_def_212,type,
sK113: ( real > nat ) > real ).
thf(func_def_213,type,
sK114: ( real > nat ) > real ).
thf(func_def_214,type,
sK115: ( int > nat ) > int ).
thf(func_def_215,type,
sK116: ( int > nat ) > int ).
thf(func_def_216,type,
sK117: ( extended_ereal > real ) > extended_ereal ).
thf(func_def_217,type,
sK118: ( extended_ereal > real ) > extended_ereal ).
thf(func_def_218,type,
sK119: ( nat > real ) > nat ).
thf(func_def_219,type,
sK120: ( nat > real ) > nat ).
thf(func_def_220,type,
sK121: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_221,type,
sK122: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_222,type,
sK123: ( extended_ereal > nat ) > extended_ereal ).
thf(func_def_223,type,
sK124: ( extended_ereal > nat ) > extended_ereal ).
thf(func_def_224,type,
sK125: ( extended_ereal > real ) > extended_ereal ).
thf(func_def_225,type,
sK126: ( extended_ereal > real ) > extended_ereal ).
thf(func_def_226,type,
sK127: ( extended_ereal > int ) > extended_ereal ).
thf(func_def_227,type,
sK128: ( extended_ereal > int ) > extended_ereal ).
thf(func_def_228,type,
sK129: ( nat > extended_ereal ) > nat ).
thf(func_def_229,type,
sK130: ( nat > extended_ereal ) > nat ).
thf(func_def_230,type,
sK131: ( nat > nat ) > nat ).
thf(func_def_231,type,
sK132: ( nat > nat ) > nat ).
thf(func_def_232,type,
sK133: ( nat > real ) > nat ).
thf(func_def_233,type,
sK134: ( nat > real ) > nat ).
thf(func_def_234,type,
sK135: ( nat > int ) > nat ).
thf(func_def_235,type,
sK136: ( nat > int ) > nat ).
thf(func_def_236,type,
sK137: ( real > extended_ereal ) > real ).
thf(func_def_237,type,
sK138: ( real > extended_ereal ) > real ).
thf(func_def_238,type,
sK139: ( real > nat ) > real ).
thf(func_def_239,type,
sK140: ( real > nat ) > real ).
thf(func_def_240,type,
sK141: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_241,type,
sK142: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_242,type,
sK143: ( extended_ereal > nat ) > extended_ereal ).
thf(func_def_243,type,
sK144: ( extended_ereal > nat ) > extended_ereal ).
thf(func_def_244,type,
sK145: ( extended_ereal > real ) > extended_ereal ).
thf(func_def_245,type,
sK146: ( extended_ereal > real ) > extended_ereal ).
thf(func_def_246,type,
sK147: ( extended_ereal > int ) > extended_ereal ).
thf(func_def_247,type,
sK148: ( extended_ereal > int ) > extended_ereal ).
thf(func_def_248,type,
sK149: ( nat > extended_ereal ) > nat ).
thf(func_def_249,type,
sK150: ( nat > extended_ereal ) > nat ).
thf(func_def_250,type,
sK151: ( nat > nat ) > nat ).
thf(func_def_251,type,
sK152: ( nat > nat ) > nat ).
thf(func_def_252,type,
sK153: ( nat > real ) > nat ).
thf(func_def_253,type,
sK154: ( nat > real ) > nat ).
thf(func_def_254,type,
sK155: ( nat > int ) > nat ).
thf(func_def_255,type,
sK156: ( nat > int ) > nat ).
thf(func_def_256,type,
sK157: ( real > extended_ereal ) > real ).
thf(func_def_257,type,
sK158: ( real > extended_ereal ) > real ).
thf(func_def_258,type,
sK159: ( real > nat ) > real ).
thf(func_def_259,type,
sK160: ( real > nat ) > real ).
thf(func_def_260,type,
sK161: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_261,type,
sK162: ( extended_ereal > extended_ereal ) > extended_ereal ).
thf(func_def_262,type,
sK163: ( extended_ereal > nat ) > extended_ereal ).
thf(func_def_263,type,
sK164: ( extended_ereal > nat ) > extended_ereal ).
thf(func_def_264,type,
sK165: ( extended_ereal > real ) > extended_ereal ).
thf(func_def_265,type,
sK166: ( extended_ereal > real ) > extended_ereal ).
thf(func_def_266,type,
sK167: ( extended_ereal > int ) > extended_ereal ).
thf(func_def_267,type,
sK168: ( extended_ereal > int ) > extended_ereal ).
thf(func_def_268,type,
sK169: ( nat > extended_ereal ) > nat ).
thf(func_def_269,type,
sK170: ( nat > extended_ereal ) > nat ).
thf(func_def_270,type,
sK171: ( nat > nat ) > nat ).
thf(func_def_271,type,
sK172: ( nat > nat ) > nat ).
thf(func_def_272,type,
sK173: ( nat > real ) > nat ).
thf(func_def_273,type,
sK174: ( nat > real ) > nat ).
thf(func_def_274,type,
sK175: ( nat > int ) > nat ).
thf(func_def_275,type,
sK176: ( nat > int ) > nat ).
thf(func_def_276,type,
sK177: ( real > extended_ereal ) > real ).
thf(func_def_277,type,
sK178: ( real > extended_ereal ) > real ).
thf(func_def_278,type,
sK179: ( real > nat ) > real ).
thf(func_def_279,type,
sK180: ( real > nat ) > real ).
thf(func_def_280,type,
sK181: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_281,type,
sK182: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_282,type,
sK183: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_283,type,
sK184: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_284,type,
sK185: ( nat > nat > $o ) > nat ).
thf(func_def_285,type,
sK186: ( nat > nat > $o ) > nat ).
thf(func_def_286,type,
sK187: ( nat > nat > $o ) > nat ).
thf(func_def_287,type,
sK188: ( nat > nat > $o ) > nat ).
thf(func_def_288,type,
sK189: ( real > real > $o ) > real ).
thf(func_def_289,type,
sK190: ( real > real > $o ) > real ).
thf(func_def_290,type,
sK191: ( real > real > $o ) > real ).
thf(func_def_291,type,
sK192: ( real > real > $o ) > real ).
thf(func_def_292,type,
sK193: ( int > int > $o ) > int ).
thf(func_def_293,type,
sK194: ( int > int > $o ) > int ).
thf(func_def_294,type,
sK195: ( int > int > $o ) > int ).
thf(func_def_295,type,
sK196: ( int > int > $o ) > int ).
thf(func_def_296,type,
sK197: real > ( nat > extended_ereal ) > nat ).
thf(func_def_297,type,
sK198: real > nat > ( nat > extended_ereal ) > nat ).
thf(func_def_298,type,
sK199: extended_ereal > extended_ereal > real ).
thf(func_def_299,type,
sK200: ( extended_ereal > $o ) > real ).
thf(func_def_300,type,
sK201: extended_ereal > real ).
thf(func_def_301,type,
sK202: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_302,type,
sK203: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_303,type,
sK204: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_304,type,
sK205: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_305,type,
sK206: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_306,type,
sK207: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_307,type,
sK208: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_308,type,
sK209: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_309,type,
sK210: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_310,type,
sK211: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_311,type,
sK212: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_312,type,
sK213: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_313,type,
sK214: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_314,type,
sK215: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_315,type,
sK216: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_316,type,
sK217: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_317,type,
sK218: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_318,type,
sK219: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_319,type,
sK220: ( extended_ereal > $o ) > real ).
thf(func_def_320,type,
sK221: extended_ereal > real ).
thf(func_def_321,type,
sK222: extended_ereal > real ).
thf(func_def_322,type,
sK223: extended_ereal > real ).
thf(func_def_323,type,
sK224: extended_ereal > real ).
thf(func_def_324,type,
sK225: extended_ereal > real ).
thf(func_def_325,type,
sK226: extended_ereal > real ).
thf(func_def_326,type,
sK227: extended_ereal > real ).
thf(func_def_327,type,
sK228: extended_ereal > real ).
thf(func_def_328,type,
sK229: extended_ereal > real ).
thf(func_def_329,type,
sK230: extended_ereal > real ).
thf(func_def_330,type,
sK231: extended_ereal > real ).
thf(func_def_331,type,
sK232: extended_ereal > real ).
thf(func_def_332,type,
sK233: extended_ereal > real ).
thf(func_def_333,type,
sK234: extended_ereal > real ).
thf(func_def_334,type,
sK235: extended_ereal > real ).
thf(func_def_335,type,
sK236: extended_ereal > real ).
thf(func_def_336,type,
sK237: extended_ereal > real ).
thf(func_def_337,type,
sK238: extended_ereal > real ).
thf(func_def_338,type,
sK239: extended_ereal > real ).
thf(func_def_339,type,
sK240: extended_ereal > real ).
thf(func_def_340,type,
sK241: extended_ereal > real ).
thf(func_def_341,type,
sK242: extended_ereal > real ).
thf(func_def_342,type,
sK243: extended_ereal > real ).
thf(func_def_343,type,
sK244: extended_ereal > real ).
thf(func_def_344,type,
sK245: extended_ereal > real ).
thf(func_def_345,type,
sK246: extended_ereal > real ).
thf(func_def_346,type,
sK247: extended_ereal > real ).
thf(func_def_347,type,
sK248: extended_ereal > real ).
thf(func_def_348,type,
sK249: extended_ereal > real ).
thf(func_def_349,type,
sK250: extended_ereal > real ).
thf(func_def_350,type,
sK251: extended_ereal > real ).
thf(func_def_351,type,
sK252: extended_ereal > real ).
thf(func_def_352,type,
sK253: extended_ereal > real ).
thf(func_def_353,type,
sK254: extended_ereal > real ).
thf(func_def_354,type,
sK255: extended_ereal > real ).
thf(func_def_355,type,
sK256: extended_ereal > real ).
thf(func_def_356,type,
sK257: extended_ereal > real ).
thf(func_def_357,type,
sK258: real > ( nat > extended_ereal ) > nat ).
thf(func_def_358,type,
sK259: nat > nat > nat ).
thf(func_def_359,type,
sK260: ( nat > $o ) > nat ).
thf(func_def_360,type,
sK261: nat > ( nat > $o ) > nat ).
thf(func_def_361,type,
sK262: extended_ereal > real ).
thf(func_def_362,type,
sK263: extended_ereal > real ).
thf(func_def_363,type,
sK264: extended_ereal > extended_ereal > extended_ereal > real ).
thf(func_def_364,type,
sK265: extended_ereal > extended_ereal > extended_ereal > real ).
thf(func_def_365,type,
sK266: real > ( nat > extended_ereal ) > nat ).
thf(func_def_366,type,
sK267: ( nat > extended_ereal ) > real ).
thf(func_def_367,type,
sK268: nat > ( nat > extended_ereal ) > nat ).
thf(func_def_368,type,
sK269: real > ( nat > extended_ereal ) > nat ).
thf(func_def_369,type,
sK270: ( nat > extended_ereal ) > real ).
thf(func_def_370,type,
sK271: nat > ( nat > extended_ereal ) > nat ).
thf(func_def_371,type,
sK272: ( nat > real ) > nat ).
thf(func_def_372,type,
sK273: ( nat > real ) > nat ).
thf(func_def_373,type,
sK274: ( nat > real ) > nat ).
thf(func_def_374,type,
sK275: ( nat > real ) > nat ).
thf(func_def_375,type,
sK276: ( a > extended_ereal ) > a > extended_ereal ).
thf(func_def_376,type,
sK277: ( a > extended_ereal ) > a > nat > extended_ereal ).
thf(func_def_377,type,
sK278: ( a > extended_ereal ) > a > nat > a ).
thf(func_def_378,type,
sK279: ( real > extended_ereal ) > real > extended_ereal ).
thf(func_def_379,type,
sK280: ( real > extended_ereal ) > real > nat > extended_ereal ).
thf(func_def_380,type,
sK281: ( real > extended_ereal ) > real > nat > real ).
thf(func_def_381,type,
sK282: ( nat > real ) > nat ).
thf(func_def_382,type,
sK283: ( nat > real ) > nat ).
thf(func_def_383,type,
sK284: ( nat > real ) > nat ).
thf(func_def_384,type,
sK285: ( nat > real ) > nat ).
thf(func_def_385,type,
sK286: ( nat > real ) > nat ).
thf(func_def_386,type,
sK287: ( nat > real ) > nat ).
thf(func_def_387,type,
sK288: ( nat > real ) > nat ).
thf(func_def_388,type,
sK289: ( nat > real ) > nat ).
thf(func_def_389,type,
sK290: ( nat > real ) > nat ).
thf(func_def_390,type,
sK291: ( nat > real ) > nat ).
thf(func_def_391,type,
sK292: ( nat > real ) > nat ).
thf(func_def_392,type,
sK293: ( nat > real ) > nat ).
thf(func_def_393,type,
sK294: ( nat > real ) > nat ).
thf(func_def_394,type,
sK295: ( nat > real ) > nat ).
thf(func_def_395,type,
sK296: ( nat > real ) > nat ).
thf(func_def_396,type,
sK297: ( nat > real ) > nat ).
thf(func_def_397,type,
sK298: ( nat > extended_ereal ) > nat ).
thf(func_def_398,type,
sK299: ( nat > extended_ereal ) > nat ).
thf(func_def_399,type,
sK300: ( nat > extended_ereal ) > nat ).
thf(func_def_400,type,
sK301: ( nat > extended_ereal ) > nat ).
thf(func_def_401,type,
sK302: ( nat > extended_ereal ) > nat ).
thf(func_def_402,type,
sK303: ( nat > extended_ereal ) > nat ).
thf(func_def_403,type,
sK304: ( nat > extended_ereal ) > nat ).
thf(func_def_404,type,
sK305: ( nat > extended_ereal ) > nat ).
thf(func_def_405,type,
sK306: ( nat > extended_ereal ) > nat ).
thf(func_def_406,type,
sK307: ( nat > extended_ereal ) > nat ).
thf(func_def_407,type,
sK308: ( nat > extended_ereal ) > nat ).
thf(func_def_408,type,
sK309: ( nat > extended_ereal ) > nat ).
thf(func_def_409,type,
sK310: ( nat > extended_ereal ) > nat ).
thf(func_def_410,type,
sK311: ( nat > extended_ereal ) > nat ).
thf(func_def_411,type,
sK312: ( nat > extended_ereal ) > nat ).
thf(func_def_412,type,
sK313: ( nat > extended_ereal ) > nat ).
thf(func_def_413,type,
sK314: ( nat > int ) > nat ).
thf(func_def_414,type,
sK315: ( nat > int ) > nat ).
thf(func_def_415,type,
sK316: ( nat > int ) > nat ).
thf(func_def_416,type,
sK317: ( nat > int ) > nat ).
thf(func_def_417,type,
sK318: ( nat > int ) > nat ).
thf(func_def_418,type,
sK319: ( nat > int ) > nat ).
thf(func_def_419,type,
sK320: ( nat > int ) > nat ).
thf(func_def_420,type,
sK321: ( nat > int ) > nat ).
thf(func_def_421,type,
sK322: ( nat > int ) > nat ).
thf(func_def_422,type,
sK323: ( nat > int ) > nat ).
thf(func_def_423,type,
sK324: ( nat > int ) > nat ).
thf(func_def_424,type,
sK325: ( nat > int ) > nat ).
thf(func_def_425,type,
sK326: ( nat > int ) > nat ).
thf(func_def_426,type,
sK327: ( nat > int ) > nat ).
thf(func_def_427,type,
sK328: ( nat > int ) > nat ).
thf(func_def_428,type,
sK329: ( nat > int ) > nat ).
thf(func_def_429,type,
sK330: ( nat > nat ) > nat ).
thf(func_def_430,type,
sK331: ( nat > nat ) > nat ).
thf(func_def_431,type,
sK332: ( nat > nat ) > nat ).
thf(func_def_432,type,
sK333: ( nat > nat ) > nat ).
thf(func_def_433,type,
sK334: ( nat > nat ) > nat ).
thf(func_def_434,type,
sK335: ( nat > nat ) > nat ).
thf(func_def_435,type,
sK336: ( nat > nat ) > nat ).
thf(func_def_436,type,
sK337: ( nat > nat ) > nat ).
thf(func_def_437,type,
sK338: ( nat > nat ) > nat ).
thf(func_def_438,type,
sK339: ( nat > nat ) > nat ).
thf(func_def_439,type,
sK340: ( nat > nat ) > nat ).
thf(func_def_440,type,
sK341: ( nat > nat ) > nat ).
thf(func_def_441,type,
sK342: ( nat > nat ) > nat ).
thf(func_def_442,type,
sK343: ( nat > nat ) > nat ).
thf(func_def_443,type,
sK344: ( nat > nat ) > nat ).
thf(func_def_444,type,
sK345: ( nat > nat ) > nat ).
thf(func_def_445,type,
sK346: ( real > int ) > real > int ).
thf(func_def_446,type,
sK347: ( real > int ) > real > nat > real ).
thf(func_def_447,type,
sK348: ( real > nat ) > real > nat ).
thf(func_def_448,type,
sK349: ( real > nat ) > real > nat > real ).
thf(func_def_449,type,
sK350: ( a > real ) > a > real ).
thf(func_def_450,type,
sK351: ( a > real ) > a > nat > a ).
thf(func_def_451,type,
sK352: ( a > extended_ereal ) > a > extended_ereal ).
thf(func_def_452,type,
sK353: ( a > extended_ereal ) > a > nat > a ).
thf(func_def_453,type,
sK354: ( a > int ) > a > int ).
thf(func_def_454,type,
sK355: ( a > int ) > a > nat > a ).
thf(func_def_455,type,
sK356: ( a > nat ) > a > nat ).
thf(func_def_456,type,
sK357: ( a > nat ) > a > nat > a ).
thf(func_def_457,type,
sK358: ( extended_ereal > real ) > extended_ereal > real ).
thf(func_def_458,type,
sK359: ( extended_ereal > real ) > extended_ereal > nat > extended_ereal ).
thf(func_def_459,type,
sK360: ( extended_ereal > extended_ereal ) > extended_ereal > extended_ereal ).
thf(func_def_460,type,
sK361: ( extended_ereal > extended_ereal ) > extended_ereal > nat > extended_ereal ).
thf(func_def_461,type,
sK362: ( extended_ereal > int ) > extended_ereal > int ).
thf(func_def_462,type,
sK363: ( extended_ereal > int ) > extended_ereal > nat > extended_ereal ).
thf(func_def_463,type,
sK364: ( extended_ereal > nat ) > extended_ereal > nat ).
thf(func_def_464,type,
sK365: ( extended_ereal > nat ) > extended_ereal > nat > extended_ereal ).
thf(func_def_465,type,
sK366: ( real > extended_ereal ) > real > extended_ereal ).
thf(func_def_466,type,
sK367: ( real > extended_ereal ) > real > nat > extended_ereal ).
thf(func_def_467,type,
sK368: ( real > extended_ereal ) > real > nat > real ).
thf(func_def_468,type,
sK369: ( real > int ) > real > int ).
thf(func_def_469,type,
sK370: ( real > int ) > real > nat > real ).
thf(func_def_470,type,
sK371: ( real > nat ) > real > nat ).
thf(func_def_471,type,
sK372: ( real > nat ) > real > nat > real ).
thf(func_def_472,type,
sK373: ( a > real ) > a > real ).
thf(func_def_473,type,
sK374: ( a > real ) > a > nat > a ).
thf(func_def_474,type,
sK375: ( a > int ) > a > int ).
thf(func_def_475,type,
sK376: ( a > int ) > a > nat > a ).
thf(func_def_476,type,
sK377: ( a > nat ) > a > nat ).
thf(func_def_477,type,
sK378: ( a > nat ) > a > nat > a ).
thf(func_def_478,type,
sK379: ( extended_ereal > real ) > extended_ereal > real ).
thf(func_def_479,type,
sK380: ( extended_ereal > real ) > extended_ereal > nat > extended_ereal ).
thf(func_def_480,type,
sK381: ( extended_ereal > extended_ereal ) > extended_ereal > extended_ereal ).
thf(func_def_481,type,
sK382: ( extended_ereal > extended_ereal ) > extended_ereal > nat > extended_ereal ).
thf(func_def_482,type,
sK383: ( extended_ereal > int ) > extended_ereal > int ).
thf(func_def_483,type,
sK384: ( extended_ereal > int ) > extended_ereal > nat > extended_ereal ).
thf(func_def_484,type,
sK385: ( extended_ereal > nat ) > extended_ereal > nat ).
thf(func_def_485,type,
sK386: ( extended_ereal > nat ) > extended_ereal > nat > extended_ereal ).
thf(func_def_486,type,
sK387: ( a > extended_ereal ) > a > extended_ereal ).
thf(func_def_487,type,
sK388: ( a > extended_ereal ) > a > nat > extended_ereal ).
thf(func_def_488,type,
sK389: ( a > extended_ereal ) > a > nat > a ).
thf(func_def_489,type,
sK390: ( real > extended_ereal ) > real > extended_ereal ).
thf(func_def_490,type,
sK391: ( real > extended_ereal ) > real > nat > extended_ereal ).
thf(func_def_491,type,
sK392: ( real > extended_ereal ) > real > nat > real ).
thf(func_def_492,type,
sK393: ( nat > a ) > ( nat > extended_ereal ) > nat ).
thf(func_def_493,type,
sK394: nat > nat ).
thf(func_def_494,type,
sK395: a > nat ).
thf(func_def_495,type,
sK396: nat > nat ).
thf(func_def_496,type,
sK397: a > nat ).
thf(func_def_497,type,
sK398: nat > nat ).
thf(func_def_498,type,
sK399: a > nat ).
thf(func_def_499,type,
sK400: a > nat ).
thf(func_def_500,type,
sK401: nat > nat ).
thf(func_def_501,type,
sK402: a > nat ).
thf(func_def_502,type,
sK403: a > nat ).
thf(func_def_503,type,
sK404: a > nat ).
thf(func_def_504,type,
sK405: nat > nat ).
thf(func_def_505,type,
sK406: a > nat ).
thf(f2,axiom,
filter1531173832_ereal @ ( comp_a1112243075al_nat @ f @ x ) @ ( topolo2140997059_ereal @ a2 ) @ at_top_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_x__def_I2_J) ).
thf(f5,axiom,
! [X0: nat > extended_ereal,X1: extended_ereal,X2: filter_nat] :
( ( filter1531173832_ereal @ X0 @ ( topolo2140997059_ereal @ X1 ) @ X2 )
=> ( filter1531173832_ereal
@ ^ [X3: nat] : ( uminus1208298309_ereal @ ( X0 @ X3 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X1 ) )
@ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_tendsto__uminus__ereal) ).
thf(f37,axiom,
( comp_a1112243075al_nat
= ( ^ [X0: a > extended_ereal,X1: nat > a,X2: nat] : ( X0 @ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_comp__apply) ).
thf(f356,conjecture,
( filter1531173832_ereal
@ ^ [X0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ X0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f357,negated_conjecture,
~ ( filter1531173832_ereal
@ ^ [X0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ X0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f360,plain,
filter1531173832_ereal @ ( comp_a1112243075al_nat @ f @ x ) @ ( topolo2140997059_ereal @ a2 ) @ at_top_nat,
inference(rectify,[],[f2]) ).
thf(f361,plain,
( ( filter1531173832_ereal @ ( comp_a1112243075al_nat @ f @ x ) @ ( topolo2140997059_ereal @ a2 ) @ at_top_nat )
= $true ),
inference(fool_elimination,[],[f360]) ).
thf(f366,plain,
! [X0: nat > extended_ereal,X1: extended_ereal,X2: filter_nat] :
( ( filter1531173832_ereal @ X0 @ ( topolo2140997059_ereal @ X1 ) @ X2 )
=> ( filter1531173832_ereal
@ ^ [X3: nat] : ( uminus1208298309_ereal @ ( X0 @ X3 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X1 ) )
@ X2 ) ),
inference(rectify,[],[f5]) ).
thf(f367,plain,
! [X0: nat > extended_ereal,X1: extended_ereal,X2: filter_nat] :
( ( ( filter1531173832_ereal @ X0 @ ( topolo2140997059_ereal @ X1 ) @ X2 )
= $true )
=> ( $true
= ( filter1531173832_ereal
@ ^ [Y0: nat] : ( uminus1208298309_ereal @ ( X0 @ Y0 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X1 ) )
@ X2 ) ) ),
inference(fool_elimination,[],[f366]) ).
thf(f422,plain,
( comp_a1112243075al_nat
= ( ^ [Y0: a > extended_ereal,Y1: nat > a,Y2: nat] : ( Y0 @ ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f967,plain,
~ ( filter1531173832_ereal
@ ^ [X0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ X0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ),
inference(rectify,[],[f357]) ).
thf(f968,plain,
( $true
!= ( filter1531173832_ereal
@ ^ [Y0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ Y0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ) ),
inference(fool_elimination,[],[f967]) ).
thf(f987,plain,
( $true
!= ( filter1531173832_ereal
@ ^ [Y0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ Y0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ) ),
inference(flattening,[],[f968]) ).
thf(f989,plain,
! [X0: nat > extended_ereal,X1: extended_ereal,X2: filter_nat] :
( ( $true
= ( filter1531173832_ereal
@ ^ [Y0: nat] : ( uminus1208298309_ereal @ ( X0 @ Y0 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X1 ) )
@ X2 ) )
| ( ( filter1531173832_ereal @ X0 @ ( topolo2140997059_ereal @ X1 ) @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f367]) ).
thf(f1661,plain,
( ( filter1531173832_ereal @ ( comp_a1112243075al_nat @ f @ x ) @ ( topolo2140997059_ereal @ a2 ) @ at_top_nat )
= $true ),
inference(cnf_transformation,[],[f361]) ).
thf(f1664,plain,
! [X2: filter_nat,X0: nat > extended_ereal,X1: extended_ereal] :
( ( ( filter1531173832_ereal @ X0 @ ( topolo2140997059_ereal @ X1 ) @ X2 )
!= $true )
| ( $true
= ( filter1531173832_ereal
@ ^ [Y0: nat] : ( uminus1208298309_ereal @ ( X0 @ Y0 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X1 ) )
@ X2 ) ) ),
inference(cnf_transformation,[],[f989]) ).
thf(f1696,plain,
( comp_a1112243075al_nat
= ( ^ [Y0: a > extended_ereal,Y1: nat > a,Y2: nat] : ( Y0 @ ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f422]) ).
thf(f2292,plain,
( $true
!= ( filter1531173832_ereal
@ ^ [Y0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ Y0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ) ),
inference(cnf_transformation,[],[f987]) ).
thf(f2306,plain,
( $true
= ( filter1531173832_ereal
@ ( ^ [Y0: a > extended_ereal,Y1: nat > a,Y2: nat] : ( Y0 @ ( Y1 @ Y2 ) )
@ f
@ x )
@ ( topolo2140997059_ereal @ a2 )
@ at_top_nat ) ),
inference(definition_unfolding,[],[f1661,f1696]) ).
thf(f3746,plain,
( $true
= ( filter1531173832_ereal
@ ^ [Y0: nat] : ( f @ ( x @ Y0 ) )
@ ( topolo2140997059_ereal @ a2 )
@ at_top_nat ) ),
inference(beta-eta_normalization,[],[f2306]) ).
thf(f6794,plain,
( ( $true != $true )
| ( $true
= ( filter1531173832_ereal
@ ^ [Y0: nat] :
( uminus1208298309_ereal
@ ( ^ [Y1: nat] : ( f @ ( x @ Y1 ) )
@ Y0 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ) ) ),
inference(constrained_superposition,[],[f1664,f3746]) ).
thf(f6798,plain,
( $true
= ( filter1531173832_ereal
@ ^ [Y0: nat] :
( uminus1208298309_ereal
@ ( ^ [Y1: nat] : ( f @ ( x @ Y1 ) )
@ Y0 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ) ),
inference(trivial_inequality_removal,[],[f6794]) ).
thf(f6799,plain,
( $true
= ( filter1531173832_ereal
@ ^ [Y0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ Y0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ) ),
inference(beta-eta_normalization,[],[f6798]) ).
thf(f6806,plain,
$false,
inference(forward_subsumption_resolution,[],[f6799,f2292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP112^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n007.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 19:53:11 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.38/0.64 % (3845653)Will run a generic schedule for satisfiability detection.
% 2.38/0.64 % (3845658)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2497773777_2999 on theBenchmark for (2999ds/0Mi)
% 2.38/0.64 % (3845659)% WARNING: option uhcvi not known.
% 2.38/0.64 % (3845659)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=74106983:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.38/0.64 % (3845663)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3687966499:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.38/0.64 % (3845660)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3157310444:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.38/0.64 % (3845661)dis+10_1_sil=32000:sp=arity:random_seed=920262297:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.38/0.64 % (3845664)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3520180429:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.38/0.64 % (3845662)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1983352165:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.38/0.64 % (3845659)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.64 % Exception at run slice level
% 2.38/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.64 % (3845672)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1367160723:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.38/0.64 % (3845663)Instruction limit reached!
% 2.38/0.64 % (3845663)------------------------------
% 2.38/0.64 % (3845663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3845663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3845663)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3845663)Termination reason: Instruction limit
% 2.38/0.64 % (3845663)Termination phase: Property scanning
% 2.38/0.64 % (3845663)Time elapsed: 0.056 s
% 2.38/0.64 % (3845663)Peak memory usage: 12 MB
% 2.38/0.64 % (3845663)Instructions burned: 132 (million)
% 2.38/0.64 % (3845662)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.64 % (3845659)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.38/0.64 % Exception at run slice level
% 2.38/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.64 % (3845674)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2974661977:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.38/0.64 % (3845675)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1596101190:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.38/0.64 % (3845661)Instruction limit reached!
% 2.38/0.64 % (3845661)------------------------------
% 2.38/0.64 % (3845661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3845661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3845661)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3845661)Termination reason: Instruction limit
% 2.38/0.64 % (3845661)Termination phase: Property scanning
% 2.38/0.64 % (3845661)Time elapsed: 0.085 s
% 2.38/0.64 % (3845661)Peak memory usage: 12 MB
% 2.38/0.64 % (3845661)Instructions burned: 103 (million)
% 2.38/0.64 % (3845675)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.64 % (3845662)Instruction limit reached!
% 2.38/0.64 % (3845662)------------------------------
% 2.38/0.64 % (3845662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3845662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3845662)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3845662)Termination reason: Instruction limit
% 2.38/0.64 % (3845662)Termination phase: Function definition elimination
% 2.38/0.64 % (3845662)Time elapsed: 0.092 s
% 2.38/0.64 % (3845662)Peak memory usage: 12 MB
% 2.38/0.64 % (3845662)Instructions burned: 116 (million)
% 2.38/0.64 % (3845675)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.38/0.64 % (3845678)ott-21_1_sil=16000:fs=off:random_seed=257901105:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.38/0.64 % (3845674)Instruction limit reached!
% 2.38/0.64 % (3845674)------------------------------
% 2.38/0.64 % (3845674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3845674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3845674)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3845674)Termination reason: Instruction limit
% 2.38/0.64 % (3845674)Termination phase: Property scanning
% 2.38/0.64 % (3845674)Time elapsed: 0.056 s
% 2.38/0.64 % (3845674)Peak memory usage: 12 MB
% 2.38/0.64 % (3845674)Instructions burned: 132 (million)
% 2.38/0.64 % (3845664)Instruction limit reached!
% 2.38/0.64 % (3845664)------------------------------
% 2.38/0.64 % (3845664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3845664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3845664)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3845664)Termination reason: Instruction limit
% 2.38/0.64 % (3845664)Termination phase: Property scanning
% 2.38/0.64 % (3845664)Time elapsed: 0.125 s
% 2.38/0.64 % (3845664)Peak memory usage: 12 MB
% 2.38/0.64 % (3845664)Instructions burned: 159 (million)
% 2.38/0.64 % (3845679)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=423778622:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.38/0.64 % (3845681)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=697086391:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.38/0.64 % (3845682)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3755640950:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.38/0.64 % (3845675)Instruction limit reached!
% 2.38/0.64 % (3845675)------------------------------
% 2.38/0.64 % (3845675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3845675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3845675)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3845675)Termination reason: Instruction limit
% 2.38/0.64 % (3845675)Termination phase: Saturation
% 2.38/0.64 % (3845675)Time elapsed: 0.163 s
% 2.38/0.64 % (3845675)Peak memory usage: 16 MB
% 2.38/0.64 % (3845675)Instructions burned: 685 (million)
% 2.38/0.64 % (3845686)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4075044528:i=889:ins=1_2996 on theBenchmark for (2996ds/889Mi)
% 2.38/0.64 % Exception at run slice level
% 2.38/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.64 % (3845678)Instruction limit reached!
% 2.38/0.64 % (3845678)------------------------------
% 2.38/0.64 % (3845678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3845678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3845678)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3845678)Termination reason: Instruction limit
% 2.38/0.64 % (3845678)Termination phase: Saturation
% 2.38/0.64 % (3845678)Time elapsed: 0.147 s
% 2.38/0.64 % (3845678)Peak memory usage: 13 MB
% 2.38/0.64 % (3845678)Instructions burned: 180 (million)
% 2.38/0.64 % Exception at run slice level
% 2.38/0.64 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.64 % (3845689)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=6442699:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 2.38/0.64 % (3845690)fmb+10_1_sil=64000:random_seed=4223578340:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.38/0.64 % (3845688)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=776198922:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 2.38/0.64 % (3845688)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.64 % (3845690)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.38/0.64 % (3845689)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.64 % (3845659) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3845653-3845659"...
% 2.38/0.64 % (3845659)...printing done.
% 2.38/0.64 % (3845659)Refutation found. Thanks to Tanya!
% 2.38/0.64 % SZS status Theorem for theBenchmark
% 2.38/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.38/0.64 % (3845659)------------------------------
% 2.38/0.64 % (3845659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3845659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3845659)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3845659)Termination reason: Refutation
% 2.38/0.64 % (3845659)Time elapsed: 0.373 s
% 2.38/0.64 % (3845659)Peak memory usage: 18 MB
% 2.38/0.64 % (3845659)Instructions burned: 780 (million)
% 2.38/0.64 % (3845653)Success in time 0.431 s
% 2.38/0.64 % Vampire exiting
%------------------------------------------------------------------------------