%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP117^1 : 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 : n004.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 08:10:45 AM UTC 2026
% Result : Theorem 0.78s 0.40s
% Output : Refutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 36 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 460 ( 11 ~; 0 |; 20 &; 429 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 19 ( 18 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 271 ( 269 usr; 21 con; 0-4 aty)
% Number of variables : 102 ( 89 ^; 13 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sigma_1422848389real_n: $tType ).
thf(type_def_6,type,
set_Si1125517487real_n: $tType ).
thf(type_def_7,type,
set_se820660888real_n: $tType ).
thf(type_def_8,type,
sigma_1466784463real_n: $tType ).
thf(type_def_9,type,
set_se2111327970real_n: $tType ).
thf(type_def_10,type,
set_se944069346_int_n: $tType ).
thf(type_def_11,type,
set_Fi1058188332real_n: $tType ).
thf(type_def_12,type,
set_Fi160064172_int_n: $tType ).
thf(type_def_13,type,
finite1489363574real_n: $tType ).
thf(type_def_14,type,
finite964658038_int_n: $tType ).
thf(type_def_15,type,
set_Ex113815278nnreal: $tType ).
thf(type_def_16,type,
set_set_nat: $tType ).
thf(type_def_17,type,
extend1728876344nnreal: $tType ).
thf(type_def_18,type,
sigma_measure_o: $tType ).
thf(type_def_19,type,
set_set_o: $tType ).
thf(type_def_20,type,
set_nat: $tType ).
thf(type_def_21,type,
set_o: $tType ).
thf(type_def_22,type,
nat: $tType ).
thf(type_def_23,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
complete_Sup_Sup_o: set_o > $o ).
thf(func_def_1,type,
comple1413366923nnreal: set_Ex113815278nnreal > extend1728876344nnreal ).
thf(func_def_2,type,
comple2042271945real_n: set_Fi1058188332real_n > finite1489363574real_n ).
thf(func_def_3,type,
comple1665300069_set_o: set_set_o > set_o ).
thf(func_def_4,type,
comple970917503_int_n: set_se944069346_int_n > set_Fi160064172_int_n ).
thf(func_def_5,type,
comple825005695real_n: set_se2111327970real_n > set_Fi1058188332real_n ).
thf(func_def_6,type,
comple1682161881et_nat: set_set_nat > set_nat ).
thf(func_def_7,type,
comple1917283637real_n: set_se820660888real_n > set_se2111327970real_n ).
thf(func_def_8,type,
comple488165692real_n: set_Si1125517487real_n > sigma_1466784463real_n ).
thf(func_def_9,type,
comple230862828real_n: sigma_1466784463real_n > sigma_1466784463real_n ).
thf(func_def_10,type,
counta1142393929_int_n: set_Fi160064172_int_n > nat > finite964658038_int_n ).
thf(func_def_11,type,
minus_1196255695_int_n: finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).
thf(func_def_12,type,
minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(func_def_13,type,
minus_1686442501real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(func_def_14,type,
one_on705384445nnreal: extend1728876344nnreal ).
thf(func_def_15,type,
one_on1253059131real_n: finite1489363574real_n ).
thf(func_def_16,type,
plus_p1763960001nnreal: extend1728876344nnreal > extend1728876344nnreal > extend1728876344nnreal ).
thf(func_def_17,type,
plus_p1654784127_int_n: finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).
thf(func_def_18,type,
plus_p585657087real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
thf(func_def_19,type,
zero_z1963244097nnreal: extend1728876344nnreal ).
thf(func_def_20,type,
zero_z200130687real_n: finite1489363574real_n ).
thf(func_def_21,type,
inf_inf_set_o: set_o > set_o > set_o ).
thf(func_def_22,type,
inf_in1108485182_int_n: set_Fi160064172_int_n > set_Fi160064172_int_n > set_Fi160064172_int_n ).
thf(func_def_23,type,
inf_in1974387902real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(func_def_24,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_25,type,
inf_in632889204real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).
thf(func_def_26,type,
lebesg260170249real_n: sigma_1466784463real_n ).
thf(func_def_27,type,
measure_null_sets_o: sigma_measure_o > set_set_o ).
thf(func_def_28,type,
measur1402256771real_n: sigma_1466784463real_n > set_se2111327970real_n ).
thf(func_def_29,type,
measur2126959417real_n: sigma_1422848389real_n > set_se820660888real_n ).
thf(func_def_30,type,
minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).
thf(func_def_31,type,
ord_le2133614988nnreal: extend1728876344nnreal > extend1728876344nnreal > $o ).
thf(func_def_32,type,
top_to287930409nt_n_o: finite964658038_int_n > $o ).
thf(func_def_33,type,
top_top_nat_o: nat > $o ).
thf(func_def_34,type,
top_top_o: $o ).
thf(func_def_35,type,
top_to1845833192nnreal: extend1728876344nnreal ).
thf(func_def_36,type,
top_top_set_o: set_o ).
thf(func_def_37,type,
top_to131672412_int_n: set_Fi160064172_int_n ).
thf(func_def_38,type,
top_to1292442332real_n: set_Fi1058188332real_n ).
thf(func_def_39,type,
top_top_set_nat: set_nat ).
thf(func_def_40,type,
top_to1587634578_int_n: set_se944069346_int_n ).
thf(func_def_41,type,
top_to20708754real_n: set_se2111327970real_n ).
thf(func_def_42,type,
top_top_set_set_nat: set_set_nat ).
thf(func_def_43,type,
sums_E1192373732nnreal: ( nat > extend1728876344nnreal ) > extend1728876344nnreal > $o ).
thf(func_def_44,type,
collect_o: ( $o > $o ) > set_o ).
thf(func_def_45,type,
collec1941932235_int_n: ( finite964658038_int_n > $o ) > set_Fi160064172_int_n ).
thf(func_def_46,type,
collec321817931real_n: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n ).
thf(func_def_47,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_48,type,
collec452821761real_n: ( set_Fi1058188332real_n > $o ) > set_se2111327970real_n ).
thf(func_def_49,type,
image_o_o: ( $o > $o ) > set_o > set_o ).
thf(func_def_50,type,
image_o_set_o: ( $o > set_o ) > set_o > set_set_o ).
thf(func_def_51,type,
image_1759008383real_n: ( $o > set_Fi1058188332real_n ) > set_o > set_se2111327970real_n ).
thf(func_def_52,type,
image_452144437real_n: ( $o > set_se2111327970real_n ) > set_o > set_se820660888real_n ).
thf(func_def_53,type,
image_1599934780real_n: ( $o > sigma_1466784463real_n ) > set_o > set_Si1125517487real_n ).
thf(func_def_54,type,
image_2066995319nnreal: ( extend1728876344nnreal > extend1728876344nnreal ) > set_Ex113815278nnreal > set_Ex113815278nnreal ).
thf(func_def_55,type,
image_216309723nt_n_o: ( finite964658038_int_n > $o ) > set_Fi160064172_int_n > set_o ).
thf(func_def_56,type,
image_1278151539_int_n: ( finite964658038_int_n > finite964658038_int_n ) > set_Fi160064172_int_n > set_Fi160064172_int_n ).
thf(func_def_57,type,
image_2058828787real_n: ( finite964658038_int_n > finite1489363574real_n ) > set_Fi160064172_int_n > set_Fi1058188332real_n ).
thf(func_def_58,type,
image_497739341_n_nat: ( finite964658038_int_n > nat ) > set_Fi160064172_int_n > set_nat ).
thf(func_def_59,type,
image_1819506345_int_n: ( finite964658038_int_n > set_Fi160064172_int_n ) > set_Fi160064172_int_n > set_se944069346_int_n ).
thf(func_def_60,type,
image_355963305real_n: ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi160064172_int_n > set_se2111327970real_n ).
thf(func_def_61,type,
image_1085873667et_nat: ( finite964658038_int_n > set_nat ) > set_Fi160064172_int_n > set_set_nat ).
thf(func_def_62,type,
image_439535603real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(func_def_63,type,
image_545463721real_n: ( finite1489363574real_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n > set_se2111327970real_n ).
thf(func_def_64,type,
image_nat_o: ( nat > $o ) > set_nat > set_o ).
thf(func_def_65,type,
image_1961920973_int_n: ( nat > finite964658038_int_n ) > set_nat > set_Fi160064172_int_n ).
thf(func_def_66,type,
image_183184717real_n: ( nat > finite1489363574real_n ) > set_nat > set_Fi1058188332real_n ).
thf(func_def_67,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_68,type,
image_968789251_int_n: ( nat > set_Fi160064172_int_n ) > set_nat > set_se944069346_int_n ).
thf(func_def_69,type,
image_1856576259real_n: ( nat > set_Fi1058188332real_n ) > set_nat > set_se2111327970real_n ).
thf(func_def_70,type,
image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
thf(func_def_71,type,
image_set_o_o: ( set_o > $o ) > set_set_o > set_o ).
thf(func_def_72,type,
image_792439519real_n: ( set_Fi160064172_int_n > set_Fi1058188332real_n ) > set_se944069346_int_n > set_se2111327970real_n ).
thf(func_def_73,type,
image_1054146965real_n: ( set_Fi160064172_int_n > set_se2111327970real_n ) > set_se944069346_int_n > set_se820660888real_n ).
thf(func_def_74,type,
image_1648361637al_n_o: ( set_Fi1058188332real_n > $o ) > set_se2111327970real_n > set_o ).
thf(func_def_75,type,
image_1687589765_set_o: ( set_Fi1058188332real_n > set_o ) > set_se2111327970real_n > set_set_o ).
thf(func_def_76,type,
image_1661509983real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_se2111327970real_n ).
thf(func_def_77,type,
image_797440021real_n: ( set_Fi1058188332real_n > set_se2111327970real_n ) > set_se2111327970real_n > set_se820660888real_n ).
thf(func_def_78,type,
image_987430492real_n: ( set_Fi1058188332real_n > sigma_1466784463real_n ) > set_se2111327970real_n > set_Si1125517487real_n ).
thf(func_def_79,type,
image_933134521real_n: ( set_nat > set_Fi1058188332real_n ) > set_set_nat > set_se2111327970real_n ).
thf(func_def_80,type,
image_1587769199real_n: ( set_nat > set_se2111327970real_n ) > set_set_nat > set_se820660888real_n ).
thf(func_def_81,type,
image_1681970287al_n_o: ( set_se2111327970real_n > $o ) > set_se820660888real_n > set_o ).
thf(func_def_82,type,
image_1298280374real_n: ( sigma_1466784463real_n > set_Fi1058188332real_n ) > set_Si1125517487real_n > set_se2111327970real_n ).
thf(func_def_83,type,
vimage_o_o: ( $o > $o ) > set_o > set_o ).
thf(func_def_84,type,
vimage961837641real_n: ( $o > set_Fi1058188332real_n ) > set_se2111327970real_n > set_o ).
thf(func_def_85,type,
vimage1122713129_int_n: ( finite964658038_int_n > finite964658038_int_n ) > set_Fi160064172_int_n > set_Fi160064172_int_n ).
thf(func_def_86,type,
vimage1276736425real_n: ( finite964658038_int_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi160064172_int_n ).
thf(func_def_87,type,
vimage1398021123_n_nat: ( finite964658038_int_n > nat ) > set_nat > set_Fi160064172_int_n ).
thf(func_def_88,type,
vimage464515423real_n: ( finite964658038_int_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_Fi160064172_int_n ).
thf(func_def_89,type,
vimage1233683625real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(func_def_90,type,
vimage714719107_int_n: ( nat > finite964658038_int_n ) > set_Fi160064172_int_n > set_nat ).
thf(func_def_91,type,
vimage1860757507real_n: ( nat > finite1489363574real_n ) > set_Fi1058188332real_n > set_nat ).
thf(func_def_92,type,
vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_93,type,
vimage3210681real_n: ( nat > set_Fi1058188332real_n ) > set_se2111327970real_n > set_nat ).
thf(func_def_94,type,
vimage851190895al_n_o: ( set_Fi1058188332real_n > $o ) > set_o > set_se2111327970real_n ).
thf(func_def_95,type,
vimage784510485real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_se2111327970real_n ).
thf(func_def_96,type,
sigma_1536574303real_n: sigma_1466784463real_n > set_Fi1058188332real_n > extend1728876344nnreal ).
thf(func_def_97,type,
sigma_1235138647real_n: sigma_1466784463real_n > set_se2111327970real_n ).
thf(func_def_98,type,
sigma_space_o: sigma_measure_o > set_o ).
thf(func_def_99,type,
sigma_476185326real_n: sigma_1466784463real_n > set_Fi1058188332real_n ).
thf(func_def_100,type,
sigma_607186084real_n: sigma_1422848389real_n > set_se2111327970real_n ).
thf(func_def_101,type,
member_o: $o > set_o > $o ).
thf(func_def_102,type,
member1217042383nnreal: extend1728876344nnreal > set_Ex113815278nnreal > $o ).
thf(func_def_103,type,
member27055245_int_n: finite964658038_int_n > set_Fi160064172_int_n > $o ).
thf(func_def_104,type,
member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ).
thf(func_def_105,type,
member_nat: nat > set_nat > $o ).
thf(func_def_106,type,
member_set_o: set_o > set_set_o > $o ).
thf(func_def_107,type,
member223413699real_n: set_Fi1058188332real_n > set_se2111327970real_n > $o ).
thf(func_def_108,type,
member1475136633real_n: set_se2111327970real_n > set_se820660888real_n > $o ).
thf(func_def_109,type,
member1000184real_n: sigma_1466784463real_n > set_Si1125517487real_n > $o ).
thf(func_def_110,type,
r: finite964658038_int_n > set_Fi1058188332real_n ).
thf(func_def_111,type,
s: set_Fi1058188332real_n ).
thf(func_def_112,type,
t: finite964658038_int_n > set_Fi1058188332real_n ).
thf(func_def_113,type,
t2: finite964658038_int_n > set_Fi1058188332real_n ).
thf(func_def_114,type,
f: nat > finite964658038_int_n ).
thf(func_def_118,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_119,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_120,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_121,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_122,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_123,type,
vIMP: $o > $o > $o ).
thf(func_def_124,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_125,type,
vAND: $o > $o > $o ).
thf(func_def_126,type,
vOR: $o > $o > $o ).
thf(func_def_127,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
vNOT: $o > $o ).
thf(func_def_129,type,
sK0: sigma_1466784463real_n > ( nat > set_Fi1058188332real_n ) > nat ).
thf(func_def_130,type,
sK1: sigma_1466784463real_n > ( nat > set_Fi1058188332real_n ) > nat ).
thf(func_def_131,type,
sK2: sigma_1466784463real_n > ( nat > set_Fi1058188332real_n ) > nat ).
thf(func_def_132,type,
sK3: sigma_1466784463real_n > ( nat > set_Fi1058188332real_n ) > nat ).
thf(func_def_133,type,
sK4: sigma_1466784463real_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > finite964658038_int_n ).
thf(func_def_134,type,
sK5: set_Fi1058188332real_n > ( set_Fi1058188332real_n > sigma_1466784463real_n ) > set_se2111327970real_n > set_Fi1058188332real_n ).
thf(func_def_135,type,
sK6: set_Fi1058188332real_n > ( $o > sigma_1466784463real_n ) > set_o > $o ).
thf(func_def_136,type,
sK7: set_Fi1058188332real_n > set_Si1125517487real_n > sigma_1466784463real_n ).
thf(func_def_137,type,
sK8: ( set_Fi1058188332real_n > sigma_1466784463real_n ) > ( set_Fi1058188332real_n > sigma_1466784463real_n ) > set_se2111327970real_n > set_Fi1058188332real_n ).
thf(func_def_138,type,
sK9: ( $o > sigma_1466784463real_n ) > ( $o > sigma_1466784463real_n ) > set_o > $o ).
thf(func_def_139,type,
sK10: ( nat > set_Fi1058188332real_n ) > ( nat > set_Fi1058188332real_n ) > set_nat > nat ).
thf(func_def_140,type,
sK11: ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > finite1489363574real_n ).
thf(func_def_141,type,
sK12: ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi160064172_int_n > finite964658038_int_n ).
thf(func_def_142,type,
sK13: ( nat > set_Fi1058188332real_n ) > ( nat > set_Fi1058188332real_n ) > set_nat > nat ).
thf(func_def_143,type,
sK14: ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > finite1489363574real_n ).
thf(func_def_144,type,
sK15: ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi160064172_int_n > finite964658038_int_n ).
thf(func_def_145,type,
sK16: ( set_Fi1058188332real_n > $o ) > set_nat > ( nat > set_Fi1058188332real_n ) > set_Fi1058188332real_n ).
thf(func_def_146,type,
sK17: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).
thf(func_def_147,type,
sK18: ( set_Fi1058188332real_n > $o ) > set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n ).
thf(func_def_148,type,
sK19: ( nat > set_Fi1058188332real_n ) > ( nat > set_Fi1058188332real_n ) > set_nat > nat ).
thf(func_def_149,type,
sK20: ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > finite1489363574real_n ).
thf(func_def_150,type,
sK21: ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi160064172_int_n > finite964658038_int_n ).
thf(func_def_151,type,
sK22: ( set_Fi1058188332real_n > $o ) > set_nat > ( nat > set_Fi1058188332real_n ) > nat ).
thf(func_def_152,type,
sK23: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).
thf(func_def_153,type,
sK24: ( set_Fi1058188332real_n > $o ) > set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > finite964658038_int_n ).
thf(func_def_154,type,
sK25: set_Fi1058188332real_n ).
thf(func_def_155,type,
sK26: $o ).
thf(func_def_156,type,
sK27: nat ).
thf(func_def_157,type,
sK28: finite964658038_int_n ).
thf(func_def_158,type,
sK29: set_se2111327970real_n > set_Fi1058188332real_n ).
thf(func_def_159,type,
sK30: set_o > $o ).
thf(func_def_160,type,
sK31: set_nat > nat ).
thf(func_def_161,type,
sK32: set_Fi160064172_int_n > finite964658038_int_n ).
thf(func_def_162,type,
sK33: set_se820660888real_n > set_Fi1058188332real_n > set_se2111327970real_n ).
thf(func_def_163,type,
sK34: set_set_o > $o > set_o ).
thf(func_def_164,type,
sK35: set_se2111327970real_n > finite1489363574real_n > set_Fi1058188332real_n ).
thf(func_def_165,type,
sK36: ( finite1489363574real_n > $o ) > ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_166,type,
sK37: set_Fi1058188332real_n > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ).
thf(func_def_167,type,
sK38: set_nat > ( nat > set_Fi1058188332real_n ) > set_Fi1058188332real_n > nat ).
thf(func_def_168,type,
sK39: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n > finite964658038_int_n ).
thf(func_def_169,type,
sK40: set_se2111327970real_n > ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(func_def_170,type,
sK41: set_o > ( $o > set_Fi1058188332real_n ) > set_Fi1058188332real_n > $o ).
thf(func_def_171,type,
sK42: set_se2111327970real_n > ( set_Fi1058188332real_n > $o ) > $o > set_Fi1058188332real_n ).
thf(func_def_172,type,
sK43: set_o > ( $o > $o ) > $o > $o ).
thf(func_def_173,type,
sK44: ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).
thf(func_def_174,type,
sK45: ( set_Fi1058188332real_n > nat ) > ( nat > set_Fi1058188332real_n ) > set_Fi1058188332real_n ).
thf(func_def_175,type,
sK46: ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_176,type,
sK47: ( finite964658038_int_n > nat ) > ( nat > finite964658038_int_n ) > finite964658038_int_n ).
thf(func_def_177,type,
sK48: ( set_Fi1058188332real_n > finite964658038_int_n ) > ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n ).
thf(func_def_178,type,
sK49: ( nat > finite964658038_int_n ) > ( finite964658038_int_n > nat ) > nat ).
thf(func_def_179,type,
sK50: ( finite964658038_int_n > finite964658038_int_n ) > ( finite964658038_int_n > finite964658038_int_n ) > finite964658038_int_n ).
thf(func_def_180,type,
sK51: finite1489363574real_n > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).
thf(func_def_181,type,
sK52: set_Fi1058188332real_n > ( nat > set_Fi1058188332real_n ) > nat ).
thf(func_def_182,type,
sK53: nat > ( nat > nat ) > nat ).
thf(func_def_183,type,
sK54: finite964658038_int_n > ( nat > finite964658038_int_n ) > nat ).
thf(func_def_184,type,
sK55: set_Fi1058188332real_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > finite964658038_int_n ).
thf(func_def_185,type,
sK56: nat > ( finite964658038_int_n > nat ) > finite964658038_int_n ).
thf(func_def_186,type,
sK57: finite964658038_int_n > ( finite964658038_int_n > finite964658038_int_n ) > finite964658038_int_n ).
thf(func_def_187,type,
sK58: finite1489363574real_n > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).
thf(func_def_188,type,
sK59: set_Fi1058188332real_n > ( nat > set_Fi1058188332real_n ) > nat ).
thf(func_def_189,type,
sK60: nat > ( nat > nat ) > nat ).
thf(func_def_190,type,
sK61: finite964658038_int_n > ( nat > finite964658038_int_n ) > nat ).
thf(func_def_191,type,
sK62: set_Fi1058188332real_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > finite964658038_int_n ).
thf(func_def_192,type,
sK63: nat > ( finite964658038_int_n > nat ) > finite964658038_int_n ).
thf(func_def_193,type,
sK64: finite964658038_int_n > ( finite964658038_int_n > finite964658038_int_n ) > finite964658038_int_n ).
thf(func_def_194,type,
sK65: ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > finite1489363574real_n ).
thf(func_def_195,type,
sK66: ( nat > set_Fi1058188332real_n ) > ( nat > set_Fi1058188332real_n ) > set_nat > nat ).
thf(func_def_196,type,
sK67: ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi160064172_int_n > finite964658038_int_n ).
thf(func_def_197,type,
sK68: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_Fi1058188332real_n ).
thf(func_def_198,type,
sK69: ( $o > set_Fi1058188332real_n ) > ( $o > set_Fi1058188332real_n ) > set_o > $o ).
thf(func_def_199,type,
sK70: ( set_Fi1058188332real_n > $o ) > ( set_Fi1058188332real_n > $o ) > set_se2111327970real_n > set_Fi1058188332real_n ).
thf(func_def_200,type,
sK71: ( $o > $o ) > ( $o > $o ) > set_o > $o ).
thf(func_def_201,type,
sK72: ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > finite1489363574real_n ).
thf(func_def_202,type,
sK73: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ).
thf(func_def_203,type,
sK74: ( nat > set_Fi1058188332real_n ) > set_Fi1058188332real_n > nat ).
thf(func_def_204,type,
sK75: ( nat > $o ) > $o > nat ).
thf(func_def_205,type,
sK76: ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n > finite964658038_int_n ).
thf(func_def_206,type,
sK77: ( finite964658038_int_n > $o ) > $o > finite964658038_int_n ).
thf(func_def_207,type,
sK78: set_se2111327970real_n > ( set_Fi1058188332real_n > set_se2111327970real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).
thf(func_def_208,type,
sK79: set_o > ( $o > set_se2111327970real_n ) > set_Fi1058188332real_n > $o ).
thf(func_def_209,type,
sK80: set_se2111327970real_n > ( set_Fi1058188332real_n > set_o ) > $o > set_Fi1058188332real_n ).
thf(func_def_210,type,
sK81: set_o > ( $o > set_o ) > $o > $o ).
thf(func_def_211,type,
sK82: set_nat > ( nat > set_Fi1058188332real_n ) > finite1489363574real_n > nat ).
thf(func_def_212,type,
sK83: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > finite1489363574real_n > finite964658038_int_n ).
thf(func_def_213,type,
sK84: set_se2111327970real_n > ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > finite1489363574real_n > set_Fi1058188332real_n ).
thf(func_def_214,type,
sK85: set_o > ( $o > set_Fi1058188332real_n ) > finite1489363574real_n > $o ).
thf(func_def_215,type,
sK86: set_Ex113815278nnreal > extend1728876344nnreal > extend1728876344nnreal ).
thf(func_def_216,type,
sK87: finite964658038_int_n > ( finite964658038_int_n > finite964658038_int_n ) > finite964658038_int_n ).
thf(func_def_217,type,
sK88: ( finite964658038_int_n > finite964658038_int_n ) > finite964658038_int_n ).
thf(func_def_218,type,
sK89: nat > ( finite964658038_int_n > nat ) > finite964658038_int_n ).
thf(func_def_219,type,
sK90: ( finite964658038_int_n > nat ) > nat ).
thf(func_def_220,type,
sK91: set_Fi1058188332real_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > finite964658038_int_n ).
thf(func_def_221,type,
sK92: ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n ).
thf(func_def_222,type,
sK93: finite964658038_int_n > ( nat > finite964658038_int_n ) > nat ).
thf(func_def_223,type,
sK94: ( nat > finite964658038_int_n ) > finite964658038_int_n ).
thf(func_def_224,type,
sK95: nat > ( nat > nat ) > nat ).
thf(func_def_225,type,
sK96: ( nat > nat ) > nat ).
thf(func_def_226,type,
sK97: set_Fi1058188332real_n > ( nat > set_Fi1058188332real_n ) > nat ).
thf(func_def_227,type,
sK98: ( nat > set_Fi1058188332real_n ) > set_Fi1058188332real_n ).
thf(func_def_228,type,
sK99: finite1489363574real_n > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).
thf(func_def_229,type,
sK100: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).
thf(func_def_230,type,
sK101: ( finite964658038_int_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n > set_Fi160064172_int_n > finite964658038_int_n ).
thf(func_def_231,type,
sK102: ( nat > set_Fi1058188332real_n ) > set_Fi1058188332real_n > set_nat > nat ).
thf(func_def_232,type,
sK103: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > set_Fi1058188332real_n > finite1489363574real_n ).
thf(func_def_233,type,
sK104: ( finite964658038_int_n > set_Fi1058188332real_n ) > finite1489363574real_n > set_Fi160064172_int_n > finite964658038_int_n ).
thf(func_def_234,type,
sK105: ( nat > set_Fi1058188332real_n ) > finite1489363574real_n > set_nat > nat ).
thf(func_def_235,type,
sK106: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_236,type,
sK107: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite964658038_int_n ).
thf(func_def_237,type,
sK108: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_238,type,
sK109: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_239,type,
sK110: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > nat ).
thf(func_def_240,type,
sK111: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_241,type,
sK112: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite964658038_int_n ).
thf(func_def_242,type,
sK113: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_243,type,
sK114: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_244,type,
sK115: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > nat ).
thf(func_def_245,type,
sK116: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_246,type,
sK117: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_247,type,
sK118: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_248,type,
sK119: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite964658038_int_n ).
thf(func_def_249,type,
sK120: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_250,type,
sK121: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_251,type,
sK122: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > nat ).
thf(func_def_252,type,
sK123: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_253,type,
sK124: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite964658038_int_n ).
thf(func_def_254,type,
sK125: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_255,type,
sK126: set_Fi160064172_int_n > ( finite964658038_int_n > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_256,type,
sK127: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > nat ).
thf(func_def_257,type,
sK128: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_258,type,
sK129: set_nat > ( nat > set_Fi1058188332real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).
thf(func_def_259,type,
sK130: ( finite1489363574real_n > $o ) > set_se2111327970real_n > finite1489363574real_n ).
thf(func_def_260,type,
sK131: ( finite1489363574real_n > $o ) > set_se2111327970real_n > set_Fi1058188332real_n ).
thf(func_def_261,type,
sK132: ( finite1489363574real_n > $o ) > set_se2111327970real_n > finite1489363574real_n ).
thf(func_def_262,type,
sK133: ( finite1489363574real_n > $o ) > set_se2111327970real_n > set_Fi1058188332real_n ).
thf(func_def_263,type,
sK134: ( finite1489363574real_n > $o ) > set_se2111327970real_n > finite1489363574real_n ).
thf(func_def_264,type,
sK135: ( finite1489363574real_n > $o ) > set_se2111327970real_n > finite1489363574real_n ).
thf(func_def_265,type,
sK136: set_se2111327970real_n > finite1489363574real_n > set_Fi1058188332real_n ).
thf(func_def_266,type,
sK137: set_set_o > $o > set_o ).
thf(func_def_267,type,
sK138: set_se820660888real_n > set_Fi1058188332real_n > set_se2111327970real_n ).
thf(func_def_268,type,
sK139: extend1728876344nnreal > set_Ex113815278nnreal > extend1728876344nnreal ).
thf(func_def_269,type,
sK140: set_Ex113815278nnreal > extend1728876344nnreal ).
thf(func_def_270,type,
sK141: nat ).
thf(f1,axiom,
! [X0: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ X0 ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_emeasure__T_H) ).
thf(f11,axiom,
( t
= ( ^ [X0: finite964658038_int_n] :
( image_439535603real_n
@ ^ [X1: finite1489363574real_n] : ( minus_1037315151real_n @ X1 @ ( minkow1134813771n_real @ X0 ) )
@ ( t2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_T_H__def) ).
thf(f12,axiom,
( f
= ( counta1142393929_int_n @ top_to131672412_int_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f__def) ).
thf(f15,axiom,
( t2
= ( ^ [X0: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_T__def) ).
thf(f130,axiom,
! [X0: set_Fi1058188332real_n,X1: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ X0 @ ( minus_1686442501real_n @ X0 @ X1 ) )
= ( inf_in1974387902real_n @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Diff__Diff__Int) ).
thf(f253,axiom,
( inf_in1974387902real_n
= ( ^ [X0: set_Fi1058188332real_n,X1: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [X2: finite1489363574real_n] :
( ( member1352538125real_n @ X2 @ X1 )
& ( member1352538125real_n @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_Int__def) ).
thf(f354,conjecture,
( ( ^ [X0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X0 ) ) ) )
= ( ^ [X0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f355,negated_conjecture,
( ( ^ [X0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X0 ) ) ) )
!= ( ^ [X0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f354]) ).
thf(f372,plain,
( t
= ( ^ [X0: finite964658038_int_n] :
( image_439535603real_n
@ ^ [X1: finite1489363574real_n] : ( minus_1037315151real_n @ X1 @ ( minkow1134813771n_real @ X0 ) )
@ ( t2 @ X0 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f373,plain,
( t
= ( ^ [Y0: finite964658038_int_n] :
( image_439535603real_n
@ ^ [Y1: finite1489363574real_n] : ( minus_1037315151real_n @ Y1 @ ( minkow1134813771n_real @ Y0 ) )
@ ( t2 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f372]) ).
thf(f377,plain,
( t2
= ( ^ [Y0: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ Y0 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f756,plain,
( inf_in1974387902real_n
= ( ^ [X0: set_Fi1058188332real_n,X1: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [X2: finite1489363574real_n] :
( ( member1352538125real_n @ X2 @ X1 )
& ( member1352538125real_n @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f253]) ).
thf(f757,plain,
( inf_in1974387902real_n
= ( ^ [Y0: set_Fi1058188332real_n,Y1: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [Y2: finite1489363574real_n] :
( ( member1352538125real_n @ Y2 @ Y0 )
& ( member1352538125real_n @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f756]) ).
thf(f885,plain,
( ( ^ [X0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ X0 ) ) ) )
!= ( ^ [X1: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ X1 ) ) ) ) ),
inference(rectify,[],[f355]) ).
thf(f886,plain,
( ( ^ [Y0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ Y0 ) ) ) )
!= ( ^ [Y0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f885]) ).
thf(f910,plain,
( ( ^ [Y0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ Y0 ) ) ) )
!= ( ^ [Y0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ Y0 ) ) ) ) ),
inference(flattening,[],[f886]) ).
thf(f1233,plain,
! [X0: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ X0 ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ X0 ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f1243,plain,
( t
= ( ^ [Y0: finite964658038_int_n] :
( image_439535603real_n
@ ^ [Y1: finite1489363574real_n] : ( minus_1037315151real_n @ Y1 @ ( minkow1134813771n_real @ Y0 ) )
@ ( t2 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f373]) ).
thf(f1244,plain,
( f
= ( counta1142393929_int_n @ top_to131672412_int_n ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f1247,plain,
( t2
= ( ^ [Y0: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f377]) ).
thf(f1368,plain,
! [X0: set_Fi1058188332real_n,X1: set_Fi1058188332real_n] :
( ( inf_in1974387902real_n @ X0 @ X1 )
= ( minus_1686442501real_n @ X0 @ ( minus_1686442501real_n @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f130]) ).
thf(f1519,plain,
( inf_in1974387902real_n
= ( ^ [Y0: set_Fi1058188332real_n,Y1: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [Y2: finite1489363574real_n] :
( ( member1352538125real_n @ Y2 @ Y0 )
& ( member1352538125real_n @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f757]) ).
thf(f1636,plain,
( ( ^ [Y0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t2 @ ( f @ Y0 ) ) ) )
!= ( ^ [Y0: nat] : ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( t @ ( f @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f910]) ).
thf(f1642,plain,
( t2
= ( ^ [Y0: finite964658038_int_n] :
( ^ [Y1: set_Fi1058188332real_n,Y2: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [Y3: finite1489363574real_n] :
( ( member1352538125real_n @ Y3 @ Y1 )
& ( member1352538125real_n @ Y3 @ Y2 ) ) )
@ s
@ ( r @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f1247,f1519]) ).
thf(f1643,plain,
( t
= ( ^ [Y0: finite964658038_int_n] :
( image_439535603real_n
@ ^ [Y1: finite1489363574real_n] : ( minus_1037315151real_n @ Y1 @ ( minkow1134813771n_real @ Y0 ) )
@ ( ^ [Y1: finite964658038_int_n] :
( ^ [Y2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [Y4: finite1489363574real_n] :
( ( member1352538125real_n @ Y4 @ Y2 )
& ( member1352538125real_n @ Y4 @ Y3 ) ) )
@ s
@ ( r @ Y1 ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f1243,f1642]) ).
thf(f1644,plain,
! [X0: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( ^ [Y0: finite964658038_int_n] :
( image_439535603real_n
@ ^ [Y1: finite1489363574real_n] : ( minus_1037315151real_n @ Y1 @ ( minkow1134813771n_real @ Y0 ) )
@ ( ^ [Y1: finite964658038_int_n] :
( ^ [Y2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [Y4: finite1489363574real_n] :
( ( member1352538125real_n @ Y4 @ Y2 )
& ( member1352538125real_n @ Y4 @ Y3 ) ) )
@ s
@ ( r @ Y1 ) )
@ Y0 ) )
@ X0 ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( ^ [Y0: finite964658038_int_n] :
( ^ [Y1: set_Fi1058188332real_n,Y2: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [Y3: finite1489363574real_n] :
( ( member1352538125real_n @ Y3 @ Y1 )
& ( member1352538125real_n @ Y3 @ Y2 ) ) )
@ s
@ ( r @ Y0 ) )
@ X0 ) ) ),
inference(definition_unfolding,[],[f1233,f1643,f1642]) ).
thf(f1714,plain,
! [X0: set_Fi1058188332real_n,X1: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ X0 @ ( minus_1686442501real_n @ X0 @ X1 ) )
= ( ^ [Y0: set_Fi1058188332real_n,Y1: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [Y2: finite1489363574real_n] :
( ( member1352538125real_n @ Y2 @ Y0 )
& ( member1352538125real_n @ Y2 @ Y1 ) ) )
@ X0
@ X1 ) ),
inference(definition_unfolding,[],[f1368,f1519]) ).
thf(f1803,plain,
( ( ^ [Y0: nat] :
( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( ^ [Y1: finite964658038_int_n] :
( ^ [Y2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [Y4: finite1489363574real_n] :
( ( member1352538125real_n @ Y4 @ Y2 )
& ( member1352538125real_n @ Y4 @ Y3 ) ) )
@ s
@ ( r @ Y1 ) )
@ ( counta1142393929_int_n @ top_to131672412_int_n @ Y0 ) ) ) )
!= ( ^ [Y0: nat] :
( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( ^ [Y1: finite964658038_int_n] :
( image_439535603real_n
@ ^ [Y2: finite1489363574real_n] : ( minus_1037315151real_n @ Y2 @ ( minkow1134813771n_real @ Y1 ) )
@ ( ^ [Y2: finite964658038_int_n] :
( ^ [Y3: set_Fi1058188332real_n,Y4: set_Fi1058188332real_n] :
( collec321817931real_n
@ ^ [Y5: finite1489363574real_n] :
( ( member1352538125real_n @ Y5 @ Y3 )
& ( member1352538125real_n @ Y5 @ Y4 ) ) )
@ s
@ ( r @ Y2 ) )
@ Y1 ) )
@ ( counta1142393929_int_n @ top_to131672412_int_n @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f1636,f1642,f1244,f1643,f1244]) ).
thf(f1860,plain,
( ( ^ [Y0: nat] :
( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( collec321817931real_n
@ ^ [Y1: finite1489363574real_n] :
( ( member1352538125real_n @ Y1 @ s )
& ( member1352538125real_n @ Y1 @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ Y0 ) ) ) ) ) ) )
!= ( ^ [Y0: nat] :
( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( image_439535603real_n
@ ^ [Y1: finite1489363574real_n] : ( minus_1037315151real_n @ Y1 @ ( minkow1134813771n_real @ ( counta1142393929_int_n @ top_to131672412_int_n @ Y0 ) ) )
@ ( collec321817931real_n
@ ^ [Y1: finite1489363574real_n] :
( ( member1352538125real_n @ Y1 @ s )
& ( member1352538125real_n @ Y1 @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1803]) ).
thf(f2138,plain,
! [X0: set_Fi1058188332real_n,X1: set_Fi1058188332real_n] :
( ( minus_1686442501real_n @ X0 @ ( minus_1686442501real_n @ X0 @ X1 ) )
= ( collec321817931real_n
@ ^ [Y0: finite1489363574real_n] :
( ( member1352538125real_n @ Y0 @ X0 )
& ( member1352538125real_n @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1714]) ).
thf(f2581,plain,
! [X0: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( image_439535603real_n
@ ^ [Y0: finite1489363574real_n] : ( minus_1037315151real_n @ Y0 @ ( minkow1134813771n_real @ X0 ) )
@ ( collec321817931real_n
@ ^ [Y0: finite1489363574real_n] :
( ( member1352538125real_n @ Y0 @ s )
& ( member1352538125real_n @ Y0 @ ( r @ X0 ) ) ) ) ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( collec321817931real_n
@ ^ [Y0: finite1489363574real_n] :
( ( member1352538125real_n @ Y0 @ s )
& ( member1352538125real_n @ Y0 @ ( r @ X0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1644]) ).
thf(f2595,plain,
! [X0: finite964658038_int_n] :
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( image_439535603real_n
@ ^ [Y0: finite1489363574real_n] : ( minus_1037315151real_n @ Y0 @ ( minkow1134813771n_real @ X0 ) )
@ ( minus_1686442501real_n @ s @ ( minus_1686442501real_n @ s @ ( r @ X0 ) ) ) ) )
= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( minus_1686442501real_n @ s @ ( minus_1686442501real_n @ s @ ( r @ X0 ) ) ) ) ),
inference(forward_demodulation,[],[f2581,f2138]) ).
thf(f3900,plain,
( ( ^ [Y0: nat] :
( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( collec321817931real_n
@ ^ [Y1: finite1489363574real_n] :
( ( member1352538125real_n @ Y1 @ s )
& ( member1352538125real_n @ Y1 @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ Y0 ) ) ) ) ) )
@ sK141 )
!= ( ^ [Y0: nat] :
( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( image_439535603real_n
@ ^ [Y1: finite1489363574real_n] : ( minus_1037315151real_n @ Y1 @ ( minkow1134813771n_real @ ( counta1142393929_int_n @ top_to131672412_int_n @ Y0 ) ) )
@ ( collec321817931real_n
@ ^ [Y1: finite1489363574real_n] :
( ( member1352538125real_n @ Y1 @ s )
& ( member1352538125real_n @ Y1 @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ Y0 ) ) ) ) ) ) )
@ sK141 ) ),
inference(negative_extensionality,[],[f1860]) ).
thf(f3901,plain,
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( collec321817931real_n
@ ^ [Y0: finite1489363574real_n] :
( ( member1352538125real_n @ Y0 @ s )
& ( member1352538125real_n @ Y0 @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ sK141 ) ) ) ) ) )
!= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( image_439535603real_n
@ ^ [Y0: finite1489363574real_n] : ( minus_1037315151real_n @ Y0 @ ( minkow1134813771n_real @ ( counta1142393929_int_n @ top_to131672412_int_n @ sK141 ) ) )
@ ( collec321817931real_n
@ ^ [Y0: finite1489363574real_n] :
( ( member1352538125real_n @ Y0 @ s )
& ( member1352538125real_n @ Y0 @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ sK141 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3900]) ).
thf(f3902,plain,
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( minus_1686442501real_n @ s @ ( minus_1686442501real_n @ s @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ sK141 ) ) ) ) )
!= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n )
@ ( image_439535603real_n
@ ^ [Y0: finite1489363574real_n] : ( minus_1037315151real_n @ Y0 @ ( minkow1134813771n_real @ ( counta1142393929_int_n @ top_to131672412_int_n @ sK141 ) ) )
@ ( minus_1686442501real_n @ s @ ( minus_1686442501real_n @ s @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ sK141 ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f3901,f2138]) ).
thf(f3903,plain,
( ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( minus_1686442501real_n @ s @ ( minus_1686442501real_n @ s @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ sK141 ) ) ) ) )
!= ( sigma_1536574303real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( minus_1686442501real_n @ s @ ( minus_1686442501real_n @ s @ ( r @ ( counta1142393929_int_n @ top_to131672412_int_n @ sK141 ) ) ) ) ) ),
inference(forward_demodulation,[],[f3902,f2595]) ).
thf(f3904,plain,
$false,
inference(trivial_inequality_removal,[],[f3903]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP117^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n004.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 19:56:07 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.78/0.40 % (1762174)Will run a generic schedule for satisfiability detection.
% 0.78/0.40 % (1762183)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2080444974:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.78/0.40 % (1762180)% WARNING: option uhcvi not known.
% 0.78/0.40 % (1762179)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1204409641_2999 on theBenchmark for (2999ds/0Mi)
% 0.78/0.40 % (1762180)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3447933137:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.78/0.40 % (1762181)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1745044011:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.78/0.40 % (1762182)dis+10_1_sil=32000:sp=arity:random_seed=791273330:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.78/0.40 % (1762184)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3995819185:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.78/0.40 % (1762185)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3973303483:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.78/0.40 % (1762183)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.78/0.40 % (1762180)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.78/0.40 % (1762183)Instruction limit reached!
% 0.78/0.40 % (1762183)------------------------------
% 0.78/0.40 % (1762183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.40 % (1762183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.40 % (1762183)CaDiCaL version: 2.1.3
% 0.78/0.40 % (1762183)Termination reason: Instruction limit
% 0.78/0.40 % (1762183)Termination phase: Saturation
% 0.78/0.40 % (1762183)Time elapsed: 0.027 s
% 0.78/0.40 % (1762183)Peak memory usage: 13 MB
% 0.78/0.40 % (1762183)Instructions burned: 118 (million)
% 0.78/0.40 % (1762193)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3972834740:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.78/0.40 % (1762182)Instruction limit reached!
% 0.78/0.40 % (1762182)------------------------------
% 0.78/0.40 % (1762182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.40 % (1762182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.40 % (1762182)CaDiCaL version: 2.1.3
% 0.78/0.40 % (1762182)Termination reason: Instruction limit
% 0.78/0.40 % (1762182)Termination phase: Property scanning
% 0.78/0.40 % (1762182)Time elapsed: 0.043 s
% 0.78/0.40 % (1762182)Peak memory usage: 11 MB
% 0.78/0.40 % (1762182)Instructions burned: 104 (million)
% 0.78/0.40 % Exception at run slice level
% 0.78/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.78/0.40 % (1762180)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.78/0.40 % Exception at run slice level
% 0.78/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.78/0.40 % (1762184)Instruction limit reached!
% 0.78/0.40 % (1762184)------------------------------
% 0.78/0.40 % (1762184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.40 % (1762184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.40 % (1762184)CaDiCaL version: 2.1.3
% 0.78/0.40 % (1762184)Termination reason: Instruction limit
% 0.78/0.40 % (1762184)Termination phase: Saturation
% 0.78/0.40 % (1762184)Time elapsed: 0.059 s
% 0.78/0.40 % (1762184)Peak memory usage: 13 MB
% 0.78/0.40 % (1762184)Instructions burned: 140 (million)
% 0.78/0.40 % (1762195)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=633981783:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.78/0.40 % (1762196)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=701024815:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.78/0.40 % (1762197)ott-21_1_sil=16000:fs=off:random_seed=285352225:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.78/0.40 % (1762185)Instruction limit reached!
% 0.78/0.40 % (1762185)------------------------------
% 0.78/0.40 % (1762185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.40 % (1762185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.40 % (1762185)CaDiCaL version: 2.1.3
% 0.78/0.40 % (1762185)Termination reason: Instruction limit
% 0.78/0.40 % (1762185)Termination phase: Saturation
% 0.78/0.40 % (1762185)Time elapsed: 0.069 s
% 0.78/0.40 % (1762185)Peak memory usage: 14 MB
% 0.78/0.40 % (1762185)Instructions burned: 160 (million)
% 0.78/0.40 % (1762198)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2931168270:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.78/0.40 % (1762196)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.78/0.40 % (1762202)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1351897866:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.78/0.40 % (1762197) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1762174-1762197"...
% 0.78/0.40 % (1762197)...printing done.
% 0.78/0.40 % (1762197)Refutation found. Thanks to Tanya!
% 0.78/0.40 % SZS status Theorem for theBenchmark
% 0.78/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.78/0.40 % (1762197)------------------------------
% 0.78/0.40 % (1762197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.40 % (1762197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.40 % (1762197)CaDiCaL version: 2.1.3
% 0.78/0.40 % (1762197)Termination reason: Refutation
% 0.78/0.40 % (1762197)Time elapsed: 0.043 s
% 0.78/0.40 % (1762197)Peak memory usage: 14 MB
% 0.78/0.40 % (1762197)Instructions burned: 181 (million)
% 0.78/0.40 % (1762174)Success in time 0.163 s
% 0.78/0.40 % Vampire exiting
%------------------------------------------------------------------------------