%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP161^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:02 AM UTC 2026
% Result : Theorem 3.85s 1.88s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 32 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 180 ( 21 ~; 11 |; 0 &; 142 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 158 ( 155 usr; 12 con; 0-4 aty)
% Number of variables : 33 ( 0 ^; 33 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
refine424419629nres_a: $tType ).
thf(type_def_7,type,
refine432681134nres_b: $tType ).
thf(type_def_8,type,
refine787176636t_unit: $tType ).
thf(type_def_9,type,
set_a: $tType ).
thf(type_def_10,type,
set_b: $tType ).
thf(type_def_11,type,
refine671810262od_a_a: $tType ).
thf(type_def_12,type,
refine1811374551od_a_b: $tType ).
thf(type_def_13,type,
refine891721109od_b_a: $tType ).
thf(type_def_14,type,
refine2031285398od_b_b: $tType ).
thf(type_def_15,type,
a: $tType ).
thf(type_def_16,type,
b: $tType ).
thf(type_def_17,type,
produc1609974940nres_a: $tType ).
thf(type_def_18,type,
produc1587512412nres_b: $tType ).
thf(type_def_19,type,
product_prod_a_a: $tType ).
thf(type_def_20,type,
product_prod_a_b: $tType ).
thf(type_def_21,type,
product_prod_b_a: $tType ).
thf(type_def_22,type,
product_prod_b_b: $tType ).
thf(type_def_23,type,
product_unit: $tType ).
thf(type_def_24,type,
set_Pr451126599t_unit: $tType ).
thf(type_def_25,type,
set_Pr1628433942t_unit: $tType ).
thf(type_def_26,type,
set_Product_prod_a_a: $tType ).
thf(type_def_27,type,
set_Product_prod_a_b: $tType ).
thf(type_def_28,type,
set_Pr1707992533t_unit: $tType ).
thf(type_def_29,type,
set_Product_prod_b_a: $tType ).
thf(type_def_30,type,
set_Product_prod_b_b: $tType ).
thf(type_def_31,type,
set_Product_unit: $tType ).
thf(func_def_0,type,
produc1587512412nres_b: $tType ).
thf(func_def_1,type,
produc1609974940nres_a: $tType ).
thf(func_def_2,type,
set_Pr451126599t_unit: $tType ).
thf(func_def_3,type,
refine2031285398od_b_b: $tType ).
thf(func_def_4,type,
refine891721109od_b_a: $tType ).
thf(func_def_5,type,
refine1811374551od_a_b: $tType ).
thf(func_def_6,type,
refine671810262od_a_a: $tType ).
thf(func_def_7,type,
refine787176636t_unit: $tType ).
thf(func_def_8,type,
set_Pr1707992533t_unit: $tType ).
thf(func_def_9,type,
set_Pr1628433942t_unit: $tType ).
thf(func_def_10,type,
refine432681134nres_b: $tType ).
thf(func_def_11,type,
refine424419629nres_a: $tType ).
thf(func_def_12,type,
set_Product_prod_b_b: $tType ).
thf(func_def_13,type,
set_Product_prod_b_a: $tType ).
thf(func_def_14,type,
set_Product_prod_a_b: $tType ).
thf(func_def_15,type,
set_Product_prod_a_a: $tType ).
thf(func_def_16,type,
set_Product_unit: $tType ).
thf(func_def_17,type,
product_prod_b_b: $tType ).
thf(func_def_18,type,
product_prod_b_a: $tType ).
thf(func_def_19,type,
product_prod_a_b: $tType ).
thf(func_def_20,type,
product_prod_a_a: $tType ).
thf(func_def_21,type,
product_unit: $tType ).
thf(func_def_22,type,
set_b: $tType ).
thf(func_def_23,type,
set_a: $tType ).
thf(func_def_24,type,
b: $tType ).
thf(func_def_25,type,
a: $tType ).
thf(func_def_26,type,
if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
thf(func_def_27,type,
if_o_R697118589nres_b: $o > ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o > refine432681134nres_b ).
thf(func_def_28,type,
if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(func_def_29,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_30,type,
if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
thf(func_def_31,type,
if_set_a: $o > set_a > set_a > set_a ).
thf(func_def_32,type,
if_set_b: $o > set_b > set_b > set_b ).
thf(func_def_33,type,
ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
thf(func_def_34,type,
ord_le1656162903nres_b: ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o ).
thf(func_def_35,type,
ord_le915866422od_a_a: refine671810262od_a_a > refine671810262od_a_a > $o ).
thf(func_def_36,type,
ord_le2055430711od_a_b: refine1811374551od_a_b > refine1811374551od_a_b > $o ).
thf(func_def_37,type,
ord_le1135777269od_b_a: refine891721109od_b_a > refine891721109od_b_a > $o ).
thf(func_def_38,type,
ord_le127857910od_b_b: refine2031285398od_b_b > refine2031285398od_b_b > $o ).
thf(func_def_39,type,
ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
thf(func_def_40,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_41,type,
ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o ).
thf(func_def_42,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_43,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(func_def_44,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(func_def_45,type,
order_1722590613nres_b: ( refine432681134nres_b > $o ) > refine432681134nres_b ).
thf(func_def_46,type,
top_top_a_o: a > $o ).
thf(func_def_47,type,
top_top_b_o: b > $o ).
thf(func_def_48,type,
top_to177290092t_unit: refine787176636t_unit ).
thf(func_def_49,type,
top_to231829469nres_a: refine424419629nres_a ).
thf(func_def_50,type,
top_to240090974nres_b: refine432681134nres_b ).
thf(func_def_51,type,
top_top_set_a: set_a ).
thf(func_def_52,type,
top_top_set_b: set_b ).
thf(func_def_53,type,
partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o ).
thf(func_def_54,type,
partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_55,type,
partia915210666nres_b: refine432681134nres_b > refine432681134nres_b > refine432681134nres_b > $o ).
thf(func_def_56,type,
produc1136923598nres_a: refine424419629nres_a > refine424419629nres_a > produc1609974940nres_a ).
thf(func_def_57,type,
produc2130641934nres_b: refine432681134nres_b > refine432681134nres_b > produc1587512412nres_b ).
thf(func_def_58,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(func_def_59,type,
product_Pair_a_b: a > b > product_prod_a_b ).
thf(func_def_60,type,
product_Pair_b_a: b > a > product_prod_b_a ).
thf(func_def_61,type,
product_Pair_b_b: b > b > product_prod_b_b ).
thf(func_def_62,type,
refine2039610767ASSERT: $o > refine787176636t_unit ).
thf(func_def_63,type,
refine1420258419t_unit: product_unit > refine787176636t_unit ).
thf(func_def_64,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(func_def_65,type,
refine2063221605TURN_b: b > refine432681134nres_b ).
thf(func_def_66,type,
refine838861686t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(func_def_67,type,
refine341651653t_unit: set_Pr1628433942t_unit > refine424419629nres_a > refine787176636t_unit ).
thf(func_def_68,type,
refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_69,type,
refine1136779703un_a_b: set_Product_prod_a_b > refine424419629nres_a > refine432681134nres_b ).
thf(func_def_70,type,
refine460904452t_unit: set_Pr1707992533t_unit > refine432681134nres_b > refine787176636t_unit ).
thf(func_def_71,type,
refine1964549109un_b_a: set_Product_prod_b_a > refine432681134nres_b > refine424419629nres_a ).
thf(func_def_72,type,
refine1964549110un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
thf(func_def_73,type,
refine988994910_a_a_b: refine671810262od_a_a > ( product_prod_a_a > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_74,type,
refine681446406t_unit: refine787176636t_unit > ( product_unit > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_75,type,
refine119808503unit_a: refine787176636t_unit > ( product_unit > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_76,type,
refine119808504unit_b: refine787176636t_unit > ( product_unit > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_77,type,
refine96995669t_unit: refine424419629nres_a > ( a > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_78,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_79,type,
refine436832839nd_a_b: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_80,type,
refine216248468t_unit: refine432681134nres_b > ( b > refine787176636t_unit ) > refine787176636t_unit ).
thf(func_def_81,type,
refine1264602245nd_b_a: refine432681134nres_b > ( b > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_82,type,
refine1264602246nd_b_b: refine432681134nres_b > ( b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_83,type,
refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit ).
thf(func_def_84,type,
refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a ).
thf(func_def_85,type,
refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_86,type,
refine1441824854un_a_b: set_Product_prod_a_b > refine432681134nres_b > refine424419629nres_a ).
thf(func_def_87,type,
refine2140306339t_unit: set_Pr1707992533t_unit > refine787176636t_unit > refine432681134nres_b ).
thf(func_def_88,type,
refine122110612un_b_a: set_Product_prod_b_a > refine424419629nres_a > refine432681134nres_b ).
thf(func_def_89,type,
refine122110613un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b ).
thf(func_def_90,type,
refine558004794t_unit: refine787176636t_unit > product_unit > $o ).
thf(func_def_91,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(func_def_92,type,
refine1001002028nres_b: refine432681134nres_b > b > $o ).
thf(func_def_93,type,
refine378960780od_a_a: refine671810262od_a_a > product_prod_a_a > $o ).
thf(func_def_94,type,
refine387222285od_a_b: refine1811374551od_a_b > product_prod_a_b > $o ).
thf(func_def_95,type,
refine1206730187od_b_a: refine891721109od_b_a > product_prod_b_a > $o ).
thf(func_def_96,type,
refine1214991692od_b_b: refine2031285398od_b_b > product_prod_b_b > $o ).
thf(func_def_97,type,
refine983493746t_unit: refine787176636t_unit > product_unit > $o ).
thf(func_def_98,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(func_def_99,type,
refine1312857700nres_b: refine432681134nres_b > b > $o ).
thf(func_def_100,type,
refine579265252t_unit: refine787176636t_unit > $o ).
thf(func_def_101,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(func_def_102,type,
refine412683990fail_b: refine432681134nres_b > $o ).
thf(func_def_103,type,
refine1607584204t_unit: refine787176636t_unit ).
thf(func_def_104,type,
refine464223677AILi_a: refine424419629nres_a ).
thf(func_def_105,type,
refine464223678AILi_b: refine432681134nres_b ).
thf(func_def_106,type,
refine622451633od_a_a: set_Product_prod_a_a > refine671810262od_a_a ).
thf(func_def_107,type,
refine630713138od_a_b: set_Product_prod_a_b > refine1811374551od_a_b ).
thf(func_def_108,type,
refine1450221040od_b_a: set_Product_prod_b_a > refine891721109od_b_a ).
thf(func_def_109,type,
refine1458482545od_b_b: set_Product_prod_b_b > refine2031285398od_b_b ).
thf(func_def_110,type,
refine1777164439t_unit: set_Product_unit > refine787176636t_unit ).
thf(func_def_111,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(func_def_112,type,
refine1198353289_RES_b: set_b > refine432681134nres_b ).
thf(func_def_113,type,
refine1208325748t_unit: refine787176636t_unit > set_Product_unit ).
thf(func_def_114,type,
refine1822134885_RES_a: refine424419629nres_a > set_a ).
thf(func_def_115,type,
refine1822134886_RES_b: refine432681134nres_b > set_b ).
thf(func_def_116,type,
domain799550107t_unit: set_Pr1628433942t_unit > set_a ).
thf(func_def_117,type,
domain_a_a: set_Product_prod_a_a > set_a ).
thf(func_def_118,type,
domain_a_b: set_Product_prod_a_b > set_a ).
thf(func_def_119,type,
domain918802906t_unit: set_Pr1707992533t_unit > set_b ).
thf(func_def_120,type,
domain_b_a: set_Product_prod_b_a > set_b ).
thf(func_def_121,type,
domain_b_b: set_Product_prod_b_b > set_b ).
thf(func_def_122,type,
image_a_a: set_Product_prod_a_a > set_a > set_a ).
thf(func_def_123,type,
image_a_b: set_Product_prod_a_b > set_a > set_b ).
thf(func_def_124,type,
image_b_a: set_Product_prod_b_a > set_b > set_a ).
thf(func_def_125,type,
image_b_b: set_Product_prod_b_b > set_b > set_b ).
thf(func_def_126,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(func_def_127,type,
collec654117139od_a_b: ( product_prod_a_b > $o ) > set_Product_prod_a_b ).
thf(func_def_128,type,
collec1473625041od_b_a: ( product_prod_b_a > $o ) > set_Product_prod_b_a ).
thf(func_def_129,type,
collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).
thf(func_def_130,type,
collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).
thf(func_def_131,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_132,type,
collect_b: ( b > $o ) > set_b ).
thf(func_def_133,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_134,type,
member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).
thf(func_def_135,type,
member1277678991od_b_a: product_prod_b_a > set_Product_prod_b_a > $o ).
thf(func_def_136,type,
member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
thf(func_def_137,type,
member_Product_unit: product_unit > set_Product_unit > $o ).
thf(func_def_138,type,
member_a: a > set_a > $o ).
thf(func_def_139,type,
member_b: b > set_b > $o ).
thf(func_def_140,type,
phi: a > $o ).
thf(func_def_141,type,
f: a > refine432681134nres_b ).
thf(func_def_142,type,
m: refine432681134nres_b ).
thf(func_def_143,type,
x: a ).
thf(func_def_157,type,
sK0: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_158,type,
sK1: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_159,type,
sK2: ( a > $o ) > set_a > a ).
thf(func_def_160,type,
sK3: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_161,type,
sK4: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_162,type,
sK5: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_163,type,
sK6: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_164,type,
sK7: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_165,type,
sK8: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_166,type,
sK9: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_167,type,
sK10: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_168,type,
sK11: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_169,type,
sK12: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_170,type,
sK13: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_171,type,
sK14: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_172,type,
sK15: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_173,type,
sK16: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_174,type,
sK17: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_175,type,
sK18: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_176,type,
sK19: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_177,type,
sK20: ( refine432681134nres_b > refine432681134nres_b ) > refine432681134nres_b ).
thf(func_def_178,type,
sK21: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_179,type,
sK22: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_180,type,
sK23: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_181,type,
sK24: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_182,type,
sK25: ( refine424419629nres_a > refine432681134nres_b ) > refine424419629nres_a ).
thf(func_def_183,type,
sK26: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_184,type,
sK27: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_185,type,
sK28: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_186,type,
sK29: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_187,type,
sK30: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_188,type,
sK31: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_189,type,
sK32: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_190,type,
sK33: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_191,type,
sK34: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_192,type,
sK35: ( refine432681134nres_b > refine424419629nres_a ) > refine432681134nres_b ).
thf(func_def_194,type,
ph37:
!>[X0: $tType] : X0 ).
thf(f1246,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1244,f1180]) ).
thf(f1180,plain,
( ( phi @ x )
= $true ),
inference(cnf_transformation,[status(thm)],[f391]) ).
thf(f391,plain,
( ( phi @ x )
= $true ),
inference(fool_elimination,[status(thm)],[f390]) ).
thf(f390,plain,
phi @ x,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
phi @ x,
file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',fact_0_assms_I1_J) ).
thf(f1244,plain,
( ( phi @ x )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1238]) ).
thf(f1238,plain,
( ( $true != $true )
| ( ( phi @ x )
!= $true ) ),
inference(superposition,[status(thm)],[f1233,f1154]) ).
thf(f1154,plain,
( ( ord_le527798542nres_b @ m @ ( f @ x ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f771]) ).
thf(f771,plain,
( ( ord_le527798542nres_b @ m @ ( f @ x ) )
= $true ),
inference(fool_elimination,[status(thm)],[f770]) ).
thf(f770,plain,
ord_le527798542nres_b @ m @ ( f @ x ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
ord_le527798542nres_b @ m @ ( f @ x ),
file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',fact_1_assms_I2_J) ).
thf(f1233,plain,
! [X0: a] :
( ( $true
!= ( ord_le527798542nres_b @ m @ ( f @ X0 ) ) )
| ( $true
!= ( phi @ X0 ) ) ),
inference(superposition,[status(thm)],[f1226,f1117]) ).
thf(f1117,plain,
! [X0: a > $o,X1: a] :
( ( X0 @ X1 )
= ( member_a @ X1 @ ( collect_a @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f979]) ).
thf(f979,plain,
! [X0: a > $o,X1: a] :
( ( X0 @ X1 )
= ( member_a @ X1 @ ( collect_a @ X0 ) ) ),
inference(rectify,[status(thm)],[f108]) ).
thf(f108,axiom,
! [X34: a > $o,X24: a] :
( ( member_a @ X24 @ ( collect_a @ X34 ) )
= ( X34 @ X24 ) ),
file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',fact_107_mem__Collect__eq) ).
thf(f1226,plain,
! [X0: a] :
( ( $true
!= ( member_a @ X0 @ ( collect_a @ phi ) ) )
| ( $true
!= ( ord_le527798542nres_b @ m @ ( f @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1219]) ).
thf(f1219,plain,
! [X0: a] :
( ( $true
!= ( member_a @ X0 @ ( collect_a @ phi ) ) )
| ( $true
!= ( ord_le527798542nres_b @ m @ ( f @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1159,f1112]) ).
thf(f1112,plain,
! [X2: refine432681134nres_b,X3: a > refine432681134nres_b,X0: a,X1: set_a] :
( ( $true
= ( ord_le527798542nres_b @ X2 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X1 ) @ X3 ) ) )
| ( $true
!= ( ord_le527798542nres_b @ X2 @ ( X3 @ X0 ) ) )
| ( $true
!= ( member_a @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f1029]) ).
thf(f1029,plain,
! [X0: a,X1: set_a,X2: refine432681134nres_b,X3: a > refine432681134nres_b] :
( ( $true
!= ( ord_le527798542nres_b @ X2 @ ( X3 @ X0 ) ) )
| ( $true
= ( ord_le527798542nres_b @ X2 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X1 ) @ X3 ) ) )
| ( $true
!= ( member_a @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f1028]) ).
thf(f1028,plain,
! [X0: a,X1: set_a,X2: refine432681134nres_b,X3: a > refine432681134nres_b] :
( ( $true
= ( ord_le527798542nres_b @ X2 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X1 ) @ X3 ) ) )
| ( $true
!= ( ord_le527798542nres_b @ X2 @ ( X3 @ X0 ) ) )
| ( $true
!= ( member_a @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f609]) ).
thf(f609,plain,
! [X0: a,X1: set_a,X2: refine432681134nres_b,X3: a > refine432681134nres_b] :
( ( $true
= ( member_a @ X0 @ X1 ) )
=> ( ( $true
= ( ord_le527798542nres_b @ X2 @ ( X3 @ X0 ) ) )
=> ( $true
= ( ord_le527798542nres_b @ X2 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X1 ) @ X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f608]) ).
thf(f608,plain,
! [X0: a,X1: set_a,X2: refine432681134nres_b,X3: a > refine432681134nres_b] :
( ( member_a @ X0 @ X1 )
=> ( ( ord_le527798542nres_b @ X2 @ ( X3 @ X0 ) )
=> ( ord_le527798542nres_b @ X2 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X1 ) @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,axiom,
! [X11: a,X0: set_a,X15: refine432681134nres_b,X18: a > refine432681134nres_b] :
( ( member_a @ X11 @ X0 )
=> ( ( ord_le527798542nres_b @ X15 @ ( X18 @ X11 ) )
=> ( ord_le527798542nres_b @ X15 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X0 ) @ X18 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',fact_35_RES__bind__choose) ).
thf(f1159,plain,
( ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f977]) ).
thf(f977,plain,
( ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) )
!= $true ),
inference(flattening,[status(thm)],[f639]) ).
thf(f639,plain,
( ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f638]) ).
thf(f638,plain,
~ ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ),
inference(rectify,[status(thm)],[f360]) ).
thf(f360,negated_conjecture,
~ ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ),
inference(negated_conjecture,[status(cth)],[f359]) ).
thf(f359,conjecture,
ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ),
file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP161^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:26:56 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : ITP161^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.46 % Domain : Interactive Theorem Proving
% 0.20/0.46 % Problem : Sledgehammer Refine_Basic problem prob_1708__3602512_1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Des21]
% 0.20/0.46 % Names : Refine_Basic/prob_1708__3602512_1 [Des21]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% 0.20/0.46 % Syntax : Number of formulae : 503 ( 146 unt; 144 typ; 0 def)
% 0.20/0.46 % Number of atoms : 1005 ( 266 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.20/0.46 % Number of connectives : 3105 ( 107 ~; 1 |; 29 &;2426 @)
% 0.20/0.46 % ( 0 <=>; 542 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 17 ( 7 avg)
% 0.20/0.46 % Number of types : 27 ( 26 usr)
% 0.20/0.46 % Number of type conns : 394 ( 394 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 121 ( 118 usr; 12 con; 0-4 aty)
% 0.20/0.46 % Number of variables : 1083 ( 62 ^;1002 !; 19 ?;1083 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:36:00.723
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (26)
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 0.20/0.46 produc1587512412nres_b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.20/0.46 produc1609974940nres_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
% 0.20/0.46 set_Pr451126599t_unit: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.20/0.46 refine2031285398od_b_b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
% 0.20/0.46 refine891721109od_b_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
% 0.20/0.46 refine1811374551od_a_b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.20/0.46 refine671810262od_a_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.20/0.46 refine787176636t_unit: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Ounit_J_J,type,
% 0.20/0.46 set_Pr1707992533t_unit: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Ounit_J_J,type,
% 0.20/0.46 set_Pr1628433942t_unit: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 0.20/0.46 refine432681134nres_b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.20/0.46 refine424419629nres_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.20/0.46 set_Product_prod_b_b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
% 0.20/0.46 set_Product_prod_b_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
% 0.20/0.46 set_Product_prod_a_b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.20/0.46 set_Product_prod_a_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.20/0.46 set_Product_unit: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 0.20/0.46 product_prod_b_b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
% 0.20/0.46 product_prod_b_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
% 0.20/0.46 product_prod_a_b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.20/0.46 product_prod_a_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Ounit,type,
% 0.20/0.46 product_unit: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_Itf__b_J,type,
% 0.20/0.46 set_b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.20/0.46 set_a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_tf__b,type,
% 0.20/0.46 b: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_tf__a,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 % Explicit typings (118)
% 0.20/0.46 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.20/0.46 if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 0.20/0.46 if_o_R697118589nres_b: $o > ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o > refine432681134nres_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 0.20/0.46 if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.20/0.46 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 0.20/0.46 if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.46 if_set_a: $o > set_a > set_a > set_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If_001t__Set__Oset_Itf__b_J,type,
% 0.20/0.46 if_set_b: $o > set_b > set_b > set_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.20/0.46 ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 0.20/0.46 ord_le1656162903nres_b: ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o ).
% 0.20/0.46
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% 0.20/0.46 refine1198353288_RES_a: set_a > refine424419629nres_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__b,type,
% 0.20/0.46 refine1198353289_RES_b: set_b > refine432681134nres_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001t__Product____Type__Ounit,type,
% 0.20/0.46 refine1208325748t_unit: refine787176636t_unit > set_Product_unit ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001tf__a,type,
% 0.20/0.46 refine1822134885_RES_a: refine424419629nres_a > set_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001tf__b,type,
% 0.20/0.46 refine1822134886_RES_b: refine432681134nres_b > set_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_ODomain_001tf__a_001t__Product____Type__Ounit,type,
% 0.20/0.46 domain799550107t_unit: set_Pr1628433942t_unit > set_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_ODomain_001tf__a_001tf__a,type,
% 0.20/0.46 domain_a_a: set_Product_prod_a_a > set_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_ODomain_001tf__a_001tf__b,type,
% 0.20/0.46 domain_a_b: set_Product_prod_a_b > set_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_ODomain_001tf__b_001t__Product____Type__Ounit,type,
% 0.20/0.46 domain918802906t_unit: set_Pr1707992533t_unit > set_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_ODomain_001tf__b_001tf__a,type,
% 0.20/0.46 domain_b_a: set_Product_prod_b_a > set_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_ODomain_001tf__b_001tf__b,type,
% 0.20/0.46 domain_b_b: set_Product_prod_b_b > set_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_OImage_001tf__a_001tf__a,type,
% 0.20/0.46 image_a_a: set_Product_prod_a_a > set_a > set_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_OImage_001tf__a_001tf__b,type,
% 0.20/0.46 image_a_b: set_Product_prod_a_b > set_a > set_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_OImage_001tf__b_001tf__a,type,
% 0.20/0.46 image_b_a: set_Product_prod_b_a > set_b > set_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Relation_OImage_001tf__b_001tf__b,type,
% 0.20/0.46 image_b_b: set_Product_prod_b_b > set_b > set_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.20/0.46 collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
% 0.20/0.46 collec654117139od_a_b: ( product_prod_a_b > $o ) > set_Product_prod_a_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
% 0.20/0.46 collec1473625041od_b_a: ( product_prod_b_a > $o ) > set_Product_prod_b_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 0.20/0.46 collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Ounit,type,
% 0.20/0.46 collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.20/0.46 collect_a: ( a > $o ) > set_a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001tf__b,type,
% 0.20/0.46 collect_b: ( b > $o ) > set_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.20/0.46 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
% 0.20/0.46 member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
% 0.20/0.46 member1277678991od_b_a: product_prod_b_a > set_Product_prod_b_a > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 0.20/0.46 member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Product____Type__Ounit,type,
% 0.20/0.46 member_Product_unit: product_unit > set_Product_unit > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001tf__a,type,
% 0.20/0.46 member_a: a > set_a > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001tf__b,type,
% 0.20/0.46 member_b: b > set_b > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v__092_060Phi_062,type,
% 0.20/0.46 phi: a > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_f,type,
% 0.20/0.46 f: a > refine432681134nres_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_m,type,
% 0.20/0.46 m: refine432681134nres_b ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_x,type,
% 0.20/0.46 x: a ).
% 0.20/0.46
% 0.20/0.46 % Relevant facts (343)
% 0.20/0.46 thf(fact_0_assms_I1_J,axiom,
% 0.20/0.46 phi @ x ).
% 0.20/0.46
% 0.20/0.46 % assms(1)
% 0.20/0.46 thf(fact_1_assms_I2_J,axiom,
% 0.20/0.46 ord_le527798542nres_b @ m @ ( f @ x ) ).
% 0.20/0.46
% 0.20/0.46 % assms(2)
% 0.20/0.46 thf(fact_2_nres__more__simps_I4_J,axiom,
% 0.20/0.46 ! [X: set_Product_unit,Y: set_Product_unit] :
% 0.20/0.46 ( ( ( refine1777164439t_unit @ X )
% 0.20/0.46 = ( refine1777164439t_unit @ Y ) )
% 0.20/0.46 = ( X = Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres_more_simps(4)
% 0.20/0.46 thf(fact_3_nres__more__simps_I4_J,axiom,
% 0.20/0.46 ! [X: set_b,Y: set_b] :
% 0.20/0.46 ( ( ( refine1198353289_RES_b @ X )
% 0.20/0.46 = ( refine1198353289_RES_b @ Y ) )
% 0.20/0.46 = ( X = Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres_more_simps(4)
% 0.20/0.46 thf(fact_4_nres__more__simps_I4_J,axiom,
% 0.20/0.46 ! [X: set_a,Y: set_a] :
% 0.20/0.46 ( ( ( refine1198353288_RES_a @ X )
% 0.20/0.46 = ( refine1198353288_RES_a @ Y ) )
% 0.20/0.46 = ( X = Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres_more_simps(4)
% 0.20/0.46 thf(fact_5_nres_Oinject,axiom,
% 0.20/0.46 ! [X2: set_Product_unit,Y2: set_Product_unit] :
% 0.20/0.46 ( ( ( refine1777164439t_unit @ X2 )
% 0.20/0.46 = ( refine1777164439t_unit @ Y2 ) )
% 0.20/0.46 = ( X2 = Y2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres.inject
% 0.20/0.46 thf(fact_6_nres_Oinject,axiom,
% 0.20/0.46 ! [X2: set_b,Y2: set_b] :
% 0.20/0.46 ( ( ( refine1198353289_RES_b @ X2 )
% 0.20/0.46 = ( refine1198353289_RES_b @ Y2 ) )
% 0.20/0.46 = ( X2 = Y2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres.inject
% 0.20/0.46 thf(fact_7_nres_Oinject,axiom,
% 0.20/0.46 ! [X2: set_a,Y2: set_a] :
% 0.20/0.46 ( ( ( refine1198353288_RES_a @ X2 )
% 0.20/0.46 = ( refine1198353288_RES_a @ Y2 ) )
% 0.20/0.46 = ( X2 = Y2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres.inject
% 0.20/0.46 thf(fact_8_if__rule,axiom,
% 0.20/0.46 ! [B: $o,S1: refine787176636t_unit,Phi: product_unit > $o,S2: refine787176636t_unit] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_le1051254044t_unit @ S1 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_le1051254044t_unit @ S2 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) )
% 0.20/0.46 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ S1 @ S2 ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % if_rule
% 0.20/0.46 thf(fact_9_if__rule,axiom,
% 0.20/0.46 ! [B: $o,S1: refine432681134nres_b,Phi: b > $o,S2: refine432681134nres_b] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_le527798542nres_b @ S1 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_le527798542nres_b @ S2 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.20/0.46 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ S1 @ S2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % if_rule
% 0.20/0.46 thf(fact_10_if__rule,axiom,
% 0.20/0.46 ! [B: $o,S1: refine424419629nres_a,Phi: a > $o,S2: refine424419629nres_a] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_le519537037nres_a @ S1 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_le519537037nres_a @ S2 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ S1 @ S2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % if_rule
% 0.20/0.46 thf(fact_11_RES__rule,axiom,
% 0.20/0.46 ! [S: set_Product_prod_a_a,Phi: product_prod_a_a > $o] :
% 0.20/0.46 ( ! [X3: product_prod_a_a] :
% 0.20/0.46 ( ( member449909584od_a_a @ X3 @ S )
% 0.20/0.46 => ( Phi @ X3 ) )
% 0.20/0.46 => ( ord_le915866422od_a_a @ ( refine622451633od_a_a @ S ) @ ( refine622451633od_a_a @ ( collec645855634od_a_a @ Phi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_rule
% 0.20/0.46 thf(fact_12_RES__rule,axiom,
% 0.20/0.46 ! [S: set_Product_prod_b_a,Phi: product_prod_b_a > $o] :
% 0.20/0.46 ( ! [X3: product_prod_b_a] :
% 0.20/0.46 ( ( member1277678991od_b_a @ X3 @ S )
% 0.20/0.46 => ( Phi @ X3 ) )
% 0.20/0.46 => ( ord_le1135777269od_b_a @ ( refine1450221040od_b_a @ S ) @ ( refine1450221040od_b_a @ ( collec1473625041od_b_a @ Phi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_rule
% 0.20/0.46 thf(fact_13_RES__rule,axiom,
% 0.20/0.46 ! [S: set_Product_prod_b_b,Phi: product_prod_b_b > $o] :
% 0.20/0.46 ( ! [X3: product_prod_b_b] :
% 0.20/0.46 ( ( member1285940496od_b_b @ X3 @ S )
% 0.20/0.46 => ( Phi @ X3 ) )
% 0.20/0.46 => ( ord_le127857910od_b_b @ ( refine1458482545od_b_b @ S ) @ ( refine1458482545od_b_b @ ( collec1481886546od_b_b @ Phi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_rule
% 0.20/0.46 thf(fact_14_RES__rule,axiom,
% 0.20/0.46 ! [S: set_Product_prod_a_b,Phi: product_prod_a_b > $o] :
% 0.20/0.46 ( ! [X3: product_prod_a_b] :
% 0.20/0.46 ( ( member458171089od_a_b @ X3 @ S )
% 0.20/0.46 => ( Phi @ X3 ) )
% 0.20/0.46 => ( ord_le2055430711od_a_b @ ( refine630713138od_a_b @ S ) @ ( refine630713138od_a_b @ ( collec654117139od_a_b @ Phi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_rule
% 0.20/0.46 thf(fact_15_RES__rule,axiom,
% 0.20/0.46 ! [S: set_Product_unit,Phi: product_unit > $o] :
% 0.20/0.46 ( ! [X3: product_unit] :
% 0.20/0.46 ( ( member_Product_unit @ X3 @ S )
% 0.20/0.46 => ( Phi @ X3 ) )
% 0.20/0.46 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ S ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_rule
% 0.20/0.46 thf(fact_16_RES__rule,axiom,
% 0.20/0.46 ! [S: set_b,Phi: b > $o] :
% 0.20/0.46 ( ! [X3: b] :
% 0.20/0.46 ( ( member_b @ X3 @ S )
% 0.20/0.46 => ( Phi @ X3 ) )
% 0.20/0.46 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_rule
% 0.20/0.46 thf(fact_17_RES__rule,axiom,
% 0.20/0.46 ! [S: set_a,Phi: a > $o] :
% 0.20/0.46 ( ! [X3: a] :
% 0.20/0.46 ( ( member_a @ X3 @ S )
% 0.20/0.46 => ( Phi @ X3 ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_rule
% 0.20/0.46 thf(fact_18_SPEC__rule,axiom,
% 0.20/0.46 ! [Phi: product_unit > $o,Phi2: product_unit > $o] :
% 0.20/0.46 ( ! [X3: product_unit] :
% 0.20/0.46 ( ( Phi @ X3 )
% 0.20/0.46 => ( Phi2 @ X3 ) )
% 0.20/0.46 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SPEC_rule
% 0.20/0.46 thf(fact_19_SPEC__rule,axiom,
% 0.20/0.46 ! [Phi: b > $o,Phi2: b > $o] :
% 0.20/0.46 ( ! [X3: b] :
% 0.20/0.46 ( ( Phi @ X3 )
% 0.20/0.46 => ( Phi2 @ X3 ) )
% 0.20/0.46 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SPEC_rule
% 0.20/0.46 thf(fact_20_SPEC__rule,axiom,
% 0.20/0.46 ! [Phi: a > $o,Phi2: a > $o] :
% 0.20/0.46 ( ! [X3: a] :
% 0.20/0.46 ( ( Phi @ X3 )
% 0.20/0.46 => ( Phi2 @ X3 ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SPEC_rule
% 0.20/0.46 thf(fact_21_SPEC__trans,axiom,
% 0.20/0.46 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit,Postcond: product_unit > $o] :
% 0.20/0.46 ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 0.20/0.46 => ( ( ord_le1051254044t_unit @ Y3 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) )
% 0.20/0.46 => ( ord_le1051254044t_unit @ X4 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SPEC_trans
% 0.20/0.46 thf(fact_22_SPEC__trans,axiom,
% 0.20/0.46 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b,Postcond: b > $o] :
% 0.20/0.46 ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 0.20/0.46 => ( ( ord_le527798542nres_b @ Y3 @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) )
% 0.20/0.46 => ( ord_le527798542nres_b @ X4 @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SPEC_trans
% 0.20/0.46 thf(fact_23_SPEC__trans,axiom,
% 0.20/0.46 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Postcond: a > $o] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ Y3 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ X4 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SPEC_trans
% 0.20/0.46 thf(fact_24_lhs__step__If,axiom,
% 0.20/0.46 ! [B: $o,T: set_b,M: set_b,E: set_b] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_less_eq_set_b @ T @ M ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_less_eq_set_b @ E @ M ) )
% 0.20/0.46 => ( ord_less_eq_set_b @ ( if_set_b @ B @ T @ E ) @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lhs_step_If
% 0.20/0.46 thf(fact_25_lhs__step__If,axiom,
% 0.20/0.46 ! [B: $o,T: set_a,M: set_a,E: set_a] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_less_eq_set_a @ T @ M ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_less_eq_set_a @ E @ M ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( if_set_a @ B @ T @ E ) @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lhs_step_If
% 0.20/0.46 thf(fact_26_lhs__step__If,axiom,
% 0.20/0.46 ! [B: $o,T: $o > refine424419629nres_a,M: $o > refine424419629nres_a,E: $o > refine424419629nres_a] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_le516598614nres_a @ T @ M ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_le516598614nres_a @ E @ M ) )
% 0.20/0.46 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B @ T @ E ) @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lhs_step_If
% 0.20/0.46 thf(fact_27_lhs__step__If,axiom,
% 0.20/0.46 ! [B: $o,T: $o > refine432681134nres_b,M: $o > refine432681134nres_b,E: $o > refine432681134nres_b] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_le1656162903nres_b @ T @ M ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_le1656162903nres_b @ E @ M ) )
% 0.20/0.46 => ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ B @ T @ E ) @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lhs_step_If
% 0.20/0.46 thf(fact_28_lhs__step__If,axiom,
% 0.20/0.46 ! [B: $o,T: refine787176636t_unit,M: refine787176636t_unit,E: refine787176636t_unit] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_le1051254044t_unit @ T @ M ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_le1051254044t_unit @ E @ M ) )
% 0.20/0.46 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ T @ E ) @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lhs_step_If
% 0.20/0.46 thf(fact_29_lhs__step__If,axiom,
% 0.20/0.46 ! [B: $o,T: refine424419629nres_a,M: refine424419629nres_a,E: refine424419629nres_a] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_le519537037nres_a @ T @ M ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_le519537037nres_a @ E @ M ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lhs_step_If
% 0.20/0.46 thf(fact_30_lhs__step__If,axiom,
% 0.20/0.46 ! [B: $o,T: refine432681134nres_b,M: refine432681134nres_b,E: refine432681134nres_b] :
% 0.20/0.46 ( ( B
% 0.20/0.46 => ( ord_le527798542nres_b @ T @ M ) )
% 0.20/0.46 => ( ( ~ B
% 0.20/0.46 => ( ord_le527798542nres_b @ E @ M ) )
% 0.20/0.46 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ T @ E ) @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lhs_step_If
% 0.20/0.46 thf(fact_31_SPEC__cons__rule,axiom,
% 0.20/0.46 ! [M: refine787176636t_unit,Phi: product_unit > $o,Psi: product_unit > $o] :
% 0.20/0.46 ( ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) )
% 0.20/0.46 => ( ! [X3: product_unit] :
% 0.20/0.46 ( ( Phi @ X3 )
% 0.20/0.46 => ( Psi @ X3 ) )
% 0.20/0.46 => ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Psi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SPEC_cons_rule
% 0.20/0.46 thf(fact_32_SPEC__cons__rule,axiom,
% 0.20/0.46 ! [M: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.20/0.46 => ( ! [X3: a] :
% 0.20/0.46 ( ( Phi @ X3 )
% 0.20/0.46 => ( Psi @ X3 ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SPEC_cons_rule
% 0.20/0.46 thf(fact_33_SPEC__cons__rule,axiom,
% 0.20/0.46 ! [M: refine432681134nres_b,Phi: b > $o,Psi: b > $o] :
% 0.20/0.46 ( ( ord_le527798542nres_b @ M @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) )
% 0.20/0.46 => ( ! [X3: b] :
% 0.20/0.46 ( ( Phi @ X3 )
% 0.20/0.46 => ( Psi @ X3 ) )
% 0.20/0.46 => ( ord_le527798542nres_b @ M @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % SPEC_cons_rule
% 0.20/0.46 thf(fact_34_RES__bind__choose,axiom,
% 0.20/0.46 ! [X4: a,X: set_a,M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.20/0.46 ( ( member_a @ X4 @ X )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ M @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_bind_choose
% 0.20/0.46 thf(fact_35_RES__bind__choose,axiom,
% 0.20/0.46 ! [X4: a,X: set_a,M: refine432681134nres_b,F: a > refine432681134nres_b] :
% 0.20/0.46 ( ( member_a @ X4 @ X )
% 0.20/0.46 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 0.20/0.46 => ( ord_le527798542nres_b @ M @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_bind_choose
% 0.20/0.46 thf(fact_36_RES__bind__choose,axiom,
% 0.20/0.46 ! [X4: b,X: set_b,M: refine432681134nres_b,F: b > refine432681134nres_b] :
% 0.20/0.46 ( ( member_b @ X4 @ X )
% 0.20/0.46 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 0.20/0.46 => ( ord_le527798542nres_b @ M @ ( refine1264602246nd_b_b @ ( refine1198353289_RES_b @ X ) @ F ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % RES_bind_choose
% 0.20/0.46 thf(fact_37_RES__bind__choose,axiom,
% 0.20/0.47 ! [X4: b,X: set_b,M: refine424419629nres_a,F: b > refine424419629nres_a] :
% 0.20/0.47 ( ( member_b @ X4 @ X )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 0.20/0.47 => ( ord_le519537037nres_a @ M @ ( refine1264602245nd_b_a @ ( refine1198353289_RES_b @ X ) @ F ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % RES_bind_choose
% 0.20/0.47 thf(fact_38_RES__bind__choose,axiom,
% 0.20/0.47 ! [X4: a,X: set_a,M: refine787176636t_unit,F: a > refine787176636t_unit] :
% 0.20/0.47 ( ( member_a @ X4 @ X )
% 0.20/0.47 => ( ( ord_le1051254044t_unit @ M @ ( F @ X4 ) )
% 0.20/0.47 => ( ord_le1051254044t_unit @ M @ ( refine96995669t_unit @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % RES_bind_choose
% 0.20/0.47 thf(fact_39_RES__bind__choose,axiom,
% 0.20/0.47 ! [X4: b,X: set_b,M: refine787176636t_unit,F: b > refine787176636t_unit] :
% 0.20/0.47 ( ( member_b @ X4 @ X )
% 0.20/0.47 => ( ( ord_le1051254044t_unit @ M @ ( F @ X4 ) )
% 0.20/0.47 => ( ord_le1051254044t_unit @ M @ ( refine216248468t_unit @ ( refine1198353289_RES_b @ X ) @ F ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % RES_bind_choose
% 0.20/0.47 thf(fact_40_RES__bind__choose,axiom,
% 0.20/0.47 ! [X4: product_unit,X: set_Product_unit,M: refine432681134nres_b,F: product_unit > refine432681134nres_b] :
% 0.20/0.47 ( ( member_Product_unit @ X4 @ X )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 0.20/0.47 => ( ord_le527798542nres_b @ M @ ( refine119808504unit_b @ ( refine1777164439t_unit @ X ) @ F ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % RES_bind_choose
% 0.20/0.47 thf(fact_41_RES__bind__choose,axiom,
% 0.20/0.47 ! [X4: product_unit,X: set_Product_unit,M: refine424419629nres_a,F: product_unit > refine424419629nres_a] :
% 0.20/0.47 ( ( member_Product_unit @ X4 @ X )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 0.20/0.47 => ( ord_le519537037nres_a @ M @ ( refine119808503unit_a @ ( refine1777164439t_unit @ X ) @ F ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % RES_bind_choose
% 0.20/0.47 thf(fact_42_RES__bind__choose,axiom,
% 0.20/0.47 ! [X4: product_unit,X: set_Product_unit,M: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 0.20/0.47 ( ( member_Product_unit @ X4 @ X )
% 0.20/0.47 => ( ( ord_le1051254044t_unit @ M @ ( F @ X4 ) )
% 0.20/0.47 => ( ord_le1051254044t_unit @ M @ ( refine681446406t_unit @ ( refine1777164439t_unit @ X ) @ F ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % RES_bind_choose
% 0.20/0.47 thf(fact_43_RES__bind__choose,axiom,
% 0.20/0.47 ! [X4: product_prod_a_a,X: set_Product_prod_a_a,M: refine432681134nres_b,F: product_prod_a_a > refine432681134nres_b] :
% 0.20/0.47 ( ( member449909584od_a_a @ X4 @ X )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 0.20/0.47 => ( ord_le527798542nres_b @ M @ ( refine988994910_a_a_b @ ( refine622451633od_a_a @ X ) @ F ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % RES_bind_choose
% 0.20/0.47 thf(fact_44_order__mono__setup_Orefl,axiom,
% 0.20/0.47 ! [X4: set_b] : ( ord_less_eq_set_b @ X4 @ X4 ) ).
% 0.20/0.47
% 0.20/0.47 % order_mono_setup.refl
% 0.20/0.47 thf(fact_45_order__mono__setup_Orefl,axiom,
% 0.20/0.47 ! [X4: set_a] : ( ord_less_eq_set_a @ X4 @ X4 ) ).
% 0.20/0.47
% 0.20/0.47 % order_mono_setup.refl
% 0.20/0.47 thf(fact_46_order__mono__setup_Orefl,axiom,
% 0.20/0.47 ! [X4: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ X4 @ X4 ) ).
% 0.20/0.47
% 0.20/0.47 % order_mono_setup.refl
% 0.20/0.47 thf(fact_47_order__mono__setup_Orefl,axiom,
% 0.20/0.47 ! [X4: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ X4 @ X4 ) ).
% 0.20/0.47
% 0.20/0.47 % order_mono_setup.refl
% 0.20/0.47 thf(fact_48_order__mono__setup_Orefl,axiom,
% 0.20/0.47 ! [X4: refine787176636t_unit] : ( ord_le1051254044t_unit @ X4 @ X4 ) ).
% 0.20/0.47
% 0.20/0.47 % order_mono_setup.refl
% 0.20/0.47 thf(fact_49_order__mono__setup_Orefl,axiom,
% 0.20/0.47 ! [X4: refine432681134nres_b] : ( ord_le527798542nres_b @ X4 @ X4 ) ).
% 0.20/0.47
% 0.20/0.47 % order_mono_setup.refl
% 0.20/0.47 thf(fact_50_order__mono__setup_Orefl,axiom,
% 0.20/0.47 ! [X4: refine424419629nres_a] : ( ord_le519537037nres_a @ X4 @ X4 ) ).
% 0.20/0.47
% 0.20/0.47 % order_mono_setup.refl
% 0.20/0.47 thf(fact_51_the__RES_Osimps,axiom,
% 0.20/0.47 ! [X: set_Product_unit] :
% 0.20/0.47 ( ( refine1208325748t_unit @ ( refine1777164439t_unit @ X ) )
% 0.20/0.47 = X ) ).
% 0.20/0.47
% 0.20/0.47 % the_RES.simps
% 0.20/0.47 thf(fact_52_the__RES_Osimps,axiom,
% 0.20/0.47 ! [X: set_a] :
% 0.20/0.47 ( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ X ) )
% 0.20/0.47 = X ) ).
% 0.20/0.47
% 0.20/0.47 % the_RES.simps
% 0.20/0.47 thf(fact_53_the__RES_Osimps,axiom,
% 0.20/0.47 ! [X: set_b] :
% 0.20/0.47 ( ( refine1822134886_RES_b @ ( refine1198353289_RES_b @ X ) )
% 0.20/0.47 = X ) ).
% 0.20/0.47
% 0.20/0.47 % the_RES.simps
% 0.20/0.47 thf(fact_54_nf__inres__RES,axiom,
% 0.20/0.47 ! [X: set_Product_prod_a_a,X4: product_prod_a_a] :
% 0.20/0.47 ( ( refine378960780od_a_a @ ( refine622451633od_a_a @ X ) @ X4 )
% 0.20/0.47 = ( member449909584od_a_a @ X4 @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_RES
% 0.20/0.47 thf(fact_55_nf__inres__RES,axiom,
% 0.20/0.47 ! [X: set_Product_prod_b_a,X4: product_prod_b_a] :
% 0.20/0.47 ( ( refine1206730187od_b_a @ ( refine1450221040od_b_a @ X ) @ X4 )
% 0.20/0.47 = ( member1277678991od_b_a @ X4 @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_RES
% 0.20/0.47 thf(fact_56_nf__inres__RES,axiom,
% 0.20/0.47 ! [X: set_Product_prod_b_b,X4: product_prod_b_b] :
% 0.20/0.47 ( ( refine1214991692od_b_b @ ( refine1458482545od_b_b @ X ) @ X4 )
% 0.20/0.47 = ( member1285940496od_b_b @ X4 @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_RES
% 0.20/0.47 thf(fact_57_nf__inres__RES,axiom,
% 0.20/0.47 ! [X: set_Product_prod_a_b,X4: product_prod_a_b] :
% 0.20/0.47 ( ( refine387222285od_a_b @ ( refine630713138od_a_b @ X ) @ X4 )
% 0.20/0.47 = ( member458171089od_a_b @ X4 @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_RES
% 0.20/0.47 thf(fact_58_nf__inres__RES,axiom,
% 0.20/0.47 ! [X: set_Product_unit,X4: product_unit] :
% 0.20/0.47 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ X ) @ X4 )
% 0.20/0.47 = ( member_Product_unit @ X4 @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_RES
% 0.20/0.47 thf(fact_59_nf__inres__RES,axiom,
% 0.20/0.47 ! [X: set_a,X4: a] :
% 0.20/0.47 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X ) @ X4 )
% 0.20/0.47 = ( member_a @ X4 @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_RES
% 0.20/0.47 thf(fact_60_nf__inres__RES,axiom,
% 0.20/0.47 ! [X: set_b,X4: b] :
% 0.20/0.47 ( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ X ) @ X4 )
% 0.20/0.47 = ( member_b @ X4 @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_RES
% 0.20/0.47 thf(fact_61_nf__inres__SPEC,axiom,
% 0.20/0.47 ! [Phi: product_unit > $o,X4: product_unit] :
% 0.20/0.47 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ X4 )
% 0.20/0.47 = ( Phi @ X4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_SPEC
% 0.20/0.47 thf(fact_62_nf__inres__SPEC,axiom,
% 0.20/0.47 ! [Phi: a > $o,X4: a] :
% 0.20/0.47 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ X4 )
% 0.20/0.47 = ( Phi @ X4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_SPEC
% 0.20/0.47 thf(fact_63_nf__inres__SPEC,axiom,
% 0.20/0.47 ! [Phi: b > $o,X4: b] :
% 0.20/0.47 ( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) @ X4 )
% 0.20/0.47 = ( Phi @ X4 ) ) ).
% 0.20/0.47
% 0.20/0.47 % nf_inres_SPEC
% 0.20/0.47 thf(fact_64_le__funD,axiom,
% 0.20/0.47 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 0.20/0.47 ( ( ord_le516598614nres_a @ F @ G )
% 0.20/0.47 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funD
% 0.20/0.47 thf(fact_65_le__funD,axiom,
% 0.20/0.47 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X4: $o] :
% 0.20/0.47 ( ( ord_le1656162903nres_b @ F @ G )
% 0.20/0.47 => ( ord_le527798542nres_b @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funD
% 0.20/0.47 thf(fact_66_le__funE,axiom,
% 0.20/0.47 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 0.20/0.47 ( ( ord_le516598614nres_a @ F @ G )
% 0.20/0.47 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funE
% 0.20/0.47 thf(fact_67_le__funE,axiom,
% 0.20/0.47 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X4: $o] :
% 0.20/0.47 ( ( ord_le1656162903nres_b @ F @ G )
% 0.20/0.47 => ( ord_le527798542nres_b @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funE
% 0.20/0.47 thf(fact_68_le__funI,axiom,
% 0.20/0.47 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a] :
% 0.20/0.47 ( ! [X3: $o] : ( ord_le519537037nres_a @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.20/0.47 => ( ord_le516598614nres_a @ F @ G ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funI
% 0.20/0.47 thf(fact_69_Refine__Misc_Oif__mono,axiom,
% 0.20/0.47 ! [B: $o,M1: refine432681134nres_b,M12: refine432681134nres_b,M2: refine432681134nres_b,M22: refine432681134nres_b] :
% 0.20/0.47 ( ( B
% 0.20/0.47 => ( ord_le527798542nres_b @ M1 @ M12 ) )
% 0.20/0.47 => ( ( ~ B
% 0.20/0.47 => ( ord_le527798542nres_b @ M2 @ M22 ) )
% 0.20/0.47 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ M1 @ M2 ) @ ( if_Ref1732808808nres_b @ B @ M12 @ M22 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Refine_Misc.if_mono
% 0.20/0.47 thf(fact_70_Refine__Misc_Oif__mono,axiom,
% 0.20/0.47 ! [B: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M2: refine424419629nres_a,M22: refine424419629nres_a] :
% 0.20/0.47 ( ( B
% 0.20/0.47 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 0.20/0.47 => ( ( ~ B
% 0.20/0.47 => ( ord_le519537037nres_a @ M2 @ M22 ) )
% 0.20/0.47 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ M1 @ M2 ) @ ( if_Ref1724547303nres_a @ B @ M12 @ M22 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Refine_Misc.if_mono
% 0.20/0.47 thf(fact_71_order__subst1,axiom,
% 0.20/0.47 ! [A: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ A @ ( F @ B ) )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ B @ C )
% 0.20/0.47 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.20/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.20/0.47 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_subst1
% 0.20/0.47 thf(fact_72_order__subst1,axiom,
% 0.20/0.47 ! [A: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ A @ ( F @ B ) )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ B @ C )
% 0.20/0.47 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.20/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.20/0.47 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_subst1
% 0.20/0.47 thf(fact_73_order__subst1,axiom,
% 0.20/0.47 ! [A: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ B @ C )
% 0.20/0.47 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.20/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.20/0.47 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_subst1
% 0.20/0.47 thf(fact_74_order__subst1,axiom,
% 0.20/0.47 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ B @ C )
% 0.20/0.47 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.20/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.20/0.47 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_subst1
% 0.20/0.47 thf(fact_75_less__eq__nres_Osimps_I2_J,axiom,
% 0.20/0.47 ! [A: set_a,B: set_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 0.20/0.47 = ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_nres.simps(2)
% 0.20/0.47 thf(fact_76_less__eq__nres_Osimps_I2_J,axiom,
% 0.20/0.47 ! [A: set_b,B: set_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine1198353289_RES_b @ B ) )
% 0.20/0.47 = ( ord_less_eq_set_b @ A @ B ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_nres.simps(2)
% 0.20/0.47 thf(fact_77_nres__order__simps_I5_J,axiom,
% 0.20/0.47 ! [X: set_a,Y: set_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine1198353288_RES_a @ Y ) )
% 0.20/0.47 = ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % nres_order_simps(5)
% 0.20/0.47 thf(fact_78_nres__order__simps_I5_J,axiom,
% 0.20/0.47 ! [X: set_b,Y: set_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ X ) @ ( refine1198353289_RES_b @ Y ) )
% 0.20/0.47 = ( ord_less_eq_set_b @ X @ Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % nres_order_simps(5)
% 0.20/0.47 thf(fact_79_order__mono__setup_Omono__if,axiom,
% 0.20/0.47 ! [T: refine432681134nres_b,T2: refine432681134nres_b,E: refine432681134nres_b,E2: refine432681134nres_b,B: $o] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ T @ T2 )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ E @ E2 )
% 0.20/0.47 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ T @ E ) @ ( if_Ref1732808808nres_b @ B @ T2 @ E2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_mono_setup.mono_if
% 0.20/0.47 thf(fact_80_order__mono__setup_Omono__if,axiom,
% 0.20/0.47 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B: $o] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ T @ T2 )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ E @ E2 )
% 0.20/0.47 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ ( if_Ref1724547303nres_a @ B @ T2 @ E2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_mono_setup.mono_if
% 0.20/0.47 thf(fact_81_dual__order_Oantisym,axiom,
% 0.20/0.47 ! [B: refine432681134nres_b,A: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ B @ A )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ A @ B )
% 0.20/0.47 => ( A = B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.antisym
% 0.20/0.47 thf(fact_82_dual__order_Oantisym,axiom,
% 0.20/0.47 ! [B: refine424419629nres_a,A: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ B @ A )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ A @ B )
% 0.20/0.47 => ( A = B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.antisym
% 0.20/0.47 thf(fact_83_dual__order_Oeq__iff,axiom,
% 0.20/0.47 ( ( ^ [Y5: refine432681134nres_b,Z: refine432681134nres_b] : ( Y5 = Z ) )
% 0.20/0.47 = ( ^ [A2: refine432681134nres_b,B2: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ B2 @ A2 )
% 0.20/0.47 & ( ord_le527798542nres_b @ A2 @ B2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.eq_iff
% 0.20/0.47 thf(fact_84_dual__order_Oeq__iff,axiom,
% 0.20/0.47 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 0.20/0.47 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.20/0.47 & ( ord_le519537037nres_a @ A2 @ B2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.eq_iff
% 0.20/0.47 thf(fact_85_dual__order_Otrans,axiom,
% 0.20/0.47 ! [B: refine432681134nres_b,A: refine432681134nres_b,C: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ B @ A )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ C @ B )
% 0.20/0.47 => ( ord_le527798542nres_b @ C @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.trans
% 0.20/0.47 thf(fact_86_dual__order_Otrans,axiom,
% 0.20/0.47 ! [B: refine424419629nres_a,A: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ B @ A )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ C @ B )
% 0.20/0.47 => ( ord_le519537037nres_a @ C @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.trans
% 0.20/0.47 thf(fact_87_dual__order_Orefl,axiom,
% 0.20/0.47 ! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.refl
% 0.20/0.47 thf(fact_88_dual__order_Orefl,axiom,
% 0.20/0.47 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.refl
% 0.20/0.47 thf(fact_89_order__trans,axiom,
% 0.20/0.47 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b,Z2: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ Y3 @ Z2 )
% 0.20/0.47 => ( ord_le527798542nres_b @ X4 @ Z2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_trans
% 0.20/0.47 thf(fact_90_order__trans,axiom,
% 0.20/0.47 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 0.20/0.47 => ( ord_le519537037nres_a @ X4 @ Z2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_trans
% 0.20/0.47 thf(fact_91_order__class_Oorder_Oantisym,axiom,
% 0.20/0.47 ! [A: refine432681134nres_b,B: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ A @ B )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ B @ A )
% 0.20/0.47 => ( A = B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_class.order.antisym
% 0.20/0.47 thf(fact_92_order__class_Oorder_Oantisym,axiom,
% 0.20/0.47 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ A @ B )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ B @ A )
% 0.20/0.47 => ( A = B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_class.order.antisym
% 0.20/0.47 thf(fact_93_ord__le__eq__trans,axiom,
% 0.20/0.47 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ A @ B )
% 0.20/0.47 => ( ( B = C )
% 0.20/0.47 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_le_eq_trans
% 0.20/0.47 thf(fact_94_ord__le__eq__trans,axiom,
% 0.20/0.47 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ A @ B )
% 0.20/0.47 => ( ( B = C )
% 0.20/0.47 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_le_eq_trans
% 0.20/0.47 thf(fact_95_ord__eq__le__trans,axiom,
% 0.20/0.47 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ B @ C )
% 0.20/0.47 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_eq_le_trans
% 0.20/0.47 thf(fact_96_ord__eq__le__trans,axiom,
% 0.20/0.47 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ B @ C )
% 0.20/0.47 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_eq_le_trans
% 0.20/0.47 thf(fact_97_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.47 ( ( ^ [Y5: refine432681134nres_b,Z: refine432681134nres_b] : ( Y5 = Z ) )
% 0.20/0.47 = ( ^ [A2: refine432681134nres_b,B2: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.20/0.47 & ( ord_le527798542nres_b @ B2 @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_class.order.eq_iff
% 0.20/0.47 thf(fact_98_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.47 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 0.20/0.47 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.47 & ( ord_le519537037nres_a @ B2 @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_class.order.eq_iff
% 0.20/0.47 thf(fact_99_antisym__conv,axiom,
% 0.20/0.47 ! [Y3: refine432681134nres_b,X4: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ Y3 @ X4 )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 0.20/0.47 = ( X4 = Y3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % antisym_conv
% 0.20/0.47 thf(fact_100_antisym__conv,axiom,
% 0.20/0.47 ! [Y3: refine424419629nres_a,X4: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.20/0.47 = ( X4 = Y3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % antisym_conv
% 0.20/0.47 thf(fact_101_order_Otrans,axiom,
% 0.20/0.47 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ A @ B )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ B @ C )
% 0.20/0.47 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order.trans
% 0.20/0.47 thf(fact_102_order_Otrans,axiom,
% 0.20/0.47 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ A @ B )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ B @ C )
% 0.20/0.47 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order.trans
% 0.20/0.47 thf(fact_103_eq__refl,axiom,
% 0.20/0.47 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.20/0.47 ( ( X4 = Y3 )
% 0.20/0.47 => ( ord_le527798542nres_b @ X4 @ Y3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_refl
% 0.20/0.47 thf(fact_104_eq__refl,axiom,
% 0.20/0.47 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.47 ( ( X4 = Y3 )
% 0.20/0.47 => ( ord_le519537037nres_a @ X4 @ Y3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_refl
% 0.20/0.47 thf(fact_105_antisym,axiom,
% 0.20/0.47 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.20/0.47 ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 0.20/0.47 => ( ( ord_le527798542nres_b @ Y3 @ X4 )
% 0.20/0.47 => ( X4 = Y3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % antisym
% 0.20/0.47 thf(fact_106_antisym,axiom,
% 0.20/0.47 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.47 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.20/0.47 => ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 0.20/0.47 => ( X4 = Y3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % antisym
% 0.20/0.47 thf(fact_107_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: a,P: a > $o] :
% 0.20/0.47 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.20/0.47 = ( P @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_108_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A: b,P: b > $o] :
% 0.20/0.47 ( ( member_b @ A @ ( collect_b @ P ) )
% 0.20/0.47 = ( P @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_109_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A3: set_a] :
% 0.20/0.47 ( ( collect_a
% 0.20/0.47 @ ^ [X5: a] : ( member_a @ X5 @ A3 ) )
% 0.20/0.47 = A3 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_110_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A3: set_b] :
% 0.20/0.47 ( ( collect_b
% 0.20/0.47 @ ^ [X5: b] : ( member_b @ X5 @ A3 ) )
% 0.20/0.47 = A3 ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_111_Collect__cong,axiom,
% 0.20/0.47 ! [P: a > $o,Q: a > $o] :
% 0.20/0.47 ( ! [X3: a] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( collect_a @ P )
% 0.20/0.47 = ( collect_a @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_112_Collect__cong,axiom,
% 0.20/0.47 ! [P: b > $o,Q: b > $o] :
% 0.20/0.47 ( ! [X3: b] :
% 0.20/0.47 ( ( P @ X3 )
% 0.20/0.47 = ( Q @ X3 ) )
% 0.20/0.47 => ( ( collect_b @ P )
% 0.20/0.47 = ( collect_b @ Q ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_cong
% 0.20/0.47 thf(fact_113_eq__iff,axiom,
% 0.20/0.47 ( ( ^ [Y5: refine432681134nres_b,Z: refine432681134nres_b] : ( Y5 = Z ) )
% 0.32/0.47 = ( ^ [X5: refine432681134nres_b,Y6: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ X5 @ Y6 )
% 0.32/0.47 & ( ord_le527798542nres_b @ Y6 @ X5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_iff
% 0.32/0.47 thf(fact_114_eq__iff,axiom,
% 0.32/0.47 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 0.32/0.47 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ X5 @ Y6 )
% 0.32/0.47 & ( ord_le519537037nres_a @ Y6 @ X5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_iff
% 0.32/0.47 thf(fact_115_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ A @ B )
% 0.32/0.47 => ( ( ( F @ B )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_116_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ A @ B )
% 0.32/0.47 => ( ( ( F @ B )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_117_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ A @ B )
% 0.32/0.47 => ( ( ( F @ B )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_118_ord__le__eq__subst,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ A @ B )
% 0.32/0.47 => ( ( ( F @ B )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_le_eq_subst
% 0.32/0.47 thf(fact_119_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.32/0.47 ( ( A
% 0.32/0.47 = ( F @ B ) )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ B @ C )
% 0.32/0.47 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_120_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.32/0.47 ( ( A
% 0.32/0.47 = ( F @ B ) )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ B @ C )
% 0.32/0.47 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_121_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.32/0.47 ( ( A
% 0.32/0.47 = ( F @ B ) )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ B @ C )
% 0.32/0.47 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_122_ord__eq__le__subst,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.32/0.47 ( ( A
% 0.32/0.47 = ( F @ B ) )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ B @ C )
% 0.32/0.47 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_subst
% 0.32/0.47 thf(fact_123_order__subst2,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ A @ B )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( F @ B ) @ C )
% 0.32/0.47 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_124_order__subst2,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ A @ B )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.32/0.47 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_125_order__subst2,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ A @ B )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( F @ B ) @ C )
% 0.32/0.47 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_126_order__subst2,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ A @ B )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.32/0.47 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order_subst2
% 0.32/0.47 thf(fact_127_the__RES__inv,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a] :
% 0.32/0.47 ( ( refine412683989fail_a @ M )
% 0.32/0.47 => ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ M ) )
% 0.32/0.47 = M ) ) ).
% 0.32/0.47
% 0.32/0.47 % the_RES_inv
% 0.32/0.47 thf(fact_128_the__RES__inv,axiom,
% 0.32/0.47 ! [M: refine432681134nres_b] :
% 0.32/0.47 ( ( refine412683990fail_b @ M )
% 0.32/0.47 => ( ( refine1198353289_RES_b @ ( refine1822134886_RES_b @ M ) )
% 0.32/0.47 = M ) ) ).
% 0.32/0.47
% 0.32/0.47 % the_RES_inv
% 0.32/0.47 thf(fact_129_Greatest__equality,axiom,
% 0.32/0.47 ! [P: refine432681134nres_b > $o,X4: refine432681134nres_b] :
% 0.32/0.47 ( ( P @ X4 )
% 0.32/0.47 => ( ! [Y4: refine432681134nres_b] :
% 0.32/0.47 ( ( P @ Y4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ Y4 @ X4 ) )
% 0.32/0.47 => ( ( order_1722590613nres_b @ P )
% 0.32/0.47 = X4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Greatest_equality
% 0.32/0.47 thf(fact_130_Greatest__equality,axiom,
% 0.32/0.47 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a] :
% 0.32/0.47 ( ( P @ X4 )
% 0.32/0.47 => ( ! [Y4: refine424419629nres_a] :
% 0.32/0.47 ( ( P @ Y4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 0.32/0.47 => ( ( order_1714329108nres_a @ P )
% 0.32/0.47 = X4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Greatest_equality
% 0.32/0.47 thf(fact_131_GreatestI2__order,axiom,
% 0.32/0.47 ! [P: refine432681134nres_b > $o,X4: refine432681134nres_b,Q: refine432681134nres_b > $o] :
% 0.32/0.47 ( ( P @ X4 )
% 0.32/0.47 => ( ! [Y4: refine432681134nres_b] :
% 0.32/0.47 ( ( P @ Y4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ Y4 @ X4 ) )
% 0.32/0.47 => ( ! [X3: refine432681134nres_b] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 => ( ! [Y7: refine432681134nres_b] :
% 0.32/0.47 ( ( P @ Y7 )
% 0.32/0.47 => ( ord_le527798542nres_b @ Y7 @ X3 ) )
% 0.32/0.47 => ( Q @ X3 ) ) )
% 0.32/0.47 => ( Q @ ( order_1722590613nres_b @ P ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % GreatestI2_order
% 0.32/0.47 thf(fact_132_GreatestI2__order,axiom,
% 0.32/0.47 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 0.32/0.47 ( ( P @ X4 )
% 0.32/0.47 => ( ! [Y4: refine424419629nres_a] :
% 0.32/0.47 ( ( P @ Y4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 0.32/0.47 => ( ! [X3: refine424419629nres_a] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 => ( ! [Y7: refine424419629nres_a] :
% 0.32/0.47 ( ( P @ Y7 )
% 0.32/0.47 => ( ord_le519537037nres_a @ Y7 @ X3 ) )
% 0.32/0.47 => ( Q @ X3 ) ) )
% 0.32/0.47 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % GreatestI2_order
% 0.32/0.47 thf(fact_133_le__rel__bool__arg__iff,axiom,
% 0.32/0.47 ( ord_le1656162903nres_b
% 0.32/0.47 = ( ^ [X6: $o > refine432681134nres_b,Y8: $o > refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 0.32/0.47 & ( ord_le527798542nres_b @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_rel_bool_arg_iff
% 0.32/0.47 thf(fact_134_le__rel__bool__arg__iff,axiom,
% 0.32/0.47 ( ord_le516598614nres_a
% 0.32/0.47 = ( ^ [X6: $o > refine424419629nres_a,Y8: $o > refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 0.32/0.47 & ( ord_le519537037nres_a @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_rel_bool_arg_iff
% 0.32/0.47 thf(fact_135_ord__eq__le__eq__trans,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
% 0.32/0.47 ( ( A = B )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ B @ C )
% 0.32/0.47 => ( ( C = D )
% 0.32/0.47 => ( ord_le527798542nres_b @ A @ D ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_eq_trans
% 0.32/0.47 thf(fact_136_ord__eq__le__eq__trans,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
% 0.32/0.47 ( ( A = B )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ B @ C )
% 0.32/0.47 => ( ( C = D )
% 0.32/0.47 => ( ord_le519537037nres_a @ A @ D ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_le_eq_trans
% 0.32/0.47 thf(fact_137_nofail__simps_I2_J,axiom,
% 0.32/0.47 ! [X: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % nofail_simps(2)
% 0.32/0.47 thf(fact_138_nofail__simps_I2_J,axiom,
% 0.32/0.47 ! [X: set_b] : ( refine412683990fail_b @ ( refine1198353289_RES_b @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % nofail_simps(2)
% 0.32/0.47 thf(fact_139_subset__Collect__conv,axiom,
% 0.32/0.47 ! [S: set_a,P: a > $o] :
% 0.32/0.47 ( ( ord_less_eq_set_a @ S @ ( collect_a @ P ) )
% 0.32/0.47 = ( ! [X5: a] :
% 0.32/0.47 ( ( member_a @ X5 @ S )
% 0.32/0.47 => ( P @ X5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_Collect_conv
% 0.32/0.47 thf(fact_140_subset__Collect__conv,axiom,
% 0.32/0.47 ! [S: set_b,P: b > $o] :
% 0.32/0.47 ( ( ord_less_eq_set_b @ S @ ( collect_b @ P ) )
% 0.32/0.47 = ( ! [X5: b] :
% 0.32/0.47 ( ( member_b @ X5 @ S )
% 0.32/0.47 => ( P @ X5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_Collect_conv
% 0.32/0.47 thf(fact_141_pwD1,axiom,
% 0.32/0.47 ! [S: refine432681134nres_b,S3: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ S @ S3 )
% 0.32/0.47 => ( ( refine412683990fail_b @ S3 )
% 0.32/0.47 => ( refine412683990fail_b @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pwD1
% 0.32/0.47 thf(fact_142_pwD1,axiom,
% 0.32/0.47 ! [S: refine424419629nres_a,S3: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ S @ S3 )
% 0.32/0.47 => ( ( refine412683989fail_a @ S3 )
% 0.32/0.47 => ( refine412683989fail_a @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pwD1
% 0.32/0.47 thf(fact_143_le__nofailI,axiom,
% 0.32/0.47 ! [M3: refine432681134nres_b,M4: refine432681134nres_b] :
% 0.32/0.47 ( ( ( refine412683990fail_b @ M3 )
% 0.32/0.47 => ( ord_le527798542nres_b @ M4 @ M3 ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ M4 @ M3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_nofailI
% 0.32/0.47 thf(fact_144_le__nofailI,axiom,
% 0.32/0.47 ! [M3: refine424419629nres_a,M4: refine424419629nres_a] :
% 0.32/0.47 ( ( ( refine412683989fail_a @ M3 )
% 0.32/0.47 => ( ord_le519537037nres_a @ M4 @ M3 ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ M4 @ M3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_nofailI
% 0.32/0.47 thf(fact_145_nofail__RES__conv,axiom,
% 0.32/0.47 ( refine412683989fail_a
% 0.32/0.47 = ( ^ [M5: refine424419629nres_a] :
% 0.32/0.47 ? [M6: set_a] :
% 0.32/0.47 ( M5
% 0.32/0.47 = ( refine1198353288_RES_a @ M6 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nofail_RES_conv
% 0.32/0.47 thf(fact_146_nofail__RES__conv,axiom,
% 0.32/0.47 ( refine412683990fail_b
% 0.32/0.47 = ( ^ [M5: refine432681134nres_b] :
% 0.32/0.47 ? [M6: set_b] :
% 0.32/0.47 ( M5
% 0.32/0.47 = ( refine1198353289_RES_b @ M6 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nofail_RES_conv
% 0.32/0.47 thf(fact_147_ref__two__step,axiom,
% 0.32/0.47 ! [A3: refine432681134nres_b,R: set_Product_prod_b_b,B3: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ A3 @ ( refine122110613un_b_b @ R @ B3 ) )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ B3 @ C2 )
% 0.32/0.47 => ( ord_le527798542nres_b @ A3 @ ( refine122110613un_b_b @ R @ C2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ref_two_step
% 0.32/0.47 thf(fact_148_ref__two__step,axiom,
% 0.32/0.47 ! [A3: refine432681134nres_b,R: set_Product_prod_b_a,B3: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ A3 @ ( refine122110612un_b_a @ R @ B3 ) )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ B3 @ C2 )
% 0.32/0.47 => ( ord_le527798542nres_b @ A3 @ ( refine122110612un_b_a @ R @ C2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ref_two_step
% 0.32/0.47 thf(fact_149_ref__two__step,axiom,
% 0.32/0.47 ! [A3: refine424419629nres_a,R: set_Product_prod_a_b,B3: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ A3 @ ( refine1441824854un_a_b @ R @ B3 ) )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ B3 @ C2 )
% 0.32/0.47 => ( ord_le519537037nres_a @ A3 @ ( refine1441824854un_a_b @ R @ C2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ref_two_step
% 0.32/0.47 thf(fact_150_ref__two__step,axiom,
% 0.32/0.47 ! [A3: refine424419629nres_a,R: set_Product_prod_a_a,B3: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ A3 @ ( refine1441824853un_a_a @ R @ B3 ) )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ B3 @ C2 )
% 0.32/0.47 => ( ord_le519537037nres_a @ A3 @ ( refine1441824853un_a_a @ R @ C2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ref_two_step
% 0.32/0.47 thf(fact_151_le__RES__nofailI,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a,X4: set_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ X4 ) )
% 0.32/0.47 => ( refine412683989fail_a @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_RES_nofailI
% 0.32/0.47 thf(fact_152_le__RES__nofailI,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b,X4: set_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ X4 ) )
% 0.32/0.47 => ( refine412683990fail_b @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_RES_nofailI
% 0.32/0.47 thf(fact_153_pw__RES__bind__choose_I1_J,axiom,
% 0.32/0.47 ! [X: set_a,F: a > refine432681134nres_b] :
% 0.32/0.47 ( ( refine412683990fail_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X ) @ F ) )
% 0.32/0.47 = ( ! [X5: a] :
% 0.32/0.47 ( ( member_a @ X5 @ X )
% 0.32/0.47 => ( refine412683990fail_b @ ( F @ X5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_RES_bind_choose(1)
% 0.32/0.47 thf(fact_154_rhs__step__bind__RES,axiom,
% 0.32/0.47 ! [X7: a,X8: set_a,M: refine432681134nres_b,R: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( member_a @ X7 @ X8 )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( F2 @ X7 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X8 ) @ F2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rhs_step_bind_RES
% 0.32/0.47 thf(fact_155_rhs__step__bind__RES,axiom,
% 0.32/0.47 ! [X7: a,X8: set_a,M: refine424419629nres_a,R: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( member_a @ X7 @ X8 )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( F2 @ X7 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X8 ) @ F2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rhs_step_bind_RES
% 0.32/0.47 thf(fact_156_rhs__step__bind__SPEC,axiom,
% 0.32/0.47 ! [Phi: a > $o,X7: a,M: refine432681134nres_b,R: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( Phi @ X7 )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( F2 @ X7 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ F2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rhs_step_bind_SPEC
% 0.32/0.47 thf(fact_157_rhs__step__bind__SPEC,axiom,
% 0.32/0.47 ! [Phi: a > $o,X7: a,M: refine424419629nres_a,R: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( Phi @ X7 )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( F2 @ X7 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ F2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rhs_step_bind_SPEC
% 0.32/0.47 thf(fact_158_subsetI,axiom,
% 0.32/0.47 ! [A3: set_a,B3: set_a] :
% 0.32/0.47 ( ! [X3: a] :
% 0.32/0.47 ( ( member_a @ X3 @ A3 )
% 0.32/0.47 => ( member_a @ X3 @ B3 ) )
% 0.32/0.47 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % subsetI
% 0.32/0.47 thf(fact_159_subsetI,axiom,
% 0.32/0.47 ! [A3: set_b,B3: set_b] :
% 0.32/0.47 ( ! [X3: b] :
% 0.32/0.47 ( ( member_b @ X3 @ A3 )
% 0.32/0.47 => ( member_b @ X3 @ B3 ) )
% 0.32/0.47 => ( ord_less_eq_set_b @ A3 @ B3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % subsetI
% 0.32/0.47 thf(fact_160_bind__sim__select__rule,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,F2: a > refine424419629nres_a,Psi: a > $o,F: a > refine432681134nres_b,Phi: b > $o] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) )
% 0.32/0.47 => ( ! [X3: a] :
% 0.32/0.47 ( ( refine412683989fail_a @ M )
% 0.32/0.47 => ( ( refine1001002027nres_a @ M @ X3 )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ ( F2 @ X3 ) @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bind_sim_select_rule
% 0.32/0.47 thf(fact_161_bind__sim__select__rule,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,F2: a > refine432681134nres_b,Psi: b > $o,F: a > refine424419629nres_a,Phi: a > $o] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 0.32/0.47 => ( ! [X3: a] :
% 0.32/0.47 ( ( refine412683989fail_a @ M )
% 0.32/0.47 => ( ( refine1001002027nres_a @ M @ X3 )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( F2 @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bind_sim_select_rule
% 0.32/0.47 thf(fact_162_bind__sim__select__rule,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,F2: a > refine432681134nres_b,Psi: b > $o,F: a > refine432681134nres_b,Phi: b > $o] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 0.32/0.47 => ( ! [X3: a] :
% 0.32/0.47 ( ( refine412683989fail_a @ M )
% 0.32/0.47 => ( ( refine1001002027nres_a @ M @ X3 )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( F2 @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bind_sim_select_rule
% 0.32/0.47 thf(fact_163_in__mono,axiom,
% 0.32/0.47 ! [A3: set_a,B3: set_a,X4: a] :
% 0.32/0.47 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.32/0.47 => ( ( member_a @ X4 @ A3 )
% 0.32/0.47 => ( member_a @ X4 @ B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_mono
% 0.32/0.47 thf(fact_164_in__mono,axiom,
% 0.32/0.47 ! [A3: set_b,B3: set_b,X4: b] :
% 0.32/0.47 ( ( ord_less_eq_set_b @ A3 @ B3 )
% 0.32/0.47 => ( ( member_b @ X4 @ A3 )
% 0.32/0.47 => ( member_b @ X4 @ B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_mono
% 0.32/0.47 thf(fact_165_subsetD,axiom,
% 0.32/0.47 ! [A3: set_a,B3: set_a,C: a] :
% 0.32/0.47 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.32/0.47 => ( ( member_a @ C @ A3 )
% 0.32/0.47 => ( member_a @ C @ B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subsetD
% 0.32/0.47 thf(fact_166_subsetD,axiom,
% 0.32/0.47 ! [A3: set_b,B3: set_b,C: b] :
% 0.32/0.47 ( ( ord_less_eq_set_b @ A3 @ B3 )
% 0.32/0.47 => ( ( member_b @ C @ A3 )
% 0.32/0.47 => ( member_b @ C @ B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subsetD
% 0.32/0.47 thf(fact_167_inres__simps_I2_J,axiom,
% 0.32/0.47 ! [X: set_a] :
% 0.32/0.47 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X ) )
% 0.32/0.47 = ( ^ [X5: a] : ( member_a @ X5 @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inres_simps(2)
% 0.32/0.47 thf(fact_168_inres__simps_I2_J,axiom,
% 0.32/0.47 ! [X: set_b] :
% 0.32/0.47 ( ( refine1001002028nres_b @ ( refine1198353289_RES_b @ X ) )
% 0.32/0.47 = ( ^ [X5: b] : ( member_b @ X5 @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inres_simps(2)
% 0.32/0.47 thf(fact_169_pwD2,axiom,
% 0.32/0.47 ! [S: refine432681134nres_b,S3: refine432681134nres_b,X4: b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ S @ S3 )
% 0.32/0.47 => ( ( refine1001002028nres_b @ S @ X4 )
% 0.32/0.47 => ( refine1001002028nres_b @ S3 @ X4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pwD2
% 0.32/0.47 thf(fact_170_pwD2,axiom,
% 0.32/0.47 ! [S: refine424419629nres_a,S3: refine424419629nres_a,X4: a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ S @ S3 )
% 0.32/0.47 => ( ( refine1001002027nres_a @ S @ X4 )
% 0.32/0.47 => ( refine1001002027nres_a @ S3 @ X4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pwD2
% 0.32/0.47 thf(fact_171_pw__RES__bind__choose_I2_J,axiom,
% 0.32/0.47 ! [X: set_a,F: a > refine432681134nres_b,Y3: b] :
% 0.32/0.47 ( ( refine1001002028nres_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X ) @ F ) @ Y3 )
% 0.32/0.47 = ( ? [X5: a] :
% 0.32/0.47 ( ( member_a @ X5 @ X )
% 0.32/0.47 & ( refine1001002028nres_b @ ( F @ X5 ) @ Y3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_RES_bind_choose(2)
% 0.32/0.47 thf(fact_172_pw__leI,axiom,
% 0.32/0.47 ! [S3: refine432681134nres_b,S: refine432681134nres_b] :
% 0.32/0.47 ( ( ( refine412683990fail_b @ S3 )
% 0.32/0.47 => ( ( refine412683990fail_b @ S )
% 0.32/0.47 & ! [X3: b] :
% 0.32/0.47 ( ( refine1001002028nres_b @ S @ X3 )
% 0.32/0.47 => ( refine1001002028nres_b @ S3 @ X3 ) ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ S @ S3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_leI
% 0.32/0.47 thf(fact_173_pw__leI,axiom,
% 0.32/0.47 ! [S3: refine424419629nres_a,S: refine424419629nres_a] :
% 0.32/0.47 ( ( ( refine412683989fail_a @ S3 )
% 0.32/0.47 => ( ( refine412683989fail_a @ S )
% 0.32/0.47 & ! [X3: a] :
% 0.32/0.47 ( ( refine1001002027nres_a @ S @ X3 )
% 0.32/0.47 => ( refine1001002027nres_a @ S3 @ X3 ) ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ S @ S3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_leI
% 0.32/0.47 thf(fact_174_pw__leI_H,axiom,
% 0.32/0.47 ! [S3: refine432681134nres_b,S: refine432681134nres_b] :
% 0.32/0.47 ( ( ( refine412683990fail_b @ S3 )
% 0.32/0.47 => ( refine412683990fail_b @ S ) )
% 0.32/0.47 => ( ! [X3: b] :
% 0.32/0.47 ( ( refine412683990fail_b @ S3 )
% 0.32/0.47 => ( ( refine1001002028nres_b @ S @ X3 )
% 0.32/0.47 => ( refine1001002028nres_b @ S3 @ X3 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ S @ S3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_leI'
% 0.32/0.47 thf(fact_175_pw__leI_H,axiom,
% 0.32/0.47 ! [S3: refine424419629nres_a,S: refine424419629nres_a] :
% 0.32/0.47 ( ( ( refine412683989fail_a @ S3 )
% 0.32/0.47 => ( refine412683989fail_a @ S ) )
% 0.32/0.47 => ( ! [X3: a] :
% 0.32/0.47 ( ( refine412683989fail_a @ S3 )
% 0.32/0.47 => ( ( refine1001002027nres_a @ S @ X3 )
% 0.32/0.47 => ( refine1001002027nres_a @ S3 @ X3 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ S @ S3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_leI'
% 0.32/0.47 thf(fact_176_pw__le__iff,axiom,
% 0.32/0.47 ( ord_le527798542nres_b
% 0.32/0.47 = ( ^ [S4: refine432681134nres_b,S5: refine432681134nres_b] :
% 0.32/0.47 ( ( refine412683990fail_b @ S5 )
% 0.32/0.47 => ( ( refine412683990fail_b @ S4 )
% 0.32/0.47 & ! [X5: b] :
% 0.32/0.47 ( ( refine1001002028nres_b @ S4 @ X5 )
% 0.32/0.47 => ( refine1001002028nres_b @ S5 @ X5 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_le_iff
% 0.32/0.47 thf(fact_177_pw__le__iff,axiom,
% 0.32/0.47 ( ord_le519537037nres_a
% 0.32/0.47 = ( ^ [S4: refine424419629nres_a,S5: refine424419629nres_a] :
% 0.32/0.47 ( ( refine412683989fail_a @ S5 )
% 0.32/0.47 => ( ( refine412683989fail_a @ S4 )
% 0.32/0.47 & ! [X5: a] :
% 0.32/0.47 ( ( refine1001002027nres_a @ S4 @ X5 )
% 0.32/0.47 => ( refine1001002027nres_a @ S5 @ X5 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_le_iff
% 0.32/0.47 thf(fact_178_pw__bind__nofail,axiom,
% 0.32/0.47 ! [M4: refine424419629nres_a,F: a > refine432681134nres_b] :
% 0.32/0.47 ( ( refine412683990fail_b @ ( refine436832839nd_a_b @ M4 @ F ) )
% 0.32/0.47 = ( ( refine412683989fail_a @ M4 )
% 0.32/0.47 & ! [X5: a] :
% 0.32/0.47 ( ( refine1001002027nres_a @ M4 @ X5 )
% 0.32/0.47 => ( refine412683990fail_b @ ( F @ X5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_bind_nofail
% 0.32/0.47 thf(fact_179_pw__bind__le__iff,axiom,
% 0.32/0.47 ! [M4: refine424419629nres_a,F: a > refine432681134nres_b,S: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ S )
% 0.32/0.47 = ( ( ( refine412683990fail_b @ S )
% 0.32/0.47 => ( refine412683989fail_a @ M4 ) )
% 0.32/0.47 & ! [X5: a] :
% 0.32/0.47 ( ( ( refine412683989fail_a @ M4 )
% 0.32/0.47 & ( refine1001002027nres_a @ M4 @ X5 ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X5 ) @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_bind_le_iff
% 0.32/0.47 thf(fact_180_pw__bind__leI,axiom,
% 0.32/0.47 ! [S: refine432681134nres_b,M4: refine424419629nres_a,F: a > refine432681134nres_b] :
% 0.32/0.47 ( ( ( refine412683990fail_b @ S )
% 0.32/0.47 => ( refine412683989fail_a @ M4 ) )
% 0.32/0.47 => ( ! [X3: a] :
% 0.32/0.47 ( ( refine412683989fail_a @ M4 )
% 0.32/0.47 => ( ( refine1001002027nres_a @ M4 @ X3 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ S ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_bind_leI
% 0.32/0.47 thf(fact_181_Collect__mono__iff,axiom,
% 0.32/0.47 ! [P: a > $o,Q: a > $o] :
% 0.32/0.47 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.32/0.47 = ( ! [X5: a] :
% 0.32/0.47 ( ( P @ X5 )
% 0.32/0.47 => ( Q @ X5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mono_iff
% 0.32/0.47 thf(fact_182_Collect__mono__iff,axiom,
% 0.32/0.47 ! [P: b > $o,Q: b > $o] :
% 0.32/0.47 ( ( ord_less_eq_set_b @ ( collect_b @ P ) @ ( collect_b @ Q ) )
% 0.32/0.47 = ( ! [X5: b] :
% 0.32/0.47 ( ( P @ X5 )
% 0.32/0.47 => ( Q @ X5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mono_iff
% 0.32/0.47 thf(fact_183_Collect__mono,axiom,
% 0.32/0.47 ! [P: a > $o,Q: a > $o] :
% 0.32/0.47 ( ! [X3: a] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 => ( Q @ X3 ) )
% 0.32/0.47 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mono
% 0.32/0.47 thf(fact_184_Collect__mono,axiom,
% 0.32/0.47 ! [P: b > $o,Q: b > $o] :
% 0.32/0.47 ( ! [X3: b] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 => ( Q @ X3 ) )
% 0.32/0.47 => ( ord_less_eq_set_b @ ( collect_b @ P ) @ ( collect_b @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mono
% 0.32/0.47 thf(fact_185_subset__iff,axiom,
% 0.32/0.47 ( ord_less_eq_set_a
% 0.32/0.47 = ( ^ [A4: set_a,B4: set_a] :
% 0.32/0.47 ! [T3: a] :
% 0.32/0.47 ( ( member_a @ T3 @ A4 )
% 0.32/0.47 => ( member_a @ T3 @ B4 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_iff
% 0.32/0.47 thf(fact_186_subset__iff,axiom,
% 0.32/0.47 ( ord_less_eq_set_b
% 0.32/0.47 = ( ^ [A4: set_b,B4: set_b] :
% 0.32/0.47 ! [T3: b] :
% 0.32/0.47 ( ( member_b @ T3 @ A4 )
% 0.32/0.47 => ( member_b @ T3 @ B4 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_iff
% 0.32/0.47 thf(fact_187_subset__eq,axiom,
% 0.32/0.47 ( ord_less_eq_set_a
% 0.32/0.47 = ( ^ [A4: set_a,B4: set_a] :
% 0.32/0.47 ! [X5: a] :
% 0.32/0.47 ( ( member_a @ X5 @ A4 )
% 0.32/0.47 => ( member_a @ X5 @ B4 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_eq
% 0.32/0.47 thf(fact_188_subset__eq,axiom,
% 0.32/0.47 ( ord_less_eq_set_b
% 0.32/0.47 = ( ^ [A4: set_b,B4: set_b] :
% 0.32/0.47 ! [X5: b] :
% 0.32/0.47 ( ( member_b @ X5 @ A4 )
% 0.32/0.47 => ( member_b @ X5 @ B4 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_eq
% 0.32/0.47 thf(fact_189_rhs__step__bind,axiom,
% 0.32/0.47 ! [M: refine432681134nres_b,R: set_Product_prod_b_a,M7: refine424419629nres_a,X4: b,Lhs: refine432681134nres_b,S: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ M @ ( refine122110612un_b_a @ R @ M7 ) )
% 0.32/0.47 => ( ( refine1001002028nres_b @ M @ X4 )
% 0.32/0.47 => ( ! [X9: a] :
% 0.32/0.47 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X9 ) @ R )
% 0.32/0.47 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( F2 @ X9 ) ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rhs_step_bind
% 0.32/0.47 thf(fact_190_rhs__step__bind,axiom,
% 0.32/0.47 ! [M: refine432681134nres_b,R: set_Product_prod_b_a,M7: refine424419629nres_a,X4: b,Lhs: refine424419629nres_a,S: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ M @ ( refine122110612un_b_a @ R @ M7 ) )
% 0.32/0.47 => ( ( refine1001002028nres_b @ M @ X4 )
% 0.32/0.47 => ( ! [X9: a] :
% 0.32/0.47 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X9 ) @ R )
% 0.32/0.47 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( F2 @ X9 ) ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rhs_step_bind
% 0.32/0.47 thf(fact_191_rhs__step__bind,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,R: set_Product_prod_a_a,M7: refine424419629nres_a,X4: a,Lhs: refine432681134nres_b,S: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ M @ ( refine1441824853un_a_a @ R @ M7 ) )
% 0.32/0.47 => ( ( refine1001002027nres_a @ M @ X4 )
% 0.32/0.47 => ( ! [X9: a] :
% 0.32/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X9 ) @ R )
% 0.32/0.47 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( F2 @ X9 ) ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rhs_step_bind
% 0.32/0.47 thf(fact_192_rhs__step__bind,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,R: set_Product_prod_a_a,M7: refine424419629nres_a,X4: a,Lhs: refine424419629nres_a,S: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ M @ ( refine1441824853un_a_a @ R @ M7 ) )
% 0.32/0.47 => ( ( refine1001002027nres_a @ M @ X4 )
% 0.32/0.47 => ( ! [X9: a] :
% 0.32/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X9 ) @ R )
% 0.32/0.47 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( F2 @ X9 ) ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rhs_step_bind
% 0.32/0.47 thf(fact_193_RES__refine,axiom,
% 0.32/0.47 ! [S: set_a,S3: set_a,R: set_Product_prod_a_a] :
% 0.32/0.47 ( ! [S6: a] :
% 0.32/0.47 ( ( member_a @ S6 @ S )
% 0.32/0.47 => ? [X10: a] :
% 0.32/0.47 ( ( member_a @ X10 @ S3 )
% 0.32/0.47 & ( member449909584od_a_a @ ( product_Pair_a_a @ S6 @ X10 ) @ R ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ S3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RES_refine
% 0.32/0.47 thf(fact_194_RES__refine,axiom,
% 0.32/0.47 ! [S: set_a,S3: set_b,R: set_Product_prod_a_b] :
% 0.32/0.47 ( ! [S6: a] :
% 0.32/0.47 ( ( member_a @ S6 @ S )
% 0.32/0.47 => ? [X10: b] :
% 0.32/0.47 ( ( member_b @ X10 @ S3 )
% 0.32/0.47 & ( member458171089od_a_b @ ( product_Pair_a_b @ S6 @ X10 ) @ R ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ S3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RES_refine
% 0.32/0.47 thf(fact_195_RES__refine,axiom,
% 0.32/0.47 ! [S: set_b,S3: set_a,R: set_Product_prod_b_a] :
% 0.32/0.47 ( ! [S6: b] :
% 0.32/0.47 ( ( member_b @ S6 @ S )
% 0.32/0.47 => ? [X10: a] :
% 0.32/0.47 ( ( member_a @ X10 @ S3 )
% 0.32/0.47 & ( member1277678991od_b_a @ ( product_Pair_b_a @ S6 @ X10 ) @ R ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine122110612un_b_a @ R @ ( refine1198353288_RES_a @ S3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RES_refine
% 0.32/0.47 thf(fact_196_RES__refine,axiom,
% 0.32/0.47 ! [S: set_b,S3: set_b,R: set_Product_prod_b_b] :
% 0.32/0.47 ( ! [S6: b] :
% 0.32/0.47 ( ( member_b @ S6 @ S )
% 0.32/0.47 => ? [X10: b] :
% 0.32/0.47 ( ( member_b @ X10 @ S3 )
% 0.32/0.47 & ( member1285940496od_b_b @ ( product_Pair_b_b @ S6 @ X10 ) @ R ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ S3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RES_refine
% 0.32/0.47 thf(fact_197_less__eq__nres_Oelims_I1_J,axiom,
% 0.32/0.47 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 0.32/0.47 ( ( ( ord_le519537037nres_a @ X4 @ Xa )
% 0.32/0.47 = Y3 )
% 0.32/0.47 => ( ( ( Xa = refine464223677AILi_a )
% 0.32/0.47 => ~ Y3 )
% 0.32/0.47 => ( ! [A5: set_a] :
% 0.32/0.47 ( ( X4
% 0.32/0.47 = ( refine1198353288_RES_a @ A5 ) )
% 0.32/0.47 => ! [B5: set_a] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( refine1198353288_RES_a @ B5 ) )
% 0.32/0.47 => ( Y3
% 0.32/0.47 = ( ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) )
% 0.32/0.47 => ~ ( ( X4 = refine464223677AILi_a )
% 0.32/0.47 => ( ? [Uv: set_a] :
% 0.32/0.47 ( Xa
% 0.32/0.47 = ( refine1198353288_RES_a @ Uv ) )
% 0.32/0.47 => Y3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.elims(1)
% 0.32/0.47 thf(fact_198_less__eq__nres_Oelims_I1_J,axiom,
% 0.32/0.47 ! [X4: refine432681134nres_b,Xa: refine432681134nres_b,Y3: $o] :
% 0.32/0.47 ( ( ( ord_le527798542nres_b @ X4 @ Xa )
% 0.32/0.47 = Y3 )
% 0.32/0.47 => ( ( ( Xa = refine464223678AILi_b )
% 0.32/0.47 => ~ Y3 )
% 0.32/0.47 => ( ! [A5: set_b] :
% 0.32/0.47 ( ( X4
% 0.32/0.47 = ( refine1198353289_RES_b @ A5 ) )
% 0.32/0.47 => ! [B5: set_b] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( refine1198353289_RES_b @ B5 ) )
% 0.32/0.47 => ( Y3
% 0.32/0.47 = ( ~ ( ord_less_eq_set_b @ A5 @ B5 ) ) ) ) )
% 0.32/0.47 => ~ ( ( X4 = refine464223678AILi_b )
% 0.32/0.47 => ( ? [Uv: set_b] :
% 0.32/0.47 ( Xa
% 0.32/0.47 = ( refine1198353289_RES_b @ Uv ) )
% 0.32/0.47 => Y3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.elims(1)
% 0.32/0.47 thf(fact_199_less__eq__nres_Oelims_I2_J,axiom,
% 0.32/0.47 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ X4 @ Xa )
% 0.32/0.47 => ( ( Xa != refine464223677AILi_a )
% 0.32/0.47 => ~ ! [A5: set_a] :
% 0.32/0.47 ( ( X4
% 0.32/0.47 = ( refine1198353288_RES_a @ A5 ) )
% 0.32/0.47 => ! [B5: set_a] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( refine1198353288_RES_a @ B5 ) )
% 0.32/0.47 => ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.elims(2)
% 0.32/0.47 thf(fact_200_less__eq__nres_Oelims_I2_J,axiom,
% 0.32/0.47 ! [X4: refine432681134nres_b,Xa: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ X4 @ Xa )
% 0.32/0.47 => ( ( Xa != refine464223678AILi_b )
% 0.32/0.47 => ~ ! [A5: set_b] :
% 0.32/0.47 ( ( X4
% 0.32/0.47 = ( refine1198353289_RES_b @ A5 ) )
% 0.32/0.47 => ! [B5: set_b] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( refine1198353289_RES_b @ B5 ) )
% 0.32/0.47 => ~ ( ord_less_eq_set_b @ A5 @ B5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.elims(2)
% 0.32/0.47 thf(fact_201_less__eq__nres_Ocases,axiom,
% 0.32/0.47 ! [X4: produc1609974940nres_a] :
% 0.32/0.47 ( ! [Uu: refine424419629nres_a] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 0.32/0.47 => ( ! [A5: set_a,B5: set_a] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) ) )
% 0.32/0.47 => ~ ! [Uv: set_a] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.cases
% 0.32/0.47 thf(fact_202_less__eq__nres_Ocases,axiom,
% 0.32/0.47 ! [X4: produc1587512412nres_b] :
% 0.32/0.47 ( ! [Uu: refine432681134nres_b] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc2130641934nres_b @ Uu @ refine464223678AILi_b ) )
% 0.32/0.47 => ( ! [A5: set_b,B5: set_b] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) ) )
% 0.32/0.47 => ~ ! [Uv: set_b] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ Uv ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.cases
% 0.32/0.47 thf(fact_203_less__nres_Ocases,axiom,
% 0.32/0.47 ! [X4: produc1609974940nres_a] :
% 0.32/0.47 ( ! [Uu: refine424419629nres_a] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc1136923598nres_a @ refine464223677AILi_a @ Uu ) )
% 0.32/0.47 => ( ! [Uv: set_a] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a ) )
% 0.32/0.47 => ~ ! [A5: set_a,B5: set_a] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_nres.cases
% 0.32/0.47 thf(fact_204_less__nres_Ocases,axiom,
% 0.32/0.47 ! [X4: produc1587512412nres_b] :
% 0.32/0.47 ( ! [Uu: refine432681134nres_b] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc2130641934nres_b @ refine464223678AILi_b @ Uu ) )
% 0.32/0.47 => ( ! [Uv: set_b] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ Uv ) @ refine464223678AILi_b ) )
% 0.32/0.47 => ~ ! [A5: set_b,B5: set_b] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_nres.cases
% 0.32/0.47 thf(fact_205_sup__nres_Ocases,axiom,
% 0.32/0.47 ! [X4: produc1609974940nres_a] :
% 0.32/0.47 ( ! [Uu: refine424419629nres_a] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 0.32/0.47 => ( ! [V: set_a] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) ) )
% 0.32/0.47 => ~ ! [A5: set_a,B5: set_a] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sup_nres.cases
% 0.32/0.47 thf(fact_206_sup__nres_Ocases,axiom,
% 0.32/0.47 ! [X4: produc1587512412nres_b] :
% 0.32/0.47 ( ! [Uu: refine432681134nres_b] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc2130641934nres_b @ Uu @ refine464223678AILi_b ) )
% 0.32/0.47 => ( ! [V: set_b] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ V ) ) )
% 0.32/0.47 => ~ ! [A5: set_b,B5: set_b] :
% 0.32/0.47 ( X4
% 0.32/0.47 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sup_nres.cases
% 0.32/0.47 thf(fact_207_less__eq__nres_Osimps_I1_J,axiom,
% 0.32/0.47 ! [Uu2: refine432681134nres_b] : ( ord_le527798542nres_b @ Uu2 @ refine464223678AILi_b ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.simps(1)
% 0.32/0.47 thf(fact_208_less__eq__nres_Osimps_I1_J,axiom,
% 0.32/0.47 ! [Uu2: refine424419629nres_a] : ( ord_le519537037nres_a @ Uu2 @ refine464223677AILi_a ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.simps(1)
% 0.32/0.47 thf(fact_209_nres_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X2: set_a] :
% 0.32/0.47 ( refine464223677AILi_a
% 0.32/0.47 != ( refine1198353288_RES_a @ X2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres.distinct(1)
% 0.32/0.47 thf(fact_210_nres_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X2: set_b] :
% 0.32/0.47 ( refine464223678AILi_b
% 0.32/0.47 != ( refine1198353289_RES_b @ X2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres.distinct(1)
% 0.32/0.47 thf(fact_211_nres_Oinduct,axiom,
% 0.32/0.47 ! [P: refine424419629nres_a > $o,Nres: refine424419629nres_a] :
% 0.32/0.47 ( ( P @ refine464223677AILi_a )
% 0.32/0.47 => ( ! [X3: set_a] : ( P @ ( refine1198353288_RES_a @ X3 ) )
% 0.32/0.47 => ( P @ Nres ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres.induct
% 0.32/0.47 thf(fact_212_nres_Oinduct,axiom,
% 0.32/0.47 ! [P: refine432681134nres_b > $o,Nres: refine432681134nres_b] :
% 0.32/0.47 ( ( P @ refine464223678AILi_b )
% 0.32/0.47 => ( ! [X3: set_b] : ( P @ ( refine1198353289_RES_b @ X3 ) )
% 0.32/0.47 => ( P @ Nres ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres.induct
% 0.32/0.47 thf(fact_213_nres_Oexhaust,axiom,
% 0.32/0.47 ! [Y3: refine424419629nres_a] :
% 0.32/0.47 ( ( Y3 != refine464223677AILi_a )
% 0.32/0.47 => ~ ! [X22: set_a] :
% 0.32/0.47 ( Y3
% 0.32/0.47 != ( refine1198353288_RES_a @ X22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres.exhaust
% 0.32/0.47 thf(fact_214_nres_Oexhaust,axiom,
% 0.32/0.47 ! [Y3: refine432681134nres_b] :
% 0.32/0.47 ( ( Y3 != refine464223678AILi_b )
% 0.32/0.47 => ~ ! [X22: set_b] :
% 0.32/0.47 ( Y3
% 0.32/0.47 != ( refine1198353289_RES_b @ X22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres.exhaust
% 0.32/0.47 thf(fact_215_sup__nres_Oinduct,axiom,
% 0.32/0.47 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.32/0.47 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.32/0.47 => ( ! [V: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) )
% 0.32/0.47 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sup_nres.induct
% 0.32/0.47 thf(fact_216_sup__nres_Oinduct,axiom,
% 0.32/0.47 ! [P: refine432681134nres_b > refine432681134nres_b > $o,A0: refine432681134nres_b,A1: refine432681134nres_b] :
% 0.32/0.47 ( ! [Uu: refine432681134nres_b] : ( P @ Uu @ refine464223678AILi_b )
% 0.32/0.47 => ( ! [V: set_b] : ( P @ refine464223678AILi_b @ ( refine1198353289_RES_b @ V ) )
% 0.32/0.47 => ( ! [A5: set_b,B5: set_b] : ( P @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sup_nres.induct
% 0.32/0.47 thf(fact_217_less__nres_Oinduct,axiom,
% 0.32/0.47 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.32/0.47 ( ! [X_1: refine424419629nres_a] : ( P @ refine464223677AILi_a @ X_1 )
% 0.32/0.47 => ( ! [Uv: set_a] : ( P @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a )
% 0.32/0.47 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_nres.induct
% 0.32/0.47 thf(fact_218_less__nres_Oinduct,axiom,
% 0.32/0.47 ! [P: refine432681134nres_b > refine432681134nres_b > $o,A0: refine432681134nres_b,A1: refine432681134nres_b] :
% 0.32/0.47 ( ! [X_1: refine432681134nres_b] : ( P @ refine464223678AILi_b @ X_1 )
% 0.32/0.47 => ( ! [Uv: set_b] : ( P @ ( refine1198353289_RES_b @ Uv ) @ refine464223678AILi_b )
% 0.32/0.47 => ( ! [A5: set_b,B5: set_b] : ( P @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_nres.induct
% 0.32/0.47 thf(fact_219_less__eq__nres_Oinduct,axiom,
% 0.32/0.47 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.32/0.47 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.32/0.47 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.32/0.47 => ( ! [Uv: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.induct
% 0.32/0.47 thf(fact_220_less__eq__nres_Oinduct,axiom,
% 0.32/0.47 ! [P: refine432681134nres_b > refine432681134nres_b > $o,A0: refine432681134nres_b,A1: refine432681134nres_b] :
% 0.32/0.47 ( ! [Uu: refine432681134nres_b] : ( P @ Uu @ refine464223678AILi_b )
% 0.32/0.47 => ( ! [A5: set_b,B5: set_b] : ( P @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) )
% 0.32/0.47 => ( ! [Uv: set_b] : ( P @ refine464223678AILi_b @ ( refine1198353289_RES_b @ Uv ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.induct
% 0.32/0.47 thf(fact_221_less__eq__nres_Osimps_I3_J,axiom,
% 0.32/0.47 ! [Uv2: set_a] :
% 0.32/0.47 ~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.simps(3)
% 0.32/0.47 thf(fact_222_less__eq__nres_Osimps_I3_J,axiom,
% 0.32/0.47 ! [Uv2: set_b] :
% 0.32/0.47 ~ ( ord_le527798542nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ Uv2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.simps(3)
% 0.32/0.47 thf(fact_223_less__eq__nres_Oelims_I3_J,axiom,
% 0.32/0.47 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.32/0.47 ( ~ ( ord_le519537037nres_a @ X4 @ Xa )
% 0.32/0.47 => ( ! [A5: set_a] :
% 0.32/0.47 ( ( X4
% 0.32/0.47 = ( refine1198353288_RES_a @ A5 ) )
% 0.32/0.47 => ! [B5: set_a] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( refine1198353288_RES_a @ B5 ) )
% 0.32/0.47 => ( ord_less_eq_set_a @ A5 @ B5 ) ) )
% 0.32/0.47 => ~ ( ( X4 = refine464223677AILi_a )
% 0.32/0.47 => ! [Uv: set_a] :
% 0.32/0.47 ( Xa
% 0.32/0.47 != ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.elims(3)
% 0.32/0.47 thf(fact_224_less__eq__nres_Oelims_I3_J,axiom,
% 0.32/0.47 ! [X4: refine432681134nres_b,Xa: refine432681134nres_b] :
% 0.32/0.47 ( ~ ( ord_le527798542nres_b @ X4 @ Xa )
% 0.32/0.47 => ( ! [A5: set_b] :
% 0.32/0.47 ( ( X4
% 0.32/0.47 = ( refine1198353289_RES_b @ A5 ) )
% 0.32/0.47 => ! [B5: set_b] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( refine1198353289_RES_b @ B5 ) )
% 0.32/0.47 => ( ord_less_eq_set_b @ A5 @ B5 ) ) )
% 0.32/0.47 => ~ ( ( X4 = refine464223678AILi_b )
% 0.32/0.47 => ! [Uv: set_b] :
% 0.32/0.47 ( Xa
% 0.32/0.47 != ( refine1198353289_RES_b @ Uv ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_eq_nres.elims(3)
% 0.32/0.47 thf(fact_225_return__refine__prop__return,axiom,
% 0.32/0.47 ! [M: refine432681134nres_b,X4: b,R: set_Product_prod_b_b] :
% 0.32/0.47 ( ( refine412683990fail_b @ M )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110613un_b_b @ R @ M ) )
% 0.32/0.47 => ~ ! [X9: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ X9 ) @ R )
% 0.32/0.47 => ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X9 ) @ M ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % return_refine_prop_return
% 0.32/0.47 thf(fact_226_return__refine__prop__return,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,X4: b,R: set_Product_prod_b_a] :
% 0.32/0.47 ( ( refine412683989fail_a @ M )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110612un_b_a @ R @ M ) )
% 0.32/0.47 => ~ ! [X9: a] :
% 0.32/0.47 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X9 ) @ R )
% 0.32/0.47 => ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X9 ) @ M ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % return_refine_prop_return
% 0.32/0.47 thf(fact_227_return__refine__prop__return,axiom,
% 0.32/0.47 ! [M: refine432681134nres_b,X4: a,R: set_Product_prod_a_b] :
% 0.32/0.47 ( ( refine412683990fail_b @ M )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824854un_a_b @ R @ M ) )
% 0.32/0.47 => ~ ! [X9: b] :
% 0.32/0.47 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X4 @ X9 ) @ R )
% 0.32/0.47 => ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X9 ) @ M ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % return_refine_prop_return
% 0.32/0.47 thf(fact_228_return__refine__prop__return,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,X4: a,R: set_Product_prod_a_a] :
% 0.32/0.47 ( ( refine412683989fail_a @ M )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824853un_a_a @ R @ M ) )
% 0.32/0.47 => ~ ! [X9: a] :
% 0.32/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X9 ) @ R )
% 0.32/0.47 => ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X9 ) @ M ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % return_refine_prop_return
% 0.32/0.47 thf(fact_229_ret__le__down__conv,axiom,
% 0.32/0.47 ! [M: refine432681134nres_b,C: b,R: set_Product_prod_b_b] :
% 0.32/0.47 ( ( refine412683990fail_b @ M )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110613un_b_b @ R @ M ) )
% 0.32/0.47 = ( ? [A2: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A2 ) @ R )
% 0.32/0.47 & ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A2 ) @ M ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ret_le_down_conv
% 0.32/0.47 thf(fact_230_ret__le__down__conv,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,C: b,R: set_Product_prod_b_a] :
% 0.32/0.47 ( ( refine412683989fail_a @ M )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110612un_b_a @ R @ M ) )
% 0.32/0.47 = ( ? [A2: a] :
% 0.32/0.47 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ C @ A2 ) @ R )
% 0.32/0.47 & ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A2 ) @ M ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ret_le_down_conv
% 0.32/0.47 thf(fact_231_ret__le__down__conv,axiom,
% 0.32/0.47 ! [M: refine432681134nres_b,C: a,R: set_Product_prod_a_b] :
% 0.32/0.47 ( ( refine412683990fail_b @ M )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824854un_a_b @ R @ M ) )
% 0.32/0.47 = ( ? [A2: b] :
% 0.32/0.47 ( ( member458171089od_a_b @ ( product_Pair_a_b @ C @ A2 ) @ R )
% 0.32/0.47 & ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A2 ) @ M ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ret_le_down_conv
% 0.32/0.47 thf(fact_232_ret__le__down__conv,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,C: a,R: set_Product_prod_a_a] :
% 0.32/0.47 ( ( refine412683989fail_a @ M )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824853un_a_a @ R @ M ) )
% 0.32/0.47 = ( ? [A2: a] :
% 0.32/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A2 ) @ R )
% 0.32/0.47 & ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A2 ) @ M ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ret_le_down_conv
% 0.32/0.47 thf(fact_233_nres__order__simps_I20_J,axiom,
% 0.32/0.47 ! [X4: b,Y3: b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine2063221605TURN_b @ Y3 ) )
% 0.32/0.47 = ( X4 = Y3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(20)
% 0.32/0.47 thf(fact_234_nres__order__simps_I20_J,axiom,
% 0.32/0.47 ! [X4: a,Y3: a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine2063221604TURN_a @ Y3 ) )
% 0.32/0.47 = ( X4 = Y3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(20)
% 0.32/0.47 thf(fact_235_nres__monad1,axiom,
% 0.32/0.47 ! [X4: a,F: a > refine432681134nres_b] :
% 0.32/0.47 ( ( refine436832839nd_a_b @ ( refine2063221604TURN_a @ X4 ) @ F )
% 0.32/0.47 = ( F @ X4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_monad1
% 0.32/0.47 thf(fact_236_nres__order__simps_I21_J,axiom,
% 0.32/0.47 ! [X4: a,Y: set_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ Y ) )
% 0.32/0.47 = ( member_a @ X4 @ Y ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(21)
% 0.32/0.47 thf(fact_237_nres__order__simps_I21_J,axiom,
% 0.32/0.47 ! [X4: b,Y: set_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine1198353289_RES_b @ Y ) )
% 0.32/0.47 = ( member_b @ X4 @ Y ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(21)
% 0.32/0.47 thf(fact_238_SPEC__eq__is__RETURN_I1_J,axiom,
% 0.32/0.47 ! [X4: a] :
% 0.32/0.47 ( ( refine1198353288_RES_a
% 0.32/0.47 @ ( collect_a
% 0.32/0.47 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 0.32/0.47 @ X4 ) ) )
% 0.32/0.47 = ( refine2063221604TURN_a @ X4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % SPEC_eq_is_RETURN(1)
% 0.32/0.47 thf(fact_239_SPEC__eq__is__RETURN_I1_J,axiom,
% 0.32/0.47 ! [X4: b] :
% 0.32/0.47 ( ( refine1198353289_RES_b
% 0.32/0.47 @ ( collect_b
% 0.32/0.47 @ ( ^ [Y5: b,Z: b] : ( Y5 = Z )
% 0.32/0.47 @ X4 ) ) )
% 0.32/0.47 = ( refine2063221605TURN_b @ X4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % SPEC_eq_is_RETURN(1)
% 0.32/0.47 thf(fact_240_RETURN__rule,axiom,
% 0.32/0.47 ! [Phi: a > $o,X4: a] :
% 0.32/0.47 ( ( Phi @ X4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_rule
% 0.32/0.47 thf(fact_241_RETURN__rule,axiom,
% 0.32/0.47 ! [Phi: b > $o,X4: b] :
% 0.32/0.47 ( ( Phi @ X4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_rule
% 0.32/0.47 thf(fact_242_lhs__step__RES,axiom,
% 0.32/0.47 ! [X: set_a,M: refine424419629nres_a] :
% 0.32/0.47 ( ! [X3: a] :
% 0.32/0.47 ( ( member_a @ X3 @ X )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ M ) ) ).
% 0.32/0.47
% 0.32/0.47 % lhs_step_RES
% 0.32/0.47 thf(fact_243_lhs__step__RES,axiom,
% 0.32/0.47 ! [X: set_b,M: refine432681134nres_b] :
% 0.32/0.47 ( ! [X3: b] :
% 0.32/0.47 ( ( member_b @ X3 @ X )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ M ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ X ) @ M ) ) ).
% 0.32/0.47
% 0.32/0.47 % lhs_step_RES
% 0.32/0.47 thf(fact_244_RETURN__to__SPEC__rule,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,V2: a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ M
% 0.32/0.47 @ ( refine1198353288_RES_a
% 0.32/0.47 @ ( collect_a
% 0.32/0.47 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 0.32/0.47 @ V2 ) ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ M @ ( refine2063221604TURN_a @ V2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_to_SPEC_rule
% 0.32/0.47 thf(fact_245_RETURN__to__SPEC__rule,axiom,
% 0.32/0.47 ! [M: refine432681134nres_b,V2: b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ M
% 0.32/0.47 @ ( refine1198353289_RES_b
% 0.32/0.47 @ ( collect_b
% 0.32/0.47 @ ( ^ [Y5: b,Z: b] : ( Y5 = Z )
% 0.32/0.47 @ V2 ) ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ M @ ( refine2063221605TURN_b @ V2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_to_SPEC_rule
% 0.32/0.47 thf(fact_246_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.32/0.47 ! [M4: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine432681134nres_b,F2: b > refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ M4 @ M3 )
% 0.32/0.47 => ( ! [X3: b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ M4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine1264602246nd_b_b @ M4 @ F ) @ ( refine1264602246nd_b_b @ M3 @ F2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.32/0.47 thf(fact_247_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.32/0.47 ! [M4: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine424419629nres_a,F2: b > refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ M4 @ M3 )
% 0.32/0.47 => ( ! [X3: b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ M4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine1264602245nd_b_a @ M4 @ F ) @ ( refine1264602245nd_b_a @ M3 @ F2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.32/0.47 thf(fact_248_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.32/0.47 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine424419629nres_a,F2: a > refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ M4 @ M3 )
% 0.32/0.47 => ( ! [X3: a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine436832838nd_a_a @ M3 @ F2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.32/0.47 thf(fact_249_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.32/0.47 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine432681134nres_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ M4 @ M3 )
% 0.32/0.47 => ( ! [X3: a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ ( refine436832839nd_a_b @ M3 @ F2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.32/0.47 thf(fact_250_bind__cong,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,M7: refine424419629nres_a,F: a > refine432681134nres_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( M = M7 )
% 0.32/0.47 => ( ! [X3: a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M7 )
% 0.32/0.47 => ( ( F @ X3 )
% 0.32/0.47 = ( F2 @ X3 ) ) )
% 0.32/0.47 => ( ( refine436832839nd_a_b @ M @ F )
% 0.32/0.47 = ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bind_cong
% 0.32/0.47 thf(fact_251_inres__def,axiom,
% 0.32/0.47 ( refine1001002028nres_b
% 0.32/0.47 = ( ^ [S4: refine432681134nres_b,X5: b] : ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X5 ) @ S4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inres_def
% 0.32/0.47 thf(fact_252_inres__def,axiom,
% 0.32/0.47 ( refine1001002027nres_a
% 0.32/0.47 = ( ^ [S4: refine424419629nres_a,X5: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X5 ) @ S4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inres_def
% 0.32/0.47 thf(fact_253_RETURN__ref__SPECD,axiom,
% 0.32/0.47 ! [C: b,R: set_Product_prod_b_a,Phi: a > $o] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110612un_b_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.32/0.47 => ~ ! [A5: a] :
% 0.32/0.47 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ C @ A5 ) @ R )
% 0.32/0.47 => ~ ( Phi @ A5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_ref_SPECD
% 0.32/0.47 thf(fact_254_RETURN__ref__SPECD,axiom,
% 0.32/0.47 ! [C: a,R: set_Product_prod_a_a,Phi: a > $o] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.32/0.47 => ~ ! [A5: a] :
% 0.32/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A5 ) @ R )
% 0.32/0.47 => ~ ( Phi @ A5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_ref_SPECD
% 0.32/0.47 thf(fact_255_RETURN__ref__SPECD,axiom,
% 0.32/0.47 ! [C: b,R: set_Product_prod_b_b,Phi: b > $o] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.32/0.47 => ~ ! [A5: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A5 ) @ R )
% 0.32/0.47 => ~ ( Phi @ A5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_ref_SPECD
% 0.32/0.47 thf(fact_256_RETURN__ref__SPECD,axiom,
% 0.32/0.47 ! [C: a,R: set_Product_prod_a_b,Phi: b > $o] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.32/0.47 => ~ ! [A5: b] :
% 0.32/0.47 ( ( member458171089od_a_b @ ( product_Pair_a_b @ C @ A5 ) @ R )
% 0.32/0.47 => ~ ( Phi @ A5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_ref_SPECD
% 0.32/0.47 thf(fact_257_RETURN__SPEC__refine,axiom,
% 0.32/0.47 ! [X4: b,R: set_Product_prod_b_a,Phi: a > $o] :
% 0.32/0.47 ( ? [X11: a] :
% 0.32/0.47 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X11 ) @ R )
% 0.32/0.47 & ( Phi @ X11 ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110612un_b_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_SPEC_refine
% 0.32/0.47 thf(fact_258_RETURN__SPEC__refine,axiom,
% 0.32/0.47 ! [X4: a,R: set_Product_prod_a_a,Phi: a > $o] :
% 0.32/0.47 ( ? [X11: a] :
% 0.32/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X11 ) @ R )
% 0.32/0.47 & ( Phi @ X11 ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_SPEC_refine
% 0.32/0.47 thf(fact_259_RETURN__SPEC__refine,axiom,
% 0.32/0.47 ! [X4: b,R: set_Product_prod_b_b,Phi: b > $o] :
% 0.32/0.47 ( ? [X11: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ X11 ) @ R )
% 0.32/0.47 & ( Phi @ X11 ) )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_SPEC_refine
% 0.32/0.47 thf(fact_260_RETURN__SPEC__refine,axiom,
% 0.32/0.47 ! [X4: a,R: set_Product_prod_a_b,Phi: b > $o] :
% 0.32/0.47 ( ? [X11: b] :
% 0.32/0.47 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X4 @ X11 ) @ R )
% 0.32/0.47 & ( Phi @ X11 ) )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RETURN_SPEC_refine
% 0.32/0.47 thf(fact_261_abs__trans__additional_I1_J,axiom,
% 0.32/0.47 ! [A3: refine432681134nres_b,B3: refine432681134nres_b,R: set_Product_prod_b_b,C2: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ A3 @ B3 )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ B3 ) @ C2 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ A3 ) @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_trans_additional(1)
% 0.32/0.47 thf(fact_262_abs__trans__additional_I1_J,axiom,
% 0.32/0.47 ! [A3: refine432681134nres_b,B3: refine432681134nres_b,R: set_Product_prod_b_a,C2: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ A3 @ B3 )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ B3 ) @ C2 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ A3 ) @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_trans_additional(1)
% 0.32/0.47 thf(fact_263_abs__trans__additional_I1_J,axiom,
% 0.32/0.47 ! [A3: refine424419629nres_a,B3: refine424419629nres_a,R: set_Product_prod_a_b,C2: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 0.32/0.47 => ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ B3 ) @ C2 )
% 0.32/0.47 => ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ A3 ) @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_trans_additional(1)
% 0.32/0.47 thf(fact_264_abs__trans__additional_I1_J,axiom,
% 0.32/0.47 ! [A3: refine424419629nres_a,B3: refine424419629nres_a,R: set_Product_prod_a_a,C2: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 0.32/0.47 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ B3 ) @ C2 )
% 0.32/0.47 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ A3 ) @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_trans_additional(1)
% 0.32/0.47 thf(fact_265_abs__fun__simps_I3_J,axiom,
% 0.32/0.47 ! [X: set_a,R: set_Pr1628433942t_unit] :
% 0.32/0.47 ( ~ ( ord_less_eq_set_a @ X @ ( domain799550107t_unit @ R ) )
% 0.32/0.47 => ( ( refine341651653t_unit @ R @ ( refine1198353288_RES_a @ X ) )
% 0.32/0.47 = top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_fun_simps(3)
% 0.32/0.47 thf(fact_266_abs__fun__simps_I3_J,axiom,
% 0.32/0.47 ! [X: set_b,R: set_Pr1707992533t_unit] :
% 0.32/0.47 ( ~ ( ord_less_eq_set_b @ X @ ( domain918802906t_unit @ R ) )
% 0.32/0.47 => ( ( refine460904452t_unit @ R @ ( refine1198353289_RES_b @ X ) )
% 0.32/0.47 = top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_fun_simps(3)
% 0.32/0.47 thf(fact_267_abs__fun__simps_I2_J,axiom,
% 0.32/0.47 ! [X: set_a,R: set_Product_prod_a_a] :
% 0.32/0.47 ( ( ord_less_eq_set_a @ X @ ( domain_a_a @ R ) )
% 0.32/0.47 => ( ( refine1136779702un_a_a @ R @ ( refine1198353288_RES_a @ X ) )
% 0.32/0.47 = ( refine1198353288_RES_a @ ( image_a_a @ R @ X ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_fun_simps(2)
% 0.32/0.47 thf(fact_268_abs__fun__simps_I2_J,axiom,
% 0.32/0.47 ! [X: set_a,R: set_Product_prod_a_b] :
% 0.32/0.47 ( ( ord_less_eq_set_a @ X @ ( domain_a_b @ R ) )
% 0.32/0.47 => ( ( refine1136779703un_a_b @ R @ ( refine1198353288_RES_a @ X ) )
% 0.32/0.47 = ( refine1198353289_RES_b @ ( image_a_b @ R @ X ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_fun_simps(2)
% 0.32/0.47 thf(fact_269_abs__fun__simps_I2_J,axiom,
% 0.32/0.47 ! [X: set_b,R: set_Product_prod_b_a] :
% 0.32/0.47 ( ( ord_less_eq_set_b @ X @ ( domain_b_a @ R ) )
% 0.32/0.47 => ( ( refine1964549109un_b_a @ R @ ( refine1198353289_RES_b @ X ) )
% 0.32/0.47 = ( refine1198353288_RES_a @ ( image_b_a @ R @ X ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_fun_simps(2)
% 0.32/0.47 thf(fact_270_abs__fun__simps_I2_J,axiom,
% 0.32/0.47 ! [X: set_b,R: set_Product_prod_b_b] :
% 0.32/0.47 ( ( ord_less_eq_set_b @ X @ ( domain_b_b @ R ) )
% 0.32/0.47 => ( ( refine1964549110un_b_b @ R @ ( refine1198353289_RES_b @ X ) )
% 0.32/0.47 = ( refine1198353289_RES_b @ ( image_b_b @ R @ X ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % abs_fun_simps(2)
% 0.32/0.47 thf(fact_271_ImageI,axiom,
% 0.32/0.47 ! [A: a,B: a,R2: set_Product_prod_a_a,A3: set_a] :
% 0.32/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R2 )
% 0.32/0.47 => ( ( member_a @ A @ A3 )
% 0.32/0.47 => ( member_a @ B @ ( image_a_a @ R2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_272_ImageI,axiom,
% 0.32/0.47 ! [A: a,B: b,R2: set_Product_prod_a_b,A3: set_a] :
% 0.32/0.47 ( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ R2 )
% 0.32/0.47 => ( ( member_a @ A @ A3 )
% 0.32/0.47 => ( member_b @ B @ ( image_a_b @ R2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_273_ImageI,axiom,
% 0.32/0.47 ! [A: b,B: a,R2: set_Product_prod_b_a,A3: set_b] :
% 0.32/0.47 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ B ) @ R2 )
% 0.32/0.47 => ( ( member_b @ A @ A3 )
% 0.32/0.47 => ( member_a @ B @ ( image_b_a @ R2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_274_ImageI,axiom,
% 0.32/0.47 ! [A: b,B: b,R2: set_Product_prod_b_b,A3: set_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ R2 )
% 0.32/0.47 => ( ( member_b @ A @ A3 )
% 0.32/0.47 => ( member_b @ B @ ( image_b_b @ R2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_275_nres__order__simps_I4_J,axiom,
% 0.32/0.47 ! [M4: refine787176636t_unit] :
% 0.32/0.47 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ M4 )
% 0.32/0.47 = ( M4 = top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(4)
% 0.32/0.47 thf(fact_276_nres__order__simps_I4_J,axiom,
% 0.32/0.47 ! [M4: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ M4 )
% 0.32/0.47 = ( M4 = top_to240090974nres_b ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(4)
% 0.32/0.47 thf(fact_277_nres__order__simps_I4_J,axiom,
% 0.32/0.47 ! [M4: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M4 )
% 0.32/0.47 = ( M4 = top_to231829469nres_a ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(4)
% 0.32/0.47 thf(fact_278_conc__fun__FAIL,axiom,
% 0.32/0.47 ! [R: set_Pr451126599t_unit] :
% 0.32/0.47 ( ( refine944483349t_unit @ R @ top_to177290092t_unit )
% 0.32/0.47 = top_to177290092t_unit ) ).
% 0.32/0.47
% 0.32/0.47 % conc_fun_FAIL
% 0.32/0.47 thf(fact_279_conc__fun__fail__iff_I1_J,axiom,
% 0.32/0.47 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.32/0.47 ( ( ( refine944483349t_unit @ R @ S )
% 0.32/0.47 = top_to177290092t_unit )
% 0.32/0.47 = ( S = top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % conc_fun_fail_iff(1)
% 0.32/0.47 thf(fact_280_conc__fun__fail__iff_I2_J,axiom,
% 0.32/0.47 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.32/0.47 ( ( top_to177290092t_unit
% 0.32/0.47 = ( refine944483349t_unit @ R @ S ) )
% 0.32/0.47 = ( S = top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % conc_fun_fail_iff(2)
% 0.32/0.47 thf(fact_281_bind__FAIL,axiom,
% 0.32/0.47 ! [F: product_unit > refine787176636t_unit] :
% 0.32/0.47 ( ( refine681446406t_unit @ top_to177290092t_unit @ F )
% 0.32/0.47 = top_to177290092t_unit ) ).
% 0.32/0.47
% 0.32/0.47 % bind_FAIL
% 0.32/0.47 thf(fact_282_bind__FAIL,axiom,
% 0.32/0.47 ! [F: a > refine432681134nres_b] :
% 0.32/0.47 ( ( refine436832839nd_a_b @ top_to231829469nres_a @ F )
% 0.32/0.47 = top_to240090974nres_b ) ).
% 0.32/0.47
% 0.32/0.47 % bind_FAIL
% 0.32/0.47 thf(fact_283_nofail__simps_I1_J,axiom,
% 0.32/0.47 ~ ( refine579265252t_unit @ top_to177290092t_unit ) ).
% 0.32/0.47
% 0.32/0.47 % nofail_simps(1)
% 0.32/0.47 thf(fact_284_inres__simps_I1_J,axiom,
% 0.32/0.47 ( ( refine558004794t_unit @ top_to177290092t_unit )
% 0.32/0.47 = ( ^ [Uu3: product_unit] : $true ) ) ).
% 0.32/0.47
% 0.32/0.47 % inres_simps(1)
% 0.32/0.47 thf(fact_285_nres__simp__internals_I2_J,axiom,
% 0.32/0.47 refine1607584204t_unit = top_to177290092t_unit ).
% 0.32/0.47
% 0.32/0.47 % nres_simp_internals(2)
% 0.32/0.47 thf(fact_286_abs__fun__simps_I1_J,axiom,
% 0.32/0.47 ! [R: set_Pr451126599t_unit] :
% 0.32/0.47 ( ( refine838861686t_unit @ R @ top_to177290092t_unit )
% 0.32/0.47 = top_to177290092t_unit ) ).
% 0.32/0.47
% 0.32/0.47 % abs_fun_simps(1)
% 0.32/0.47 thf(fact_287_FAIL__refine,axiom,
% 0.32/0.47 ! [X: refine432681134nres_b,R: set_Pr1707992533t_unit] : ( ord_le527798542nres_b @ X @ ( refine2140306339t_unit @ R @ top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % FAIL_refine
% 0.32/0.47 thf(fact_288_FAIL__refine,axiom,
% 0.32/0.47 ! [X: refine424419629nres_a,R: set_Pr1628433942t_unit] : ( ord_le519537037nres_a @ X @ ( refine2021053540t_unit @ R @ top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % FAIL_refine
% 0.32/0.47 thf(fact_289_rev__ImageI,axiom,
% 0.32/0.47 ! [A: a,A3: set_a,B: a,R2: set_Product_prod_a_a] :
% 0.32/0.47 ( ( member_a @ A @ A3 )
% 0.32/0.47 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R2 )
% 0.32/0.47 => ( member_a @ B @ ( image_a_a @ R2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_290_rev__ImageI,axiom,
% 0.32/0.47 ! [A: a,A3: set_a,B: b,R2: set_Product_prod_a_b] :
% 0.32/0.47 ( ( member_a @ A @ A3 )
% 0.32/0.47 => ( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ R2 )
% 0.32/0.47 => ( member_b @ B @ ( image_a_b @ R2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_291_rev__ImageI,axiom,
% 0.32/0.47 ! [A: b,A3: set_b,B: a,R2: set_Product_prod_b_a] :
% 0.32/0.47 ( ( member_b @ A @ A3 )
% 0.32/0.47 => ( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ B ) @ R2 )
% 0.32/0.47 => ( member_a @ B @ ( image_b_a @ R2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_292_rev__ImageI,axiom,
% 0.32/0.47 ! [A: b,A3: set_b,B: b,R2: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member_b @ A @ A3 )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ R2 )
% 0.32/0.47 => ( member_b @ B @ ( image_b_b @ R2 @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_293_ImageE,axiom,
% 0.32/0.47 ! [B: a,R2: set_Product_prod_a_a,A3: set_a] :
% 0.32/0.47 ( ( member_a @ B @ ( image_a_a @ R2 @ A3 ) )
% 0.32/0.47 => ~ ! [X3: a] :
% 0.32/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ B ) @ R2 )
% 0.32/0.47 => ~ ( member_a @ X3 @ A3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_294_ImageE,axiom,
% 0.32/0.47 ! [B: a,R2: set_Product_prod_b_a,A3: set_b] :
% 0.32/0.47 ( ( member_a @ B @ ( image_b_a @ R2 @ A3 ) )
% 0.32/0.47 => ~ ! [X3: b] :
% 0.32/0.47 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X3 @ B ) @ R2 )
% 0.32/0.47 => ~ ( member_b @ X3 @ A3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_295_ImageE,axiom,
% 0.32/0.47 ! [B: b,R2: set_Product_prod_a_b,A3: set_a] :
% 0.32/0.47 ( ( member_b @ B @ ( image_a_b @ R2 @ A3 ) )
% 0.32/0.47 => ~ ! [X3: a] :
% 0.32/0.47 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X3 @ B ) @ R2 )
% 0.32/0.47 => ~ ( member_a @ X3 @ A3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_296_ImageE,axiom,
% 0.32/0.47 ! [B: b,R2: set_Product_prod_b_b,A3: set_b] :
% 0.32/0.47 ( ( member_b @ B @ ( image_b_b @ R2 @ A3 ) )
% 0.32/0.47 => ~ ! [X3: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X3 @ B ) @ R2 )
% 0.32/0.47 => ~ ( member_b @ X3 @ A3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_297_nres__inequalities_I3_J,axiom,
% 0.32/0.47 ! [X4: product_unit] :
% 0.32/0.47 ( top_to177290092t_unit
% 0.32/0.47 != ( refine1420258419t_unit @ X4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_inequalities(3)
% 0.32/0.47 thf(fact_298_top__nres__def,axiom,
% 0.32/0.47 top_to177290092t_unit = refine1607584204t_unit ).
% 0.32/0.47
% 0.32/0.47 % top_nres_def
% 0.32/0.47 thf(fact_299_top__greatest,axiom,
% 0.32/0.47 ! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ) ).
% 0.32/0.47
% 0.32/0.47 % top_greatest
% 0.32/0.47 thf(fact_300_top__greatest,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ) ).
% 0.32/0.47
% 0.32/0.47 % top_greatest
% 0.32/0.47 thf(fact_301_top__greatest,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ) ).
% 0.32/0.47
% 0.32/0.47 % top_greatest
% 0.32/0.47 thf(fact_302_top_Oextremum__unique,axiom,
% 0.32/0.47 ! [A: refine787176636t_unit] :
% 0.32/0.47 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
% 0.32/0.47 = ( A = top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % top.extremum_unique
% 0.32/0.47 thf(fact_303_top_Oextremum__unique,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
% 0.32/0.47 = ( A = top_to240090974nres_b ) ) ).
% 0.32/0.47
% 0.32/0.47 % top.extremum_unique
% 0.32/0.47 thf(fact_304_top_Oextremum__unique,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 0.32/0.47 = ( A = top_to231829469nres_a ) ) ).
% 0.32/0.47
% 0.32/0.47 % top.extremum_unique
% 0.32/0.47 thf(fact_305_top_Oextremum__uniqueI,axiom,
% 0.32/0.47 ! [A: refine787176636t_unit] :
% 0.32/0.47 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
% 0.32/0.47 => ( A = top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % top.extremum_uniqueI
% 0.32/0.47 thf(fact_306_top_Oextremum__uniqueI,axiom,
% 0.32/0.47 ! [A: refine432681134nres_b] :
% 0.32/0.47 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
% 0.32/0.47 => ( A = top_to240090974nres_b ) ) ).
% 0.32/0.47
% 0.32/0.47 % top.extremum_uniqueI
% 0.32/0.47 thf(fact_307_top_Oextremum__uniqueI,axiom,
% 0.32/0.47 ! [A: refine424419629nres_a] :
% 0.32/0.47 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 0.32/0.47 => ( A = top_to231829469nres_a ) ) ).
% 0.32/0.47
% 0.32/0.47 % top.extremum_uniqueI
% 0.32/0.47 thf(fact_308_nres__order__simps_I3_J,axiom,
% 0.32/0.47 ! [M4: refine787176636t_unit] : ( ord_le1051254044t_unit @ M4 @ top_to177290092t_unit ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(3)
% 0.32/0.47 thf(fact_309_nres__order__simps_I3_J,axiom,
% 0.32/0.47 ! [M4: refine432681134nres_b] : ( ord_le527798542nres_b @ M4 @ top_to240090974nres_b ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(3)
% 0.32/0.47 thf(fact_310_nres__order__simps_I3_J,axiom,
% 0.32/0.47 ! [M4: refine424419629nres_a] : ( ord_le519537037nres_a @ M4 @ top_to231829469nres_a ) ).
% 0.32/0.47
% 0.32/0.47 % nres_order_simps(3)
% 0.32/0.47 thf(fact_311_nres__inequalities_I1_J,axiom,
% 0.32/0.47 ! [X: set_Product_unit] :
% 0.32/0.47 ( top_to177290092t_unit
% 0.32/0.47 != ( refine1777164439t_unit @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_inequalities(1)
% 0.32/0.47 thf(fact_312_nres__inequalities_I1_J,axiom,
% 0.32/0.47 ! [X: set_a] :
% 0.32/0.47 ( top_to231829469nres_a
% 0.32/0.47 != ( refine1198353288_RES_a @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_inequalities(1)
% 0.32/0.47 thf(fact_313_nres__inequalities_I1_J,axiom,
% 0.32/0.47 ! [X: set_b] :
% 0.32/0.47 ( top_to240090974nres_b
% 0.32/0.47 != ( refine1198353289_RES_b @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_inequalities(1)
% 0.32/0.47 thf(fact_314_nres__cases,axiom,
% 0.32/0.47 ! [M4: refine787176636t_unit] :
% 0.32/0.47 ( ( M4 != top_to177290092t_unit )
% 0.32/0.47 => ~ ! [X12: set_Product_unit] :
% 0.32/0.47 ( M4
% 0.32/0.47 != ( refine1777164439t_unit @ X12 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_cases
% 0.32/0.47 thf(fact_315_nres__cases,axiom,
% 0.32/0.47 ! [M4: refine424419629nres_a] :
% 0.32/0.47 ( ( M4 != top_to231829469nres_a )
% 0.32/0.47 => ~ ! [X12: set_a] :
% 0.32/0.47 ( M4
% 0.32/0.47 != ( refine1198353288_RES_a @ X12 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_cases
% 0.32/0.47 thf(fact_316_nres__cases,axiom,
% 0.32/0.47 ! [M4: refine432681134nres_b] :
% 0.32/0.47 ( ( M4 != top_to240090974nres_b )
% 0.32/0.47 => ~ ! [X12: set_b] :
% 0.32/0.47 ( M4
% 0.32/0.47 != ( refine1198353289_RES_b @ X12 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nres_cases
% 0.32/0.47 thf(fact_317_not__nofail__iff,axiom,
% 0.32/0.47 ! [S: refine787176636t_unit] :
% 0.32/0.47 ( ( ~ ( refine579265252t_unit @ S ) )
% 0.32/0.47 = ( S = top_to177290092t_unit ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_nofail_iff
% 0.32/0.47 thf(fact_318_nofail__def,axiom,
% 0.32/0.47 ( refine579265252t_unit
% 0.32/0.47 = ( ^ [S4: refine787176636t_unit] : ( S4 != top_to177290092t_unit ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nofail_def
% 0.32/0.47 thf(fact_319_intro__nofail_I2_J,axiom,
% 0.32/0.47 ! [S: refine787176636t_unit] :
% 0.32/0.47 ( ( top_to177290092t_unit != S )
% 0.32/0.47 = ( refine579265252t_unit @ S ) ) ).
% 0.32/0.47
% 0.32/0.47 % intro_nofail(2)
% 0.32/0.47 thf(fact_320_ibind__strict_I2_J,axiom,
% 0.32/0.47 ! [F: product_unit > refine787176636t_unit] :
% 0.32/0.47 ( ( refine681446406t_unit @ top_to177290092t_unit @ F )
% 0.32/0.47 = top_to177290092t_unit ) ).
% 0.32/0.47
% 0.32/0.47 % ibind_strict(2)
% 0.32/0.47 thf(fact_321_meta__le__everything__if__top,axiom,
% 0.32/0.47 ! [M: refine787176636t_unit,X4: refine787176636t_unit] :
% 0.32/0.47 ( ( M = top_to177290092t_unit )
% 0.32/0.47 => ( ord_le1051254044t_unit @ X4 @ M ) ) ).
% 0.32/0.47
% 0.32/0.47 % meta_le_everything_if_top
% 0.32/0.47 thf(fact_322_meta__le__everything__if__top,axiom,
% 0.32/0.47 ! [M: refine432681134nres_b,X4: refine432681134nres_b] :
% 0.32/0.47 ( ( M = top_to240090974nres_b )
% 0.32/0.47 => ( ord_le527798542nres_b @ X4 @ M ) ) ).
% 0.32/0.47
% 0.32/0.47 % meta_le_everything_if_top
% 0.32/0.47 thf(fact_323_meta__le__everything__if__top,axiom,
% 0.32/0.47 ! [M: refine424419629nres_a,X4: refine424419629nres_a] :
% 0.32/0.47 ( ( M = top_to231829469nres_a )
% 0.32/0.47 => ( ord_le519537037nres_a @ X4 @ M ) ) ).
% 0.32/0.47
% 0.32/0.47 % meta_le_everything_if_top
% 0.32/0.47 thf(fact_324_pw__flat__ge__iff,axiom,
% 0.32/0.47 ! [S: refine787176636t_unit,S3: refine787176636t_unit] :
% 0.32/0.47 ( ( partia1658438072t_unit @ top_to177290092t_unit @ S @ S3 )
% 0.32/0.47 = ( ( refine579265252t_unit @ S )
% 0.32/0.47 => ( ( refine579265252t_unit @ S3 )
% 0.32/0.47 & ! [X5: product_unit] :
% 0.32/0.47 ( ( refine558004794t_unit @ S @ X5 )
% 0.32/0.47 = ( refine558004794t_unit @ S3 @ X5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % pw_flat_ge_iff
% 0.32/0.47 thf(fact_325_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.32/0.47 ! [M4: refine787176636t_unit,M3: refine787176636t_unit,F: product_unit > refine787176636t_unit,F2: product_unit > refine787176636t_unit] :
% 0.32/0.47 ( ( partia1658438072t_unit @ top_to177290092t_unit @ M4 @ M3 )
% 0.32/0.47 => ( ! [X3: product_unit] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 0.32/0.47 => ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine681446406t_unit @ M4 @ F ) @ ( refine681446406t_unit @ M3 @ F2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(2)
% 0.32/0.47 thf(fact_326_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.32/0.47 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine432681134nres_b,F2: a > refine432681134nres_b] :
% 0.32/0.47 ( ( partia906949161nres_a @ top_to231829469nres_a @ M4 @ M3 )
% 0.32/0.47 => ( ! [X3: a] : ( partia915210666nres_b @ top_to240090974nres_b @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 0.32/0.47 => ( partia915210666nres_b @ top_to240090974nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ ( refine436832839nd_a_b @ M3 @ F2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(2)
% 0.32/0.47 thf(fact_327_flat__ord__compat_I2_J,axiom,
% 0.32/0.47 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.32/0.47 ( ( partia1658438072t_unit @ top_to177290092t_unit @ X4 @ Y3 )
% 0.32/0.47 => ( ord_le1051254044t_unit @ Y3 @ X4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % flat_ord_compat(2)
% 0.32/0.47 thf(fact_328_flat__ord__compat_I2_J,axiom,
% 0.32/0.47 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.32/0.47 ( ( partia915210666nres_b @ top_to240090974nres_b @ X4 @ Y3 )
% 0.32/0.47 => ( ord_le527798542nres_b @ Y3 @ X4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % flat_ord_compat(2)
% 0.32/0.47 thf(fact_329_flat__ord__compat_I2_J,axiom,
% 0.32/0.47 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.32/0.47 ( ( partia906949161nres_a @ top_to231829469nres_a @ X4 @ Y3 )
% 0.32/0.47 => ( ord_le519537037nres_a @ Y3 @ X4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % flat_ord_compat(2)
% 0.32/0.47 thf(fact_330_UNIV__I,axiom,
% 0.32/0.47 ! [X4: a] : ( member_a @ X4 @ top_top_set_a ) ).
% 0.32/0.47
% 0.32/0.47 % UNIV_I
% 0.32/0.47 thf(fact_331_UNIV__I,axiom,
% 0.32/0.47 ! [X4: b] : ( member_b @ X4 @ top_top_set_b ) ).
% 0.32/0.47
% 0.32/0.47 % UNIV_I
% 0.32/0.47 thf(fact_332_eq__UNIV__iff,axiom,
% 0.32/0.47 ! [S: set_a] :
% 0.32/0.47 ( ( S = top_top_set_a )
% 0.32/0.47 = ( ! [X5: a] : ( member_a @ X5 @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_UNIV_iff
% 0.32/0.47 thf(fact_333_eq__UNIV__iff,axiom,
% 0.32/0.47 ! [S: set_b] :
% 0.32/0.47 ( ( S = top_top_set_b )
% 0.32/0.47 = ( ! [X5: b] : ( member_b @ X5 @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_UNIV_iff
% 0.32/0.47 thf(fact_334_UNIV__witness,axiom,
% 0.32/0.47 ? [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).
% 0.32/0.47
% 0.32/0.47 % UNIV_witness
% 0.32/0.47 thf(fact_335_UNIV__witness,axiom,
% 0.32/0.47 ? [X3: b] : ( member_b @ X3 @ top_top_set_b ) ).
% 0.32/0.47
% 0.32/0.47 % UNIV_witness
% 0.32/0.47 thf(fact_336_top__set__def,axiom,
% 0.32/0.47 ( top_top_set_a
% 0.32/0.47 = ( collect_a @ top_top_a_o ) ) ).
% 0.32/0.47
% 0.32/0.47 % top_set_def
% 0.32/0.47 thf(fact_337_top__set__def,axiom,
% 0.32/0.47 ( top_top_set_b
% 0.32/0.47 = ( collect_b @ top_top_b_o ) ) ).
% 0.32/0.47
% 0.32/0.47 % top_set_def
% 0.32/0.47 thf(fact_338_UNIV__eq__I,axiom,
% 0.32/0.47 ! [A3: set_a] :
% 0.32/0.47 ( ! [X3: a] : ( member_a @ X3 @ A3 )
% 0.32/0.47 => ( top_top_set_a = A3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % UNIV_eq_I
% 0.32/0.47 thf(fact_339_UNIV__eq__I,axiom,
% 0.32/0.47 ! [A3: set_b] :
% 0.32/0.47 ( ! [X3: b] : ( member_b @ X3 @ A3 )
% 0.32/0.47 => ( top_top_set_b = A3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % UNIV_eq_I
% 0.32/0.47 thf(fact_340_top__empty__eq,axiom,
% 0.32/0.47 ( top_top_a_o
% 0.32/0.47 = ( ^ [X5: a] : ( member_a @ X5 @ top_top_set_a ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % top_empty_eq
% 0.32/0.47 thf(fact_341_top__empty__eq,axiom,
% 0.32/0.47 ( top_top_b_o
% 0.32/0.47 = ( ^ [X5: b] : ( member_b @ X5 @ top_top_set_b ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % top_empty_eq
% 0.32/0.47 thf(fact_342_ASSERT__simps_I2_J,axiom,
% 0.32/0.47 ( ( refine2039610767ASSERT @ $false )
% 0.32/0.47 = top_to177290092t_unit ) ).
% 0.32/0.47
% 0.32/0.47 % ASSERT_simps(2)
% 0.32/0.47
% 0.32/0.47 % Helper facts (15)
% 0.32/0.47 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.32/0.47 ! [X4: set_a,Y3: set_a] :
% 0.32/0.47 ( ( if_set_a @ $false @ X4 @ Y3 )
% 0.32/0.47 = Y3 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.32/0.47 ! [X4: set_a,Y3: set_a] :
% 0.32/0.47 ( ( if_set_a @ $true @ X4 @ Y3 )
% 0.32/0.47 = X4 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_2_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 0.32/0.47 ! [X4: set_b,Y3: set_b] :
% 0.32/0.47 ( ( if_set_b @ $false @ X4 @ Y3 )
% 0.32/0.47 = Y3 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 0.32/0.47 ! [X4: set_b,Y3: set_b] :
% 0.32/0.47 ( ( if_set_b @ $true @ X4 @ Y3 )
% 0.32/0.47 = X4 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.32/0.47 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.32/0.47 ( ( if_Ref1724547303nres_a @ $false @ X4 @ Y3 )
% 0.32/0.47 = Y3 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.32/0.47 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.32/0.47 ( ( if_Ref1724547303nres_a @ $true @ X4 @ Y3 )
% 0.32/0.47 = X4 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 0.32/0.47 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.32/0.47 ( ( if_Ref1732808808nres_b @ $false @ X4 @ Y3 )
% 0.32/0.47 = Y3 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 0.32/0.47 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.32/0.47 ( ( if_Ref1732808808nres_b @ $true @ X4 @ Y3 )
% 0.32/0.47 = X4 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 0.32/0.47 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 0.32/0.47 ( ( if_o_R1705037948nres_a @ $false @ X4 @ Y3 )
% 0.32/0.47 = Y3 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 0.32/0.47 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 0.32/0.47 ( ( if_o_R1705037948nres_a @ $true @ X4 @ Y3 )
% 0.32/0.47 = X4 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 0.32/0.47 ! [X4: $o > refine432681134nres_b,Y3: $o > refine432681134nres_b] :
% 0.32/0.47 ( ( if_o_R697118589nres_b @ $false @ X4 @ Y3 )
% 0.32/0.47 = Y3 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 0.32/0.47 ! [X4: $o > refine432681134nres_b,Y3: $o > refine432681134nres_b] :
% 0.32/0.47 ( ( if_o_R697118589nres_b @ $true @ X4 @ Y3 )
% 0.32/0.47 = X4 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.32/0.47 ! [P: $o] :
% 0.32/0.47 ( ( P = $true )
% 0.32/0.47 | ( P = $false ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.32/0.47 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.32/0.47 ( ( if_Ref1369692790t_unit @ $false @ X4 @ Y3 )
% 0.32/0.47 = Y3 ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.32/0.47 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.32/0.47 ( ( if_Ref1369692790t_unit @ $true @ X4 @ Y3 )
% 0.32/0.47 = X4 ) ).
% 0.32/0.47
% 0.32/0.47 % Conjectures (1)
% 0.32/0.47 thf(conj_0,conjecture,
% 0.32/0.47 ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 3.76/1.71 ---- Embedded in THF ---
% 3.76/1.72 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.76/1.72 %%% Generated on Tue Feb 24 08:26:57 EST 2026
% 3.76/1.72 %%% using '$$dhol' embedding, version 1.3.0.
% 3.76/1.72 %%% Logic specification used:
% 3.76/1.72 %%% thf(spec, logic, $$dhol).
% 3.76/1.72
% 3.76/1.72 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2DTF19091.p
% See solution above
% 3.76/1.72 ------------------------
% 3.76/1.78 ---- Cleaned THF ---
% 3.76/1.78 thf(ty_n_t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 3.76/1.78 produc1587512412nres_b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 3.76/1.78 produc1609974940nres_a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
% 3.76/1.78 set_Pr451126599t_unit: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.76/1.78 refine2031285398od_b_b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
% 3.76/1.78 refine891721109od_b_a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
% 3.76/1.78 refine1811374551od_a_b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 3.76/1.78 refine671810262od_a_a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 3.76/1.78 refine787176636t_unit: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Ounit_J_J,type,
% 3.76/1.78 set_Pr1707992533t_unit: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Ounit_J_J,type,
% 3.76/1.78 set_Pr1628433942t_unit: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 3.76/1.78 refine432681134nres_b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.76/1.78 refine424419629nres_a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.76/1.78 set_Product_prod_b_b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
% 3.76/1.78 set_Product_prod_b_a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
% 3.76/1.78 set_Product_prod_a_b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 3.76/1.78 set_Product_prod_a_a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 3.76/1.78 set_Product_unit: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 3.76/1.78 product_prod_b_b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
% 3.76/1.78 product_prod_b_a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
% 3.76/1.78 product_prod_a_b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 3.76/1.78 product_prod_a_a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Product____Type__Ounit,type,
% 3.76/1.78 product_unit: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_Itf__b_J,type,
% 3.76/1.78 set_b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 3.76/1.78 set_a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_tf__b,type,
% 3.76/1.78 b: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(ty_n_tf__a,type,
% 3.76/1.78 a: $tType ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 3.76/1.78 if_o_R1705037948nres_a: $o > ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o > refine424419629nres_a ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 3.76/1.78 if_o_R697118589nres_b: $o > ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o > refine432681134nres_b ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 3.76/1.78 if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.76/1.78 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 3.76/1.78 if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 3.76/1.78 if_set_a: $o > set_a > set_a > set_a ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_If_001t__Set__Oset_Itf__b_J,type,
% 3.76/1.78 if_set_b: $o > set_b > set_b > set_b ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 3.76/1.78 ord_le516598614nres_a: ( $o > refine424419629nres_a ) > ( $o > refine424419629nres_a ) > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J,type,
% 3.76/1.78 ord_le1656162903nres_b: ( $o > refine432681134nres_b ) > ( $o > refine432681134nres_b ) > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 3.76/1.78 ord_le915866422od_a_a: refine671810262od_a_a > refine671810262od_a_a > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
% 3.76/1.78 ord_le2055430711od_a_b: refine1811374551od_a_b > refine1811374551od_a_b > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__b_Mtf__a_J_J,type,
% 3.76/1.78 ord_le1135777269od_b_a: refine891721109od_b_a > refine891721109od_b_a > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.76/1.78 ord_le127857910od_b_b: refine2031285398od_b_b > refine2031285398od_b_b > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 3.76/1.78 ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.76/1.78 ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 3.76/1.78 ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 3.76/1.78 ord_less_eq_set_a: set_a > set_a > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__b_J,type,
% 3.76/1.78 ord_less_eq_set_b: set_b > set_b > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.76/1.78 order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J,type,
% 3.76/1.78 order_1722590613nres_b: ( refine432681134nres_b > $o ) > refine432681134nres_b ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Otop__class_Otop_001_062_Itf__a_M_Eo_J,type,
% 3.76/1.78 top_top_a_o: a > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Otop__class_Otop_001_062_Itf__b_M_Eo_J,type,
% 3.76/1.78 top_top_b_o: b > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J,type,
% 3.76/1.78 top_to177290092t_unit: refine787176636t_unit ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Orderings_Otop__class_Otop_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
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% 3.76/1.78
% 3.76/1.78 thf(sy_c_Set_OCollect_001tf__a,type,
% 3.76/1.78 collect_a: ( a > $o ) > set_a ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_Set_OCollect_001tf__b,type,
% 3.76/1.78 collect_b: ( b > $o ) > set_b ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 3.76/1.78 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
% 3.76/1.78 member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
% 3.76/1.78 member1277678991od_b_a: product_prod_b_a > set_Product_prod_b_a > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 3.76/1.78 member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_member_001t__Product____Type__Ounit,type,
% 3.76/1.78 member_Product_unit: product_unit > set_Product_unit > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_member_001tf__a,type,
% 3.76/1.78 member_a: a > set_a > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_c_member_001tf__b,type,
% 3.76/1.78 member_b: b > set_b > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_v__092_060Phi_062,type,
% 3.76/1.78 phi: a > $o ).
% 3.76/1.78
% 3.76/1.78 thf(sy_v_f,type,
% 3.76/1.78 f: a > refine432681134nres_b ).
% 3.76/1.78
% 3.76/1.78 thf(sy_v_m,type,
% 3.76/1.78 m: refine432681134nres_b ).
% 3.76/1.78
% 3.76/1.78 thf(sy_v_x,type,
% 3.76/1.78 x: a ).
% 3.76/1.78
% 3.76/1.78 thf(fact_0_assms_I1_J,axiom,
% 3.76/1.78 phi @ x ).
% 3.76/1.78
% 3.76/1.78 thf(fact_1_assms_I2_J,axiom,
% 3.76/1.78 ord_le527798542nres_b @ m @ ( f @ x ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_2_nres__more__simps_I4_J,axiom,
% 3.76/1.78 ! [X: set_Product_unit,Y: set_Product_unit] :
% 3.76/1.78 ( ( ( refine1777164439t_unit @ X )
% 3.76/1.78 = ( refine1777164439t_unit @ Y ) )
% 3.76/1.78 = ( X = Y ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_3_nres__more__simps_I4_J,axiom,
% 3.76/1.78 ! [X: set_b,Y: set_b] :
% 3.76/1.78 ( ( ( refine1198353289_RES_b @ X )
% 3.76/1.78 = ( refine1198353289_RES_b @ Y ) )
% 3.76/1.78 = ( X = Y ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_4_nres__more__simps_I4_J,axiom,
% 3.76/1.78 ! [X: set_a,Y: set_a] :
% 3.76/1.78 ( ( ( refine1198353288_RES_a @ X )
% 3.76/1.78 = ( refine1198353288_RES_a @ Y ) )
% 3.76/1.78 = ( X = Y ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_5_nres_Oinject,axiom,
% 3.76/1.78 ! [X2: set_Product_unit,Y2: set_Product_unit] :
% 3.76/1.78 ( ( ( refine1777164439t_unit @ X2 )
% 3.76/1.78 = ( refine1777164439t_unit @ Y2 ) )
% 3.76/1.78 = ( X2 = Y2 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_6_nres_Oinject,axiom,
% 3.76/1.78 ! [X2: set_b,Y2: set_b] :
% 3.76/1.78 ( ( ( refine1198353289_RES_b @ X2 )
% 3.76/1.78 = ( refine1198353289_RES_b @ Y2 ) )
% 3.76/1.78 = ( X2 = Y2 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_7_nres_Oinject,axiom,
% 3.76/1.78 ! [X2: set_a,Y2: set_a] :
% 3.76/1.78 ( ( ( refine1198353288_RES_a @ X2 )
% 3.76/1.78 = ( refine1198353288_RES_a @ Y2 ) )
% 3.76/1.78 = ( X2 = Y2 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_8_if__rule,axiom,
% 3.76/1.78 ! [B: $o,S1: refine787176636t_unit,Phi: product_unit > $o,S2: refine787176636t_unit] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le1051254044t_unit @ S1 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le1051254044t_unit @ S2 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) )
% 3.76/1.78 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ S1 @ S2 ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_9_if__rule,axiom,
% 3.76/1.78 ! [B: $o,S1: refine432681134nres_b,Phi: b > $o,S2: refine432681134nres_b] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le527798542nres_b @ S1 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le527798542nres_b @ S2 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ S1 @ S2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_10_if__rule,axiom,
% 3.76/1.78 ! [B: $o,S1: refine424419629nres_a,Phi: a > $o,S2: refine424419629nres_a] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le519537037nres_a @ S1 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le519537037nres_a @ S2 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ S1 @ S2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_11_RES__rule,axiom,
% 3.76/1.78 ! [S: set_Product_prod_a_a,Phi: product_prod_a_a > $o] :
% 3.76/1.78 ( ! [X3: product_prod_a_a] :
% 3.76/1.78 ( ( member449909584od_a_a @ X3 @ S )
% 3.76/1.78 => ( Phi @ X3 ) )
% 3.76/1.78 => ( ord_le915866422od_a_a @ ( refine622451633od_a_a @ S ) @ ( refine622451633od_a_a @ ( collec645855634od_a_a @ Phi ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_12_RES__rule,axiom,
% 3.76/1.78 ! [S: set_Product_prod_b_a,Phi: product_prod_b_a > $o] :
% 3.76/1.78 ( ! [X3: product_prod_b_a] :
% 3.76/1.78 ( ( member1277678991od_b_a @ X3 @ S )
% 3.76/1.78 => ( Phi @ X3 ) )
% 3.76/1.78 => ( ord_le1135777269od_b_a @ ( refine1450221040od_b_a @ S ) @ ( refine1450221040od_b_a @ ( collec1473625041od_b_a @ Phi ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_13_RES__rule,axiom,
% 3.76/1.78 ! [S: set_Product_prod_b_b,Phi: product_prod_b_b > $o] :
% 3.76/1.78 ( ! [X3: product_prod_b_b] :
% 3.76/1.78 ( ( member1285940496od_b_b @ X3 @ S )
% 3.76/1.78 => ( Phi @ X3 ) )
% 3.76/1.78 => ( ord_le127857910od_b_b @ ( refine1458482545od_b_b @ S ) @ ( refine1458482545od_b_b @ ( collec1481886546od_b_b @ Phi ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_14_RES__rule,axiom,
% 3.76/1.78 ! [S: set_Product_prod_a_b,Phi: product_prod_a_b > $o] :
% 3.76/1.78 ( ! [X3: product_prod_a_b] :
% 3.76/1.78 ( ( member458171089od_a_b @ X3 @ S )
% 3.76/1.78 => ( Phi @ X3 ) )
% 3.76/1.78 => ( ord_le2055430711od_a_b @ ( refine630713138od_a_b @ S ) @ ( refine630713138od_a_b @ ( collec654117139od_a_b @ Phi ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_15_RES__rule,axiom,
% 3.76/1.78 ! [S: set_Product_unit,Phi: product_unit > $o] :
% 3.76/1.78 ( ! [X3: product_unit] :
% 3.76/1.78 ( ( member_Product_unit @ X3 @ S )
% 3.76/1.78 => ( Phi @ X3 ) )
% 3.76/1.78 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ S ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_16_RES__rule,axiom,
% 3.76/1.78 ! [S: set_b,Phi: b > $o] :
% 3.76/1.78 ( ! [X3: b] :
% 3.76/1.78 ( ( member_b @ X3 @ S )
% 3.76/1.78 => ( Phi @ X3 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_17_RES__rule,axiom,
% 3.76/1.78 ! [S: set_a,Phi: a > $o] :
% 3.76/1.78 ( ! [X3: a] :
% 3.76/1.78 ( ( member_a @ X3 @ S )
% 3.76/1.78 => ( Phi @ X3 ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_18_SPEC__rule,axiom,
% 3.76/1.78 ! [Phi: product_unit > $o,Phi2: product_unit > $o] :
% 3.76/1.78 ( ! [X3: product_unit] :
% 3.76/1.78 ( ( Phi @ X3 )
% 3.76/1.78 => ( Phi2 @ X3 ) )
% 3.76/1.78 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_19_SPEC__rule,axiom,
% 3.76/1.78 ! [Phi: b > $o,Phi2: b > $o] :
% 3.76/1.78 ( ! [X3: b] :
% 3.76/1.78 ( ( Phi @ X3 )
% 3.76/1.78 => ( Phi2 @ X3 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_20_SPEC__rule,axiom,
% 3.76/1.78 ! [Phi: a > $o,Phi2: a > $o] :
% 3.76/1.78 ( ! [X3: a] :
% 3.76/1.78 ( ( Phi @ X3 )
% 3.76/1.78 => ( Phi2 @ X3 ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_21_SPEC__trans,axiom,
% 3.76/1.78 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit,Postcond: product_unit > $o] :
% 3.76/1.78 ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 3.76/1.78 => ( ( ord_le1051254044t_unit @ Y3 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) )
% 3.76/1.78 => ( ord_le1051254044t_unit @ X4 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_22_SPEC__trans,axiom,
% 3.76/1.78 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b,Postcond: b > $o] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ Y3 @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ X4 @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_23_SPEC__trans,axiom,
% 3.76/1.78 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Postcond: a > $o] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ Y3 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ X4 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_24_lhs__step__If,axiom,
% 3.76/1.78 ! [B: $o,T: set_b,M: set_b,E: set_b] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_less_eq_set_b @ T @ M ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_less_eq_set_b @ E @ M ) )
% 3.76/1.78 => ( ord_less_eq_set_b @ ( if_set_b @ B @ T @ E ) @ M ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_25_lhs__step__If,axiom,
% 3.76/1.78 ! [B: $o,T: set_a,M: set_a,E: set_a] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_less_eq_set_a @ T @ M ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_less_eq_set_a @ E @ M ) )
% 3.76/1.78 => ( ord_less_eq_set_a @ ( if_set_a @ B @ T @ E ) @ M ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_26_lhs__step__If,axiom,
% 3.76/1.78 ! [B: $o,T: $o > refine424419629nres_a,M: $o > refine424419629nres_a,E: $o > refine424419629nres_a] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le516598614nres_a @ T @ M ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le516598614nres_a @ E @ M ) )
% 3.76/1.78 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B @ T @ E ) @ M ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_27_lhs__step__If,axiom,
% 3.76/1.78 ! [B: $o,T: $o > refine432681134nres_b,M: $o > refine432681134nres_b,E: $o > refine432681134nres_b] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le1656162903nres_b @ T @ M ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le1656162903nres_b @ E @ M ) )
% 3.76/1.78 => ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ B @ T @ E ) @ M ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_28_lhs__step__If,axiom,
% 3.76/1.78 ! [B: $o,T: refine787176636t_unit,M: refine787176636t_unit,E: refine787176636t_unit] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le1051254044t_unit @ T @ M ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le1051254044t_unit @ E @ M ) )
% 3.76/1.78 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ T @ E ) @ M ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_29_lhs__step__If,axiom,
% 3.76/1.78 ! [B: $o,T: refine424419629nres_a,M: refine424419629nres_a,E: refine424419629nres_a] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le519537037nres_a @ T @ M ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le519537037nres_a @ E @ M ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ M ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_30_lhs__step__If,axiom,
% 3.76/1.78 ! [B: $o,T: refine432681134nres_b,M: refine432681134nres_b,E: refine432681134nres_b] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le527798542nres_b @ T @ M ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le527798542nres_b @ E @ M ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ T @ E ) @ M ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_31_SPEC__cons__rule,axiom,
% 3.76/1.78 ! [M: refine787176636t_unit,Phi: product_unit > $o,Psi: product_unit > $o] :
% 3.76/1.78 ( ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) )
% 3.76/1.78 => ( ! [X3: product_unit] :
% 3.76/1.78 ( ( Phi @ X3 )
% 3.76/1.78 => ( Psi @ X3 ) )
% 3.76/1.78 => ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Psi ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_32_SPEC__cons__rule,axiom,
% 3.76/1.78 ! [M: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 3.76/1.78 => ( ! [X3: a] :
% 3.76/1.78 ( ( Phi @ X3 )
% 3.76/1.78 => ( Psi @ X3 ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_33_SPEC__cons__rule,axiom,
% 3.76/1.78 ! [M: refine432681134nres_b,Phi: b > $o,Psi: b > $o] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ M @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) )
% 3.76/1.78 => ( ! [X3: b] :
% 3.76/1.78 ( ( Phi @ X3 )
% 3.76/1.78 => ( Psi @ X3 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ M @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_34_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: a,X: set_a,M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 3.76/1.78 ( ( member_a @ X4 @ X )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ M @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_35_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: a,X: set_a,M: refine432681134nres_b,F: a > refine432681134nres_b] :
% 3.76/1.78 ( ( member_a @ X4 @ X )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ M @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_36_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: b,X: set_b,M: refine432681134nres_b,F: b > refine432681134nres_b] :
% 3.76/1.78 ( ( member_b @ X4 @ X )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ M @ ( refine1264602246nd_b_b @ ( refine1198353289_RES_b @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_37_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: b,X: set_b,M: refine424419629nres_a,F: b > refine424419629nres_a] :
% 3.76/1.78 ( ( member_b @ X4 @ X )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ M @ ( refine1264602245nd_b_a @ ( refine1198353289_RES_b @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_38_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: a,X: set_a,M: refine787176636t_unit,F: a > refine787176636t_unit] :
% 3.76/1.78 ( ( member_a @ X4 @ X )
% 3.76/1.78 => ( ( ord_le1051254044t_unit @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le1051254044t_unit @ M @ ( refine96995669t_unit @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_39_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: b,X: set_b,M: refine787176636t_unit,F: b > refine787176636t_unit] :
% 3.76/1.78 ( ( member_b @ X4 @ X )
% 3.76/1.78 => ( ( ord_le1051254044t_unit @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le1051254044t_unit @ M @ ( refine216248468t_unit @ ( refine1198353289_RES_b @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_40_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: product_unit,X: set_Product_unit,M: refine432681134nres_b,F: product_unit > refine432681134nres_b] :
% 3.76/1.78 ( ( member_Product_unit @ X4 @ X )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ M @ ( refine119808504unit_b @ ( refine1777164439t_unit @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_41_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: product_unit,X: set_Product_unit,M: refine424419629nres_a,F: product_unit > refine424419629nres_a] :
% 3.76/1.78 ( ( member_Product_unit @ X4 @ X )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ M @ ( refine119808503unit_a @ ( refine1777164439t_unit @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_42_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: product_unit,X: set_Product_unit,M: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 3.76/1.78 ( ( member_Product_unit @ X4 @ X )
% 3.76/1.78 => ( ( ord_le1051254044t_unit @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le1051254044t_unit @ M @ ( refine681446406t_unit @ ( refine1777164439t_unit @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_43_RES__bind__choose,axiom,
% 3.76/1.78 ! [X4: product_prod_a_a,X: set_Product_prod_a_a,M: refine432681134nres_b,F: product_prod_a_a > refine432681134nres_b] :
% 3.76/1.78 ( ( member449909584od_a_a @ X4 @ X )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ M @ ( refine988994910_a_a_b @ ( refine622451633od_a_a @ X ) @ F ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_44_order__mono__setup_Orefl,axiom,
% 3.76/1.78 ! [X4: set_b] : ( ord_less_eq_set_b @ X4 @ X4 ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_45_order__mono__setup_Orefl,axiom,
% 3.76/1.78 ! [X4: set_a] : ( ord_less_eq_set_a @ X4 @ X4 ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_46_order__mono__setup_Orefl,axiom,
% 3.76/1.78 ! [X4: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ X4 @ X4 ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_47_order__mono__setup_Orefl,axiom,
% 3.76/1.78 ! [X4: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ X4 @ X4 ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_48_order__mono__setup_Orefl,axiom,
% 3.76/1.78 ! [X4: refine787176636t_unit] : ( ord_le1051254044t_unit @ X4 @ X4 ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_49_order__mono__setup_Orefl,axiom,
% 3.76/1.78 ! [X4: refine432681134nres_b] : ( ord_le527798542nres_b @ X4 @ X4 ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_50_order__mono__setup_Orefl,axiom,
% 3.76/1.78 ! [X4: refine424419629nres_a] : ( ord_le519537037nres_a @ X4 @ X4 ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_51_the__RES_Osimps,axiom,
% 3.76/1.78 ! [X: set_Product_unit] :
% 3.76/1.78 ( ( refine1208325748t_unit @ ( refine1777164439t_unit @ X ) )
% 3.76/1.78 = X ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_52_the__RES_Osimps,axiom,
% 3.76/1.78 ! [X: set_a] :
% 3.76/1.78 ( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ X ) )
% 3.76/1.78 = X ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_53_the__RES_Osimps,axiom,
% 3.76/1.78 ! [X: set_b] :
% 3.76/1.78 ( ( refine1822134886_RES_b @ ( refine1198353289_RES_b @ X ) )
% 3.76/1.78 = X ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_54_nf__inres__RES,axiom,
% 3.76/1.78 ! [X: set_Product_prod_a_a,X4: product_prod_a_a] :
% 3.76/1.78 ( ( refine378960780od_a_a @ ( refine622451633od_a_a @ X ) @ X4 )
% 3.76/1.78 = ( member449909584od_a_a @ X4 @ X ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_55_nf__inres__RES,axiom,
% 3.76/1.78 ! [X: set_Product_prod_b_a,X4: product_prod_b_a] :
% 3.76/1.78 ( ( refine1206730187od_b_a @ ( refine1450221040od_b_a @ X ) @ X4 )
% 3.76/1.78 = ( member1277678991od_b_a @ X4 @ X ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_56_nf__inres__RES,axiom,
% 3.76/1.78 ! [X: set_Product_prod_b_b,X4: product_prod_b_b] :
% 3.76/1.78 ( ( refine1214991692od_b_b @ ( refine1458482545od_b_b @ X ) @ X4 )
% 3.76/1.78 = ( member1285940496od_b_b @ X4 @ X ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_57_nf__inres__RES,axiom,
% 3.76/1.78 ! [X: set_Product_prod_a_b,X4: product_prod_a_b] :
% 3.76/1.78 ( ( refine387222285od_a_b @ ( refine630713138od_a_b @ X ) @ X4 )
% 3.76/1.78 = ( member458171089od_a_b @ X4 @ X ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_58_nf__inres__RES,axiom,
% 3.76/1.78 ! [X: set_Product_unit,X4: product_unit] :
% 3.76/1.78 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ X ) @ X4 )
% 3.76/1.78 = ( member_Product_unit @ X4 @ X ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_59_nf__inres__RES,axiom,
% 3.76/1.78 ! [X: set_a,X4: a] :
% 3.76/1.78 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X ) @ X4 )
% 3.76/1.78 = ( member_a @ X4 @ X ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_60_nf__inres__RES,axiom,
% 3.76/1.78 ! [X: set_b,X4: b] :
% 3.76/1.78 ( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ X ) @ X4 )
% 3.76/1.78 = ( member_b @ X4 @ X ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_61_nf__inres__SPEC,axiom,
% 3.76/1.78 ! [Phi: product_unit > $o,X4: product_unit] :
% 3.76/1.78 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ X4 )
% 3.76/1.78 = ( Phi @ X4 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_62_nf__inres__SPEC,axiom,
% 3.76/1.78 ! [Phi: a > $o,X4: a] :
% 3.76/1.78 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ X4 )
% 3.76/1.78 = ( Phi @ X4 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_63_nf__inres__SPEC,axiom,
% 3.76/1.78 ! [Phi: b > $o,X4: b] :
% 3.76/1.78 ( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) @ X4 )
% 3.76/1.78 = ( Phi @ X4 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_64_le__funD,axiom,
% 3.76/1.78 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 3.76/1.78 ( ( ord_le516598614nres_a @ F @ G )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_65_le__funD,axiom,
% 3.76/1.78 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X4: $o] :
% 3.76/1.78 ( ( ord_le1656162903nres_b @ F @ G )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_66_le__funE,axiom,
% 3.76/1.78 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 3.76/1.78 ( ( ord_le516598614nres_a @ F @ G )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_67_le__funE,axiom,
% 3.76/1.78 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X4: $o] :
% 3.76/1.78 ( ( ord_le1656162903nres_b @ F @ G )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_68_le__funI,axiom,
% 3.76/1.78 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a] :
% 3.76/1.78 ( ! [X3: $o] : ( ord_le519537037nres_a @ ( F @ X3 ) @ ( G @ X3 ) )
% 3.76/1.78 => ( ord_le516598614nres_a @ F @ G ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_69_Refine__Misc_Oif__mono,axiom,
% 3.76/1.78 ! [B: $o,M1: refine432681134nres_b,M12: refine432681134nres_b,M2: refine432681134nres_b,M22: refine432681134nres_b] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le527798542nres_b @ M1 @ M12 ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le527798542nres_b @ M2 @ M22 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ M1 @ M2 ) @ ( if_Ref1732808808nres_b @ B @ M12 @ M22 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_70_Refine__Misc_Oif__mono,axiom,
% 3.76/1.78 ! [B: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M2: refine424419629nres_a,M22: refine424419629nres_a] :
% 3.76/1.78 ( ( B
% 3.76/1.78 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 3.76/1.78 => ( ( ~ B
% 3.76/1.78 => ( ord_le519537037nres_a @ M2 @ M22 ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ M1 @ M2 ) @ ( if_Ref1724547303nres_a @ B @ M12 @ M22 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_71_order__subst1,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ ( F @ B ) )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B @ C )
% 3.76/1.78 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_72_order__subst1,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ ( F @ B ) )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B @ C )
% 3.76/1.78 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_73_order__subst1,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B: refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B @ C )
% 3.76/1.78 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_74_order__subst1,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B @ C )
% 3.76/1.78 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_75_less__eq__nres_Osimps_I2_J,axiom,
% 3.76/1.78 ! [A: set_a,B: set_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 3.76/1.78 = ( ord_less_eq_set_a @ A @ B ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_76_less__eq__nres_Osimps_I2_J,axiom,
% 3.76/1.78 ! [A: set_b,B: set_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine1198353289_RES_b @ B ) )
% 3.76/1.78 = ( ord_less_eq_set_b @ A @ B ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_77_nres__order__simps_I5_J,axiom,
% 3.76/1.78 ! [X: set_a,Y: set_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine1198353288_RES_a @ Y ) )
% 3.76/1.78 = ( ord_less_eq_set_a @ X @ Y ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_78_nres__order__simps_I5_J,axiom,
% 3.76/1.78 ! [X: set_b,Y: set_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ X ) @ ( refine1198353289_RES_b @ Y ) )
% 3.76/1.78 = ( ord_less_eq_set_b @ X @ Y ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_79_order__mono__setup_Omono__if,axiom,
% 3.76/1.78 ! [T: refine432681134nres_b,T2: refine432681134nres_b,E: refine432681134nres_b,E2: refine432681134nres_b,B: $o] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ T @ T2 )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ E @ E2 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ T @ E ) @ ( if_Ref1732808808nres_b @ B @ T2 @ E2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_80_order__mono__setup_Omono__if,axiom,
% 3.76/1.78 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B: $o] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ T @ T2 )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ E @ E2 )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ ( if_Ref1724547303nres_a @ B @ T2 @ E2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_81_dual__order_Oantisym,axiom,
% 3.76/1.78 ! [B: refine432681134nres_b,A: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ B @ A )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ A @ B )
% 3.76/1.78 => ( A = B ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_82_dual__order_Oantisym,axiom,
% 3.76/1.78 ! [B: refine424419629nres_a,A: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ B @ A )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ A @ B )
% 3.76/1.78 => ( A = B ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_83_dual__order_Oeq__iff,axiom,
% 3.76/1.78 ( ( ^ [Y5: refine432681134nres_b,Z: refine432681134nres_b] : ( Y5 = Z ) )
% 3.76/1.78 = ( ^ [A2: refine432681134nres_b,B2: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ B2 @ A2 )
% 3.76/1.78 & ( ord_le527798542nres_b @ A2 @ B2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_84_dual__order_Oeq__iff,axiom,
% 3.76/1.78 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 3.76/1.78 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 3.76/1.78 & ( ord_le519537037nres_a @ A2 @ B2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_85_dual__order_Otrans,axiom,
% 3.76/1.78 ! [B: refine432681134nres_b,A: refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ B @ A )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ C @ B )
% 3.76/1.78 => ( ord_le527798542nres_b @ C @ A ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_86_dual__order_Otrans,axiom,
% 3.76/1.78 ! [B: refine424419629nres_a,A: refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ B @ A )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ C @ B )
% 3.76/1.78 => ( ord_le519537037nres_a @ C @ A ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_87_dual__order_Orefl,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_88_dual__order_Orefl,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_89_order__trans,axiom,
% 3.76/1.78 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b,Z2: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ Y3 @ Z2 )
% 3.76/1.78 => ( ord_le527798542nres_b @ X4 @ Z2 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_90_order__trans,axiom,
% 3.76/1.78 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 3.76/1.78 => ( ord_le519537037nres_a @ X4 @ Z2 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_91_order__class_Oorder_Oantisym,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,B: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ B )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B @ A )
% 3.76/1.78 => ( A = B ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_92_order__class_Oorder_Oantisym,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ B )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B @ A )
% 3.76/1.78 => ( A = B ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_93_ord__le__eq__trans,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ B )
% 3.76/1.78 => ( ( B = C )
% 3.76/1.78 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_94_ord__le__eq__trans,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ B )
% 3.76/1.78 => ( ( B = C )
% 3.76/1.78 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_95_ord__eq__le__trans,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( A = B )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B @ C )
% 3.76/1.78 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_96_ord__eq__le__trans,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( A = B )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B @ C )
% 3.76/1.78 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_97_order__class_Oorder_Oeq__iff,axiom,
% 3.76/1.78 ( ( ^ [Y5: refine432681134nres_b,Z: refine432681134nres_b] : ( Y5 = Z ) )
% 3.76/1.78 = ( ^ [A2: refine432681134nres_b,B2: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 3.76/1.78 & ( ord_le527798542nres_b @ B2 @ A2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_98_order__class_Oorder_Oeq__iff,axiom,
% 3.76/1.78 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 3.76/1.78 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.76/1.78 & ( ord_le519537037nres_a @ B2 @ A2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_99_antisym__conv,axiom,
% 3.76/1.78 ! [Y3: refine432681134nres_b,X4: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ Y3 @ X4 )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 3.76/1.78 = ( X4 = Y3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_100_antisym__conv,axiom,
% 3.76/1.78 ! [Y3: refine424419629nres_a,X4: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.76/1.78 = ( X4 = Y3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_101_order_Otrans,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ B )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B @ C )
% 3.76/1.78 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_102_order_Otrans,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ B )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B @ C )
% 3.76/1.78 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_103_eq__refl,axiom,
% 3.76/1.78 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 3.76/1.78 ( ( X4 = Y3 )
% 3.76/1.78 => ( ord_le527798542nres_b @ X4 @ Y3 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_104_eq__refl,axiom,
% 3.76/1.78 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.76/1.78 ( ( X4 = Y3 )
% 3.76/1.78 => ( ord_le519537037nres_a @ X4 @ Y3 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_105_antisym,axiom,
% 3.76/1.78 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ Y3 @ X4 )
% 3.76/1.78 => ( X4 = Y3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_106_antisym,axiom,
% 3.76/1.78 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 3.76/1.78 => ( X4 = Y3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_107_mem__Collect__eq,axiom,
% 3.76/1.78 ! [A: a,P: a > $o] :
% 3.76/1.78 ( ( member_a @ A @ ( collect_a @ P ) )
% 3.76/1.78 = ( P @ A ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_108_mem__Collect__eq,axiom,
% 3.76/1.78 ! [A: b,P: b > $o] :
% 3.76/1.78 ( ( member_b @ A @ ( collect_b @ P ) )
% 3.76/1.78 = ( P @ A ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_109_Collect__mem__eq,axiom,
% 3.76/1.78 ! [A3: set_a] :
% 3.76/1.78 ( ( collect_a
% 3.76/1.78 @ ^ [X5: a] : ( member_a @ X5 @ A3 ) )
% 3.76/1.78 = A3 ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_110_Collect__mem__eq,axiom,
% 3.76/1.78 ! [A3: set_b] :
% 3.76/1.78 ( ( collect_b
% 3.76/1.78 @ ^ [X5: b] : ( member_b @ X5 @ A3 ) )
% 3.76/1.78 = A3 ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_111_Collect__cong,axiom,
% 3.76/1.78 ! [P: a > $o,Q: a > $o] :
% 3.76/1.78 ( ! [X3: a] :
% 3.76/1.78 ( ( P @ X3 )
% 3.76/1.78 = ( Q @ X3 ) )
% 3.76/1.78 => ( ( collect_a @ P )
% 3.76/1.78 = ( collect_a @ Q ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_112_Collect__cong,axiom,
% 3.76/1.78 ! [P: b > $o,Q: b > $o] :
% 3.76/1.78 ( ! [X3: b] :
% 3.76/1.78 ( ( P @ X3 )
% 3.76/1.78 = ( Q @ X3 ) )
% 3.76/1.78 => ( ( collect_b @ P )
% 3.76/1.78 = ( collect_b @ Q ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_113_eq__iff,axiom,
% 3.76/1.78 ( ( ^ [Y5: refine432681134nres_b,Z: refine432681134nres_b] : ( Y5 = Z ) )
% 3.76/1.78 = ( ^ [X5: refine432681134nres_b,Y6: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X5 @ Y6 )
% 3.76/1.78 & ( ord_le527798542nres_b @ Y6 @ X5 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_114_eq__iff,axiom,
% 3.76/1.78 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 3.76/1.78 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X5 @ Y6 )
% 3.76/1.78 & ( ord_le519537037nres_a @ Y6 @ X5 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_115_ord__le__eq__subst,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ B )
% 3.76/1.78 => ( ( ( F @ B )
% 3.76/1.78 = C )
% 3.76/1.78 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_116_ord__le__eq__subst,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ B )
% 3.76/1.78 => ( ( ( F @ B )
% 3.76/1.78 = C )
% 3.76/1.78 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_117_ord__le__eq__subst,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ B )
% 3.76/1.78 => ( ( ( F @ B )
% 3.76/1.78 = C )
% 3.76/1.78 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_118_ord__le__eq__subst,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ B )
% 3.76/1.78 => ( ( ( F @ B )
% 3.76/1.78 = C )
% 3.76/1.78 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_119_ord__eq__le__subst,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( A
% 3.76/1.78 = ( F @ B ) )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B @ C )
% 3.76/1.78 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_120_ord__eq__le__subst,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B: refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( A
% 3.76/1.78 = ( F @ B ) )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B @ C )
% 3.76/1.78 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_121_ord__eq__le__subst,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( A
% 3.76/1.78 = ( F @ B ) )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B @ C )
% 3.76/1.78 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_122_ord__eq__le__subst,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( A
% 3.76/1.78 = ( F @ B ) )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B @ C )
% 3.76/1.78 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_123_order__subst2,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ B )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ ( F @ B ) @ C )
% 3.76/1.78 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_124_order__subst2,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ B )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 3.76/1.78 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_125_order__subst2,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ B )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ ( F @ B ) @ C )
% 3.76/1.78 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_126_order__subst2,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ B )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 3.76/1.78 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_127_the__RES__inv,axiom,
% 3.76/1.78 ! [M: refine424419629nres_a] :
% 3.76/1.78 ( ( refine412683989fail_a @ M )
% 3.76/1.78 => ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ M ) )
% 3.76/1.78 = M ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_128_the__RES__inv,axiom,
% 3.76/1.78 ! [M: refine432681134nres_b] :
% 3.76/1.78 ( ( refine412683990fail_b @ M )
% 3.76/1.78 => ( ( refine1198353289_RES_b @ ( refine1822134886_RES_b @ M ) )
% 3.76/1.78 = M ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_129_Greatest__equality,axiom,
% 3.76/1.78 ! [P: refine432681134nres_b > $o,X4: refine432681134nres_b] :
% 3.76/1.78 ( ( P @ X4 )
% 3.76/1.78 => ( ! [Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( P @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ Y4 @ X4 ) )
% 3.76/1.78 => ( ( order_1722590613nres_b @ P )
% 3.76/1.78 = X4 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_130_Greatest__equality,axiom,
% 3.76/1.78 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a] :
% 3.76/1.78 ( ( P @ X4 )
% 3.76/1.78 => ( ! [Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( P @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 3.76/1.78 => ( ( order_1714329108nres_a @ P )
% 3.76/1.78 = X4 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_131_GreatestI2__order,axiom,
% 3.76/1.78 ! [P: refine432681134nres_b > $o,X4: refine432681134nres_b,Q: refine432681134nres_b > $o] :
% 3.76/1.78 ( ( P @ X4 )
% 3.76/1.78 => ( ! [Y4: refine432681134nres_b] :
% 3.76/1.78 ( ( P @ Y4 )
% 3.76/1.78 => ( ord_le527798542nres_b @ Y4 @ X4 ) )
% 3.76/1.78 => ( ! [X3: refine432681134nres_b] :
% 3.76/1.78 ( ( P @ X3 )
% 3.76/1.78 => ( ! [Y7: refine432681134nres_b] :
% 3.76/1.78 ( ( P @ Y7 )
% 3.76/1.78 => ( ord_le527798542nres_b @ Y7 @ X3 ) )
% 3.76/1.78 => ( Q @ X3 ) ) )
% 3.76/1.78 => ( Q @ ( order_1722590613nres_b @ P ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_132_GreatestI2__order,axiom,
% 3.76/1.78 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 3.76/1.78 ( ( P @ X4 )
% 3.76/1.78 => ( ! [Y4: refine424419629nres_a] :
% 3.76/1.78 ( ( P @ Y4 )
% 3.76/1.78 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 3.76/1.78 => ( ! [X3: refine424419629nres_a] :
% 3.76/1.78 ( ( P @ X3 )
% 3.76/1.78 => ( ! [Y7: refine424419629nres_a] :
% 3.76/1.78 ( ( P @ Y7 )
% 3.76/1.78 => ( ord_le519537037nres_a @ Y7 @ X3 ) )
% 3.76/1.78 => ( Q @ X3 ) ) )
% 3.76/1.78 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_133_le__rel__bool__arg__iff,axiom,
% 3.76/1.78 ( ord_le1656162903nres_b
% 3.76/1.78 = ( ^ [X6: $o > refine432681134nres_b,Y8: $o > refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 3.76/1.78 & ( ord_le527798542nres_b @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_134_le__rel__bool__arg__iff,axiom,
% 3.76/1.78 ( ord_le516598614nres_a
% 3.76/1.78 = ( ^ [X6: $o > refine424419629nres_a,Y8: $o > refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 3.76/1.78 & ( ord_le519537037nres_a @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_135_ord__eq__le__eq__trans,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
% 3.76/1.78 ( ( A = B )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B @ C )
% 3.76/1.78 => ( ( C = D )
% 3.76/1.78 => ( ord_le527798542nres_b @ A @ D ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_136_ord__eq__le__eq__trans,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
% 3.76/1.78 ( ( A = B )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B @ C )
% 3.76/1.78 => ( ( C = D )
% 3.76/1.78 => ( ord_le519537037nres_a @ A @ D ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_137_nofail__simps_I2_J,axiom,
% 3.76/1.78 ! [X: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_138_nofail__simps_I2_J,axiom,
% 3.76/1.78 ! [X: set_b] : ( refine412683990fail_b @ ( refine1198353289_RES_b @ X ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_139_subset__Collect__conv,axiom,
% 3.76/1.78 ! [S: set_a,P: a > $o] :
% 3.76/1.78 ( ( ord_less_eq_set_a @ S @ ( collect_a @ P ) )
% 3.76/1.78 = ( ! [X5: a] :
% 3.76/1.78 ( ( member_a @ X5 @ S )
% 3.76/1.78 => ( P @ X5 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_140_subset__Collect__conv,axiom,
% 3.76/1.78 ! [S: set_b,P: b > $o] :
% 3.76/1.78 ( ( ord_less_eq_set_b @ S @ ( collect_b @ P ) )
% 3.76/1.78 = ( ! [X5: b] :
% 3.76/1.78 ( ( member_b @ X5 @ S )
% 3.76/1.78 => ( P @ X5 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_141_pwD1,axiom,
% 3.76/1.78 ! [S: refine432681134nres_b,S3: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ S @ S3 )
% 3.76/1.78 => ( ( refine412683990fail_b @ S3 )
% 3.76/1.78 => ( refine412683990fail_b @ S ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_142_pwD1,axiom,
% 3.76/1.78 ! [S: refine424419629nres_a,S3: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ S @ S3 )
% 3.76/1.78 => ( ( refine412683989fail_a @ S3 )
% 3.76/1.78 => ( refine412683989fail_a @ S ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_143_le__nofailI,axiom,
% 3.76/1.78 ! [M3: refine432681134nres_b,M4: refine432681134nres_b] :
% 3.76/1.78 ( ( ( refine412683990fail_b @ M3 )
% 3.76/1.78 => ( ord_le527798542nres_b @ M4 @ M3 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ M4 @ M3 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_144_le__nofailI,axiom,
% 3.76/1.78 ! [M3: refine424419629nres_a,M4: refine424419629nres_a] :
% 3.76/1.78 ( ( ( refine412683989fail_a @ M3 )
% 3.76/1.78 => ( ord_le519537037nres_a @ M4 @ M3 ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ M4 @ M3 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_145_nofail__RES__conv,axiom,
% 3.76/1.78 ( refine412683989fail_a
% 3.76/1.78 = ( ^ [M5: refine424419629nres_a] :
% 3.76/1.78 ? [M6: set_a] :
% 3.76/1.78 ( M5
% 3.76/1.78 = ( refine1198353288_RES_a @ M6 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_146_nofail__RES__conv,axiom,
% 3.76/1.78 ( refine412683990fail_b
% 3.76/1.78 = ( ^ [M5: refine432681134nres_b] :
% 3.76/1.78 ? [M6: set_b] :
% 3.76/1.78 ( M5
% 3.76/1.78 = ( refine1198353289_RES_b @ M6 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_147_ref__two__step,axiom,
% 3.76/1.78 ! [A3: refine432681134nres_b,R: set_Product_prod_b_b,B3: refine432681134nres_b,C2: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A3 @ ( refine122110613un_b_b @ R @ B3 ) )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B3 @ C2 )
% 3.76/1.78 => ( ord_le527798542nres_b @ A3 @ ( refine122110613un_b_b @ R @ C2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_148_ref__two__step,axiom,
% 3.76/1.78 ! [A3: refine432681134nres_b,R: set_Product_prod_b_a,B3: refine424419629nres_a,C2: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A3 @ ( refine122110612un_b_a @ R @ B3 ) )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B3 @ C2 )
% 3.76/1.78 => ( ord_le527798542nres_b @ A3 @ ( refine122110612un_b_a @ R @ C2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_149_ref__two__step,axiom,
% 3.76/1.78 ! [A3: refine424419629nres_a,R: set_Product_prod_a_b,B3: refine432681134nres_b,C2: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A3 @ ( refine1441824854un_a_b @ R @ B3 ) )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ B3 @ C2 )
% 3.76/1.78 => ( ord_le519537037nres_a @ A3 @ ( refine1441824854un_a_b @ R @ C2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_150_ref__two__step,axiom,
% 3.76/1.78 ! [A3: refine424419629nres_a,R: set_Product_prod_a_a,B3: refine424419629nres_a,C2: refine424419629nres_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A3 @ ( refine1441824853un_a_a @ R @ B3 ) )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ B3 @ C2 )
% 3.76/1.78 => ( ord_le519537037nres_a @ A3 @ ( refine1441824853un_a_a @ R @ C2 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_151_le__RES__nofailI,axiom,
% 3.76/1.78 ! [A: refine424419629nres_a,X4: set_a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ X4 ) )
% 3.76/1.78 => ( refine412683989fail_a @ A ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_152_le__RES__nofailI,axiom,
% 3.76/1.78 ! [A: refine432681134nres_b,X4: set_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ X4 ) )
% 3.76/1.78 => ( refine412683990fail_b @ A ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_153_pw__RES__bind__choose_I1_J,axiom,
% 3.76/1.78 ! [X: set_a,F: a > refine432681134nres_b] :
% 3.76/1.78 ( ( refine412683990fail_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X ) @ F ) )
% 3.76/1.78 = ( ! [X5: a] :
% 3.76/1.78 ( ( member_a @ X5 @ X )
% 3.76/1.78 => ( refine412683990fail_b @ ( F @ X5 ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_154_rhs__step__bind__RES,axiom,
% 3.76/1.78 ! [X7: a,X8: set_a,M: refine432681134nres_b,R: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 3.76/1.78 ( ( member_a @ X7 @ X8 )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( F2 @ X7 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X8 ) @ F2 ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_155_rhs__step__bind__RES,axiom,
% 3.76/1.78 ! [X7: a,X8: set_a,M: refine424419629nres_a,R: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 3.76/1.78 ( ( member_a @ X7 @ X8 )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( F2 @ X7 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X8 ) @ F2 ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_156_rhs__step__bind__SPEC,axiom,
% 3.76/1.78 ! [Phi: a > $o,X7: a,M: refine432681134nres_b,R: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 3.76/1.78 ( ( Phi @ X7 )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( F2 @ X7 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ F2 ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_157_rhs__step__bind__SPEC,axiom,
% 3.76/1.78 ! [Phi: a > $o,X7: a,M: refine424419629nres_a,R: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 3.76/1.78 ( ( Phi @ X7 )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( F2 @ X7 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ F2 ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_158_subsetI,axiom,
% 3.76/1.78 ! [A3: set_a,B3: set_a] :
% 3.76/1.78 ( ! [X3: a] :
% 3.76/1.78 ( ( member_a @ X3 @ A3 )
% 3.76/1.78 => ( member_a @ X3 @ B3 ) )
% 3.76/1.78 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_159_subsetI,axiom,
% 3.76/1.78 ! [A3: set_b,B3: set_b] :
% 3.76/1.78 ( ! [X3: b] :
% 3.76/1.78 ( ( member_b @ X3 @ A3 )
% 3.76/1.78 => ( member_b @ X3 @ B3 ) )
% 3.76/1.78 => ( ord_less_eq_set_b @ A3 @ B3 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_160_bind__sim__select__rule,axiom,
% 3.76/1.78 ! [M: refine424419629nres_a,F2: a > refine424419629nres_a,Psi: a > $o,F: a > refine432681134nres_b,Phi: b > $o] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) )
% 3.76/1.78 => ( ! [X3: a] :
% 3.76/1.78 ( ( refine412683989fail_a @ M )
% 3.76/1.78 => ( ( refine1001002027nres_a @ M @ X3 )
% 3.76/1.78 => ( ( ord_le519537037nres_a @ ( F2 @ X3 ) @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_161_bind__sim__select__rule,axiom,
% 3.76/1.78 ! [M: refine424419629nres_a,F2: a > refine432681134nres_b,Psi: b > $o,F: a > refine424419629nres_a,Phi: a > $o] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 3.76/1.78 => ( ! [X3: a] :
% 3.76/1.78 ( ( refine412683989fail_a @ M )
% 3.76/1.78 => ( ( refine1001002027nres_a @ M @ X3 )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ ( F2 @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_162_bind__sim__select__rule,axiom,
% 3.76/1.78 ! [M: refine424419629nres_a,F2: a > refine432681134nres_b,Psi: b > $o,F: a > refine432681134nres_b,Phi: b > $o] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 3.76/1.78 => ( ! [X3: a] :
% 3.76/1.78 ( ( refine412683989fail_a @ M )
% 3.76/1.78 => ( ( refine1001002027nres_a @ M @ X3 )
% 3.76/1.78 => ( ( ord_le527798542nres_b @ ( F2 @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_163_in__mono,axiom,
% 3.76/1.78 ! [A3: set_a,B3: set_a,X4: a] :
% 3.76/1.78 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 3.76/1.78 => ( ( member_a @ X4 @ A3 )
% 3.76/1.78 => ( member_a @ X4 @ B3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_164_in__mono,axiom,
% 3.76/1.78 ! [A3: set_b,B3: set_b,X4: b] :
% 3.76/1.78 ( ( ord_less_eq_set_b @ A3 @ B3 )
% 3.76/1.78 => ( ( member_b @ X4 @ A3 )
% 3.76/1.78 => ( member_b @ X4 @ B3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_165_subsetD,axiom,
% 3.76/1.78 ! [A3: set_a,B3: set_a,C: a] :
% 3.76/1.78 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 3.76/1.78 => ( ( member_a @ C @ A3 )
% 3.76/1.78 => ( member_a @ C @ B3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_166_subsetD,axiom,
% 3.76/1.78 ! [A3: set_b,B3: set_b,C: b] :
% 3.76/1.78 ( ( ord_less_eq_set_b @ A3 @ B3 )
% 3.76/1.78 => ( ( member_b @ C @ A3 )
% 3.76/1.78 => ( member_b @ C @ B3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_167_inres__simps_I2_J,axiom,
% 3.76/1.78 ! [X: set_a] :
% 3.76/1.78 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X ) )
% 3.76/1.78 = ( ^ [X5: a] : ( member_a @ X5 @ X ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_168_inres__simps_I2_J,axiom,
% 3.76/1.78 ! [X: set_b] :
% 3.76/1.78 ( ( refine1001002028nres_b @ ( refine1198353289_RES_b @ X ) )
% 3.76/1.78 = ( ^ [X5: b] : ( member_b @ X5 @ X ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_169_pwD2,axiom,
% 3.76/1.78 ! [S: refine432681134nres_b,S3: refine432681134nres_b,X4: b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ S @ S3 )
% 3.76/1.78 => ( ( refine1001002028nres_b @ S @ X4 )
% 3.76/1.78 => ( refine1001002028nres_b @ S3 @ X4 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_170_pwD2,axiom,
% 3.76/1.78 ! [S: refine424419629nres_a,S3: refine424419629nres_a,X4: a] :
% 3.76/1.78 ( ( ord_le519537037nres_a @ S @ S3 )
% 3.76/1.78 => ( ( refine1001002027nres_a @ S @ X4 )
% 3.76/1.78 => ( refine1001002027nres_a @ S3 @ X4 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_171_pw__RES__bind__choose_I2_J,axiom,
% 3.76/1.78 ! [X: set_a,F: a > refine432681134nres_b,Y3: b] :
% 3.76/1.78 ( ( refine1001002028nres_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X ) @ F ) @ Y3 )
% 3.76/1.78 = ( ? [X5: a] :
% 3.76/1.78 ( ( member_a @ X5 @ X )
% 3.76/1.78 & ( refine1001002028nres_b @ ( F @ X5 ) @ Y3 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_172_pw__leI,axiom,
% 3.76/1.78 ! [S3: refine432681134nres_b,S: refine432681134nres_b] :
% 3.76/1.78 ( ( ( refine412683990fail_b @ S3 )
% 3.76/1.78 => ( ( refine412683990fail_b @ S )
% 3.76/1.78 & ! [X3: b] :
% 3.76/1.78 ( ( refine1001002028nres_b @ S @ X3 )
% 3.76/1.78 => ( refine1001002028nres_b @ S3 @ X3 ) ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ S @ S3 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_173_pw__leI,axiom,
% 3.76/1.78 ! [S3: refine424419629nres_a,S: refine424419629nres_a] :
% 3.76/1.78 ( ( ( refine412683989fail_a @ S3 )
% 3.76/1.78 => ( ( refine412683989fail_a @ S )
% 3.76/1.78 & ! [X3: a] :
% 3.76/1.78 ( ( refine1001002027nres_a @ S @ X3 )
% 3.76/1.78 => ( refine1001002027nres_a @ S3 @ X3 ) ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ S @ S3 ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_174_pw__leI_H,axiom,
% 3.76/1.78 ! [S3: refine432681134nres_b,S: refine432681134nres_b] :
% 3.76/1.78 ( ( ( refine412683990fail_b @ S3 )
% 3.76/1.78 => ( refine412683990fail_b @ S ) )
% 3.76/1.78 => ( ! [X3: b] :
% 3.76/1.78 ( ( refine412683990fail_b @ S3 )
% 3.76/1.78 => ( ( refine1001002028nres_b @ S @ X3 )
% 3.76/1.78 => ( refine1001002028nres_b @ S3 @ X3 ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ S @ S3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_175_pw__leI_H,axiom,
% 3.76/1.78 ! [S3: refine424419629nres_a,S: refine424419629nres_a] :
% 3.76/1.78 ( ( ( refine412683989fail_a @ S3 )
% 3.76/1.78 => ( refine412683989fail_a @ S ) )
% 3.76/1.78 => ( ! [X3: a] :
% 3.76/1.78 ( ( refine412683989fail_a @ S3 )
% 3.76/1.78 => ( ( refine1001002027nres_a @ S @ X3 )
% 3.76/1.78 => ( refine1001002027nres_a @ S3 @ X3 ) ) )
% 3.76/1.78 => ( ord_le519537037nres_a @ S @ S3 ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_176_pw__le__iff,axiom,
% 3.76/1.78 ( ord_le527798542nres_b
% 3.76/1.78 = ( ^ [S4: refine432681134nres_b,S5: refine432681134nres_b] :
% 3.76/1.78 ( ( refine412683990fail_b @ S5 )
% 3.76/1.78 => ( ( refine412683990fail_b @ S4 )
% 3.76/1.78 & ! [X5: b] :
% 3.76/1.78 ( ( refine1001002028nres_b @ S4 @ X5 )
% 3.76/1.78 => ( refine1001002028nres_b @ S5 @ X5 ) ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_177_pw__le__iff,axiom,
% 3.76/1.78 ( ord_le519537037nres_a
% 3.76/1.78 = ( ^ [S4: refine424419629nres_a,S5: refine424419629nres_a] :
% 3.76/1.78 ( ( refine412683989fail_a @ S5 )
% 3.76/1.78 => ( ( refine412683989fail_a @ S4 )
% 3.76/1.78 & ! [X5: a] :
% 3.76/1.78 ( ( refine1001002027nres_a @ S4 @ X5 )
% 3.76/1.78 => ( refine1001002027nres_a @ S5 @ X5 ) ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_178_pw__bind__nofail,axiom,
% 3.76/1.78 ! [M4: refine424419629nres_a,F: a > refine432681134nres_b] :
% 3.76/1.78 ( ( refine412683990fail_b @ ( refine436832839nd_a_b @ M4 @ F ) )
% 3.76/1.78 = ( ( refine412683989fail_a @ M4 )
% 3.76/1.78 & ! [X5: a] :
% 3.76/1.78 ( ( refine1001002027nres_a @ M4 @ X5 )
% 3.76/1.78 => ( refine412683990fail_b @ ( F @ X5 ) ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_179_pw__bind__le__iff,axiom,
% 3.76/1.78 ! [M4: refine424419629nres_a,F: a > refine432681134nres_b,S: refine432681134nres_b] :
% 3.76/1.78 ( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ S )
% 3.76/1.78 = ( ( ( refine412683990fail_b @ S )
% 3.76/1.78 => ( refine412683989fail_a @ M4 ) )
% 3.76/1.78 & ! [X5: a] :
% 3.76/1.78 ( ( ( refine412683989fail_a @ M4 )
% 3.76/1.78 & ( refine1001002027nres_a @ M4 @ X5 ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X5 ) @ S ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_180_pw__bind__leI,axiom,
% 3.76/1.78 ! [S: refine432681134nres_b,M4: refine424419629nres_a,F: a > refine432681134nres_b] :
% 3.76/1.78 ( ( ( refine412683990fail_b @ S )
% 3.76/1.78 => ( refine412683989fail_a @ M4 ) )
% 3.76/1.78 => ( ! [X3: a] :
% 3.76/1.78 ( ( refine412683989fail_a @ M4 )
% 3.76/1.78 => ( ( refine1001002027nres_a @ M4 @ X3 )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( F @ X3 ) @ S ) ) )
% 3.76/1.78 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ S ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_181_Collect__mono__iff,axiom,
% 3.76/1.78 ! [P: a > $o,Q: a > $o] :
% 3.76/1.78 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 3.76/1.78 = ( ! [X5: a] :
% 3.76/1.78 ( ( P @ X5 )
% 3.76/1.78 => ( Q @ X5 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_182_Collect__mono__iff,axiom,
% 3.76/1.78 ! [P: b > $o,Q: b > $o] :
% 3.76/1.78 ( ( ord_less_eq_set_b @ ( collect_b @ P ) @ ( collect_b @ Q ) )
% 3.76/1.78 = ( ! [X5: b] :
% 3.76/1.78 ( ( P @ X5 )
% 3.76/1.78 => ( Q @ X5 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_183_Collect__mono,axiom,
% 3.76/1.78 ! [P: a > $o,Q: a > $o] :
% 3.76/1.78 ( ! [X3: a] :
% 3.76/1.78 ( ( P @ X3 )
% 3.76/1.78 => ( Q @ X3 ) )
% 3.76/1.78 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_184_Collect__mono,axiom,
% 3.76/1.78 ! [P: b > $o,Q: b > $o] :
% 3.76/1.78 ( ! [X3: b] :
% 3.76/1.78 ( ( P @ X3 )
% 3.76/1.78 => ( Q @ X3 ) )
% 3.76/1.78 => ( ord_less_eq_set_b @ ( collect_b @ P ) @ ( collect_b @ Q ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_185_subset__iff,axiom,
% 3.76/1.78 ( ord_less_eq_set_a
% 3.76/1.78 = ( ^ [A4: set_a,B4: set_a] :
% 3.76/1.78 ! [T3: a] :
% 3.76/1.78 ( ( member_a @ T3 @ A4 )
% 3.76/1.78 => ( member_a @ T3 @ B4 ) ) ) ) ).
% 3.76/1.78
% 3.76/1.78 thf(fact_186_subset__iff,axiom,
% 3.76/1.79 ( ord_less_eq_set_b
% 3.76/1.79 = ( ^ [A4: set_b,B4: set_b] :
% 3.76/1.79 ! [T3: b] :
% 3.76/1.79 ( ( member_b @ T3 @ A4 )
% 3.76/1.79 => ( member_b @ T3 @ B4 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_187_subset__eq,axiom,
% 3.76/1.79 ( ord_less_eq_set_a
% 3.76/1.79 = ( ^ [A4: set_a,B4: set_a] :
% 3.76/1.79 ! [X5: a] :
% 3.76/1.79 ( ( member_a @ X5 @ A4 )
% 3.76/1.79 => ( member_a @ X5 @ B4 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_188_subset__eq,axiom,
% 3.76/1.79 ( ord_less_eq_set_b
% 3.76/1.79 = ( ^ [A4: set_b,B4: set_b] :
% 3.76/1.79 ! [X5: b] :
% 3.76/1.79 ( ( member_b @ X5 @ A4 )
% 3.76/1.79 => ( member_b @ X5 @ B4 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_189_rhs__step__bind,axiom,
% 3.76/1.79 ! [M: refine432681134nres_b,R: set_Product_prod_b_a,M7: refine424419629nres_a,X4: b,Lhs: refine432681134nres_b,S: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ M @ ( refine122110612un_b_a @ R @ M7 ) )
% 3.76/1.79 => ( ( refine1001002028nres_b @ M @ X4 )
% 3.76/1.79 => ( ! [X9: a] :
% 3.76/1.79 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X9 ) @ R )
% 3.76/1.79 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( F2 @ X9 ) ) ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_190_rhs__step__bind,axiom,
% 3.76/1.79 ! [M: refine432681134nres_b,R: set_Product_prod_b_a,M7: refine424419629nres_a,X4: b,Lhs: refine424419629nres_a,S: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ M @ ( refine122110612un_b_a @ R @ M7 ) )
% 3.76/1.79 => ( ( refine1001002028nres_b @ M @ X4 )
% 3.76/1.79 => ( ! [X9: a] :
% 3.76/1.79 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X9 ) @ R )
% 3.76/1.79 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( F2 @ X9 ) ) ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_191_rhs__step__bind,axiom,
% 3.76/1.79 ! [M: refine424419629nres_a,R: set_Product_prod_a_a,M7: refine424419629nres_a,X4: a,Lhs: refine432681134nres_b,S: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ M @ ( refine1441824853un_a_a @ R @ M7 ) )
% 3.76/1.79 => ( ( refine1001002027nres_a @ M @ X4 )
% 3.76/1.79 => ( ! [X9: a] :
% 3.76/1.79 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X9 ) @ R )
% 3.76/1.79 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( F2 @ X9 ) ) ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_192_rhs__step__bind,axiom,
% 3.76/1.79 ! [M: refine424419629nres_a,R: set_Product_prod_a_a,M7: refine424419629nres_a,X4: a,Lhs: refine424419629nres_a,S: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ M @ ( refine1441824853un_a_a @ R @ M7 ) )
% 3.76/1.79 => ( ( refine1001002027nres_a @ M @ X4 )
% 3.76/1.79 => ( ! [X9: a] :
% 3.76/1.79 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X9 ) @ R )
% 3.76/1.79 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( F2 @ X9 ) ) ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_193_RES__refine,axiom,
% 3.76/1.79 ! [S: set_a,S3: set_a,R: set_Product_prod_a_a] :
% 3.76/1.79 ( ! [S6: a] :
% 3.76/1.79 ( ( member_a @ S6 @ S )
% 3.76/1.79 => ? [X10: a] :
% 3.76/1.79 ( ( member_a @ X10 @ S3 )
% 3.76/1.79 & ( member449909584od_a_a @ ( product_Pair_a_a @ S6 @ X10 ) @ R ) ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ S3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_194_RES__refine,axiom,
% 3.76/1.79 ! [S: set_a,S3: set_b,R: set_Product_prod_a_b] :
% 3.76/1.79 ( ! [S6: a] :
% 3.76/1.79 ( ( member_a @ S6 @ S )
% 3.76/1.79 => ? [X10: b] :
% 3.76/1.79 ( ( member_b @ X10 @ S3 )
% 3.76/1.79 & ( member458171089od_a_b @ ( product_Pair_a_b @ S6 @ X10 ) @ R ) ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ S3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_195_RES__refine,axiom,
% 3.76/1.79 ! [S: set_b,S3: set_a,R: set_Product_prod_b_a] :
% 3.76/1.79 ( ! [S6: b] :
% 3.76/1.79 ( ( member_b @ S6 @ S )
% 3.76/1.79 => ? [X10: a] :
% 3.76/1.79 ( ( member_a @ X10 @ S3 )
% 3.76/1.79 & ( member1277678991od_b_a @ ( product_Pair_b_a @ S6 @ X10 ) @ R ) ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine122110612un_b_a @ R @ ( refine1198353288_RES_a @ S3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_196_RES__refine,axiom,
% 3.76/1.79 ! [S: set_b,S3: set_b,R: set_Product_prod_b_b] :
% 3.76/1.79 ( ! [S6: b] :
% 3.76/1.79 ( ( member_b @ S6 @ S )
% 3.76/1.79 => ? [X10: b] :
% 3.76/1.79 ( ( member_b @ X10 @ S3 )
% 3.76/1.79 & ( member1285940496od_b_b @ ( product_Pair_b_b @ S6 @ X10 ) @ R ) ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ S3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_197_less__eq__nres_Oelims_I1_J,axiom,
% 3.76/1.79 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 3.76/1.79 ( ( ( ord_le519537037nres_a @ X4 @ Xa )
% 3.76/1.79 = Y3 )
% 3.76/1.79 => ( ( ( Xa = refine464223677AILi_a )
% 3.76/1.79 => ~ Y3 )
% 3.76/1.79 => ( ! [A5: set_a] :
% 3.76/1.79 ( ( X4
% 3.76/1.79 = ( refine1198353288_RES_a @ A5 ) )
% 3.76/1.79 => ! [B5: set_a] :
% 3.76/1.79 ( ( Xa
% 3.76/1.79 = ( refine1198353288_RES_a @ B5 ) )
% 3.76/1.79 => ( Y3
% 3.76/1.79 = ( ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) )
% 3.76/1.79 => ~ ( ( X4 = refine464223677AILi_a )
% 3.76/1.79 => ( ? [Uv: set_a] :
% 3.76/1.79 ( Xa
% 3.76/1.79 = ( refine1198353288_RES_a @ Uv ) )
% 3.76/1.79 => Y3 ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_198_less__eq__nres_Oelims_I1_J,axiom,
% 3.76/1.79 ! [X4: refine432681134nres_b,Xa: refine432681134nres_b,Y3: $o] :
% 3.76/1.79 ( ( ( ord_le527798542nres_b @ X4 @ Xa )
% 3.76/1.79 = Y3 )
% 3.76/1.79 => ( ( ( Xa = refine464223678AILi_b )
% 3.76/1.79 => ~ Y3 )
% 3.76/1.79 => ( ! [A5: set_b] :
% 3.76/1.79 ( ( X4
% 3.76/1.79 = ( refine1198353289_RES_b @ A5 ) )
% 3.76/1.79 => ! [B5: set_b] :
% 3.76/1.79 ( ( Xa
% 3.76/1.79 = ( refine1198353289_RES_b @ B5 ) )
% 3.76/1.79 => ( Y3
% 3.76/1.79 = ( ~ ( ord_less_eq_set_b @ A5 @ B5 ) ) ) ) )
% 3.76/1.79 => ~ ( ( X4 = refine464223678AILi_b )
% 3.76/1.79 => ( ? [Uv: set_b] :
% 3.76/1.79 ( Xa
% 3.76/1.79 = ( refine1198353289_RES_b @ Uv ) )
% 3.76/1.79 => Y3 ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_199_less__eq__nres_Oelims_I2_J,axiom,
% 3.76/1.79 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ X4 @ Xa )
% 3.76/1.79 => ( ( Xa != refine464223677AILi_a )
% 3.76/1.79 => ~ ! [A5: set_a] :
% 3.76/1.79 ( ( X4
% 3.76/1.79 = ( refine1198353288_RES_a @ A5 ) )
% 3.76/1.79 => ! [B5: set_a] :
% 3.76/1.79 ( ( Xa
% 3.76/1.79 = ( refine1198353288_RES_a @ B5 ) )
% 3.76/1.79 => ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_200_less__eq__nres_Oelims_I2_J,axiom,
% 3.76/1.79 ! [X4: refine432681134nres_b,Xa: refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ X4 @ Xa )
% 3.76/1.79 => ( ( Xa != refine464223678AILi_b )
% 3.76/1.79 => ~ ! [A5: set_b] :
% 3.76/1.79 ( ( X4
% 3.76/1.79 = ( refine1198353289_RES_b @ A5 ) )
% 3.76/1.79 => ! [B5: set_b] :
% 3.76/1.79 ( ( Xa
% 3.76/1.79 = ( refine1198353289_RES_b @ B5 ) )
% 3.76/1.79 => ~ ( ord_less_eq_set_b @ A5 @ B5 ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_201_less__eq__nres_Ocases,axiom,
% 3.76/1.79 ! [X4: produc1609974940nres_a] :
% 3.76/1.79 ( ! [Uu: refine424419629nres_a] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 3.76/1.79 => ( ! [A5: set_a,B5: set_a] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) ) )
% 3.76/1.79 => ~ ! [Uv: set_a] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_202_less__eq__nres_Ocases,axiom,
% 3.76/1.79 ! [X4: produc1587512412nres_b] :
% 3.76/1.79 ( ! [Uu: refine432681134nres_b] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc2130641934nres_b @ Uu @ refine464223678AILi_b ) )
% 3.76/1.79 => ( ! [A5: set_b,B5: set_b] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) ) )
% 3.76/1.79 => ~ ! [Uv: set_b] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ Uv ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_203_less__nres_Ocases,axiom,
% 3.76/1.79 ! [X4: produc1609974940nres_a] :
% 3.76/1.79 ( ! [Uu: refine424419629nres_a] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc1136923598nres_a @ refine464223677AILi_a @ Uu ) )
% 3.76/1.79 => ( ! [Uv: set_a] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a ) )
% 3.76/1.79 => ~ ! [A5: set_a,B5: set_a] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_204_less__nres_Ocases,axiom,
% 3.76/1.79 ! [X4: produc1587512412nres_b] :
% 3.76/1.79 ( ! [Uu: refine432681134nres_b] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc2130641934nres_b @ refine464223678AILi_b @ Uu ) )
% 3.76/1.79 => ( ! [Uv: set_b] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ Uv ) @ refine464223678AILi_b ) )
% 3.76/1.79 => ~ ! [A5: set_b,B5: set_b] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_205_sup__nres_Ocases,axiom,
% 3.76/1.79 ! [X4: produc1609974940nres_a] :
% 3.76/1.79 ( ! [Uu: refine424419629nres_a] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 3.76/1.79 => ( ! [V: set_a] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) ) )
% 3.76/1.79 => ~ ! [A5: set_a,B5: set_a] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_206_sup__nres_Ocases,axiom,
% 3.76/1.79 ! [X4: produc1587512412nres_b] :
% 3.76/1.79 ( ! [Uu: refine432681134nres_b] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc2130641934nres_b @ Uu @ refine464223678AILi_b ) )
% 3.76/1.79 => ( ! [V: set_b] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ V ) ) )
% 3.76/1.79 => ~ ! [A5: set_b,B5: set_b] :
% 3.76/1.79 ( X4
% 3.76/1.79 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_207_less__eq__nres_Osimps_I1_J,axiom,
% 3.76/1.79 ! [Uu2: refine432681134nres_b] : ( ord_le527798542nres_b @ Uu2 @ refine464223678AILi_b ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_208_less__eq__nres_Osimps_I1_J,axiom,
% 3.76/1.79 ! [Uu2: refine424419629nres_a] : ( ord_le519537037nres_a @ Uu2 @ refine464223677AILi_a ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_209_nres_Odistinct_I1_J,axiom,
% 3.76/1.79 ! [X2: set_a] :
% 3.76/1.79 ( refine464223677AILi_a
% 3.76/1.79 != ( refine1198353288_RES_a @ X2 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_210_nres_Odistinct_I1_J,axiom,
% 3.76/1.79 ! [X2: set_b] :
% 3.76/1.79 ( refine464223678AILi_b
% 3.76/1.79 != ( refine1198353289_RES_b @ X2 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_211_nres_Oinduct,axiom,
% 3.76/1.79 ! [P: refine424419629nres_a > $o,Nres: refine424419629nres_a] :
% 3.76/1.79 ( ( P @ refine464223677AILi_a )
% 3.76/1.79 => ( ! [X3: set_a] : ( P @ ( refine1198353288_RES_a @ X3 ) )
% 3.76/1.79 => ( P @ Nres ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_212_nres_Oinduct,axiom,
% 3.76/1.79 ! [P: refine432681134nres_b > $o,Nres: refine432681134nres_b] :
% 3.76/1.79 ( ( P @ refine464223678AILi_b )
% 3.76/1.79 => ( ! [X3: set_b] : ( P @ ( refine1198353289_RES_b @ X3 ) )
% 3.76/1.79 => ( P @ Nres ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_213_nres_Oexhaust,axiom,
% 3.76/1.79 ! [Y3: refine424419629nres_a] :
% 3.76/1.79 ( ( Y3 != refine464223677AILi_a )
% 3.76/1.79 => ~ ! [X22: set_a] :
% 3.76/1.79 ( Y3
% 3.76/1.79 != ( refine1198353288_RES_a @ X22 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_214_nres_Oexhaust,axiom,
% 3.76/1.79 ! [Y3: refine432681134nres_b] :
% 3.76/1.79 ( ( Y3 != refine464223678AILi_b )
% 3.76/1.79 => ~ ! [X22: set_b] :
% 3.76/1.79 ( Y3
% 3.76/1.79 != ( refine1198353289_RES_b @ X22 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_215_sup__nres_Oinduct,axiom,
% 3.76/1.79 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 3.76/1.79 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 3.76/1.79 => ( ! [V: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) )
% 3.76/1.79 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 3.76/1.79 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_216_sup__nres_Oinduct,axiom,
% 3.76/1.79 ! [P: refine432681134nres_b > refine432681134nres_b > $o,A0: refine432681134nres_b,A1: refine432681134nres_b] :
% 3.76/1.79 ( ! [Uu: refine432681134nres_b] : ( P @ Uu @ refine464223678AILi_b )
% 3.76/1.79 => ( ! [V: set_b] : ( P @ refine464223678AILi_b @ ( refine1198353289_RES_b @ V ) )
% 3.76/1.79 => ( ! [A5: set_b,B5: set_b] : ( P @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) )
% 3.76/1.79 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_217_less__nres_Oinduct,axiom,
% 3.76/1.79 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 3.76/1.79 ( ! [X_1: refine424419629nres_a] : ( P @ refine464223677AILi_a @ X_1 )
% 3.76/1.79 => ( ! [Uv: set_a] : ( P @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a )
% 3.76/1.79 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 3.76/1.79 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_218_less__nres_Oinduct,axiom,
% 3.76/1.79 ! [P: refine432681134nres_b > refine432681134nres_b > $o,A0: refine432681134nres_b,A1: refine432681134nres_b] :
% 3.76/1.79 ( ! [X_1: refine432681134nres_b] : ( P @ refine464223678AILi_b @ X_1 )
% 3.76/1.79 => ( ! [Uv: set_b] : ( P @ ( refine1198353289_RES_b @ Uv ) @ refine464223678AILi_b )
% 3.76/1.79 => ( ! [A5: set_b,B5: set_b] : ( P @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) )
% 3.76/1.79 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_219_less__eq__nres_Oinduct,axiom,
% 3.76/1.79 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 3.76/1.79 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 3.76/1.79 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 3.76/1.79 => ( ! [Uv: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) )
% 3.76/1.79 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_220_less__eq__nres_Oinduct,axiom,
% 3.76/1.79 ! [P: refine432681134nres_b > refine432681134nres_b > $o,A0: refine432681134nres_b,A1: refine432681134nres_b] :
% 3.76/1.79 ( ! [Uu: refine432681134nres_b] : ( P @ Uu @ refine464223678AILi_b )
% 3.76/1.79 => ( ! [A5: set_b,B5: set_b] : ( P @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) )
% 3.76/1.79 => ( ! [Uv: set_b] : ( P @ refine464223678AILi_b @ ( refine1198353289_RES_b @ Uv ) )
% 3.76/1.79 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_221_less__eq__nres_Osimps_I3_J,axiom,
% 3.76/1.79 ! [Uv2: set_a] :
% 3.76/1.79 ~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv2 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_222_less__eq__nres_Osimps_I3_J,axiom,
% 3.76/1.79 ! [Uv2: set_b] :
% 3.76/1.79 ~ ( ord_le527798542nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ Uv2 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_223_less__eq__nres_Oelims_I3_J,axiom,
% 3.76/1.79 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.76/1.79 ( ~ ( ord_le519537037nres_a @ X4 @ Xa )
% 3.76/1.79 => ( ! [A5: set_a] :
% 3.76/1.79 ( ( X4
% 3.76/1.79 = ( refine1198353288_RES_a @ A5 ) )
% 3.76/1.79 => ! [B5: set_a] :
% 3.76/1.79 ( ( Xa
% 3.76/1.79 = ( refine1198353288_RES_a @ B5 ) )
% 3.76/1.79 => ( ord_less_eq_set_a @ A5 @ B5 ) ) )
% 3.76/1.79 => ~ ( ( X4 = refine464223677AILi_a )
% 3.76/1.79 => ! [Uv: set_a] :
% 3.76/1.79 ( Xa
% 3.76/1.79 != ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_224_less__eq__nres_Oelims_I3_J,axiom,
% 3.76/1.79 ! [X4: refine432681134nres_b,Xa: refine432681134nres_b] :
% 3.76/1.79 ( ~ ( ord_le527798542nres_b @ X4 @ Xa )
% 3.76/1.79 => ( ! [A5: set_b] :
% 3.76/1.79 ( ( X4
% 3.76/1.79 = ( refine1198353289_RES_b @ A5 ) )
% 3.76/1.79 => ! [B5: set_b] :
% 3.76/1.79 ( ( Xa
% 3.76/1.79 = ( refine1198353289_RES_b @ B5 ) )
% 3.76/1.79 => ( ord_less_eq_set_b @ A5 @ B5 ) ) )
% 3.76/1.79 => ~ ( ( X4 = refine464223678AILi_b )
% 3.76/1.79 => ! [Uv: set_b] :
% 3.76/1.79 ( Xa
% 3.76/1.79 != ( refine1198353289_RES_b @ Uv ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_225_return__refine__prop__return,axiom,
% 3.76/1.79 ! [M: refine432681134nres_b,X4: b,R: set_Product_prod_b_b] :
% 3.76/1.79 ( ( refine412683990fail_b @ M )
% 3.76/1.79 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110613un_b_b @ R @ M ) )
% 3.76/1.79 => ~ ! [X9: b] :
% 3.76/1.79 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ X9 ) @ R )
% 3.76/1.79 => ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X9 ) @ M ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_226_return__refine__prop__return,axiom,
% 3.76/1.79 ! [M: refine424419629nres_a,X4: b,R: set_Product_prod_b_a] :
% 3.76/1.79 ( ( refine412683989fail_a @ M )
% 3.76/1.79 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110612un_b_a @ R @ M ) )
% 3.76/1.79 => ~ ! [X9: a] :
% 3.76/1.79 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X9 ) @ R )
% 3.76/1.79 => ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X9 ) @ M ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_227_return__refine__prop__return,axiom,
% 3.76/1.79 ! [M: refine432681134nres_b,X4: a,R: set_Product_prod_a_b] :
% 3.76/1.79 ( ( refine412683990fail_b @ M )
% 3.76/1.79 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824854un_a_b @ R @ M ) )
% 3.76/1.79 => ~ ! [X9: b] :
% 3.76/1.79 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X4 @ X9 ) @ R )
% 3.76/1.79 => ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X9 ) @ M ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_228_return__refine__prop__return,axiom,
% 3.76/1.79 ! [M: refine424419629nres_a,X4: a,R: set_Product_prod_a_a] :
% 3.76/1.79 ( ( refine412683989fail_a @ M )
% 3.76/1.79 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824853un_a_a @ R @ M ) )
% 3.76/1.79 => ~ ! [X9: a] :
% 3.76/1.79 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X9 ) @ R )
% 3.76/1.79 => ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X9 ) @ M ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_229_ret__le__down__conv,axiom,
% 3.76/1.79 ! [M: refine432681134nres_b,C: b,R: set_Product_prod_b_b] :
% 3.76/1.79 ( ( refine412683990fail_b @ M )
% 3.76/1.79 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110613un_b_b @ R @ M ) )
% 3.76/1.79 = ( ? [A2: b] :
% 3.76/1.79 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A2 ) @ R )
% 3.76/1.79 & ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A2 ) @ M ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_230_ret__le__down__conv,axiom,
% 3.76/1.79 ! [M: refine424419629nres_a,C: b,R: set_Product_prod_b_a] :
% 3.76/1.79 ( ( refine412683989fail_a @ M )
% 3.76/1.79 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110612un_b_a @ R @ M ) )
% 3.76/1.79 = ( ? [A2: a] :
% 3.76/1.79 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ C @ A2 ) @ R )
% 3.76/1.79 & ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A2 ) @ M ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_231_ret__le__down__conv,axiom,
% 3.76/1.79 ! [M: refine432681134nres_b,C: a,R: set_Product_prod_a_b] :
% 3.76/1.79 ( ( refine412683990fail_b @ M )
% 3.76/1.79 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824854un_a_b @ R @ M ) )
% 3.76/1.79 = ( ? [A2: b] :
% 3.76/1.79 ( ( member458171089od_a_b @ ( product_Pair_a_b @ C @ A2 ) @ R )
% 3.76/1.79 & ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A2 ) @ M ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_232_ret__le__down__conv,axiom,
% 3.76/1.79 ! [M: refine424419629nres_a,C: a,R: set_Product_prod_a_a] :
% 3.76/1.79 ( ( refine412683989fail_a @ M )
% 3.76/1.79 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824853un_a_a @ R @ M ) )
% 3.76/1.79 = ( ? [A2: a] :
% 3.76/1.79 ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A2 ) @ R )
% 3.76/1.79 & ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A2 ) @ M ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_233_nres__order__simps_I20_J,axiom,
% 3.76/1.79 ! [X4: b,Y3: b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine2063221605TURN_b @ Y3 ) )
% 3.76/1.79 = ( X4 = Y3 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_234_nres__order__simps_I20_J,axiom,
% 3.76/1.79 ! [X4: a,Y3: a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine2063221604TURN_a @ Y3 ) )
% 3.76/1.79 = ( X4 = Y3 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_235_nres__monad1,axiom,
% 3.76/1.79 ! [X4: a,F: a > refine432681134nres_b] :
% 3.76/1.79 ( ( refine436832839nd_a_b @ ( refine2063221604TURN_a @ X4 ) @ F )
% 3.76/1.79 = ( F @ X4 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_236_nres__order__simps_I21_J,axiom,
% 3.76/1.79 ! [X4: a,Y: set_a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ Y ) )
% 3.76/1.79 = ( member_a @ X4 @ Y ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_237_nres__order__simps_I21_J,axiom,
% 3.76/1.79 ! [X4: b,Y: set_b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine1198353289_RES_b @ Y ) )
% 3.76/1.79 = ( member_b @ X4 @ Y ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_238_SPEC__eq__is__RETURN_I1_J,axiom,
% 3.76/1.79 ! [X4: a] :
% 3.76/1.79 ( ( refine1198353288_RES_a
% 3.76/1.79 @ ( collect_a
% 3.76/1.79 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 3.76/1.79 @ X4 ) ) )
% 3.76/1.79 = ( refine2063221604TURN_a @ X4 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_239_SPEC__eq__is__RETURN_I1_J,axiom,
% 3.76/1.79 ! [X4: b] :
% 3.76/1.79 ( ( refine1198353289_RES_b
% 3.76/1.79 @ ( collect_b
% 3.76/1.79 @ ( ^ [Y5: b,Z: b] : ( Y5 = Z )
% 3.76/1.79 @ X4 ) ) )
% 3.76/1.79 = ( refine2063221605TURN_b @ X4 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_240_RETURN__rule,axiom,
% 3.76/1.79 ! [Phi: a > $o,X4: a] :
% 3.76/1.79 ( ( Phi @ X4 )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_241_RETURN__rule,axiom,
% 3.76/1.79 ! [Phi: b > $o,X4: b] :
% 3.76/1.79 ( ( Phi @ X4 )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_242_lhs__step__RES,axiom,
% 3.76/1.79 ! [X: set_a,M: refine424419629nres_a] :
% 3.76/1.79 ( ! [X3: a] :
% 3.76/1.79 ( ( member_a @ X3 @ X )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ M ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_243_lhs__step__RES,axiom,
% 3.76/1.79 ! [X: set_b,M: refine432681134nres_b] :
% 3.76/1.79 ( ! [X3: b] :
% 3.76/1.79 ( ( member_b @ X3 @ X )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ M ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ X ) @ M ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_244_RETURN__to__SPEC__rule,axiom,
% 3.76/1.79 ! [M: refine424419629nres_a,V2: a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ M
% 3.76/1.79 @ ( refine1198353288_RES_a
% 3.76/1.79 @ ( collect_a
% 3.76/1.79 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 3.76/1.79 @ V2 ) ) ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ M @ ( refine2063221604TURN_a @ V2 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_245_RETURN__to__SPEC__rule,axiom,
% 3.76/1.79 ! [M: refine432681134nres_b,V2: b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ M
% 3.76/1.79 @ ( refine1198353289_RES_b
% 3.76/1.79 @ ( collect_b
% 3.76/1.79 @ ( ^ [Y5: b,Z: b] : ( Y5 = Z )
% 3.76/1.79 @ V2 ) ) ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ M @ ( refine2063221605TURN_b @ V2 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_246_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 3.76/1.79 ! [M4: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine432681134nres_b,F2: b > refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ M4 @ M3 )
% 3.76/1.79 => ( ! [X3: b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ M4 )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine1264602246nd_b_b @ M4 @ F ) @ ( refine1264602246nd_b_b @ M3 @ F2 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_247_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 3.76/1.79 ! [M4: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine424419629nres_a,F2: b > refine424419629nres_a] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ M4 @ M3 )
% 3.76/1.79 => ( ! [X3: b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ M4 )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine1264602245nd_b_a @ M4 @ F ) @ ( refine1264602245nd_b_a @ M3 @ F2 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_248_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 3.76/1.79 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine424419629nres_a,F2: a > refine424419629nres_a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ M4 @ M3 )
% 3.76/1.79 => ( ! [X3: a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine436832838nd_a_a @ M3 @ F2 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_249_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 3.76/1.79 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine432681134nres_b,F2: a > refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ M4 @ M3 )
% 3.76/1.79 => ( ! [X3: a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ ( refine436832839nd_a_b @ M3 @ F2 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_250_bind__cong,axiom,
% 3.76/1.79 ! [M: refine424419629nres_a,M7: refine424419629nres_a,F: a > refine432681134nres_b,F2: a > refine432681134nres_b] :
% 3.76/1.79 ( ( M = M7 )
% 3.76/1.79 => ( ! [X3: a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M7 )
% 3.76/1.79 => ( ( F @ X3 )
% 3.76/1.79 = ( F2 @ X3 ) ) )
% 3.76/1.79 => ( ( refine436832839nd_a_b @ M @ F )
% 3.76/1.79 = ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_251_inres__def,axiom,
% 3.76/1.79 ( refine1001002028nres_b
% 3.76/1.79 = ( ^ [S4: refine432681134nres_b,X5: b] : ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X5 ) @ S4 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_252_inres__def,axiom,
% 3.76/1.79 ( refine1001002027nres_a
% 3.76/1.79 = ( ^ [S4: refine424419629nres_a,X5: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X5 ) @ S4 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_253_RETURN__ref__SPECD,axiom,
% 3.76/1.79 ! [C: b,R: set_Product_prod_b_a,Phi: a > $o] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110612un_b_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 3.76/1.79 => ~ ! [A5: a] :
% 3.76/1.79 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ C @ A5 ) @ R )
% 3.76/1.79 => ~ ( Phi @ A5 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_254_RETURN__ref__SPECD,axiom,
% 3.76/1.79 ! [C: a,R: set_Product_prod_a_a,Phi: a > $o] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 3.76/1.79 => ~ ! [A5: a] :
% 3.76/1.79 ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A5 ) @ R )
% 3.76/1.79 => ~ ( Phi @ A5 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_255_RETURN__ref__SPECD,axiom,
% 3.76/1.79 ! [C: b,R: set_Product_prod_b_b,Phi: b > $o] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 3.76/1.79 => ~ ! [A5: b] :
% 3.76/1.79 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A5 ) @ R )
% 3.76/1.79 => ~ ( Phi @ A5 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_256_RETURN__ref__SPECD,axiom,
% 3.76/1.79 ! [C: a,R: set_Product_prod_a_b,Phi: b > $o] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 3.76/1.79 => ~ ! [A5: b] :
% 3.76/1.79 ( ( member458171089od_a_b @ ( product_Pair_a_b @ C @ A5 ) @ R )
% 3.76/1.79 => ~ ( Phi @ A5 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_257_RETURN__SPEC__refine,axiom,
% 3.76/1.79 ! [X4: b,R: set_Product_prod_b_a,Phi: a > $o] :
% 3.76/1.79 ( ? [X11: a] :
% 3.76/1.79 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X11 ) @ R )
% 3.76/1.79 & ( Phi @ X11 ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110612un_b_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_258_RETURN__SPEC__refine,axiom,
% 3.76/1.79 ! [X4: a,R: set_Product_prod_a_a,Phi: a > $o] :
% 3.76/1.79 ( ? [X11: a] :
% 3.76/1.79 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X11 ) @ R )
% 3.76/1.79 & ( Phi @ X11 ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_259_RETURN__SPEC__refine,axiom,
% 3.76/1.79 ! [X4: b,R: set_Product_prod_b_b,Phi: b > $o] :
% 3.76/1.79 ( ? [X11: b] :
% 3.76/1.79 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ X11 ) @ R )
% 3.76/1.79 & ( Phi @ X11 ) )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_260_RETURN__SPEC__refine,axiom,
% 3.76/1.79 ! [X4: a,R: set_Product_prod_a_b,Phi: b > $o] :
% 3.76/1.79 ( ? [X11: b] :
% 3.76/1.79 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X4 @ X11 ) @ R )
% 3.76/1.79 & ( Phi @ X11 ) )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_261_abs__trans__additional_I1_J,axiom,
% 3.76/1.79 ! [A3: refine432681134nres_b,B3: refine432681134nres_b,R: set_Product_prod_b_b,C2: refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ A3 @ B3 )
% 3.76/1.79 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ B3 ) @ C2 )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ A3 ) @ C2 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_262_abs__trans__additional_I1_J,axiom,
% 3.76/1.79 ! [A3: refine432681134nres_b,B3: refine432681134nres_b,R: set_Product_prod_b_a,C2: refine424419629nres_a] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ A3 @ B3 )
% 3.76/1.79 => ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ B3 ) @ C2 )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ A3 ) @ C2 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_263_abs__trans__additional_I1_J,axiom,
% 3.76/1.79 ! [A3: refine424419629nres_a,B3: refine424419629nres_a,R: set_Product_prod_a_b,C2: refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 3.76/1.79 => ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ B3 ) @ C2 )
% 3.76/1.79 => ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ A3 ) @ C2 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_264_abs__trans__additional_I1_J,axiom,
% 3.76/1.79 ! [A3: refine424419629nres_a,B3: refine424419629nres_a,R: set_Product_prod_a_a,C2: refine424419629nres_a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 3.76/1.79 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ B3 ) @ C2 )
% 3.76/1.79 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ A3 ) @ C2 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_265_abs__fun__simps_I3_J,axiom,
% 3.76/1.79 ! [X: set_a,R: set_Pr1628433942t_unit] :
% 3.76/1.79 ( ~ ( ord_less_eq_set_a @ X @ ( domain799550107t_unit @ R ) )
% 3.76/1.79 => ( ( refine341651653t_unit @ R @ ( refine1198353288_RES_a @ X ) )
% 3.76/1.79 = top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_266_abs__fun__simps_I3_J,axiom,
% 3.76/1.79 ! [X: set_b,R: set_Pr1707992533t_unit] :
% 3.76/1.79 ( ~ ( ord_less_eq_set_b @ X @ ( domain918802906t_unit @ R ) )
% 3.76/1.79 => ( ( refine460904452t_unit @ R @ ( refine1198353289_RES_b @ X ) )
% 3.76/1.79 = top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_267_abs__fun__simps_I2_J,axiom,
% 3.76/1.79 ! [X: set_a,R: set_Product_prod_a_a] :
% 3.76/1.79 ( ( ord_less_eq_set_a @ X @ ( domain_a_a @ R ) )
% 3.76/1.79 => ( ( refine1136779702un_a_a @ R @ ( refine1198353288_RES_a @ X ) )
% 3.76/1.79 = ( refine1198353288_RES_a @ ( image_a_a @ R @ X ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_268_abs__fun__simps_I2_J,axiom,
% 3.76/1.79 ! [X: set_a,R: set_Product_prod_a_b] :
% 3.76/1.79 ( ( ord_less_eq_set_a @ X @ ( domain_a_b @ R ) )
% 3.76/1.79 => ( ( refine1136779703un_a_b @ R @ ( refine1198353288_RES_a @ X ) )
% 3.76/1.79 = ( refine1198353289_RES_b @ ( image_a_b @ R @ X ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_269_abs__fun__simps_I2_J,axiom,
% 3.76/1.79 ! [X: set_b,R: set_Product_prod_b_a] :
% 3.76/1.79 ( ( ord_less_eq_set_b @ X @ ( domain_b_a @ R ) )
% 3.76/1.79 => ( ( refine1964549109un_b_a @ R @ ( refine1198353289_RES_b @ X ) )
% 3.76/1.79 = ( refine1198353288_RES_a @ ( image_b_a @ R @ X ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_270_abs__fun__simps_I2_J,axiom,
% 3.76/1.79 ! [X: set_b,R: set_Product_prod_b_b] :
% 3.76/1.79 ( ( ord_less_eq_set_b @ X @ ( domain_b_b @ R ) )
% 3.76/1.79 => ( ( refine1964549110un_b_b @ R @ ( refine1198353289_RES_b @ X ) )
% 3.76/1.79 = ( refine1198353289_RES_b @ ( image_b_b @ R @ X ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_271_ImageI,axiom,
% 3.76/1.79 ! [A: a,B: a,R2: set_Product_prod_a_a,A3: set_a] :
% 3.76/1.79 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R2 )
% 3.76/1.79 => ( ( member_a @ A @ A3 )
% 3.76/1.79 => ( member_a @ B @ ( image_a_a @ R2 @ A3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_272_ImageI,axiom,
% 3.76/1.79 ! [A: a,B: b,R2: set_Product_prod_a_b,A3: set_a] :
% 3.76/1.79 ( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ R2 )
% 3.76/1.79 => ( ( member_a @ A @ A3 )
% 3.76/1.79 => ( member_b @ B @ ( image_a_b @ R2 @ A3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_273_ImageI,axiom,
% 3.76/1.79 ! [A: b,B: a,R2: set_Product_prod_b_a,A3: set_b] :
% 3.76/1.79 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ B ) @ R2 )
% 3.76/1.79 => ( ( member_b @ A @ A3 )
% 3.76/1.79 => ( member_a @ B @ ( image_b_a @ R2 @ A3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_274_ImageI,axiom,
% 3.76/1.79 ! [A: b,B: b,R2: set_Product_prod_b_b,A3: set_b] :
% 3.76/1.79 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ R2 )
% 3.76/1.79 => ( ( member_b @ A @ A3 )
% 3.76/1.79 => ( member_b @ B @ ( image_b_b @ R2 @ A3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_275_nres__order__simps_I4_J,axiom,
% 3.76/1.79 ! [M4: refine787176636t_unit] :
% 3.76/1.79 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ M4 )
% 3.76/1.79 = ( M4 = top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_276_nres__order__simps_I4_J,axiom,
% 3.76/1.79 ! [M4: refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ M4 )
% 3.76/1.79 = ( M4 = top_to240090974nres_b ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_277_nres__order__simps_I4_J,axiom,
% 3.76/1.79 ! [M4: refine424419629nres_a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M4 )
% 3.76/1.79 = ( M4 = top_to231829469nres_a ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_278_conc__fun__FAIL,axiom,
% 3.76/1.79 ! [R: set_Pr451126599t_unit] :
% 3.76/1.79 ( ( refine944483349t_unit @ R @ top_to177290092t_unit )
% 3.76/1.79 = top_to177290092t_unit ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_279_conc__fun__fail__iff_I1_J,axiom,
% 3.76/1.79 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 3.76/1.79 ( ( ( refine944483349t_unit @ R @ S )
% 3.76/1.79 = top_to177290092t_unit )
% 3.76/1.79 = ( S = top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_280_conc__fun__fail__iff_I2_J,axiom,
% 3.76/1.79 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 3.76/1.79 ( ( top_to177290092t_unit
% 3.76/1.79 = ( refine944483349t_unit @ R @ S ) )
% 3.76/1.79 = ( S = top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_281_bind__FAIL,axiom,
% 3.76/1.79 ! [F: product_unit > refine787176636t_unit] :
% 3.76/1.79 ( ( refine681446406t_unit @ top_to177290092t_unit @ F )
% 3.76/1.79 = top_to177290092t_unit ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_282_bind__FAIL,axiom,
% 3.76/1.79 ! [F: a > refine432681134nres_b] :
% 3.76/1.79 ( ( refine436832839nd_a_b @ top_to231829469nres_a @ F )
% 3.76/1.79 = top_to240090974nres_b ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_283_nofail__simps_I1_J,axiom,
% 3.76/1.79 ~ ( refine579265252t_unit @ top_to177290092t_unit ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_284_inres__simps_I1_J,axiom,
% 3.76/1.79 ( ( refine558004794t_unit @ top_to177290092t_unit )
% 3.76/1.79 = ( ^ [Uu3: product_unit] : $true ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_285_nres__simp__internals_I2_J,axiom,
% 3.76/1.79 refine1607584204t_unit = top_to177290092t_unit ).
% 3.76/1.79
% 3.76/1.79 thf(fact_286_abs__fun__simps_I1_J,axiom,
% 3.76/1.79 ! [R: set_Pr451126599t_unit] :
% 3.76/1.79 ( ( refine838861686t_unit @ R @ top_to177290092t_unit )
% 3.76/1.79 = top_to177290092t_unit ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_287_FAIL__refine,axiom,
% 3.76/1.79 ! [X: refine432681134nres_b,R: set_Pr1707992533t_unit] : ( ord_le527798542nres_b @ X @ ( refine2140306339t_unit @ R @ top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_288_FAIL__refine,axiom,
% 3.76/1.79 ! [X: refine424419629nres_a,R: set_Pr1628433942t_unit] : ( ord_le519537037nres_a @ X @ ( refine2021053540t_unit @ R @ top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_289_rev__ImageI,axiom,
% 3.76/1.79 ! [A: a,A3: set_a,B: a,R2: set_Product_prod_a_a] :
% 3.76/1.79 ( ( member_a @ A @ A3 )
% 3.76/1.79 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R2 )
% 3.76/1.79 => ( member_a @ B @ ( image_a_a @ R2 @ A3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_290_rev__ImageI,axiom,
% 3.76/1.79 ! [A: a,A3: set_a,B: b,R2: set_Product_prod_a_b] :
% 3.76/1.79 ( ( member_a @ A @ A3 )
% 3.76/1.79 => ( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ R2 )
% 3.76/1.79 => ( member_b @ B @ ( image_a_b @ R2 @ A3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_291_rev__ImageI,axiom,
% 3.76/1.79 ! [A: b,A3: set_b,B: a,R2: set_Product_prod_b_a] :
% 3.76/1.79 ( ( member_b @ A @ A3 )
% 3.76/1.79 => ( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ B ) @ R2 )
% 3.76/1.79 => ( member_a @ B @ ( image_b_a @ R2 @ A3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_292_rev__ImageI,axiom,
% 3.76/1.79 ! [A: b,A3: set_b,B: b,R2: set_Product_prod_b_b] :
% 3.76/1.79 ( ( member_b @ A @ A3 )
% 3.76/1.79 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ R2 )
% 3.76/1.79 => ( member_b @ B @ ( image_b_b @ R2 @ A3 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_293_ImageE,axiom,
% 3.76/1.79 ! [B: a,R2: set_Product_prod_a_a,A3: set_a] :
% 3.76/1.79 ( ( member_a @ B @ ( image_a_a @ R2 @ A3 ) )
% 3.76/1.79 => ~ ! [X3: a] :
% 3.76/1.79 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ B ) @ R2 )
% 3.76/1.79 => ~ ( member_a @ X3 @ A3 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_294_ImageE,axiom,
% 3.76/1.79 ! [B: a,R2: set_Product_prod_b_a,A3: set_b] :
% 3.76/1.79 ( ( member_a @ B @ ( image_b_a @ R2 @ A3 ) )
% 3.76/1.79 => ~ ! [X3: b] :
% 3.76/1.79 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X3 @ B ) @ R2 )
% 3.76/1.79 => ~ ( member_b @ X3 @ A3 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_295_ImageE,axiom,
% 3.76/1.79 ! [B: b,R2: set_Product_prod_a_b,A3: set_a] :
% 3.76/1.79 ( ( member_b @ B @ ( image_a_b @ R2 @ A3 ) )
% 3.76/1.79 => ~ ! [X3: a] :
% 3.76/1.79 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X3 @ B ) @ R2 )
% 3.76/1.79 => ~ ( member_a @ X3 @ A3 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_296_ImageE,axiom,
% 3.76/1.79 ! [B: b,R2: set_Product_prod_b_b,A3: set_b] :
% 3.76/1.79 ( ( member_b @ B @ ( image_b_b @ R2 @ A3 ) )
% 3.76/1.79 => ~ ! [X3: b] :
% 3.76/1.79 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X3 @ B ) @ R2 )
% 3.76/1.79 => ~ ( member_b @ X3 @ A3 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_297_nres__inequalities_I3_J,axiom,
% 3.76/1.79 ! [X4: product_unit] :
% 3.76/1.79 ( top_to177290092t_unit
% 3.76/1.79 != ( refine1420258419t_unit @ X4 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_298_top__nres__def,axiom,
% 3.76/1.79 top_to177290092t_unit = refine1607584204t_unit ).
% 3.76/1.79
% 3.76/1.79 thf(fact_299_top__greatest,axiom,
% 3.76/1.79 ! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_300_top__greatest,axiom,
% 3.76/1.79 ! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_301_top__greatest,axiom,
% 3.76/1.79 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_302_top_Oextremum__unique,axiom,
% 3.76/1.79 ! [A: refine787176636t_unit] :
% 3.76/1.79 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
% 3.76/1.79 = ( A = top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_303_top_Oextremum__unique,axiom,
% 3.76/1.79 ! [A: refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
% 3.76/1.79 = ( A = top_to240090974nres_b ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_304_top_Oextremum__unique,axiom,
% 3.76/1.79 ! [A: refine424419629nres_a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 3.76/1.79 = ( A = top_to231829469nres_a ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_305_top_Oextremum__uniqueI,axiom,
% 3.76/1.79 ! [A: refine787176636t_unit] :
% 3.76/1.79 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
% 3.76/1.79 => ( A = top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_306_top_Oextremum__uniqueI,axiom,
% 3.76/1.79 ! [A: refine432681134nres_b] :
% 3.76/1.79 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
% 3.76/1.79 => ( A = top_to240090974nres_b ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_307_top_Oextremum__uniqueI,axiom,
% 3.76/1.79 ! [A: refine424419629nres_a] :
% 3.76/1.79 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 3.76/1.79 => ( A = top_to231829469nres_a ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_308_nres__order__simps_I3_J,axiom,
% 3.76/1.79 ! [M4: refine787176636t_unit] : ( ord_le1051254044t_unit @ M4 @ top_to177290092t_unit ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_309_nres__order__simps_I3_J,axiom,
% 3.76/1.79 ! [M4: refine432681134nres_b] : ( ord_le527798542nres_b @ M4 @ top_to240090974nres_b ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_310_nres__order__simps_I3_J,axiom,
% 3.76/1.79 ! [M4: refine424419629nres_a] : ( ord_le519537037nres_a @ M4 @ top_to231829469nres_a ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_311_nres__inequalities_I1_J,axiom,
% 3.76/1.79 ! [X: set_Product_unit] :
% 3.76/1.79 ( top_to177290092t_unit
% 3.76/1.79 != ( refine1777164439t_unit @ X ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_312_nres__inequalities_I1_J,axiom,
% 3.76/1.79 ! [X: set_a] :
% 3.76/1.79 ( top_to231829469nres_a
% 3.76/1.79 != ( refine1198353288_RES_a @ X ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_313_nres__inequalities_I1_J,axiom,
% 3.76/1.79 ! [X: set_b] :
% 3.76/1.79 ( top_to240090974nres_b
% 3.76/1.79 != ( refine1198353289_RES_b @ X ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_314_nres__cases,axiom,
% 3.76/1.79 ! [M4: refine787176636t_unit] :
% 3.76/1.79 ( ( M4 != top_to177290092t_unit )
% 3.76/1.79 => ~ ! [X12: set_Product_unit] :
% 3.76/1.79 ( M4
% 3.76/1.79 != ( refine1777164439t_unit @ X12 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_315_nres__cases,axiom,
% 3.76/1.79 ! [M4: refine424419629nres_a] :
% 3.76/1.79 ( ( M4 != top_to231829469nres_a )
% 3.76/1.79 => ~ ! [X12: set_a] :
% 3.76/1.79 ( M4
% 3.76/1.79 != ( refine1198353288_RES_a @ X12 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_316_nres__cases,axiom,
% 3.76/1.79 ! [M4: refine432681134nres_b] :
% 3.76/1.79 ( ( M4 != top_to240090974nres_b )
% 3.76/1.79 => ~ ! [X12: set_b] :
% 3.76/1.79 ( M4
% 3.76/1.79 != ( refine1198353289_RES_b @ X12 ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_317_not__nofail__iff,axiom,
% 3.76/1.79 ! [S: refine787176636t_unit] :
% 3.76/1.79 ( ( ~ ( refine579265252t_unit @ S ) )
% 3.76/1.79 = ( S = top_to177290092t_unit ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_318_nofail__def,axiom,
% 3.76/1.79 ( refine579265252t_unit
% 3.76/1.79 = ( ^ [S4: refine787176636t_unit] : ( S4 != top_to177290092t_unit ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_319_intro__nofail_I2_J,axiom,
% 3.76/1.79 ! [S: refine787176636t_unit] :
% 3.76/1.79 ( ( top_to177290092t_unit != S )
% 3.76/1.79 = ( refine579265252t_unit @ S ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_320_ibind__strict_I2_J,axiom,
% 3.76/1.79 ! [F: product_unit > refine787176636t_unit] :
% 3.76/1.79 ( ( refine681446406t_unit @ top_to177290092t_unit @ F )
% 3.76/1.79 = top_to177290092t_unit ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_321_meta__le__everything__if__top,axiom,
% 3.76/1.79 ! [M: refine787176636t_unit,X4: refine787176636t_unit] :
% 3.76/1.79 ( ( M = top_to177290092t_unit )
% 3.76/1.79 => ( ord_le1051254044t_unit @ X4 @ M ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_322_meta__le__everything__if__top,axiom,
% 3.76/1.79 ! [M: refine432681134nres_b,X4: refine432681134nres_b] :
% 3.76/1.79 ( ( M = top_to240090974nres_b )
% 3.76/1.79 => ( ord_le527798542nres_b @ X4 @ M ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_323_meta__le__everything__if__top,axiom,
% 3.76/1.79 ! [M: refine424419629nres_a,X4: refine424419629nres_a] :
% 3.76/1.79 ( ( M = top_to231829469nres_a )
% 3.76/1.79 => ( ord_le519537037nres_a @ X4 @ M ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_324_pw__flat__ge__iff,axiom,
% 3.76/1.79 ! [S: refine787176636t_unit,S3: refine787176636t_unit] :
% 3.76/1.79 ( ( partia1658438072t_unit @ top_to177290092t_unit @ S @ S3 )
% 3.76/1.79 = ( ( refine579265252t_unit @ S )
% 3.76/1.79 => ( ( refine579265252t_unit @ S3 )
% 3.76/1.79 & ! [X5: product_unit] :
% 3.76/1.79 ( ( refine558004794t_unit @ S @ X5 )
% 3.76/1.79 = ( refine558004794t_unit @ S3 @ X5 ) ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_325_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 3.76/1.79 ! [M4: refine787176636t_unit,M3: refine787176636t_unit,F: product_unit > refine787176636t_unit,F2: product_unit > refine787176636t_unit] :
% 3.76/1.79 ( ( partia1658438072t_unit @ top_to177290092t_unit @ M4 @ M3 )
% 3.76/1.79 => ( ! [X3: product_unit] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 3.76/1.79 => ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine681446406t_unit @ M4 @ F ) @ ( refine681446406t_unit @ M3 @ F2 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_326_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 3.76/1.79 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine432681134nres_b,F2: a > refine432681134nres_b] :
% 3.76/1.79 ( ( partia906949161nres_a @ top_to231829469nres_a @ M4 @ M3 )
% 3.76/1.79 => ( ! [X3: a] : ( partia915210666nres_b @ top_to240090974nres_b @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 3.76/1.79 => ( partia915210666nres_b @ top_to240090974nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ ( refine436832839nd_a_b @ M3 @ F2 ) ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_327_flat__ord__compat_I2_J,axiom,
% 3.76/1.79 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 3.76/1.79 ( ( partia1658438072t_unit @ top_to177290092t_unit @ X4 @ Y3 )
% 3.76/1.79 => ( ord_le1051254044t_unit @ Y3 @ X4 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_328_flat__ord__compat_I2_J,axiom,
% 3.76/1.79 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 3.76/1.79 ( ( partia915210666nres_b @ top_to240090974nres_b @ X4 @ Y3 )
% 3.76/1.79 => ( ord_le527798542nres_b @ Y3 @ X4 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_329_flat__ord__compat_I2_J,axiom,
% 3.76/1.79 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.76/1.79 ( ( partia906949161nres_a @ top_to231829469nres_a @ X4 @ Y3 )
% 3.76/1.79 => ( ord_le519537037nres_a @ Y3 @ X4 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_330_UNIV__I,axiom,
% 3.76/1.79 ! [X4: a] : ( member_a @ X4 @ top_top_set_a ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_331_UNIV__I,axiom,
% 3.76/1.79 ! [X4: b] : ( member_b @ X4 @ top_top_set_b ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_332_eq__UNIV__iff,axiom,
% 3.76/1.79 ! [S: set_a] :
% 3.76/1.79 ( ( S = top_top_set_a )
% 3.76/1.79 = ( ! [X5: a] : ( member_a @ X5 @ S ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_333_eq__UNIV__iff,axiom,
% 3.76/1.79 ! [S: set_b] :
% 3.76/1.79 ( ( S = top_top_set_b )
% 3.76/1.79 = ( ! [X5: b] : ( member_b @ X5 @ S ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_334_UNIV__witness,axiom,
% 3.76/1.79 ? [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_335_UNIV__witness,axiom,
% 3.76/1.79 ? [X3: b] : ( member_b @ X3 @ top_top_set_b ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_336_top__set__def,axiom,
% 3.76/1.79 ( top_top_set_a
% 3.76/1.79 = ( collect_a @ top_top_a_o ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_337_top__set__def,axiom,
% 3.76/1.79 ( top_top_set_b
% 3.76/1.79 = ( collect_b @ top_top_b_o ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_338_UNIV__eq__I,axiom,
% 3.76/1.79 ! [A3: set_a] :
% 3.76/1.79 ( ! [X3: a] : ( member_a @ X3 @ A3 )
% 3.76/1.79 => ( top_top_set_a = A3 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_339_UNIV__eq__I,axiom,
% 3.76/1.79 ! [A3: set_b] :
% 3.76/1.79 ( ! [X3: b] : ( member_b @ X3 @ A3 )
% 3.76/1.79 => ( top_top_set_b = A3 ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_340_top__empty__eq,axiom,
% 3.76/1.79 ( top_top_a_o
% 3.76/1.79 = ( ^ [X5: a] : ( member_a @ X5 @ top_top_set_a ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_341_top__empty__eq,axiom,
% 3.76/1.79 ( top_top_b_o
% 3.76/1.79 = ( ^ [X5: b] : ( member_b @ X5 @ top_top_set_b ) ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(fact_342_ASSERT__simps_I2_J,axiom,
% 3.76/1.79 ( ( refine2039610767ASSERT @ $false )
% 3.76/1.79 = top_to177290092t_unit ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 3.76/1.79 ! [X4: set_a,Y3: set_a] :
% 3.76/1.79 ( ( if_set_a @ $false @ X4 @ Y3 )
% 3.76/1.79 = Y3 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 3.76/1.79 ! [X4: set_a,Y3: set_a] :
% 3.76/1.79 ( ( if_set_a @ $true @ X4 @ Y3 )
% 3.76/1.79 = X4 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_2_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 3.76/1.79 ! [X4: set_b,Y3: set_b] :
% 3.76/1.79 ( ( if_set_b @ $false @ X4 @ Y3 )
% 3.76/1.79 = Y3 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_1_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 3.76/1.79 ! [X4: set_b,Y3: set_b] :
% 3.76/1.79 ( ( if_set_b @ $true @ X4 @ Y3 )
% 3.76/1.79 = X4 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 3.76/1.79 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.76/1.79 ( ( if_Ref1724547303nres_a @ $false @ X4 @ Y3 )
% 3.76/1.79 = Y3 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 3.76/1.79 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.76/1.79 ( ( if_Ref1724547303nres_a @ $true @ X4 @ Y3 )
% 3.76/1.79 = X4 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 3.76/1.79 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 3.76/1.79 ( ( if_Ref1732808808nres_b @ $false @ X4 @ Y3 )
% 3.76/1.79 = Y3 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 3.76/1.79 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 3.76/1.79 ( ( if_Ref1732808808nres_b @ $true @ X4 @ Y3 )
% 3.76/1.79 = X4 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 3.76/1.79 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 3.76/1.79 ( ( if_o_R1705037948nres_a @ $false @ X4 @ Y3 )
% 3.76/1.79 = Y3 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 3.76/1.79 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 3.76/1.79 ( ( if_o_R1705037948nres_a @ $true @ X4 @ Y3 )
% 3.76/1.79 = X4 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 3.76/1.79 ! [X4: $o > refine432681134nres_b,Y3: $o > refine432681134nres_b] :
% 3.76/1.79 ( ( if_o_R697118589nres_b @ $false @ X4 @ Y3 )
% 3.76/1.79 = Y3 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 3.76/1.79 ! [X4: $o > refine432681134nres_b,Y3: $o > refine432681134nres_b] :
% 3.76/1.79 ( ( if_o_R697118589nres_b @ $true @ X4 @ Y3 )
% 3.76/1.79 = X4 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 3.76/1.79 ! [P: $o] :
% 3.76/1.79 ( ( P = $true )
% 3.76/1.79 | ( P = $false ) ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 3.76/1.79 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 3.76/1.79 ( ( if_Ref1369692790t_unit @ $false @ X4 @ Y3 )
% 3.76/1.79 = Y3 ) ).
% 3.76/1.79
% 3.76/1.79 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 3.76/1.79 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 3.76/1.79 ( ( if_Ref1369692790t_unit @ $true @ X4 @ Y3 )
% 3.76/1.79 = X4 ) ).
% 3.76/1.79
% 3.76/1.79 thf(conj_0,conjecture,
% 3.76/1.79 ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ).
% 3.76/1.79 ------------------------
% 3.85/1.83 % (19199)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/27Mi)
% 3.85/1.83 % (19202)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/275Mi)
% 3.85/1.83 % (19203)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/18Mi)
% 3.85/1.83 % (19198)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/4Mi)
% 3.85/1.83 % (19197)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/183Mi)
% 3.85/1.83 % (19201)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/2Mi)
% 3.85/1.83 % (19200)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/2Mi)
% 3.85/1.83 % (19201)Instruction limit reached!
% 3.85/1.83 % (19201)------------------------------
% 3.85/1.83 % (19201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.83 % (19201)Termination reason: Unknown
% 3.85/1.83 % (19201)Termination phase: shuffling
% 3.85/1.83
% 3.85/1.83 % (19201)Memory used [KB]: 1535
% 3.85/1.83 % (19201)Time elapsed: 0.003 s
% 3.85/1.83 % (19201)Instructions burned: 2 (million)
% 3.85/1.83 % (19201)------------------------------
% 3.85/1.83 % (19201)------------------------------
% 3.85/1.84 % (19200)Instruction limit reached!
% 3.85/1.84 % (19200)------------------------------
% 3.85/1.84 % (19200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.84 % (19200)Termination reason: Unknown
% 3.85/1.84 % (19200)Termination phase: shuffling
% 3.85/1.84
% 3.85/1.84 % (19200)Memory used [KB]: 1535
% 3.85/1.84 % (19200)Time elapsed: 0.004 s
% 3.85/1.84 % (19200)Instructions burned: 3 (million)
% 3.85/1.84 % (19200)------------------------------
% 3.85/1.84 % (19200)------------------------------
% 3.85/1.84 % (19198)Instruction limit reached!
% 3.85/1.84 % (19198)------------------------------
% 3.85/1.84 % (19198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.84 % (19198)Termination reason: Unknown
% 3.85/1.84 % (19198)Termination phase: shuffling
% 3.85/1.84
% 3.85/1.84 % (19198)Memory used [KB]: 1663
% 3.85/1.84 % (19198)Time elapsed: 0.005 s
% 3.85/1.84 % (19198)Instructions burned: 5 (million)
% 3.85/1.84 % (19198)------------------------------
% 3.85/1.84 % (19198)------------------------------
% 3.85/1.84 % (19203)Instruction limit reached!
% 3.85/1.84 % (19203)------------------------------
% 3.85/1.84 % (19203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.84 % (19203)Termination reason: Unknown
% 3.85/1.84 % (19203)Termination phase: shuffling
% 3.85/1.84
% 3.85/1.84 % (19203)Memory used [KB]: 1918
% 3.85/1.84 % (19203)Time elapsed: 0.013 s
% 3.85/1.84 % (19203)Instructions burned: 19 (million)
% 3.85/1.84 % (19203)------------------------------
% 3.85/1.84 % (19203)------------------------------
% 3.85/1.85 % (19199)Instruction limit reached!
% 3.85/1.85 % (19199)------------------------------
% 3.85/1.85 % (19199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.85 % (19199)Termination reason: Unknown
% 3.85/1.85 % (19199)Termination phase: shuffling
% 3.85/1.85
% 3.85/1.85 % (19199)Memory used [KB]: 2046
% 3.85/1.85 % (19199)Time elapsed: 0.017 s
% 3.85/1.85 % (19199)Instructions burned: 27 (million)
% 3.85/1.85 % (19199)------------------------------
% 3.85/1.85 % (19199)------------------------------
% 3.85/1.85 % (19204)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/3Mi)
% 3.85/1.85 % (19205)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/37Mi)
% 3.85/1.85 % (19206)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/15Mi)
% 3.85/1.86 % (19204)Instruction limit reached!
% 3.85/1.86 % (19204)------------------------------
% 3.85/1.86 % (19204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.86 % (19204)Termination reason: Unknown
% 3.85/1.86 % (19204)Termination phase: shuffling
% 3.85/1.86
% 3.85/1.86 % (19204)Memory used [KB]: 1535
% 3.85/1.86 % (19204)Time elapsed: 0.004 s
% 3.85/1.86 % (19204)Instructions burned: 3 (million)
% 3.85/1.86 % (19204)------------------------------
% 3.85/1.86 % (19204)------------------------------
% 3.85/1.86 % (19206)Instruction limit reached!
% 3.85/1.86 % (19206)------------------------------
% 3.85/1.86 % (19206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.86 % (19206)Termination reason: Unknown
% 3.85/1.86 % (19206)Termination phase: shuffling
% 3.85/1.86
% 3.85/1.86 % (19206)Memory used [KB]: 1791
% 3.85/1.86 % (19206)Time elapsed: 0.010 s
% 3.85/1.86 % (19206)Instructions burned: 15 (million)
% 3.85/1.86 % (19206)------------------------------
% 3.85/1.86 % (19206)------------------------------
% 3.85/1.86 % (19207)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/3Mi)
% 3.85/1.87 % (19207)Instruction limit reached!
% 3.85/1.87 % (19207)------------------------------
% 3.85/1.87 % (19207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.87 % (19207)Termination reason: Unknown
% 3.85/1.87 % (19207)Termination phase: shuffling
% 3.85/1.87
% 3.85/1.87 % (19207)Memory used [KB]: 1535
% 3.85/1.87 % (19207)Time elapsed: 0.004 s
% 3.85/1.87 % (19207)Instructions burned: 3 (million)
% 3.85/1.87 % (19207)------------------------------
% 3.85/1.87 % (19207)------------------------------
% 3.85/1.87 % (19208)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/1041Mi)
% 3.85/1.87 % (19205)Instruction limit reached!
% 3.85/1.87 % (19205)------------------------------
% 3.85/1.87 % (19205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.87 % (19205)Termination reason: Unknown
% 3.85/1.87 % (19205)Termination phase: shuffling
% 3.85/1.87
% 3.85/1.87 % (19205)Memory used [KB]: 2302
% 3.85/1.87 % (19205)Time elapsed: 0.021 s
% 3.85/1.87 % (19205)Instructions burned: 38 (million)
% 3.85/1.87 % (19205)------------------------------
% 3.85/1.87 % (19205)------------------------------
% 3.85/1.87 % (19209)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19091 for (2999ds/7Mi)
% 3.85/1.87 % (19202)First to succeed.
% 3.85/1.88 % (19202)Refutation found. Thanks to Tanya!
% 3.85/1.88 % SZS status Theorem for DTF2THF_19091
% 3.85/1.88 % SZS output start Proof for DTF2THF_19091
% 3.85/1.88 thf(type_def_5, type, refine424419629nres_a: $tType).
% 3.85/1.88 thf(type_def_7, type, refine432681134nres_b: $tType).
% 3.85/1.88 thf(type_def_8, type, refine787176636t_unit: $tType).
% 3.85/1.88 thf(type_def_9, type, set_a: $tType).
% 3.85/1.88 thf(type_def_10, type, set_b: $tType).
% 3.85/1.88 thf(type_def_11, type, refine671810262od_a_a: $tType).
% 3.85/1.88 thf(type_def_12, type, refine1811374551od_a_b: $tType).
% 3.85/1.88 thf(type_def_13, type, refine891721109od_b_a: $tType).
% 3.85/1.88 thf(type_def_14, type, refine2031285398od_b_b: $tType).
% 3.85/1.88 thf(type_def_15, type, a: $tType).
% 3.85/1.88 thf(type_def_16, type, b: $tType).
% 3.85/1.88 thf(type_def_17, type, produc1609974940nres_a: $tType).
% 3.85/1.88 thf(type_def_18, type, produc1587512412nres_b: $tType).
% 3.85/1.88 thf(type_def_19, type, product_prod_a_a: $tType).
% 3.85/1.88 thf(type_def_20, type, product_prod_a_b: $tType).
% 3.85/1.88 thf(type_def_21, type, product_prod_b_a: $tType).
% 3.85/1.88 thf(type_def_22, type, product_prod_b_b: $tType).
% 3.85/1.88 thf(type_def_23, type, product_unit: $tType).
% 3.85/1.88 thf(type_def_24, type, set_Pr451126599t_unit: $tType).
% 3.85/1.88 thf(type_def_25, type, set_Pr1628433942t_unit: $tType).
% 3.85/1.88 thf(type_def_26, type, set_Product_prod_a_a: $tType).
% 3.85/1.88 thf(type_def_27, type, set_Product_prod_a_b: $tType).
% 3.85/1.88 thf(type_def_28, type, set_Pr1707992533t_unit: $tType).
% 3.85/1.88 thf(type_def_29, type, set_Product_prod_b_a: $tType).
% 3.85/1.88 thf(type_def_30, type, set_Product_prod_b_b: $tType).
% 3.85/1.88 thf(type_def_31, type, set_Product_unit: $tType).
% 3.85/1.88 thf(func_def_0, type, produc1587512412nres_b: $tType).
% 3.85/1.88 thf(func_def_1, type, produc1609974940nres_a: $tType).
% 3.85/1.88 thf(func_def_2, type, set_Pr451126599t_unit: $tType).
% 3.85/1.88 thf(func_def_3, type, refine2031285398od_b_b: $tType).
% 3.85/1.88 thf(func_def_4, type, refine891721109od_b_a: $tType).
% 3.85/1.88 thf(func_def_5, type, refine1811374551od_a_b: $tType).
% 3.85/1.88 thf(func_def_6, type, refine671810262od_a_a: $tType).
% 3.85/1.88 thf(func_def_7, type, refine787176636t_unit: $tType).
% 3.85/1.88 thf(func_def_8, type, set_Pr1707992533t_unit: $tType).
% 3.85/1.88 thf(func_def_9, type, set_Pr1628433942t_unit: $tType).
% 3.85/1.88 thf(func_def_10, type, refine432681134nres_b: $tType).
% 3.85/1.88 thf(func_def_11, type, refine424419629nres_a: $tType).
% 3.85/1.88 thf(func_def_12, type, set_Product_prod_b_b: $tType).
% 3.85/1.88 thf(func_def_13, type, set_Product_prod_b_a: $tType).
% 3.85/1.88 thf(func_def_14, type, set_Product_prod_a_b: $tType).
% 3.85/1.88 thf(func_def_15, type, set_Product_prod_a_a: $tType).
% 3.85/1.88 thf(func_def_16, type, set_Product_unit: $tType).
% 3.85/1.88 thf(func_def_17, type, product_prod_b_b: $tType).
% 3.85/1.88 thf(func_def_18, type, product_prod_b_a: $tType).
% 3.85/1.88 thf(func_def_19, type, product_prod_a_b: $tType).
% 3.85/1.88 thf(func_def_20, type, product_prod_a_a: $tType).
% 3.85/1.88 thf(func_def_21, type, product_unit: $tType).
% 3.85/1.88 thf(func_def_22, type, set_b: $tType).
% 3.85/1.88 thf(func_def_23, type, set_a: $tType).
% 3.85/1.88 thf(func_def_24, type, b: $tType).
% 3.85/1.88 thf(func_def_25, type, a: $tType).
% 3.85/1.88 thf(func_def_26, type, if_o_R1705037948nres_a: $o > ($o > refine424419629nres_a) > ($o > refine424419629nres_a) > $o > refine424419629nres_a).
% 3.85/1.88 thf(func_def_27, type, if_o_R697118589nres_b: $o > ($o > refine432681134nres_b) > ($o > refine432681134nres_b) > $o > refine432681134nres_b).
% 3.85/1.88 thf(func_def_28, type, if_Ref1369692790t_unit: $o > refine787176636t_unit > refine787176636t_unit > refine787176636t_unit).
% 3.85/1.88 thf(func_def_29, type, if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a).
% 3.85/1.88 thf(func_def_30, type, if_Ref1732808808nres_b: $o > refine432681134nres_b > refine432681134nres_b > refine432681134nres_b).
% 3.85/1.88 thf(func_def_31, type, if_set_a: $o > set_a > set_a > set_a).
% 3.85/1.88 thf(func_def_32, type, if_set_b: $o > set_b > set_b > set_b).
% 3.85/1.88 thf(func_def_33, type, ord_le516598614nres_a: ($o > refine424419629nres_a) > ($o > refine424419629nres_a) > $o).
% 3.85/1.88 thf(func_def_34, type, ord_le1656162903nres_b: ($o > refine432681134nres_b) > ($o > refine432681134nres_b) > $o).
% 3.85/1.88 thf(func_def_35, type, ord_le915866422od_a_a: refine671810262od_a_a > refine671810262od_a_a > $o).
% 3.85/1.88 thf(func_def_36, type, ord_le2055430711od_a_b: refine1811374551od_a_b > refine1811374551od_a_b > $o).
% 3.85/1.88 thf(func_def_37, type, ord_le1135777269od_b_a: refine891721109od_b_a > refine891721109od_b_a > $o).
% 3.85/1.88 thf(func_def_38, type, ord_le127857910od_b_b: refine2031285398od_b_b > refine2031285398od_b_b > $o).
% 3.85/1.88 thf(func_def_39, type, ord_le1051254044t_unit: refine787176636t_unit > refine787176636t_unit > $o).
% 3.85/1.88 thf(func_def_40, type, ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o).
% 3.85/1.88 thf(func_def_41, type, ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o).
% 3.85/1.88 thf(func_def_42, type, ord_less_eq_set_a: set_a > set_a > $o).
% 3.85/1.88 thf(func_def_43, type, ord_less_eq_set_b: set_b > set_b > $o).
% 3.85/1.88 thf(func_def_44, type, order_1714329108nres_a: (refine424419629nres_a > $o) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_45, type, order_1722590613nres_b: (refine432681134nres_b > $o) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_46, type, top_top_a_o: a > $o).
% 3.85/1.88 thf(func_def_47, type, top_top_b_o: b > $o).
% 3.85/1.88 thf(func_def_48, type, top_to177290092t_unit: refine787176636t_unit).
% 3.85/1.88 thf(func_def_49, type, top_to231829469nres_a: refine424419629nres_a).
% 3.85/1.88 thf(func_def_50, type, top_to240090974nres_b: refine432681134nres_b).
% 3.85/1.88 thf(func_def_51, type, top_top_set_a: set_a).
% 3.85/1.88 thf(func_def_52, type, top_top_set_b: set_b).
% 3.85/1.88 thf(func_def_53, type, partia1658438072t_unit: refine787176636t_unit > refine787176636t_unit > refine787176636t_unit > $o).
% 3.85/1.88 thf(func_def_54, type, partia906949161nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a > $o).
% 3.85/1.88 thf(func_def_55, type, partia915210666nres_b: refine432681134nres_b > refine432681134nres_b > refine432681134nres_b > $o).
% 3.85/1.88 thf(func_def_56, type, produc1136923598nres_a: refine424419629nres_a > refine424419629nres_a > produc1609974940nres_a).
% 3.85/1.88 thf(func_def_57, type, produc2130641934nres_b: refine432681134nres_b > refine432681134nres_b > produc1587512412nres_b).
% 3.85/1.88 thf(func_def_58, type, product_Pair_a_a: a > a > product_prod_a_a).
% 3.85/1.88 thf(func_def_59, type, product_Pair_a_b: a > b > product_prod_a_b).
% 3.85/1.88 thf(func_def_60, type, product_Pair_b_a: b > a > product_prod_b_a).
% 3.85/1.88 thf(func_def_61, type, product_Pair_b_b: b > b > product_prod_b_b).
% 3.85/1.88 thf(func_def_62, type, refine2039610767ASSERT: $o > refine787176636t_unit).
% 3.85/1.88 thf(func_def_63, type, refine1420258419t_unit: product_unit > refine787176636t_unit).
% 3.85/1.88 thf(func_def_64, type, refine2063221604TURN_a: a > refine424419629nres_a).
% 3.85/1.88 thf(func_def_65, type, refine2063221605TURN_b: b > refine432681134nres_b).
% 3.85/1.88 thf(func_def_66, type, refine838861686t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit).
% 3.85/1.88 thf(func_def_67, type, refine341651653t_unit: set_Pr1628433942t_unit > refine424419629nres_a > refine787176636t_unit).
% 3.85/1.88 thf(func_def_68, type, refine1136779702un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a).
% 3.85/1.88 thf(func_def_69, type, refine1136779703un_a_b: set_Product_prod_a_b > refine424419629nres_a > refine432681134nres_b).
% 3.85/1.88 thf(func_def_70, type, refine460904452t_unit: set_Pr1707992533t_unit > refine432681134nres_b > refine787176636t_unit).
% 3.85/1.88 thf(func_def_71, type, refine1964549109un_b_a: set_Product_prod_b_a > refine432681134nres_b > refine424419629nres_a).
% 3.85/1.88 thf(func_def_72, type, refine1964549110un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b).
% 3.85/1.88 thf(func_def_73, type, refine988994910_a_a_b: refine671810262od_a_a > (product_prod_a_a > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_74, type, refine681446406t_unit: refine787176636t_unit > (product_unit > refine787176636t_unit) > refine787176636t_unit).
% 3.85/1.88 thf(func_def_75, type, refine119808503unit_a: refine787176636t_unit > (product_unit > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_76, type, refine119808504unit_b: refine787176636t_unit > (product_unit > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_77, type, refine96995669t_unit: refine424419629nres_a > (a > refine787176636t_unit) > refine787176636t_unit).
% 3.85/1.88 thf(func_def_78, type, refine436832838nd_a_a: refine424419629nres_a > (a > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_79, type, refine436832839nd_a_b: refine424419629nres_a > (a > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_80, type, refine216248468t_unit: refine432681134nres_b > (b > refine787176636t_unit) > refine787176636t_unit).
% 3.85/1.88 thf(func_def_81, type, refine1264602245nd_b_a: refine432681134nres_b > (b > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_82, type, refine1264602246nd_b_b: refine432681134nres_b > (b > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_83, type, refine944483349t_unit: set_Pr451126599t_unit > refine787176636t_unit > refine787176636t_unit).
% 3.85/1.88 thf(func_def_84, type, refine2021053540t_unit: set_Pr1628433942t_unit > refine787176636t_unit > refine424419629nres_a).
% 3.85/1.88 thf(func_def_85, type, refine1441824853un_a_a: set_Product_prod_a_a > refine424419629nres_a > refine424419629nres_a).
% 3.85/1.88 thf(func_def_86, type, refine1441824854un_a_b: set_Product_prod_a_b > refine432681134nres_b > refine424419629nres_a).
% 3.85/1.88 thf(func_def_87, type, refine2140306339t_unit: set_Pr1707992533t_unit > refine787176636t_unit > refine432681134nres_b).
% 3.85/1.88 thf(func_def_88, type, refine122110612un_b_a: set_Product_prod_b_a > refine424419629nres_a > refine432681134nres_b).
% 3.85/1.88 thf(func_def_89, type, refine122110613un_b_b: set_Product_prod_b_b > refine432681134nres_b > refine432681134nres_b).
% 3.85/1.88 thf(func_def_90, type, refine558004794t_unit: refine787176636t_unit > product_unit > $o).
% 3.85/1.88 thf(func_def_91, type, refine1001002027nres_a: refine424419629nres_a > a > $o).
% 3.85/1.88 thf(func_def_92, type, refine1001002028nres_b: refine432681134nres_b > b > $o).
% 3.85/1.88 thf(func_def_93, type, refine378960780od_a_a: refine671810262od_a_a > product_prod_a_a > $o).
% 3.85/1.88 thf(func_def_94, type, refine387222285od_a_b: refine1811374551od_a_b > product_prod_a_b > $o).
% 3.85/1.88 thf(func_def_95, type, refine1206730187od_b_a: refine891721109od_b_a > product_prod_b_a > $o).
% 3.85/1.88 thf(func_def_96, type, refine1214991692od_b_b: refine2031285398od_b_b > product_prod_b_b > $o).
% 3.85/1.88 thf(func_def_97, type, refine983493746t_unit: refine787176636t_unit > product_unit > $o).
% 3.85/1.88 thf(func_def_98, type, refine1312857699nres_a: refine424419629nres_a > a > $o).
% 3.85/1.88 thf(func_def_99, type, refine1312857700nres_b: refine432681134nres_b > b > $o).
% 3.85/1.88 thf(func_def_100, type, refine579265252t_unit: refine787176636t_unit > $o).
% 3.85/1.88 thf(func_def_101, type, refine412683989fail_a: refine424419629nres_a > $o).
% 3.85/1.88 thf(func_def_102, type, refine412683990fail_b: refine432681134nres_b > $o).
% 3.85/1.88 thf(func_def_103, type, refine1607584204t_unit: refine787176636t_unit).
% 3.85/1.88 thf(func_def_104, type, refine464223677AILi_a: refine424419629nres_a).
% 3.85/1.88 thf(func_def_105, type, refine464223678AILi_b: refine432681134nres_b).
% 3.85/1.88 thf(func_def_106, type, refine622451633od_a_a: set_Product_prod_a_a > refine671810262od_a_a).
% 3.85/1.88 thf(func_def_107, type, refine630713138od_a_b: set_Product_prod_a_b > refine1811374551od_a_b).
% 3.85/1.88 thf(func_def_108, type, refine1450221040od_b_a: set_Product_prod_b_a > refine891721109od_b_a).
% 3.85/1.88 thf(func_def_109, type, refine1458482545od_b_b: set_Product_prod_b_b > refine2031285398od_b_b).
% 3.85/1.88 thf(func_def_110, type, refine1777164439t_unit: set_Product_unit > refine787176636t_unit).
% 3.85/1.88 thf(func_def_111, type, refine1198353288_RES_a: set_a > refine424419629nres_a).
% 3.85/1.88 thf(func_def_112, type, refine1198353289_RES_b: set_b > refine432681134nres_b).
% 3.85/1.88 thf(func_def_113, type, refine1208325748t_unit: refine787176636t_unit > set_Product_unit).
% 3.85/1.88 thf(func_def_114, type, refine1822134885_RES_a: refine424419629nres_a > set_a).
% 3.85/1.88 thf(func_def_115, type, refine1822134886_RES_b: refine432681134nres_b > set_b).
% 3.85/1.88 thf(func_def_116, type, domain799550107t_unit: set_Pr1628433942t_unit > set_a).
% 3.85/1.88 thf(func_def_117, type, domain_a_a: set_Product_prod_a_a > set_a).
% 3.85/1.88 thf(func_def_118, type, domain_a_b: set_Product_prod_a_b > set_a).
% 3.85/1.88 thf(func_def_119, type, domain918802906t_unit: set_Pr1707992533t_unit > set_b).
% 3.85/1.88 thf(func_def_120, type, domain_b_a: set_Product_prod_b_a > set_b).
% 3.85/1.88 thf(func_def_121, type, domain_b_b: set_Product_prod_b_b > set_b).
% 3.85/1.88 thf(func_def_122, type, image_a_a: set_Product_prod_a_a > set_a > set_a).
% 3.85/1.88 thf(func_def_123, type, image_a_b: set_Product_prod_a_b > set_a > set_b).
% 3.85/1.88 thf(func_def_124, type, image_b_a: set_Product_prod_b_a > set_b > set_a).
% 3.85/1.88 thf(func_def_125, type, image_b_b: set_Product_prod_b_b > set_b > set_b).
% 3.85/1.88 thf(func_def_126, type, collec645855634od_a_a: (product_prod_a_a > $o) > set_Product_prod_a_a).
% 3.85/1.88 thf(func_def_127, type, collec654117139od_a_b: (product_prod_a_b > $o) > set_Product_prod_a_b).
% 3.85/1.88 thf(func_def_128, type, collec1473625041od_b_a: (product_prod_b_a > $o) > set_Product_prod_b_a).
% 3.85/1.88 thf(func_def_129, type, collec1481886546od_b_b: (product_prod_b_b > $o) > set_Product_prod_b_b).
% 3.85/1.88 thf(func_def_130, type, collect_Product_unit: (product_unit > $o) > set_Product_unit).
% 3.85/1.88 thf(func_def_131, type, collect_a: (a > $o) > set_a).
% 3.85/1.88 thf(func_def_132, type, collect_b: (b > $o) > set_b).
% 3.85/1.88 thf(func_def_133, type, member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o).
% 3.85/1.88 thf(func_def_134, type, member458171089od_a_b: product_prod_a_b > set_Product_prod_a_b > $o).
% 3.85/1.88 thf(func_def_135, type, member1277678991od_b_a: product_prod_b_a > set_Product_prod_b_a > $o).
% 3.85/1.88 thf(func_def_136, type, member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o).
% 3.85/1.88 thf(func_def_137, type, member_Product_unit: product_unit > set_Product_unit > $o).
% 3.85/1.88 thf(func_def_138, type, member_a: a > set_a > $o).
% 3.85/1.88 thf(func_def_139, type, member_b: b > set_b > $o).
% 3.85/1.88 thf(func_def_140, type, phi: a > $o).
% 3.85/1.88 thf(func_def_141, type, f: a > refine432681134nres_b).
% 3.85/1.88 thf(func_def_142, type, m: refine432681134nres_b).
% 3.85/1.88 thf(func_def_143, type, x: a).
% 3.85/1.88 thf(func_def_157, type, sK0: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_158, type, sK1: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_159, type, sK2: (a > $o) > set_a > a).
% 3.85/1.88 thf(func_def_160, type, sK3: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_161, type, sK4: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_162, type, sK5: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_163, type, sK6: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_164, type, sK7: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_165, type, sK8: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_166, type, sK9: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_167, type, sK10: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_168, type, sK11: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_169, type, sK12: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_170, type, sK13: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_171, type, sK14: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_172, type, sK15: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_173, type, sK16: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_174, type, sK17: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_175, type, sK18: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_176, type, sK19: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_177, type, sK20: (refine432681134nres_b > refine432681134nres_b) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_178, type, sK21: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_179, type, sK22: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_180, type, sK23: (a > $o) > (a > $o) > a).
% 3.85/1.88 thf(func_def_181, type, sK24: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_182, type, sK25: (refine424419629nres_a > refine432681134nres_b) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_183, type, sK26: (a > $o) > (a > $o) > a).
% 3.85/1.88 thf(func_def_184, type, sK27: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_185, type, sK28: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.85/1.88 thf(func_def_186, type, sK29: (a > $o) > (a > $o) > a).
% 3.85/1.88 thf(func_def_187, type, sK30: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_188, type, sK31: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_189, type, sK32: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_190, type, sK33: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_191, type, sK34: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_192, type, sK35: (refine432681134nres_b > refine424419629nres_a) > refine432681134nres_b).
% 3.85/1.88 thf(func_def_194, type, ph37: !>[X0: $tType]:(X0)).
% 3.85/1.88 thf(f1246,plain,(
% 3.85/1.88 $false),
% 3.85/1.88 inference(subsumption_resolution,[status(thm)],[f1244,f1180])).
% 3.85/1.88 thf(f1180,plain,(
% 3.85/1.88 ((phi @ x) = $true)),
% 3.85/1.88 inference(cnf_transformation,[status(thm)],[f391])).
% 3.85/1.88 thf(f391,plain,(
% 3.85/1.88 ((phi @ x) = $true)),
% 3.85/1.88 inference(fool_elimination,[status(thm)],[f390])).
% 3.85/1.88 thf(f390,plain,(
% 3.85/1.88 (phi @ x)),
% 3.85/1.88 inference(rectify,[status(thm)],[f1])).
% 3.85/1.88 thf(f1,axiom,(
% 3.85/1.88 (phi @ x)),
% 3.85/1.88 file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',fact_0_assms_I1_J)).
% 3.85/1.88 thf(f1244,plain,(
% 3.85/1.88 ((phi @ x) != $true)),
% 3.85/1.88 inference(trivial_inequality_removal,[status(thm)],[f1238])).
% 3.85/1.88 thf(f1238,plain,(
% 3.85/1.88 ($true != $true) | ((phi @ x) != $true)),
% 3.85/1.88 inference(superposition,[status(thm)],[f1233,f1154])).
% 3.85/1.88 thf(f1154,plain,(
% 3.85/1.88 ((ord_le527798542nres_b @ m @ (f @ x)) = $true)),
% 3.85/1.88 inference(cnf_transformation,[status(thm)],[f771])).
% 3.85/1.88 thf(f771,plain,(
% 3.85/1.88 ((ord_le527798542nres_b @ m @ (f @ x)) = $true)),
% 3.85/1.88 inference(fool_elimination,[status(thm)],[f770])).
% 3.85/1.88 thf(f770,plain,(
% 3.85/1.88 (ord_le527798542nres_b @ m @ (f @ x))),
% 3.85/1.88 inference(rectify,[status(thm)],[f2])).
% 3.85/1.88 thf(f2,axiom,(
% 3.85/1.88 (ord_le527798542nres_b @ m @ (f @ x))),
% 3.85/1.88 file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',fact_1_assms_I2_J)).
% 3.85/1.88 thf(f1233,plain,(
% 3.85/1.88 ( ! [X0 : a] : (($true != (ord_le527798542nres_b @ m @ (f @ X0))) | ($true != (phi @ X0))) )),
% 3.85/1.88 inference(superposition,[status(thm)],[f1226,f1117])).
% 3.85/1.88 thf(f1117,plain,(
% 3.85/1.88 ( ! [X0 : a > $o,X1 : a] : (((X0 @ X1) = (member_a @ X1 @ (collect_a @ X0)))) )),
% 3.85/1.88 inference(cnf_transformation,[status(thm)],[f979])).
% 3.85/1.88 thf(f979,plain,(
% 3.85/1.88 ! [X0 : a > $o,X1 : a] : ((X0 @ X1) = (member_a @ X1 @ (collect_a @ X0)))),
% 3.85/1.88 inference(rectify,[status(thm)],[f108])).
% 3.85/1.88 thf(f108,axiom,(
% 3.85/1.88 ! [X34 : a > $o,X24 : a] : ((member_a @ X24 @ (collect_a @ X34)) = (X34 @ X24))),
% 3.85/1.88 file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',fact_107_mem__Collect__eq)).
% 3.85/1.88 thf(f1226,plain,(
% 3.85/1.88 ( ! [X0 : a] : (($true != (member_a @ X0 @ (collect_a @ phi))) | ($true != (ord_le527798542nres_b @ m @ (f @ X0)))) )),
% 3.85/1.88 inference(trivial_inequality_removal,[status(thm)],[f1219])).
% 3.85/1.88 thf(f1219,plain,(
% 3.85/1.88 ( ! [X0 : a] : (($true != (member_a @ X0 @ (collect_a @ phi))) | ($true != (ord_le527798542nres_b @ m @ (f @ X0))) | ($true != $true)) )),
% 3.85/1.88 inference(superposition,[status(thm)],[f1159,f1112])).
% 3.85/1.88 thf(f1112,plain,(
% 3.85/1.88 ( ! [X2 : refine432681134nres_b,X3 : a > refine432681134nres_b,X0 : a,X1 : set_a] : (($true = (ord_le527798542nres_b @ X2 @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ X1) @ X3))) | ($true != (ord_le527798542nres_b @ X2 @ (X3 @ X0))) | ($true != (member_a @ X0 @ X1))) )),
% 3.85/1.88 inference(cnf_transformation,[status(thm)],[f1029])).
% 3.85/1.88 thf(f1029,plain,(
% 3.85/1.88 ! [X0 : a,X1 : set_a,X2 : refine432681134nres_b,X3 : a > refine432681134nres_b] : (($true != (ord_le527798542nres_b @ X2 @ (X3 @ X0))) | ($true = (ord_le527798542nres_b @ X2 @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ X1) @ X3))) | ($true != (member_a @ X0 @ X1)))),
% 3.85/1.88 inference(flattening,[status(thm)],[f1028])).
% 3.85/1.88 thf(f1028,plain,(
% 3.85/1.88 ! [X0 : a,X1 : set_a,X2 : refine432681134nres_b,X3 : a > refine432681134nres_b] : ((($true = (ord_le527798542nres_b @ X2 @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ X1) @ X3))) | ($true != (ord_le527798542nres_b @ X2 @ (X3 @ X0)))) | ($true != (member_a @ X0 @ X1)))),
% 3.85/1.88 inference(ennf_transformation,[status(thm)],[f609])).
% 3.85/1.88 thf(f609,plain,(
% 3.85/1.88 ! [X0 : a,X1 : set_a,X2 : refine432681134nres_b,X3 : a > refine432681134nres_b] : (($true = (member_a @ X0 @ X1)) => (($true = (ord_le527798542nres_b @ X2 @ (X3 @ X0))) => ($true = (ord_le527798542nres_b @ X2 @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ X1) @ X3)))))),
% 3.85/1.88 inference(fool_elimination,[status(thm)],[f608])).
% 3.85/1.88 thf(f608,plain,(
% 3.85/1.88 ! [X0 : a,X1 : set_a,X2 : refine432681134nres_b,X3 : a > refine432681134nres_b] : ((member_a @ X0 @ X1) => ((ord_le527798542nres_b @ X2 @ (X3 @ X0)) => (ord_le527798542nres_b @ X2 @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ X1) @ X3))))),
% 3.85/1.88 inference(rectify,[status(thm)],[f36])).
% 3.85/1.88 thf(f36,axiom,(
% 3.85/1.88 ! [X11 : a,X0 : set_a,X15 : refine432681134nres_b,X18 : a > refine432681134nres_b] : ((member_a @ X11 @ X0) => ((ord_le527798542nres_b @ X15 @ (X18 @ X11)) => (ord_le527798542nres_b @ X15 @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ X0) @ X18))))),
% 3.85/1.88 file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',fact_35_RES__bind__choose)).
% 3.85/1.88 thf(f1159,plain,(
% 3.85/1.88 ((ord_le527798542nres_b @ m @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ (collect_a @ phi)) @ f)) != $true)),
% 3.85/1.88 inference(cnf_transformation,[status(thm)],[f977])).
% 3.85/1.88 thf(f977,plain,(
% 3.85/1.88 ((ord_le527798542nres_b @ m @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ (collect_a @ phi)) @ f)) != $true)),
% 3.85/1.88 inference(flattening,[status(thm)],[f639])).
% 3.85/1.88 thf(f639,plain,(
% 3.85/1.88 ~((ord_le527798542nres_b @ m @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ (collect_a @ phi)) @ f)) = $true)),
% 3.85/1.88 inference(fool_elimination,[status(thm)],[f638])).
% 3.85/1.88 thf(f638,plain,(
% 3.85/1.88 ~(ord_le527798542nres_b @ m @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ (collect_a @ phi)) @ f))),
% 3.85/1.88 inference(rectify,[status(thm)],[f360])).
% 3.85/1.88 thf(f360,negated_conjecture,(
% 3.85/1.88 ~(ord_le527798542nres_b @ m @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ (collect_a @ phi)) @ f))),
% 3.85/1.88 inference(negated_conjecture,[status(cth)],[f359])).
% 3.85/1.88 thf(f359,conjecture,(
% 3.85/1.88 (ord_le527798542nres_b @ m @ (refine436832839nd_a_b @ (refine1198353288_RES_a @ (collect_a @ phi)) @ f))),
% 3.85/1.88 file('/export/starexec/sandbox/tmp/tmp.QdJ518ZbBB/DTF2THF_19091.p',conj_0)).
% 3.85/1.88 % SZS output end Proof for DTF2THF_19091
% 3.85/1.88 % (19202)------------------------------
% 3.85/1.88 % (19202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.85/1.88 % (19202)Termination reason: Refutation
% 3.85/1.88
% 3.85/1.88 % (19202)Memory used [KB]: 6780
% 3.85/1.88 % (19202)Time elapsed: 0.044 s
% 3.85/1.88 % (19202)Instructions burned: 73 (million)
% 3.85/1.88 % (19202)------------------------------
% 3.85/1.88 % (19202)------------------------------
% 3.85/1.88 % (19196)Success in time 0.094 s
%------------------------------------------------------------------------------