%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP071^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 08:55:19 AM UTC 2026
% Result : Theorem 2.87s 1.64s
% Output : Refutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 91 ( 9 ~; 2 |; 0 &; 78 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 232 ( 229 usr; 5 con; 0-6 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1070816379Tree_a: $tType ).
thf(type_def_6,type,
produc143150363Tree_a: $tType ).
thf(type_def_7,type,
tree_a: $tType ).
thf(type_def_9,type,
produc1689254567Tree_a: $tType ).
thf(type_def_10,type,
product_prod_a_a: $tType ).
thf(type_def_11,type,
a: $tType ).
thf(type_def_12,type,
set_Product_prod_a_a: $tType ).
thf(type_def_13,type,
produc981471411ee_a_a: $tType ).
thf(type_def_14,type,
set_Pr921883667ee_a_a: $tType ).
thf(type_def_15,type,
set_a: $tType ).
thf(type_def_16,type,
list_a: $tType ).
thf(type_def_17,type,
multiset_a: $tType ).
thf(func_def_0,type,
produc1689254567Tree_a: $tType ).
thf(func_def_1,type,
set_Pr1070816379Tree_a: $tType ).
thf(func_def_2,type,
set_Pr921883667ee_a_a: $tType ).
thf(func_def_3,type,
produc143150363Tree_a: $tType ).
thf(func_def_4,type,
produc981471411ee_a_a: $tType ).
thf(func_def_5,type,
set_Product_prod_a_a: $tType ).
thf(func_def_6,type,
product_prod_a_a: $tType ).
thf(func_def_7,type,
multiset_a: $tType ).
thf(func_def_8,type,
list_a: $tType ).
thf(func_def_9,type,
tree_a: $tType ).
thf(func_def_10,type,
set_a: $tType ).
thf(func_def_11,type,
a: $tType ).
thf(func_def_12,type,
bNF_cs1091007358Tree_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > tree_a ) > ( produc1689254567Tree_a > tree_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > ( produc143150363Tree_a > produc1689254567Tree_a ) > $o ).
thf(func_def_13,type,
bNF_cs739966834Tree_a: set_Pr1070816379Tree_a > ( product_prod_a_a > a ) > ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > product_prod_a_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > $o ).
thf(func_def_14,type,
bNF_cs1095035134ee_a_a: set_Product_prod_a_a > ( produc143150363Tree_a > tree_a ) > ( produc981471411ee_a_a > tree_a ) > ( product_prod_a_a > produc143150363Tree_a ) > ( product_prod_a_a > produc981471411ee_a_a ) > $o ).
thf(func_def_15,type,
bNF_fstOp_Tree_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_16,type,
bNF_fs1579355852Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_17,type,
bNF_fstOp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > product_prod_a_a > produc143150363Tree_a ).
thf(func_def_18,type,
bNF_fstOp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > product_prod_a_a ).
thf(func_def_19,type,
bNF_pi1059296282ee_a_a: ( tree_a > tree_a > $o ) > ( tree_a > a > $o ) > tree_a > a > tree_a ).
thf(func_def_20,type,
bNF_pi1407460238_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > tree_a > a > a ).
thf(func_def_21,type,
bNF_pi1536086554Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > a > tree_a > tree_a ).
thf(func_def_22,type,
bNF_pi207687054Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > a > tree_a > a ).
thf(func_def_23,type,
bNF_sn210385162ee_a_a: ( tree_a > tree_a > $o ) > ( tree_a > a > $o ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_24,type,
bNF_sn687175434Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > produc143150363Tree_a > produc1689254567Tree_a ).
thf(func_def_25,type,
bNF_sndOp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > product_prod_a_a > produc981471411ee_a_a ).
thf(func_def_26,type,
bNF_sndOp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_27,type,
bNF_Gr2005589581ee_a_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > tree_a ) > ( produc143150363Tree_a > a ) > set_Pr921883667ee_a_a ).
thf(func_def_28,type,
bNF_Gr2042500789Tree_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > tree_a ) > set_Pr1070816379Tree_a ).
thf(func_def_29,type,
bNF_Gr614734384ee_a_a: set_a > ( a > tree_a ) > ( a > a ) > set_Pr921883667ee_a_a ).
thf(func_def_30,type,
bNF_Gr651645592Tree_a: set_a > ( a > a ) > ( a > tree_a ) > set_Pr1070816379Tree_a ).
thf(func_def_31,type,
comp_T59512783Tree_a: ( tree_a > tree_a ) > ( tree_a > tree_a ) > tree_a > tree_a ).
thf(func_def_32,type,
comp_T1074491280ee_a_a: ( tree_a > tree_a ) > ( produc981471411ee_a_a > tree_a ) > produc981471411ee_a_a > tree_a ).
thf(func_def_33,type,
comp_T236170232Tree_a: ( tree_a > tree_a ) > ( produc143150363Tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_34,type,
comp_P1066590417ee_a_a: ( produc981471411ee_a_a > tree_a ) > ( produc981471411ee_a_a > produc981471411ee_a_a ) > produc981471411ee_a_a > tree_a ).
thf(func_def_35,type,
comp_P228269369Tree_a: ( produc981471411ee_a_a > tree_a ) > ( produc143150363Tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_36,type,
comp_P342079405Tree_a: ( produc981471411ee_a_a > a ) > ( produc143150363Tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > a ).
thf(func_def_37,type,
comp_P1663859001ee_a_a: ( produc143150363Tree_a > tree_a ) > ( produc981471411ee_a_a > produc143150363Tree_a ) > produc981471411ee_a_a > tree_a ).
thf(func_def_38,type,
comp_P825537953Tree_a: ( produc143150363Tree_a > tree_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_39,type,
comp_P1103783853ee_a_a: ( produc143150363Tree_a > a ) > ( produc981471411ee_a_a > produc143150363Tree_a ) > produc981471411ee_a_a > a ).
thf(func_def_40,type,
comp_P265462805Tree_a: ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > produc143150363Tree_a > a ).
thf(func_def_41,type,
comp_a608639864Tree_a: ( a > a ) > ( produc143150363Tree_a > a ) > produc143150363Tree_a > a ).
thf(func_def_42,type,
heapIm970322378pify_a: tree_a > tree_a ).
thf(func_def_43,type,
heapIm229596386mpty_a: tree_a > $o ).
thf(func_def_44,type,
heapIm915766629_max_a: tree_a > produc143150363Tree_a ).
thf(func_def_45,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(func_def_46,type,
heapIm837449470Leaf_a: tree_a > produc143150363Tree_a ).
thf(func_def_47,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(func_def_48,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(func_def_49,type,
heap_Tree_a_a: tree_a > ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > tree_a ) > ( tree_a > produc143150363Tree_a ) > $o ).
thf(func_def_50,type,
heap_axioms_Tree_a_a: ( tree_a > $o ) > ( list_a > tree_a ) > ( tree_a > multiset_a ) > ( tree_a > tree_a ) > ( tree_a > produc143150363Tree_a ) > $o ).
thf(func_def_51,type,
e_a: tree_a ).
thf(func_def_52,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(func_def_53,type,
in_tree_a: a > tree_a > $o ).
thf(func_def_54,type,
is_heap_a: tree_a > $o ).
thf(func_def_55,type,
multiset_a2: tree_a > multiset_a ).
thf(func_def_56,type,
val_a: tree_a > a ).
thf(func_def_57,type,
if_Pro1144176865Tree_a: $o > produc143150363Tree_a > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_58,type,
lattic146396397_Max_a: set_a > a ).
thf(func_def_59,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(func_def_60,type,
set_mset_a: multiset_a > set_a ).
thf(func_def_61,type,
ord_le1748873858_a_a_o: ( tree_a > a > $o ) > ( tree_a > a > $o ) > $o ).
thf(func_def_62,type,
ord_le1601593986ee_a_o: ( produc143150363Tree_a > $o ) > ( produc143150363Tree_a > $o ) > $o ).
thf(func_def_63,type,
ord_le1327026842ee_a_o: ( a > tree_a > $o ) > ( a > tree_a > $o ) > $o ).
thf(func_def_64,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_65,type,
ord_le864074675ee_a_a: set_Pr921883667ee_a_a > set_Pr921883667ee_a_a > $o ).
thf(func_def_66,type,
ord_le1013007387Tree_a: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > $o ).
thf(func_def_67,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_68,type,
ord_less_eq_a: a > a > $o ).
thf(func_def_69,type,
order_Greatest_a: ( a > $o ) > a ).
thf(func_def_70,type,
produc649172771ee_a_a: tree_a > a > produc981471411ee_a_a ).
thf(func_def_71,type,
produc686083979Tree_a: a > tree_a > produc143150363Tree_a ).
thf(func_def_72,type,
produc569472578ee_a_a: ( tree_a > tree_a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_73,type,
produc606383786Tree_a: ( tree_a > a ) > produc1689254567Tree_a > produc143150363Tree_a ).
thf(func_def_74,type,
produc159857078_a_a_a: ( tree_a > a ) > produc981471411ee_a_a > product_prod_a_a ).
thf(func_def_75,type,
produc1046262850Tree_a: ( a > tree_a ) > produc143150363Tree_a > produc1689254567Tree_a ).
thf(func_def_76,type,
produc1070656334ee_a_a: ( a > tree_a ) > product_prod_a_a > produc981471411ee_a_a ).
thf(func_def_77,type,
produc1107567542Tree_a: ( a > a ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_78,type,
produc819961216ee_a_a: ( tree_a > tree_a ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_79,type,
produc856872424Tree_a: ( tree_a > a ) > produc1689254567Tree_a > produc981471411ee_a_a ).
thf(func_def_80,type,
produc21534708_a_a_a: ( tree_a > a ) > produc143150363Tree_a > product_prod_a_a ).
thf(func_def_81,type,
produc1296751488Tree_a: ( a > tree_a ) > produc981471411ee_a_a > produc1689254567Tree_a ).
thf(func_def_82,type,
produc932333964ee_a_a: ( a > tree_a ) > product_prod_a_a > produc143150363Tree_a ).
thf(func_def_83,type,
produc969245172Tree_a: ( a > a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_84,type,
produc1205515265_a_a_o: ( produc981471411ee_a_a > $o ) > tree_a > a > $o ).
thf(func_def_85,type,
produc1808426884Tree_a: ( produc981471411ee_a_a > produc143150363Tree_a ) > tree_a > a > produc143150363Tree_a ).
thf(func_def_86,type,
produc1291432345ee_a_o: ( produc143150363Tree_a > $o ) > a > tree_a > $o ).
thf(func_def_87,type,
produc740705523Tree_a: ( produc143150363Tree_a > tree_a ) > a > tree_a > tree_a ).
thf(func_def_88,type,
produc623433908ee_a_a: ( produc143150363Tree_a > produc981471411ee_a_a ) > a > tree_a > produc981471411ee_a_a ).
thf(func_def_89,type,
produc126329485Tree_a: ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > produc143150363Tree_a ).
thf(func_def_90,type,
produc1405823650ee_a_o: ( a > tree_a > $o ) > produc143150363Tree_a > $o ).
thf(func_def_91,type,
produc534868220Tree_a: ( a > tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_92,type,
produc1088820157ee_a_a: ( a > tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > produc981471411ee_a_a ).
thf(func_def_93,type,
produc1587316832_a_a_o: ( tree_a > a > $o ) > produc981471411ee_a_a > $o ).
thf(func_def_94,type,
produc433477818Tree_a: ( tree_a > a > tree_a ) > produc981471411ee_a_a > tree_a ).
thf(func_def_95,type,
produc1207340411ee_a_a: ( tree_a > a > produc981471411ee_a_a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
thf(func_def_96,type,
produc369019363Tree_a: ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > produc143150363Tree_a ).
thf(func_def_97,type,
produc951236931Tree_a: ( tree_a > a > set_Pr1070816379Tree_a ) > produc981471411ee_a_a > set_Pr1070816379Tree_a ).
thf(func_def_98,type,
produc136688934_set_a: ( tree_a > a > set_a ) > produc981471411ee_a_a > set_a ).
thf(func_def_99,type,
produc1673233912ee_a_o: ( a > tree_a > $o ) > produc143150363Tree_a > $o ).
thf(func_def_100,type,
produc873356882Tree_a: ( a > tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
thf(func_def_101,type,
produc1331510035ee_a_a: ( a > tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > produc981471411ee_a_a ).
thf(func_def_102,type,
produc493188987Tree_a: ( a > tree_a > produc143150363Tree_a ) > produc143150363Tree_a > produc143150363Tree_a ).
thf(func_def_103,type,
produc802621147Tree_a: ( a > tree_a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > set_Pr1070816379Tree_a ).
thf(func_def_104,type,
produc1902270_set_a: ( a > tree_a > set_a ) > produc143150363Tree_a > set_a ).
thf(func_def_105,type,
produc950721886ee_a_a: ( a > tree_a > a ) > produc143150363Tree_a > a ).
thf(func_def_106,type,
produc1206152067Tree_a: produc1689254567Tree_a > tree_a ).
thf(func_def_107,type,
product_fst_Tree_a_a: produc981471411ee_a_a > tree_a ).
thf(func_def_108,type,
product_fst_a_Tree_a: produc143150363Tree_a > a ).
thf(func_def_109,type,
product_snd_Tree_a_a: produc981471411ee_a_a > a ).
thf(func_def_110,type,
product_snd_a_Tree_a: produc143150363Tree_a > tree_a ).
thf(func_def_111,type,
product_snd_a_a: product_prod_a_a > a ).
thf(func_def_112,type,
produc1478296771ee_a_a: produc981471411ee_a_a > produc143150363Tree_a ).
thf(func_def_113,type,
produc1515207979Tree_a: produc143150363Tree_a > produc981471411ee_a_a ).
thf(func_def_114,type,
relcom439193229Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > a > tree_a > $o ).
thf(func_def_115,type,
relcompp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > a > a > $o ).
thf(func_def_116,type,
relcompp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > a > tree_a > $o ).
thf(func_def_117,type,
collec1324690334ee_a_a: ( produc981471411ee_a_a > $o ) > set_Pr921883667ee_a_a ).
thf(func_def_118,type,
collec486369286Tree_a: ( produc143150363Tree_a > $o ) > set_Pr1070816379Tree_a ).
thf(func_def_119,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(func_def_120,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_121,type,
member1092636252ee_a_a: produc981471411ee_a_a > set_Pr921883667ee_a_a > $o ).
thf(func_def_122,type,
member254315204Tree_a: produc143150363Tree_a > set_Pr1070816379Tree_a > $o ).
thf(func_def_123,type,
member_a: a > set_a > $o ).
thf(func_def_124,type,
t: tree_a ).
thf(func_def_125,type,
v: a ).
thf(func_def_142,type,
sP0: a > a > a > $o ).
thf(func_def_143,type,
sP1: a > a > a > $o ).
thf(func_def_144,type,
sP2: a > a > a > $o ).
thf(func_def_145,type,
sP3: ( tree_a > $o ) > $o ).
thf(func_def_146,type,
sP4: ( tree_a > $o ) > $o ).
thf(func_def_147,type,
sP5: ( tree_a > $o ) > $o ).
thf(func_def_148,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_149,type,
sK7: ( a > a > $o ) > a ).
thf(func_def_150,type,
sK8: ( a > a > $o ) > a ).
thf(func_def_151,type,
sK9: ( a > a > $o ) > a ).
thf(func_def_152,type,
sK10: produc143150363Tree_a > a ).
thf(func_def_153,type,
sK11: produc143150363Tree_a > tree_a ).
thf(func_def_154,type,
sK12: tree_a > a ).
thf(func_def_155,type,
sK13: tree_a > tree_a ).
thf(func_def_156,type,
sK14: tree_a > a ).
thf(func_def_157,type,
sK15: tree_a > tree_a ).
thf(func_def_158,type,
sK16: tree_a > tree_a ).
thf(func_def_159,type,
sK17: tree_a > a ).
thf(func_def_160,type,
sK18: tree_a > tree_a ).
thf(func_def_161,type,
sK19: tree_a > a ).
thf(func_def_162,type,
sK20: tree_a > tree_a ).
thf(func_def_163,type,
sK21: tree_a > tree_a ).
thf(func_def_164,type,
sK22: tree_a > a ).
thf(func_def_165,type,
sK23: tree_a > a ).
thf(func_def_166,type,
sK24: tree_a > a ).
thf(func_def_167,type,
sK25: tree_a > a ).
thf(func_def_168,type,
sK26: tree_a > tree_a ).
thf(func_def_169,type,
sK27: tree_a > a ).
thf(func_def_170,type,
sK28: tree_a > tree_a ).
thf(func_def_171,type,
sK29: tree_a > tree_a ).
thf(func_def_172,type,
sK30: tree_a > tree_a ).
thf(func_def_173,type,
sK31: tree_a > tree_a ).
thf(func_def_174,type,
sK32: tree_a > a ).
thf(func_def_175,type,
sK33: tree_a > tree_a ).
thf(func_def_176,type,
sK34: tree_a > a ).
thf(func_def_177,type,
sK35: ( tree_a > $o ) > a ).
thf(func_def_178,type,
sK36: ( tree_a > $o ) > tree_a ).
thf(func_def_179,type,
sK37: ( tree_a > $o ) > tree_a ).
thf(func_def_180,type,
sK38: tree_a > a ).
thf(func_def_181,type,
sK39: tree_a > a ).
thf(func_def_182,type,
sK40: tree_a > tree_a ).
thf(func_def_183,type,
sK41: tree_a > tree_a ).
thf(func_def_184,type,
sK42: tree_a > tree_a ).
thf(func_def_185,type,
sK43: tree_a > a ).
thf(func_def_186,type,
sK44: tree_a > tree_a ).
thf(func_def_187,type,
sK45: tree_a > tree_a ).
thf(func_def_188,type,
sK46: tree_a > tree_a ).
thf(func_def_189,type,
sK47: tree_a > a ).
thf(func_def_190,type,
sK48: tree_a > a ).
thf(func_def_191,type,
sK49: tree_a > tree_a ).
thf(func_def_192,type,
sK50: tree_a > a ).
thf(func_def_193,type,
sK51: tree_a > tree_a ).
thf(func_def_194,type,
sK52: tree_a > a ).
thf(func_def_195,type,
sK53: tree_a > a ).
thf(func_def_196,type,
sK54: ( tree_a > a > $o ) > tree_a ).
thf(func_def_197,type,
sK55: ( tree_a > a > $o ) > a ).
thf(func_def_198,type,
sK56: produc143150363Tree_a > tree_a > a ).
thf(func_def_199,type,
sK57: produc143150363Tree_a > a > tree_a ).
thf(func_def_200,type,
sK58: ( a > a ) > a ).
thf(func_def_201,type,
sK59: ( a > a ) > a ).
thf(func_def_202,type,
sK60: tree_a > a ).
thf(func_def_203,type,
sK61: tree_a > tree_a ).
thf(func_def_204,type,
sK62: tree_a > tree_a ).
thf(func_def_205,type,
sK63: ( a > a ) > a ).
thf(func_def_206,type,
sK64: ( a > a ) > a ).
thf(func_def_207,type,
sK65: ( a > a ) > a ).
thf(func_def_208,type,
sK66: ( a > a ) > a ).
thf(func_def_209,type,
sK67: ( tree_a > $o ) > a ).
thf(func_def_210,type,
sK68: ( tree_a > $o ) > tree_a ).
thf(func_def_211,type,
sK69: ( tree_a > $o ) > tree_a ).
thf(func_def_212,type,
sK70: ( tree_a > $o ) > tree_a ).
thf(func_def_213,type,
sK71: ( tree_a > $o ) > a ).
thf(func_def_214,type,
sK72: ( tree_a > $o ) > a ).
thf(func_def_215,type,
sK73: ( tree_a > $o ) > tree_a ).
thf(func_def_216,type,
sK74: ( tree_a > $o ) > a ).
thf(func_def_217,type,
sK75: ( tree_a > $o ) > tree_a ).
thf(func_def_218,type,
sK76: ( tree_a > $o ) > tree_a ).
thf(func_def_219,type,
sK77: ( tree_a > $o ) > tree_a ).
thf(func_def_220,type,
sK78: ( tree_a > $o ) > a ).
thf(func_def_221,type,
sK79: ( tree_a > $o ) > a ).
thf(func_def_222,type,
sK80: ( tree_a > $o ) > tree_a ).
thf(func_def_223,type,
sK81: ( tree_a > $o ) > tree_a ).
thf(func_def_224,type,
sK82: ( tree_a > $o ) > tree_a ).
thf(func_def_225,type,
sK83: ( tree_a > $o ) > a ).
thf(func_def_226,type,
sK84: ( tree_a > $o ) > a ).
thf(func_def_227,type,
sK85: ( tree_a > $o ) > tree_a ).
thf(func_def_228,type,
sK86: ( tree_a > $o ) > tree_a ).
thf(func_def_229,type,
sK87: ( tree_a > $o ) > a ).
thf(func_def_230,type,
sK88: ( tree_a > $o ) > a ).
thf(func_def_231,type,
sK89: ( tree_a > $o ) > a ).
thf(func_def_232,type,
sK90: ( produc143150363Tree_a > $o ) > a ).
thf(func_def_233,type,
sK91: ( produc143150363Tree_a > $o ) > tree_a ).
thf(func_def_234,type,
sK92: ( a > a ) > a ).
thf(func_def_235,type,
sK93: ( a > a ) > a ).
thf(func_def_236,type,
sK94: ( produc143150363Tree_a > $o ) > a ).
thf(func_def_237,type,
sK95: ( produc143150363Tree_a > $o ) > tree_a ).
thf(func_def_238,type,
sK96: produc143150363Tree_a > a ).
thf(func_def_239,type,
sK97: produc143150363Tree_a > tree_a ).
thf(func_def_240,type,
sK98: tree_a > tree_a ).
thf(func_def_241,type,
sK99: tree_a > tree_a ).
thf(func_def_242,type,
sK100: tree_a > a ).
thf(func_def_243,type,
sK101: tree_a > tree_a ).
thf(func_def_244,type,
sK102: tree_a > a ).
thf(func_def_245,type,
sK103: tree_a > tree_a ).
thf(func_def_246,type,
sK104: tree_a > a ).
thf(func_def_247,type,
sK105: tree_a > a ).
thf(func_def_248,type,
sK106: tree_a > tree_a ).
thf(func_def_249,type,
sK107: tree_a > a ).
thf(func_def_250,type,
sK108: tree_a > tree_a ).
thf(func_def_251,type,
sK109: tree_a > a ).
thf(func_def_252,type,
sK110: tree_a > tree_a ).
thf(func_def_253,type,
sK111: tree_a > a ).
thf(func_def_254,type,
sK112: tree_a > a ).
thf(func_def_255,type,
sK113: tree_a > tree_a ).
thf(func_def_257,type,
ph115:
!>[X0: $tType] : X0 ).
thf(f1164,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1163,f1032]) ).
thf(f1032,plain,
( ( is_heap_a @ e_a )
= $true ),
inference(cnf_transformation,[status(thm)],[f392]) ).
thf(f392,plain,
( ( is_heap_a @ e_a )
= $true ),
inference(fool_elimination,[status(thm)],[f391]) ).
thf(f391,plain,
is_heap_a @ e_a,
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
is_heap_a @ e_a,
file('/export/starexec/sandbox2/tmp/tmp.YD8GTuktd0/DTF2THF_14883.p',fact_10_is__heap_Osimps_I1_J) ).
thf(f1163,plain,
( ( is_heap_a @ e_a )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1162,f1159]) ).
thf(f1159,plain,
! [X2: tree_a,X0: a] :
( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X0 @ X2 ) )
= X2 ),
inference(equality_resolution,[status(thm)],[f1126]) ).
thf(f1126,plain,
! [X2: tree_a,X0: a,X1: tree_a] :
( ( X1 = X2 )
| ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X0 @ X2 ) )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f904]) ).
thf(f904,plain,
! [X0: a,X1: tree_a,X2: tree_a] :
( ( X1 = X2 )
| ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X0 @ X2 ) )
!= X1 ) ),
inference(ennf_transformation,[status(thm)],[f832]) ).
thf(f832,plain,
! [X0: a,X1: tree_a,X2: tree_a] :
( ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X0 @ X2 ) )
= X1 )
=> ( X1 = X2 ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,axiom,
! [X0: a,X35: tree_a,X22: tree_a] :
( ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X0 @ X22 ) )
= X35 )
=> ( X22 = X35 ) ),
file('/export/starexec/sandbox2/tmp/tmp.YD8GTuktd0/DTF2THF_14883.p',fact_31_snd__eqD) ).
thf(f1162,plain,
( ( is_heap_a @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ v @ e_a ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1133,f1064]) ).
thf(f1064,plain,
! [X0: a] :
( ( produc686083979Tree_a @ X0 @ e_a )
= ( heapIm837449470Leaf_a @ ( t_a @ X0 @ e_a @ e_a ) ) ),
inference(cnf_transformation,[status(thm)],[f822]) ).
thf(f822,plain,
! [X0: a] :
( ( produc686083979Tree_a @ X0 @ e_a )
= ( heapIm837449470Leaf_a @ ( t_a @ X0 @ e_a @ e_a ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,axiom,
! [X10: a] :
( ( heapIm837449470Leaf_a @ ( t_a @ X10 @ e_a @ e_a ) )
= ( produc686083979Tree_a @ X10 @ e_a ) ),
file('/export/starexec/sandbox2/tmp/tmp.YD8GTuktd0/DTF2THF_14883.p',fact_16_removeLeaf_Osimps_I1_J) ).
thf(f1133,plain,
( ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f819]) ).
thf(f819,plain,
( ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f438]) ).
thf(f438,plain,
( ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f437]) ).
thf(f437,plain,
~ ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ),
inference(rectify,[status(thm)],[f359]) ).
thf(f359,negated_conjecture,
~ ( is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f358,conjecture,
is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YD8GTuktd0/DTF2THF_14883.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP071^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:25:18 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.44 ---- Original DTF file ---
% 0.20/0.44 thf(spec,logic,$$dhol).
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % File : ITP071^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.44 % Domain : Interactive Theorem Proving
% 0.20/0.44 % Problem : Sledgehammer HeapImperative problem prob_933__5350368_1
% 0.20/0.44 % Version : Especial.
% 0.20/0.44 % English :
% 0.20/0.44
% 0.20/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.44 % Source : [Des21]
% 0.20/0.44 % Names : HeapImperative/prob_933__5350368_1 [Des21]
% 0.20/0.44
% 0.20/0.44 % Status : Theorem
% 0.20/0.44 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.20/0.44 % Syntax : Number of formulae : 484 ( 221 unt; 126 typ; 0 def)
% 0.20/0.44 % Number of atoms : 784 ( 429 equ; 0 cnn)
% 0.20/0.44 % Maximal formula atoms : 12 ( 2 avg)
% 0.20/0.44 % Number of connectives : 3437 ( 93 ~; 4 |; 57 &;2949 @)
% 0.20/0.44 % ( 0 <=>; 334 =>; 0 <=; 0 <~>)
% 0.20/0.44 % Maximal formula depth : 23 ( 6 avg)
% 0.20/0.44 % Number of types : 13 ( 12 usr)
% 0.20/0.44 % Number of type conns : 911 ( 911 >; 0 *; 0 +; 0 <<)
% 0.20/0.44 % Number of symbols : 117 ( 114 usr; 5 con; 0-6 aty)
% 0.20/0.44 % Number of variables : 1245 ( 189 ^;1045 !; 11 ?;1245 :)
% 0.20/0.44 % SPC : TH0_THM_EQU_NAR
% 0.20/0.44
% 0.20/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:34.981
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % Could-be-implicit typings (12)
% 0.20/0.44 thf(ty_n_t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mt__Heap__OTree_Itf__a_J_J,type,
% 0.20/0.44 produc1689254567Tree_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_J,type,
% 0.20/0.44 set_Pr1070816379Tree_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J_J,type,
% 0.20/0.44 set_Pr921883667ee_a_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
% 0.20/0.44 produc143150363Tree_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
% 0.20/0.44 produc981471411ee_a_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 0.20/0.44 set_Product_prod_a_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 0.20/0.44 product_prod_a_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
% 0.20/0.44 multiset_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.20/0.44 list_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Heap__OTree_Itf__a_J,type,
% 0.20/0.44 tree_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.20/0.44 set_a: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(ty_n_tf__a,type,
% 0.20/0.44 a: $tType ).
% 0.20/0.44
% 0.20/0.44 % Explicit typings (114)
% 0.20/0.44 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001t__Heap__OTree_Itf__a_J_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mt__Heap__OTree_Itf__a_J_J,type,
% 0.20/0.44 bNF_cs1091007358Tree_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > tree_a ) > ( produc1689254567Tree_a > tree_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > ( produc143150363Tree_a > produc1689254567Tree_a ) > $o ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001tf__a_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
% 0.20/0.44 bNF_cs739966834Tree_a: set_Pr1070816379Tree_a > ( product_prod_a_a > a ) > ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > product_prod_a_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > $o ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001t__Heap__OTree_Itf__a_J_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
% 0.20/0.44 bNF_cs1095035134ee_a_a: set_Product_prod_a_a > ( produc143150363Tree_a > tree_a ) > ( produc981471411ee_a_a > tree_a ) > ( product_prod_a_a > produc143150363Tree_a ) > ( product_prod_a_a > produc981471411ee_a_a ) > $o ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_OfstOp_001t__Heap__OTree_Itf__a_J_001tf__a_001tf__a,type,
% 0.20/0.44 bNF_fstOp_Tree_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > produc981471411ee_a_a > produc981471411ee_a_a ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_OfstOp_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
% 0.20/0.44 bNF_fs1579355852Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > produc143150363Tree_a > produc143150363Tree_a ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_OfstOp_001tf__a_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.20/0.44 bNF_fstOp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > product_prod_a_a > produc143150363Tree_a ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_OfstOp_001tf__a_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 0.20/0.44 bNF_fstOp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > product_prod_a_a ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_Opick__middlep_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.20/0.44 bNF_pi1059296282ee_a_a: ( tree_a > tree_a > $o ) > ( tree_a > a > $o ) > tree_a > a > tree_a ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_Opick__middlep_001t__Heap__OTree_Itf__a_J_001tf__a_001tf__a,type,
% 0.20/0.44 bNF_pi1407460238_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > tree_a > a > a ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_Opick__middlep_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
% 0.20/0.44 bNF_pi1536086554Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > a > tree_a > tree_a ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_Opick__middlep_001tf__a_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 0.20/0.44 bNF_pi207687054Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > a > tree_a > a ).
% 0.20/0.44
% 0.20/0.44 thf(sy_c_BNF__Def_OsndOp_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J_001tf__a,type,
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% 0.20/0.45 produc534868220Tree_a: ( a > tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Ointernal__case__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__OTree_Itf__a_J_001tf__a_001_Eo,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__OTree_Itf__a_J_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 0.20/0.45 produc433477818Tree_a: ( tree_a > a > tree_a ) > produc981471411ee_a_a > tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__OTree_Itf__a_J_001tf__a_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
% 0.20/0.45 produc1207340411ee_a_a: ( tree_a > a > produc981471411ee_a_a ) > produc981471411ee_a_a > produc981471411ee_a_a ).
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% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__OTree_Itf__a_J_001tf__a_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
% 0.20/0.45 produc369019363Tree_a: ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > produc143150363Tree_a ).
% 0.20/0.45
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__OTree_Itf__a_J_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 produc136688934_set_a: ( tree_a > a > set_a ) > produc981471411ee_a_a > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001_Eo,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
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% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_J,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 produc1902270_set_a: ( a > tree_a > set_a ) > produc143150363Tree_a > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001tf__a,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ofst_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ofst_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.20/0.45 product_fst_Tree_a_a: produc981471411ee_a_a > tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Ofst_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 0.20/0.45 product_fst_a_Tree_a: produc143150363Tree_a > a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Osnd_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 0.20/0.45 product_snd_Tree_a_a: produc981471411ee_a_a > a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 0.20/0.45 product_snd_a_Tree_a: produc143150363Tree_a > tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001tf__a,type,
% 0.20/0.45 product_snd_a_a: product_prod_a_a > a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Oswap_001t__Heap__OTree_Itf__a_J_001tf__a,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_Oprod_Oswap_001tf__a_001t__Heap__OTree_Itf__a_J,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Relation_Orelcompp_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
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% 0.20/0.45 thf(sy_c_Relation_Orelcompp_001tf__a_001t__Heap__OTree_Itf__a_J_001tf__a,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Relation_Orelcompp_001tf__a_001tf__a_001t__Heap__OTree_Itf__a_J,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_c_Set_OCollect_001tf__a,type,
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% 0.20/0.45
% 0.20/0.45 thf(sy_v_t,type,
% 0.20/0.45 t: tree_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_v____,type,
% 0.20/0.45 v: a ).
% 0.20/0.45
% 0.20/0.45 % Relevant facts (354)
% 0.20/0.45 thf(fact_0_assms_I2_J,axiom,
% 0.20/0.45 t != e_a ).
% 0.20/0.45
% 0.20/0.45 % assms(2)
% 0.20/0.45 thf(fact_1_assms_I1_J,axiom,
% 0.20/0.45 is_heap_a @ t ).
% 0.20/0.45
% 0.20/0.45 % assms(1)
% 0.20/0.45 thf(fact_2__C1_Oprems_C_I2_J,axiom,
% 0.20/0.45 ( ( t_a @ v @ e_a @ e_a )
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% 0.20/0.45
% 0.20/0.45 % "1.prems"(2)
% 0.20/0.45 thf(fact_3__C1_Oprems_C_I1_J,axiom,
% 0.20/0.45 is_heap_a @ ( t_a @ v @ e_a @ e_a ) ).
% 0.20/0.45
% 0.20/0.45 % "1.prems"(1)
% 0.20/0.45 thf(fact_4_siftDown_Ocases,axiom,
% 0.20/0.45 ! [X: tree_a] :
% 0.20/0.45 ( ( X != e_a )
% 0.20/0.45 => ( ! [V: a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ e_a @ e_a ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.20/0.45 => ~ ! [V: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.cases
% 0.20/0.45 thf(fact_5_removeLeaf_Ocases,axiom,
% 0.20/0.45 ! [X: tree_a] :
% 0.20/0.45 ( ! [V: a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ e_a @ e_a ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) )
% 0.20/0.45 => ( ! [V: a,Vd: a,Ve: tree_a,Vf: tree_a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.20/0.45 => ( X = e_a ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % removeLeaf.cases
% 0.20/0.45 thf(fact_6_removeLeaf_Oinduct,axiom,
% 0.20/0.45 ! [P: tree_a > $o,A0: tree_a] :
% 0.20/0.45 ( ! [V: a] : ( P @ ( t_a @ V @ e_a @ e_a ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 0.20/0.45 => ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 0.20/0.45 => ( P @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) ) ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 0.20/0.45 => ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 0.20/0.45 => ( P @ ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) ) ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.20/0.45 ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 0.20/0.45 => ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 0.20/0.45 => ( P @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) )
% 0.20/0.45 => ( ! [V: a,Vd: a,Ve: tree_a,Vf: tree_a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( ( P @ ( t_a @ Vd @ Ve @ Vf ) )
% 0.20/0.45 => ( ( P @ ( t_a @ Vd @ Ve @ Vf ) )
% 0.20/0.45 => ( P @ ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) ) ) )
% 0.20/0.45 => ( ( P @ e_a )
% 0.20/0.45 => ( P @ A0 ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % removeLeaf.induct
% 0.20/0.45 thf(fact_7_is__heap_Osimps_I2_J,axiom,
% 0.20/0.45 ! [V2: a] : ( is_heap_a @ ( t_a @ V2 @ e_a @ e_a ) ) ).
% 0.20/0.45
% 0.20/0.45 % is_heap.simps(2)
% 0.20/0.45 thf(fact_8_Tree_Oinject,axiom,
% 0.20/0.45 ! [X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 0.20/0.45 ( ( ( t_a @ X21 @ X22 @ X23 )
% 0.20/0.45 = ( t_a @ Y21 @ Y22 @ Y23 ) )
% 0.20/0.45 = ( ( X21 = Y21 )
% 0.20/0.45 & ( X22 = Y22 )
% 0.20/0.45 & ( X23 = Y23 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.inject
% 0.20/0.45 thf(fact_9_hs__is__empty__def,axiom,
% 0.20/0.45 ( heapIm229596386mpty_a
% 0.20/0.45 = ( ^ [T: tree_a] : ( T = e_a ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % hs_is_empty_def
% 0.20/0.45 thf(fact_10_is__heap_Osimps_I1_J,axiom,
% 0.20/0.45 is_heap_a @ e_a ).
% 0.20/0.45
% 0.20/0.45 % is_heap.simps(1)
% 0.20/0.45 thf(fact_11_Tree_Odistinct_I1_J,axiom,
% 0.20/0.45 ! [X21: a,X22: tree_a,X23: tree_a] :
% 0.20/0.45 ( e_a
% 0.20/0.45 != ( t_a @ X21 @ X22 @ X23 ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.distinct(1)
% 0.20/0.45 thf(fact_12_Tree_Oinduct,axiom,
% 0.20/0.45 ! [P: tree_a > $o,Tree: tree_a] :
% 0.20/0.45 ( ( P @ e_a )
% 0.20/0.45 => ( ! [X1: a,X2: tree_a,X3: tree_a] :
% 0.20/0.45 ( ( P @ X2 )
% 0.20/0.45 => ( ( P @ X3 )
% 0.20/0.45 => ( P @ ( t_a @ X1 @ X2 @ X3 ) ) ) )
% 0.20/0.45 => ( P @ Tree ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.induct
% 0.20/0.45 thf(fact_13_Tree_Oexhaust,axiom,
% 0.20/0.45 ! [Y: tree_a] :
% 0.20/0.45 ( ( Y != e_a )
% 0.20/0.45 => ~ ! [X212: a,X222: tree_a,X232: tree_a] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( t_a @ X212 @ X222 @ X232 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Tree.exhaust
% 0.20/0.45 thf(fact_14_is__heap_Ocases,axiom,
% 0.20/0.45 ! [X: tree_a] :
% 0.20/0.45 ( ( X != e_a )
% 0.20/0.45 => ( ! [V: a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ e_a @ e_a ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 0.20/0.45 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 0.20/0.45 => ~ ! [V: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 0.20/0.45 ( X
% 0.20/0.45 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % is_heap.cases
% 0.20/0.45 thf(fact_15_removeLeaf__val__val,axiom,
% 0.20/0.45 ! [T2: tree_a] :
% 0.20/0.45 ( ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T2 ) )
% 0.20/0.45 != e_a )
% 0.20/0.45 => ( ( T2 != e_a )
% 0.20/0.45 => ( ( val_a @ T2 )
% 0.20/0.45 = ( val_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T2 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % removeLeaf_val_val
% 0.20/0.45 thf(fact_16_removeLeaf_Osimps_I1_J,axiom,
% 0.20/0.45 ! [V2: a] :
% 0.20/0.45 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ e_a @ e_a ) )
% 0.20/0.45 = ( produc686083979Tree_a @ V2 @ e_a ) ) ).
% 0.20/0.45
% 0.20/0.45 % removeLeaf.simps(1)
% 0.20/0.45 thf(fact_17_siftDown__heap__is__heap,axiom,
% 0.20/0.45 ! [L: tree_a,R: tree_a,T2: tree_a,V2: a] :
% 0.20/0.45 ( ( is_heap_a @ L )
% 0.20/0.45 => ( ( is_heap_a @ R )
% 0.20/0.45 => ( ( T2
% 0.20/0.45 = ( t_a @ V2 @ L @ R ) )
% 0.20/0.45 => ( is_heap_a @ ( heapIm1091024090Down_a @ T2 ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown_heap_is_heap
% 0.20/0.45 thf(fact_18_siftDown_Osimps_I2_J,axiom,
% 0.20/0.45 ! [V2: a] :
% 0.20/0.45 ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ e_a @ e_a ) )
% 0.20/0.45 = ( t_a @ V2 @ e_a @ e_a ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(2)
% 0.20/0.45 thf(fact_19_val_Osimps,axiom,
% 0.20/0.45 ! [V2: a,Uu: tree_a,Uv: tree_a] :
% 0.20/0.45 ( ( val_a @ ( t_a @ V2 @ Uu @ Uv ) )
% 0.20/0.45 = V2 ) ).
% 0.20/0.45
% 0.20/0.45 % val.simps
% 0.20/0.45 thf(fact_20_siftDown_Osimps_I1_J,axiom,
% 0.20/0.45 ( ( heapIm1091024090Down_a @ e_a )
% 0.20/0.45 = e_a ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(1)
% 0.20/0.45 thf(fact_21_prod_Oinject,axiom,
% 0.20/0.45 ! [X12: a,X24: tree_a,Y1: a,Y2: tree_a] :
% 0.20/0.45 ( ( ( produc686083979Tree_a @ X12 @ X24 )
% 0.20/0.45 = ( produc686083979Tree_a @ Y1 @ Y2 ) )
% 0.20/0.45 = ( ( X12 = Y1 )
% 0.20/0.45 & ( X24 = Y2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.inject
% 0.20/0.45 thf(fact_22_prod_Oinject,axiom,
% 0.20/0.45 ! [X12: tree_a,X24: a,Y1: tree_a,Y2: a] :
% 0.20/0.45 ( ( ( produc649172771ee_a_a @ X12 @ X24 )
% 0.20/0.45 = ( produc649172771ee_a_a @ Y1 @ Y2 ) )
% 0.20/0.45 = ( ( X12 = Y1 )
% 0.20/0.45 & ( X24 = Y2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.inject
% 0.20/0.45 thf(fact_23_old_Oprod_Oinject,axiom,
% 0.20/0.45 ! [A: a,B: tree_a,A2: a,B2: tree_a] :
% 0.20/0.45 ( ( ( produc686083979Tree_a @ A @ B )
% 0.20/0.45 = ( produc686083979Tree_a @ A2 @ B2 ) )
% 0.20/0.45 = ( ( A = A2 )
% 0.20/0.45 & ( B = B2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.inject
% 0.20/0.45 thf(fact_24_old_Oprod_Oinject,axiom,
% 0.20/0.45 ! [A: tree_a,B: a,A2: tree_a,B2: a] :
% 0.20/0.45 ( ( ( produc649172771ee_a_a @ A @ B )
% 0.20/0.45 = ( produc649172771ee_a_a @ A2 @ B2 ) )
% 0.20/0.45 = ( ( A = A2 )
% 0.20/0.45 & ( B = B2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.inject
% 0.20/0.45 thf(fact_25_siftDown__in__tree,axiom,
% 0.20/0.45 ! [T2: tree_a] :
% 0.20/0.45 ( ( T2 != e_a )
% 0.20/0.45 => ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ T2 ) ) @ T2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown_in_tree
% 0.20/0.45 thf(fact_26_eq__snd__iff,axiom,
% 0.20/0.45 ! [B: a,P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( B
% 0.20/0.45 = ( product_snd_Tree_a_a @ P2 ) )
% 0.20/0.45 = ( ? [A3: tree_a] :
% 0.20/0.45 ( P2
% 0.20/0.45 = ( produc649172771ee_a_a @ A3 @ B ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % eq_snd_iff
% 0.20/0.45 thf(fact_27_eq__snd__iff,axiom,
% 0.20/0.45 ! [B: tree_a,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( B
% 0.20/0.45 = ( product_snd_a_Tree_a @ P2 ) )
% 0.20/0.45 = ( ? [A3: a] :
% 0.20/0.45 ( P2
% 0.20/0.45 = ( produc686083979Tree_a @ A3 @ B ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % eq_snd_iff
% 0.20/0.45 thf(fact_28_snd__conv,axiom,
% 0.20/0.45 ! [X12: tree_a,X24: a] :
% 0.20/0.45 ( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ X12 @ X24 ) )
% 0.20/0.45 = X24 ) ).
% 0.20/0.45
% 0.20/0.45 % snd_conv
% 0.20/0.45 thf(fact_29_snd__conv,axiom,
% 0.20/0.45 ! [X12: a,X24: tree_a] :
% 0.20/0.45 ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 0.20/0.45 = X24 ) ).
% 0.20/0.45
% 0.20/0.45 % snd_conv
% 0.20/0.45 thf(fact_30_snd__eqD,axiom,
% 0.20/0.45 ! [X: tree_a,Y: a,A: a] :
% 0.20/0.45 ( ( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ X @ Y ) )
% 0.20/0.45 = A )
% 0.20/0.45 => ( Y = A ) ) ).
% 0.20/0.45
% 0.20/0.45 % snd_eqD
% 0.20/0.45 thf(fact_31_snd__eqD,axiom,
% 0.20/0.45 ! [X: a,Y: tree_a,A: tree_a] :
% 0.20/0.45 ( ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X @ Y ) )
% 0.20/0.45 = A )
% 0.20/0.45 => ( Y = A ) ) ).
% 0.20/0.45
% 0.20/0.45 % snd_eqD
% 0.20/0.45 thf(fact_32_sndI,axiom,
% 0.20/0.45 ! [X: produc981471411ee_a_a,Y: tree_a,Z: a] :
% 0.20/0.45 ( ( X
% 0.20/0.45 = ( produc649172771ee_a_a @ Y @ Z ) )
% 0.20/0.45 => ( ( product_snd_Tree_a_a @ X )
% 0.20/0.45 = Z ) ) ).
% 0.20/0.45
% 0.20/0.45 % sndI
% 0.20/0.45 thf(fact_33_sndI,axiom,
% 0.20/0.45 ! [X: produc143150363Tree_a,Y: a,Z: tree_a] :
% 0.20/0.45 ( ( X
% 0.20/0.45 = ( produc686083979Tree_a @ Y @ Z ) )
% 0.20/0.45 => ( ( product_snd_a_Tree_a @ X )
% 0.20/0.45 = Z ) ) ).
% 0.20/0.45
% 0.20/0.45 % sndI
% 0.20/0.45 thf(fact_34_removeLeaf_Osimps_I2_J,axiom,
% 0.20/0.45 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.20/0.45 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ ( t_a @ V2 @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ e_a ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % removeLeaf.simps(2)
% 0.20/0.45 thf(fact_35_removeLeaf_Osimps_I3_J,axiom,
% 0.20/0.45 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.20/0.45 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ ( t_a @ V2 @ e_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % removeLeaf.simps(3)
% 0.20/0.45 thf(fact_36_removeLeaf_Osimps_I4_J,axiom,
% 0.20/0.45 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 0.20/0.45 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ ( t_a @ V2 @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % removeLeaf.simps(4)
% 0.20/0.45 thf(fact_37_prod_Ocollapse,axiom,
% 0.20/0.45 ! [Prod: produc981471411ee_a_a] :
% 0.20/0.45 ( ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) )
% 0.20/0.45 = Prod ) ).
% 0.20/0.45
% 0.20/0.45 % prod.collapse
% 0.20/0.45 thf(fact_38_prod_Ocollapse,axiom,
% 0.20/0.45 ! [Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) )
% 0.20/0.45 = Prod ) ).
% 0.20/0.45
% 0.20/0.45 % prod.collapse
% 0.20/0.45 thf(fact_39_eq__fst__iff,axiom,
% 0.20/0.45 ! [A: a,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( A
% 0.20/0.45 = ( product_fst_a_Tree_a @ P2 ) )
% 0.20/0.45 = ( ? [B3: tree_a] :
% 0.20/0.45 ( P2
% 0.20/0.45 = ( produc686083979Tree_a @ A @ B3 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % eq_fst_iff
% 0.20/0.45 thf(fact_40_eq__fst__iff,axiom,
% 0.20/0.45 ! [A: tree_a,P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( A
% 0.20/0.45 = ( product_fst_Tree_a_a @ P2 ) )
% 0.20/0.45 = ( ? [B3: a] :
% 0.20/0.45 ( P2
% 0.20/0.45 = ( produc649172771ee_a_a @ A @ B3 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % eq_fst_iff
% 0.20/0.45 thf(fact_41_fst__conv,axiom,
% 0.20/0.45 ! [X12: a,X24: tree_a] :
% 0.20/0.45 ( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 0.20/0.45 = X12 ) ).
% 0.20/0.45
% 0.20/0.45 % fst_conv
% 0.20/0.45 thf(fact_42_fst__conv,axiom,
% 0.20/0.45 ! [X12: tree_a,X24: a] :
% 0.20/0.45 ( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ X12 @ X24 ) )
% 0.20/0.45 = X12 ) ).
% 0.20/0.45
% 0.20/0.45 % fst_conv
% 0.20/0.45 thf(fact_43_fst__eqD,axiom,
% 0.20/0.45 ! [X: a,Y: tree_a,A: a] :
% 0.20/0.45 ( ( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ X @ Y ) )
% 0.20/0.45 = A )
% 0.20/0.45 => ( X = A ) ) ).
% 0.20/0.45
% 0.20/0.45 % fst_eqD
% 0.20/0.45 thf(fact_44_fst__eqD,axiom,
% 0.20/0.45 ! [X: tree_a,Y: a,A: tree_a] :
% 0.20/0.45 ( ( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ X @ Y ) )
% 0.20/0.45 = A )
% 0.20/0.45 => ( X = A ) ) ).
% 0.20/0.45
% 0.20/0.45 % fst_eqD
% 0.20/0.45 thf(fact_45_fstI,axiom,
% 0.20/0.45 ! [X: produc143150363Tree_a,Y: a,Z: tree_a] :
% 0.20/0.45 ( ( X
% 0.20/0.45 = ( produc686083979Tree_a @ Y @ Z ) )
% 0.20/0.45 => ( ( product_fst_a_Tree_a @ X )
% 0.20/0.45 = Y ) ) ).
% 0.20/0.45
% 0.20/0.45 % fstI
% 0.20/0.45 thf(fact_46_fstI,axiom,
% 0.20/0.45 ! [X: produc981471411ee_a_a,Y: tree_a,Z: a] :
% 0.20/0.45 ( ( X
% 0.20/0.45 = ( produc649172771ee_a_a @ Y @ Z ) )
% 0.20/0.45 => ( ( product_fst_Tree_a_a @ X )
% 0.20/0.45 = Y ) ) ).
% 0.20/0.45
% 0.20/0.45 % fstI
% 0.20/0.45 thf(fact_47_prod__eqI,axiom,
% 0.20/0.45 ! [P2: produc981471411ee_a_a,Q: produc981471411ee_a_a] :
% 0.20/0.45 ( ( ( product_fst_Tree_a_a @ P2 )
% 0.20/0.45 = ( product_fst_Tree_a_a @ Q ) )
% 0.20/0.45 => ( ( ( product_snd_Tree_a_a @ P2 )
% 0.20/0.45 = ( product_snd_Tree_a_a @ Q ) )
% 0.20/0.45 => ( P2 = Q ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_eqI
% 0.20/0.45 thf(fact_48_prod__eqI,axiom,
% 0.20/0.45 ! [P2: produc143150363Tree_a,Q: produc143150363Tree_a] :
% 0.20/0.45 ( ( ( product_fst_a_Tree_a @ P2 )
% 0.20/0.45 = ( product_fst_a_Tree_a @ Q ) )
% 0.20/0.45 => ( ( ( product_snd_a_Tree_a @ P2 )
% 0.20/0.45 = ( product_snd_a_Tree_a @ Q ) )
% 0.20/0.45 => ( P2 = Q ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_eqI
% 0.20/0.45 thf(fact_49_prod_Oexpand,axiom,
% 0.20/0.45 ! [Prod: produc981471411ee_a_a,Prod2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( ( ( product_fst_Tree_a_a @ Prod )
% 0.20/0.45 = ( product_fst_Tree_a_a @ Prod2 ) )
% 0.20/0.45 & ( ( product_snd_Tree_a_a @ Prod )
% 0.20/0.45 = ( product_snd_Tree_a_a @ Prod2 ) ) )
% 0.20/0.45 => ( Prod = Prod2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.expand
% 0.20/0.45 thf(fact_50_prod_Oexpand,axiom,
% 0.20/0.45 ! [Prod: produc143150363Tree_a,Prod2: produc143150363Tree_a] :
% 0.20/0.45 ( ( ( ( product_fst_a_Tree_a @ Prod )
% 0.20/0.45 = ( product_fst_a_Tree_a @ Prod2 ) )
% 0.20/0.45 & ( ( product_snd_a_Tree_a @ Prod )
% 0.20/0.45 = ( product_snd_a_Tree_a @ Prod2 ) ) )
% 0.20/0.45 => ( Prod = Prod2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.expand
% 0.20/0.45 thf(fact_51_prod__eq__iff,axiom,
% 0.20/0.45 ( ( ^ [Y3: produc981471411ee_a_a,Z2: produc981471411ee_a_a] : ( Y3 = Z2 ) )
% 0.20/0.45 = ( ^ [S: produc981471411ee_a_a,T: produc981471411ee_a_a] :
% 0.20/0.45 ( ( ( product_fst_Tree_a_a @ S )
% 0.20/0.45 = ( product_fst_Tree_a_a @ T ) )
% 0.20/0.45 & ( ( product_snd_Tree_a_a @ S )
% 0.20/0.45 = ( product_snd_Tree_a_a @ T ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_eq_iff
% 0.20/0.45 thf(fact_52_prod__eq__iff,axiom,
% 0.20/0.45 ( ( ^ [Y3: produc143150363Tree_a,Z2: produc143150363Tree_a] : ( Y3 = Z2 ) )
% 0.20/0.45 = ( ^ [S: produc143150363Tree_a,T: produc143150363Tree_a] :
% 0.20/0.45 ( ( ( product_fst_a_Tree_a @ S )
% 0.20/0.45 = ( product_fst_a_Tree_a @ T ) )
% 0.20/0.45 & ( ( product_snd_a_Tree_a @ S )
% 0.20/0.45 = ( product_snd_a_Tree_a @ T ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_eq_iff
% 0.20/0.45 thf(fact_53_surjective__pairing,axiom,
% 0.20/0.45 ! [T2: produc981471411ee_a_a] :
% 0.20/0.45 ( T2
% 0.20/0.45 = ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ T2 ) @ ( product_snd_Tree_a_a @ T2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % surjective_pairing
% 0.20/0.45 thf(fact_54_surjective__pairing,axiom,
% 0.20/0.45 ! [T2: produc143150363Tree_a] :
% 0.20/0.45 ( T2
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ T2 ) @ ( product_snd_a_Tree_a @ T2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % surjective_pairing
% 0.20/0.45 thf(fact_55_prod_Oexhaust__sel,axiom,
% 0.20/0.45 ! [Prod: produc981471411ee_a_a] :
% 0.20/0.45 ( Prod
% 0.20/0.45 = ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.exhaust_sel
% 0.20/0.45 thf(fact_56_prod_Oexhaust__sel,axiom,
% 0.20/0.45 ! [Prod: produc143150363Tree_a] :
% 0.20/0.45 ( Prod
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.exhaust_sel
% 0.20/0.45 thf(fact_57_in__tree_Osimps_I2_J,axiom,
% 0.20/0.45 ! [V2: a,V3: a,L: tree_a,R: tree_a] :
% 0.20/0.45 ( ( in_tree_a @ V2 @ ( t_a @ V3 @ L @ R ) )
% 0.20/0.45 = ( ( V2 = V3 )
% 0.20/0.45 | ( in_tree_a @ V2 @ L )
% 0.20/0.45 | ( in_tree_a @ V2 @ R ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % in_tree.simps(2)
% 0.20/0.45 thf(fact_58_in__tree_Osimps_I1_J,axiom,
% 0.20/0.45 ! [V2: a] :
% 0.20/0.45 ~ ( in_tree_a @ V2 @ e_a ) ).
% 0.20/0.45
% 0.20/0.45 % in_tree.simps(1)
% 0.20/0.45 thf(fact_59_siftDown__in__tree__set,axiom,
% 0.20/0.45 ( in_tree_a
% 0.20/0.45 = ( ^ [V4: a,T: tree_a] : ( in_tree_a @ V4 @ ( heapIm1091024090Down_a @ T ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown_in_tree_set
% 0.20/0.45 thf(fact_60_old_Oprod_Oinducts,axiom,
% 0.20/0.45 ! [P: produc143150363Tree_a > $o,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ! [A4: a,B4: tree_a] : ( P @ ( produc686083979Tree_a @ A4 @ B4 ) )
% 0.20/0.45 => ( P @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.inducts
% 0.20/0.45 thf(fact_61_old_Oprod_Oinducts,axiom,
% 0.20/0.45 ! [P: produc981471411ee_a_a > $o,Prod: produc981471411ee_a_a] :
% 0.20/0.45 ( ! [A4: tree_a,B4: a] : ( P @ ( produc649172771ee_a_a @ A4 @ B4 ) )
% 0.20/0.45 => ( P @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.inducts
% 0.20/0.45 thf(fact_62_mem__Collect__eq,axiom,
% 0.20/0.45 ! [A: a,P: a > $o] :
% 0.20/0.45 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.20/0.45 = ( P @ A ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_Collect_eq
% 0.20/0.45 thf(fact_63_mem__Collect__eq,axiom,
% 0.20/0.45 ! [A: produc143150363Tree_a,P: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ P ) )
% 0.20/0.45 = ( P @ A ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_Collect_eq
% 0.20/0.45 thf(fact_64_Collect__mem__eq,axiom,
% 0.20/0.45 ! [A5: set_a] :
% 0.20/0.45 ( ( collect_a
% 0.20/0.45 @ ^ [X4: a] : ( member_a @ X4 @ A5 ) )
% 0.20/0.45 = A5 ) ).
% 0.20/0.45
% 0.20/0.45 % Collect_mem_eq
% 0.20/0.45 thf(fact_65_Collect__mem__eq,axiom,
% 0.20/0.45 ! [A5: set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ( collec486369286Tree_a
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ A5 ) )
% 0.20/0.45 = A5 ) ).
% 0.20/0.45
% 0.20/0.45 % Collect_mem_eq
% 0.20/0.45 thf(fact_66_Collect__cong,axiom,
% 0.20/0.45 ! [P: produc143150363Tree_a > $o,Q2: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ! [X5: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ X5 )
% 0.20/0.45 = ( Q2 @ X5 ) )
% 0.20/0.45 => ( ( collec486369286Tree_a @ P )
% 0.20/0.45 = ( collec486369286Tree_a @ Q2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Collect_cong
% 0.20/0.45 thf(fact_67_old_Oprod_Oexhaust,axiom,
% 0.20/0.45 ! [Y: produc143150363Tree_a] :
% 0.20/0.45 ~ ! [A4: a,B4: tree_a] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( produc686083979Tree_a @ A4 @ B4 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.exhaust
% 0.20/0.45 thf(fact_68_old_Oprod_Oexhaust,axiom,
% 0.20/0.45 ! [Y: produc981471411ee_a_a] :
% 0.20/0.45 ~ ! [A4: tree_a,B4: a] :
% 0.20/0.45 ( Y
% 0.20/0.45 != ( produc649172771ee_a_a @ A4 @ B4 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.exhaust
% 0.20/0.45 thf(fact_69_Pair__inject,axiom,
% 0.20/0.45 ! [A: a,B: tree_a,A2: a,B2: tree_a] :
% 0.20/0.45 ( ( ( produc686083979Tree_a @ A @ B )
% 0.20/0.45 = ( produc686083979Tree_a @ A2 @ B2 ) )
% 0.20/0.45 => ~ ( ( A = A2 )
% 0.20/0.45 => ( B != B2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Pair_inject
% 0.20/0.45 thf(fact_70_Pair__inject,axiom,
% 0.20/0.45 ! [A: tree_a,B: a,A2: tree_a,B2: a] :
% 0.20/0.45 ( ( ( produc649172771ee_a_a @ A @ B )
% 0.20/0.45 = ( produc649172771ee_a_a @ A2 @ B2 ) )
% 0.20/0.45 => ~ ( ( A = A2 )
% 0.20/0.45 => ( B != B2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Pair_inject
% 0.20/0.45 thf(fact_71_prod__cases,axiom,
% 0.20/0.45 ! [P: produc143150363Tree_a > $o,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ! [A4: a,B4: tree_a] : ( P @ ( produc686083979Tree_a @ A4 @ B4 ) )
% 0.20/0.45 => ( P @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_cases
% 0.20/0.45 thf(fact_72_prod__cases,axiom,
% 0.20/0.45 ! [P: produc981471411ee_a_a > $o,P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ! [A4: tree_a,B4: a] : ( P @ ( produc649172771ee_a_a @ A4 @ B4 ) )
% 0.20/0.45 => ( P @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod_cases
% 0.20/0.45 thf(fact_73_surj__pair,axiom,
% 0.20/0.45 ! [P2: produc143150363Tree_a] :
% 0.20/0.45 ? [X5: a,Y4: tree_a] :
% 0.20/0.45 ( P2
% 0.20/0.45 = ( produc686083979Tree_a @ X5 @ Y4 ) ) ).
% 0.20/0.45
% 0.20/0.45 % surj_pair
% 0.20/0.45 thf(fact_74_surj__pair,axiom,
% 0.20/0.45 ! [P2: produc981471411ee_a_a] :
% 0.20/0.45 ? [X5: tree_a,Y4: a] :
% 0.20/0.45 ( P2
% 0.20/0.45 = ( produc649172771ee_a_a @ X5 @ Y4 ) ) ).
% 0.20/0.45
% 0.20/0.45 % surj_pair
% 0.20/0.45 thf(fact_75_removeLeaf_Osimps_I5_J,axiom,
% 0.20/0.45 ! [V2: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.20/0.45 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) @ ( t_a @ V2 @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % removeLeaf.simps(5)
% 0.20/0.45 thf(fact_76_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.45 ! [P: tree_a > a > $o,X: tree_a,Y: a,A: produc981471411ee_a_a] :
% 0.20/0.45 ( ( P @ X @ Y )
% 0.20/0.45 => ( ( A
% 0.20/0.45 = ( produc649172771ee_a_a @ X @ Y ) )
% 0.20/0.45 => ( P @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.45 thf(fact_77_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.20/0.45 ! [P: a > tree_a > $o,X: a,Y: tree_a,A: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ X @ Y )
% 0.20/0.45 => ( ( A
% 0.20/0.45 = ( produc686083979Tree_a @ X @ Y ) )
% 0.20/0.45 => ( P @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % BNF_Greatest_Fixpoint.subst_Pair
% 0.20/0.45 thf(fact_78_conjI__realizer,axiom,
% 0.20/0.45 ! [P: tree_a > $o,P2: tree_a,Q2: a > $o,Q: a] :
% 0.20/0.45 ( ( P @ P2 )
% 0.20/0.45 => ( ( Q2 @ Q )
% 0.20/0.45 => ( ( P @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ P2 @ Q ) ) )
% 0.20/0.45 & ( Q2 @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ P2 @ Q ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % conjI_realizer
% 0.20/0.45 thf(fact_79_conjI__realizer,axiom,
% 0.20/0.45 ! [P: a > $o,P2: a,Q2: tree_a > $o,Q: tree_a] :
% 0.20/0.45 ( ( P @ P2 )
% 0.20/0.45 => ( ( Q2 @ Q )
% 0.20/0.45 => ( ( P @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ P2 @ Q ) ) )
% 0.20/0.45 & ( Q2 @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ P2 @ Q ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % conjI_realizer
% 0.20/0.45 thf(fact_80_exI__realizer,axiom,
% 0.20/0.45 ! [P: a > tree_a > $o,Y: a,X: tree_a] :
% 0.20/0.45 ( ( P @ Y @ X )
% 0.20/0.45 => ( P @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ X @ Y ) ) @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ X @ Y ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exI_realizer
% 0.20/0.45 thf(fact_81_exI__realizer,axiom,
% 0.20/0.45 ! [P: tree_a > a > $o,Y: tree_a,X: a] :
% 0.20/0.45 ( ( P @ Y @ X )
% 0.20/0.45 => ( P @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X @ Y ) ) @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ X @ Y ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % exI_realizer
% 0.20/0.45 thf(fact_82_exE__realizer_H,axiom,
% 0.20/0.45 ! [P: a > tree_a > $o,P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( P @ ( product_snd_Tree_a_a @ P2 ) @ ( product_fst_Tree_a_a @ P2 ) )
% 0.20/0.45 => ~ ! [X5: tree_a,Y4: a] :
% 0.20/0.45 ~ ( P @ Y4 @ X5 ) ) ).
% 0.20/0.45
% 0.20/0.45 % exE_realizer'
% 0.20/0.45 thf(fact_83_exE__realizer_H,axiom,
% 0.20/0.45 ! [P: tree_a > a > $o,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ ( product_snd_a_Tree_a @ P2 ) @ ( product_fst_a_Tree_a @ P2 ) )
% 0.20/0.45 => ~ ! [X5: a,Y4: tree_a] :
% 0.20/0.45 ~ ( P @ Y4 @ X5 ) ) ).
% 0.20/0.45
% 0.20/0.45 % exE_realizer'
% 0.20/0.45 thf(fact_84_prod_Oswap__def,axiom,
% 0.20/0.45 ( produc1478296771ee_a_a
% 0.20/0.45 = ( ^ [P3: produc981471411ee_a_a] : ( produc686083979Tree_a @ ( product_snd_Tree_a_a @ P3 ) @ ( product_fst_Tree_a_a @ P3 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.swap_def
% 0.20/0.45 thf(fact_85_prod_Oswap__def,axiom,
% 0.20/0.45 ( produc1515207979Tree_a
% 0.20/0.45 = ( ^ [P3: produc143150363Tree_a] : ( produc649172771ee_a_a @ ( product_snd_a_Tree_a @ P3 ) @ ( product_fst_a_Tree_a @ P3 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.swap_def
% 0.20/0.45 thf(fact_86_heapify_Osimps_I2_J,axiom,
% 0.20/0.45 ! [V2: a,L: tree_a,R: tree_a] :
% 0.20/0.45 ( ( heapIm970322378pify_a @ ( t_a @ V2 @ L @ R ) )
% 0.20/0.45 = ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm970322378pify_a @ L ) @ ( heapIm970322378pify_a @ R ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % heapify.simps(2)
% 0.20/0.45 thf(fact_87_is__heap_Osimps_I4_J,axiom,
% 0.20/0.45 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.20/0.45 ( ( is_heap_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.20/0.45 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % is_heap.simps(4)
% 0.20/0.45 thf(fact_88_is__heap_Osimps_I3_J,axiom,
% 0.20/0.45 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.20/0.45 ( ( is_heap_a @ ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % is_heap.simps(3)
% 0.20/0.45 thf(fact_89_swap__swap,axiom,
% 0.20/0.45 ! [P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( produc1515207979Tree_a @ ( produc1478296771ee_a_a @ P2 ) )
% 0.20/0.45 = P2 ) ).
% 0.20/0.45
% 0.20/0.45 % swap_swap
% 0.20/0.45 thf(fact_90_swap__swap,axiom,
% 0.20/0.45 ! [P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( produc1478296771ee_a_a @ ( produc1515207979Tree_a @ P2 ) )
% 0.20/0.45 = P2 ) ).
% 0.20/0.45
% 0.20/0.45 % swap_swap
% 0.20/0.45 thf(fact_91_swap__simp,axiom,
% 0.20/0.45 ! [X: a,Y: tree_a] :
% 0.20/0.45 ( ( produc1515207979Tree_a @ ( produc686083979Tree_a @ X @ Y ) )
% 0.20/0.45 = ( produc649172771ee_a_a @ Y @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % swap_simp
% 0.20/0.45 thf(fact_92_swap__simp,axiom,
% 0.20/0.45 ! [X: tree_a,Y: a] :
% 0.20/0.45 ( ( produc1478296771ee_a_a @ ( produc649172771ee_a_a @ X @ Y ) )
% 0.20/0.45 = ( produc686083979Tree_a @ Y @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % swap_simp
% 0.20/0.45 thf(fact_93_fst__swap,axiom,
% 0.20/0.45 ! [X: produc981471411ee_a_a] :
% 0.20/0.45 ( ( product_fst_a_Tree_a @ ( produc1478296771ee_a_a @ X ) )
% 0.20/0.45 = ( product_snd_Tree_a_a @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % fst_swap
% 0.20/0.45 thf(fact_94_fst__swap,axiom,
% 0.20/0.45 ! [X: produc143150363Tree_a] :
% 0.20/0.45 ( ( product_fst_Tree_a_a @ ( produc1515207979Tree_a @ X ) )
% 0.20/0.45 = ( product_snd_a_Tree_a @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % fst_swap
% 0.20/0.45 thf(fact_95_snd__swap,axiom,
% 0.20/0.45 ! [X: produc143150363Tree_a] :
% 0.20/0.45 ( ( product_snd_Tree_a_a @ ( produc1515207979Tree_a @ X ) )
% 0.20/0.45 = ( product_fst_a_Tree_a @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % snd_swap
% 0.20/0.45 thf(fact_96_snd__swap,axiom,
% 0.20/0.45 ! [X: produc981471411ee_a_a] :
% 0.20/0.45 ( ( product_snd_a_Tree_a @ ( produc1478296771ee_a_a @ X ) )
% 0.20/0.45 = ( product_fst_Tree_a_a @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % snd_swap
% 0.20/0.45 thf(fact_97_siftDown__Node,axiom,
% 0.20/0.45 ! [T2: tree_a,V2: a,L: tree_a,R: tree_a] :
% 0.20/0.45 ( ( T2
% 0.20/0.45 = ( t_a @ V2 @ L @ R ) )
% 0.20/0.45 => ? [L2: tree_a,V5: a,R2: tree_a] :
% 0.20/0.45 ( ( ( heapIm1091024090Down_a @ T2 )
% 0.20/0.45 = ( t_a @ V5 @ L2 @ R2 ) )
% 0.20/0.45 & ( ord_less_eq_a @ V2 @ V5 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown_Node
% 0.20/0.45 thf(fact_98_heapify_Osimps_I1_J,axiom,
% 0.20/0.45 ( ( heapIm970322378pify_a @ e_a )
% 0.20/0.45 = e_a ) ).
% 0.20/0.45
% 0.20/0.45 % heapify.simps(1)
% 0.20/0.45 thf(fact_99_heapify__heap__is__heap,axiom,
% 0.20/0.45 ! [T2: tree_a] : ( is_heap_a @ ( heapIm970322378pify_a @ T2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % heapify_heap_is_heap
% 0.20/0.45 thf(fact_100_is__heap_Osimps_I5_J,axiom,
% 0.20/0.45 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 0.20/0.45 ( ( is_heap_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 0.20/0.45 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) )
% 0.20/0.45 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % is_heap.simps(5)
% 0.20/0.45 thf(fact_101_is__heap_Osimps_I6_J,axiom,
% 0.20/0.45 ! [V2: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 0.20/0.45 ( ( is_heap_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 0.20/0.45 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 0.20/0.45 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % is_heap.simps(6)
% 0.20/0.45 thf(fact_102_is__heap__max,axiom,
% 0.20/0.45 ! [V2: a,T2: tree_a] :
% 0.20/0.45 ( ( in_tree_a @ V2 @ T2 )
% 0.20/0.45 => ( ( is_heap_a @ T2 )
% 0.20/0.45 => ( ord_less_eq_a @ V2 @ ( val_a @ T2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % is_heap_max
% 0.20/0.45 thf(fact_103_order__refl,axiom,
% 0.20/0.45 ! [X: a] : ( ord_less_eq_a @ X @ X ) ).
% 0.20/0.45
% 0.20/0.45 % order_refl
% 0.20/0.45 thf(fact_104_siftDown_Osimps_I3_J,axiom,
% 0.20/0.45 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V2: a] :
% 0.20/0.45 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.20/0.45 = ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 0.20/0.45 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ e_a ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(3)
% 0.20/0.45 thf(fact_105_siftDown_Osimps_I4_J,axiom,
% 0.20/0.45 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V2: a] :
% 0.20/0.45 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(4)
% 0.20/0.45 thf(fact_106_siftDown_Osimps_I6_J,axiom,
% 0.20/0.45 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a,V2: a] :
% 0.20/0.45 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(6)
% 0.20/0.45 thf(fact_107_siftDown_Osimps_I5_J,axiom,
% 0.20/0.45 ! [Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a,V2: a] :
% 0.20/0.45 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 0.20/0.45 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 0.20/0.45 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 0.20/0.45 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown.simps(5)
% 0.20/0.45 thf(fact_108_left_Osimps,axiom,
% 0.20/0.45 ! [V2: a,L: tree_a,R: tree_a] :
% 0.20/0.45 ( ( heapIm1140443833left_a @ ( t_a @ V2 @ L @ R ) )
% 0.20/0.45 = L ) ).
% 0.20/0.45
% 0.20/0.45 % left.simps
% 0.20/0.45 thf(fact_109_right_Osimps,axiom,
% 0.20/0.45 ! [V2: a,L: tree_a,R: tree_a] :
% 0.20/0.45 ( ( heapIm1257206334ight_a @ ( t_a @ V2 @ L @ R ) )
% 0.20/0.45 = R ) ).
% 0.20/0.45
% 0.20/0.45 % right.simps
% 0.20/0.45 thf(fact_110_dual__order_Oantisym,axiom,
% 0.20/0.45 ! [B: a,A: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ B @ A )
% 0.20/0.45 => ( ( ord_less_eq_a @ A @ B )
% 0.20/0.45 => ( A = B ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % dual_order.antisym
% 0.20/0.45 thf(fact_111_dual__order_Oeq__iff,axiom,
% 0.20/0.45 ( ( ^ [Y3: a,Z2: a] : ( Y3 = Z2 ) )
% 0.20/0.45 = ( ^ [A3: a,B3: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ B3 @ A3 )
% 0.20/0.45 & ( ord_less_eq_a @ A3 @ B3 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % dual_order.eq_iff
% 0.20/0.45 thf(fact_112_dual__order_Otrans,axiom,
% 0.20/0.45 ! [B: a,A: a,C: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ B @ A )
% 0.20/0.45 => ( ( ord_less_eq_a @ C @ B )
% 0.20/0.45 => ( ord_less_eq_a @ C @ A ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % dual_order.trans
% 0.20/0.45 thf(fact_113_linorder__wlog,axiom,
% 0.20/0.45 ! [P: a > a > $o,A: a,B: a] :
% 0.20/0.45 ( ! [A4: a,B4: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ A4 @ B4 )
% 0.20/0.45 => ( P @ A4 @ B4 ) )
% 0.20/0.45 => ( ! [A4: a,B4: a] :
% 0.20/0.45 ( ( P @ B4 @ A4 )
% 0.20/0.45 => ( P @ A4 @ B4 ) )
% 0.20/0.45 => ( P @ A @ B ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % linorder_wlog
% 0.20/0.45 thf(fact_114_dual__order_Orefl,axiom,
% 0.20/0.45 ! [A: a] : ( ord_less_eq_a @ A @ A ) ).
% 0.20/0.45
% 0.20/0.45 % dual_order.refl
% 0.20/0.45 thf(fact_115_order__trans,axiom,
% 0.20/0.45 ! [X: a,Y: a,Z: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.45 => ( ( ord_less_eq_a @ Y @ Z )
% 0.20/0.45 => ( ord_less_eq_a @ X @ Z ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % order_trans
% 0.20/0.45 thf(fact_116_order__class_Oorder_Oantisym,axiom,
% 0.20/0.45 ! [A: a,B: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.45 => ( ( ord_less_eq_a @ B @ A )
% 0.20/0.45 => ( A = B ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % order_class.order.antisym
% 0.20/0.45 thf(fact_117_ord__le__eq__trans,axiom,
% 0.20/0.45 ! [A: a,B: a,C: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.45 => ( ( B = C )
% 0.20/0.45 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % ord_le_eq_trans
% 0.20/0.45 thf(fact_118_ord__eq__le__trans,axiom,
% 0.20/0.45 ! [A: a,B: a,C: a] :
% 0.20/0.45 ( ( A = B )
% 0.20/0.45 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.45 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % ord_eq_le_trans
% 0.20/0.45 thf(fact_119_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.45 ( ( ^ [Y3: a,Z2: a] : ( Y3 = Z2 ) )
% 0.20/0.45 = ( ^ [A3: a,B3: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ A3 @ B3 )
% 0.20/0.45 & ( ord_less_eq_a @ B3 @ A3 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % order_class.order.eq_iff
% 0.20/0.45 thf(fact_120_antisym__conv,axiom,
% 0.20/0.45 ! [Y: a,X: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ Y @ X )
% 0.20/0.45 => ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.45 = ( X = Y ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % antisym_conv
% 0.20/0.45 thf(fact_121_le__cases3,axiom,
% 0.20/0.45 ! [X: a,Y: a,Z: a] :
% 0.20/0.45 ( ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.45 => ~ ( ord_less_eq_a @ Y @ Z ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ Y @ X )
% 0.20/0.45 => ~ ( ord_less_eq_a @ X @ Z ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ X @ Z )
% 0.20/0.45 => ~ ( ord_less_eq_a @ Z @ Y ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ Z @ Y )
% 0.20/0.45 => ~ ( ord_less_eq_a @ Y @ X ) )
% 0.20/0.45 => ( ( ( ord_less_eq_a @ Y @ Z )
% 0.20/0.45 => ~ ( ord_less_eq_a @ Z @ X ) )
% 0.20/0.45 => ~ ( ( ord_less_eq_a @ Z @ X )
% 0.20/0.45 => ~ ( ord_less_eq_a @ X @ Y ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % le_cases3
% 0.20/0.45 thf(fact_122_order_Otrans,axiom,
% 0.20/0.45 ! [A: a,B: a,C: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.45 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.45 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % order.trans
% 0.20/0.45 thf(fact_123_le__cases,axiom,
% 0.20/0.45 ! [X: a,Y: a] :
% 0.20/0.45 ( ~ ( ord_less_eq_a @ X @ Y )
% 0.20/0.45 => ( ord_less_eq_a @ Y @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % le_cases
% 0.20/0.45 thf(fact_124_eq__refl,axiom,
% 0.20/0.45 ! [X: a,Y: a] :
% 0.20/0.45 ( ( X = Y )
% 0.20/0.45 => ( ord_less_eq_a @ X @ Y ) ) ).
% 0.20/0.45
% 0.20/0.45 % eq_refl
% 0.20/0.45 thf(fact_125_linear,axiom,
% 0.20/0.45 ! [X: a,Y: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.45 | ( ord_less_eq_a @ Y @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % linear
% 0.20/0.45 thf(fact_126_antisym,axiom,
% 0.20/0.45 ! [X: a,Y: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ X @ Y )
% 0.20/0.45 => ( ( ord_less_eq_a @ Y @ X )
% 0.20/0.45 => ( X = Y ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % antisym
% 0.20/0.45 thf(fact_127_eq__iff,axiom,
% 0.20/0.45 ( ( ^ [Y3: a,Z2: a] : ( Y3 = Z2 ) )
% 0.20/0.45 = ( ^ [X4: a,Y5: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ X4 @ Y5 )
% 0.20/0.45 & ( ord_less_eq_a @ Y5 @ X4 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % eq_iff
% 0.20/0.45 thf(fact_128_ord__le__eq__subst,axiom,
% 0.20/0.45 ! [A: a,B: a,F: a > a,C: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.45 => ( ( ( F @ B )
% 0.20/0.45 = C )
% 0.20/0.45 => ( ! [X5: a,Y4: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.45 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.45 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % ord_le_eq_subst
% 0.20/0.45 thf(fact_129_ord__eq__le__subst,axiom,
% 0.20/0.45 ! [A: a,F: a > a,B: a,C: a] :
% 0.20/0.45 ( ( A
% 0.20/0.45 = ( F @ B ) )
% 0.20/0.45 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.45 => ( ! [X5: a,Y4: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.45 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.45 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % ord_eq_le_subst
% 0.20/0.45 thf(fact_130_order__subst2,axiom,
% 0.20/0.45 ! [A: a,B: a,F: a > a,C: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ A @ B )
% 0.20/0.45 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 0.20/0.45 => ( ! [X5: a,Y4: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.45 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.45 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % order_subst2
% 0.20/0.45 thf(fact_131_order__subst1,axiom,
% 0.20/0.45 ! [A: a,F: a > a,B: a,C: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 0.20/0.45 => ( ( ord_less_eq_a @ B @ C )
% 0.20/0.45 => ( ! [X5: a,Y4: a] :
% 0.20/0.45 ( ( ord_less_eq_a @ X5 @ Y4 )
% 0.20/0.45 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.20/0.45 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % order_subst1
% 0.20/0.45 thf(fact_132_hs__remove__max__def,axiom,
% 0.20/0.45 ( heapIm915766629_max_a
% 0.20/0.45 = ( ^ [T: tree_a] :
% 0.20/0.45 ( if_Pro1144176865Tree_a
% 0.20/0.45 @ ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T ) )
% 0.20/0.45 = e_a )
% 0.20/0.45 @ ( produc686083979Tree_a @ ( val_a @ T ) @ e_a )
% 0.20/0.45 @ ( produc686083979Tree_a @ ( val_a @ T ) @ ( heapIm1091024090Down_a @ ( t_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ T ) ) @ ( heapIm1140443833left_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T ) ) ) @ ( heapIm1257206334ight_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T ) ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % hs_remove_max_def
% 0.20/0.45 thf(fact_133_Heap_Oremove__max__is__heap,axiom,
% 0.20/0.45 ! [Empty: tree_a,Is_empty: tree_a > $o,Of_list: list_a > tree_a,Multiset: tree_a > multiset_a,As_tree: tree_a > tree_a,Remove_max: tree_a > produc143150363Tree_a,L: tree_a,M: a,L3: tree_a] :
% 0.20/0.45 ( ( heap_Tree_a_a @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.20/0.45 => ( ~ ( Is_empty @ L )
% 0.20/0.45 => ( ( is_heap_a @ ( As_tree @ L ) )
% 0.20/0.45 => ( ( ( produc686083979Tree_a @ M @ L3 )
% 0.20/0.45 = ( Remove_max @ L ) )
% 0.20/0.45 => ( is_heap_a @ ( As_tree @ L3 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Heap.remove_max_is_heap
% 0.20/0.45 thf(fact_134_Heap_Oremove__max__val,axiom,
% 0.20/0.45 ! [Empty: tree_a,Is_empty: tree_a > $o,Of_list: list_a > tree_a,Multiset: tree_a > multiset_a,As_tree: tree_a > tree_a,Remove_max: tree_a > produc143150363Tree_a,T2: tree_a,M: a,T3: tree_a] :
% 0.20/0.45 ( ( heap_Tree_a_a @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.20/0.45 => ( ~ ( Is_empty @ T2 )
% 0.20/0.45 => ( ( ( produc686083979Tree_a @ M @ T3 )
% 0.20/0.45 = ( Remove_max @ T2 ) )
% 0.20/0.45 => ( M
% 0.20/0.45 = ( val_a @ ( As_tree @ T2 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Heap.remove_max_val
% 0.20/0.45 thf(fact_135_sndOp__def,axiom,
% 0.20/0.45 ( bNF_sn210385162ee_a_a
% 0.20/0.45 = ( ^ [P4: tree_a > tree_a > $o,Q3: tree_a > a > $o,Ac: produc981471411ee_a_a] : ( produc649172771ee_a_a @ ( bNF_pi1059296282ee_a_a @ P4 @ Q3 @ ( product_fst_Tree_a_a @ Ac ) @ ( product_snd_Tree_a_a @ Ac ) ) @ ( product_snd_Tree_a_a @ Ac ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % sndOp_def
% 0.20/0.45 thf(fact_136_sndOp__def,axiom,
% 0.20/0.45 ( bNF_sndOp_a_a_Tree_a
% 0.20/0.45 = ( ^ [P4: a > a > $o,Q3: a > tree_a > $o,Ac: produc143150363Tree_a] : ( produc686083979Tree_a @ ( bNF_pi207687054Tree_a @ P4 @ Q3 @ ( product_fst_a_Tree_a @ Ac ) @ ( product_snd_a_Tree_a @ Ac ) ) @ ( product_snd_a_Tree_a @ Ac ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % sndOp_def
% 0.20/0.45 thf(fact_137_fstOp__def,axiom,
% 0.20/0.45 ( bNF_fstOp_Tree_a_a_a
% 0.20/0.45 = ( ^ [P4: tree_a > a > $o,Q3: a > a > $o,Ac: produc981471411ee_a_a] : ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Ac ) @ ( bNF_pi1407460238_a_a_a @ P4 @ Q3 @ ( product_fst_Tree_a_a @ Ac ) @ ( product_snd_Tree_a_a @ Ac ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % fstOp_def
% 0.20/0.45 thf(fact_138_fstOp__def,axiom,
% 0.20/0.45 ( bNF_fs1579355852Tree_a
% 0.20/0.45 = ( ^ [P4: a > tree_a > $o,Q3: tree_a > tree_a > $o,Ac: produc143150363Tree_a] : ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Ac ) @ ( bNF_pi1536086554Tree_a @ P4 @ Q3 @ ( product_fst_a_Tree_a @ Ac ) @ ( product_snd_a_Tree_a @ Ac ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % fstOp_def
% 0.20/0.45 thf(fact_139_pred__subset__eq2,axiom,
% 0.20/0.45 ! [R3: set_Pr1070816379Tree_a,S2: set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ( ord_le1327026842ee_a_o
% 0.20/0.45 @ ^ [X4: a,Y5: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ X4 @ Y5 ) @ R3 )
% 0.20/0.45 @ ^ [X4: a,Y5: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ X4 @ Y5 ) @ S2 ) )
% 0.20/0.45 = ( ord_le1013007387Tree_a @ R3 @ S2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % pred_subset_eq2
% 0.20/0.45 thf(fact_140_pred__subset__eq2,axiom,
% 0.20/0.45 ! [R3: set_Pr921883667ee_a_a,S2: set_Pr921883667ee_a_a] :
% 0.20/0.45 ( ( ord_le1748873858_a_a_o
% 0.20/0.45 @ ^ [X4: tree_a,Y5: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X4 @ Y5 ) @ R3 )
% 0.20/0.45 @ ^ [X4: tree_a,Y5: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X4 @ Y5 ) @ S2 ) )
% 0.20/0.45 = ( ord_le864074675ee_a_a @ R3 @ S2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % pred_subset_eq2
% 0.20/0.45 thf(fact_141_pred__equals__eq2,axiom,
% 0.20/0.45 ! [R3: set_Pr1070816379Tree_a,S2: set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ( ( ^ [X4: a,Y5: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ X4 @ Y5 ) @ R3 ) )
% 0.20/0.45 = ( ^ [X4: a,Y5: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ X4 @ Y5 ) @ S2 ) ) )
% 0.20/0.45 = ( R3 = S2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % pred_equals_eq2
% 0.20/0.45 thf(fact_142_pred__equals__eq2,axiom,
% 0.20/0.45 ! [R3: set_Pr921883667ee_a_a,S2: set_Pr921883667ee_a_a] :
% 0.20/0.45 ( ( ( ^ [X4: tree_a,Y5: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X4 @ Y5 ) @ R3 ) )
% 0.20/0.45 = ( ^ [X4: tree_a,Y5: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X4 @ Y5 ) @ S2 ) ) )
% 0.20/0.45 = ( R3 = S2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % pred_equals_eq2
% 0.20/0.45 thf(fact_143_csquare__fstOp__sndOp,axiom,
% 0.20/0.45 ! [F: ( a > tree_a > $o ) > produc143150363Tree_a > $o,P: a > a > $o,Q2: a > tree_a > $o] : ( bNF_cs739966834Tree_a @ ( collec486369286Tree_a @ ( F @ ( relcompp_a_a_Tree_a @ P @ Q2 ) ) ) @ product_snd_a_a @ product_fst_a_Tree_a @ ( bNF_fstOp_a_a_Tree_a @ P @ Q2 ) @ ( bNF_sndOp_a_a_Tree_a @ P @ Q2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % csquare_fstOp_sndOp
% 0.20/0.45 thf(fact_144_csquare__fstOp__sndOp,axiom,
% 0.20/0.45 ! [F: ( a > tree_a > $o ) > produc143150363Tree_a > $o,P: a > tree_a > $o,Q2: tree_a > tree_a > $o] : ( bNF_cs1091007358Tree_a @ ( collec486369286Tree_a @ ( F @ ( relcom439193229Tree_a @ P @ Q2 ) ) ) @ product_snd_a_Tree_a @ produc1206152067Tree_a @ ( bNF_fs1579355852Tree_a @ P @ Q2 ) @ ( bNF_sn687175434Tree_a @ P @ Q2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % csquare_fstOp_sndOp
% 0.20/0.45 thf(fact_145_csquare__fstOp__sndOp,axiom,
% 0.20/0.45 ! [F: ( a > a > $o ) > product_prod_a_a > $o,P: a > tree_a > $o,Q2: tree_a > a > $o] : ( bNF_cs1095035134ee_a_a @ ( collec645855634od_a_a @ ( F @ ( relcompp_a_Tree_a_a @ P @ Q2 ) ) ) @ product_snd_a_Tree_a @ product_fst_Tree_a_a @ ( bNF_fstOp_a_Tree_a_a @ P @ Q2 ) @ ( bNF_sndOp_a_Tree_a_a @ P @ Q2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % csquare_fstOp_sndOp
% 0.20/0.45 thf(fact_146_subset__Collect__iff,axiom,
% 0.20/0.45 ! [B5: set_a,A5: set_a,P: a > $o] :
% 0.20/0.45 ( ( ord_less_eq_set_a @ B5 @ A5 )
% 0.20/0.45 => ( ( ord_less_eq_set_a @ B5
% 0.20/0.45 @ ( collect_a
% 0.20/0.45 @ ^ [X4: a] :
% 0.20/0.45 ( ( member_a @ X4 @ A5 )
% 0.20/0.45 & ( P @ X4 ) ) ) )
% 0.20/0.45 = ( ! [X4: a] :
% 0.20/0.45 ( ( member_a @ X4 @ B5 )
% 0.20/0.45 => ( P @ X4 ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subset_Collect_iff
% 0.20/0.45 thf(fact_147_subset__Collect__iff,axiom,
% 0.20/0.45 ! [B5: set_Pr1070816379Tree_a,A5: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ( ord_le1013007387Tree_a @ B5 @ A5 )
% 0.20/0.45 => ( ( ord_le1013007387Tree_a @ B5
% 0.20/0.45 @ ( collec486369286Tree_a
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X4 @ A5 )
% 0.20/0.45 & ( P @ X4 ) ) ) )
% 0.20/0.45 = ( ! [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X4 @ B5 )
% 0.20/0.45 => ( P @ X4 ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subset_Collect_iff
% 0.20/0.45 thf(fact_148_subset__CollectI,axiom,
% 0.20/0.45 ! [B5: set_a,A5: set_a,Q2: a > $o,P: a > $o] :
% 0.20/0.45 ( ( ord_less_eq_set_a @ B5 @ A5 )
% 0.20/0.45 => ( ! [X5: a] :
% 0.20/0.45 ( ( member_a @ X5 @ B5 )
% 0.20/0.45 => ( ( Q2 @ X5 )
% 0.20/0.45 => ( P @ X5 ) ) )
% 0.20/0.45 => ( ord_less_eq_set_a
% 0.20/0.45 @ ( collect_a
% 0.20/0.45 @ ^ [X4: a] :
% 0.20/0.45 ( ( member_a @ X4 @ B5 )
% 0.20/0.45 & ( Q2 @ X4 ) ) )
% 0.20/0.45 @ ( collect_a
% 0.20/0.45 @ ^ [X4: a] :
% 0.20/0.45 ( ( member_a @ X4 @ A5 )
% 0.20/0.45 & ( P @ X4 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subset_CollectI
% 0.20/0.45 thf(fact_149_subset__CollectI,axiom,
% 0.20/0.45 ! [B5: set_Pr1070816379Tree_a,A5: set_Pr1070816379Tree_a,Q2: produc143150363Tree_a > $o,P: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ( ord_le1013007387Tree_a @ B5 @ A5 )
% 0.20/0.45 => ( ! [X5: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X5 @ B5 )
% 0.20/0.45 => ( ( Q2 @ X5 )
% 0.20/0.45 => ( P @ X5 ) ) )
% 0.20/0.45 => ( ord_le1013007387Tree_a
% 0.20/0.45 @ ( collec486369286Tree_a
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X4 @ B5 )
% 0.20/0.45 & ( Q2 @ X4 ) ) )
% 0.20/0.45 @ ( collec486369286Tree_a
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X4 @ A5 )
% 0.20/0.45 & ( P @ X4 ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subset_CollectI
% 0.20/0.45 thf(fact_150_pred__subset__eq,axiom,
% 0.20/0.45 ! [R3: set_a,S2: set_a] :
% 0.20/0.45 ( ( ord_less_eq_a_o
% 0.20/0.45 @ ^ [X4: a] : ( member_a @ X4 @ R3 )
% 0.20/0.45 @ ^ [X4: a] : ( member_a @ X4 @ S2 ) )
% 0.20/0.45 = ( ord_less_eq_set_a @ R3 @ S2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % pred_subset_eq
% 0.20/0.45 thf(fact_151_pred__subset__eq,axiom,
% 0.20/0.45 ! [R3: set_Pr1070816379Tree_a,S2: set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ( ord_le1601593986ee_a_o
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ R3 )
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ S2 ) )
% 0.20/0.45 = ( ord_le1013007387Tree_a @ R3 @ S2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % pred_subset_eq
% 0.20/0.45 thf(fact_152_subrelI,axiom,
% 0.20/0.45 ! [R: set_Pr1070816379Tree_a,S3: set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ! [X5: a,Y4: tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ ( produc686083979Tree_a @ X5 @ Y4 ) @ R )
% 0.20/0.45 => ( member254315204Tree_a @ ( produc686083979Tree_a @ X5 @ Y4 ) @ S3 ) )
% 0.20/0.45 => ( ord_le1013007387Tree_a @ R @ S3 ) ) ).
% 0.20/0.45
% 0.20/0.45 % subrelI
% 0.20/0.45 thf(fact_153_subrelI,axiom,
% 0.20/0.45 ! [R: set_Pr921883667ee_a_a,S3: set_Pr921883667ee_a_a] :
% 0.20/0.45 ( ! [X5: tree_a,Y4: a] :
% 0.20/0.45 ( ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X5 @ Y4 ) @ R )
% 0.20/0.45 => ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X5 @ Y4 ) @ S3 ) )
% 0.20/0.45 => ( ord_le864074675ee_a_a @ R @ S3 ) ) ).
% 0.20/0.45
% 0.20/0.45 % subrelI
% 0.20/0.45 thf(fact_154_subsetI,axiom,
% 0.20/0.45 ! [A5: set_a,B5: set_a] :
% 0.20/0.45 ( ! [X5: a] :
% 0.20/0.45 ( ( member_a @ X5 @ A5 )
% 0.20/0.45 => ( member_a @ X5 @ B5 ) )
% 0.20/0.45 => ( ord_less_eq_set_a @ A5 @ B5 ) ) ).
% 0.20/0.45
% 0.20/0.45 % subsetI
% 0.20/0.45 thf(fact_155_subsetI,axiom,
% 0.20/0.45 ! [A5: set_Pr1070816379Tree_a,B5: set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ! [X5: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X5 @ A5 )
% 0.20/0.45 => ( member254315204Tree_a @ X5 @ B5 ) )
% 0.20/0.45 => ( ord_le1013007387Tree_a @ A5 @ B5 ) ) ).
% 0.20/0.45
% 0.20/0.45 % subsetI
% 0.20/0.45 thf(fact_156_Collect__restrict,axiom,
% 0.20/0.45 ! [X6: set_a,P: a > $o] :
% 0.20/0.45 ( ord_less_eq_set_a
% 0.20/0.45 @ ( collect_a
% 0.20/0.45 @ ^ [X4: a] :
% 0.20/0.45 ( ( member_a @ X4 @ X6 )
% 0.20/0.45 & ( P @ X4 ) ) )
% 0.20/0.45 @ X6 ) ).
% 0.20/0.45
% 0.20/0.45 % Collect_restrict
% 0.20/0.45 thf(fact_157_Collect__restrict,axiom,
% 0.20/0.45 ! [X6: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ord_le1013007387Tree_a
% 0.20/0.45 @ ( collec486369286Tree_a
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X4 @ X6 )
% 0.20/0.45 & ( P @ X4 ) ) )
% 0.20/0.45 @ X6 ) ).
% 0.20/0.45
% 0.20/0.45 % Collect_restrict
% 0.20/0.45 thf(fact_158_ssubst__Pair__rhs,axiom,
% 0.20/0.45 ! [R: a,S3: tree_a,R3: set_Pr1070816379Tree_a,S4: tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ ( produc686083979Tree_a @ R @ S3 ) @ R3 )
% 0.20/0.45 => ( ( S4 = S3 )
% 0.20/0.45 => ( member254315204Tree_a @ ( produc686083979Tree_a @ R @ S4 ) @ R3 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % ssubst_Pair_rhs
% 0.20/0.45 thf(fact_159_ssubst__Pair__rhs,axiom,
% 0.20/0.45 ! [R: tree_a,S3: a,R3: set_Pr921883667ee_a_a,S4: a] :
% 0.20/0.45 ( ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ R @ S3 ) @ R3 )
% 0.20/0.45 => ( ( S4 = S3 )
% 0.20/0.45 => ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ R @ S4 ) @ R3 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % ssubst_Pair_rhs
% 0.20/0.45 thf(fact_160_in__mono,axiom,
% 0.20/0.45 ! [A5: set_a,B5: set_a,X: a] :
% 0.20/0.45 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 0.20/0.45 => ( ( member_a @ X @ A5 )
% 0.20/0.45 => ( member_a @ X @ B5 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % in_mono
% 0.20/0.45 thf(fact_161_in__mono,axiom,
% 0.20/0.45 ! [A5: set_Pr1070816379Tree_a,B5: set_Pr1070816379Tree_a,X: produc143150363Tree_a] :
% 0.20/0.45 ( ( ord_le1013007387Tree_a @ A5 @ B5 )
% 0.20/0.45 => ( ( member254315204Tree_a @ X @ A5 )
% 0.20/0.45 => ( member254315204Tree_a @ X @ B5 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % in_mono
% 0.20/0.45 thf(fact_162_subsetD,axiom,
% 0.20/0.45 ! [A5: set_a,B5: set_a,C: a] :
% 0.20/0.45 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 0.20/0.45 => ( ( member_a @ C @ A5 )
% 0.20/0.45 => ( member_a @ C @ B5 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subsetD
% 0.20/0.45 thf(fact_163_subsetD,axiom,
% 0.20/0.45 ! [A5: set_Pr1070816379Tree_a,B5: set_Pr1070816379Tree_a,C: produc143150363Tree_a] :
% 0.20/0.45 ( ( ord_le1013007387Tree_a @ A5 @ B5 )
% 0.20/0.45 => ( ( member254315204Tree_a @ C @ A5 )
% 0.20/0.45 => ( member254315204Tree_a @ C @ B5 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subsetD
% 0.20/0.45 thf(fact_164_subset__eq,axiom,
% 0.20/0.45 ( ord_less_eq_set_a
% 0.20/0.45 = ( ^ [A6: set_a,B6: set_a] :
% 0.20/0.45 ! [X4: a] :
% 0.20/0.45 ( ( member_a @ X4 @ A6 )
% 0.20/0.45 => ( member_a @ X4 @ B6 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subset_eq
% 0.20/0.45 thf(fact_165_subset__eq,axiom,
% 0.20/0.45 ( ord_le1013007387Tree_a
% 0.20/0.45 = ( ^ [A6: set_Pr1070816379Tree_a,B6: set_Pr1070816379Tree_a] :
% 0.20/0.45 ! [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X4 @ A6 )
% 0.20/0.45 => ( member254315204Tree_a @ X4 @ B6 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subset_eq
% 0.20/0.45 thf(fact_166_subset__iff,axiom,
% 0.20/0.45 ( ord_less_eq_set_a
% 0.20/0.45 = ( ^ [A6: set_a,B6: set_a] :
% 0.20/0.45 ! [T: a] :
% 0.20/0.45 ( ( member_a @ T @ A6 )
% 0.20/0.45 => ( member_a @ T @ B6 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subset_iff
% 0.20/0.45 thf(fact_167_subset__iff,axiom,
% 0.20/0.45 ( ord_le1013007387Tree_a
% 0.20/0.45 = ( ^ [A6: set_Pr1070816379Tree_a,B6: set_Pr1070816379Tree_a] :
% 0.20/0.45 ! [T: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ T @ A6 )
% 0.20/0.45 => ( member254315204Tree_a @ T @ B6 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % subset_iff
% 0.20/0.45 thf(fact_168_Collect__mono,axiom,
% 0.20/0.45 ! [P: produc143150363Tree_a > $o,Q2: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ! [X5: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ X5 )
% 0.20/0.45 => ( Q2 @ X5 ) )
% 0.20/0.45 => ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ P ) @ ( collec486369286Tree_a @ Q2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Collect_mono
% 0.20/0.45 thf(fact_169_Collect__mono__iff,axiom,
% 0.20/0.45 ! [P: produc143150363Tree_a > $o,Q2: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ P ) @ ( collec486369286Tree_a @ Q2 ) )
% 0.20/0.45 = ( ! [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ X4 )
% 0.20/0.45 => ( Q2 @ X4 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Collect_mono_iff
% 0.20/0.45 thf(fact_170_Collect__subset,axiom,
% 0.20/0.45 ! [A5: set_a,P: a > $o] :
% 0.20/0.45 ( ord_less_eq_set_a
% 0.20/0.45 @ ( collect_a
% 0.20/0.45 @ ^ [X4: a] :
% 0.20/0.45 ( ( member_a @ X4 @ A5 )
% 0.20/0.45 & ( P @ X4 ) ) )
% 0.20/0.45 @ A5 ) ).
% 0.20/0.45
% 0.20/0.45 % Collect_subset
% 0.20/0.45 thf(fact_171_Collect__subset,axiom,
% 0.20/0.45 ! [A5: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ord_le1013007387Tree_a
% 0.20/0.45 @ ( collec486369286Tree_a
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X4 @ A5 )
% 0.20/0.45 & ( P @ X4 ) ) )
% 0.20/0.45 @ A5 ) ).
% 0.20/0.45
% 0.20/0.45 % Collect_subset
% 0.20/0.45 thf(fact_172_less__eq__set__def,axiom,
% 0.20/0.45 ( ord_less_eq_set_a
% 0.20/0.45 = ( ^ [A6: set_a,B6: set_a] :
% 0.20/0.45 ( ord_less_eq_a_o
% 0.20/0.45 @ ^ [X4: a] : ( member_a @ X4 @ A6 )
% 0.20/0.45 @ ^ [X4: a] : ( member_a @ X4 @ B6 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % less_eq_set_def
% 0.20/0.45 thf(fact_173_less__eq__set__def,axiom,
% 0.20/0.45 ( ord_le1013007387Tree_a
% 0.20/0.45 = ( ^ [A6: set_Pr1070816379Tree_a,B6: set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ord_le1601593986ee_a_o
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ A6 )
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ B6 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % less_eq_set_def
% 0.20/0.45 thf(fact_174_prop__restrict,axiom,
% 0.20/0.45 ! [X: a,Z3: set_a,X6: set_a,P: a > $o] :
% 0.20/0.45 ( ( member_a @ X @ Z3 )
% 0.20/0.45 => ( ( ord_less_eq_set_a @ Z3
% 0.20/0.45 @ ( collect_a
% 0.20/0.45 @ ^ [X4: a] :
% 0.20/0.45 ( ( member_a @ X4 @ X6 )
% 0.20/0.45 & ( P @ X4 ) ) ) )
% 0.20/0.45 => ( P @ X ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prop_restrict
% 0.20/0.45 thf(fact_175_prop__restrict,axiom,
% 0.20/0.45 ! [X: produc143150363Tree_a,Z3: set_Pr1070816379Tree_a,X6: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ( member254315204Tree_a @ X @ Z3 )
% 0.20/0.45 => ( ( ord_le1013007387Tree_a @ Z3
% 0.20/0.45 @ ( collec486369286Tree_a
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ X4 @ X6 )
% 0.20/0.45 & ( P @ X4 ) ) ) )
% 0.20/0.45 => ( P @ X ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prop_restrict
% 0.20/0.45 thf(fact_176_conj__subset__def,axiom,
% 0.20/0.45 ! [A5: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o,Q2: produc143150363Tree_a > $o] :
% 0.20/0.45 ( ( ord_le1013007387Tree_a @ A5
% 0.20/0.45 @ ( collec486369286Tree_a
% 0.20/0.45 @ ^ [X4: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ X4 )
% 0.20/0.45 & ( Q2 @ X4 ) ) ) )
% 0.20/0.45 = ( ( ord_le1013007387Tree_a @ A5 @ ( collec486369286Tree_a @ P ) )
% 0.20/0.45 & ( ord_le1013007387Tree_a @ A5 @ ( collec486369286Tree_a @ Q2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % conj_subset_def
% 0.20/0.45 thf(fact_177_image2__eqI,axiom,
% 0.20/0.45 ! [B: a,F: a > a,X: a,C: tree_a,G: a > tree_a,A5: set_a] :
% 0.20/0.45 ( ( B
% 0.20/0.45 = ( F @ X ) )
% 0.20/0.45 => ( ( C
% 0.20/0.45 = ( G @ X ) )
% 0.20/0.45 => ( ( member_a @ X @ A5 )
% 0.20/0.45 => ( member254315204Tree_a @ ( produc686083979Tree_a @ B @ C ) @ ( bNF_Gr651645592Tree_a @ A5 @ F @ G ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % image2_eqI
% 0.20/0.45 thf(fact_178_image2__eqI,axiom,
% 0.20/0.45 ! [B: a,F: produc143150363Tree_a > a,X: produc143150363Tree_a,C: tree_a,G: produc143150363Tree_a > tree_a,A5: set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ( B
% 0.20/0.45 = ( F @ X ) )
% 0.20/0.45 => ( ( C
% 0.20/0.45 = ( G @ X ) )
% 0.20/0.45 => ( ( member254315204Tree_a @ X @ A5 )
% 0.20/0.45 => ( member254315204Tree_a @ ( produc686083979Tree_a @ B @ C ) @ ( bNF_Gr2042500789Tree_a @ A5 @ F @ G ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % image2_eqI
% 0.20/0.45 thf(fact_179_image2__eqI,axiom,
% 0.20/0.45 ! [B: tree_a,F: a > tree_a,X: a,C: a,G: a > a,A5: set_a] :
% 0.20/0.45 ( ( B
% 0.20/0.45 = ( F @ X ) )
% 0.20/0.45 => ( ( C
% 0.20/0.45 = ( G @ X ) )
% 0.20/0.45 => ( ( member_a @ X @ A5 )
% 0.20/0.45 => ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ B @ C ) @ ( bNF_Gr614734384ee_a_a @ A5 @ F @ G ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % image2_eqI
% 0.20/0.45 thf(fact_180_image2__eqI,axiom,
% 0.20/0.45 ! [B: tree_a,F: produc143150363Tree_a > tree_a,X: produc143150363Tree_a,C: a,G: produc143150363Tree_a > a,A5: set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ( B
% 0.20/0.45 = ( F @ X ) )
% 0.20/0.45 => ( ( C
% 0.20/0.45 = ( G @ X ) )
% 0.20/0.45 => ( ( member254315204Tree_a @ X @ A5 )
% 0.20/0.45 => ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ B @ C ) @ ( bNF_Gr2005589581ee_a_a @ A5 @ F @ G ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % image2_eqI
% 0.20/0.45 thf(fact_181_GreatestI2__order,axiom,
% 0.20/0.45 ! [P: a > $o,X: a,Q2: a > $o] :
% 0.20/0.45 ( ( P @ X )
% 0.20/0.45 => ( ! [Y4: a] :
% 0.20/0.45 ( ( P @ Y4 )
% 0.20/0.45 => ( ord_less_eq_a @ Y4 @ X ) )
% 0.20/0.45 => ( ! [X5: a] :
% 0.20/0.45 ( ( P @ X5 )
% 0.20/0.45 => ( ! [Y6: a] :
% 0.20/0.45 ( ( P @ Y6 )
% 0.20/0.45 => ( ord_less_eq_a @ Y6 @ X5 ) )
% 0.20/0.45 => ( Q2 @ X5 ) ) )
% 0.20/0.45 => ( Q2 @ ( order_Greatest_a @ P ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % GreatestI2_order
% 0.20/0.45 thf(fact_182_Greatest__equality,axiom,
% 0.20/0.45 ! [P: a > $o,X: a] :
% 0.20/0.45 ( ( P @ X )
% 0.20/0.45 => ( ! [Y4: a] :
% 0.20/0.45 ( ( P @ Y4 )
% 0.20/0.45 => ( ord_less_eq_a @ Y4 @ X ) )
% 0.20/0.45 => ( ( order_Greatest_a @ P )
% 0.20/0.45 = X ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Greatest_equality
% 0.20/0.45 thf(fact_183_Heap__axioms__def,axiom,
% 0.20/0.45 ( heap_axioms_Tree_a_a
% 0.20/0.45 = ( ^ [Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,As_tree2: tree_a > tree_a,Remove_max2: tree_a > produc143150363Tree_a] :
% 0.20/0.45 ( ! [L4: tree_a] :
% 0.20/0.45 ( ( Multiset2 @ L4 )
% 0.20/0.45 = ( multiset_a2 @ ( As_tree2 @ L4 ) ) )
% 0.20/0.45 & ! [I: list_a] : ( is_heap_a @ ( As_tree2 @ ( Of_list2 @ I ) ) )
% 0.20/0.45 & ! [T: tree_a] :
% 0.20/0.45 ( ( ( As_tree2 @ T )
% 0.20/0.45 = e_a )
% 0.20/0.45 = ( Is_empty2 @ T ) )
% 0.20/0.45 & ! [L4: tree_a,M2: a,L5: tree_a] :
% 0.20/0.45 ( ~ ( Is_empty2 @ L4 )
% 0.20/0.45 => ( ( ( produc686083979Tree_a @ M2 @ L5 )
% 0.20/0.45 = ( Remove_max2 @ L4 ) )
% 0.20/0.45 => ( ( add_mset_a @ M2 @ ( Multiset2 @ L5 ) )
% 0.20/0.45 = ( Multiset2 @ L4 ) ) ) )
% 0.20/0.45 & ! [L4: tree_a,M2: a,L5: tree_a] :
% 0.20/0.45 ( ~ ( Is_empty2 @ L4 )
% 0.20/0.45 => ( ( is_heap_a @ ( As_tree2 @ L4 ) )
% 0.20/0.45 => ( ( ( produc686083979Tree_a @ M2 @ L5 )
% 0.20/0.45 = ( Remove_max2 @ L4 ) )
% 0.20/0.45 => ( is_heap_a @ ( As_tree2 @ L5 ) ) ) ) )
% 0.20/0.45 & ! [T: tree_a,M2: a,T4: tree_a] :
% 0.20/0.45 ( ~ ( Is_empty2 @ T )
% 0.20/0.45 => ( ( ( produc686083979Tree_a @ M2 @ T4 )
% 0.20/0.45 = ( Remove_max2 @ T ) )
% 0.20/0.45 => ( M2
% 0.20/0.45 = ( val_a @ ( As_tree2 @ T ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Heap_axioms_def
% 0.20/0.45 thf(fact_184_siftDown__multiset,axiom,
% 0.20/0.45 ! [T2: tree_a] :
% 0.20/0.45 ( ( multiset_a2 @ ( heapIm1091024090Down_a @ T2 ) )
% 0.20/0.45 = ( multiset_a2 @ T2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % siftDown_multiset
% 0.20/0.45 thf(fact_185_Heap_Oremove__max__multiset_H,axiom,
% 0.20/0.45 ! [Empty: tree_a,Is_empty: tree_a > $o,Of_list: list_a > tree_a,Multiset: tree_a > multiset_a,As_tree: tree_a > tree_a,Remove_max: tree_a > produc143150363Tree_a,L: tree_a,M: a,L3: tree_a] :
% 0.20/0.45 ( ( heap_Tree_a_a @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 0.20/0.45 => ( ~ ( Is_empty @ L )
% 0.20/0.45 => ( ( ( produc686083979Tree_a @ M @ L3 )
% 0.20/0.45 = ( Remove_max @ L ) )
% 0.20/0.45 => ( ( add_mset_a @ M @ ( Multiset @ L3 ) )
% 0.20/0.45 = ( Multiset @ L ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Heap.remove_max_multiset'
% 0.20/0.45 thf(fact_186_multiset__heapify,axiom,
% 0.20/0.45 ! [T2: tree_a] :
% 0.20/0.45 ( ( multiset_a2 @ ( heapIm970322378pify_a @ T2 ) )
% 0.20/0.45 = ( multiset_a2 @ T2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % multiset_heapify
% 0.20/0.45 thf(fact_187_Heap__axioms_Ointro,axiom,
% 0.20/0.45 ! [Multiset: tree_a > multiset_a,As_tree: tree_a > tree_a,Of_list: list_a > tree_a,Is_empty: tree_a > $o,Remove_max: tree_a > produc143150363Tree_a] :
% 0.20/0.45 ( ! [L6: tree_a] :
% 0.20/0.45 ( ( Multiset @ L6 )
% 0.20/0.45 = ( multiset_a2 @ ( As_tree @ L6 ) ) )
% 0.20/0.45 => ( ! [I2: list_a] : ( is_heap_a @ ( As_tree @ ( Of_list @ I2 ) ) )
% 0.20/0.45 => ( ! [T5: tree_a] :
% 0.20/0.45 ( ( ( As_tree @ T5 )
% 0.20/0.45 = e_a )
% 0.20/0.45 = ( Is_empty @ T5 ) )
% 0.20/0.45 => ( ! [L6: tree_a,M3: a,L2: tree_a] :
% 0.20/0.45 ( ~ ( Is_empty @ L6 )
% 0.20/0.45 => ( ( ( produc686083979Tree_a @ M3 @ L2 )
% 0.20/0.45 = ( Remove_max @ L6 ) )
% 0.20/0.45 => ( ( add_mset_a @ M3 @ ( Multiset @ L2 ) )
% 0.20/0.45 = ( Multiset @ L6 ) ) ) )
% 0.20/0.45 => ( ! [L6: tree_a,M3: a,L2: tree_a] :
% 0.20/0.45 ( ~ ( Is_empty @ L6 )
% 0.20/0.45 => ( ( is_heap_a @ ( As_tree @ L6 ) )
% 0.20/0.45 => ( ( ( produc686083979Tree_a @ M3 @ L2 )
% 0.20/0.45 = ( Remove_max @ L6 ) )
% 0.20/0.45 => ( is_heap_a @ ( As_tree @ L2 ) ) ) ) )
% 0.20/0.45 => ( ! [T5: tree_a,M3: a,T6: tree_a] :
% 0.20/0.45 ( ~ ( Is_empty @ T5 )
% 0.20/0.45 => ( ( ( produc686083979Tree_a @ M3 @ T6 )
% 0.20/0.45 = ( Remove_max @ T5 ) )
% 0.20/0.45 => ( M3
% 0.20/0.45 = ( val_a @ ( As_tree @ T5 ) ) ) ) )
% 0.20/0.45 => ( heap_axioms_Tree_a_a @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Heap_axioms.intro
% 0.20/0.45 thf(fact_188_heap__top__geq,axiom,
% 0.20/0.45 ! [A: a,T2: tree_a] :
% 0.20/0.45 ( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ T2 ) ) )
% 0.20/0.45 => ( ( is_heap_a @ T2 )
% 0.20/0.45 => ( ord_less_eq_a @ A @ ( val_a @ T2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % heap_top_geq
% 0.20/0.45 thf(fact_189_prod_Osplit__sel__asm,axiom,
% 0.20/0.45 ! [P: $o > $o,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 0.20/0.45 = ( ~ ( ( Prod
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 0.20/0.45 & ~ ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.split_sel_asm
% 0.20/0.45 thf(fact_190_prod_Osplit__sel__asm,axiom,
% 0.20/0.45 ! [P: tree_a > $o,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ ( produc873356882Tree_a @ F @ Prod ) )
% 0.20/0.45 = ( ~ ( ( Prod
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 0.20/0.45 & ~ ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.split_sel_asm
% 0.20/0.45 thf(fact_191_prod_Osplit__sel__asm,axiom,
% 0.20/0.45 ! [P: produc143150363Tree_a > $o,F: tree_a > a > produc143150363Tree_a,Prod: produc981471411ee_a_a] :
% 0.20/0.45 ( ( P @ ( produc369019363Tree_a @ F @ Prod ) )
% 0.20/0.45 = ( ~ ( ( Prod
% 0.20/0.45 = ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) )
% 0.20/0.45 & ~ ( P @ ( F @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.split_sel_asm
% 0.20/0.45 thf(fact_192_prod_Osplit__sel__asm,axiom,
% 0.20/0.45 ! [P: produc981471411ee_a_a > $o,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 0.20/0.45 = ( ~ ( ( Prod
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 0.20/0.45 & ~ ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.split_sel_asm
% 0.20/0.45 thf(fact_193_prod_Osplit__sel,axiom,
% 0.20/0.45 ! [P: $o > $o,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 0.20/0.45 = ( ( Prod
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 0.20/0.45 => ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.split_sel
% 0.20/0.45 thf(fact_194_prod_Osplit__sel,axiom,
% 0.20/0.45 ! [P: tree_a > $o,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ ( produc873356882Tree_a @ F @ Prod ) )
% 0.20/0.45 = ( ( Prod
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 0.20/0.45 => ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.split_sel
% 0.20/0.45 thf(fact_195_prod_Osplit__sel,axiom,
% 0.20/0.45 ! [P: produc143150363Tree_a > $o,F: tree_a > a > produc143150363Tree_a,Prod: produc981471411ee_a_a] :
% 0.20/0.45 ( ( P @ ( produc369019363Tree_a @ F @ Prod ) )
% 0.20/0.45 = ( ( Prod
% 0.20/0.45 = ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) )
% 0.20/0.45 => ( P @ ( F @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.split_sel
% 0.20/0.45 thf(fact_196_prod_Osplit__sel,axiom,
% 0.20/0.45 ! [P: produc981471411ee_a_a > $o,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( P @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 0.20/0.45 = ( ( Prod
% 0.20/0.45 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 0.20/0.45 => ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.split_sel
% 0.20/0.45 thf(fact_197_mem__case__prodI,axiom,
% 0.20/0.45 ! [Z: a,C: a > tree_a > set_a,A: a,B: tree_a] :
% 0.20/0.45 ( ( member_a @ Z @ ( C @ A @ B ) )
% 0.20/0.45 => ( member_a @ Z @ ( produc1902270_set_a @ C @ ( produc686083979Tree_a @ A @ B ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_case_prodI
% 0.20/0.45 thf(fact_198_mem__case__prodI,axiom,
% 0.20/0.45 ! [Z: produc143150363Tree_a,C: a > tree_a > set_Pr1070816379Tree_a,A: a,B: tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ Z @ ( C @ A @ B ) )
% 0.20/0.45 => ( member254315204Tree_a @ Z @ ( produc802621147Tree_a @ C @ ( produc686083979Tree_a @ A @ B ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_case_prodI
% 0.20/0.45 thf(fact_199_mem__case__prodI,axiom,
% 0.20/0.45 ! [Z: a,C: tree_a > a > set_a,A: tree_a,B: a] :
% 0.20/0.45 ( ( member_a @ Z @ ( C @ A @ B ) )
% 0.20/0.45 => ( member_a @ Z @ ( produc136688934_set_a @ C @ ( produc649172771ee_a_a @ A @ B ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_case_prodI
% 0.20/0.45 thf(fact_200_mem__case__prodI,axiom,
% 0.20/0.45 ! [Z: produc143150363Tree_a,C: tree_a > a > set_Pr1070816379Tree_a,A: tree_a,B: a] :
% 0.20/0.45 ( ( member254315204Tree_a @ Z @ ( C @ A @ B ) )
% 0.20/0.45 => ( member254315204Tree_a @ Z @ ( produc951236931Tree_a @ C @ ( produc649172771ee_a_a @ A @ B ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_case_prodI
% 0.20/0.45 thf(fact_201_mem__case__prodI2,axiom,
% 0.20/0.45 ! [P2: produc143150363Tree_a,Z: a,C: a > tree_a > set_a] :
% 0.20/0.45 ( ! [A4: a,B4: tree_a] :
% 0.20/0.45 ( ( P2
% 0.20/0.45 = ( produc686083979Tree_a @ A4 @ B4 ) )
% 0.20/0.45 => ( member_a @ Z @ ( C @ A4 @ B4 ) ) )
% 0.20/0.45 => ( member_a @ Z @ ( produc1902270_set_a @ C @ P2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_case_prodI2
% 0.20/0.45 thf(fact_202_mem__case__prodI2,axiom,
% 0.20/0.45 ! [P2: produc143150363Tree_a,Z: produc143150363Tree_a,C: a > tree_a > set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ! [A4: a,B4: tree_a] :
% 0.20/0.45 ( ( P2
% 0.20/0.45 = ( produc686083979Tree_a @ A4 @ B4 ) )
% 0.20/0.45 => ( member254315204Tree_a @ Z @ ( C @ A4 @ B4 ) ) )
% 0.20/0.45 => ( member254315204Tree_a @ Z @ ( produc802621147Tree_a @ C @ P2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_case_prodI2
% 0.20/0.45 thf(fact_203_mem__case__prodI2,axiom,
% 0.20/0.45 ! [P2: produc981471411ee_a_a,Z: a,C: tree_a > a > set_a] :
% 0.20/0.45 ( ! [A4: tree_a,B4: a] :
% 0.20/0.45 ( ( P2
% 0.20/0.45 = ( produc649172771ee_a_a @ A4 @ B4 ) )
% 0.20/0.45 => ( member_a @ Z @ ( C @ A4 @ B4 ) ) )
% 0.20/0.45 => ( member_a @ Z @ ( produc136688934_set_a @ C @ P2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_case_prodI2
% 0.20/0.45 thf(fact_204_mem__case__prodI2,axiom,
% 0.20/0.45 ! [P2: produc981471411ee_a_a,Z: produc143150363Tree_a,C: tree_a > a > set_Pr1070816379Tree_a] :
% 0.20/0.45 ( ! [A4: tree_a,B4: a] :
% 0.20/0.45 ( ( P2
% 0.20/0.45 = ( produc649172771ee_a_a @ A4 @ B4 ) )
% 0.20/0.45 => ( member254315204Tree_a @ Z @ ( C @ A4 @ B4 ) ) )
% 0.20/0.45 => ( member254315204Tree_a @ Z @ ( produc951236931Tree_a @ C @ P2 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_case_prodI2
% 0.20/0.45 thf(fact_205_case__prodI,axiom,
% 0.20/0.45 ! [F: tree_a > a > $o,A: tree_a,B: a] :
% 0.20/0.45 ( ( F @ A @ B )
% 0.20/0.45 => ( produc1587316832_a_a_o @ F @ ( produc649172771ee_a_a @ A @ B ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prodI
% 0.20/0.45 thf(fact_206_case__prodI,axiom,
% 0.20/0.45 ! [F: a > tree_a > $o,A: a,B: tree_a] :
% 0.20/0.45 ( ( F @ A @ B )
% 0.20/0.45 => ( produc1673233912ee_a_o @ F @ ( produc686083979Tree_a @ A @ B ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prodI
% 0.20/0.45 thf(fact_207_case__prodI2,axiom,
% 0.20/0.45 ! [P2: produc981471411ee_a_a,C: tree_a > a > $o] :
% 0.20/0.45 ( ! [A4: tree_a,B4: a] :
% 0.20/0.45 ( ( P2
% 0.20/0.45 = ( produc649172771ee_a_a @ A4 @ B4 ) )
% 0.20/0.45 => ( C @ A4 @ B4 ) )
% 0.20/0.45 => ( produc1587316832_a_a_o @ C @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prodI2
% 0.20/0.45 thf(fact_208_case__prodI2,axiom,
% 0.20/0.45 ! [P2: produc143150363Tree_a,C: a > tree_a > $o] :
% 0.20/0.45 ( ! [A4: a,B4: tree_a] :
% 0.20/0.45 ( ( P2
% 0.20/0.45 = ( produc686083979Tree_a @ A4 @ B4 ) )
% 0.20/0.45 => ( C @ A4 @ B4 ) )
% 0.20/0.45 => ( produc1673233912ee_a_o @ C @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prodI2
% 0.20/0.45 thf(fact_209_case__prod__conv,axiom,
% 0.20/0.45 ! [F: a > tree_a > $o,A: a,B: tree_a] :
% 0.20/0.45 ( ( produc1673233912ee_a_o @ F @ ( produc686083979Tree_a @ A @ B ) )
% 0.20/0.45 = ( F @ A @ B ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prod_conv
% 0.20/0.45 thf(fact_210_case__prod__conv,axiom,
% 0.20/0.45 ! [F: a > tree_a > tree_a,A: a,B: tree_a] :
% 0.20/0.45 ( ( produc873356882Tree_a @ F @ ( produc686083979Tree_a @ A @ B ) )
% 0.20/0.45 = ( F @ A @ B ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prod_conv
% 0.20/0.45 thf(fact_211_case__prod__conv,axiom,
% 0.20/0.45 ! [F: tree_a > a > produc143150363Tree_a,A: tree_a,B: a] :
% 0.20/0.45 ( ( produc369019363Tree_a @ F @ ( produc649172771ee_a_a @ A @ B ) )
% 0.20/0.45 = ( F @ A @ B ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prod_conv
% 0.20/0.45 thf(fact_212_case__prod__conv,axiom,
% 0.20/0.45 ! [F: a > tree_a > produc981471411ee_a_a,A: a,B: tree_a] :
% 0.20/0.45 ( ( produc1331510035ee_a_a @ F @ ( produc686083979Tree_a @ A @ B ) )
% 0.20/0.45 = ( F @ A @ B ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prod_conv
% 0.20/0.45 thf(fact_213_case__swap,axiom,
% 0.20/0.45 ! [F: a > tree_a > $o,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( produc1587316832_a_a_o
% 0.20/0.45 @ ^ [Y5: tree_a,X4: a] : ( F @ X4 @ Y5 )
% 0.20/0.45 @ ( produc1515207979Tree_a @ P2 ) )
% 0.20/0.45 = ( produc1673233912ee_a_o @ F @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_swap
% 0.20/0.45 thf(fact_214_case__swap,axiom,
% 0.20/0.45 ! [F: a > tree_a > tree_a,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( produc433477818Tree_a
% 0.20/0.45 @ ^ [Y5: tree_a,X4: a] : ( F @ X4 @ Y5 )
% 0.20/0.45 @ ( produc1515207979Tree_a @ P2 ) )
% 0.20/0.45 = ( produc873356882Tree_a @ F @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_swap
% 0.20/0.45 thf(fact_215_case__swap,axiom,
% 0.20/0.45 ! [F: tree_a > a > produc143150363Tree_a,P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( produc493188987Tree_a
% 0.20/0.45 @ ^ [Y5: a,X4: tree_a] : ( F @ X4 @ Y5 )
% 0.20/0.45 @ ( produc1478296771ee_a_a @ P2 ) )
% 0.20/0.45 = ( produc369019363Tree_a @ F @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_swap
% 0.20/0.45 thf(fact_216_case__swap,axiom,
% 0.20/0.45 ! [F: a > tree_a > produc981471411ee_a_a,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( produc1207340411ee_a_a
% 0.20/0.45 @ ^ [Y5: tree_a,X4: a] : ( F @ X4 @ Y5 )
% 0.20/0.45 @ ( produc1515207979Tree_a @ P2 ) )
% 0.20/0.45 = ( produc1331510035ee_a_a @ F @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_swap
% 0.20/0.45 thf(fact_217_case__swap,axiom,
% 0.20/0.45 ! [F: tree_a > a > $o,P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( produc1673233912ee_a_o
% 0.20/0.45 @ ^ [Y5: a,X4: tree_a] : ( F @ X4 @ Y5 )
% 0.20/0.45 @ ( produc1478296771ee_a_a @ P2 ) )
% 0.20/0.45 = ( produc1587316832_a_a_o @ F @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_swap
% 0.20/0.45 thf(fact_218_case__swap,axiom,
% 0.20/0.45 ! [F: tree_a > a > tree_a,P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( produc873356882Tree_a
% 0.20/0.45 @ ^ [Y5: a,X4: tree_a] : ( F @ X4 @ Y5 )
% 0.20/0.45 @ ( produc1478296771ee_a_a @ P2 ) )
% 0.20/0.45 = ( produc433477818Tree_a @ F @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_swap
% 0.20/0.45 thf(fact_219_case__swap,axiom,
% 0.20/0.45 ! [F: a > tree_a > produc143150363Tree_a,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( produc369019363Tree_a
% 0.20/0.45 @ ^ [Y5: tree_a,X4: a] : ( F @ X4 @ Y5 )
% 0.20/0.45 @ ( produc1515207979Tree_a @ P2 ) )
% 0.20/0.45 = ( produc493188987Tree_a @ F @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_swap
% 0.20/0.45 thf(fact_220_case__swap,axiom,
% 0.20/0.45 ! [F: tree_a > a > produc981471411ee_a_a,P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( produc1331510035ee_a_a
% 0.20/0.45 @ ^ [Y5: a,X4: tree_a] : ( F @ X4 @ Y5 )
% 0.20/0.45 @ ( produc1478296771ee_a_a @ P2 ) )
% 0.20/0.45 = ( produc1207340411ee_a_a @ F @ P2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_swap
% 0.20/0.45 thf(fact_221_Product__Type_OCollect__case__prodD,axiom,
% 0.20/0.45 ! [X: produc981471411ee_a_a,A5: tree_a > a > $o] :
% 0.20/0.45 ( ( member1092636252ee_a_a @ X @ ( collec1324690334ee_a_a @ ( produc1587316832_a_a_o @ A5 ) ) )
% 0.20/0.45 => ( A5 @ ( product_fst_Tree_a_a @ X ) @ ( product_snd_Tree_a_a @ X ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Product_Type.Collect_case_prodD
% 0.20/0.45 thf(fact_222_Product__Type_OCollect__case__prodD,axiom,
% 0.20/0.45 ! [X: produc143150363Tree_a,A5: a > tree_a > $o] :
% 0.20/0.45 ( ( member254315204Tree_a @ X @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ A5 ) ) )
% 0.20/0.45 => ( A5 @ ( product_fst_a_Tree_a @ X ) @ ( product_snd_a_Tree_a @ X ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % Product_Type.Collect_case_prodD
% 0.20/0.45 thf(fact_223_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: $o > $o,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( H @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 0.20/0.45 = ( produc1673233912ee_a_o
% 0.20/0.45 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_224_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: $o > tree_a,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( H @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 0.20/0.45 = ( produc873356882Tree_a
% 0.20/0.45 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_225_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: $o > produc981471411ee_a_a,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( H @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 0.20/0.45 = ( produc1331510035ee_a_a
% 0.20/0.45 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_226_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: tree_a > $o,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( H @ ( produc873356882Tree_a @ F @ Prod ) )
% 0.20/0.45 = ( produc1673233912ee_a_o
% 0.20/0.45 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_227_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: tree_a > tree_a,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( H @ ( produc873356882Tree_a @ F @ Prod ) )
% 0.20/0.45 = ( produc873356882Tree_a
% 0.20/0.45 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_228_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: tree_a > produc981471411ee_a_a,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( H @ ( produc873356882Tree_a @ F @ Prod ) )
% 0.20/0.45 = ( produc1331510035ee_a_a
% 0.20/0.45 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_229_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: produc143150363Tree_a > produc143150363Tree_a,F: tree_a > a > produc143150363Tree_a,Prod: produc981471411ee_a_a] :
% 0.20/0.45 ( ( H @ ( produc369019363Tree_a @ F @ Prod ) )
% 0.20/0.45 = ( produc369019363Tree_a
% 0.20/0.45 @ ^ [X13: tree_a,X25: a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_230_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: produc981471411ee_a_a > $o,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( H @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 0.20/0.45 = ( produc1673233912ee_a_o
% 0.20/0.45 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_231_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: produc981471411ee_a_a > tree_a,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( H @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 0.20/0.45 = ( produc873356882Tree_a
% 0.20/0.45 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_232_prod_Ocase__distrib,axiom,
% 0.20/0.45 ! [H: produc981471411ee_a_a > produc981471411ee_a_a,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 0.20/0.45 ( ( H @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 0.20/0.45 = ( produc1331510035ee_a_a
% 0.20/0.45 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 0.20/0.45 @ Prod ) ) ).
% 0.20/0.45
% 0.20/0.45 % prod.case_distrib
% 0.20/0.45 thf(fact_233_case__prodE,axiom,
% 0.20/0.45 ! [C: tree_a > a > $o,P2: produc981471411ee_a_a] :
% 0.20/0.45 ( ( produc1587316832_a_a_o @ C @ P2 )
% 0.20/0.45 => ~ ! [X5: tree_a,Y4: a] :
% 0.20/0.45 ( ( P2
% 0.20/0.45 = ( produc649172771ee_a_a @ X5 @ Y4 ) )
% 0.20/0.45 => ~ ( C @ X5 @ Y4 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prodE
% 0.20/0.45 thf(fact_234_case__prodE,axiom,
% 0.20/0.45 ! [C: a > tree_a > $o,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( produc1673233912ee_a_o @ C @ P2 )
% 0.20/0.45 => ~ ! [X5: a,Y4: tree_a] :
% 0.20/0.45 ( ( P2
% 0.20/0.45 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 0.20/0.45 => ~ ( C @ X5 @ Y4 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prodE
% 0.20/0.45 thf(fact_235_case__prodD,axiom,
% 0.20/0.45 ! [F: tree_a > a > $o,A: tree_a,B: a] :
% 0.20/0.45 ( ( produc1587316832_a_a_o @ F @ ( produc649172771ee_a_a @ A @ B ) )
% 0.20/0.45 => ( F @ A @ B ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prodD
% 0.20/0.45 thf(fact_236_case__prodD,axiom,
% 0.20/0.45 ! [F: a > tree_a > $o,A: a,B: tree_a] :
% 0.20/0.45 ( ( produc1673233912ee_a_o @ F @ ( produc686083979Tree_a @ A @ B ) )
% 0.20/0.45 => ( F @ A @ B ) ) ).
% 0.20/0.45
% 0.20/0.45 % case_prodD
% 0.20/0.45 thf(fact_237_old_Oprod_Ocase,axiom,
% 0.20/0.45 ! [F: a > tree_a > $o,X12: a,X24: tree_a] :
% 0.20/0.45 ( ( produc1673233912ee_a_o @ F @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 0.20/0.45 = ( F @ X12 @ X24 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.case
% 0.20/0.45 thf(fact_238_old_Oprod_Ocase,axiom,
% 0.20/0.45 ! [F: a > tree_a > tree_a,X12: a,X24: tree_a] :
% 0.20/0.45 ( ( produc873356882Tree_a @ F @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 0.20/0.45 = ( F @ X12 @ X24 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.case
% 0.20/0.45 thf(fact_239_old_Oprod_Ocase,axiom,
% 0.20/0.45 ! [F: tree_a > a > produc143150363Tree_a,X12: tree_a,X24: a] :
% 0.20/0.45 ( ( produc369019363Tree_a @ F @ ( produc649172771ee_a_a @ X12 @ X24 ) )
% 0.20/0.45 = ( F @ X12 @ X24 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.case
% 0.20/0.45 thf(fact_240_old_Oprod_Ocase,axiom,
% 0.20/0.45 ! [F: a > tree_a > produc981471411ee_a_a,X12: a,X24: tree_a] :
% 0.20/0.45 ( ( produc1331510035ee_a_a @ F @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 0.20/0.45 = ( F @ X12 @ X24 ) ) ).
% 0.20/0.45
% 0.20/0.45 % old.prod.case
% 0.20/0.45 thf(fact_241_mem__case__prodE,axiom,
% 0.20/0.45 ! [Z: a,C: a > tree_a > set_a,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( member_a @ Z @ ( produc1902270_set_a @ C @ P2 ) )
% 0.20/0.45 => ~ ! [X5: a,Y4: tree_a] :
% 0.20/0.45 ( ( P2
% 0.20/0.45 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 0.20/0.45 => ~ ( member_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % mem_case_prodE
% 0.20/0.45 thf(fact_242_mem__case__prodE,axiom,
% 0.20/0.45 ! [Z: produc143150363Tree_a,C: a > tree_a > set_Pr1070816379Tree_a,P2: produc143150363Tree_a] :
% 0.20/0.45 ( ( member254315204Tree_a @ Z @ ( produc802621147Tree_a @ C @ P2 ) )
% 0.20/0.45 => ~ ! [X5: a,Y4: tree_a] :
% 0.20/0.45 ( ( P2
% 0.31/0.45 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 0.31/0.45 => ~ ( member254315204Tree_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % mem_case_prodE
% 0.31/0.45 thf(fact_243_mem__case__prodE,axiom,
% 0.31/0.45 ! [Z: a,C: tree_a > a > set_a,P2: produc981471411ee_a_a] :
% 0.31/0.45 ( ( member_a @ Z @ ( produc136688934_set_a @ C @ P2 ) )
% 0.31/0.45 => ~ ! [X5: tree_a,Y4: a] :
% 0.31/0.45 ( ( P2
% 0.31/0.45 = ( produc649172771ee_a_a @ X5 @ Y4 ) )
% 0.31/0.45 => ~ ( member_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % mem_case_prodE
% 0.31/0.45 thf(fact_244_mem__case__prodE,axiom,
% 0.31/0.45 ! [Z: produc143150363Tree_a,C: tree_a > a > set_Pr1070816379Tree_a,P2: produc981471411ee_a_a] :
% 0.31/0.45 ( ( member254315204Tree_a @ Z @ ( produc951236931Tree_a @ C @ P2 ) )
% 0.31/0.45 => ~ ! [X5: tree_a,Y4: a] :
% 0.31/0.45 ( ( P2
% 0.31/0.45 = ( produc649172771ee_a_a @ X5 @ Y4 ) )
% 0.31/0.45 => ~ ( member254315204Tree_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % mem_case_prodE
% 0.31/0.45 thf(fact_245_snd__def,axiom,
% 0.31/0.45 ( product_snd_a_Tree_a
% 0.31/0.45 = ( produc873356882Tree_a
% 0.31/0.45 @ ^ [X13: a,X25: tree_a] : X25 ) ) ).
% 0.31/0.45
% 0.31/0.45 % snd_def
% 0.31/0.45 thf(fact_246_fst__def,axiom,
% 0.31/0.45 ( product_fst_a_Tree_a
% 0.31/0.45 = ( produc950721886ee_a_a
% 0.31/0.45 @ ^ [X13: a,X25: tree_a] : X13 ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_def
% 0.31/0.45 thf(fact_247_fst__def,axiom,
% 0.31/0.45 ( product_fst_Tree_a_a
% 0.31/0.45 = ( produc433477818Tree_a
% 0.31/0.45 @ ^ [X13: tree_a,X25: a] : X13 ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_def
% 0.31/0.45 thf(fact_248_case__prodE2,axiom,
% 0.31/0.45 ! [Q2: $o > $o,P: a > tree_a > $o,Z: produc143150363Tree_a] :
% 0.31/0.45 ( ( Q2 @ ( produc1673233912ee_a_o @ P @ Z ) )
% 0.31/0.45 => ~ ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( Z
% 0.31/0.45 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 0.31/0.45 => ~ ( Q2 @ ( P @ X5 @ Y4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prodE2
% 0.31/0.45 thf(fact_249_case__prodE2,axiom,
% 0.31/0.45 ! [Q2: tree_a > $o,P: a > tree_a > tree_a,Z: produc143150363Tree_a] :
% 0.31/0.45 ( ( Q2 @ ( produc873356882Tree_a @ P @ Z ) )
% 0.31/0.45 => ~ ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( Z
% 0.31/0.45 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 0.31/0.45 => ~ ( Q2 @ ( P @ X5 @ Y4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prodE2
% 0.31/0.45 thf(fact_250_case__prodE2,axiom,
% 0.31/0.45 ! [Q2: produc143150363Tree_a > $o,P: tree_a > a > produc143150363Tree_a,Z: produc981471411ee_a_a] :
% 0.31/0.45 ( ( Q2 @ ( produc369019363Tree_a @ P @ Z ) )
% 0.31/0.45 => ~ ! [X5: tree_a,Y4: a] :
% 0.31/0.45 ( ( Z
% 0.31/0.45 = ( produc649172771ee_a_a @ X5 @ Y4 ) )
% 0.31/0.45 => ~ ( Q2 @ ( P @ X5 @ Y4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prodE2
% 0.31/0.45 thf(fact_251_case__prodE2,axiom,
% 0.31/0.45 ! [Q2: produc981471411ee_a_a > $o,P: a > tree_a > produc981471411ee_a_a,Z: produc143150363Tree_a] :
% 0.31/0.45 ( ( Q2 @ ( produc1331510035ee_a_a @ P @ Z ) )
% 0.31/0.45 => ~ ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( Z
% 0.31/0.45 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 0.31/0.45 => ~ ( Q2 @ ( P @ X5 @ Y4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prodE2
% 0.31/0.45 thf(fact_252_case__prod__eta,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > $o] :
% 0.31/0.45 ( ( produc1673233912ee_a_o
% 0.31/0.45 @ ^ [X4: a,Y5: tree_a] : ( F @ ( produc686083979Tree_a @ X4 @ Y5 ) ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_eta
% 0.31/0.45 thf(fact_253_case__prod__eta,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > tree_a] :
% 0.31/0.45 ( ( produc873356882Tree_a
% 0.31/0.45 @ ^ [X4: a,Y5: tree_a] : ( F @ ( produc686083979Tree_a @ X4 @ Y5 ) ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_eta
% 0.31/0.45 thf(fact_254_case__prod__eta,axiom,
% 0.31/0.45 ! [F: produc981471411ee_a_a > produc143150363Tree_a] :
% 0.31/0.45 ( ( produc369019363Tree_a
% 0.31/0.45 @ ^ [X4: tree_a,Y5: a] : ( F @ ( produc649172771ee_a_a @ X4 @ Y5 ) ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_eta
% 0.31/0.45 thf(fact_255_case__prod__eta,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > produc981471411ee_a_a] :
% 0.31/0.45 ( ( produc1331510035ee_a_a
% 0.31/0.45 @ ^ [X4: a,Y5: tree_a] : ( F @ ( produc686083979Tree_a @ X4 @ Y5 ) ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_eta
% 0.31/0.45 thf(fact_256_cond__case__prod__eta,axiom,
% 0.31/0.45 ! [F: a > tree_a > $o,G: produc143150363Tree_a > $o] :
% 0.31/0.45 ( ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( F @ X5 @ Y4 )
% 0.31/0.45 = ( G @ ( produc686083979Tree_a @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( ( produc1673233912ee_a_o @ F )
% 0.31/0.45 = G ) ) ).
% 0.31/0.45
% 0.31/0.45 % cond_case_prod_eta
% 0.31/0.45 thf(fact_257_cond__case__prod__eta,axiom,
% 0.31/0.45 ! [F: a > tree_a > tree_a,G: produc143150363Tree_a > tree_a] :
% 0.31/0.45 ( ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( F @ X5 @ Y4 )
% 0.31/0.45 = ( G @ ( produc686083979Tree_a @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( ( produc873356882Tree_a @ F )
% 0.31/0.45 = G ) ) ).
% 0.31/0.45
% 0.31/0.45 % cond_case_prod_eta
% 0.31/0.45 thf(fact_258_cond__case__prod__eta,axiom,
% 0.31/0.45 ! [F: tree_a > a > produc143150363Tree_a,G: produc981471411ee_a_a > produc143150363Tree_a] :
% 0.31/0.45 ( ! [X5: tree_a,Y4: a] :
% 0.31/0.45 ( ( F @ X5 @ Y4 )
% 0.31/0.45 = ( G @ ( produc649172771ee_a_a @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( ( produc369019363Tree_a @ F )
% 0.31/0.45 = G ) ) ).
% 0.31/0.45
% 0.31/0.45 % cond_case_prod_eta
% 0.31/0.45 thf(fact_259_cond__case__prod__eta,axiom,
% 0.31/0.45 ! [F: a > tree_a > produc981471411ee_a_a,G: produc143150363Tree_a > produc981471411ee_a_a] :
% 0.31/0.45 ( ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( F @ X5 @ Y4 )
% 0.31/0.45 = ( G @ ( produc686083979Tree_a @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( ( produc1331510035ee_a_a @ F )
% 0.31/0.45 = G ) ) ).
% 0.31/0.45
% 0.31/0.45 % cond_case_prod_eta
% 0.31/0.45 thf(fact_260_case__prod__Pair__iden,axiom,
% 0.31/0.45 ! [P2: produc143150363Tree_a] :
% 0.31/0.45 ( ( produc493188987Tree_a @ produc686083979Tree_a @ P2 )
% 0.31/0.45 = P2 ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_Pair_iden
% 0.31/0.45 thf(fact_261_case__prod__Pair__iden,axiom,
% 0.31/0.45 ! [P2: produc981471411ee_a_a] :
% 0.31/0.45 ( ( produc1207340411ee_a_a @ produc649172771ee_a_a @ P2 )
% 0.31/0.45 = P2 ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_Pair_iden
% 0.31/0.45 thf(fact_262_Collect__case__prod__mono,axiom,
% 0.31/0.45 ! [A5: a > tree_a > $o,B5: a > tree_a > $o] :
% 0.31/0.45 ( ( ord_le1327026842ee_a_o @ A5 @ B5 )
% 0.31/0.45 => ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ A5 ) ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ B5 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % Collect_case_prod_mono
% 0.31/0.45 thf(fact_263_prod_Ocase__eq__if,axiom,
% 0.31/0.45 ( produc1673233912ee_a_o
% 0.31/0.45 = ( ^ [F2: a > tree_a > $o,Prod3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ Prod3 ) @ ( product_snd_a_Tree_a @ Prod3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % prod.case_eq_if
% 0.31/0.45 thf(fact_264_prod_Ocase__eq__if,axiom,
% 0.31/0.45 ( produc873356882Tree_a
% 0.31/0.45 = ( ^ [F2: a > tree_a > tree_a,Prod3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ Prod3 ) @ ( product_snd_a_Tree_a @ Prod3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % prod.case_eq_if
% 0.31/0.45 thf(fact_265_prod_Ocase__eq__if,axiom,
% 0.31/0.45 ( produc369019363Tree_a
% 0.31/0.45 = ( ^ [F2: tree_a > a > produc143150363Tree_a,Prod3: produc981471411ee_a_a] : ( F2 @ ( product_fst_Tree_a_a @ Prod3 ) @ ( product_snd_Tree_a_a @ Prod3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % prod.case_eq_if
% 0.31/0.45 thf(fact_266_prod_Ocase__eq__if,axiom,
% 0.31/0.45 ( produc1331510035ee_a_a
% 0.31/0.45 = ( ^ [F2: a > tree_a > produc981471411ee_a_a,Prod3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ Prod3 ) @ ( product_snd_a_Tree_a @ Prod3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % prod.case_eq_if
% 0.31/0.45 thf(fact_267_case__prod__beta,axiom,
% 0.31/0.45 ( produc1673233912ee_a_o
% 0.31/0.45 = ( ^ [F2: a > tree_a > $o,P3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_beta
% 0.31/0.45 thf(fact_268_case__prod__beta,axiom,
% 0.31/0.45 ( produc873356882Tree_a
% 0.31/0.45 = ( ^ [F2: a > tree_a > tree_a,P3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_beta
% 0.31/0.45 thf(fact_269_case__prod__beta,axiom,
% 0.31/0.45 ( produc369019363Tree_a
% 0.31/0.45 = ( ^ [F2: tree_a > a > produc143150363Tree_a,P3: produc981471411ee_a_a] : ( F2 @ ( product_fst_Tree_a_a @ P3 ) @ ( product_snd_Tree_a_a @ P3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_beta
% 0.31/0.45 thf(fact_270_case__prod__beta,axiom,
% 0.31/0.45 ( produc1331510035ee_a_a
% 0.31/0.45 = ( ^ [F2: a > tree_a > produc981471411ee_a_a,P3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_beta
% 0.31/0.45 thf(fact_271_internal__case__prod__def,axiom,
% 0.31/0.45 produc1405823650ee_a_o = produc1673233912ee_a_o ).
% 0.31/0.45
% 0.31/0.45 % internal_case_prod_def
% 0.31/0.45 thf(fact_272_internal__case__prod__def,axiom,
% 0.31/0.45 produc534868220Tree_a = produc873356882Tree_a ).
% 0.31/0.45
% 0.31/0.45 % internal_case_prod_def
% 0.31/0.45 thf(fact_273_internal__case__prod__def,axiom,
% 0.31/0.45 produc126329485Tree_a = produc369019363Tree_a ).
% 0.31/0.45
% 0.31/0.45 % internal_case_prod_def
% 0.31/0.45 thf(fact_274_internal__case__prod__def,axiom,
% 0.31/0.45 produc1088820157ee_a_a = produc1331510035ee_a_a ).
% 0.31/0.45
% 0.31/0.45 % internal_case_prod_def
% 0.31/0.45 thf(fact_275_fstOp__in,axiom,
% 0.31/0.45 ! [Ac2: produc143150363Tree_a,P: a > tree_a > $o,Q2: tree_a > tree_a > $o] :
% 0.31/0.45 ( ( member254315204Tree_a @ Ac2 @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ ( relcom439193229Tree_a @ P @ Q2 ) ) ) )
% 0.31/0.45 => ( member254315204Tree_a @ ( bNF_fs1579355852Tree_a @ P @ Q2 @ Ac2 ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ P ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % fstOp_in
% 0.31/0.45 thf(fact_276_sndOp__in,axiom,
% 0.31/0.45 ! [Ac2: produc143150363Tree_a,P: a > a > $o,Q2: a > tree_a > $o] :
% 0.31/0.45 ( ( member254315204Tree_a @ Ac2 @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ ( relcompp_a_a_Tree_a @ P @ Q2 ) ) ) )
% 0.31/0.45 => ( member254315204Tree_a @ ( bNF_sndOp_a_a_Tree_a @ P @ Q2 @ Ac2 ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ Q2 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % sndOp_in
% 0.31/0.45 thf(fact_277_case__prod__beta_H,axiom,
% 0.31/0.45 ( produc1673233912ee_a_o
% 0.31/0.45 = ( ^ [F2: a > tree_a > $o,X4: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ X4 ) @ ( product_snd_a_Tree_a @ X4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_beta'
% 0.31/0.45 thf(fact_278_case__prod__beta_H,axiom,
% 0.31/0.45 ( produc873356882Tree_a
% 0.31/0.45 = ( ^ [F2: a > tree_a > tree_a,X4: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ X4 ) @ ( product_snd_a_Tree_a @ X4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_beta'
% 0.31/0.45 thf(fact_279_case__prod__beta_H,axiom,
% 0.31/0.45 ( produc369019363Tree_a
% 0.31/0.45 = ( ^ [F2: tree_a > a > produc143150363Tree_a,X4: produc981471411ee_a_a] : ( F2 @ ( product_fst_Tree_a_a @ X4 ) @ ( product_snd_Tree_a_a @ X4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_beta'
% 0.31/0.45 thf(fact_280_case__prod__beta_H,axiom,
% 0.31/0.45 ( produc1331510035ee_a_a
% 0.31/0.45 = ( ^ [F2: a > tree_a > produc981471411ee_a_a,X4: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ X4 ) @ ( product_snd_a_Tree_a @ X4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_beta'
% 0.31/0.45 thf(fact_281_case__prod__unfold,axiom,
% 0.31/0.45 ( produc1673233912ee_a_o
% 0.31/0.45 = ( ^ [C2: a > tree_a > $o,P3: produc143150363Tree_a] : ( C2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_unfold
% 0.31/0.45 thf(fact_282_case__prod__unfold,axiom,
% 0.31/0.45 ( produc873356882Tree_a
% 0.31/0.45 = ( ^ [C2: a > tree_a > tree_a,P3: produc143150363Tree_a] : ( C2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_unfold
% 0.31/0.45 thf(fact_283_case__prod__unfold,axiom,
% 0.31/0.45 ( produc369019363Tree_a
% 0.31/0.45 = ( ^ [C2: tree_a > a > produc143150363Tree_a,P3: produc981471411ee_a_a] : ( C2 @ ( product_fst_Tree_a_a @ P3 ) @ ( product_snd_Tree_a_a @ P3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_unfold
% 0.31/0.45 thf(fact_284_case__prod__unfold,axiom,
% 0.31/0.45 ( produc1331510035ee_a_a
% 0.31/0.45 = ( ^ [C2: a > tree_a > produc981471411ee_a_a,P3: produc143150363Tree_a] : ( C2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_unfold
% 0.31/0.45 thf(fact_285_exE__realizer,axiom,
% 0.31/0.45 ! [P: tree_a > a > $o,P2: produc143150363Tree_a,Q2: $o > $o,F: a > tree_a > $o] :
% 0.31/0.45 ( ( P @ ( product_snd_a_Tree_a @ P2 ) @ ( product_fst_a_Tree_a @ P2 ) )
% 0.31/0.45 => ( ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( P @ Y4 @ X5 )
% 0.31/0.45 => ( Q2 @ ( F @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( Q2 @ ( produc1673233912ee_a_o @ F @ P2 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % exE_realizer
% 0.31/0.45 thf(fact_286_exE__realizer,axiom,
% 0.31/0.45 ! [P: tree_a > a > $o,P2: produc143150363Tree_a,Q2: tree_a > $o,F: a > tree_a > tree_a] :
% 0.31/0.45 ( ( P @ ( product_snd_a_Tree_a @ P2 ) @ ( product_fst_a_Tree_a @ P2 ) )
% 0.31/0.45 => ( ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( P @ Y4 @ X5 )
% 0.31/0.45 => ( Q2 @ ( F @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( Q2 @ ( produc873356882Tree_a @ F @ P2 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % exE_realizer
% 0.31/0.45 thf(fact_287_exE__realizer,axiom,
% 0.31/0.45 ! [P: a > tree_a > $o,P2: produc981471411ee_a_a,Q2: produc143150363Tree_a > $o,F: tree_a > a > produc143150363Tree_a] :
% 0.31/0.45 ( ( P @ ( product_snd_Tree_a_a @ P2 ) @ ( product_fst_Tree_a_a @ P2 ) )
% 0.31/0.45 => ( ! [X5: tree_a,Y4: a] :
% 0.31/0.45 ( ( P @ Y4 @ X5 )
% 0.31/0.45 => ( Q2 @ ( F @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( Q2 @ ( produc369019363Tree_a @ F @ P2 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % exE_realizer
% 0.31/0.45 thf(fact_288_exE__realizer,axiom,
% 0.31/0.45 ! [P: tree_a > a > $o,P2: produc143150363Tree_a,Q2: produc981471411ee_a_a > $o,F: a > tree_a > produc981471411ee_a_a] :
% 0.31/0.45 ( ( P @ ( product_snd_a_Tree_a @ P2 ) @ ( product_fst_a_Tree_a @ P2 ) )
% 0.31/0.45 => ( ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( P @ Y4 @ X5 )
% 0.31/0.45 => ( Q2 @ ( F @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( Q2 @ ( produc1331510035ee_a_a @ F @ P2 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % exE_realizer
% 0.31/0.45 thf(fact_289_split__cong,axiom,
% 0.31/0.45 ! [Q: produc143150363Tree_a,F: a > tree_a > $o,G: a > tree_a > $o,P2: produc143150363Tree_a] :
% 0.31/0.45 ( ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( ( produc686083979Tree_a @ X5 @ Y4 )
% 0.31/0.45 = Q )
% 0.31/0.45 => ( ( F @ X5 @ Y4 )
% 0.31/0.45 = ( G @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( ( P2 = Q )
% 0.31/0.45 => ( ( produc1673233912ee_a_o @ F @ P2 )
% 0.31/0.45 = ( produc1673233912ee_a_o @ G @ Q ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % split_cong
% 0.31/0.45 thf(fact_290_split__cong,axiom,
% 0.31/0.45 ! [Q: produc143150363Tree_a,F: a > tree_a > tree_a,G: a > tree_a > tree_a,P2: produc143150363Tree_a] :
% 0.31/0.45 ( ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( ( produc686083979Tree_a @ X5 @ Y4 )
% 0.31/0.45 = Q )
% 0.31/0.45 => ( ( F @ X5 @ Y4 )
% 0.31/0.45 = ( G @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( ( P2 = Q )
% 0.31/0.45 => ( ( produc873356882Tree_a @ F @ P2 )
% 0.31/0.45 = ( produc873356882Tree_a @ G @ Q ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % split_cong
% 0.31/0.45 thf(fact_291_split__cong,axiom,
% 0.31/0.45 ! [Q: produc981471411ee_a_a,F: tree_a > a > produc143150363Tree_a,G: tree_a > a > produc143150363Tree_a,P2: produc981471411ee_a_a] :
% 0.31/0.45 ( ! [X5: tree_a,Y4: a] :
% 0.31/0.45 ( ( ( produc649172771ee_a_a @ X5 @ Y4 )
% 0.31/0.45 = Q )
% 0.31/0.45 => ( ( F @ X5 @ Y4 )
% 0.31/0.45 = ( G @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( ( P2 = Q )
% 0.31/0.45 => ( ( produc369019363Tree_a @ F @ P2 )
% 0.31/0.45 = ( produc369019363Tree_a @ G @ Q ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % split_cong
% 0.31/0.45 thf(fact_292_split__cong,axiom,
% 0.31/0.45 ! [Q: produc143150363Tree_a,F: a > tree_a > produc981471411ee_a_a,G: a > tree_a > produc981471411ee_a_a,P2: produc143150363Tree_a] :
% 0.31/0.45 ( ! [X5: a,Y4: tree_a] :
% 0.31/0.45 ( ( ( produc686083979Tree_a @ X5 @ Y4 )
% 0.31/0.45 = Q )
% 0.31/0.45 => ( ( F @ X5 @ Y4 )
% 0.31/0.45 = ( G @ X5 @ Y4 ) ) )
% 0.31/0.45 => ( ( P2 = Q )
% 0.31/0.45 => ( ( produc1331510035ee_a_a @ F @ P2 )
% 0.31/0.45 = ( produc1331510035ee_a_a @ G @ Q ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % split_cong
% 0.31/0.45 thf(fact_293_heap__top__max,axiom,
% 0.31/0.45 ! [T2: tree_a] :
% 0.31/0.45 ( ( T2 != e_a )
% 0.31/0.45 => ( ( is_heap_a @ T2 )
% 0.31/0.45 => ( ( val_a @ T2 )
% 0.31/0.45 = ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ T2 ) ) ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % heap_top_max
% 0.31/0.45 thf(fact_294_curry__case__prod,axiom,
% 0.31/0.45 ! [F: a > tree_a > $o] :
% 0.31/0.45 ( ( produc1291432345ee_a_o @ ( produc1673233912ee_a_o @ F ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % curry_case_prod
% 0.31/0.45 thf(fact_295_curry__case__prod,axiom,
% 0.31/0.45 ! [F: a > tree_a > tree_a] :
% 0.31/0.45 ( ( produc740705523Tree_a @ ( produc873356882Tree_a @ F ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % curry_case_prod
% 0.31/0.45 thf(fact_296_curry__case__prod,axiom,
% 0.31/0.45 ! [F: tree_a > a > produc143150363Tree_a] :
% 0.31/0.45 ( ( produc1808426884Tree_a @ ( produc369019363Tree_a @ F ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % curry_case_prod
% 0.31/0.45 thf(fact_297_curry__case__prod,axiom,
% 0.31/0.45 ! [F: a > tree_a > produc981471411ee_a_a] :
% 0.31/0.45 ( ( produc623433908ee_a_a @ ( produc1331510035ee_a_a @ F ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % curry_case_prod
% 0.31/0.45 thf(fact_298_curryI,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > $o,A: a,B: tree_a] :
% 0.31/0.45 ( ( F @ ( produc686083979Tree_a @ A @ B ) )
% 0.31/0.45 => ( produc1291432345ee_a_o @ F @ A @ B ) ) ).
% 0.31/0.45
% 0.31/0.45 % curryI
% 0.31/0.45 thf(fact_299_curryI,axiom,
% 0.31/0.45 ! [F: produc981471411ee_a_a > $o,A: tree_a,B: a] :
% 0.31/0.45 ( ( F @ ( produc649172771ee_a_a @ A @ B ) )
% 0.31/0.45 => ( produc1205515265_a_a_o @ F @ A @ B ) ) ).
% 0.31/0.45
% 0.31/0.45 % curryI
% 0.31/0.45 thf(fact_300_split__part,axiom,
% 0.31/0.45 ! [P: $o,Q2: a > tree_a > $o] :
% 0.31/0.45 ( ( produc1673233912ee_a_o
% 0.31/0.45 @ ^ [A3: a,B3: tree_a] :
% 0.31/0.45 ( P
% 0.31/0.45 & ( Q2 @ A3 @ B3 ) ) )
% 0.31/0.45 = ( ^ [Ab: produc143150363Tree_a] :
% 0.31/0.45 ( P
% 0.31/0.45 & ( produc1673233912ee_a_o @ Q2 @ Ab ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % split_part
% 0.31/0.45 thf(fact_301_case__prod__curry,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > $o] :
% 0.31/0.45 ( ( produc1673233912ee_a_o @ ( produc1291432345ee_a_o @ F ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_curry
% 0.31/0.45 thf(fact_302_case__prod__curry,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > tree_a] :
% 0.31/0.45 ( ( produc873356882Tree_a @ ( produc740705523Tree_a @ F ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_curry
% 0.31/0.45 thf(fact_303_case__prod__curry,axiom,
% 0.31/0.45 ! [F: produc981471411ee_a_a > produc143150363Tree_a] :
% 0.31/0.45 ( ( produc369019363Tree_a @ ( produc1808426884Tree_a @ F ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_curry
% 0.31/0.45 thf(fact_304_case__prod__curry,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > produc981471411ee_a_a] :
% 0.31/0.45 ( ( produc1331510035ee_a_a @ ( produc623433908ee_a_a @ F ) )
% 0.31/0.45 = F ) ).
% 0.31/0.45
% 0.31/0.45 % case_prod_curry
% 0.31/0.45 thf(fact_305_prod_Odisc__eq__case,axiom,
% 0.31/0.45 ! [Prod: produc143150363Tree_a] :
% 0.31/0.45 ( produc1673233912ee_a_o
% 0.31/0.45 @ ^ [Uu2: a,Uv2: tree_a] : $true
% 0.31/0.45 @ Prod ) ).
% 0.31/0.45
% 0.31/0.45 % prod.disc_eq_case
% 0.31/0.45 thf(fact_306_curryD,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > $o,A: a,B: tree_a] :
% 0.31/0.45 ( ( produc1291432345ee_a_o @ F @ A @ B )
% 0.31/0.45 => ( F @ ( produc686083979Tree_a @ A @ B ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % curryD
% 0.31/0.45 thf(fact_307_curryD,axiom,
% 0.31/0.45 ! [F: produc981471411ee_a_a > $o,A: tree_a,B: a] :
% 0.31/0.45 ( ( produc1205515265_a_a_o @ F @ A @ B )
% 0.31/0.45 => ( F @ ( produc649172771ee_a_a @ A @ B ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % curryD
% 0.31/0.45 thf(fact_308_curryE,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > $o,A: a,B: tree_a] :
% 0.31/0.45 ( ( produc1291432345ee_a_o @ F @ A @ B )
% 0.31/0.45 => ( F @ ( produc686083979Tree_a @ A @ B ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % curryE
% 0.31/0.45 thf(fact_309_curryE,axiom,
% 0.31/0.45 ! [F: produc981471411ee_a_a > $o,A: tree_a,B: a] :
% 0.31/0.45 ( ( produc1205515265_a_a_o @ F @ A @ B )
% 0.31/0.45 => ( F @ ( produc649172771ee_a_a @ A @ B ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % curryE
% 0.31/0.45 thf(fact_310_fst__snd__flip,axiom,
% 0.31/0.45 ( product_fst_a_Tree_a
% 0.31/0.45 = ( comp_P342079405Tree_a @ product_snd_Tree_a_a
% 0.31/0.45 @ ( produc1331510035ee_a_a
% 0.31/0.45 @ ^ [X4: a,Y5: tree_a] : ( produc649172771ee_a_a @ Y5 @ X4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_snd_flip
% 0.31/0.45 thf(fact_311_fst__snd__flip,axiom,
% 0.31/0.45 ( product_fst_Tree_a_a
% 0.31/0.45 = ( comp_P1663859001ee_a_a @ product_snd_a_Tree_a
% 0.31/0.45 @ ( produc369019363Tree_a
% 0.31/0.45 @ ^ [X4: tree_a,Y5: a] : ( produc686083979Tree_a @ Y5 @ X4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_snd_flip
% 0.31/0.45 thf(fact_312_snd__fst__flip,axiom,
% 0.31/0.45 ( product_snd_Tree_a_a
% 0.31/0.45 = ( comp_P1103783853ee_a_a @ product_fst_a_Tree_a
% 0.31/0.45 @ ( produc369019363Tree_a
% 0.31/0.45 @ ^ [X4: tree_a,Y5: a] : ( produc686083979Tree_a @ Y5 @ X4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % snd_fst_flip
% 0.31/0.45 thf(fact_313_snd__fst__flip,axiom,
% 0.31/0.45 ( product_snd_a_Tree_a
% 0.31/0.45 = ( comp_P228269369Tree_a @ product_fst_Tree_a_a
% 0.31/0.45 @ ( produc1331510035ee_a_a
% 0.31/0.45 @ ^ [X4: a,Y5: tree_a] : ( produc649172771ee_a_a @ Y5 @ X4 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % snd_fst_flip
% 0.31/0.45 thf(fact_314_fst__fstOp,axiom,
% 0.31/0.45 ! [P: a > tree_a > $o,Q2: tree_a > tree_a > $o] :
% 0.31/0.45 ( product_fst_a_Tree_a
% 0.31/0.45 = ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( bNF_fs1579355852Tree_a @ P @ Q2 ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_fstOp
% 0.31/0.45 thf(fact_315_fst__fstOp,axiom,
% 0.31/0.45 ! [P: tree_a > a > $o,Q2: a > a > $o] :
% 0.31/0.45 ( product_fst_Tree_a_a
% 0.31/0.45 = ( comp_P1066590417ee_a_a @ product_fst_Tree_a_a @ ( bNF_fstOp_Tree_a_a_a @ P @ Q2 ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_fstOp
% 0.31/0.45 thf(fact_316_snd__sndOp,axiom,
% 0.31/0.45 ! [P: a > a > $o,Q2: a > tree_a > $o] :
% 0.31/0.45 ( product_snd_a_Tree_a
% 0.31/0.45 = ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( bNF_sndOp_a_a_Tree_a @ P @ Q2 ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % snd_sndOp
% 0.31/0.45 thf(fact_317_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > tree_a,G: produc981471411ee_a_a > produc143150363Tree_a,X: produc981471411ee_a_a,H: produc143150363Tree_a > tree_a,K: produc981471411ee_a_a > produc143150363Tree_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_P1663859001ee_a_a @ F @ G @ X )
% 0.31/0.45 = ( comp_P1663859001ee_a_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_318_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: produc981471411ee_a_a > tree_a,G: produc143150363Tree_a > produc981471411ee_a_a,X: produc143150363Tree_a,H: produc981471411ee_a_a > tree_a,K: produc143150363Tree_a > produc981471411ee_a_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_P228269369Tree_a @ F @ G @ X )
% 0.31/0.45 = ( comp_P228269369Tree_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_319_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: produc981471411ee_a_a > tree_a,G: produc143150363Tree_a > produc981471411ee_a_a,X: produc143150363Tree_a,H: produc143150363Tree_a > tree_a,K: produc143150363Tree_a > produc143150363Tree_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_P228269369Tree_a @ F @ G @ X )
% 0.31/0.45 = ( comp_P825537953Tree_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_320_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: produc981471411ee_a_a > tree_a,G: produc143150363Tree_a > produc981471411ee_a_a,X: produc143150363Tree_a,H: tree_a > tree_a,K: produc143150363Tree_a > tree_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_P228269369Tree_a @ F @ G @ X )
% 0.31/0.45 = ( comp_T236170232Tree_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_321_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > tree_a,G: produc143150363Tree_a > produc143150363Tree_a,X: produc143150363Tree_a,H: produc981471411ee_a_a > tree_a,K: produc143150363Tree_a > produc981471411ee_a_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_P825537953Tree_a @ F @ G @ X )
% 0.31/0.45 = ( comp_P228269369Tree_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_322_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > tree_a,G: produc143150363Tree_a > produc143150363Tree_a,X: produc143150363Tree_a,H: produc143150363Tree_a > tree_a,K: produc143150363Tree_a > produc143150363Tree_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_P825537953Tree_a @ F @ G @ X )
% 0.31/0.45 = ( comp_P825537953Tree_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_323_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: produc143150363Tree_a > tree_a,G: produc143150363Tree_a > produc143150363Tree_a,X: produc143150363Tree_a,H: tree_a > tree_a,K: produc143150363Tree_a > tree_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_P825537953Tree_a @ F @ G @ X )
% 0.31/0.45 = ( comp_T236170232Tree_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_324_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,G: produc143150363Tree_a > tree_a,X: produc143150363Tree_a,H: produc981471411ee_a_a > tree_a,K: produc143150363Tree_a > produc981471411ee_a_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_T236170232Tree_a @ F @ G @ X )
% 0.31/0.45 = ( comp_P228269369Tree_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_325_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,G: produc143150363Tree_a > tree_a,X: produc143150363Tree_a,H: produc143150363Tree_a > tree_a,K: produc143150363Tree_a > produc143150363Tree_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_T236170232Tree_a @ F @ G @ X )
% 0.31/0.45 = ( comp_P825537953Tree_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_326_comp__apply__eq,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,G: produc143150363Tree_a > tree_a,X: produc143150363Tree_a,H: tree_a > tree_a,K: produc143150363Tree_a > tree_a] :
% 0.31/0.45 ( ( ( F @ ( G @ X ) )
% 0.31/0.45 = ( H @ ( K @ X ) ) )
% 0.31/0.45 => ( ( comp_T236170232Tree_a @ F @ G @ X )
% 0.31/0.45 = ( comp_T236170232Tree_a @ H @ K @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % comp_apply_eq
% 0.31/0.45 thf(fact_327_snd__comp__apsnd,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a] :
% 0.31/0.45 ( ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( produc819961216ee_a_a @ F ) )
% 0.31/0.45 = ( comp_T236170232Tree_a @ F @ product_snd_a_Tree_a ) ) ).
% 0.31/0.45
% 0.31/0.45 % snd_comp_apsnd
% 0.31/0.45 thf(fact_328_fst__comp__apfst,axiom,
% 0.31/0.45 ! [F: a > a] :
% 0.31/0.45 ( ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( produc1107567542Tree_a @ F ) )
% 0.31/0.45 = ( comp_a608639864Tree_a @ F @ product_fst_a_Tree_a ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_comp_apfst
% 0.31/0.45 thf(fact_329_fst__comp__apfst,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a] :
% 0.31/0.45 ( ( comp_P1066590417ee_a_a @ product_fst_Tree_a_a @ ( produc569472578ee_a_a @ F ) )
% 0.31/0.45 = ( comp_T1074491280ee_a_a @ F @ product_fst_Tree_a_a ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_comp_apfst
% 0.31/0.45 thf(fact_330_apfst__conv,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,X: tree_a,Y: a] :
% 0.31/0.45 ( ( produc569472578ee_a_a @ F @ ( produc649172771ee_a_a @ X @ Y ) )
% 0.31/0.45 = ( produc649172771ee_a_a @ ( F @ X ) @ Y ) ) ).
% 0.31/0.45
% 0.31/0.45 % apfst_conv
% 0.31/0.45 thf(fact_331_apfst__conv,axiom,
% 0.31/0.45 ! [F: a > a,X: a,Y: tree_a] :
% 0.31/0.45 ( ( produc1107567542Tree_a @ F @ ( produc686083979Tree_a @ X @ Y ) )
% 0.31/0.45 = ( produc686083979Tree_a @ ( F @ X ) @ Y ) ) ).
% 0.31/0.45
% 0.31/0.45 % apfst_conv
% 0.31/0.45 thf(fact_332_apsnd__conv,axiom,
% 0.31/0.45 ! [F: a > a,X: tree_a,Y: a] :
% 0.31/0.45 ( ( produc969245172Tree_a @ F @ ( produc649172771ee_a_a @ X @ Y ) )
% 0.31/0.45 = ( produc649172771ee_a_a @ X @ ( F @ Y ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apsnd_conv
% 0.31/0.45 thf(fact_333_apsnd__conv,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,X: a,Y: tree_a] :
% 0.31/0.45 ( ( produc819961216ee_a_a @ F @ ( produc686083979Tree_a @ X @ Y ) )
% 0.31/0.45 = ( produc686083979Tree_a @ X @ ( F @ Y ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apsnd_conv
% 0.31/0.45 thf(fact_334_fst__apfst,axiom,
% 0.31/0.45 ! [F: a > a,X: produc143150363Tree_a] :
% 0.31/0.45 ( ( product_fst_a_Tree_a @ ( produc1107567542Tree_a @ F @ X ) )
% 0.31/0.45 = ( F @ ( product_fst_a_Tree_a @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_apfst
% 0.31/0.45 thf(fact_335_fst__apfst,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,X: produc981471411ee_a_a] :
% 0.31/0.45 ( ( product_fst_Tree_a_a @ ( produc569472578ee_a_a @ F @ X ) )
% 0.31/0.45 = ( F @ ( product_fst_Tree_a_a @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_apfst
% 0.31/0.45 thf(fact_336_apfst__eq__conv,axiom,
% 0.31/0.45 ! [F: a > a,X: produc143150363Tree_a,G: a > a] :
% 0.31/0.45 ( ( ( produc1107567542Tree_a @ F @ X )
% 0.31/0.45 = ( produc1107567542Tree_a @ G @ X ) )
% 0.31/0.45 = ( ( F @ ( product_fst_a_Tree_a @ X ) )
% 0.31/0.45 = ( G @ ( product_fst_a_Tree_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apfst_eq_conv
% 0.31/0.45 thf(fact_337_snd__apfst,axiom,
% 0.31/0.45 ! [F: a > a,X: produc143150363Tree_a] :
% 0.31/0.45 ( ( product_snd_a_Tree_a @ ( produc1107567542Tree_a @ F @ X ) )
% 0.31/0.45 = ( product_snd_a_Tree_a @ X ) ) ).
% 0.31/0.45
% 0.31/0.45 % snd_apfst
% 0.31/0.45 thf(fact_338_fst__apsnd,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,X: produc143150363Tree_a] :
% 0.31/0.45 ( ( product_fst_a_Tree_a @ ( produc819961216ee_a_a @ F @ X ) )
% 0.31/0.45 = ( product_fst_a_Tree_a @ X ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_apsnd
% 0.31/0.45 thf(fact_339_fst__apsnd,axiom,
% 0.31/0.45 ! [F: a > a,X: produc981471411ee_a_a] :
% 0.31/0.45 ( ( product_fst_Tree_a_a @ ( produc969245172Tree_a @ F @ X ) )
% 0.31/0.45 = ( product_fst_Tree_a_a @ X ) ) ).
% 0.31/0.45
% 0.31/0.45 % fst_apsnd
% 0.31/0.45 thf(fact_340_apsnd__eq__conv,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,X: produc143150363Tree_a,G: tree_a > tree_a] :
% 0.31/0.45 ( ( ( produc819961216ee_a_a @ F @ X )
% 0.31/0.45 = ( produc819961216ee_a_a @ G @ X ) )
% 0.31/0.45 = ( ( F @ ( product_snd_a_Tree_a @ X ) )
% 0.31/0.45 = ( G @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apsnd_eq_conv
% 0.31/0.45 thf(fact_341_snd__apsnd,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,X: produc143150363Tree_a] :
% 0.31/0.45 ( ( product_snd_a_Tree_a @ ( produc819961216ee_a_a @ F @ X ) )
% 0.31/0.45 = ( F @ ( product_snd_a_Tree_a @ X ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % snd_apsnd
% 0.31/0.45 thf(fact_342_snd__comp__apfst,axiom,
% 0.31/0.45 ! [F: a > a] :
% 0.31/0.45 ( ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( produc1107567542Tree_a @ F ) )
% 0.31/0.45 = product_snd_a_Tree_a ) ).
% 0.31/0.45
% 0.31/0.45 % snd_comp_apfst
% 0.31/0.45 thf(fact_343_fst__comp__apsnd,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a] :
% 0.31/0.45 ( ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( produc819961216ee_a_a @ F ) )
% 0.31/0.45 = product_fst_a_Tree_a ) ).
% 0.31/0.45
% 0.31/0.45 % fst_comp_apsnd
% 0.31/0.45 thf(fact_344_fst__comp__apsnd,axiom,
% 0.31/0.45 ! [F: a > a] :
% 0.31/0.45 ( ( comp_P1066590417ee_a_a @ product_fst_Tree_a_a @ ( produc969245172Tree_a @ F ) )
% 0.31/0.45 = product_fst_Tree_a_a ) ).
% 0.31/0.45
% 0.31/0.45 % fst_comp_apsnd
% 0.31/0.45 thf(fact_345_apfst__apsnd,axiom,
% 0.31/0.45 ! [F: tree_a > a,G: a > tree_a,X: produc981471411ee_a_a] :
% 0.31/0.45 ( ( produc606383786Tree_a @ F @ ( produc1296751488Tree_a @ G @ X ) )
% 0.31/0.45 = ( produc686083979Tree_a @ ( F @ ( product_fst_Tree_a_a @ X ) ) @ ( G @ ( product_snd_Tree_a_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apfst_apsnd
% 0.31/0.45 thf(fact_346_apfst__apsnd,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,G: a > a,X: produc981471411ee_a_a] :
% 0.31/0.45 ( ( produc569472578ee_a_a @ F @ ( produc969245172Tree_a @ G @ X ) )
% 0.31/0.45 = ( produc649172771ee_a_a @ ( F @ ( product_fst_Tree_a_a @ X ) ) @ ( G @ ( product_snd_Tree_a_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apfst_apsnd
% 0.31/0.45 thf(fact_347_apfst__apsnd,axiom,
% 0.31/0.45 ! [F: a > tree_a,G: tree_a > a,X: produc143150363Tree_a] :
% 0.31/0.45 ( ( produc1070656334ee_a_a @ F @ ( produc21534708_a_a_a @ G @ X ) )
% 0.31/0.45 = ( produc649172771ee_a_a @ ( F @ ( product_fst_a_Tree_a @ X ) ) @ ( G @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apfst_apsnd
% 0.31/0.45 thf(fact_348_apfst__apsnd,axiom,
% 0.31/0.45 ! [F: a > a,G: tree_a > tree_a,X: produc143150363Tree_a] :
% 0.31/0.45 ( ( produc1107567542Tree_a @ F @ ( produc819961216ee_a_a @ G @ X ) )
% 0.31/0.45 = ( produc686083979Tree_a @ ( F @ ( product_fst_a_Tree_a @ X ) ) @ ( G @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apfst_apsnd
% 0.31/0.45 thf(fact_349_apsnd__apfst,axiom,
% 0.31/0.45 ! [F: a > tree_a,G: tree_a > a,X: produc981471411ee_a_a] :
% 0.31/0.45 ( ( produc932333964ee_a_a @ F @ ( produc159857078_a_a_a @ G @ X ) )
% 0.31/0.45 = ( produc686083979Tree_a @ ( G @ ( product_fst_Tree_a_a @ X ) ) @ ( F @ ( product_snd_Tree_a_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apsnd_apfst
% 0.31/0.45 thf(fact_350_apsnd__apfst,axiom,
% 0.31/0.45 ! [F: a > a,G: tree_a > tree_a,X: produc981471411ee_a_a] :
% 0.31/0.45 ( ( produc969245172Tree_a @ F @ ( produc569472578ee_a_a @ G @ X ) )
% 0.31/0.45 = ( produc649172771ee_a_a @ ( G @ ( product_fst_Tree_a_a @ X ) ) @ ( F @ ( product_snd_Tree_a_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apsnd_apfst
% 0.31/0.45 thf(fact_351_apsnd__apfst,axiom,
% 0.31/0.45 ! [F: tree_a > a,G: a > tree_a,X: produc143150363Tree_a] :
% 0.31/0.45 ( ( produc856872424Tree_a @ F @ ( produc1046262850Tree_a @ G @ X ) )
% 0.31/0.45 = ( produc649172771ee_a_a @ ( G @ ( product_fst_a_Tree_a @ X ) ) @ ( F @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apsnd_apfst
% 0.31/0.45 thf(fact_352_apsnd__apfst,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,G: a > a,X: produc143150363Tree_a] :
% 0.31/0.45 ( ( produc819961216ee_a_a @ F @ ( produc1107567542Tree_a @ G @ X ) )
% 0.31/0.45 = ( produc686083979Tree_a @ ( G @ ( product_fst_a_Tree_a @ X ) ) @ ( F @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 % apsnd_apfst
% 0.31/0.45 thf(fact_353_apsnd__compose,axiom,
% 0.31/0.45 ! [F: tree_a > tree_a,G: tree_a > tree_a,X: produc143150363Tree_a] :
% 0.31/0.45 ( ( produc819961216ee_a_a @ F @ ( produc819961216ee_a_a @ G @ X ) )
% 0.31/0.45 = ( produc819961216ee_a_a @ ( comp_T59512783Tree_a @ F @ G ) @ X ) ) ).
% 0.31/0.45
% 0.31/0.45 % apsnd_compose
% 0.31/0.45
% 0.31/0.45 % Helper facts (3)
% 0.31/0.45 thf(help_If_3_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T,axiom,
% 0.31/0.45 ! [P: $o] :
% 0.31/0.45 ( ( P = $true )
% 0.31/0.45 | ( P = $false ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(help_If_2_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T,axiom,
% 0.31/0.45 ! [X: produc143150363Tree_a,Y: produc143150363Tree_a] :
% 0.31/0.45 ( ( if_Pro1144176865Tree_a @ $false @ X @ Y )
% 0.31/0.45 = Y ) ).
% 0.31/0.45
% 0.31/0.45 thf(help_If_1_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T,axiom,
% 0.31/0.45 ! [X: produc143150363Tree_a,Y: produc143150363Tree_a] :
% 0.31/0.45 ( ( if_Pro1144176865Tree_a @ $true @ X @ Y )
% 0.31/0.45 = X ) ).
% 0.31/0.45
% 0.31/0.45 % Conjectures (1)
% 0.31/0.45 thf(conj_0,conjecture,
% 0.31/0.45 is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 2.55/1.49 ---- Embedded in THF ---
% 2.55/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.55/1.50 %%% Generated on Tue Feb 24 08:25:19 EST 2026
% 2.55/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 2.55/1.50 %%% Logic specification used:
% 2.55/1.50 %%% thf(spec, logic, $$dhol).
% 2.55/1.50
% 2.55/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YD8GTuktd0/DTF2DTF14883.p
% See solution above
% 2.80/1.50 ------------------------
% 2.80/1.56 ---- Cleaned THF ---
% 2.80/1.56 thf(ty_n_t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mt__Heap__OTree_Itf__a_J_J,type,
% 2.80/1.56 produc1689254567Tree_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_J,type,
% 2.80/1.56 set_Pr1070816379Tree_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J_J,type,
% 2.80/1.56 set_Pr921883667ee_a_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
% 2.80/1.56 produc143150363Tree_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
% 2.80/1.56 produc981471411ee_a_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 2.80/1.56 set_Product_prod_a_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 2.80/1.56 product_prod_a_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
% 2.80/1.56 multiset_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 2.80/1.56 list_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 tree_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.80/1.56 set_a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(ty_n_tf__a,type,
% 2.80/1.56 a: $tType ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001t__Heap__OTree_Itf__a_J_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mt__Heap__OTree_Itf__a_J_J,type,
% 2.80/1.56 bNF_cs1091007358Tree_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > tree_a ) > ( produc1689254567Tree_a > tree_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > ( produc143150363Tree_a > produc1689254567Tree_a ) > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001tf__a_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
% 2.80/1.56 bNF_cs739966834Tree_a: set_Pr1070816379Tree_a > ( product_prod_a_a > a ) > ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > product_prod_a_a ) > ( produc143150363Tree_a > produc143150363Tree_a ) > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001t__Heap__OTree_Itf__a_J_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
% 2.80/1.56 bNF_cs1095035134ee_a_a: set_Product_prod_a_a > ( produc143150363Tree_a > tree_a ) > ( produc981471411ee_a_a > tree_a ) > ( product_prod_a_a > produc143150363Tree_a ) > ( product_prod_a_a > produc981471411ee_a_a ) > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_OfstOp_001t__Heap__OTree_Itf__a_J_001tf__a_001tf__a,type,
% 2.80/1.56 bNF_fstOp_Tree_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > produc981471411ee_a_a > produc981471411ee_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_OfstOp_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 bNF_fs1579355852Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > produc143150363Tree_a > produc143150363Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_OfstOp_001tf__a_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 bNF_fstOp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > product_prod_a_a > produc143150363Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_OfstOp_001tf__a_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 bNF_fstOp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > product_prod_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_Opick__middlep_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 bNF_pi1059296282ee_a_a: ( tree_a > tree_a > $o ) > ( tree_a > a > $o ) > tree_a > a > tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_Opick__middlep_001t__Heap__OTree_Itf__a_J_001tf__a_001tf__a,type,
% 2.80/1.56 bNF_pi1407460238_a_a_a: ( tree_a > a > $o ) > ( a > a > $o ) > tree_a > a > a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_Opick__middlep_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 bNF_pi1536086554Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > a > tree_a > tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_Opick__middlep_001tf__a_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 bNF_pi207687054Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > a > tree_a > a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_OsndOp_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 bNF_sn210385162ee_a_a: ( tree_a > tree_a > $o ) > ( tree_a > a > $o ) > produc981471411ee_a_a > produc981471411ee_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_OsndOp_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 bNF_sn687175434Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > produc143150363Tree_a > produc1689254567Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_OsndOp_001tf__a_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 bNF_sndOp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > product_prod_a_a > produc981471411ee_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Def_OsndOp_001tf__a_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 bNF_sndOp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > produc143150363Tree_a > produc143150363Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 bNF_Gr2005589581ee_a_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > tree_a ) > ( produc143150363Tree_a > a ) > set_Pr921883667ee_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 bNF_Gr2042500789Tree_a: set_Pr1070816379Tree_a > ( produc143150363Tree_a > a ) > ( produc143150363Tree_a > tree_a ) > set_Pr1070816379Tree_a ).
% 2.80/1.56
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% 2.80/1.56 produc369019363Tree_a: ( tree_a > a > produc143150363Tree_a ) > produc981471411ee_a_a > produc143150363Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__OTree_Itf__a_J_001tf__a_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_J,type,
% 2.80/1.56 produc951236931Tree_a: ( tree_a > a > set_Pr1070816379Tree_a ) > produc981471411ee_a_a > set_Pr1070816379Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__OTree_Itf__a_J_001tf__a_001t__Set__Oset_Itf__a_J,type,
% 2.80/1.56 produc136688934_set_a: ( tree_a > a > set_a ) > produc981471411ee_a_a > set_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001_Eo,type,
% 2.80/1.56 produc1673233912ee_a_o: ( a > tree_a > $o ) > produc143150363Tree_a > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 produc873356882Tree_a: ( a > tree_a > tree_a ) > produc143150363Tree_a > tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
% 2.80/1.56 produc1331510035ee_a_a: ( a > tree_a > produc981471411ee_a_a ) > produc143150363Tree_a > produc981471411ee_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
% 2.80/1.56 produc493188987Tree_a: ( a > tree_a > produc143150363Tree_a ) > produc143150363Tree_a > produc143150363Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_J,type,
% 2.80/1.56 produc802621147Tree_a: ( a > tree_a > set_Pr1070816379Tree_a ) > produc143150363Tree_a > set_Pr1070816379Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
% 2.80/1.56 produc1902270_set_a: ( a > tree_a > set_a ) > produc143150363Tree_a > set_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 produc950721886ee_a_a: ( a > tree_a > a ) > produc143150363Tree_a > a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ofst_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 produc1206152067Tree_a: produc1689254567Tree_a > tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ofst_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 product_fst_Tree_a_a: produc981471411ee_a_a > tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Ofst_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 product_fst_a_Tree_a: produc143150363Tree_a > a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Osnd_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 product_snd_Tree_a_a: produc981471411ee_a_a > a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 product_snd_a_Tree_a: produc143150363Tree_a > tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Osnd_001tf__a_001tf__a,type,
% 2.80/1.56 product_snd_a_a: product_prod_a_a > a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Oswap_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 produc1478296771ee_a_a: produc981471411ee_a_a > produc143150363Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Product__Type_Oprod_Oswap_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 produc1515207979Tree_a: produc143150363Tree_a > produc981471411ee_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Relation_Orelcompp_001tf__a_001t__Heap__OTree_Itf__a_J_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 relcom439193229Tree_a: ( a > tree_a > $o ) > ( tree_a > tree_a > $o ) > a > tree_a > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Relation_Orelcompp_001tf__a_001t__Heap__OTree_Itf__a_J_001tf__a,type,
% 2.80/1.56 relcompp_a_Tree_a_a: ( a > tree_a > $o ) > ( tree_a > a > $o ) > a > a > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Relation_Orelcompp_001tf__a_001tf__a_001t__Heap__OTree_Itf__a_J,type,
% 2.80/1.56 relcompp_a_a_Tree_a: ( a > a > $o ) > ( a > tree_a > $o ) > a > tree_a > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
% 2.80/1.56 collec1324690334ee_a_a: ( produc981471411ee_a_a > $o ) > set_Pr921883667ee_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
% 2.80/1.56 collec486369286Tree_a: ( produc143150363Tree_a > $o ) > set_Pr1070816379Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 2.80/1.56 collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.80/1.56 collect_a: ( a > $o ) > set_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_member_001t__Product____Type__Oprod_It__Heap__OTree_Itf__a_J_Mtf__a_J,type,
% 2.80/1.56 member1092636252ee_a_a: produc981471411ee_a_a > set_Pr921883667ee_a_a > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J,type,
% 2.80/1.56 member254315204Tree_a: produc143150363Tree_a > set_Pr1070816379Tree_a > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_c_member_001tf__a,type,
% 2.80/1.56 member_a: a > set_a > $o ).
% 2.80/1.56
% 2.80/1.56 thf(sy_v_t,type,
% 2.80/1.56 t: tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(sy_v_v____,type,
% 2.80/1.56 v: a ).
% 2.80/1.56
% 2.80/1.56 thf(fact_0_assms_I2_J,axiom,
% 2.80/1.56 t != e_a ).
% 2.80/1.56
% 2.80/1.56 thf(fact_1_assms_I1_J,axiom,
% 2.80/1.56 is_heap_a @ t ).
% 2.80/1.56
% 2.80/1.56 thf(fact_2__C1_Oprems_C_I2_J,axiom,
% 2.80/1.56 ( ( t_a @ v @ e_a @ e_a )
% 2.80/1.56 != e_a ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_3__C1_Oprems_C_I1_J,axiom,
% 2.80/1.56 is_heap_a @ ( t_a @ v @ e_a @ e_a ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_4_siftDown_Ocases,axiom,
% 2.80/1.56 ! [X: tree_a] :
% 2.80/1.56 ( ( X != e_a )
% 2.80/1.56 => ( ! [V: a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ e_a @ e_a ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 2.80/1.56 => ~ ! [V: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_5_removeLeaf_Ocases,axiom,
% 2.80/1.56 ! [X: tree_a] :
% 2.80/1.56 ( ! [V: a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ e_a @ e_a ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) )
% 2.80/1.56 => ( ! [V: a,Vd: a,Ve: tree_a,Vf: tree_a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) )
% 2.80/1.56 => ( X = e_a ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_6_removeLeaf_Oinduct,axiom,
% 2.80/1.56 ! [P: tree_a > $o,A0: tree_a] :
% 2.80/1.56 ( ! [V: a] : ( P @ ( t_a @ V @ e_a @ e_a ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 2.80/1.56 => ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 2.80/1.56 => ( P @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) ) ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 2.80/1.56 => ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 2.80/1.56 => ( P @ ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) ) ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 2.80/1.56 ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 2.80/1.56 => ( ( P @ ( t_a @ Va @ Vb @ Vc ) )
% 2.80/1.56 => ( P @ ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) )
% 2.80/1.56 => ( ! [V: a,Vd: a,Ve: tree_a,Vf: tree_a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( ( P @ ( t_a @ Vd @ Ve @ Vf ) )
% 2.80/1.56 => ( ( P @ ( t_a @ Vd @ Ve @ Vf ) )
% 2.80/1.56 => ( P @ ( t_a @ V @ ( t_a @ Vd @ Ve @ Vf ) @ ( t_a @ Va @ Vb @ Vc ) ) ) ) )
% 2.80/1.56 => ( ( P @ e_a )
% 2.80/1.56 => ( P @ A0 ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_7_is__heap_Osimps_I2_J,axiom,
% 2.80/1.56 ! [V2: a] : ( is_heap_a @ ( t_a @ V2 @ e_a @ e_a ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_8_Tree_Oinject,axiom,
% 2.80/1.56 ! [X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
% 2.80/1.56 ( ( ( t_a @ X21 @ X22 @ X23 )
% 2.80/1.56 = ( t_a @ Y21 @ Y22 @ Y23 ) )
% 2.80/1.56 = ( ( X21 = Y21 )
% 2.80/1.56 & ( X22 = Y22 )
% 2.80/1.56 & ( X23 = Y23 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_9_hs__is__empty__def,axiom,
% 2.80/1.56 ( heapIm229596386mpty_a
% 2.80/1.56 = ( ^ [T: tree_a] : ( T = e_a ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_10_is__heap_Osimps_I1_J,axiom,
% 2.80/1.56 is_heap_a @ e_a ).
% 2.80/1.56
% 2.80/1.56 thf(fact_11_Tree_Odistinct_I1_J,axiom,
% 2.80/1.56 ! [X21: a,X22: tree_a,X23: tree_a] :
% 2.80/1.56 ( e_a
% 2.80/1.56 != ( t_a @ X21 @ X22 @ X23 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_12_Tree_Oinduct,axiom,
% 2.80/1.56 ! [P: tree_a > $o,Tree: tree_a] :
% 2.80/1.56 ( ( P @ e_a )
% 2.80/1.56 => ( ! [X1: a,X2: tree_a,X3: tree_a] :
% 2.80/1.56 ( ( P @ X2 )
% 2.80/1.56 => ( ( P @ X3 )
% 2.80/1.56 => ( P @ ( t_a @ X1 @ X2 @ X3 ) ) ) )
% 2.80/1.56 => ( P @ Tree ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_13_Tree_Oexhaust,axiom,
% 2.80/1.56 ! [Y: tree_a] :
% 2.80/1.56 ( ( Y != e_a )
% 2.80/1.56 => ~ ! [X212: a,X222: tree_a,X232: tree_a] :
% 2.80/1.56 ( Y
% 2.80/1.56 != ( t_a @ X212 @ X222 @ X232 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_14_is__heap_Ocases,axiom,
% 2.80/1.56 ! [X: tree_a] :
% 2.80/1.56 ( ( X != e_a )
% 2.80/1.56 => ( ! [V: a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ e_a @ e_a ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ e_a @ ( t_a @ Va @ Vb @ Vc ) ) )
% 2.80/1.56 => ( ! [V: a,Va: a,Vb: tree_a,Vc: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ e_a ) )
% 2.80/1.56 => ~ ! [V: a,Va: a,Vb: tree_a,Vc: tree_a,Vd: a,Ve: tree_a,Vf: tree_a] :
% 2.80/1.56 ( X
% 2.80/1.56 != ( t_a @ V @ ( t_a @ Va @ Vb @ Vc ) @ ( t_a @ Vd @ Ve @ Vf ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_15_removeLeaf__val__val,axiom,
% 2.80/1.56 ! [T2: tree_a] :
% 2.80/1.56 ( ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T2 ) )
% 2.80/1.56 != e_a )
% 2.80/1.56 => ( ( T2 != e_a )
% 2.80/1.56 => ( ( val_a @ T2 )
% 2.80/1.56 = ( val_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T2 ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_16_removeLeaf_Osimps_I1_J,axiom,
% 2.80/1.56 ! [V2: a] :
% 2.80/1.56 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ e_a @ e_a ) )
% 2.80/1.56 = ( produc686083979Tree_a @ V2 @ e_a ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_17_siftDown__heap__is__heap,axiom,
% 2.80/1.56 ! [L: tree_a,R: tree_a,T2: tree_a,V2: a] :
% 2.80/1.56 ( ( is_heap_a @ L )
% 2.80/1.56 => ( ( is_heap_a @ R )
% 2.80/1.56 => ( ( T2
% 2.80/1.56 = ( t_a @ V2 @ L @ R ) )
% 2.80/1.56 => ( is_heap_a @ ( heapIm1091024090Down_a @ T2 ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_18_siftDown_Osimps_I2_J,axiom,
% 2.80/1.56 ! [V2: a] :
% 2.80/1.56 ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ e_a @ e_a ) )
% 2.80/1.56 = ( t_a @ V2 @ e_a @ e_a ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_19_val_Osimps,axiom,
% 2.80/1.56 ! [V2: a,Uu: tree_a,Uv: tree_a] :
% 2.80/1.56 ( ( val_a @ ( t_a @ V2 @ Uu @ Uv ) )
% 2.80/1.56 = V2 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_20_siftDown_Osimps_I1_J,axiom,
% 2.80/1.56 ( ( heapIm1091024090Down_a @ e_a )
% 2.80/1.56 = e_a ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_21_prod_Oinject,axiom,
% 2.80/1.56 ! [X12: a,X24: tree_a,Y1: a,Y2: tree_a] :
% 2.80/1.56 ( ( ( produc686083979Tree_a @ X12 @ X24 )
% 2.80/1.56 = ( produc686083979Tree_a @ Y1 @ Y2 ) )
% 2.80/1.56 = ( ( X12 = Y1 )
% 2.80/1.56 & ( X24 = Y2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_22_prod_Oinject,axiom,
% 2.80/1.56 ! [X12: tree_a,X24: a,Y1: tree_a,Y2: a] :
% 2.80/1.56 ( ( ( produc649172771ee_a_a @ X12 @ X24 )
% 2.80/1.56 = ( produc649172771ee_a_a @ Y1 @ Y2 ) )
% 2.80/1.56 = ( ( X12 = Y1 )
% 2.80/1.56 & ( X24 = Y2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_23_old_Oprod_Oinject,axiom,
% 2.80/1.56 ! [A: a,B: tree_a,A2: a,B2: tree_a] :
% 2.80/1.56 ( ( ( produc686083979Tree_a @ A @ B )
% 2.80/1.56 = ( produc686083979Tree_a @ A2 @ B2 ) )
% 2.80/1.56 = ( ( A = A2 )
% 2.80/1.56 & ( B = B2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_24_old_Oprod_Oinject,axiom,
% 2.80/1.56 ! [A: tree_a,B: a,A2: tree_a,B2: a] :
% 2.80/1.56 ( ( ( produc649172771ee_a_a @ A @ B )
% 2.80/1.56 = ( produc649172771ee_a_a @ A2 @ B2 ) )
% 2.80/1.56 = ( ( A = A2 )
% 2.80/1.56 & ( B = B2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_25_siftDown__in__tree,axiom,
% 2.80/1.56 ! [T2: tree_a] :
% 2.80/1.56 ( ( T2 != e_a )
% 2.80/1.56 => ( in_tree_a @ ( val_a @ ( heapIm1091024090Down_a @ T2 ) ) @ T2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_26_eq__snd__iff,axiom,
% 2.80/1.56 ! [B: a,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( B
% 2.80/1.56 = ( product_snd_Tree_a_a @ P2 ) )
% 2.80/1.56 = ( ? [A3: tree_a] :
% 2.80/1.56 ( P2
% 2.80/1.56 = ( produc649172771ee_a_a @ A3 @ B ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_27_eq__snd__iff,axiom,
% 2.80/1.56 ! [B: tree_a,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( B
% 2.80/1.56 = ( product_snd_a_Tree_a @ P2 ) )
% 2.80/1.56 = ( ? [A3: a] :
% 2.80/1.56 ( P2
% 2.80/1.56 = ( produc686083979Tree_a @ A3 @ B ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_28_snd__conv,axiom,
% 2.80/1.56 ! [X12: tree_a,X24: a] :
% 2.80/1.56 ( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ X12 @ X24 ) )
% 2.80/1.56 = X24 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_29_snd__conv,axiom,
% 2.80/1.56 ! [X12: a,X24: tree_a] :
% 2.80/1.56 ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 2.80/1.56 = X24 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_30_snd__eqD,axiom,
% 2.80/1.56 ! [X: tree_a,Y: a,A: a] :
% 2.80/1.56 ( ( ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ X @ Y ) )
% 2.80/1.56 = A )
% 2.80/1.56 => ( Y = A ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_31_snd__eqD,axiom,
% 2.80/1.56 ! [X: a,Y: tree_a,A: tree_a] :
% 2.80/1.56 ( ( ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X @ Y ) )
% 2.80/1.56 = A )
% 2.80/1.56 => ( Y = A ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_32_sndI,axiom,
% 2.80/1.56 ! [X: produc981471411ee_a_a,Y: tree_a,Z: a] :
% 2.80/1.56 ( ( X
% 2.80/1.56 = ( produc649172771ee_a_a @ Y @ Z ) )
% 2.80/1.56 => ( ( product_snd_Tree_a_a @ X )
% 2.80/1.56 = Z ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_33_sndI,axiom,
% 2.80/1.56 ! [X: produc143150363Tree_a,Y: a,Z: tree_a] :
% 2.80/1.56 ( ( X
% 2.80/1.56 = ( produc686083979Tree_a @ Y @ Z ) )
% 2.80/1.56 => ( ( product_snd_a_Tree_a @ X )
% 2.80/1.56 = Z ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_34_removeLeaf_Osimps_I2_J,axiom,
% 2.80/1.56 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.80/1.56 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ ( t_a @ V2 @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ e_a ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_35_removeLeaf_Osimps_I3_J,axiom,
% 2.80/1.56 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.80/1.56 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ ( t_a @ V2 @ e_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_36_removeLeaf_Osimps_I4_J,axiom,
% 2.80/1.56 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 2.80/1.56 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ ( t_a @ V2 @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_37_prod_Ocollapse,axiom,
% 2.80/1.56 ! [Prod: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) )
% 2.80/1.56 = Prod ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_38_prod_Ocollapse,axiom,
% 2.80/1.56 ! [Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) )
% 2.80/1.56 = Prod ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_39_eq__fst__iff,axiom,
% 2.80/1.56 ! [A: a,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( A
% 2.80/1.56 = ( product_fst_a_Tree_a @ P2 ) )
% 2.80/1.56 = ( ? [B3: tree_a] :
% 2.80/1.56 ( P2
% 2.80/1.56 = ( produc686083979Tree_a @ A @ B3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_40_eq__fst__iff,axiom,
% 2.80/1.56 ! [A: tree_a,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( A
% 2.80/1.56 = ( product_fst_Tree_a_a @ P2 ) )
% 2.80/1.56 = ( ? [B3: a] :
% 2.80/1.56 ( P2
% 2.80/1.56 = ( produc649172771ee_a_a @ A @ B3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_41_fst__conv,axiom,
% 2.80/1.56 ! [X12: a,X24: tree_a] :
% 2.80/1.56 ( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 2.80/1.56 = X12 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_42_fst__conv,axiom,
% 2.80/1.56 ! [X12: tree_a,X24: a] :
% 2.80/1.56 ( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ X12 @ X24 ) )
% 2.80/1.56 = X12 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_43_fst__eqD,axiom,
% 2.80/1.56 ! [X: a,Y: tree_a,A: a] :
% 2.80/1.56 ( ( ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ X @ Y ) )
% 2.80/1.56 = A )
% 2.80/1.56 => ( X = A ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_44_fst__eqD,axiom,
% 2.80/1.56 ! [X: tree_a,Y: a,A: tree_a] :
% 2.80/1.56 ( ( ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ X @ Y ) )
% 2.80/1.56 = A )
% 2.80/1.56 => ( X = A ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_45_fstI,axiom,
% 2.80/1.56 ! [X: produc143150363Tree_a,Y: a,Z: tree_a] :
% 2.80/1.56 ( ( X
% 2.80/1.56 = ( produc686083979Tree_a @ Y @ Z ) )
% 2.80/1.56 => ( ( product_fst_a_Tree_a @ X )
% 2.80/1.56 = Y ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_46_fstI,axiom,
% 2.80/1.56 ! [X: produc981471411ee_a_a,Y: tree_a,Z: a] :
% 2.80/1.56 ( ( X
% 2.80/1.56 = ( produc649172771ee_a_a @ Y @ Z ) )
% 2.80/1.56 => ( ( product_fst_Tree_a_a @ X )
% 2.80/1.56 = Y ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_47_prod__eqI,axiom,
% 2.80/1.56 ! [P2: produc981471411ee_a_a,Q: produc981471411ee_a_a] :
% 2.80/1.56 ( ( ( product_fst_Tree_a_a @ P2 )
% 2.80/1.56 = ( product_fst_Tree_a_a @ Q ) )
% 2.80/1.56 => ( ( ( product_snd_Tree_a_a @ P2 )
% 2.80/1.56 = ( product_snd_Tree_a_a @ Q ) )
% 2.80/1.56 => ( P2 = Q ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_48_prod__eqI,axiom,
% 2.80/1.56 ! [P2: produc143150363Tree_a,Q: produc143150363Tree_a] :
% 2.80/1.56 ( ( ( product_fst_a_Tree_a @ P2 )
% 2.80/1.56 = ( product_fst_a_Tree_a @ Q ) )
% 2.80/1.56 => ( ( ( product_snd_a_Tree_a @ P2 )
% 2.80/1.56 = ( product_snd_a_Tree_a @ Q ) )
% 2.80/1.56 => ( P2 = Q ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_49_prod_Oexpand,axiom,
% 2.80/1.56 ! [Prod: produc981471411ee_a_a,Prod2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( ( ( product_fst_Tree_a_a @ Prod )
% 2.80/1.56 = ( product_fst_Tree_a_a @ Prod2 ) )
% 2.80/1.56 & ( ( product_snd_Tree_a_a @ Prod )
% 2.80/1.56 = ( product_snd_Tree_a_a @ Prod2 ) ) )
% 2.80/1.56 => ( Prod = Prod2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_50_prod_Oexpand,axiom,
% 2.80/1.56 ! [Prod: produc143150363Tree_a,Prod2: produc143150363Tree_a] :
% 2.80/1.56 ( ( ( ( product_fst_a_Tree_a @ Prod )
% 2.80/1.56 = ( product_fst_a_Tree_a @ Prod2 ) )
% 2.80/1.56 & ( ( product_snd_a_Tree_a @ Prod )
% 2.80/1.56 = ( product_snd_a_Tree_a @ Prod2 ) ) )
% 2.80/1.56 => ( Prod = Prod2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_51_prod__eq__iff,axiom,
% 2.80/1.56 ( ( ^ [Y3: produc981471411ee_a_a,Z2: produc981471411ee_a_a] : ( Y3 = Z2 ) )
% 2.80/1.56 = ( ^ [S: produc981471411ee_a_a,T: produc981471411ee_a_a] :
% 2.80/1.56 ( ( ( product_fst_Tree_a_a @ S )
% 2.80/1.56 = ( product_fst_Tree_a_a @ T ) )
% 2.80/1.56 & ( ( product_snd_Tree_a_a @ S )
% 2.80/1.56 = ( product_snd_Tree_a_a @ T ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_52_prod__eq__iff,axiom,
% 2.80/1.56 ( ( ^ [Y3: produc143150363Tree_a,Z2: produc143150363Tree_a] : ( Y3 = Z2 ) )
% 2.80/1.56 = ( ^ [S: produc143150363Tree_a,T: produc143150363Tree_a] :
% 2.80/1.56 ( ( ( product_fst_a_Tree_a @ S )
% 2.80/1.56 = ( product_fst_a_Tree_a @ T ) )
% 2.80/1.56 & ( ( product_snd_a_Tree_a @ S )
% 2.80/1.56 = ( product_snd_a_Tree_a @ T ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_53_surjective__pairing,axiom,
% 2.80/1.56 ! [T2: produc981471411ee_a_a] :
% 2.80/1.56 ( T2
% 2.80/1.56 = ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ T2 ) @ ( product_snd_Tree_a_a @ T2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_54_surjective__pairing,axiom,
% 2.80/1.56 ! [T2: produc143150363Tree_a] :
% 2.80/1.56 ( T2
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ T2 ) @ ( product_snd_a_Tree_a @ T2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_55_prod_Oexhaust__sel,axiom,
% 2.80/1.56 ! [Prod: produc981471411ee_a_a] :
% 2.80/1.56 ( Prod
% 2.80/1.56 = ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_56_prod_Oexhaust__sel,axiom,
% 2.80/1.56 ! [Prod: produc143150363Tree_a] :
% 2.80/1.56 ( Prod
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_57_in__tree_Osimps_I2_J,axiom,
% 2.80/1.56 ! [V2: a,V3: a,L: tree_a,R: tree_a] :
% 2.80/1.56 ( ( in_tree_a @ V2 @ ( t_a @ V3 @ L @ R ) )
% 2.80/1.56 = ( ( V2 = V3 )
% 2.80/1.56 | ( in_tree_a @ V2 @ L )
% 2.80/1.56 | ( in_tree_a @ V2 @ R ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_58_in__tree_Osimps_I1_J,axiom,
% 2.80/1.56 ! [V2: a] :
% 2.80/1.56 ~ ( in_tree_a @ V2 @ e_a ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_59_siftDown__in__tree__set,axiom,
% 2.80/1.56 ( in_tree_a
% 2.80/1.56 = ( ^ [V4: a,T: tree_a] : ( in_tree_a @ V4 @ ( heapIm1091024090Down_a @ T ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_60_old_Oprod_Oinducts,axiom,
% 2.80/1.56 ! [P: produc143150363Tree_a > $o,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ! [A4: a,B4: tree_a] : ( P @ ( produc686083979Tree_a @ A4 @ B4 ) )
% 2.80/1.56 => ( P @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_61_old_Oprod_Oinducts,axiom,
% 2.80/1.56 ! [P: produc981471411ee_a_a > $o,Prod: produc981471411ee_a_a] :
% 2.80/1.56 ( ! [A4: tree_a,B4: a] : ( P @ ( produc649172771ee_a_a @ A4 @ B4 ) )
% 2.80/1.56 => ( P @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_62_mem__Collect__eq,axiom,
% 2.80/1.56 ! [A: a,P: a > $o] :
% 2.80/1.56 ( ( member_a @ A @ ( collect_a @ P ) )
% 2.80/1.56 = ( P @ A ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_63_mem__Collect__eq,axiom,
% 2.80/1.56 ! [A: produc143150363Tree_a,P: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ( member254315204Tree_a @ A @ ( collec486369286Tree_a @ P ) )
% 2.80/1.56 = ( P @ A ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_64_Collect__mem__eq,axiom,
% 2.80/1.56 ! [A5: set_a] :
% 2.80/1.56 ( ( collect_a
% 2.80/1.56 @ ^ [X4: a] : ( member_a @ X4 @ A5 ) )
% 2.80/1.56 = A5 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_65_Collect__mem__eq,axiom,
% 2.80/1.56 ! [A5: set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ( collec486369286Tree_a
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ A5 ) )
% 2.80/1.56 = A5 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_66_Collect__cong,axiom,
% 2.80/1.56 ! [P: produc143150363Tree_a > $o,Q2: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ! [X5: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ X5 )
% 2.80/1.56 = ( Q2 @ X5 ) )
% 2.80/1.56 => ( ( collec486369286Tree_a @ P )
% 2.80/1.56 = ( collec486369286Tree_a @ Q2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_67_old_Oprod_Oexhaust,axiom,
% 2.80/1.56 ! [Y: produc143150363Tree_a] :
% 2.80/1.56 ~ ! [A4: a,B4: tree_a] :
% 2.80/1.56 ( Y
% 2.80/1.56 != ( produc686083979Tree_a @ A4 @ B4 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_68_old_Oprod_Oexhaust,axiom,
% 2.80/1.56 ! [Y: produc981471411ee_a_a] :
% 2.80/1.56 ~ ! [A4: tree_a,B4: a] :
% 2.80/1.56 ( Y
% 2.80/1.56 != ( produc649172771ee_a_a @ A4 @ B4 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_69_Pair__inject,axiom,
% 2.80/1.56 ! [A: a,B: tree_a,A2: a,B2: tree_a] :
% 2.80/1.56 ( ( ( produc686083979Tree_a @ A @ B )
% 2.80/1.56 = ( produc686083979Tree_a @ A2 @ B2 ) )
% 2.80/1.56 => ~ ( ( A = A2 )
% 2.80/1.56 => ( B != B2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_70_Pair__inject,axiom,
% 2.80/1.56 ! [A: tree_a,B: a,A2: tree_a,B2: a] :
% 2.80/1.56 ( ( ( produc649172771ee_a_a @ A @ B )
% 2.80/1.56 = ( produc649172771ee_a_a @ A2 @ B2 ) )
% 2.80/1.56 => ~ ( ( A = A2 )
% 2.80/1.56 => ( B != B2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_71_prod__cases,axiom,
% 2.80/1.56 ! [P: produc143150363Tree_a > $o,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ! [A4: a,B4: tree_a] : ( P @ ( produc686083979Tree_a @ A4 @ B4 ) )
% 2.80/1.56 => ( P @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_72_prod__cases,axiom,
% 2.80/1.56 ! [P: produc981471411ee_a_a > $o,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ! [A4: tree_a,B4: a] : ( P @ ( produc649172771ee_a_a @ A4 @ B4 ) )
% 2.80/1.56 => ( P @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_73_surj__pair,axiom,
% 2.80/1.56 ! [P2: produc143150363Tree_a] :
% 2.80/1.56 ? [X5: a,Y4: tree_a] :
% 2.80/1.56 ( P2
% 2.80/1.56 = ( produc686083979Tree_a @ X5 @ Y4 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_74_surj__pair,axiom,
% 2.80/1.56 ! [P2: produc981471411ee_a_a] :
% 2.80/1.56 ? [X5: tree_a,Y4: a] :
% 2.80/1.56 ( P2
% 2.80/1.56 = ( produc649172771ee_a_a @ X5 @ Y4 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_75_removeLeaf_Osimps_I5_J,axiom,
% 2.80/1.56 ! [V2: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.80/1.56 ( ( heapIm837449470Leaf_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) @ ( t_a @ V2 @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_76_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 2.80/1.56 ! [P: tree_a > a > $o,X: tree_a,Y: a,A: produc981471411ee_a_a] :
% 2.80/1.56 ( ( P @ X @ Y )
% 2.80/1.56 => ( ( A
% 2.80/1.56 = ( produc649172771ee_a_a @ X @ Y ) )
% 2.80/1.56 => ( P @ ( product_fst_Tree_a_a @ A ) @ ( product_snd_Tree_a_a @ A ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_77_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 2.80/1.56 ! [P: a > tree_a > $o,X: a,Y: tree_a,A: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ X @ Y )
% 2.80/1.56 => ( ( A
% 2.80/1.56 = ( produc686083979Tree_a @ X @ Y ) )
% 2.80/1.56 => ( P @ ( product_fst_a_Tree_a @ A ) @ ( product_snd_a_Tree_a @ A ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_78_conjI__realizer,axiom,
% 2.80/1.56 ! [P: tree_a > $o,P2: tree_a,Q2: a > $o,Q: a] :
% 2.80/1.56 ( ( P @ P2 )
% 2.80/1.56 => ( ( Q2 @ Q )
% 2.80/1.56 => ( ( P @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ P2 @ Q ) ) )
% 2.80/1.56 & ( Q2 @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ P2 @ Q ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_79_conjI__realizer,axiom,
% 2.80/1.56 ! [P: a > $o,P2: a,Q2: tree_a > $o,Q: tree_a] :
% 2.80/1.56 ( ( P @ P2 )
% 2.80/1.56 => ( ( Q2 @ Q )
% 2.80/1.56 => ( ( P @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ P2 @ Q ) ) )
% 2.80/1.56 & ( Q2 @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ P2 @ Q ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_80_exI__realizer,axiom,
% 2.80/1.56 ! [P: a > tree_a > $o,Y: a,X: tree_a] :
% 2.80/1.56 ( ( P @ Y @ X )
% 2.80/1.56 => ( P @ ( product_snd_Tree_a_a @ ( produc649172771ee_a_a @ X @ Y ) ) @ ( product_fst_Tree_a_a @ ( produc649172771ee_a_a @ X @ Y ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_81_exI__realizer,axiom,
% 2.80/1.56 ! [P: tree_a > a > $o,Y: tree_a,X: a] :
% 2.80/1.56 ( ( P @ Y @ X )
% 2.80/1.56 => ( P @ ( product_snd_a_Tree_a @ ( produc686083979Tree_a @ X @ Y ) ) @ ( product_fst_a_Tree_a @ ( produc686083979Tree_a @ X @ Y ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_82_exE__realizer_H,axiom,
% 2.80/1.56 ! [P: a > tree_a > $o,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( P @ ( product_snd_Tree_a_a @ P2 ) @ ( product_fst_Tree_a_a @ P2 ) )
% 2.80/1.56 => ~ ! [X5: tree_a,Y4: a] :
% 2.80/1.56 ~ ( P @ Y4 @ X5 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_83_exE__realizer_H,axiom,
% 2.80/1.56 ! [P: tree_a > a > $o,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ ( product_snd_a_Tree_a @ P2 ) @ ( product_fst_a_Tree_a @ P2 ) )
% 2.80/1.56 => ~ ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ~ ( P @ Y4 @ X5 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_84_prod_Oswap__def,axiom,
% 2.80/1.56 ( produc1478296771ee_a_a
% 2.80/1.56 = ( ^ [P3: produc981471411ee_a_a] : ( produc686083979Tree_a @ ( product_snd_Tree_a_a @ P3 ) @ ( product_fst_Tree_a_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_85_prod_Oswap__def,axiom,
% 2.80/1.56 ( produc1515207979Tree_a
% 2.80/1.56 = ( ^ [P3: produc143150363Tree_a] : ( produc649172771ee_a_a @ ( product_snd_a_Tree_a @ P3 ) @ ( product_fst_a_Tree_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_86_heapify_Osimps_I2_J,axiom,
% 2.80/1.56 ! [V2: a,L: tree_a,R: tree_a] :
% 2.80/1.56 ( ( heapIm970322378pify_a @ ( t_a @ V2 @ L @ R ) )
% 2.80/1.56 = ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm970322378pify_a @ L ) @ ( heapIm970322378pify_a @ R ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_87_is__heap_Osimps_I4_J,axiom,
% 2.80/1.56 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.80/1.56 ( ( is_heap_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.80/1.56 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_88_is__heap_Osimps_I3_J,axiom,
% 2.80/1.56 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.80/1.56 ( ( is_heap_a @ ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_89_swap__swap,axiom,
% 2.80/1.56 ! [P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc1515207979Tree_a @ ( produc1478296771ee_a_a @ P2 ) )
% 2.80/1.56 = P2 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_90_swap__swap,axiom,
% 2.80/1.56 ! [P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc1478296771ee_a_a @ ( produc1515207979Tree_a @ P2 ) )
% 2.80/1.56 = P2 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_91_swap__simp,axiom,
% 2.80/1.56 ! [X: a,Y: tree_a] :
% 2.80/1.56 ( ( produc1515207979Tree_a @ ( produc686083979Tree_a @ X @ Y ) )
% 2.80/1.56 = ( produc649172771ee_a_a @ Y @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_92_swap__simp,axiom,
% 2.80/1.56 ! [X: tree_a,Y: a] :
% 2.80/1.56 ( ( produc1478296771ee_a_a @ ( produc649172771ee_a_a @ X @ Y ) )
% 2.80/1.56 = ( produc686083979Tree_a @ Y @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_93_fst__swap,axiom,
% 2.80/1.56 ! [X: produc981471411ee_a_a] :
% 2.80/1.56 ( ( product_fst_a_Tree_a @ ( produc1478296771ee_a_a @ X ) )
% 2.80/1.56 = ( product_snd_Tree_a_a @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_94_fst__swap,axiom,
% 2.80/1.56 ! [X: produc143150363Tree_a] :
% 2.80/1.56 ( ( product_fst_Tree_a_a @ ( produc1515207979Tree_a @ X ) )
% 2.80/1.56 = ( product_snd_a_Tree_a @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_95_snd__swap,axiom,
% 2.80/1.56 ! [X: produc143150363Tree_a] :
% 2.80/1.56 ( ( product_snd_Tree_a_a @ ( produc1515207979Tree_a @ X ) )
% 2.80/1.56 = ( product_fst_a_Tree_a @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_96_snd__swap,axiom,
% 2.80/1.56 ! [X: produc981471411ee_a_a] :
% 2.80/1.56 ( ( product_snd_a_Tree_a @ ( produc1478296771ee_a_a @ X ) )
% 2.80/1.56 = ( product_fst_Tree_a_a @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_97_siftDown__Node,axiom,
% 2.80/1.56 ! [T2: tree_a,V2: a,L: tree_a,R: tree_a] :
% 2.80/1.56 ( ( T2
% 2.80/1.56 = ( t_a @ V2 @ L @ R ) )
% 2.80/1.56 => ? [L2: tree_a,V5: a,R2: tree_a] :
% 2.80/1.56 ( ( ( heapIm1091024090Down_a @ T2 )
% 2.80/1.56 = ( t_a @ V5 @ L2 @ R2 ) )
% 2.80/1.56 & ( ord_less_eq_a @ V2 @ V5 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_98_heapify_Osimps_I1_J,axiom,
% 2.80/1.56 ( ( heapIm970322378pify_a @ e_a )
% 2.80/1.56 = e_a ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_99_heapify__heap__is__heap,axiom,
% 2.80/1.56 ! [T2: tree_a] : ( is_heap_a @ ( heapIm970322378pify_a @ T2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_100_is__heap_Osimps_I5_J,axiom,
% 2.80/1.56 ! [V2: a,Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a] :
% 2.80/1.56 ( ( is_heap_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.80/1.56 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 2.80/1.56 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) )
% 2.80/1.56 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_101_is__heap_Osimps_I6_J,axiom,
% 2.80/1.56 ! [V2: a,Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
% 2.80/1.56 ( ( is_heap_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 & ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) )
% 2.80/1.56 & ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 2.80/1.56 & ( is_heap_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_102_is__heap__max,axiom,
% 2.80/1.56 ! [V2: a,T2: tree_a] :
% 2.80/1.56 ( ( in_tree_a @ V2 @ T2 )
% 2.80/1.56 => ( ( is_heap_a @ T2 )
% 2.80/1.56 => ( ord_less_eq_a @ V2 @ ( val_a @ T2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_103_order__refl,axiom,
% 2.80/1.56 ! [X: a] : ( ord_less_eq_a @ X @ X ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_104_siftDown_Osimps_I3_J,axiom,
% 2.80/1.56 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V2: a] :
% 2.80/1.56 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.80/1.56 = ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) ) )
% 2.80/1.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ e_a ) )
% 2.80/1.56 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ e_a ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_105_siftDown_Osimps_I4_J,axiom,
% 2.80/1.56 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,V2: a] :
% 2.80/1.56 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.80/1.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_106_siftDown_Osimps_I6_J,axiom,
% 2.80/1.56 ! [Va2: a,Vb2: tree_a,Vc2: tree_a,Vd2: a,Ve2: tree_a,Vf2: tree_a,V2: a] :
% 2.80/1.56 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.80/1.56 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.80/1.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) )
% 2.80/1.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.80/1.56 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
% 2.80/1.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_107_siftDown_Osimps_I5_J,axiom,
% 2.80/1.56 ! [Vd2: a,Ve2: tree_a,Vf2: tree_a,Va2: a,Vb2: tree_a,Vc2: tree_a,V2: a] :
% 2.80/1.56 ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.80/1.56 = ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 2.80/1.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.80/1.56 = ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) )
% 2.80/1.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
% 2.80/1.56 => ( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.80/1.56 = ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) )
% 2.80/1.56 & ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ V2 )
% 2.80/1.56 => ( ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) )
% 2.80/1.56 = ( t_a @ ( val_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( t_a @ Va2 @ Vb2 @ Vc2 ) @ ( heapIm1091024090Down_a @ ( t_a @ V2 @ ( heapIm1140443833left_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Vd2 @ Ve2 @ Vf2 ) ) ) ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_108_left_Osimps,axiom,
% 2.80/1.56 ! [V2: a,L: tree_a,R: tree_a] :
% 2.80/1.56 ( ( heapIm1140443833left_a @ ( t_a @ V2 @ L @ R ) )
% 2.80/1.56 = L ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_109_right_Osimps,axiom,
% 2.80/1.56 ! [V2: a,L: tree_a,R: tree_a] :
% 2.80/1.56 ( ( heapIm1257206334ight_a @ ( t_a @ V2 @ L @ R ) )
% 2.80/1.56 = R ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_110_dual__order_Oantisym,axiom,
% 2.80/1.56 ! [B: a,A: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ B @ A )
% 2.80/1.56 => ( ( ord_less_eq_a @ A @ B )
% 2.80/1.56 => ( A = B ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_111_dual__order_Oeq__iff,axiom,
% 2.80/1.56 ( ( ^ [Y3: a,Z2: a] : ( Y3 = Z2 ) )
% 2.80/1.56 = ( ^ [A3: a,B3: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ B3 @ A3 )
% 2.80/1.56 & ( ord_less_eq_a @ A3 @ B3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_112_dual__order_Otrans,axiom,
% 2.80/1.56 ! [B: a,A: a,C: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ B @ A )
% 2.80/1.56 => ( ( ord_less_eq_a @ C @ B )
% 2.80/1.56 => ( ord_less_eq_a @ C @ A ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_113_linorder__wlog,axiom,
% 2.80/1.56 ! [P: a > a > $o,A: a,B: a] :
% 2.80/1.56 ( ! [A4: a,B4: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ A4 @ B4 )
% 2.80/1.56 => ( P @ A4 @ B4 ) )
% 2.80/1.56 => ( ! [A4: a,B4: a] :
% 2.80/1.56 ( ( P @ B4 @ A4 )
% 2.80/1.56 => ( P @ A4 @ B4 ) )
% 2.80/1.56 => ( P @ A @ B ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_114_dual__order_Orefl,axiom,
% 2.80/1.56 ! [A: a] : ( ord_less_eq_a @ A @ A ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_115_order__trans,axiom,
% 2.80/1.56 ! [X: a,Y: a,Z: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ X @ Y )
% 2.80/1.56 => ( ( ord_less_eq_a @ Y @ Z )
% 2.80/1.56 => ( ord_less_eq_a @ X @ Z ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_116_order__class_Oorder_Oantisym,axiom,
% 2.80/1.56 ! [A: a,B: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ A @ B )
% 2.80/1.56 => ( ( ord_less_eq_a @ B @ A )
% 2.80/1.56 => ( A = B ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_117_ord__le__eq__trans,axiom,
% 2.80/1.56 ! [A: a,B: a,C: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ A @ B )
% 2.80/1.56 => ( ( B = C )
% 2.80/1.56 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_118_ord__eq__le__trans,axiom,
% 2.80/1.56 ! [A: a,B: a,C: a] :
% 2.80/1.56 ( ( A = B )
% 2.80/1.56 => ( ( ord_less_eq_a @ B @ C )
% 2.80/1.56 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_119_order__class_Oorder_Oeq__iff,axiom,
% 2.80/1.56 ( ( ^ [Y3: a,Z2: a] : ( Y3 = Z2 ) )
% 2.80/1.56 = ( ^ [A3: a,B3: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ A3 @ B3 )
% 2.80/1.56 & ( ord_less_eq_a @ B3 @ A3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_120_antisym__conv,axiom,
% 2.80/1.56 ! [Y: a,X: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ Y @ X )
% 2.80/1.56 => ( ( ord_less_eq_a @ X @ Y )
% 2.80/1.56 = ( X = Y ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_121_le__cases3,axiom,
% 2.80/1.56 ! [X: a,Y: a,Z: a] :
% 2.80/1.56 ( ( ( ord_less_eq_a @ X @ Y )
% 2.80/1.56 => ~ ( ord_less_eq_a @ Y @ Z ) )
% 2.80/1.56 => ( ( ( ord_less_eq_a @ Y @ X )
% 2.80/1.56 => ~ ( ord_less_eq_a @ X @ Z ) )
% 2.80/1.56 => ( ( ( ord_less_eq_a @ X @ Z )
% 2.80/1.56 => ~ ( ord_less_eq_a @ Z @ Y ) )
% 2.80/1.56 => ( ( ( ord_less_eq_a @ Z @ Y )
% 2.80/1.56 => ~ ( ord_less_eq_a @ Y @ X ) )
% 2.80/1.56 => ( ( ( ord_less_eq_a @ Y @ Z )
% 2.80/1.56 => ~ ( ord_less_eq_a @ Z @ X ) )
% 2.80/1.56 => ~ ( ( ord_less_eq_a @ Z @ X )
% 2.80/1.56 => ~ ( ord_less_eq_a @ X @ Y ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_122_order_Otrans,axiom,
% 2.80/1.56 ! [A: a,B: a,C: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ A @ B )
% 2.80/1.56 => ( ( ord_less_eq_a @ B @ C )
% 2.80/1.56 => ( ord_less_eq_a @ A @ C ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_123_le__cases,axiom,
% 2.80/1.56 ! [X: a,Y: a] :
% 2.80/1.56 ( ~ ( ord_less_eq_a @ X @ Y )
% 2.80/1.56 => ( ord_less_eq_a @ Y @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_124_eq__refl,axiom,
% 2.80/1.56 ! [X: a,Y: a] :
% 2.80/1.56 ( ( X = Y )
% 2.80/1.56 => ( ord_less_eq_a @ X @ Y ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_125_linear,axiom,
% 2.80/1.56 ! [X: a,Y: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ X @ Y )
% 2.80/1.56 | ( ord_less_eq_a @ Y @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_126_antisym,axiom,
% 2.80/1.56 ! [X: a,Y: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ X @ Y )
% 2.80/1.56 => ( ( ord_less_eq_a @ Y @ X )
% 2.80/1.56 => ( X = Y ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_127_eq__iff,axiom,
% 2.80/1.56 ( ( ^ [Y3: a,Z2: a] : ( Y3 = Z2 ) )
% 2.80/1.56 = ( ^ [X4: a,Y5: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ X4 @ Y5 )
% 2.80/1.56 & ( ord_less_eq_a @ Y5 @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_128_ord__le__eq__subst,axiom,
% 2.80/1.56 ! [A: a,B: a,F: a > a,C: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ A @ B )
% 2.80/1.56 => ( ( ( F @ B )
% 2.80/1.56 = C )
% 2.80/1.56 => ( ! [X5: a,Y4: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.80/1.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.80/1.56 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_129_ord__eq__le__subst,axiom,
% 2.80/1.56 ! [A: a,F: a > a,B: a,C: a] :
% 2.80/1.56 ( ( A
% 2.80/1.56 = ( F @ B ) )
% 2.80/1.56 => ( ( ord_less_eq_a @ B @ C )
% 2.80/1.56 => ( ! [X5: a,Y4: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.80/1.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.80/1.56 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_130_order__subst2,axiom,
% 2.80/1.56 ! [A: a,B: a,F: a > a,C: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ A @ B )
% 2.80/1.56 => ( ( ord_less_eq_a @ ( F @ B ) @ C )
% 2.80/1.56 => ( ! [X5: a,Y4: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.80/1.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.80/1.56 => ( ord_less_eq_a @ ( F @ A ) @ C ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_131_order__subst1,axiom,
% 2.80/1.56 ! [A: a,F: a > a,B: a,C: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ A @ ( F @ B ) )
% 2.80/1.56 => ( ( ord_less_eq_a @ B @ C )
% 2.80/1.56 => ( ! [X5: a,Y4: a] :
% 2.80/1.56 ( ( ord_less_eq_a @ X5 @ Y4 )
% 2.80/1.56 => ( ord_less_eq_a @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 2.80/1.56 => ( ord_less_eq_a @ A @ ( F @ C ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_132_hs__remove__max__def,axiom,
% 2.80/1.56 ( heapIm915766629_max_a
% 2.80/1.56 = ( ^ [T: tree_a] :
% 2.80/1.56 ( if_Pro1144176865Tree_a
% 2.80/1.56 @ ( ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T ) )
% 2.80/1.56 = e_a )
% 2.80/1.56 @ ( produc686083979Tree_a @ ( val_a @ T ) @ e_a )
% 2.80/1.56 @ ( produc686083979Tree_a @ ( val_a @ T ) @ ( heapIm1091024090Down_a @ ( t_a @ ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ T ) ) @ ( heapIm1140443833left_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T ) ) ) @ ( heapIm1257206334ight_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ T ) ) ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_133_Heap_Oremove__max__is__heap,axiom,
% 2.80/1.56 ! [Empty: tree_a,Is_empty: tree_a > $o,Of_list: list_a > tree_a,Multiset: tree_a > multiset_a,As_tree: tree_a > tree_a,Remove_max: tree_a > produc143150363Tree_a,L: tree_a,M: a,L3: tree_a] :
% 2.80/1.56 ( ( heap_Tree_a_a @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.80/1.56 => ( ~ ( Is_empty @ L )
% 2.80/1.56 => ( ( is_heap_a @ ( As_tree @ L ) )
% 2.80/1.56 => ( ( ( produc686083979Tree_a @ M @ L3 )
% 2.80/1.56 = ( Remove_max @ L ) )
% 2.80/1.56 => ( is_heap_a @ ( As_tree @ L3 ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_134_Heap_Oremove__max__val,axiom,
% 2.80/1.56 ! [Empty: tree_a,Is_empty: tree_a > $o,Of_list: list_a > tree_a,Multiset: tree_a > multiset_a,As_tree: tree_a > tree_a,Remove_max: tree_a > produc143150363Tree_a,T2: tree_a,M: a,T3: tree_a] :
% 2.80/1.56 ( ( heap_Tree_a_a @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.80/1.56 => ( ~ ( Is_empty @ T2 )
% 2.80/1.56 => ( ( ( produc686083979Tree_a @ M @ T3 )
% 2.80/1.56 = ( Remove_max @ T2 ) )
% 2.80/1.56 => ( M
% 2.80/1.56 = ( val_a @ ( As_tree @ T2 ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_135_sndOp__def,axiom,
% 2.80/1.56 ( bNF_sn210385162ee_a_a
% 2.80/1.56 = ( ^ [P4: tree_a > tree_a > $o,Q3: tree_a > a > $o,Ac: produc981471411ee_a_a] : ( produc649172771ee_a_a @ ( bNF_pi1059296282ee_a_a @ P4 @ Q3 @ ( product_fst_Tree_a_a @ Ac ) @ ( product_snd_Tree_a_a @ Ac ) ) @ ( product_snd_Tree_a_a @ Ac ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_136_sndOp__def,axiom,
% 2.80/1.56 ( bNF_sndOp_a_a_Tree_a
% 2.80/1.56 = ( ^ [P4: a > a > $o,Q3: a > tree_a > $o,Ac: produc143150363Tree_a] : ( produc686083979Tree_a @ ( bNF_pi207687054Tree_a @ P4 @ Q3 @ ( product_fst_a_Tree_a @ Ac ) @ ( product_snd_a_Tree_a @ Ac ) ) @ ( product_snd_a_Tree_a @ Ac ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_137_fstOp__def,axiom,
% 2.80/1.56 ( bNF_fstOp_Tree_a_a_a
% 2.80/1.56 = ( ^ [P4: tree_a > a > $o,Q3: a > a > $o,Ac: produc981471411ee_a_a] : ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Ac ) @ ( bNF_pi1407460238_a_a_a @ P4 @ Q3 @ ( product_fst_Tree_a_a @ Ac ) @ ( product_snd_Tree_a_a @ Ac ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_138_fstOp__def,axiom,
% 2.80/1.56 ( bNF_fs1579355852Tree_a
% 2.80/1.56 = ( ^ [P4: a > tree_a > $o,Q3: tree_a > tree_a > $o,Ac: produc143150363Tree_a] : ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Ac ) @ ( bNF_pi1536086554Tree_a @ P4 @ Q3 @ ( product_fst_a_Tree_a @ Ac ) @ ( product_snd_a_Tree_a @ Ac ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_139_pred__subset__eq2,axiom,
% 2.80/1.56 ! [R3: set_Pr1070816379Tree_a,S2: set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ( ord_le1327026842ee_a_o
% 2.80/1.56 @ ^ [X4: a,Y5: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ X4 @ Y5 ) @ R3 )
% 2.80/1.56 @ ^ [X4: a,Y5: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ X4 @ Y5 ) @ S2 ) )
% 2.80/1.56 = ( ord_le1013007387Tree_a @ R3 @ S2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_140_pred__subset__eq2,axiom,
% 2.80/1.56 ! [R3: set_Pr921883667ee_a_a,S2: set_Pr921883667ee_a_a] :
% 2.80/1.56 ( ( ord_le1748873858_a_a_o
% 2.80/1.56 @ ^ [X4: tree_a,Y5: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X4 @ Y5 ) @ R3 )
% 2.80/1.56 @ ^ [X4: tree_a,Y5: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X4 @ Y5 ) @ S2 ) )
% 2.80/1.56 = ( ord_le864074675ee_a_a @ R3 @ S2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_141_pred__equals__eq2,axiom,
% 2.80/1.56 ! [R3: set_Pr1070816379Tree_a,S2: set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ( ( ^ [X4: a,Y5: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ X4 @ Y5 ) @ R3 ) )
% 2.80/1.56 = ( ^ [X4: a,Y5: tree_a] : ( member254315204Tree_a @ ( produc686083979Tree_a @ X4 @ Y5 ) @ S2 ) ) )
% 2.80/1.56 = ( R3 = S2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_142_pred__equals__eq2,axiom,
% 2.80/1.56 ! [R3: set_Pr921883667ee_a_a,S2: set_Pr921883667ee_a_a] :
% 2.80/1.56 ( ( ( ^ [X4: tree_a,Y5: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X4 @ Y5 ) @ R3 ) )
% 2.80/1.56 = ( ^ [X4: tree_a,Y5: a] : ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X4 @ Y5 ) @ S2 ) ) )
% 2.80/1.56 = ( R3 = S2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_143_csquare__fstOp__sndOp,axiom,
% 2.80/1.56 ! [F: ( a > tree_a > $o ) > produc143150363Tree_a > $o,P: a > a > $o,Q2: a > tree_a > $o] : ( bNF_cs739966834Tree_a @ ( collec486369286Tree_a @ ( F @ ( relcompp_a_a_Tree_a @ P @ Q2 ) ) ) @ product_snd_a_a @ product_fst_a_Tree_a @ ( bNF_fstOp_a_a_Tree_a @ P @ Q2 ) @ ( bNF_sndOp_a_a_Tree_a @ P @ Q2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_144_csquare__fstOp__sndOp,axiom,
% 2.80/1.56 ! [F: ( a > tree_a > $o ) > produc143150363Tree_a > $o,P: a > tree_a > $o,Q2: tree_a > tree_a > $o] : ( bNF_cs1091007358Tree_a @ ( collec486369286Tree_a @ ( F @ ( relcom439193229Tree_a @ P @ Q2 ) ) ) @ product_snd_a_Tree_a @ produc1206152067Tree_a @ ( bNF_fs1579355852Tree_a @ P @ Q2 ) @ ( bNF_sn687175434Tree_a @ P @ Q2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_145_csquare__fstOp__sndOp,axiom,
% 2.80/1.56 ! [F: ( a > a > $o ) > product_prod_a_a > $o,P: a > tree_a > $o,Q2: tree_a > a > $o] : ( bNF_cs1095035134ee_a_a @ ( collec645855634od_a_a @ ( F @ ( relcompp_a_Tree_a_a @ P @ Q2 ) ) ) @ product_snd_a_Tree_a @ product_fst_Tree_a_a @ ( bNF_fstOp_a_Tree_a_a @ P @ Q2 ) @ ( bNF_sndOp_a_Tree_a_a @ P @ Q2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_146_subset__Collect__iff,axiom,
% 2.80/1.56 ! [B5: set_a,A5: set_a,P: a > $o] :
% 2.80/1.56 ( ( ord_less_eq_set_a @ B5 @ A5 )
% 2.80/1.56 => ( ( ord_less_eq_set_a @ B5
% 2.80/1.56 @ ( collect_a
% 2.80/1.56 @ ^ [X4: a] :
% 2.80/1.56 ( ( member_a @ X4 @ A5 )
% 2.80/1.56 & ( P @ X4 ) ) ) )
% 2.80/1.56 = ( ! [X4: a] :
% 2.80/1.56 ( ( member_a @ X4 @ B5 )
% 2.80/1.56 => ( P @ X4 ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_147_subset__Collect__iff,axiom,
% 2.80/1.56 ! [B5: set_Pr1070816379Tree_a,A5: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ( ord_le1013007387Tree_a @ B5 @ A5 )
% 2.80/1.56 => ( ( ord_le1013007387Tree_a @ B5
% 2.80/1.56 @ ( collec486369286Tree_a
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X4 @ A5 )
% 2.80/1.56 & ( P @ X4 ) ) ) )
% 2.80/1.56 = ( ! [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X4 @ B5 )
% 2.80/1.56 => ( P @ X4 ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_148_subset__CollectI,axiom,
% 2.80/1.56 ! [B5: set_a,A5: set_a,Q2: a > $o,P: a > $o] :
% 2.80/1.56 ( ( ord_less_eq_set_a @ B5 @ A5 )
% 2.80/1.56 => ( ! [X5: a] :
% 2.80/1.56 ( ( member_a @ X5 @ B5 )
% 2.80/1.56 => ( ( Q2 @ X5 )
% 2.80/1.56 => ( P @ X5 ) ) )
% 2.80/1.56 => ( ord_less_eq_set_a
% 2.80/1.56 @ ( collect_a
% 2.80/1.56 @ ^ [X4: a] :
% 2.80/1.56 ( ( member_a @ X4 @ B5 )
% 2.80/1.56 & ( Q2 @ X4 ) ) )
% 2.80/1.56 @ ( collect_a
% 2.80/1.56 @ ^ [X4: a] :
% 2.80/1.56 ( ( member_a @ X4 @ A5 )
% 2.80/1.56 & ( P @ X4 ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_149_subset__CollectI,axiom,
% 2.80/1.56 ! [B5: set_Pr1070816379Tree_a,A5: set_Pr1070816379Tree_a,Q2: produc143150363Tree_a > $o,P: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ( ord_le1013007387Tree_a @ B5 @ A5 )
% 2.80/1.56 => ( ! [X5: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X5 @ B5 )
% 2.80/1.56 => ( ( Q2 @ X5 )
% 2.80/1.56 => ( P @ X5 ) ) )
% 2.80/1.56 => ( ord_le1013007387Tree_a
% 2.80/1.56 @ ( collec486369286Tree_a
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X4 @ B5 )
% 2.80/1.56 & ( Q2 @ X4 ) ) )
% 2.80/1.56 @ ( collec486369286Tree_a
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X4 @ A5 )
% 2.80/1.56 & ( P @ X4 ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_150_pred__subset__eq,axiom,
% 2.80/1.56 ! [R3: set_a,S2: set_a] :
% 2.80/1.56 ( ( ord_less_eq_a_o
% 2.80/1.56 @ ^ [X4: a] : ( member_a @ X4 @ R3 )
% 2.80/1.56 @ ^ [X4: a] : ( member_a @ X4 @ S2 ) )
% 2.80/1.56 = ( ord_less_eq_set_a @ R3 @ S2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_151_pred__subset__eq,axiom,
% 2.80/1.56 ! [R3: set_Pr1070816379Tree_a,S2: set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ( ord_le1601593986ee_a_o
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ R3 )
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ S2 ) )
% 2.80/1.56 = ( ord_le1013007387Tree_a @ R3 @ S2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_152_subrelI,axiom,
% 2.80/1.56 ! [R: set_Pr1070816379Tree_a,S3: set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ ( produc686083979Tree_a @ X5 @ Y4 ) @ R )
% 2.80/1.56 => ( member254315204Tree_a @ ( produc686083979Tree_a @ X5 @ Y4 ) @ S3 ) )
% 2.80/1.56 => ( ord_le1013007387Tree_a @ R @ S3 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_153_subrelI,axiom,
% 2.80/1.56 ! [R: set_Pr921883667ee_a_a,S3: set_Pr921883667ee_a_a] :
% 2.80/1.56 ( ! [X5: tree_a,Y4: a] :
% 2.80/1.56 ( ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X5 @ Y4 ) @ R )
% 2.80/1.56 => ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ X5 @ Y4 ) @ S3 ) )
% 2.80/1.56 => ( ord_le864074675ee_a_a @ R @ S3 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_154_subsetI,axiom,
% 2.80/1.56 ! [A5: set_a,B5: set_a] :
% 2.80/1.56 ( ! [X5: a] :
% 2.80/1.56 ( ( member_a @ X5 @ A5 )
% 2.80/1.56 => ( member_a @ X5 @ B5 ) )
% 2.80/1.56 => ( ord_less_eq_set_a @ A5 @ B5 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_155_subsetI,axiom,
% 2.80/1.56 ! [A5: set_Pr1070816379Tree_a,B5: set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ! [X5: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X5 @ A5 )
% 2.80/1.56 => ( member254315204Tree_a @ X5 @ B5 ) )
% 2.80/1.56 => ( ord_le1013007387Tree_a @ A5 @ B5 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_156_Collect__restrict,axiom,
% 2.80/1.56 ! [X6: set_a,P: a > $o] :
% 2.80/1.56 ( ord_less_eq_set_a
% 2.80/1.56 @ ( collect_a
% 2.80/1.56 @ ^ [X4: a] :
% 2.80/1.56 ( ( member_a @ X4 @ X6 )
% 2.80/1.56 & ( P @ X4 ) ) )
% 2.80/1.56 @ X6 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_157_Collect__restrict,axiom,
% 2.80/1.56 ! [X6: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ord_le1013007387Tree_a
% 2.80/1.56 @ ( collec486369286Tree_a
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X4 @ X6 )
% 2.80/1.56 & ( P @ X4 ) ) )
% 2.80/1.56 @ X6 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_158_ssubst__Pair__rhs,axiom,
% 2.80/1.56 ! [R: a,S3: tree_a,R3: set_Pr1070816379Tree_a,S4: tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ ( produc686083979Tree_a @ R @ S3 ) @ R3 )
% 2.80/1.56 => ( ( S4 = S3 )
% 2.80/1.56 => ( member254315204Tree_a @ ( produc686083979Tree_a @ R @ S4 ) @ R3 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_159_ssubst__Pair__rhs,axiom,
% 2.80/1.56 ! [R: tree_a,S3: a,R3: set_Pr921883667ee_a_a,S4: a] :
% 2.80/1.56 ( ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ R @ S3 ) @ R3 )
% 2.80/1.56 => ( ( S4 = S3 )
% 2.80/1.56 => ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ R @ S4 ) @ R3 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_160_in__mono,axiom,
% 2.80/1.56 ! [A5: set_a,B5: set_a,X: a] :
% 2.80/1.56 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 2.80/1.56 => ( ( member_a @ X @ A5 )
% 2.80/1.56 => ( member_a @ X @ B5 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_161_in__mono,axiom,
% 2.80/1.56 ! [A5: set_Pr1070816379Tree_a,B5: set_Pr1070816379Tree_a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( ord_le1013007387Tree_a @ A5 @ B5 )
% 2.80/1.56 => ( ( member254315204Tree_a @ X @ A5 )
% 2.80/1.56 => ( member254315204Tree_a @ X @ B5 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_162_subsetD,axiom,
% 2.80/1.56 ! [A5: set_a,B5: set_a,C: a] :
% 2.80/1.56 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 2.80/1.56 => ( ( member_a @ C @ A5 )
% 2.80/1.56 => ( member_a @ C @ B5 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_163_subsetD,axiom,
% 2.80/1.56 ! [A5: set_Pr1070816379Tree_a,B5: set_Pr1070816379Tree_a,C: produc143150363Tree_a] :
% 2.80/1.56 ( ( ord_le1013007387Tree_a @ A5 @ B5 )
% 2.80/1.56 => ( ( member254315204Tree_a @ C @ A5 )
% 2.80/1.56 => ( member254315204Tree_a @ C @ B5 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_164_subset__eq,axiom,
% 2.80/1.56 ( ord_less_eq_set_a
% 2.80/1.56 = ( ^ [A6: set_a,B6: set_a] :
% 2.80/1.56 ! [X4: a] :
% 2.80/1.56 ( ( member_a @ X4 @ A6 )
% 2.80/1.56 => ( member_a @ X4 @ B6 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_165_subset__eq,axiom,
% 2.80/1.56 ( ord_le1013007387Tree_a
% 2.80/1.56 = ( ^ [A6: set_Pr1070816379Tree_a,B6: set_Pr1070816379Tree_a] :
% 2.80/1.56 ! [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X4 @ A6 )
% 2.80/1.56 => ( member254315204Tree_a @ X4 @ B6 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_166_subset__iff,axiom,
% 2.80/1.56 ( ord_less_eq_set_a
% 2.80/1.56 = ( ^ [A6: set_a,B6: set_a] :
% 2.80/1.56 ! [T: a] :
% 2.80/1.56 ( ( member_a @ T @ A6 )
% 2.80/1.56 => ( member_a @ T @ B6 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_167_subset__iff,axiom,
% 2.80/1.56 ( ord_le1013007387Tree_a
% 2.80/1.56 = ( ^ [A6: set_Pr1070816379Tree_a,B6: set_Pr1070816379Tree_a] :
% 2.80/1.56 ! [T: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ T @ A6 )
% 2.80/1.56 => ( member254315204Tree_a @ T @ B6 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_168_Collect__mono,axiom,
% 2.80/1.56 ! [P: produc143150363Tree_a > $o,Q2: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ! [X5: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ X5 )
% 2.80/1.56 => ( Q2 @ X5 ) )
% 2.80/1.56 => ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ P ) @ ( collec486369286Tree_a @ Q2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_169_Collect__mono__iff,axiom,
% 2.80/1.56 ! [P: produc143150363Tree_a > $o,Q2: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ P ) @ ( collec486369286Tree_a @ Q2 ) )
% 2.80/1.56 = ( ! [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ X4 )
% 2.80/1.56 => ( Q2 @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_170_Collect__subset,axiom,
% 2.80/1.56 ! [A5: set_a,P: a > $o] :
% 2.80/1.56 ( ord_less_eq_set_a
% 2.80/1.56 @ ( collect_a
% 2.80/1.56 @ ^ [X4: a] :
% 2.80/1.56 ( ( member_a @ X4 @ A5 )
% 2.80/1.56 & ( P @ X4 ) ) )
% 2.80/1.56 @ A5 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_171_Collect__subset,axiom,
% 2.80/1.56 ! [A5: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ord_le1013007387Tree_a
% 2.80/1.56 @ ( collec486369286Tree_a
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X4 @ A5 )
% 2.80/1.56 & ( P @ X4 ) ) )
% 2.80/1.56 @ A5 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_172_less__eq__set__def,axiom,
% 2.80/1.56 ( ord_less_eq_set_a
% 2.80/1.56 = ( ^ [A6: set_a,B6: set_a] :
% 2.80/1.56 ( ord_less_eq_a_o
% 2.80/1.56 @ ^ [X4: a] : ( member_a @ X4 @ A6 )
% 2.80/1.56 @ ^ [X4: a] : ( member_a @ X4 @ B6 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_173_less__eq__set__def,axiom,
% 2.80/1.56 ( ord_le1013007387Tree_a
% 2.80/1.56 = ( ^ [A6: set_Pr1070816379Tree_a,B6: set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ord_le1601593986ee_a_o
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ A6 )
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] : ( member254315204Tree_a @ X4 @ B6 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_174_prop__restrict,axiom,
% 2.80/1.56 ! [X: a,Z3: set_a,X6: set_a,P: a > $o] :
% 2.80/1.56 ( ( member_a @ X @ Z3 )
% 2.80/1.56 => ( ( ord_less_eq_set_a @ Z3
% 2.80/1.56 @ ( collect_a
% 2.80/1.56 @ ^ [X4: a] :
% 2.80/1.56 ( ( member_a @ X4 @ X6 )
% 2.80/1.56 & ( P @ X4 ) ) ) )
% 2.80/1.56 => ( P @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_175_prop__restrict,axiom,
% 2.80/1.56 ! [X: produc143150363Tree_a,Z3: set_Pr1070816379Tree_a,X6: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ( member254315204Tree_a @ X @ Z3 )
% 2.80/1.56 => ( ( ord_le1013007387Tree_a @ Z3
% 2.80/1.56 @ ( collec486369286Tree_a
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ X4 @ X6 )
% 2.80/1.56 & ( P @ X4 ) ) ) )
% 2.80/1.56 => ( P @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_176_conj__subset__def,axiom,
% 2.80/1.56 ! [A5: set_Pr1070816379Tree_a,P: produc143150363Tree_a > $o,Q2: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ( ord_le1013007387Tree_a @ A5
% 2.80/1.56 @ ( collec486369286Tree_a
% 2.80/1.56 @ ^ [X4: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ X4 )
% 2.80/1.56 & ( Q2 @ X4 ) ) ) )
% 2.80/1.56 = ( ( ord_le1013007387Tree_a @ A5 @ ( collec486369286Tree_a @ P ) )
% 2.80/1.56 & ( ord_le1013007387Tree_a @ A5 @ ( collec486369286Tree_a @ Q2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_177_image2__eqI,axiom,
% 2.80/1.56 ! [B: a,F: a > a,X: a,C: tree_a,G: a > tree_a,A5: set_a] :
% 2.80/1.56 ( ( B
% 2.80/1.56 = ( F @ X ) )
% 2.80/1.56 => ( ( C
% 2.80/1.56 = ( G @ X ) )
% 2.80/1.56 => ( ( member_a @ X @ A5 )
% 2.80/1.56 => ( member254315204Tree_a @ ( produc686083979Tree_a @ B @ C ) @ ( bNF_Gr651645592Tree_a @ A5 @ F @ G ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_178_image2__eqI,axiom,
% 2.80/1.56 ! [B: a,F: produc143150363Tree_a > a,X: produc143150363Tree_a,C: tree_a,G: produc143150363Tree_a > tree_a,A5: set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ( B
% 2.80/1.56 = ( F @ X ) )
% 2.80/1.56 => ( ( C
% 2.80/1.56 = ( G @ X ) )
% 2.80/1.56 => ( ( member254315204Tree_a @ X @ A5 )
% 2.80/1.56 => ( member254315204Tree_a @ ( produc686083979Tree_a @ B @ C ) @ ( bNF_Gr2042500789Tree_a @ A5 @ F @ G ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_179_image2__eqI,axiom,
% 2.80/1.56 ! [B: tree_a,F: a > tree_a,X: a,C: a,G: a > a,A5: set_a] :
% 2.80/1.56 ( ( B
% 2.80/1.56 = ( F @ X ) )
% 2.80/1.56 => ( ( C
% 2.80/1.56 = ( G @ X ) )
% 2.80/1.56 => ( ( member_a @ X @ A5 )
% 2.80/1.56 => ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ B @ C ) @ ( bNF_Gr614734384ee_a_a @ A5 @ F @ G ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_180_image2__eqI,axiom,
% 2.80/1.56 ! [B: tree_a,F: produc143150363Tree_a > tree_a,X: produc143150363Tree_a,C: a,G: produc143150363Tree_a > a,A5: set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ( B
% 2.80/1.56 = ( F @ X ) )
% 2.80/1.56 => ( ( C
% 2.80/1.56 = ( G @ X ) )
% 2.80/1.56 => ( ( member254315204Tree_a @ X @ A5 )
% 2.80/1.56 => ( member1092636252ee_a_a @ ( produc649172771ee_a_a @ B @ C ) @ ( bNF_Gr2005589581ee_a_a @ A5 @ F @ G ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_181_GreatestI2__order,axiom,
% 2.80/1.56 ! [P: a > $o,X: a,Q2: a > $o] :
% 2.80/1.56 ( ( P @ X )
% 2.80/1.56 => ( ! [Y4: a] :
% 2.80/1.56 ( ( P @ Y4 )
% 2.80/1.56 => ( ord_less_eq_a @ Y4 @ X ) )
% 2.80/1.56 => ( ! [X5: a] :
% 2.80/1.56 ( ( P @ X5 )
% 2.80/1.56 => ( ! [Y6: a] :
% 2.80/1.56 ( ( P @ Y6 )
% 2.80/1.56 => ( ord_less_eq_a @ Y6 @ X5 ) )
% 2.80/1.56 => ( Q2 @ X5 ) ) )
% 2.80/1.56 => ( Q2 @ ( order_Greatest_a @ P ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_182_Greatest__equality,axiom,
% 2.80/1.56 ! [P: a > $o,X: a] :
% 2.80/1.56 ( ( P @ X )
% 2.80/1.56 => ( ! [Y4: a] :
% 2.80/1.56 ( ( P @ Y4 )
% 2.80/1.56 => ( ord_less_eq_a @ Y4 @ X ) )
% 2.80/1.56 => ( ( order_Greatest_a @ P )
% 2.80/1.56 = X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_183_Heap__axioms__def,axiom,
% 2.80/1.56 ( heap_axioms_Tree_a_a
% 2.80/1.56 = ( ^ [Is_empty2: tree_a > $o,Of_list2: list_a > tree_a,Multiset2: tree_a > multiset_a,As_tree2: tree_a > tree_a,Remove_max2: tree_a > produc143150363Tree_a] :
% 2.80/1.56 ( ! [L4: tree_a] :
% 2.80/1.56 ( ( Multiset2 @ L4 )
% 2.80/1.56 = ( multiset_a2 @ ( As_tree2 @ L4 ) ) )
% 2.80/1.56 & ! [I: list_a] : ( is_heap_a @ ( As_tree2 @ ( Of_list2 @ I ) ) )
% 2.80/1.56 & ! [T: tree_a] :
% 2.80/1.56 ( ( ( As_tree2 @ T )
% 2.80/1.56 = e_a )
% 2.80/1.56 = ( Is_empty2 @ T ) )
% 2.80/1.56 & ! [L4: tree_a,M2: a,L5: tree_a] :
% 2.80/1.56 ( ~ ( Is_empty2 @ L4 )
% 2.80/1.56 => ( ( ( produc686083979Tree_a @ M2 @ L5 )
% 2.80/1.56 = ( Remove_max2 @ L4 ) )
% 2.80/1.56 => ( ( add_mset_a @ M2 @ ( Multiset2 @ L5 ) )
% 2.80/1.56 = ( Multiset2 @ L4 ) ) ) )
% 2.80/1.56 & ! [L4: tree_a,M2: a,L5: tree_a] :
% 2.80/1.56 ( ~ ( Is_empty2 @ L4 )
% 2.80/1.56 => ( ( is_heap_a @ ( As_tree2 @ L4 ) )
% 2.80/1.56 => ( ( ( produc686083979Tree_a @ M2 @ L5 )
% 2.80/1.56 = ( Remove_max2 @ L4 ) )
% 2.80/1.56 => ( is_heap_a @ ( As_tree2 @ L5 ) ) ) ) )
% 2.80/1.56 & ! [T: tree_a,M2: a,T4: tree_a] :
% 2.80/1.56 ( ~ ( Is_empty2 @ T )
% 2.80/1.56 => ( ( ( produc686083979Tree_a @ M2 @ T4 )
% 2.80/1.56 = ( Remove_max2 @ T ) )
% 2.80/1.56 => ( M2
% 2.80/1.56 = ( val_a @ ( As_tree2 @ T ) ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_184_siftDown__multiset,axiom,
% 2.80/1.56 ! [T2: tree_a] :
% 2.80/1.56 ( ( multiset_a2 @ ( heapIm1091024090Down_a @ T2 ) )
% 2.80/1.56 = ( multiset_a2 @ T2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_185_Heap_Oremove__max__multiset_H,axiom,
% 2.80/1.56 ! [Empty: tree_a,Is_empty: tree_a > $o,Of_list: list_a > tree_a,Multiset: tree_a > multiset_a,As_tree: tree_a > tree_a,Remove_max: tree_a > produc143150363Tree_a,L: tree_a,M: a,L3: tree_a] :
% 2.80/1.56 ( ( heap_Tree_a_a @ Empty @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max )
% 2.80/1.56 => ( ~ ( Is_empty @ L )
% 2.80/1.56 => ( ( ( produc686083979Tree_a @ M @ L3 )
% 2.80/1.56 = ( Remove_max @ L ) )
% 2.80/1.56 => ( ( add_mset_a @ M @ ( Multiset @ L3 ) )
% 2.80/1.56 = ( Multiset @ L ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_186_multiset__heapify,axiom,
% 2.80/1.56 ! [T2: tree_a] :
% 2.80/1.56 ( ( multiset_a2 @ ( heapIm970322378pify_a @ T2 ) )
% 2.80/1.56 = ( multiset_a2 @ T2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_187_Heap__axioms_Ointro,axiom,
% 2.80/1.56 ! [Multiset: tree_a > multiset_a,As_tree: tree_a > tree_a,Of_list: list_a > tree_a,Is_empty: tree_a > $o,Remove_max: tree_a > produc143150363Tree_a] :
% 2.80/1.56 ( ! [L6: tree_a] :
% 2.80/1.56 ( ( Multiset @ L6 )
% 2.80/1.56 = ( multiset_a2 @ ( As_tree @ L6 ) ) )
% 2.80/1.56 => ( ! [I2: list_a] : ( is_heap_a @ ( As_tree @ ( Of_list @ I2 ) ) )
% 2.80/1.56 => ( ! [T5: tree_a] :
% 2.80/1.56 ( ( ( As_tree @ T5 )
% 2.80/1.56 = e_a )
% 2.80/1.56 = ( Is_empty @ T5 ) )
% 2.80/1.56 => ( ! [L6: tree_a,M3: a,L2: tree_a] :
% 2.80/1.56 ( ~ ( Is_empty @ L6 )
% 2.80/1.56 => ( ( ( produc686083979Tree_a @ M3 @ L2 )
% 2.80/1.56 = ( Remove_max @ L6 ) )
% 2.80/1.56 => ( ( add_mset_a @ M3 @ ( Multiset @ L2 ) )
% 2.80/1.56 = ( Multiset @ L6 ) ) ) )
% 2.80/1.56 => ( ! [L6: tree_a,M3: a,L2: tree_a] :
% 2.80/1.56 ( ~ ( Is_empty @ L6 )
% 2.80/1.56 => ( ( is_heap_a @ ( As_tree @ L6 ) )
% 2.80/1.56 => ( ( ( produc686083979Tree_a @ M3 @ L2 )
% 2.80/1.56 = ( Remove_max @ L6 ) )
% 2.80/1.56 => ( is_heap_a @ ( As_tree @ L2 ) ) ) ) )
% 2.80/1.56 => ( ! [T5: tree_a,M3: a,T6: tree_a] :
% 2.80/1.56 ( ~ ( Is_empty @ T5 )
% 2.80/1.56 => ( ( ( produc686083979Tree_a @ M3 @ T6 )
% 2.80/1.56 = ( Remove_max @ T5 ) )
% 2.80/1.56 => ( M3
% 2.80/1.56 = ( val_a @ ( As_tree @ T5 ) ) ) ) )
% 2.80/1.56 => ( heap_axioms_Tree_a_a @ Is_empty @ Of_list @ Multiset @ As_tree @ Remove_max ) ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_188_heap__top__geq,axiom,
% 2.80/1.56 ! [A: a,T2: tree_a] :
% 2.80/1.56 ( ( member_a @ A @ ( set_mset_a @ ( multiset_a2 @ T2 ) ) )
% 2.80/1.56 => ( ( is_heap_a @ T2 )
% 2.80/1.56 => ( ord_less_eq_a @ A @ ( val_a @ T2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_189_prod_Osplit__sel__asm,axiom,
% 2.80/1.56 ! [P: $o > $o,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 2.80/1.56 = ( ~ ( ( Prod
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 2.80/1.56 & ~ ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_190_prod_Osplit__sel__asm,axiom,
% 2.80/1.56 ! [P: tree_a > $o,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ ( produc873356882Tree_a @ F @ Prod ) )
% 2.80/1.56 = ( ~ ( ( Prod
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 2.80/1.56 & ~ ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_191_prod_Osplit__sel__asm,axiom,
% 2.80/1.56 ! [P: produc143150363Tree_a > $o,F: tree_a > a > produc143150363Tree_a,Prod: produc981471411ee_a_a] :
% 2.80/1.56 ( ( P @ ( produc369019363Tree_a @ F @ Prod ) )
% 2.80/1.56 = ( ~ ( ( Prod
% 2.80/1.56 = ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) )
% 2.80/1.56 & ~ ( P @ ( F @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_192_prod_Osplit__sel__asm,axiom,
% 2.80/1.56 ! [P: produc981471411ee_a_a > $o,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 2.80/1.56 = ( ~ ( ( Prod
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 2.80/1.56 & ~ ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_193_prod_Osplit__sel,axiom,
% 2.80/1.56 ! [P: $o > $o,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 2.80/1.56 = ( ( Prod
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 2.80/1.56 => ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_194_prod_Osplit__sel,axiom,
% 2.80/1.56 ! [P: tree_a > $o,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ ( produc873356882Tree_a @ F @ Prod ) )
% 2.80/1.56 = ( ( Prod
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 2.80/1.56 => ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_195_prod_Osplit__sel,axiom,
% 2.80/1.56 ! [P: produc143150363Tree_a > $o,F: tree_a > a > produc143150363Tree_a,Prod: produc981471411ee_a_a] :
% 2.80/1.56 ( ( P @ ( produc369019363Tree_a @ F @ Prod ) )
% 2.80/1.56 = ( ( Prod
% 2.80/1.56 = ( produc649172771ee_a_a @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) )
% 2.80/1.56 => ( P @ ( F @ ( product_fst_Tree_a_a @ Prod ) @ ( product_snd_Tree_a_a @ Prod ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_196_prod_Osplit__sel,axiom,
% 2.80/1.56 ! [P: produc981471411ee_a_a > $o,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 2.80/1.56 = ( ( Prod
% 2.80/1.56 = ( produc686083979Tree_a @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) )
% 2.80/1.56 => ( P @ ( F @ ( product_fst_a_Tree_a @ Prod ) @ ( product_snd_a_Tree_a @ Prod ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_197_mem__case__prodI,axiom,
% 2.80/1.56 ! [Z: a,C: a > tree_a > set_a,A: a,B: tree_a] :
% 2.80/1.56 ( ( member_a @ Z @ ( C @ A @ B ) )
% 2.80/1.56 => ( member_a @ Z @ ( produc1902270_set_a @ C @ ( produc686083979Tree_a @ A @ B ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_198_mem__case__prodI,axiom,
% 2.80/1.56 ! [Z: produc143150363Tree_a,C: a > tree_a > set_Pr1070816379Tree_a,A: a,B: tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ Z @ ( C @ A @ B ) )
% 2.80/1.56 => ( member254315204Tree_a @ Z @ ( produc802621147Tree_a @ C @ ( produc686083979Tree_a @ A @ B ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_199_mem__case__prodI,axiom,
% 2.80/1.56 ! [Z: a,C: tree_a > a > set_a,A: tree_a,B: a] :
% 2.80/1.56 ( ( member_a @ Z @ ( C @ A @ B ) )
% 2.80/1.56 => ( member_a @ Z @ ( produc136688934_set_a @ C @ ( produc649172771ee_a_a @ A @ B ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_200_mem__case__prodI,axiom,
% 2.80/1.56 ! [Z: produc143150363Tree_a,C: tree_a > a > set_Pr1070816379Tree_a,A: tree_a,B: a] :
% 2.80/1.56 ( ( member254315204Tree_a @ Z @ ( C @ A @ B ) )
% 2.80/1.56 => ( member254315204Tree_a @ Z @ ( produc951236931Tree_a @ C @ ( produc649172771ee_a_a @ A @ B ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_201_mem__case__prodI2,axiom,
% 2.80/1.56 ! [P2: produc143150363Tree_a,Z: a,C: a > tree_a > set_a] :
% 2.80/1.56 ( ! [A4: a,B4: tree_a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc686083979Tree_a @ A4 @ B4 ) )
% 2.80/1.56 => ( member_a @ Z @ ( C @ A4 @ B4 ) ) )
% 2.80/1.56 => ( member_a @ Z @ ( produc1902270_set_a @ C @ P2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_202_mem__case__prodI2,axiom,
% 2.80/1.56 ! [P2: produc143150363Tree_a,Z: produc143150363Tree_a,C: a > tree_a > set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ! [A4: a,B4: tree_a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc686083979Tree_a @ A4 @ B4 ) )
% 2.80/1.56 => ( member254315204Tree_a @ Z @ ( C @ A4 @ B4 ) ) )
% 2.80/1.56 => ( member254315204Tree_a @ Z @ ( produc802621147Tree_a @ C @ P2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_203_mem__case__prodI2,axiom,
% 2.80/1.56 ! [P2: produc981471411ee_a_a,Z: a,C: tree_a > a > set_a] :
% 2.80/1.56 ( ! [A4: tree_a,B4: a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc649172771ee_a_a @ A4 @ B4 ) )
% 2.80/1.56 => ( member_a @ Z @ ( C @ A4 @ B4 ) ) )
% 2.80/1.56 => ( member_a @ Z @ ( produc136688934_set_a @ C @ P2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_204_mem__case__prodI2,axiom,
% 2.80/1.56 ! [P2: produc981471411ee_a_a,Z: produc143150363Tree_a,C: tree_a > a > set_Pr1070816379Tree_a] :
% 2.80/1.56 ( ! [A4: tree_a,B4: a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc649172771ee_a_a @ A4 @ B4 ) )
% 2.80/1.56 => ( member254315204Tree_a @ Z @ ( C @ A4 @ B4 ) ) )
% 2.80/1.56 => ( member254315204Tree_a @ Z @ ( produc951236931Tree_a @ C @ P2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_205_case__prodI,axiom,
% 2.80/1.56 ! [F: tree_a > a > $o,A: tree_a,B: a] :
% 2.80/1.56 ( ( F @ A @ B )
% 2.80/1.56 => ( produc1587316832_a_a_o @ F @ ( produc649172771ee_a_a @ A @ B ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_206_case__prodI,axiom,
% 2.80/1.56 ! [F: a > tree_a > $o,A: a,B: tree_a] :
% 2.80/1.56 ( ( F @ A @ B )
% 2.80/1.56 => ( produc1673233912ee_a_o @ F @ ( produc686083979Tree_a @ A @ B ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_207_case__prodI2,axiom,
% 2.80/1.56 ! [P2: produc981471411ee_a_a,C: tree_a > a > $o] :
% 2.80/1.56 ( ! [A4: tree_a,B4: a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc649172771ee_a_a @ A4 @ B4 ) )
% 2.80/1.56 => ( C @ A4 @ B4 ) )
% 2.80/1.56 => ( produc1587316832_a_a_o @ C @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_208_case__prodI2,axiom,
% 2.80/1.56 ! [P2: produc143150363Tree_a,C: a > tree_a > $o] :
% 2.80/1.56 ( ! [A4: a,B4: tree_a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc686083979Tree_a @ A4 @ B4 ) )
% 2.80/1.56 => ( C @ A4 @ B4 ) )
% 2.80/1.56 => ( produc1673233912ee_a_o @ C @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_209_case__prod__conv,axiom,
% 2.80/1.56 ! [F: a > tree_a > $o,A: a,B: tree_a] :
% 2.80/1.56 ( ( produc1673233912ee_a_o @ F @ ( produc686083979Tree_a @ A @ B ) )
% 2.80/1.56 = ( F @ A @ B ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_210_case__prod__conv,axiom,
% 2.80/1.56 ! [F: a > tree_a > tree_a,A: a,B: tree_a] :
% 2.80/1.56 ( ( produc873356882Tree_a @ F @ ( produc686083979Tree_a @ A @ B ) )
% 2.80/1.56 = ( F @ A @ B ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_211_case__prod__conv,axiom,
% 2.80/1.56 ! [F: tree_a > a > produc143150363Tree_a,A: tree_a,B: a] :
% 2.80/1.56 ( ( produc369019363Tree_a @ F @ ( produc649172771ee_a_a @ A @ B ) )
% 2.80/1.56 = ( F @ A @ B ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_212_case__prod__conv,axiom,
% 2.80/1.56 ! [F: a > tree_a > produc981471411ee_a_a,A: a,B: tree_a] :
% 2.80/1.56 ( ( produc1331510035ee_a_a @ F @ ( produc686083979Tree_a @ A @ B ) )
% 2.80/1.56 = ( F @ A @ B ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_213_case__swap,axiom,
% 2.80/1.56 ! [F: a > tree_a > $o,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc1587316832_a_a_o
% 2.80/1.56 @ ^ [Y5: tree_a,X4: a] : ( F @ X4 @ Y5 )
% 2.80/1.56 @ ( produc1515207979Tree_a @ P2 ) )
% 2.80/1.56 = ( produc1673233912ee_a_o @ F @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_214_case__swap,axiom,
% 2.80/1.56 ! [F: a > tree_a > tree_a,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc433477818Tree_a
% 2.80/1.56 @ ^ [Y5: tree_a,X4: a] : ( F @ X4 @ Y5 )
% 2.80/1.56 @ ( produc1515207979Tree_a @ P2 ) )
% 2.80/1.56 = ( produc873356882Tree_a @ F @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_215_case__swap,axiom,
% 2.80/1.56 ! [F: tree_a > a > produc143150363Tree_a,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc493188987Tree_a
% 2.80/1.56 @ ^ [Y5: a,X4: tree_a] : ( F @ X4 @ Y5 )
% 2.80/1.56 @ ( produc1478296771ee_a_a @ P2 ) )
% 2.80/1.56 = ( produc369019363Tree_a @ F @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_216_case__swap,axiom,
% 2.80/1.56 ! [F: a > tree_a > produc981471411ee_a_a,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc1207340411ee_a_a
% 2.80/1.56 @ ^ [Y5: tree_a,X4: a] : ( F @ X4 @ Y5 )
% 2.80/1.56 @ ( produc1515207979Tree_a @ P2 ) )
% 2.80/1.56 = ( produc1331510035ee_a_a @ F @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_217_case__swap,axiom,
% 2.80/1.56 ! [F: tree_a > a > $o,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc1673233912ee_a_o
% 2.80/1.56 @ ^ [Y5: a,X4: tree_a] : ( F @ X4 @ Y5 )
% 2.80/1.56 @ ( produc1478296771ee_a_a @ P2 ) )
% 2.80/1.56 = ( produc1587316832_a_a_o @ F @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_218_case__swap,axiom,
% 2.80/1.56 ! [F: tree_a > a > tree_a,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc873356882Tree_a
% 2.80/1.56 @ ^ [Y5: a,X4: tree_a] : ( F @ X4 @ Y5 )
% 2.80/1.56 @ ( produc1478296771ee_a_a @ P2 ) )
% 2.80/1.56 = ( produc433477818Tree_a @ F @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_219_case__swap,axiom,
% 2.80/1.56 ! [F: a > tree_a > produc143150363Tree_a,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc369019363Tree_a
% 2.80/1.56 @ ^ [Y5: tree_a,X4: a] : ( F @ X4 @ Y5 )
% 2.80/1.56 @ ( produc1515207979Tree_a @ P2 ) )
% 2.80/1.56 = ( produc493188987Tree_a @ F @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_220_case__swap,axiom,
% 2.80/1.56 ! [F: tree_a > a > produc981471411ee_a_a,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc1331510035ee_a_a
% 2.80/1.56 @ ^ [Y5: a,X4: tree_a] : ( F @ X4 @ Y5 )
% 2.80/1.56 @ ( produc1478296771ee_a_a @ P2 ) )
% 2.80/1.56 = ( produc1207340411ee_a_a @ F @ P2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_221_Product__Type_OCollect__case__prodD,axiom,
% 2.80/1.56 ! [X: produc981471411ee_a_a,A5: tree_a > a > $o] :
% 2.80/1.56 ( ( member1092636252ee_a_a @ X @ ( collec1324690334ee_a_a @ ( produc1587316832_a_a_o @ A5 ) ) )
% 2.80/1.56 => ( A5 @ ( product_fst_Tree_a_a @ X ) @ ( product_snd_Tree_a_a @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_222_Product__Type_OCollect__case__prodD,axiom,
% 2.80/1.56 ! [X: produc143150363Tree_a,A5: a > tree_a > $o] :
% 2.80/1.56 ( ( member254315204Tree_a @ X @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ A5 ) ) )
% 2.80/1.56 => ( A5 @ ( product_fst_a_Tree_a @ X ) @ ( product_snd_a_Tree_a @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_223_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: $o > $o,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( H @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 2.80/1.56 = ( produc1673233912ee_a_o
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_224_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: $o > tree_a,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( H @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 2.80/1.56 = ( produc873356882Tree_a
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_225_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: $o > produc981471411ee_a_a,F: a > tree_a > $o,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( H @ ( produc1673233912ee_a_o @ F @ Prod ) )
% 2.80/1.56 = ( produc1331510035ee_a_a
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_226_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: tree_a > $o,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( H @ ( produc873356882Tree_a @ F @ Prod ) )
% 2.80/1.56 = ( produc1673233912ee_a_o
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_227_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: tree_a > tree_a,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( H @ ( produc873356882Tree_a @ F @ Prod ) )
% 2.80/1.56 = ( produc873356882Tree_a
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_228_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: tree_a > produc981471411ee_a_a,F: a > tree_a > tree_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( H @ ( produc873356882Tree_a @ F @ Prod ) )
% 2.80/1.56 = ( produc1331510035ee_a_a
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_229_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: produc143150363Tree_a > produc143150363Tree_a,F: tree_a > a > produc143150363Tree_a,Prod: produc981471411ee_a_a] :
% 2.80/1.56 ( ( H @ ( produc369019363Tree_a @ F @ Prod ) )
% 2.80/1.56 = ( produc369019363Tree_a
% 2.80/1.56 @ ^ [X13: tree_a,X25: a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_230_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: produc981471411ee_a_a > $o,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( H @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 2.80/1.56 = ( produc1673233912ee_a_o
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_231_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: produc981471411ee_a_a > tree_a,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( H @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 2.80/1.56 = ( produc873356882Tree_a
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_232_prod_Ocase__distrib,axiom,
% 2.80/1.56 ! [H: produc981471411ee_a_a > produc981471411ee_a_a,F: a > tree_a > produc981471411ee_a_a,Prod: produc143150363Tree_a] :
% 2.80/1.56 ( ( H @ ( produc1331510035ee_a_a @ F @ Prod ) )
% 2.80/1.56 = ( produc1331510035ee_a_a
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : ( H @ ( F @ X13 @ X25 ) )
% 2.80/1.56 @ Prod ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_233_case__prodE,axiom,
% 2.80/1.56 ! [C: tree_a > a > $o,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc1587316832_a_a_o @ C @ P2 )
% 2.80/1.56 => ~ ! [X5: tree_a,Y4: a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc649172771ee_a_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( C @ X5 @ Y4 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_234_case__prodE,axiom,
% 2.80/1.56 ! [C: a > tree_a > $o,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc1673233912ee_a_o @ C @ P2 )
% 2.80/1.56 => ~ ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( C @ X5 @ Y4 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_235_case__prodD,axiom,
% 2.80/1.56 ! [F: tree_a > a > $o,A: tree_a,B: a] :
% 2.80/1.56 ( ( produc1587316832_a_a_o @ F @ ( produc649172771ee_a_a @ A @ B ) )
% 2.80/1.56 => ( F @ A @ B ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_236_case__prodD,axiom,
% 2.80/1.56 ! [F: a > tree_a > $o,A: a,B: tree_a] :
% 2.80/1.56 ( ( produc1673233912ee_a_o @ F @ ( produc686083979Tree_a @ A @ B ) )
% 2.80/1.56 => ( F @ A @ B ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_237_old_Oprod_Ocase,axiom,
% 2.80/1.56 ! [F: a > tree_a > $o,X12: a,X24: tree_a] :
% 2.80/1.56 ( ( produc1673233912ee_a_o @ F @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 2.80/1.56 = ( F @ X12 @ X24 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_238_old_Oprod_Ocase,axiom,
% 2.80/1.56 ! [F: a > tree_a > tree_a,X12: a,X24: tree_a] :
% 2.80/1.56 ( ( produc873356882Tree_a @ F @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 2.80/1.56 = ( F @ X12 @ X24 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_239_old_Oprod_Ocase,axiom,
% 2.80/1.56 ! [F: tree_a > a > produc143150363Tree_a,X12: tree_a,X24: a] :
% 2.80/1.56 ( ( produc369019363Tree_a @ F @ ( produc649172771ee_a_a @ X12 @ X24 ) )
% 2.80/1.56 = ( F @ X12 @ X24 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_240_old_Oprod_Ocase,axiom,
% 2.80/1.56 ! [F: a > tree_a > produc981471411ee_a_a,X12: a,X24: tree_a] :
% 2.80/1.56 ( ( produc1331510035ee_a_a @ F @ ( produc686083979Tree_a @ X12 @ X24 ) )
% 2.80/1.56 = ( F @ X12 @ X24 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_241_mem__case__prodE,axiom,
% 2.80/1.56 ! [Z: a,C: a > tree_a > set_a,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( member_a @ Z @ ( produc1902270_set_a @ C @ P2 ) )
% 2.80/1.56 => ~ ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( member_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_242_mem__case__prodE,axiom,
% 2.80/1.56 ! [Z: produc143150363Tree_a,C: a > tree_a > set_Pr1070816379Tree_a,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ Z @ ( produc802621147Tree_a @ C @ P2 ) )
% 2.80/1.56 => ~ ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( member254315204Tree_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_243_mem__case__prodE,axiom,
% 2.80/1.56 ! [Z: a,C: tree_a > a > set_a,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( member_a @ Z @ ( produc136688934_set_a @ C @ P2 ) )
% 2.80/1.56 => ~ ! [X5: tree_a,Y4: a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc649172771ee_a_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( member_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_244_mem__case__prodE,axiom,
% 2.80/1.56 ! [Z: produc143150363Tree_a,C: tree_a > a > set_Pr1070816379Tree_a,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( member254315204Tree_a @ Z @ ( produc951236931Tree_a @ C @ P2 ) )
% 2.80/1.56 => ~ ! [X5: tree_a,Y4: a] :
% 2.80/1.56 ( ( P2
% 2.80/1.56 = ( produc649172771ee_a_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( member254315204Tree_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_245_snd__def,axiom,
% 2.80/1.56 ( product_snd_a_Tree_a
% 2.80/1.56 = ( produc873356882Tree_a
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : X25 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_246_fst__def,axiom,
% 2.80/1.56 ( product_fst_a_Tree_a
% 2.80/1.56 = ( produc950721886ee_a_a
% 2.80/1.56 @ ^ [X13: a,X25: tree_a] : X13 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_247_fst__def,axiom,
% 2.80/1.56 ( product_fst_Tree_a_a
% 2.80/1.56 = ( produc433477818Tree_a
% 2.80/1.56 @ ^ [X13: tree_a,X25: a] : X13 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_248_case__prodE2,axiom,
% 2.80/1.56 ! [Q2: $o > $o,P: a > tree_a > $o,Z: produc143150363Tree_a] :
% 2.80/1.56 ( ( Q2 @ ( produc1673233912ee_a_o @ P @ Z ) )
% 2.80/1.56 => ~ ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( Z
% 2.80/1.56 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( Q2 @ ( P @ X5 @ Y4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_249_case__prodE2,axiom,
% 2.80/1.56 ! [Q2: tree_a > $o,P: a > tree_a > tree_a,Z: produc143150363Tree_a] :
% 2.80/1.56 ( ( Q2 @ ( produc873356882Tree_a @ P @ Z ) )
% 2.80/1.56 => ~ ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( Z
% 2.80/1.56 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( Q2 @ ( P @ X5 @ Y4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_250_case__prodE2,axiom,
% 2.80/1.56 ! [Q2: produc143150363Tree_a > $o,P: tree_a > a > produc143150363Tree_a,Z: produc981471411ee_a_a] :
% 2.80/1.56 ( ( Q2 @ ( produc369019363Tree_a @ P @ Z ) )
% 2.80/1.56 => ~ ! [X5: tree_a,Y4: a] :
% 2.80/1.56 ( ( Z
% 2.80/1.56 = ( produc649172771ee_a_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( Q2 @ ( P @ X5 @ Y4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_251_case__prodE2,axiom,
% 2.80/1.56 ! [Q2: produc981471411ee_a_a > $o,P: a > tree_a > produc981471411ee_a_a,Z: produc143150363Tree_a] :
% 2.80/1.56 ( ( Q2 @ ( produc1331510035ee_a_a @ P @ Z ) )
% 2.80/1.56 => ~ ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( Z
% 2.80/1.56 = ( produc686083979Tree_a @ X5 @ Y4 ) )
% 2.80/1.56 => ~ ( Q2 @ ( P @ X5 @ Y4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_252_case__prod__eta,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ( produc1673233912ee_a_o
% 2.80/1.56 @ ^ [X4: a,Y5: tree_a] : ( F @ ( produc686083979Tree_a @ X4 @ Y5 ) ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_253_case__prod__eta,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > tree_a] :
% 2.80/1.56 ( ( produc873356882Tree_a
% 2.80/1.56 @ ^ [X4: a,Y5: tree_a] : ( F @ ( produc686083979Tree_a @ X4 @ Y5 ) ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_254_case__prod__eta,axiom,
% 2.80/1.56 ! [F: produc981471411ee_a_a > produc143150363Tree_a] :
% 2.80/1.56 ( ( produc369019363Tree_a
% 2.80/1.56 @ ^ [X4: tree_a,Y5: a] : ( F @ ( produc649172771ee_a_a @ X4 @ Y5 ) ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_255_case__prod__eta,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc1331510035ee_a_a
% 2.80/1.56 @ ^ [X4: a,Y5: tree_a] : ( F @ ( produc686083979Tree_a @ X4 @ Y5 ) ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_256_cond__case__prod__eta,axiom,
% 2.80/1.56 ! [F: a > tree_a > $o,G: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( F @ X5 @ Y4 )
% 2.80/1.56 = ( G @ ( produc686083979Tree_a @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( ( produc1673233912ee_a_o @ F )
% 2.80/1.56 = G ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_257_cond__case__prod__eta,axiom,
% 2.80/1.56 ! [F: a > tree_a > tree_a,G: produc143150363Tree_a > tree_a] :
% 2.80/1.56 ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( F @ X5 @ Y4 )
% 2.80/1.56 = ( G @ ( produc686083979Tree_a @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( ( produc873356882Tree_a @ F )
% 2.80/1.56 = G ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_258_cond__case__prod__eta,axiom,
% 2.80/1.56 ! [F: tree_a > a > produc143150363Tree_a,G: produc981471411ee_a_a > produc143150363Tree_a] :
% 2.80/1.56 ( ! [X5: tree_a,Y4: a] :
% 2.80/1.56 ( ( F @ X5 @ Y4 )
% 2.80/1.56 = ( G @ ( produc649172771ee_a_a @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( ( produc369019363Tree_a @ F )
% 2.80/1.56 = G ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_259_cond__case__prod__eta,axiom,
% 2.80/1.56 ! [F: a > tree_a > produc981471411ee_a_a,G: produc143150363Tree_a > produc981471411ee_a_a] :
% 2.80/1.56 ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( F @ X5 @ Y4 )
% 2.80/1.56 = ( G @ ( produc686083979Tree_a @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( ( produc1331510035ee_a_a @ F )
% 2.80/1.56 = G ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_260_case__prod__Pair__iden,axiom,
% 2.80/1.56 ! [P2: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc493188987Tree_a @ produc686083979Tree_a @ P2 )
% 2.80/1.56 = P2 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_261_case__prod__Pair__iden,axiom,
% 2.80/1.56 ! [P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc1207340411ee_a_a @ produc649172771ee_a_a @ P2 )
% 2.80/1.56 = P2 ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_262_Collect__case__prod__mono,axiom,
% 2.80/1.56 ! [A5: a > tree_a > $o,B5: a > tree_a > $o] :
% 2.80/1.56 ( ( ord_le1327026842ee_a_o @ A5 @ B5 )
% 2.80/1.56 => ( ord_le1013007387Tree_a @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ A5 ) ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ B5 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_263_prod_Ocase__eq__if,axiom,
% 2.80/1.56 ( produc1673233912ee_a_o
% 2.80/1.56 = ( ^ [F2: a > tree_a > $o,Prod3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ Prod3 ) @ ( product_snd_a_Tree_a @ Prod3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_264_prod_Ocase__eq__if,axiom,
% 2.80/1.56 ( produc873356882Tree_a
% 2.80/1.56 = ( ^ [F2: a > tree_a > tree_a,Prod3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ Prod3 ) @ ( product_snd_a_Tree_a @ Prod3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_265_prod_Ocase__eq__if,axiom,
% 2.80/1.56 ( produc369019363Tree_a
% 2.80/1.56 = ( ^ [F2: tree_a > a > produc143150363Tree_a,Prod3: produc981471411ee_a_a] : ( F2 @ ( product_fst_Tree_a_a @ Prod3 ) @ ( product_snd_Tree_a_a @ Prod3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_266_prod_Ocase__eq__if,axiom,
% 2.80/1.56 ( produc1331510035ee_a_a
% 2.80/1.56 = ( ^ [F2: a > tree_a > produc981471411ee_a_a,Prod3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ Prod3 ) @ ( product_snd_a_Tree_a @ Prod3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_267_case__prod__beta,axiom,
% 2.80/1.56 ( produc1673233912ee_a_o
% 2.80/1.56 = ( ^ [F2: a > tree_a > $o,P3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_268_case__prod__beta,axiom,
% 2.80/1.56 ( produc873356882Tree_a
% 2.80/1.56 = ( ^ [F2: a > tree_a > tree_a,P3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_269_case__prod__beta,axiom,
% 2.80/1.56 ( produc369019363Tree_a
% 2.80/1.56 = ( ^ [F2: tree_a > a > produc143150363Tree_a,P3: produc981471411ee_a_a] : ( F2 @ ( product_fst_Tree_a_a @ P3 ) @ ( product_snd_Tree_a_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_270_case__prod__beta,axiom,
% 2.80/1.56 ( produc1331510035ee_a_a
% 2.80/1.56 = ( ^ [F2: a > tree_a > produc981471411ee_a_a,P3: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_271_internal__case__prod__def,axiom,
% 2.80/1.56 produc1405823650ee_a_o = produc1673233912ee_a_o ).
% 2.80/1.56
% 2.80/1.56 thf(fact_272_internal__case__prod__def,axiom,
% 2.80/1.56 produc534868220Tree_a = produc873356882Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(fact_273_internal__case__prod__def,axiom,
% 2.80/1.56 produc126329485Tree_a = produc369019363Tree_a ).
% 2.80/1.56
% 2.80/1.56 thf(fact_274_internal__case__prod__def,axiom,
% 2.80/1.56 produc1088820157ee_a_a = produc1331510035ee_a_a ).
% 2.80/1.56
% 2.80/1.56 thf(fact_275_fstOp__in,axiom,
% 2.80/1.56 ! [Ac2: produc143150363Tree_a,P: a > tree_a > $o,Q2: tree_a > tree_a > $o] :
% 2.80/1.56 ( ( member254315204Tree_a @ Ac2 @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ ( relcom439193229Tree_a @ P @ Q2 ) ) ) )
% 2.80/1.56 => ( member254315204Tree_a @ ( bNF_fs1579355852Tree_a @ P @ Q2 @ Ac2 ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ P ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_276_sndOp__in,axiom,
% 2.80/1.56 ! [Ac2: produc143150363Tree_a,P: a > a > $o,Q2: a > tree_a > $o] :
% 2.80/1.56 ( ( member254315204Tree_a @ Ac2 @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ ( relcompp_a_a_Tree_a @ P @ Q2 ) ) ) )
% 2.80/1.56 => ( member254315204Tree_a @ ( bNF_sndOp_a_a_Tree_a @ P @ Q2 @ Ac2 ) @ ( collec486369286Tree_a @ ( produc1673233912ee_a_o @ Q2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_277_case__prod__beta_H,axiom,
% 2.80/1.56 ( produc1673233912ee_a_o
% 2.80/1.56 = ( ^ [F2: a > tree_a > $o,X4: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ X4 ) @ ( product_snd_a_Tree_a @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_278_case__prod__beta_H,axiom,
% 2.80/1.56 ( produc873356882Tree_a
% 2.80/1.56 = ( ^ [F2: a > tree_a > tree_a,X4: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ X4 ) @ ( product_snd_a_Tree_a @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_279_case__prod__beta_H,axiom,
% 2.80/1.56 ( produc369019363Tree_a
% 2.80/1.56 = ( ^ [F2: tree_a > a > produc143150363Tree_a,X4: produc981471411ee_a_a] : ( F2 @ ( product_fst_Tree_a_a @ X4 ) @ ( product_snd_Tree_a_a @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_280_case__prod__beta_H,axiom,
% 2.80/1.56 ( produc1331510035ee_a_a
% 2.80/1.56 = ( ^ [F2: a > tree_a > produc981471411ee_a_a,X4: produc143150363Tree_a] : ( F2 @ ( product_fst_a_Tree_a @ X4 ) @ ( product_snd_a_Tree_a @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_281_case__prod__unfold,axiom,
% 2.80/1.56 ( produc1673233912ee_a_o
% 2.80/1.56 = ( ^ [C2: a > tree_a > $o,P3: produc143150363Tree_a] : ( C2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_282_case__prod__unfold,axiom,
% 2.80/1.56 ( produc873356882Tree_a
% 2.80/1.56 = ( ^ [C2: a > tree_a > tree_a,P3: produc143150363Tree_a] : ( C2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_283_case__prod__unfold,axiom,
% 2.80/1.56 ( produc369019363Tree_a
% 2.80/1.56 = ( ^ [C2: tree_a > a > produc143150363Tree_a,P3: produc981471411ee_a_a] : ( C2 @ ( product_fst_Tree_a_a @ P3 ) @ ( product_snd_Tree_a_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_284_case__prod__unfold,axiom,
% 2.80/1.56 ( produc1331510035ee_a_a
% 2.80/1.56 = ( ^ [C2: a > tree_a > produc981471411ee_a_a,P3: produc143150363Tree_a] : ( C2 @ ( product_fst_a_Tree_a @ P3 ) @ ( product_snd_a_Tree_a @ P3 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_285_exE__realizer,axiom,
% 2.80/1.56 ! [P: tree_a > a > $o,P2: produc143150363Tree_a,Q2: $o > $o,F: a > tree_a > $o] :
% 2.80/1.56 ( ( P @ ( product_snd_a_Tree_a @ P2 ) @ ( product_fst_a_Tree_a @ P2 ) )
% 2.80/1.56 => ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( P @ Y4 @ X5 )
% 2.80/1.56 => ( Q2 @ ( F @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( Q2 @ ( produc1673233912ee_a_o @ F @ P2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_286_exE__realizer,axiom,
% 2.80/1.56 ! [P: tree_a > a > $o,P2: produc143150363Tree_a,Q2: tree_a > $o,F: a > tree_a > tree_a] :
% 2.80/1.56 ( ( P @ ( product_snd_a_Tree_a @ P2 ) @ ( product_fst_a_Tree_a @ P2 ) )
% 2.80/1.56 => ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( P @ Y4 @ X5 )
% 2.80/1.56 => ( Q2 @ ( F @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( Q2 @ ( produc873356882Tree_a @ F @ P2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_287_exE__realizer,axiom,
% 2.80/1.56 ! [P: a > tree_a > $o,P2: produc981471411ee_a_a,Q2: produc143150363Tree_a > $o,F: tree_a > a > produc143150363Tree_a] :
% 2.80/1.56 ( ( P @ ( product_snd_Tree_a_a @ P2 ) @ ( product_fst_Tree_a_a @ P2 ) )
% 2.80/1.56 => ( ! [X5: tree_a,Y4: a] :
% 2.80/1.56 ( ( P @ Y4 @ X5 )
% 2.80/1.56 => ( Q2 @ ( F @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( Q2 @ ( produc369019363Tree_a @ F @ P2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_288_exE__realizer,axiom,
% 2.80/1.56 ! [P: tree_a > a > $o,P2: produc143150363Tree_a,Q2: produc981471411ee_a_a > $o,F: a > tree_a > produc981471411ee_a_a] :
% 2.80/1.56 ( ( P @ ( product_snd_a_Tree_a @ P2 ) @ ( product_fst_a_Tree_a @ P2 ) )
% 2.80/1.56 => ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( P @ Y4 @ X5 )
% 2.80/1.56 => ( Q2 @ ( F @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( Q2 @ ( produc1331510035ee_a_a @ F @ P2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_289_split__cong,axiom,
% 2.80/1.56 ! [Q: produc143150363Tree_a,F: a > tree_a > $o,G: a > tree_a > $o,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( ( produc686083979Tree_a @ X5 @ Y4 )
% 2.80/1.56 = Q )
% 2.80/1.56 => ( ( F @ X5 @ Y4 )
% 2.80/1.56 = ( G @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( ( P2 = Q )
% 2.80/1.56 => ( ( produc1673233912ee_a_o @ F @ P2 )
% 2.80/1.56 = ( produc1673233912ee_a_o @ G @ Q ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_290_split__cong,axiom,
% 2.80/1.56 ! [Q: produc143150363Tree_a,F: a > tree_a > tree_a,G: a > tree_a > tree_a,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( ( produc686083979Tree_a @ X5 @ Y4 )
% 2.80/1.56 = Q )
% 2.80/1.56 => ( ( F @ X5 @ Y4 )
% 2.80/1.56 = ( G @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( ( P2 = Q )
% 2.80/1.56 => ( ( produc873356882Tree_a @ F @ P2 )
% 2.80/1.56 = ( produc873356882Tree_a @ G @ Q ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_291_split__cong,axiom,
% 2.80/1.56 ! [Q: produc981471411ee_a_a,F: tree_a > a > produc143150363Tree_a,G: tree_a > a > produc143150363Tree_a,P2: produc981471411ee_a_a] :
% 2.80/1.56 ( ! [X5: tree_a,Y4: a] :
% 2.80/1.56 ( ( ( produc649172771ee_a_a @ X5 @ Y4 )
% 2.80/1.56 = Q )
% 2.80/1.56 => ( ( F @ X5 @ Y4 )
% 2.80/1.56 = ( G @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( ( P2 = Q )
% 2.80/1.56 => ( ( produc369019363Tree_a @ F @ P2 )
% 2.80/1.56 = ( produc369019363Tree_a @ G @ Q ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_292_split__cong,axiom,
% 2.80/1.56 ! [Q: produc143150363Tree_a,F: a > tree_a > produc981471411ee_a_a,G: a > tree_a > produc981471411ee_a_a,P2: produc143150363Tree_a] :
% 2.80/1.56 ( ! [X5: a,Y4: tree_a] :
% 2.80/1.56 ( ( ( produc686083979Tree_a @ X5 @ Y4 )
% 2.80/1.56 = Q )
% 2.80/1.56 => ( ( F @ X5 @ Y4 )
% 2.80/1.56 = ( G @ X5 @ Y4 ) ) )
% 2.80/1.56 => ( ( P2 = Q )
% 2.80/1.56 => ( ( produc1331510035ee_a_a @ F @ P2 )
% 2.80/1.56 = ( produc1331510035ee_a_a @ G @ Q ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_293_heap__top__max,axiom,
% 2.80/1.56 ! [T2: tree_a] :
% 2.80/1.56 ( ( T2 != e_a )
% 2.80/1.56 => ( ( is_heap_a @ T2 )
% 2.80/1.56 => ( ( val_a @ T2 )
% 2.80/1.56 = ( lattic146396397_Max_a @ ( set_mset_a @ ( multiset_a2 @ T2 ) ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_294_curry__case__prod,axiom,
% 2.80/1.56 ! [F: a > tree_a > $o] :
% 2.80/1.56 ( ( produc1291432345ee_a_o @ ( produc1673233912ee_a_o @ F ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_295_curry__case__prod,axiom,
% 2.80/1.56 ! [F: a > tree_a > tree_a] :
% 2.80/1.56 ( ( produc740705523Tree_a @ ( produc873356882Tree_a @ F ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_296_curry__case__prod,axiom,
% 2.80/1.56 ! [F: tree_a > a > produc143150363Tree_a] :
% 2.80/1.56 ( ( produc1808426884Tree_a @ ( produc369019363Tree_a @ F ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_297_curry__case__prod,axiom,
% 2.80/1.56 ! [F: a > tree_a > produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc623433908ee_a_a @ ( produc1331510035ee_a_a @ F ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_298_curryI,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > $o,A: a,B: tree_a] :
% 2.80/1.56 ( ( F @ ( produc686083979Tree_a @ A @ B ) )
% 2.80/1.56 => ( produc1291432345ee_a_o @ F @ A @ B ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_299_curryI,axiom,
% 2.80/1.56 ! [F: produc981471411ee_a_a > $o,A: tree_a,B: a] :
% 2.80/1.56 ( ( F @ ( produc649172771ee_a_a @ A @ B ) )
% 2.80/1.56 => ( produc1205515265_a_a_o @ F @ A @ B ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_300_split__part,axiom,
% 2.80/1.56 ! [P: $o,Q2: a > tree_a > $o] :
% 2.80/1.56 ( ( produc1673233912ee_a_o
% 2.80/1.56 @ ^ [A3: a,B3: tree_a] :
% 2.80/1.56 ( P
% 2.80/1.56 & ( Q2 @ A3 @ B3 ) ) )
% 2.80/1.56 = ( ^ [Ab: produc143150363Tree_a] :
% 2.80/1.56 ( P
% 2.80/1.56 & ( produc1673233912ee_a_o @ Q2 @ Ab ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_301_case__prod__curry,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > $o] :
% 2.80/1.56 ( ( produc1673233912ee_a_o @ ( produc1291432345ee_a_o @ F ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_302_case__prod__curry,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > tree_a] :
% 2.80/1.56 ( ( produc873356882Tree_a @ ( produc740705523Tree_a @ F ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_303_case__prod__curry,axiom,
% 2.80/1.56 ! [F: produc981471411ee_a_a > produc143150363Tree_a] :
% 2.80/1.56 ( ( produc369019363Tree_a @ ( produc1808426884Tree_a @ F ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_304_case__prod__curry,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc1331510035ee_a_a @ ( produc623433908ee_a_a @ F ) )
% 2.80/1.56 = F ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_305_prod_Odisc__eq__case,axiom,
% 2.80/1.56 ! [Prod: produc143150363Tree_a] :
% 2.80/1.56 ( produc1673233912ee_a_o
% 2.80/1.56 @ ^ [Uu2: a,Uv2: tree_a] : $true
% 2.80/1.56 @ Prod ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_306_curryD,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > $o,A: a,B: tree_a] :
% 2.80/1.56 ( ( produc1291432345ee_a_o @ F @ A @ B )
% 2.80/1.56 => ( F @ ( produc686083979Tree_a @ A @ B ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_307_curryD,axiom,
% 2.80/1.56 ! [F: produc981471411ee_a_a > $o,A: tree_a,B: a] :
% 2.80/1.56 ( ( produc1205515265_a_a_o @ F @ A @ B )
% 2.80/1.56 => ( F @ ( produc649172771ee_a_a @ A @ B ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_308_curryE,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > $o,A: a,B: tree_a] :
% 2.80/1.56 ( ( produc1291432345ee_a_o @ F @ A @ B )
% 2.80/1.56 => ( F @ ( produc686083979Tree_a @ A @ B ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_309_curryE,axiom,
% 2.80/1.56 ! [F: produc981471411ee_a_a > $o,A: tree_a,B: a] :
% 2.80/1.56 ( ( produc1205515265_a_a_o @ F @ A @ B )
% 2.80/1.56 => ( F @ ( produc649172771ee_a_a @ A @ B ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_310_fst__snd__flip,axiom,
% 2.80/1.56 ( product_fst_a_Tree_a
% 2.80/1.56 = ( comp_P342079405Tree_a @ product_snd_Tree_a_a
% 2.80/1.56 @ ( produc1331510035ee_a_a
% 2.80/1.56 @ ^ [X4: a,Y5: tree_a] : ( produc649172771ee_a_a @ Y5 @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_311_fst__snd__flip,axiom,
% 2.80/1.56 ( product_fst_Tree_a_a
% 2.80/1.56 = ( comp_P1663859001ee_a_a @ product_snd_a_Tree_a
% 2.80/1.56 @ ( produc369019363Tree_a
% 2.80/1.56 @ ^ [X4: tree_a,Y5: a] : ( produc686083979Tree_a @ Y5 @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_312_snd__fst__flip,axiom,
% 2.80/1.56 ( product_snd_Tree_a_a
% 2.80/1.56 = ( comp_P1103783853ee_a_a @ product_fst_a_Tree_a
% 2.80/1.56 @ ( produc369019363Tree_a
% 2.80/1.56 @ ^ [X4: tree_a,Y5: a] : ( produc686083979Tree_a @ Y5 @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_313_snd__fst__flip,axiom,
% 2.80/1.56 ( product_snd_a_Tree_a
% 2.80/1.56 = ( comp_P228269369Tree_a @ product_fst_Tree_a_a
% 2.80/1.56 @ ( produc1331510035ee_a_a
% 2.80/1.56 @ ^ [X4: a,Y5: tree_a] : ( produc649172771ee_a_a @ Y5 @ X4 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_314_fst__fstOp,axiom,
% 2.80/1.56 ! [P: a > tree_a > $o,Q2: tree_a > tree_a > $o] :
% 2.80/1.56 ( product_fst_a_Tree_a
% 2.80/1.56 = ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( bNF_fs1579355852Tree_a @ P @ Q2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_315_fst__fstOp,axiom,
% 2.80/1.56 ! [P: tree_a > a > $o,Q2: a > a > $o] :
% 2.80/1.56 ( product_fst_Tree_a_a
% 2.80/1.56 = ( comp_P1066590417ee_a_a @ product_fst_Tree_a_a @ ( bNF_fstOp_Tree_a_a_a @ P @ Q2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_316_snd__sndOp,axiom,
% 2.80/1.56 ! [P: a > a > $o,Q2: a > tree_a > $o] :
% 2.80/1.56 ( product_snd_a_Tree_a
% 2.80/1.56 = ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( bNF_sndOp_a_a_Tree_a @ P @ Q2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_317_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > tree_a,G: produc981471411ee_a_a > produc143150363Tree_a,X: produc981471411ee_a_a,H: produc143150363Tree_a > tree_a,K: produc981471411ee_a_a > produc143150363Tree_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_P1663859001ee_a_a @ F @ G @ X )
% 2.80/1.56 = ( comp_P1663859001ee_a_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_318_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: produc981471411ee_a_a > tree_a,G: produc143150363Tree_a > produc981471411ee_a_a,X: produc143150363Tree_a,H: produc981471411ee_a_a > tree_a,K: produc143150363Tree_a > produc981471411ee_a_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_P228269369Tree_a @ F @ G @ X )
% 2.80/1.56 = ( comp_P228269369Tree_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_319_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: produc981471411ee_a_a > tree_a,G: produc143150363Tree_a > produc981471411ee_a_a,X: produc143150363Tree_a,H: produc143150363Tree_a > tree_a,K: produc143150363Tree_a > produc143150363Tree_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_P228269369Tree_a @ F @ G @ X )
% 2.80/1.56 = ( comp_P825537953Tree_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_320_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: produc981471411ee_a_a > tree_a,G: produc143150363Tree_a > produc981471411ee_a_a,X: produc143150363Tree_a,H: tree_a > tree_a,K: produc143150363Tree_a > tree_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_P228269369Tree_a @ F @ G @ X )
% 2.80/1.56 = ( comp_T236170232Tree_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_321_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > tree_a,G: produc143150363Tree_a > produc143150363Tree_a,X: produc143150363Tree_a,H: produc981471411ee_a_a > tree_a,K: produc143150363Tree_a > produc981471411ee_a_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_P825537953Tree_a @ F @ G @ X )
% 2.80/1.56 = ( comp_P228269369Tree_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_322_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > tree_a,G: produc143150363Tree_a > produc143150363Tree_a,X: produc143150363Tree_a,H: produc143150363Tree_a > tree_a,K: produc143150363Tree_a > produc143150363Tree_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_P825537953Tree_a @ F @ G @ X )
% 2.80/1.56 = ( comp_P825537953Tree_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_323_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: produc143150363Tree_a > tree_a,G: produc143150363Tree_a > produc143150363Tree_a,X: produc143150363Tree_a,H: tree_a > tree_a,K: produc143150363Tree_a > tree_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_P825537953Tree_a @ F @ G @ X )
% 2.80/1.56 = ( comp_T236170232Tree_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_324_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,G: produc143150363Tree_a > tree_a,X: produc143150363Tree_a,H: produc981471411ee_a_a > tree_a,K: produc143150363Tree_a > produc981471411ee_a_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_T236170232Tree_a @ F @ G @ X )
% 2.80/1.56 = ( comp_P228269369Tree_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_325_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,G: produc143150363Tree_a > tree_a,X: produc143150363Tree_a,H: produc143150363Tree_a > tree_a,K: produc143150363Tree_a > produc143150363Tree_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_T236170232Tree_a @ F @ G @ X )
% 2.80/1.56 = ( comp_P825537953Tree_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_326_comp__apply__eq,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,G: produc143150363Tree_a > tree_a,X: produc143150363Tree_a,H: tree_a > tree_a,K: produc143150363Tree_a > tree_a] :
% 2.80/1.56 ( ( ( F @ ( G @ X ) )
% 2.80/1.56 = ( H @ ( K @ X ) ) )
% 2.80/1.56 => ( ( comp_T236170232Tree_a @ F @ G @ X )
% 2.80/1.56 = ( comp_T236170232Tree_a @ H @ K @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_327_snd__comp__apsnd,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a] :
% 2.80/1.56 ( ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( produc819961216ee_a_a @ F ) )
% 2.80/1.56 = ( comp_T236170232Tree_a @ F @ product_snd_a_Tree_a ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_328_fst__comp__apfst,axiom,
% 2.80/1.56 ! [F: a > a] :
% 2.80/1.56 ( ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( produc1107567542Tree_a @ F ) )
% 2.80/1.56 = ( comp_a608639864Tree_a @ F @ product_fst_a_Tree_a ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_329_fst__comp__apfst,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a] :
% 2.80/1.56 ( ( comp_P1066590417ee_a_a @ product_fst_Tree_a_a @ ( produc569472578ee_a_a @ F ) )
% 2.80/1.56 = ( comp_T1074491280ee_a_a @ F @ product_fst_Tree_a_a ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_330_apfst__conv,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,X: tree_a,Y: a] :
% 2.80/1.56 ( ( produc569472578ee_a_a @ F @ ( produc649172771ee_a_a @ X @ Y ) )
% 2.80/1.56 = ( produc649172771ee_a_a @ ( F @ X ) @ Y ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_331_apfst__conv,axiom,
% 2.80/1.56 ! [F: a > a,X: a,Y: tree_a] :
% 2.80/1.56 ( ( produc1107567542Tree_a @ F @ ( produc686083979Tree_a @ X @ Y ) )
% 2.80/1.56 = ( produc686083979Tree_a @ ( F @ X ) @ Y ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_332_apsnd__conv,axiom,
% 2.80/1.56 ! [F: a > a,X: tree_a,Y: a] :
% 2.80/1.56 ( ( produc969245172Tree_a @ F @ ( produc649172771ee_a_a @ X @ Y ) )
% 2.80/1.56 = ( produc649172771ee_a_a @ X @ ( F @ Y ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_333_apsnd__conv,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,X: a,Y: tree_a] :
% 2.80/1.56 ( ( produc819961216ee_a_a @ F @ ( produc686083979Tree_a @ X @ Y ) )
% 2.80/1.56 = ( produc686083979Tree_a @ X @ ( F @ Y ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_334_fst__apfst,axiom,
% 2.80/1.56 ! [F: a > a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( product_fst_a_Tree_a @ ( produc1107567542Tree_a @ F @ X ) )
% 2.80/1.56 = ( F @ ( product_fst_a_Tree_a @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_335_fst__apfst,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,X: produc981471411ee_a_a] :
% 2.80/1.56 ( ( product_fst_Tree_a_a @ ( produc569472578ee_a_a @ F @ X ) )
% 2.80/1.56 = ( F @ ( product_fst_Tree_a_a @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_336_apfst__eq__conv,axiom,
% 2.80/1.56 ! [F: a > a,X: produc143150363Tree_a,G: a > a] :
% 2.80/1.56 ( ( ( produc1107567542Tree_a @ F @ X )
% 2.80/1.56 = ( produc1107567542Tree_a @ G @ X ) )
% 2.80/1.56 = ( ( F @ ( product_fst_a_Tree_a @ X ) )
% 2.80/1.56 = ( G @ ( product_fst_a_Tree_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_337_snd__apfst,axiom,
% 2.80/1.56 ! [F: a > a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( product_snd_a_Tree_a @ ( produc1107567542Tree_a @ F @ X ) )
% 2.80/1.56 = ( product_snd_a_Tree_a @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_338_fst__apsnd,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( product_fst_a_Tree_a @ ( produc819961216ee_a_a @ F @ X ) )
% 2.80/1.56 = ( product_fst_a_Tree_a @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_339_fst__apsnd,axiom,
% 2.80/1.56 ! [F: a > a,X: produc981471411ee_a_a] :
% 2.80/1.56 ( ( product_fst_Tree_a_a @ ( produc969245172Tree_a @ F @ X ) )
% 2.80/1.56 = ( product_fst_Tree_a_a @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_340_apsnd__eq__conv,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,X: produc143150363Tree_a,G: tree_a > tree_a] :
% 2.80/1.56 ( ( ( produc819961216ee_a_a @ F @ X )
% 2.80/1.56 = ( produc819961216ee_a_a @ G @ X ) )
% 2.80/1.56 = ( ( F @ ( product_snd_a_Tree_a @ X ) )
% 2.80/1.56 = ( G @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_341_snd__apsnd,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( product_snd_a_Tree_a @ ( produc819961216ee_a_a @ F @ X ) )
% 2.80/1.56 = ( F @ ( product_snd_a_Tree_a @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_342_snd__comp__apfst,axiom,
% 2.80/1.56 ! [F: a > a] :
% 2.80/1.56 ( ( comp_P825537953Tree_a @ product_snd_a_Tree_a @ ( produc1107567542Tree_a @ F ) )
% 2.80/1.56 = product_snd_a_Tree_a ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_343_fst__comp__apsnd,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a] :
% 2.80/1.56 ( ( comp_P265462805Tree_a @ product_fst_a_Tree_a @ ( produc819961216ee_a_a @ F ) )
% 2.80/1.56 = product_fst_a_Tree_a ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_344_fst__comp__apsnd,axiom,
% 2.80/1.56 ! [F: a > a] :
% 2.80/1.56 ( ( comp_P1066590417ee_a_a @ product_fst_Tree_a_a @ ( produc969245172Tree_a @ F ) )
% 2.80/1.56 = product_fst_Tree_a_a ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_345_apfst__apsnd,axiom,
% 2.80/1.56 ! [F: tree_a > a,G: a > tree_a,X: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc606383786Tree_a @ F @ ( produc1296751488Tree_a @ G @ X ) )
% 2.80/1.56 = ( produc686083979Tree_a @ ( F @ ( product_fst_Tree_a_a @ X ) ) @ ( G @ ( product_snd_Tree_a_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_346_apfst__apsnd,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,G: a > a,X: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc569472578ee_a_a @ F @ ( produc969245172Tree_a @ G @ X ) )
% 2.80/1.56 = ( produc649172771ee_a_a @ ( F @ ( product_fst_Tree_a_a @ X ) ) @ ( G @ ( product_snd_Tree_a_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_347_apfst__apsnd,axiom,
% 2.80/1.56 ! [F: a > tree_a,G: tree_a > a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc1070656334ee_a_a @ F @ ( produc21534708_a_a_a @ G @ X ) )
% 2.80/1.56 = ( produc649172771ee_a_a @ ( F @ ( product_fst_a_Tree_a @ X ) ) @ ( G @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_348_apfst__apsnd,axiom,
% 2.80/1.56 ! [F: a > a,G: tree_a > tree_a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc1107567542Tree_a @ F @ ( produc819961216ee_a_a @ G @ X ) )
% 2.80/1.56 = ( produc686083979Tree_a @ ( F @ ( product_fst_a_Tree_a @ X ) ) @ ( G @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_349_apsnd__apfst,axiom,
% 2.80/1.56 ! [F: a > tree_a,G: tree_a > a,X: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc932333964ee_a_a @ F @ ( produc159857078_a_a_a @ G @ X ) )
% 2.80/1.56 = ( produc686083979Tree_a @ ( G @ ( product_fst_Tree_a_a @ X ) ) @ ( F @ ( product_snd_Tree_a_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_350_apsnd__apfst,axiom,
% 2.80/1.56 ! [F: a > a,G: tree_a > tree_a,X: produc981471411ee_a_a] :
% 2.80/1.56 ( ( produc969245172Tree_a @ F @ ( produc569472578ee_a_a @ G @ X ) )
% 2.80/1.56 = ( produc649172771ee_a_a @ ( G @ ( product_fst_Tree_a_a @ X ) ) @ ( F @ ( product_snd_Tree_a_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_351_apsnd__apfst,axiom,
% 2.80/1.56 ! [F: tree_a > a,G: a > tree_a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc856872424Tree_a @ F @ ( produc1046262850Tree_a @ G @ X ) )
% 2.80/1.56 = ( produc649172771ee_a_a @ ( G @ ( product_fst_a_Tree_a @ X ) ) @ ( F @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_352_apsnd__apfst,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,G: a > a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc819961216ee_a_a @ F @ ( produc1107567542Tree_a @ G @ X ) )
% 2.80/1.56 = ( produc686083979Tree_a @ ( G @ ( product_fst_a_Tree_a @ X ) ) @ ( F @ ( product_snd_a_Tree_a @ X ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_353_apsnd__compose,axiom,
% 2.80/1.56 ! [F: tree_a > tree_a,G: tree_a > tree_a,X: produc143150363Tree_a] :
% 2.80/1.56 ( ( produc819961216ee_a_a @ F @ ( produc819961216ee_a_a @ G @ X ) )
% 2.80/1.56 = ( produc819961216ee_a_a @ ( comp_T59512783Tree_a @ F @ G ) @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(help_If_3_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T,axiom,
% 2.80/1.56 ! [P: $o] :
% 2.80/1.56 ( ( P = $true )
% 2.80/1.56 | ( P = $false ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(help_If_2_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T,axiom,
% 2.80/1.56 ! [X: produc143150363Tree_a,Y: produc143150363Tree_a] :
% 2.80/1.56 ( ( if_Pro1144176865Tree_a @ $false @ X @ Y )
% 2.80/1.56 = Y ) ).
% 2.80/1.56
% 2.80/1.56 thf(help_If_1_1_If_001t__Product____Type__Oprod_Itf__a_Mt__Heap__OTree_Itf__a_J_J_T,axiom,
% 2.80/1.56 ! [X: produc143150363Tree_a,Y: produc143150363Tree_a] :
% 2.80/1.56 ( ( if_Pro1144176865Tree_a @ $true @ X @ Y )
% 2.80/1.56 = X ) ).
% 2.80/1.56
% 2.80/1.56 thf(conj_0,conjecture,
% 2.80/1.56 is_heap_a @ ( product_snd_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v @ e_a @ e_a ) ) ) ).
% 2.80/1.56 ------------------------
% 2.87/1.61 % (15102)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14883 for (2999ds/183Mi)
% 2.87/1.61 % (15107)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_14883 for (2999ds/275Mi)
% 2.87/1.61 % (15105)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14883 for (2999ds/2Mi)
% 2.87/1.61 % (15104)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_14883 for (2999ds/27Mi)
% 2.87/1.61 % (15103)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_14883 for (2999ds/4Mi)
% 2.87/1.61 % (15106)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_14883 for (2999ds/2Mi)
% 2.87/1.61 % (15108)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14883 for (2999ds/18Mi)
% 2.87/1.61 % (15105)Instruction limit reached!
% 2.87/1.61 % (15105)------------------------------
% 2.87/1.61 % (15105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.61 % (15105)Termination reason: Unknown
% 2.87/1.61 % (15105)Termination phase: shuffling
% 2.87/1.61
% 2.87/1.61 % (15105)Memory used [KB]: 1535
% 2.87/1.61 % (15105)Time elapsed: 0.003 s
% 2.87/1.61 % (15105)Instructions burned: 2 (million)
% 2.87/1.61 % (15105)------------------------------
% 2.87/1.61 % (15105)------------------------------
% 2.87/1.61 % (15106)Instruction limit reached!
% 2.87/1.61 % (15106)------------------------------
% 2.87/1.61 % (15106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.61 % (15106)Termination reason: Unknown
% 2.87/1.61 % (15106)Termination phase: shuffling
% 2.87/1.61
% 2.87/1.61 % (15106)Memory used [KB]: 1535
% 2.87/1.61 % (15106)Time elapsed: 0.003 s
% 2.87/1.61 % (15106)Instructions burned: 2 (million)
% 2.87/1.61 % (15106)------------------------------
% 2.87/1.61 % (15106)------------------------------
% 2.87/1.62 % (15103)Instruction limit reached!
% 2.87/1.62 % (15103)------------------------------
% 2.87/1.62 % (15103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.62 % (15103)Termination reason: Unknown
% 2.87/1.62 % (15103)Termination phase: shuffling
% 2.87/1.62
% 2.87/1.62 % (15103)Memory used [KB]: 1663
% 2.87/1.62 % (15103)Time elapsed: 0.005 s
% 2.87/1.62 % (15103)Instructions burned: 5 (million)
% 2.87/1.62 % (15103)------------------------------
% 2.87/1.62 % (15103)------------------------------
% 2.87/1.62 % (15108)Instruction limit reached!
% 2.87/1.62 % (15108)------------------------------
% 2.87/1.62 % (15108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.62 % (15108)Termination reason: Unknown
% 2.87/1.62 % (15108)Termination phase: shuffling
% 2.87/1.62
% 2.87/1.62 % (15108)Memory used [KB]: 1918
% 2.87/1.62 % (15108)Time elapsed: 0.013 s
% 2.87/1.62 % (15108)Instructions burned: 19 (million)
% 2.87/1.62 % (15108)------------------------------
% 2.87/1.62 % (15108)------------------------------
% 2.87/1.63 % (15104)Instruction limit reached!
% 2.87/1.63 % (15104)------------------------------
% 2.87/1.63 % (15104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.63 % (15104)Termination reason: Unknown
% 2.87/1.63 % (15104)Termination phase: shuffling
% 2.87/1.63
% 2.87/1.63 % (15104)Memory used [KB]: 2046
% 2.87/1.63 % (15104)Time elapsed: 0.018 s
% 2.87/1.63 % (15104)Instructions burned: 27 (million)
% 2.87/1.63 % (15104)------------------------------
% 2.87/1.63 % (15104)------------------------------
% 2.87/1.63 % (15109)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14883 for (2999ds/3Mi)
% 2.87/1.63 % (15110)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_14883 for (2999ds/37Mi)
% 2.87/1.63 % (15107)First to succeed.
% 2.87/1.63 % (15111)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_14883 for (2999ds/15Mi)
% 2.87/1.63 % (15109)Instruction limit reached!
% 2.87/1.63 % (15109)------------------------------
% 2.87/1.63 % (15109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.63 % (15109)Termination reason: Unknown
% 2.87/1.63 % (15109)Termination phase: shuffling
% 2.87/1.63
% 2.87/1.63 % (15109)Memory used [KB]: 1535
% 2.87/1.63 % (15109)Time elapsed: 0.004 s
% 2.87/1.63 % (15109)Instructions burned: 3 (million)
% 2.87/1.63 % (15109)------------------------------
% 2.87/1.63 % (15109)------------------------------
% 2.87/1.64 % (15107)Refutation found. Thanks to Tanya!
% 2.87/1.64 % SZS status Theorem for DTF2THF_14883
% 2.87/1.64 % SZS output start Proof for DTF2THF_14883
% 2.87/1.64 thf(type_def_5, type, set_Pr1070816379Tree_a: $tType).
% 2.87/1.64 thf(type_def_6, type, produc143150363Tree_a: $tType).
% 2.87/1.64 thf(type_def_7, type, tree_a: $tType).
% 2.87/1.64 thf(type_def_9, type, produc1689254567Tree_a: $tType).
% 2.87/1.64 thf(type_def_10, type, product_prod_a_a: $tType).
% 2.87/1.64 thf(type_def_11, type, a: $tType).
% 2.87/1.64 thf(type_def_12, type, set_Product_prod_a_a: $tType).
% 2.87/1.64 thf(type_def_13, type, produc981471411ee_a_a: $tType).
% 2.87/1.64 thf(type_def_14, type, set_Pr921883667ee_a_a: $tType).
% 2.87/1.64 thf(type_def_15, type, set_a: $tType).
% 2.87/1.64 thf(type_def_16, type, list_a: $tType).
% 2.87/1.64 thf(type_def_17, type, multiset_a: $tType).
% 2.87/1.64 thf(func_def_0, type, produc1689254567Tree_a: $tType).
% 2.87/1.64 thf(func_def_1, type, set_Pr1070816379Tree_a: $tType).
% 2.87/1.64 thf(func_def_2, type, set_Pr921883667ee_a_a: $tType).
% 2.87/1.64 thf(func_def_3, type, produc143150363Tree_a: $tType).
% 2.87/1.64 thf(func_def_4, type, produc981471411ee_a_a: $tType).
% 2.87/1.64 thf(func_def_5, type, set_Product_prod_a_a: $tType).
% 2.87/1.64 thf(func_def_6, type, product_prod_a_a: $tType).
% 2.87/1.64 thf(func_def_7, type, multiset_a: $tType).
% 2.87/1.64 thf(func_def_8, type, list_a: $tType).
% 2.87/1.64 thf(func_def_9, type, tree_a: $tType).
% 2.87/1.64 thf(func_def_10, type, set_a: $tType).
% 2.87/1.64 thf(func_def_11, type, a: $tType).
% 2.87/1.64 thf(func_def_12, type, bNF_cs1091007358Tree_a: set_Pr1070816379Tree_a > (produc143150363Tree_a > tree_a) > (produc1689254567Tree_a > tree_a) > (produc143150363Tree_a > produc143150363Tree_a) > (produc143150363Tree_a > produc1689254567Tree_a) > $o).
% 2.87/1.64 thf(func_def_13, type, bNF_cs739966834Tree_a: set_Pr1070816379Tree_a > (product_prod_a_a > a) > (produc143150363Tree_a > a) > (produc143150363Tree_a > product_prod_a_a) > (produc143150363Tree_a > produc143150363Tree_a) > $o).
% 2.87/1.64 thf(func_def_14, type, bNF_cs1095035134ee_a_a: set_Product_prod_a_a > (produc143150363Tree_a > tree_a) > (produc981471411ee_a_a > tree_a) > (product_prod_a_a > produc143150363Tree_a) > (product_prod_a_a > produc981471411ee_a_a) > $o).
% 2.87/1.64 thf(func_def_15, type, bNF_fstOp_Tree_a_a_a: (tree_a > a > $o) > (a > a > $o) > produc981471411ee_a_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_16, type, bNF_fs1579355852Tree_a: (a > tree_a > $o) > (tree_a > tree_a > $o) > produc143150363Tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_17, type, bNF_fstOp_a_Tree_a_a: (a > tree_a > $o) > (tree_a > a > $o) > product_prod_a_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_18, type, bNF_fstOp_a_a_Tree_a: (a > a > $o) > (a > tree_a > $o) > produc143150363Tree_a > product_prod_a_a).
% 2.87/1.64 thf(func_def_19, type, bNF_pi1059296282ee_a_a: (tree_a > tree_a > $o) > (tree_a > a > $o) > tree_a > a > tree_a).
% 2.87/1.64 thf(func_def_20, type, bNF_pi1407460238_a_a_a: (tree_a > a > $o) > (a > a > $o) > tree_a > a > a).
% 2.87/1.64 thf(func_def_21, type, bNF_pi1536086554Tree_a: (a > tree_a > $o) > (tree_a > tree_a > $o) > a > tree_a > tree_a).
% 2.87/1.64 thf(func_def_22, type, bNF_pi207687054Tree_a: (a > a > $o) > (a > tree_a > $o) > a > tree_a > a).
% 2.87/1.64 thf(func_def_23, type, bNF_sn210385162ee_a_a: (tree_a > tree_a > $o) > (tree_a > a > $o) > produc981471411ee_a_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_24, type, bNF_sn687175434Tree_a: (a > tree_a > $o) > (tree_a > tree_a > $o) > produc143150363Tree_a > produc1689254567Tree_a).
% 2.87/1.64 thf(func_def_25, type, bNF_sndOp_a_Tree_a_a: (a > tree_a > $o) > (tree_a > a > $o) > product_prod_a_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_26, type, bNF_sndOp_a_a_Tree_a: (a > a > $o) > (a > tree_a > $o) > produc143150363Tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_27, type, bNF_Gr2005589581ee_a_a: set_Pr1070816379Tree_a > (produc143150363Tree_a > tree_a) > (produc143150363Tree_a > a) > set_Pr921883667ee_a_a).
% 2.87/1.64 thf(func_def_28, type, bNF_Gr2042500789Tree_a: set_Pr1070816379Tree_a > (produc143150363Tree_a > a) > (produc143150363Tree_a > tree_a) > set_Pr1070816379Tree_a).
% 2.87/1.64 thf(func_def_29, type, bNF_Gr614734384ee_a_a: set_a > (a > tree_a) > (a > a) > set_Pr921883667ee_a_a).
% 2.87/1.64 thf(func_def_30, type, bNF_Gr651645592Tree_a: set_a > (a > a) > (a > tree_a) > set_Pr1070816379Tree_a).
% 2.87/1.64 thf(func_def_31, type, comp_T59512783Tree_a: (tree_a > tree_a) > (tree_a > tree_a) > tree_a > tree_a).
% 2.87/1.64 thf(func_def_32, type, comp_T1074491280ee_a_a: (tree_a > tree_a) > (produc981471411ee_a_a > tree_a) > produc981471411ee_a_a > tree_a).
% 2.87/1.64 thf(func_def_33, type, comp_T236170232Tree_a: (tree_a > tree_a) > (produc143150363Tree_a > tree_a) > produc143150363Tree_a > tree_a).
% 2.87/1.64 thf(func_def_34, type, comp_P1066590417ee_a_a: (produc981471411ee_a_a > tree_a) > (produc981471411ee_a_a > produc981471411ee_a_a) > produc981471411ee_a_a > tree_a).
% 2.87/1.64 thf(func_def_35, type, comp_P228269369Tree_a: (produc981471411ee_a_a > tree_a) > (produc143150363Tree_a > produc981471411ee_a_a) > produc143150363Tree_a > tree_a).
% 2.87/1.64 thf(func_def_36, type, comp_P342079405Tree_a: (produc981471411ee_a_a > a) > (produc143150363Tree_a > produc981471411ee_a_a) > produc143150363Tree_a > a).
% 2.87/1.64 thf(func_def_37, type, comp_P1663859001ee_a_a: (produc143150363Tree_a > tree_a) > (produc981471411ee_a_a > produc143150363Tree_a) > produc981471411ee_a_a > tree_a).
% 2.87/1.64 thf(func_def_38, type, comp_P825537953Tree_a: (produc143150363Tree_a > tree_a) > (produc143150363Tree_a > produc143150363Tree_a) > produc143150363Tree_a > tree_a).
% 2.87/1.64 thf(func_def_39, type, comp_P1103783853ee_a_a: (produc143150363Tree_a > a) > (produc981471411ee_a_a > produc143150363Tree_a) > produc981471411ee_a_a > a).
% 2.87/1.64 thf(func_def_40, type, comp_P265462805Tree_a: (produc143150363Tree_a > a) > (produc143150363Tree_a > produc143150363Tree_a) > produc143150363Tree_a > a).
% 2.87/1.64 thf(func_def_41, type, comp_a608639864Tree_a: (a > a) > (produc143150363Tree_a > a) > produc143150363Tree_a > a).
% 2.87/1.64 thf(func_def_42, type, heapIm970322378pify_a: tree_a > tree_a).
% 2.87/1.64 thf(func_def_43, type, heapIm229596386mpty_a: tree_a > $o).
% 2.87/1.64 thf(func_def_44, type, heapIm915766629_max_a: tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_45, type, heapIm1140443833left_a: tree_a > tree_a).
% 2.87/1.64 thf(func_def_46, type, heapIm837449470Leaf_a: tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_47, type, heapIm1257206334ight_a: tree_a > tree_a).
% 2.87/1.64 thf(func_def_48, type, heapIm1091024090Down_a: tree_a > tree_a).
% 2.87/1.64 thf(func_def_49, type, heap_Tree_a_a: tree_a > (tree_a > $o) > (list_a > tree_a) > (tree_a > multiset_a) > (tree_a > tree_a) > (tree_a > produc143150363Tree_a) > $o).
% 2.87/1.64 thf(func_def_50, type, heap_axioms_Tree_a_a: (tree_a > $o) > (list_a > tree_a) > (tree_a > multiset_a) > (tree_a > tree_a) > (tree_a > produc143150363Tree_a) > $o).
% 2.87/1.64 thf(func_def_51, type, e_a: tree_a).
% 2.87/1.64 thf(func_def_52, type, t_a: a > tree_a > tree_a > tree_a).
% 2.87/1.64 thf(func_def_53, type, in_tree_a: a > tree_a > $o).
% 2.87/1.64 thf(func_def_54, type, is_heap_a: tree_a > $o).
% 2.87/1.64 thf(func_def_55, type, multiset_a2: tree_a > multiset_a).
% 2.87/1.64 thf(func_def_56, type, val_a: tree_a > a).
% 2.87/1.64 thf(func_def_57, type, if_Pro1144176865Tree_a: $o > produc143150363Tree_a > produc143150363Tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_58, type, lattic146396397_Max_a: set_a > a).
% 2.87/1.64 thf(func_def_59, type, add_mset_a: a > multiset_a > multiset_a).
% 2.87/1.64 thf(func_def_60, type, set_mset_a: multiset_a > set_a).
% 2.87/1.64 thf(func_def_61, type, ord_le1748873858_a_a_o: (tree_a > a > $o) > (tree_a > a > $o) > $o).
% 2.87/1.64 thf(func_def_62, type, ord_le1601593986ee_a_o: (produc143150363Tree_a > $o) > (produc143150363Tree_a > $o) > $o).
% 2.87/1.64 thf(func_def_63, type, ord_le1327026842ee_a_o: (a > tree_a > $o) > (a > tree_a > $o) > $o).
% 2.87/1.64 thf(func_def_64, type, ord_less_eq_a_o: (a > $o) > (a > $o) > $o).
% 2.87/1.64 thf(func_def_65, type, ord_le864074675ee_a_a: set_Pr921883667ee_a_a > set_Pr921883667ee_a_a > $o).
% 2.87/1.64 thf(func_def_66, type, ord_le1013007387Tree_a: set_Pr1070816379Tree_a > set_Pr1070816379Tree_a > $o).
% 2.87/1.64 thf(func_def_67, type, ord_less_eq_set_a: set_a > set_a > $o).
% 2.87/1.64 thf(func_def_68, type, ord_less_eq_a: a > a > $o).
% 2.87/1.64 thf(func_def_69, type, order_Greatest_a: (a > $o) > a).
% 2.87/1.64 thf(func_def_70, type, produc649172771ee_a_a: tree_a > a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_71, type, produc686083979Tree_a: a > tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_72, type, produc569472578ee_a_a: (tree_a > tree_a) > produc981471411ee_a_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_73, type, produc606383786Tree_a: (tree_a > a) > produc1689254567Tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_74, type, produc159857078_a_a_a: (tree_a > a) > produc981471411ee_a_a > product_prod_a_a).
% 2.87/1.64 thf(func_def_75, type, produc1046262850Tree_a: (a > tree_a) > produc143150363Tree_a > produc1689254567Tree_a).
% 2.87/1.64 thf(func_def_76, type, produc1070656334ee_a_a: (a > tree_a) > product_prod_a_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_77, type, produc1107567542Tree_a: (a > a) > produc143150363Tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_78, type, produc819961216ee_a_a: (tree_a > tree_a) > produc143150363Tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_79, type, produc856872424Tree_a: (tree_a > a) > produc1689254567Tree_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_80, type, produc21534708_a_a_a: (tree_a > a) > produc143150363Tree_a > product_prod_a_a).
% 2.87/1.64 thf(func_def_81, type, produc1296751488Tree_a: (a > tree_a) > produc981471411ee_a_a > produc1689254567Tree_a).
% 2.87/1.64 thf(func_def_82, type, produc932333964ee_a_a: (a > tree_a) > product_prod_a_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_83, type, produc969245172Tree_a: (a > a) > produc981471411ee_a_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_84, type, produc1205515265_a_a_o: (produc981471411ee_a_a > $o) > tree_a > a > $o).
% 2.87/1.64 thf(func_def_85, type, produc1808426884Tree_a: (produc981471411ee_a_a > produc143150363Tree_a) > tree_a > a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_86, type, produc1291432345ee_a_o: (produc143150363Tree_a > $o) > a > tree_a > $o).
% 2.87/1.64 thf(func_def_87, type, produc740705523Tree_a: (produc143150363Tree_a > tree_a) > a > tree_a > tree_a).
% 2.87/1.64 thf(func_def_88, type, produc623433908ee_a_a: (produc143150363Tree_a > produc981471411ee_a_a) > a > tree_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_89, type, produc126329485Tree_a: (tree_a > a > produc143150363Tree_a) > produc981471411ee_a_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_90, type, produc1405823650ee_a_o: (a > tree_a > $o) > produc143150363Tree_a > $o).
% 2.87/1.64 thf(func_def_91, type, produc534868220Tree_a: (a > tree_a > tree_a) > produc143150363Tree_a > tree_a).
% 2.87/1.64 thf(func_def_92, type, produc1088820157ee_a_a: (a > tree_a > produc981471411ee_a_a) > produc143150363Tree_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_93, type, produc1587316832_a_a_o: (tree_a > a > $o) > produc981471411ee_a_a > $o).
% 2.87/1.64 thf(func_def_94, type, produc433477818Tree_a: (tree_a > a > tree_a) > produc981471411ee_a_a > tree_a).
% 2.87/1.64 thf(func_def_95, type, produc1207340411ee_a_a: (tree_a > a > produc981471411ee_a_a) > produc981471411ee_a_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_96, type, produc369019363Tree_a: (tree_a > a > produc143150363Tree_a) > produc981471411ee_a_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_97, type, produc951236931Tree_a: (tree_a > a > set_Pr1070816379Tree_a) > produc981471411ee_a_a > set_Pr1070816379Tree_a).
% 2.87/1.64 thf(func_def_98, type, produc136688934_set_a: (tree_a > a > set_a) > produc981471411ee_a_a > set_a).
% 2.87/1.64 thf(func_def_99, type, produc1673233912ee_a_o: (a > tree_a > $o) > produc143150363Tree_a > $o).
% 2.87/1.64 thf(func_def_100, type, produc873356882Tree_a: (a > tree_a > tree_a) > produc143150363Tree_a > tree_a).
% 2.87/1.64 thf(func_def_101, type, produc1331510035ee_a_a: (a > tree_a > produc981471411ee_a_a) > produc143150363Tree_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_102, type, produc493188987Tree_a: (a > tree_a > produc143150363Tree_a) > produc143150363Tree_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_103, type, produc802621147Tree_a: (a > tree_a > set_Pr1070816379Tree_a) > produc143150363Tree_a > set_Pr1070816379Tree_a).
% 2.87/1.64 thf(func_def_104, type, produc1902270_set_a: (a > tree_a > set_a) > produc143150363Tree_a > set_a).
% 2.87/1.64 thf(func_def_105, type, produc950721886ee_a_a: (a > tree_a > a) > produc143150363Tree_a > a).
% 2.87/1.64 thf(func_def_106, type, produc1206152067Tree_a: produc1689254567Tree_a > tree_a).
% 2.87/1.64 thf(func_def_107, type, product_fst_Tree_a_a: produc981471411ee_a_a > tree_a).
% 2.87/1.64 thf(func_def_108, type, product_fst_a_Tree_a: produc143150363Tree_a > a).
% 2.87/1.64 thf(func_def_109, type, product_snd_Tree_a_a: produc981471411ee_a_a > a).
% 2.87/1.64 thf(func_def_110, type, product_snd_a_Tree_a: produc143150363Tree_a > tree_a).
% 2.87/1.64 thf(func_def_111, type, product_snd_a_a: product_prod_a_a > a).
% 2.87/1.64 thf(func_def_112, type, produc1478296771ee_a_a: produc981471411ee_a_a > produc143150363Tree_a).
% 2.87/1.64 thf(func_def_113, type, produc1515207979Tree_a: produc143150363Tree_a > produc981471411ee_a_a).
% 2.87/1.64 thf(func_def_114, type, relcom439193229Tree_a: (a > tree_a > $o) > (tree_a > tree_a > $o) > a > tree_a > $o).
% 2.87/1.64 thf(func_def_115, type, relcompp_a_Tree_a_a: (a > tree_a > $o) > (tree_a > a > $o) > a > a > $o).
% 2.87/1.64 thf(func_def_116, type, relcompp_a_a_Tree_a: (a > a > $o) > (a > tree_a > $o) > a > tree_a > $o).
% 2.87/1.64 thf(func_def_117, type, collec1324690334ee_a_a: (produc981471411ee_a_a > $o) > set_Pr921883667ee_a_a).
% 2.87/1.64 thf(func_def_118, type, collec486369286Tree_a: (produc143150363Tree_a > $o) > set_Pr1070816379Tree_a).
% 2.87/1.64 thf(func_def_119, type, collec645855634od_a_a: (product_prod_a_a > $o) > set_Product_prod_a_a).
% 2.87/1.64 thf(func_def_120, type, collect_a: (a > $o) > set_a).
% 2.87/1.64 thf(func_def_121, type, member1092636252ee_a_a: produc981471411ee_a_a > set_Pr921883667ee_a_a > $o).
% 2.87/1.64 thf(func_def_122, type, member254315204Tree_a: produc143150363Tree_a > set_Pr1070816379Tree_a > $o).
% 2.87/1.64 thf(func_def_123, type, member_a: a > set_a > $o).
% 2.87/1.64 thf(func_def_124, type, t: tree_a).
% 2.87/1.64 thf(func_def_125, type, v: a).
% 2.87/1.64 thf(func_def_142, type, sP0: a > a > a > $o).
% 2.87/1.64 thf(func_def_143, type, sP1: a > a > a > $o).
% 2.87/1.64 thf(func_def_144, type, sP2: a > a > a > $o).
% 2.87/1.64 thf(func_def_145, type, sP3: (tree_a > $o) > $o).
% 2.87/1.64 thf(func_def_146, type, sP4: (tree_a > $o) > $o).
% 2.87/1.64 thf(func_def_147, type, sP5: (tree_a > $o) > $o).
% 2.87/1.64 thf(func_def_148, type, sK6: (a > a > $o) > a).
% 2.87/1.64 thf(func_def_149, type, sK7: (a > a > $o) > a).
% 2.87/1.64 thf(func_def_150, type, sK8: (a > a > $o) > a).
% 2.87/1.64 thf(func_def_151, type, sK9: (a > a > $o) > a).
% 2.87/1.64 thf(func_def_152, type, sK10: produc143150363Tree_a > a).
% 2.87/1.64 thf(func_def_153, type, sK11: produc143150363Tree_a > tree_a).
% 2.87/1.64 thf(func_def_154, type, sK12: tree_a > a).
% 2.87/1.64 thf(func_def_155, type, sK13: tree_a > tree_a).
% 2.87/1.64 thf(func_def_156, type, sK14: tree_a > a).
% 2.87/1.64 thf(func_def_157, type, sK15: tree_a > tree_a).
% 2.87/1.64 thf(func_def_158, type, sK16: tree_a > tree_a).
% 2.87/1.64 thf(func_def_159, type, sK17: tree_a > a).
% 2.87/1.64 thf(func_def_160, type, sK18: tree_a > tree_a).
% 2.87/1.64 thf(func_def_161, type, sK19: tree_a > a).
% 2.87/1.64 thf(func_def_162, type, sK20: tree_a > tree_a).
% 2.87/1.64 thf(func_def_163, type, sK21: tree_a > tree_a).
% 2.87/1.64 thf(func_def_164, type, sK22: tree_a > a).
% 2.87/1.64 thf(func_def_165, type, sK23: tree_a > a).
% 2.87/1.64 thf(func_def_166, type, sK24: tree_a > a).
% 2.87/1.64 thf(func_def_167, type, sK25: tree_a > a).
% 2.87/1.64 thf(func_def_168, type, sK26: tree_a > tree_a).
% 2.87/1.64 thf(func_def_169, type, sK27: tree_a > a).
% 2.87/1.64 thf(func_def_170, type, sK28: tree_a > tree_a).
% 2.87/1.64 thf(func_def_171, type, sK29: tree_a > tree_a).
% 2.87/1.64 thf(func_def_172, type, sK30: tree_a > tree_a).
% 2.87/1.64 thf(func_def_173, type, sK31: tree_a > tree_a).
% 2.87/1.64 thf(func_def_174, type, sK32: tree_a > a).
% 2.87/1.64 thf(func_def_175, type, sK33: tree_a > tree_a).
% 2.87/1.64 thf(func_def_176, type, sK34: tree_a > a).
% 2.87/1.64 thf(func_def_177, type, sK35: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_178, type, sK36: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_179, type, sK37: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_180, type, sK38: tree_a > a).
% 2.87/1.64 thf(func_def_181, type, sK39: tree_a > a).
% 2.87/1.64 thf(func_def_182, type, sK40: tree_a > tree_a).
% 2.87/1.64 thf(func_def_183, type, sK41: tree_a > tree_a).
% 2.87/1.64 thf(func_def_184, type, sK42: tree_a > tree_a).
% 2.87/1.64 thf(func_def_185, type, sK43: tree_a > a).
% 2.87/1.64 thf(func_def_186, type, sK44: tree_a > tree_a).
% 2.87/1.64 thf(func_def_187, type, sK45: tree_a > tree_a).
% 2.87/1.64 thf(func_def_188, type, sK46: tree_a > tree_a).
% 2.87/1.64 thf(func_def_189, type, sK47: tree_a > a).
% 2.87/1.64 thf(func_def_190, type, sK48: tree_a > a).
% 2.87/1.64 thf(func_def_191, type, sK49: tree_a > tree_a).
% 2.87/1.64 thf(func_def_192, type, sK50: tree_a > a).
% 2.87/1.64 thf(func_def_193, type, sK51: tree_a > tree_a).
% 2.87/1.64 thf(func_def_194, type, sK52: tree_a > a).
% 2.87/1.64 thf(func_def_195, type, sK53: tree_a > a).
% 2.87/1.64 thf(func_def_196, type, sK54: (tree_a > a > $o) > tree_a).
% 2.87/1.64 thf(func_def_197, type, sK55: (tree_a > a > $o) > a).
% 2.87/1.64 thf(func_def_198, type, sK56: produc143150363Tree_a > tree_a > a).
% 2.87/1.64 thf(func_def_199, type, sK57: produc143150363Tree_a > a > tree_a).
% 2.87/1.64 thf(func_def_200, type, sK58: (a > a) > a).
% 2.87/1.64 thf(func_def_201, type, sK59: (a > a) > a).
% 2.87/1.64 thf(func_def_202, type, sK60: tree_a > a).
% 2.87/1.64 thf(func_def_203, type, sK61: tree_a > tree_a).
% 2.87/1.64 thf(func_def_204, type, sK62: tree_a > tree_a).
% 2.87/1.64 thf(func_def_205, type, sK63: (a > a) > a).
% 2.87/1.64 thf(func_def_206, type, sK64: (a > a) > a).
% 2.87/1.64 thf(func_def_207, type, sK65: (a > a) > a).
% 2.87/1.64 thf(func_def_208, type, sK66: (a > a) > a).
% 2.87/1.64 thf(func_def_209, type, sK67: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_210, type, sK68: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_211, type, sK69: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_212, type, sK70: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_213, type, sK71: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_214, type, sK72: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_215, type, sK73: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_216, type, sK74: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_217, type, sK75: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_218, type, sK76: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_219, type, sK77: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_220, type, sK78: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_221, type, sK79: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_222, type, sK80: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_223, type, sK81: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_224, type, sK82: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_225, type, sK83: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_226, type, sK84: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_227, type, sK85: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_228, type, sK86: (tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_229, type, sK87: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_230, type, sK88: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_231, type, sK89: (tree_a > $o) > a).
% 2.87/1.64 thf(func_def_232, type, sK90: (produc143150363Tree_a > $o) > a).
% 2.87/1.64 thf(func_def_233, type, sK91: (produc143150363Tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_234, type, sK92: (a > a) > a).
% 2.87/1.64 thf(func_def_235, type, sK93: (a > a) > a).
% 2.87/1.64 thf(func_def_236, type, sK94: (produc143150363Tree_a > $o) > a).
% 2.87/1.64 thf(func_def_237, type, sK95: (produc143150363Tree_a > $o) > tree_a).
% 2.87/1.64 thf(func_def_238, type, sK96: produc143150363Tree_a > a).
% 2.87/1.64 thf(func_def_239, type, sK97: produc143150363Tree_a > tree_a).
% 2.87/1.64 thf(func_def_240, type, sK98: tree_a > tree_a).
% 2.87/1.64 thf(func_def_241, type, sK99: tree_a > tree_a).
% 2.87/1.64 thf(func_def_242, type, sK100: tree_a > a).
% 2.87/1.64 thf(func_def_243, type, sK101: tree_a > tree_a).
% 2.87/1.64 thf(func_def_244, type, sK102: tree_a > a).
% 2.87/1.64 thf(func_def_245, type, sK103: tree_a > tree_a).
% 2.87/1.64 thf(func_def_246, type, sK104: tree_a > a).
% 2.87/1.64 thf(func_def_247, type, sK105: tree_a > a).
% 2.87/1.64 thf(func_def_248, type, sK106: tree_a > tree_a).
% 2.87/1.64 thf(func_def_249, type, sK107: tree_a > a).
% 2.87/1.64 thf(func_def_250, type, sK108: tree_a > tree_a).
% 2.87/1.64 thf(func_def_251, type, sK109: tree_a > a).
% 2.87/1.64 thf(func_def_252, type, sK110: tree_a > tree_a).
% 2.87/1.64 thf(func_def_253, type, sK111: tree_a > a).
% 2.87/1.64 thf(func_def_254, type, sK112: tree_a > a).
% 2.87/1.64 thf(func_def_255, type, sK113: tree_a > tree_a).
% 2.87/1.64 thf(func_def_257, type, ph115: !>[X0: $tType]:(X0)).
% 2.87/1.64 thf(f1164,plain,(
% 2.87/1.64 $false),
% 2.87/1.64 inference(subsumption_resolution,[status(thm)],[f1163,f1032])).
% 2.87/1.64 thf(f1032,plain,(
% 2.87/1.64 ((is_heap_a @ e_a) = $true)),
% 2.87/1.64 inference(cnf_transformation,[status(thm)],[f392])).
% 2.87/1.64 thf(f392,plain,(
% 2.87/1.64 ((is_heap_a @ e_a) = $true)),
% 2.87/1.64 inference(fool_elimination,[status(thm)],[f391])).
% 2.87/1.64 thf(f391,plain,(
% 2.87/1.64 (is_heap_a @ e_a)),
% 2.87/1.64 inference(rectify,[status(thm)],[f11])).
% 2.87/1.64 thf(f11,axiom,(
% 2.87/1.64 (is_heap_a @ e_a)),
% 2.87/1.64 file('/export/starexec/sandbox2/tmp/tmp.YD8GTuktd0/DTF2THF_14883.p',fact_10_is__heap_Osimps_I1_J)).
% 2.87/1.64 thf(f1163,plain,(
% 2.87/1.64 ((is_heap_a @ e_a) != $true)),
% 2.87/1.64 inference(forward_demodulation,[status(thm)],[f1162,f1159])).
% 2.87/1.64 thf(f1159,plain,(
% 2.87/1.64 ( ! [X2 : tree_a,X0 : a] : (((product_snd_a_Tree_a @ (produc686083979Tree_a @ X0 @ X2)) = X2)) )),
% 2.87/1.64 inference(equality_resolution,[status(thm)],[f1126])).
% 2.87/1.64 thf(f1126,plain,(
% 2.87/1.64 ( ! [X2 : tree_a,X0 : a,X1 : tree_a] : ((X1 = X2) | ((product_snd_a_Tree_a @ (produc686083979Tree_a @ X0 @ X2)) != X1)) )),
% 2.87/1.64 inference(cnf_transformation,[status(thm)],[f904])).
% 2.87/1.64 thf(f904,plain,(
% 2.87/1.64 ! [X0 : a,X1 : tree_a,X2 : tree_a] : ((X1 = X2) | ((product_snd_a_Tree_a @ (produc686083979Tree_a @ X0 @ X2)) != X1))),
% 2.87/1.64 inference(ennf_transformation,[status(thm)],[f832])).
% 2.87/1.64 thf(f832,plain,(
% 2.87/1.64 ! [X0 : a,X1 : tree_a,X2 : tree_a] : (((product_snd_a_Tree_a @ (produc686083979Tree_a @ X0 @ X2)) = X1) => (X1 = X2))),
% 2.87/1.64 inference(rectify,[status(thm)],[f32])).
% 2.87/1.64 thf(f32,axiom,(
% 2.87/1.64 ! [X0 : a,X35 : tree_a,X22 : tree_a] : (((product_snd_a_Tree_a @ (produc686083979Tree_a @ X0 @ X22)) = X35) => (X22 = X35))),
% 2.87/1.64 file('/export/starexec/sandbox2/tmp/tmp.YD8GTuktd0/DTF2THF_14883.p',fact_31_snd__eqD)).
% 2.87/1.64 thf(f1162,plain,(
% 2.87/1.64 ((is_heap_a @ (product_snd_a_Tree_a @ (produc686083979Tree_a @ v @ e_a))) != $true)),
% 2.87/1.64 inference(forward_demodulation,[status(thm)],[f1133,f1064])).
% 2.87/1.64 thf(f1064,plain,(
% 2.87/1.64 ( ! [X0 : a] : (((produc686083979Tree_a @ X0 @ e_a) = (heapIm837449470Leaf_a @ (t_a @ X0 @ e_a @ e_a)))) )),
% 2.87/1.64 inference(cnf_transformation,[status(thm)],[f822])).
% 2.87/1.64 thf(f822,plain,(
% 2.87/1.64 ! [X0 : a] : ((produc686083979Tree_a @ X0 @ e_a) = (heapIm837449470Leaf_a @ (t_a @ X0 @ e_a @ e_a)))),
% 2.87/1.64 inference(rectify,[status(thm)],[f17])).
% 2.87/1.64 thf(f17,axiom,(
% 2.87/1.64 ! [X10 : a] : ((heapIm837449470Leaf_a @ (t_a @ X10 @ e_a @ e_a)) = (produc686083979Tree_a @ X10 @ e_a))),
% 2.87/1.64 file('/export/starexec/sandbox2/tmp/tmp.YD8GTuktd0/DTF2THF_14883.p',fact_16_removeLeaf_Osimps_I1_J)).
% 2.87/1.64 thf(f1133,plain,(
% 2.87/1.64 ((is_heap_a @ (product_snd_a_Tree_a @ (heapIm837449470Leaf_a @ (t_a @ v @ e_a @ e_a)))) != $true)),
% 2.87/1.64 inference(cnf_transformation,[status(thm)],[f819])).
% 2.87/1.64 thf(f819,plain,(
% 2.87/1.64 ((is_heap_a @ (product_snd_a_Tree_a @ (heapIm837449470Leaf_a @ (t_a @ v @ e_a @ e_a)))) != $true)),
% 2.87/1.64 inference(flattening,[status(thm)],[f438])).
% 2.87/1.64 thf(f438,plain,(
% 2.87/1.64 ~((is_heap_a @ (product_snd_a_Tree_a @ (heapIm837449470Leaf_a @ (t_a @ v @ e_a @ e_a)))) = $true)),
% 2.87/1.64 inference(fool_elimination,[status(thm)],[f437])).
% 2.87/1.64 thf(f437,plain,(
% 2.87/1.64 ~(is_heap_a @ (product_snd_a_Tree_a @ (heapIm837449470Leaf_a @ (t_a @ v @ e_a @ e_a))))),
% 2.87/1.64 inference(rectify,[status(thm)],[f359])).
% 2.87/1.64 thf(f359,negated_conjecture,(
% 2.87/1.64 ~(is_heap_a @ (product_snd_a_Tree_a @ (heapIm837449470Leaf_a @ (t_a @ v @ e_a @ e_a))))),
% 2.87/1.64 inference(negated_conjecture,[status(cth)],[f358])).
% 2.87/1.64 thf(f358,conjecture,(
% 2.87/1.64 (is_heap_a @ (product_snd_a_Tree_a @ (heapIm837449470Leaf_a @ (t_a @ v @ e_a @ e_a))))),
% 2.87/1.64 file('/export/starexec/sandbox2/tmp/tmp.YD8GTuktd0/DTF2THF_14883.p',conj_0)).
% 2.87/1.64 % SZS output end Proof for DTF2THF_14883
% 2.87/1.64 % (15107)------------------------------
% 2.87/1.64 % (15107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.64 % (15107)Termination reason: Refutation
% 2.87/1.64
% 2.87/1.64 % (15107)Memory used [KB]: 7036
% 2.87/1.64 % (15107)Time elapsed: 0.030 s
% 2.87/1.64 % (15107)Instructions burned: 86 (million)
% 2.87/1.64 % (15107)------------------------------
% 2.87/1.64 % (15107)------------------------------
% 2.87/1.64 % (15101)Success in time 0.066 s
%------------------------------------------------------------------------------