%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP037^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 08:55:02 AM UTC 2026
% Result : Theorem 2.90s 1.52s
% Output : Refutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 5 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 25 ( 5 ~; 0 |; 0 &; 20 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 53 ( 52 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 144 ( 141 usr; 37 con; 0-10 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
produc190496183real_c: $tType ).
thf(type_def_6,type,
set_Sum_sum_c_c: $tType ).
thf(type_def_8,type,
produc1149990247eal_sz: $tType ).
thf(type_def_9,type,
set_Sum_sum_sz_sz: $tType ).
thf(type_def_10,type,
denota231621370t_unit: $tType ).
thf(type_def_11,type,
trm_a_c: $tType ).
thf(type_def_12,type,
real: $tType ).
thf(type_def_13,type,
finite1398487019real_c: $tType ).
thf(type_def_14,type,
frechet_strm_a_c: $tType ).
thf(type_def_15,type,
trm_sf_sz: $tType ).
thf(type_def_16,type,
frechet_strm_sf_sz: $tType ).
thf(type_def_17,type,
produc99145217real_c: $tType ).
thf(type_def_18,type,
produc133347448c_real: $tType ).
thf(type_def_19,type,
produc1952288593real_c: $tType ).
thf(type_def_20,type,
produc640052711real_c: $tType ).
thf(type_def_21,type,
produc906325778c_real: $tType ).
thf(type_def_22,type,
produc1471603704real_c: $tType ).
thf(type_def_23,type,
produc1295591296real_c: $tType ).
thf(type_def_24,type,
produc957004601l_real: $tType ).
thf(type_def_25,type,
sz: $tType ).
thf(type_def_26,type,
sf: $tType ).
thf(type_def_27,type,
sc: $tType ).
thf(type_def_28,type,
produc802386618_set_c: $tType ).
thf(type_def_29,type,
produc189019228set_sz: $tType ).
thf(type_def_30,type,
produc1299700144real_c: $tType ).
thf(type_def_31,type,
produc621499498um_c_c: $tType ).
thf(type_def_32,type,
produc756982951_set_c: $tType ).
thf(type_def_33,type,
produc313687471set_sz: $tType ).
thf(type_def_34,type,
produc729314338real_c: $tType ).
thf(type_def_35,type,
produc44682460um_c_c: $tType ).
thf(type_def_36,type,
produc1631500469_set_c: $tType ).
thf(type_def_37,type,
produc2057661729set_sz: $tType ).
thf(type_def_38,type,
set_Fi1407883041real_c: $tType ).
thf(type_def_39,type,
set_Pr1389752855real_c: $tType ).
thf(type_def_40,type,
set_c: $tType ).
thf(type_def_41,type,
set_sz: $tType ).
thf(type_def_42,type,
denota610675952t_unit: $tType ).
thf(type_def_43,type,
produc866628903_sc_sz: $tType ).
thf(type_def_44,type,
produc1821101996_sc_sz: $tType ).
thf(type_def_45,type,
finite824932053eal_sz: $tType ).
thf(type_def_46,type,
list_f1238882004_sc_sz: $tType ).
thf(type_def_47,type,
produc999471430t_unit: $tType ).
thf(type_def_48,type,
produc861709536_sz_sz: $tType ).
thf(type_def_49,type,
set_Pr2041213564t_unit: $tType ).
thf(type_def_50,type,
set_trm_a_c: $tType ).
thf(type_def_51,type,
set_trm_sf_sz: $tType ).
thf(type_def_52,type,
a: $tType ).
thf(type_def_53,type,
set_a: $tType ).
thf(type_def_54,type,
set_sf: $tType ).
thf(type_def_55,type,
set_Pr1169339874_sc_sz: $tType ).
thf(type_def_56,type,
c: $tType ).
thf(type_def_57,type,
formula_sf_sc_sz: $tType ).
thf(func_def_0,type,
produc640052711real_c: $tType ).
thf(func_def_1,type,
set_Pr2041213564t_unit: $tType ).
thf(func_def_2,type,
set_Pr1169339874_sc_sz: $tType ).
thf(func_def_3,type,
produc999471430t_unit: $tType ).
thf(func_def_4,type,
produc1821101996_sc_sz: $tType ).
thf(func_def_5,type,
produc1952288593real_c: $tType ).
thf(func_def_6,type,
produc99145217real_c: $tType ).
thf(func_def_7,type,
produc1295591296real_c: $tType ).
thf(func_def_8,type,
produc906325778c_real: $tType ).
thf(func_def_9,type,
set_Pr1389752855real_c: $tType ).
thf(func_def_10,type,
produc1149990247eal_sz: $tType ).
thf(func_def_11,type,
produc190496183real_c: $tType ).
thf(func_def_12,type,
produc866628903_sc_sz: $tType ).
thf(func_def_13,type,
produc729314338real_c: $tType ).
thf(func_def_14,type,
produc1299700144real_c: $tType ).
thf(func_def_15,type,
produc1471603704real_c: $tType ).
thf(func_def_16,type,
produc133347448c_real: $tType ).
thf(func_def_17,type,
denota610675952t_unit: $tType ).
thf(func_def_18,type,
produc44682460um_c_c: $tType ).
thf(func_def_19,type,
produc189019228set_sz: $tType ).
thf(func_def_20,type,
produc621499498um_c_c: $tType ).
thf(func_def_21,type,
produc802386618_set_c: $tType ).
thf(func_def_22,type,
denota231621370t_unit: $tType ).
thf(func_def_23,type,
set_Fi1407883041real_c: $tType ).
thf(func_def_24,type,
produc2057661729set_sz: $tType ).
thf(func_def_25,type,
produc1631500469_set_c: $tType ).
thf(func_def_26,type,
produc313687471set_sz: $tType ).
thf(func_def_27,type,
produc756982951_set_c: $tType ).
thf(func_def_28,type,
produc861709536_sz_sz: $tType ).
thf(func_def_29,type,
finite824932053eal_sz: $tType ).
thf(func_def_30,type,
finite1398487019real_c: $tType ).
thf(func_def_31,type,
list_f1238882004_sc_sz: $tType ).
thf(func_def_32,type,
produc957004601l_real: $tType ).
thf(func_def_33,type,
frechet_strm_sf_sz: $tType ).
thf(func_def_34,type,
set_Sum_sum_sz_sz: $tType ).
thf(func_def_35,type,
frechet_strm_a_c: $tType ).
thf(func_def_36,type,
set_Sum_sum_c_c: $tType ).
thf(func_def_37,type,
set_trm_sf_sz: $tType ).
thf(func_def_38,type,
set_trm_a_c: $tType ).
thf(func_def_39,type,
formula_sf_sc_sz: $tType ).
thf(func_def_40,type,
trm_sf_sz: $tType ).
thf(func_def_41,type,
trm_a_c: $tType ).
thf(func_def_42,type,
set_sz: $tType ).
thf(func_def_43,type,
set_sf: $tType ).
thf(func_def_44,type,
set_c: $tType ).
thf(func_def_45,type,
set_a: $tType ).
thf(func_def_46,type,
real: $tType ).
thf(func_def_47,type,
sz: $tType ).
thf(func_def_48,type,
sf: $tType ).
thf(func_def_49,type,
sc: $tType ).
thf(func_def_50,type,
c: $tType ).
thf(func_def_51,type,
a: $tType ).
thf(func_def_52,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(func_def_53,type,
denota102713844ree_sz: produc1149990247eal_sz > produc1149990247eal_sz > set_Sum_sum_sz_sz > $o ).
thf(func_def_54,type,
denota2112424896_a_b_c: denota231621370t_unit > trm_a_c > produc190496183real_c > real ).
thf(func_def_55,type,
denota229585092_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > finite1398487019real_c > real ).
thf(func_def_56,type,
frechet_cr_strm_a_c: trm_a_c > frechet_strm_a_c > $o ).
thf(func_def_57,type,
freche1244000341_sf_sz: trm_sf_sz > frechet_strm_sf_sz > $o ).
thf(func_def_58,type,
zero_z109254132real_c: finite1398487019real_c ).
thf(func_def_59,type,
zero_z1506780526real_c: produc190496183real_c ).
thf(func_def_60,type,
zero_z735295626real_c: produc99145217real_c ).
thf(func_def_61,type,
zero_z1273814959c_real: produc133347448c_real ).
thf(func_def_62,type,
zero_z440955354real_c: produc1952288593real_c ).
thf(func_def_63,type,
zero_z993734942real_c: produc640052711real_c ).
thf(func_def_64,type,
zero_z1830236699c_real: produc906325778c_real ).
thf(func_def_65,type,
zero_z464587567real_c: produc1471603704real_c ).
thf(func_def_66,type,
zero_z72018569real_c: produc1295591296real_c ).
thf(func_def_67,type,
zero_z659284464l_real: produc957004601l_real ).
thf(func_def_68,type,
zero_zero_real: real ).
thf(func_def_69,type,
ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o ).
thf(func_def_70,type,
if_trm_sf_sz: $o > trm_sf_sz > trm_sf_sz > trm_sf_sz ).
thf(func_def_71,type,
top_to1309524330_set_c: produc802386618_set_c ).
thf(func_def_72,type,
top_to1246597548set_sz: produc189019228set_sz ).
thf(func_def_73,type,
top_to1783191648real_c: produc1299700144real_c ).
thf(func_def_74,type,
top_to1128637210um_c_c: produc621499498um_c_c ).
thf(func_def_75,type,
top_to543326711_set_c: produc756982951_set_c ).
thf(func_def_76,type,
top_to1303770207set_sz: produc313687471set_sz ).
thf(func_def_77,type,
top_to1102487922real_c: produc729314338real_c ).
thf(func_def_78,type,
top_to1102260780um_c_c: produc44682460um_c_c ).
thf(func_def_79,type,
top_to474099557_set_c: produc1631500469_set_c ).
thf(func_def_80,type,
top_to1999610481set_sz: produc2057661729set_sz ).
thf(func_def_81,type,
top_to1642137041real_c: set_Fi1407883041real_c ).
thf(func_def_82,type,
top_to226056039real_c: set_Pr1389752855real_c ).
thf(func_def_83,type,
top_to1660572043um_c_c: set_Sum_sum_c_c ).
thf(func_def_84,type,
top_to1246370329_sz_sz: set_Sum_sum_sz_sz ).
thf(func_def_85,type,
top_top_set_c: set_c ).
thf(func_def_86,type,
top_top_set_sz: set_sz ).
thf(func_def_87,type,
produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz ).
thf(func_def_88,type,
produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(func_def_89,type,
produc1563404851real_c: finite1398487019real_c > produc190496183real_c > produc99145217real_c ).
thf(func_def_90,type,
produc1715747632c_real: finite1398487019real_c > real > produc133347448c_real ).
thf(func_def_91,type,
produc1308130519eal_sz: finite824932053eal_sz > finite824932053eal_sz > produc1149990247eal_sz ).
thf(func_def_92,type,
produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz ).
thf(func_def_93,type,
produc116546123real_c: produc190496183real_c > finite1398487019real_c > produc1952288593real_c ).
thf(func_def_94,type,
produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c ).
thf(func_def_95,type,
produc171591948c_real: produc190496183real_c > real > produc906325778c_real ).
thf(func_def_96,type,
produc502616768t_unit: produc866628903_sc_sz > denota610675952t_unit > produc999471430t_unit ).
thf(func_def_97,type,
produc1327150128real_c: real > finite1398487019real_c > produc1471603704real_c ).
thf(func_def_98,type,
produc2134005810real_c: real > produc190496183real_c > produc1295591296real_c ).
thf(func_def_99,type,
produc705216881l_real: real > real > produc957004601l_real ).
thf(func_def_100,type,
produc1767696108_set_c: set_Sum_sum_c_c > set_c > produc802386618_set_c ).
thf(func_def_101,type,
produc1251379220set_sz: set_Sum_sum_c_c > set_sz > produc189019228set_sz ).
thf(func_def_102,type,
produc280329770real_c: set_c > set_Fi1407883041real_c > produc1299700144real_c ).
thf(func_def_103,type,
produc1519884516um_c_c: set_c > set_Sum_sum_c_c > produc621499498um_c_c ).
thf(func_def_104,type,
produc878845847_set_c: set_c > set_c > produc756982951_set_c ).
thf(func_def_105,type,
produc2039118377set_sz: set_c > set_sz > produc313687471set_sz ).
thf(func_def_106,type,
produc1915663706real_c: set_sz > set_Fi1407883041real_c > produc729314338real_c ).
thf(func_def_107,type,
produc590684180um_c_c: set_sz > set_Sum_sum_c_c > produc44682460um_c_c ).
thf(func_def_108,type,
produc760013927_set_c: set_sz > set_c > produc1631500469_set_c ).
thf(func_def_109,type,
produc2156889set_sz: set_sz > set_sz > produc2057661729set_sz ).
thf(func_def_110,type,
produc792909658_sz_sz: trm_sf_sz > sz > produc861709536_sz_sz ).
thf(func_def_111,type,
produc403791768_sc_sz: ( denota610675952t_unit > denota610675952t_unit ) > ( produc866628903_sc_sz > produc866628903_sc_sz ) > produc1821101996_sc_sz > produc1821101996_sc_sz ).
thf(func_def_112,type,
produc368345510real_c: ( finite1398487019real_c > finite1398487019real_c ) > ( finite1398487019real_c > finite1398487019real_c ) > produc190496183real_c > produc190496183real_c ).
thf(func_def_113,type,
produc1503602930_sc_sz: produc1821101996_sc_sz > denota610675952t_unit ).
thf(func_def_114,type,
produc2010422875real_c: produc190496183real_c > finite1398487019real_c ).
thf(func_def_115,type,
produc548504323_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
thf(func_def_116,type,
produc1216682964t_unit: produc999471430t_unit > produc866628903_sc_sz ).
thf(func_def_117,type,
produc2069561454_sz_sz: produc861709536_sz_sz > trm_sf_sz ).
thf(func_def_118,type,
produc974239792_sc_sz: produc1821101996_sc_sz > produc866628903_sc_sz ).
thf(func_def_119,type,
produc314122909real_c: produc190496183real_c > finite1398487019real_c ).
thf(func_def_120,type,
produc4753477_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
thf(func_def_121,type,
produc687319826t_unit: produc999471430t_unit > denota610675952t_unit ).
thf(func_def_122,type,
produc181739436_sz_sz: produc861709536_sz_sz > sz ).
thf(func_def_123,type,
produc532048446_sc_sz: produc1821101996_sc_sz > produc999471430t_unit ).
thf(func_def_124,type,
produc704157711real_c: produc190496183real_c > produc190496183real_c ).
thf(func_def_125,type,
produc245128480t_unit: produc999471430t_unit > produc1821101996_sc_sz ).
thf(func_def_126,type,
domain2047240575rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > trm_a_c > $o ).
thf(func_def_127,type,
domain512309999_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > trm_sf_sz > $o ).
thf(func_def_128,type,
collec377961627t_unit: ( produc999471430t_unit > $o ) > set_Pr2041213564t_unit ).
thf(func_def_129,type,
collect_trm_a_c: ( trm_a_c > $o ) > set_trm_a_c ).
thf(func_def_130,type,
collect_trm_sf_sz: ( trm_sf_sz > $o ) > set_trm_sf_sz ).
thf(func_def_131,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_132,type,
collect_sf: ( sf > $o ) > set_sf ).
thf(func_def_133,type,
image_1726193375_sc_sz: ( produc1821101996_sc_sz > produc1821101996_sc_sz ) > set_Pr1169339874_sc_sz > set_Pr1169339874_sc_sz ).
thf(func_def_134,type,
image_904562809t_unit: ( produc1821101996_sc_sz > produc999471430t_unit ) > set_Pr1169339874_sc_sz > set_Pr2041213564t_unit ).
thf(func_def_135,type,
image_14429021real_c: ( produc190496183real_c > finite1398487019real_c ) > set_Pr1389752855real_c > set_Fi1407883041real_c ).
thf(func_def_136,type,
image_1426741113_sc_sz: ( produc999471430t_unit > produc1821101996_sc_sz ) > set_Pr2041213564t_unit > set_Pr1169339874_sc_sz ).
thf(func_def_137,type,
image_c_trm_a_c: ( c > trm_a_c ) > set_c > set_trm_a_c ).
thf(func_def_138,type,
image_sz_trm_sf_sz: ( sz > trm_sf_sz ) > set_sz > set_trm_sf_sz ).
thf(func_def_139,type,
static_FVDiff_a_c: trm_a_c > set_Sum_sum_c_c ).
thf(func_def_140,type,
static_FVDiff_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
thf(func_def_141,type,
predic913887884_sf_sz: sc > formula_sf_sc_sz ).
thf(func_def_142,type,
dfree_a_c: trm_a_c > $o ).
thf(func_def_143,type,
dfree_sf_sz: trm_sf_sz > $o ).
thf(func_def_144,type,
dsafe_a_c: trm_a_c > $o ).
thf(func_def_145,type,
dsafe_sf_sz: trm_sf_sz > $o ).
thf(func_def_146,type,
ffree_sf_sc_sz: formula_sf_sc_sz > $o ).
thf(func_def_147,type,
prop_sz_sf_sc: sz > ( sz > trm_sf_sz ) > formula_sf_sc_sz ).
thf(func_def_148,type,
set1_f989022726_sc_sz: formula_sf_sc_sz > set_sf ).
thf(func_def_149,type,
p_sc_sf_sz: sc > formula_sf_sc_sz ).
thf(func_def_150,type,
empty_c_a: c > trm_a_c ).
thf(func_def_151,type,
empty_sz_sf: sz > trm_sf_sz ).
thf(func_def_152,type,
f0_sf_sz: sf > trm_sf_sz ).
thf(func_def_153,type,
f1_sz_sf: sz > sf > sz > trm_sf_sz ).
thf(func_def_154,type,
p1_sz_sf_sc: sz > sz > sz > formula_sf_sc_sz ).
thf(func_def_155,type,
singleton_sz_sf: sz > trm_sf_sz > sz > trm_sf_sz ).
thf(func_def_156,type,
singleton_rel_sf_sz: produc861709536_sz_sz > produc861709536_sz_sz > $o ).
thf(func_def_157,type,
const_a_c: real > trm_a_c ).
thf(func_def_158,type,
const_sf_sz: real > trm_sf_sz ).
thf(func_def_159,type,
diffVar_c_a: c > trm_a_c ).
thf(func_def_160,type,
diffVar_sz_sf: sz > trm_sf_sz ).
thf(func_def_161,type,
differential_a_c: trm_a_c > trm_a_c ).
thf(func_def_162,type,
differential_sf_sz: trm_sf_sz > trm_sf_sz ).
thf(func_def_163,type,
function_a_c: a > ( c > trm_a_c ) > trm_a_c ).
thf(func_def_164,type,
function_sf_sz: sf > ( sz > trm_sf_sz ) > trm_sf_sz ).
thf(func_def_165,type,
plus_a_c: trm_a_c > trm_a_c > trm_a_c ).
thf(func_def_166,type,
plus_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
thf(func_def_167,type,
times_a_c: trm_a_c > trm_a_c > trm_a_c ).
thf(func_def_168,type,
times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
thf(func_def_169,type,
var_c_a: c > trm_a_c ).
thf(func_def_170,type,
var_sz_sf: sz > trm_sf_sz ).
thf(func_def_171,type,
set_trm_a_c2: trm_a_c > set_a ).
thf(func_def_172,type,
set_trm_sf_sz2: trm_sf_sz > set_sf ).
thf(func_def_173,type,
left_u968903956rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > $o ).
thf(func_def_174,type,
left_u638806404_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > $o ).
thf(func_def_175,type,
right_1933252621rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > $o ).
thf(func_def_176,type,
right_963419005_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > $o ).
thf(func_def_177,type,
accp_P529224471_sz_sz: ( produc861709536_sz_sz > produc861709536_sz_sz > $o ) > produc861709536_sz_sz > $o ).
thf(func_def_178,type,
member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o ).
thf(func_def_179,type,
member235934813t_unit: produc999471430t_unit > set_Pr2041213564t_unit > $o ).
thf(func_def_180,type,
member_trm_a_c: trm_a_c > set_trm_a_c > $o ).
thf(func_def_181,type,
member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
thf(func_def_182,type,
member_a: a > set_a > $o ).
thf(func_def_183,type,
member_sf: sf > set_sf > $o ).
thf(func_def_184,type,
i: denota231621370t_unit ).
thf(func_def_185,type,
nu: produc190496183real_c ).
thf(func_def_186,type,
nu2: produc190496183real_c ).
thf(func_def_187,type,
args: c > trm_a_c ).
thf(func_def_188,type,
i2: c ).
thf(func_def_189,type,
var: a ).
thf(func_def_190,type,
vid1: sz ).
thf(func_def_191,type,
vid2: sz ).
thf(func_def_192,type,
vid3: sz ).
thf(f743,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f740,f739]) ).
thf(f739,plain,
! [X0: c] :
( ( dfree_a_c @ ( args @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f705]) ).
thf(f705,plain,
! [X0: c] :
( ( dfree_a_c @ ( args @ X0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f704]) ).
thf(f704,plain,
! [X0: c] : ( dfree_a_c @ ( args @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: c] : ( dfree_a_c @ ( args @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.ItXc5YzKVO/DTF2THF_27746.p',fact_0_free) ).
thf(f740,plain,
( ( dfree_a_c @ ( args @ i2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f736]) ).
thf(f736,plain,
( ( dfree_a_c @ ( args @ i2 ) )
!= $true ),
inference(flattening,[status(thm)],[f607]) ).
thf(f607,plain,
( ( dfree_a_c @ ( args @ i2 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f606]) ).
thf(f606,plain,
~ ( dfree_a_c @ ( args @ i2 ) ),
inference(rectify,[status(thm)],[f358]) ).
thf(f358,negated_conjecture,
~ ( dfree_a_c @ ( args @ i2 ) ),
inference(negated_conjecture,[status(cth)],[f357]) ).
thf(f357,conjecture,
dfree_a_c @ ( args @ i2 ),
file('/export/starexec/sandbox/tmp/tmp.ItXc5YzKVO/DTF2THF_27746.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP037^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:24:16 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP037^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer Coincidence problem prob_129__7211024_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : Coincidence/prob_129__7211024_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.40 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 550 ( 245 unt; 193 typ; 0 def)
% 0.30/0.46 % Number of atoms : 778 ( 464 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 15 ( 2 avg)
% 0.30/0.46 % Number of connectives : 2327 ( 159 ~; 21 |; 61 &;1765 @)
% 0.30/0.46 % ( 0 <=>; 321 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 25 ( 6 avg)
% 0.30/0.46 % Number of types : 53 ( 52 usr)
% 0.30/0.46 % Number of type conns : 332 ( 332 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 144 ( 141 usr; 37 con; 0-10 aty)
% 0.30/0.46 % Number of variables : 1076 ( 37 ^; 978 !; 61 ?;1076 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:37:05.819
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (52)
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 produc640052711real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J_J,type,
% 0.30/0.46 set_Pr2041213564t_unit: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_J,type,
% 0.30/0.46 set_Pr1169339874_sc_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 0.30/0.46 produc999471430t_unit: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 0.30/0.46 produc1821101996_sc_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 produc1952288593real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 produc99145217real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 produc1295591296real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Real__Oreal_J,type,
% 0.30/0.46 produc906325778c_real: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 set_Pr1389752855real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 0.30/0.46 produc1149990247eal_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 produc190496183real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.30/0.46 produc866628903_sc_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 produc729314338real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 produc1299700144real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 produc1471603704real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Real__Oreal_J,type,
% 0.30/0.46 produc133347448c_real: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.30/0.46 denota610675952t_unit: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 0.30/0.46 produc44682460um_c_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 0.30/0.46 produc189019228set_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 0.30/0.46 produc621499498um_c_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_Itf__c_J_J,type,
% 0.30/0.46 produc802386618_set_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J,type,
% 0.30/0.46 denota231621370t_unit: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 set_Fi1407883041real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 0.30/0.46 produc2057661729set_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_Itf__c_J_J,type,
% 0.30/0.46 produc1631500469_set_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 0.30/0.46 produc313687471set_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_Itf__c_J_J,type,
% 0.30/0.46 produc756982951_set_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_Mtf__sz_J,type,
% 0.30/0.46 produc861709536_sz_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 0.30/0.46 finite824932053eal_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 finite1398487019real_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 0.30/0.46 list_f1238882004_sc_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 0.30/0.46 produc957004601l_real: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J,type,
% 0.30/0.46 frechet_strm_sf_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__sz_Mtf__sz_J_J,type,
% 0.30/0.46 set_Sum_sum_sz_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__c_J,type,
% 0.30/0.46 frechet_strm_a_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 0.30/0.46 set_Sum_sum_c_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_J,type,
% 0.30/0.46 set_trm_sf_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_It__Syntax__Otrm_Itf__a_Mtf__c_J_J,type,
% 0.30/0.46 set_trm_a_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J,type,
% 0.30/0.46 formula_sf_sc_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 0.30/0.46 trm_sf_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 0.30/0.46 trm_a_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_Itf__sz_J,type,
% 0.30/0.46 set_sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_Itf__sf_J,type,
% 0.30/0.46 set_sf: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_Itf__c_J,type,
% 0.30/0.46 set_c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.30/0.46 set_a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t__Real__Oreal,type,
% 0.30/0.46 real: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__sz,type,
% 0.30/0.46 sz: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__sf,type,
% 0.30/0.46 sf: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__sc,type,
% 0.30/0.46 sc: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__c,type,
% 0.30/0.46 c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_tf__a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (141)
% 0.30/0.46 thf(sy_c_Denotational__Semantics_OVagree_001tf__c,type,
% 0.30/0.46 denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Denotational__Semantics_OVagree_001tf__sz,type,
% 0.30/0.46 denota102713844ree_sz: produc1149990247eal_sz > produc1149990247eal_sz > set_Sum_sum_sz_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Denotational__Semantics_Odirectional__derivative_001tf__a_001tf__b_001tf__c,type,
% 0.30/0.46 denota2112424896_a_b_c: denota231621370t_unit > trm_a_c > produc190496183real_c > real ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Denotational__Semantics_Ofrechet_001tf__a_001tf__b_001tf__c,type,
% 0.30/0.46 denota229585092_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > finite1398487019real_c > real ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm_001tf__a_001tf__c,type,
% 0.30/0.46 frechet_cr_strm_a_c: trm_a_c > frechet_strm_a_c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm_001tf__sf_001tf__sz,type,
% 0.30/0.46 freche1244000341_sf_sz: trm_sf_sz > frechet_strm_sf_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 zero_z109254132real_c: finite1398487019real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 zero_z1506780526real_c: produc190496183real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 zero_z735295626real_c: produc99145217real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Real__Oreal_J,type,
% 0.30/0.46 zero_z1273814959c_real: produc133347448c_real ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 zero_z440955354real_c: produc1952288593real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 zero_z993734942real_c: produc640052711real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Real__Oreal_J,type,
% 0.30/0.46 zero_z1830236699c_real: produc906325778c_real ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 zero_z464587567real_c: produc1471603704real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 zero_z72018569real_c: produc1295591296real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 0.30/0.46 zero_z659284464l_real: produc957004601l_real ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.30/0.46 zero_zero_real: real ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Ids_Oids_001tf__sz_001tf__sf_001tf__sc,type,
% 0.30/0.46 ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_If_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 0.30/0.46 if_trm_sf_sz: $o > trm_sf_sz > trm_sf_sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_Itf__c_J_J,type,
% 0.30/0.46 top_to1309524330_set_c: produc802386618_set_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 0.30/0.46 top_to1246597548set_sz: produc189019228set_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 top_to1783191648real_c: produc1299700144real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 0.30/0.46 top_to1128637210um_c_c: produc621499498um_c_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_Itf__c_J_J,type,
% 0.30/0.46 top_to543326711_set_c: produc756982951_set_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 0.30/0.46 top_to1303770207set_sz: produc313687471set_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 top_to1102487922real_c: produc729314338real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 0.30/0.46 top_to1102260780um_c_c: produc44682460um_c_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_Itf__c_J_J,type,
% 0.30/0.46 top_to474099557_set_c: produc1631500469_set_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 0.30/0.46 top_to1999610481set_sz: produc2057661729set_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 top_to1642137041real_c: set_Fi1407883041real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.30/0.46 top_to226056039real_c: set_Pr1389752855real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 0.30/0.46 top_to1660572043um_c_c: set_Sum_sum_c_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__sz_Mtf__sz_J_J,type,
% 0.30/0.46 top_to1246370329_sz_sz: set_Sum_sum_sz_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__c_J,type,
% 0.30/0.46 top_top_set_c: set_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__sz_J,type,
% 0.30/0.46 top_top_set_sz: set_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.30/0.46 produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 produc1563404851real_c: finite1398487019real_c > produc190496183real_c > produc99145217real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Real__Oreal,type,
% 0.30/0.46 produc1715747632c_real: finite1398487019real_c > real > produc133347448c_real ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 0.30/0.46 produc1308130519eal_sz: finite824932053eal_sz > finite824932053eal_sz > produc1149990247eal_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 0.30/0.46 produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 produc116546123real_c: produc190496183real_c > finite1398487019real_c > produc1952288593real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Real__Oreal,type,
% 0.30/0.46 produc171591948c_real: produc190496183real_c > real > produc906325778c_real ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.30/0.46 produc502616768t_unit: produc866628903_sc_sz > denota610675952t_unit > produc999471430t_unit ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 produc1327150128real_c: real > finite1398487019real_c > produc1471603704real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 produc2134005810real_c: real > produc190496183real_c > produc1295591296real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.30/0.46 produc705216881l_real: real > real > produc957004601l_real ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_001t__Set__Oset_Itf__c_J,type,
% 0.30/0.46 produc1767696108_set_c: set_Sum_sum_c_c > set_c > produc802386618_set_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_001t__Set__Oset_Itf__sz_J,type,
% 0.30/0.46 produc1251379220set_sz: set_Sum_sum_c_c > set_sz > produc189019228set_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c_J_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 produc280329770real_c: set_c > set_Fi1407883041real_c > produc1299700144real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c_J_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 0.30/0.46 produc1519884516um_c_c: set_c > set_Sum_sum_c_c > produc621499498um_c_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c_J_001t__Set__Oset_Itf__c_J,type,
% 0.30/0.46 produc878845847_set_c: set_c > set_c > produc756982951_set_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c_J_001t__Set__Oset_Itf__sz_J,type,
% 0.30/0.46 produc2039118377set_sz: set_c > set_sz > produc313687471set_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__sz_J_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.30/0.46 produc1915663706real_c: set_sz > set_Fi1407883041real_c > produc729314338real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__sz_J_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 0.30/0.46 produc590684180um_c_c: set_sz > set_Sum_sum_c_c > produc44682460um_c_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__sz_J_001t__Set__Oset_Itf__c_J,type,
% 0.30/0.46 produc760013927_set_c: set_sz > set_c > produc1631500469_set_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__sz_J_001t__Set__Oset_Itf__sz_J,type,
% 0.30/0.46 produc2156889set_sz: set_sz > set_sz > produc2057661729set_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001tf__sz,type,
% 0.30/0.46 produc792909658_sz_sz: trm_sf_sz > sz > produc861709536_sz_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Omap__prod_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.30/0.46 produc403791768_sc_sz: ( denota610675952t_unit > denota610675952t_unit ) > ( produc866628903_sc_sz > produc866628903_sc_sz ) > produc1821101996_sc_sz > produc1821101996_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Omap__prod_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 produc368345510real_c: ( finite1398487019real_c > finite1398487019real_c ) > ( finite1398487019real_c > finite1398487019real_c ) > produc190496183real_c > produc190496183real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.30/0.46 produc1503602930_sc_sz: produc1821101996_sc_sz > denota610675952t_unit ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 produc2010422875real_c: produc190496183real_c > finite1398487019real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 0.30/0.46 produc548504323_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.30/0.46 produc1216682964t_unit: produc999471430t_unit > produc866628903_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Ofst_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001tf__sz,type,
% 0.30/0.46 produc2069561454_sz_sz: produc861709536_sz_sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Osnd_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.30/0.46 produc974239792_sc_sz: produc1821101996_sc_sz > produc866628903_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Osnd_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 produc314122909real_c: produc190496183real_c > finite1398487019real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Osnd_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 0.30/0.46 produc4753477_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.30/0.46 produc687319826t_unit: produc999471430t_unit > denota610675952t_unit ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Osnd_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001tf__sz,type,
% 0.30/0.46 produc181739436_sz_sz: produc861709536_sz_sz > sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Oswap_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.30/0.46 produc532048446_sc_sz: produc1821101996_sc_sz > produc999471430t_unit ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Oswap_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 produc704157711real_c: produc190496183real_c > produc190496183real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_Oprod_Oswap_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.30/0.46 produc245128480t_unit: produc999471430t_unit > produc1821101996_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_ODomainp_001t__Syntax__Otrm_Itf__a_Mtf__c_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__c_J,type,
% 0.30/0.46 domain2047240575rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > trm_a_c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Relation_ODomainp_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J,type,
% 0.30/0.46 domain512309999_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > trm_sf_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 0.30/0.46 collec377961627t_unit: ( produc999471430t_unit > $o ) > set_Pr2041213564t_unit ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 0.30/0.46 collect_trm_a_c: ( trm_a_c > $o ) > set_trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 0.30/0.46 collect_trm_sf_sz: ( trm_sf_sz > $o ) > set_trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.30/0.46 collect_a: ( a > $o ) > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001tf__sf,type,
% 0.30/0.46 collect_sf: ( sf > $o ) > set_sf ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 0.30/0.46 image_1726193375_sc_sz: ( produc1821101996_sc_sz > produc1821101996_sc_sz ) > set_Pr1169339874_sc_sz > set_Pr1169339874_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 0.30/0.46 image_904562809t_unit: ( produc1821101996_sc_sz > produc999471430t_unit ) > set_Pr1169339874_sc_sz > set_Pr2041213564t_unit ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.30/0.46 image_14429021real_c: ( produc190496183real_c > finite1398487019real_c ) > set_Pr1389752855real_c > set_Fi1407883041real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 0.30/0.46 image_1426741113_sc_sz: ( produc999471430t_unit > produc1821101996_sc_sz ) > set_Pr2041213564t_unit > set_Pr1169339874_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oimage_001tf__c_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 0.30/0.46 image_c_trm_a_c: ( c > trm_a_c ) > set_c > set_trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oimage_001tf__sz_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 0.30/0.46 image_sz_trm_sf_sz: ( sz > trm_sf_sz ) > set_sz > set_trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Static__Semantics_OFVDiff_001tf__a_001tf__c,type,
% 0.30/0.46 static_FVDiff_a_c: trm_a_c > set_Sum_sum_c_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Static__Semantics_OFVDiff_001tf__sf_001tf__sz,type,
% 0.30/0.46 static_FVDiff_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_OPredicational_001tf__sc_001tf__sf_001tf__sz,type,
% 0.30/0.46 predic913887884_sf_sz: sc > formula_sf_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Odfree_001tf__a_001tf__c,type,
% 0.30/0.46 dfree_a_c: trm_a_c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Odfree_001tf__sf_001tf__sz,type,
% 0.30/0.46 dfree_sf_sz: trm_sf_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Odsafe_001tf__a_001tf__c,type,
% 0.30/0.46 dsafe_a_c: trm_a_c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Odsafe_001tf__sf_001tf__sz,type,
% 0.30/0.46 dsafe_sf_sz: trm_sf_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Offree_001tf__sf_001tf__sc_001tf__sz,type,
% 0.30/0.46 ffree_sf_sc_sz: formula_sf_sc_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oformula_OProp_001tf__sz_001tf__sf_001tf__sc,type,
% 0.30/0.46 prop_sz_sf_sc: sz > ( sz > trm_sf_sz ) > formula_sf_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oformula_Oset1__formula_001tf__sf_001tf__sc_001tf__sz,type,
% 0.30/0.46 set1_f989022726_sc_sz: formula_sf_sc_sz > set_sf ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oids_OP_001tf__sc_001tf__sf_001tf__sz,type,
% 0.30/0.46 p_sc_sf_sz: sc > formula_sf_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oids_Oempty_001tf__c_001tf__a,type,
% 0.30/0.46 empty_c_a: c > trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oids_Oempty_001tf__sz_001tf__sf,type,
% 0.30/0.46 empty_sz_sf: sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oids_Of0_001tf__sf_001tf__sz,type,
% 0.30/0.46 f0_sf_sz: sf > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oids_Of1_001tf__sz_001tf__sf,type,
% 0.30/0.46 f1_sz_sf: sz > sf > sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oids_Op1_001tf__sz_001tf__sf_001tf__sc,type,
% 0.30/0.46 p1_sz_sf_sc: sz > sz > sz > formula_sf_sc_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oids_Osingleton_001tf__sz_001tf__sf,type,
% 0.30/0.46 singleton_sz_sf: sz > trm_sf_sz > sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Oids_Osingleton__rel_001tf__sf_001tf__sz,type,
% 0.30/0.46 singleton_rel_sf_sz: produc861709536_sz_sz > produc861709536_sz_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OConst_001tf__a_001tf__c,type,
% 0.30/0.46 const_a_c: real > trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OConst_001tf__sf_001tf__sz,type,
% 0.30/0.46 const_sf_sz: real > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_ODiffVar_001tf__c_001tf__a,type,
% 0.30/0.46 diffVar_c_a: c > trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_ODiffVar_001tf__sz_001tf__sf,type,
% 0.30/0.46 diffVar_sz_sf: sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_ODifferential_001tf__a_001tf__c,type,
% 0.30/0.46 differential_a_c: trm_a_c > trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_ODifferential_001tf__sf_001tf__sz,type,
% 0.30/0.46 differential_sf_sz: trm_sf_sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OFunction_001tf__a_001tf__c,type,
% 0.30/0.46 function_a_c: a > ( c > trm_a_c ) > trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OFunction_001tf__sf_001tf__sz,type,
% 0.30/0.46 function_sf_sz: sf > ( sz > trm_sf_sz ) > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OPlus_001tf__a_001tf__c,type,
% 0.30/0.46 plus_a_c: trm_a_c > trm_a_c > trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OPlus_001tf__sf_001tf__sz,type,
% 0.30/0.46 plus_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OTimes_001tf__a_001tf__c,type,
% 0.30/0.46 times_a_c: trm_a_c > trm_a_c > trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OTimes_001tf__sf_001tf__sz,type,
% 0.30/0.46 times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OVar_001tf__c_001tf__a,type,
% 0.30/0.46 var_c_a: c > trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_OVar_001tf__sz_001tf__sf,type,
% 0.30/0.46 var_sz_sf: sz > trm_sf_sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_Oset__trm_001tf__a_001tf__c,type,
% 0.30/0.46 set_trm_a_c2: trm_a_c > set_a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Syntax_Otrm_Oset__trm_001tf__sf_001tf__sz,type,
% 0.30/0.46 set_trm_sf_sz2: trm_sf_sz > set_sf ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Transfer_Oleft__unique_001t__Syntax__Otrm_Itf__a_Mtf__c_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__c_J,type,
% 0.30/0.46 left_u968903956rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Transfer_Oleft__unique_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J,type,
% 0.30/0.46 left_u638806404_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Transfer_Oright__unique_001t__Syntax__Otrm_Itf__a_Mtf__c_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__c_J,type,
% 0.30/0.46 right_1933252621rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Transfer_Oright__unique_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J,type,
% 0.30/0.46 right_963419005_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_Mtf__sz_J,type,
% 0.30/0.46 accp_P529224471_sz_sz: ( produc861709536_sz_sz > produc861709536_sz_sz > $o ) > produc861709536_sz_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 0.30/0.46 member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 0.30/0.46 member235934813t_unit: produc999471430t_unit > set_Pr2041213564t_unit > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 0.30/0.46 member_trm_a_c: trm_a_c > set_trm_a_c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 0.30/0.46 member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001tf__a,type,
% 0.30/0.46 member_a: a > set_a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001tf__sf,type,
% 0.30/0.46 member_sf: sf > set_sf > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_I,type,
% 0.30/0.46 i: denota231621370t_unit ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v__092_060nu_062,type,
% 0.30/0.46 nu: produc190496183real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v__092_060nu_062_H,type,
% 0.30/0.46 nu2: produc190496183real_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_args____,type,
% 0.30/0.46 args: c > trm_a_c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_i,type,
% 0.30/0.46 i2: c ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_var____,type,
% 0.30/0.46 var: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_vid1,type,
% 0.30/0.46 vid1: sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_vid2,type,
% 0.30/0.46 vid2: sz ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_vid3,type,
% 0.30/0.46 vid3: sz ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (353)
% 0.30/0.46 thf(fact_0_free,axiom,
% 0.30/0.46 ! [I: c] : ( dfree_a_c @ ( args @ I ) ) ).
% 0.30/0.46
% 0.30/0.46 % free
% 0.30/0.46 thf(fact_1_P__def,axiom,
% 0.30/0.46 p_sc_sf_sz = predic913887884_sf_sz ).
% 0.30/0.46
% 0.30/0.46 % P_def
% 0.30/0.46 thf(fact_2_strm_Odomain,axiom,
% 0.30/0.46 ( ( domain512309999_sf_sz @ freche1244000341_sf_sz )
% 0.30/0.46 = dfree_sf_sz ) ).
% 0.30/0.46
% 0.30/0.46 % strm.domain
% 0.30/0.46 thf(fact_3_strm_Odomain,axiom,
% 0.30/0.46 ( ( domain2047240575rm_a_c @ frechet_cr_strm_a_c )
% 0.30/0.46 = dfree_a_c ) ).
% 0.30/0.46
% 0.30/0.46 % strm.domain
% 0.30/0.46 thf(fact_4_dfree__DiffVar__simps,axiom,
% 0.30/0.46 ! [X: sz] :
% 0.30/0.46 ~ ( dfree_sf_sz @ ( diffVar_sz_sf @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_DiffVar_simps
% 0.30/0.46 thf(fact_5_dfree__DiffVar__simps,axiom,
% 0.30/0.46 ! [X: c] :
% 0.30/0.46 ~ ( dfree_a_c @ ( diffVar_c_a @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_DiffVar_simps
% 0.30/0.46 thf(fact_6_seq__sem_Ocases,axiom,
% 0.30/0.46 ! [X: produc1821101996_sc_sz] :
% 0.30/0.46 ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( produc789536734_sc_sz @ I2 @ S ) ) ).
% 0.30/0.46
% 0.30/0.46 % seq_sem.cases
% 0.30/0.46 thf(fact_7_singleton_Ocases,axiom,
% 0.30/0.46 ! [X: produc861709536_sz_sz] :
% 0.30/0.46 ~ ! [T: trm_sf_sz,I3: sz] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( produc792909658_sz_sz @ T @ I3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton.cases
% 0.30/0.46 thf(fact_8_dfree__Differential__simps,axiom,
% 0.30/0.46 ! [X: trm_sf_sz] :
% 0.30/0.46 ~ ( dfree_sf_sz @ ( differential_sf_sz @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Differential_simps
% 0.30/0.46 thf(fact_9_dfree__Differential__simps,axiom,
% 0.30/0.46 ! [X: trm_a_c] :
% 0.30/0.46 ~ ( dfree_a_c @ ( differential_a_c @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Differential_simps
% 0.30/0.46 thf(fact_10_dfree__Var__simps,axiom,
% 0.30/0.46 ! [X: c] : ( dfree_a_c @ ( var_c_a @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Var_simps
% 0.30/0.46 thf(fact_11_dfree__Var__simps,axiom,
% 0.30/0.46 ! [X: sz] : ( dfree_sf_sz @ ( var_sz_sf @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Var_simps
% 0.30/0.46 thf(fact_12_dfree__Times__simps,axiom,
% 0.30/0.46 ! [A: trm_a_c,B: trm_a_c] :
% 0.30/0.46 ( ( dfree_a_c @ ( times_a_c @ A @ B ) )
% 0.30/0.46 = ( ( dfree_a_c @ A )
% 0.30/0.46 & ( dfree_a_c @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Times_simps
% 0.30/0.46 thf(fact_13_dfree__Times__simps,axiom,
% 0.30/0.46 ! [A: trm_sf_sz,B: trm_sf_sz] :
% 0.30/0.46 ( ( dfree_sf_sz @ ( times_sf_sz @ A @ B ) )
% 0.30/0.46 = ( ( dfree_sf_sz @ A )
% 0.30/0.46 & ( dfree_sf_sz @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Times_simps
% 0.30/0.46 thf(fact_14_dfree__Plus__simps,axiom,
% 0.30/0.46 ! [A: trm_a_c,B: trm_a_c] :
% 0.30/0.46 ( ( dfree_a_c @ ( plus_a_c @ A @ B ) )
% 0.30/0.46 = ( ( dfree_a_c @ A )
% 0.30/0.46 & ( dfree_a_c @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Plus_simps
% 0.30/0.46 thf(fact_15_dfree__Plus__simps,axiom,
% 0.30/0.46 ! [A: trm_sf_sz,B: trm_sf_sz] :
% 0.30/0.46 ( ( dfree_sf_sz @ ( plus_sf_sz @ A @ B ) )
% 0.30/0.46 = ( ( dfree_sf_sz @ A )
% 0.30/0.46 & ( dfree_sf_sz @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Plus_simps
% 0.30/0.46 thf(fact_16_dfree__Fun_Oprems,axiom,
% 0.30/0.46 denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( function_a_c @ var @ args ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Fun.prems
% 0.30/0.46 thf(fact_17_trm_Oinject_I3_J,axiom,
% 0.30/0.46 ! [X31: a,X32: c > trm_a_c,Y31: a,Y32: c > trm_a_c] :
% 0.30/0.46 ( ( ( function_a_c @ X31 @ X32 )
% 0.30/0.46 = ( function_a_c @ Y31 @ Y32 ) )
% 0.30/0.46 = ( ( X31 = Y31 )
% 0.30/0.46 & ( X32 = Y32 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(3)
% 0.30/0.46 thf(fact_18_trm_Oinject_I3_J,axiom,
% 0.30/0.46 ! [X31: sf,X32: sz > trm_sf_sz,Y31: sf,Y32: sz > trm_sf_sz] :
% 0.30/0.46 ( ( ( function_sf_sz @ X31 @ X32 )
% 0.30/0.46 = ( function_sf_sz @ Y31 @ Y32 ) )
% 0.30/0.46 = ( ( X31 = Y31 )
% 0.30/0.46 & ( X32 = Y32 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(3)
% 0.30/0.46 thf(fact_19_trm_Oinject_I4_J,axiom,
% 0.30/0.46 ! [X41: trm_sf_sz,X42: trm_sf_sz,Y41: trm_sf_sz,Y42: trm_sf_sz] :
% 0.30/0.46 ( ( ( plus_sf_sz @ X41 @ X42 )
% 0.30/0.46 = ( plus_sf_sz @ Y41 @ Y42 ) )
% 0.30/0.46 = ( ( X41 = Y41 )
% 0.30/0.46 & ( X42 = Y42 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(4)
% 0.30/0.46 thf(fact_20_trm_Oinject_I4_J,axiom,
% 0.30/0.46 ! [X41: trm_a_c,X42: trm_a_c,Y41: trm_a_c,Y42: trm_a_c] :
% 0.30/0.46 ( ( ( plus_a_c @ X41 @ X42 )
% 0.30/0.46 = ( plus_a_c @ Y41 @ Y42 ) )
% 0.30/0.46 = ( ( X41 = Y41 )
% 0.30/0.46 & ( X42 = Y42 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(4)
% 0.30/0.46 thf(fact_21_trm_Oinject_I5_J,axiom,
% 0.30/0.46 ! [X51: trm_sf_sz,X52: trm_sf_sz,Y51: trm_sf_sz,Y52: trm_sf_sz] :
% 0.30/0.46 ( ( ( times_sf_sz @ X51 @ X52 )
% 0.30/0.46 = ( times_sf_sz @ Y51 @ Y52 ) )
% 0.30/0.46 = ( ( X51 = Y51 )
% 0.30/0.46 & ( X52 = Y52 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(5)
% 0.30/0.46 thf(fact_22_trm_Oinject_I5_J,axiom,
% 0.30/0.46 ! [X51: trm_a_c,X52: trm_a_c,Y51: trm_a_c,Y52: trm_a_c] :
% 0.30/0.46 ( ( ( times_a_c @ X51 @ X52 )
% 0.30/0.46 = ( times_a_c @ Y51 @ Y52 ) )
% 0.30/0.46 = ( ( X51 = Y51 )
% 0.30/0.46 & ( X52 = Y52 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(5)
% 0.30/0.46 thf(fact_23_trm_Oinject_I1_J,axiom,
% 0.30/0.46 ! [X1: sz,Y1: sz] :
% 0.30/0.46 ( ( ( var_sz_sf @ X1 )
% 0.30/0.46 = ( var_sz_sf @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(1)
% 0.30/0.46 thf(fact_24_trm_Oinject_I1_J,axiom,
% 0.30/0.46 ! [X1: c,Y1: c] :
% 0.30/0.46 ( ( ( var_c_a @ X1 )
% 0.30/0.46 = ( var_c_a @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(1)
% 0.30/0.46 thf(fact_25_trm_Oinject_I7_J,axiom,
% 0.30/0.46 ! [X7: trm_sf_sz,Y7: trm_sf_sz] :
% 0.30/0.46 ( ( ( differential_sf_sz @ X7 )
% 0.30/0.46 = ( differential_sf_sz @ Y7 ) )
% 0.30/0.46 = ( X7 = Y7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(7)
% 0.30/0.46 thf(fact_26_trm_Oinject_I7_J,axiom,
% 0.30/0.46 ! [X7: trm_a_c,Y7: trm_a_c] :
% 0.30/0.46 ( ( ( differential_a_c @ X7 )
% 0.30/0.46 = ( differential_a_c @ Y7 ) )
% 0.30/0.46 = ( X7 = Y7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(7)
% 0.30/0.46 thf(fact_27_trm_Oinject_I6_J,axiom,
% 0.30/0.46 ! [X6: sz,Y6: sz] :
% 0.30/0.46 ( ( ( diffVar_sz_sf @ X6 )
% 0.30/0.46 = ( diffVar_sz_sf @ Y6 ) )
% 0.30/0.46 = ( X6 = Y6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(6)
% 0.30/0.46 thf(fact_28_trm_Oinject_I6_J,axiom,
% 0.30/0.46 ! [X6: c,Y6: c] :
% 0.30/0.46 ( ( ( diffVar_c_a @ X6 )
% 0.30/0.46 = ( diffVar_c_a @ Y6 ) )
% 0.30/0.46 = ( X6 = Y6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(6)
% 0.30/0.46 thf(fact_29_dfree__Fun__simps,axiom,
% 0.30/0.46 ! [I: a,Args: c > trm_a_c] :
% 0.30/0.46 ( ( dfree_a_c @ ( function_a_c @ I @ Args ) )
% 0.30/0.46 = ( ! [X2: c] : ( dfree_a_c @ ( Args @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Fun_simps
% 0.30/0.46 thf(fact_30_dfree__Fun__simps,axiom,
% 0.30/0.46 ! [I: sf,Args: sz > trm_sf_sz] :
% 0.30/0.46 ( ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) )
% 0.30/0.46 = ( ! [X2: sz] : ( dfree_sf_sz @ ( Args @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Fun_simps
% 0.30/0.46 thf(fact_31_trm_Odistinct_I41_J,axiom,
% 0.30/0.46 ! [X6: sz,X7: trm_sf_sz] :
% 0.30/0.46 ( ( diffVar_sz_sf @ X6 )
% 0.30/0.46 != ( differential_sf_sz @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(41)
% 0.30/0.46 thf(fact_32_trm_Odistinct_I41_J,axiom,
% 0.30/0.46 ! [X6: c,X7: trm_a_c] :
% 0.30/0.46 ( ( diffVar_c_a @ X6 )
% 0.30/0.46 != ( differential_a_c @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(41)
% 0.30/0.46 thf(fact_33_trm_Odistinct_I39_J,axiom,
% 0.30/0.46 ! [X51: trm_sf_sz,X52: trm_sf_sz,X7: trm_sf_sz] :
% 0.30/0.46 ( ( times_sf_sz @ X51 @ X52 )
% 0.30/0.46 != ( differential_sf_sz @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(39)
% 0.30/0.46 thf(fact_34_trm_Odistinct_I39_J,axiom,
% 0.30/0.46 ! [X51: trm_a_c,X52: trm_a_c,X7: trm_a_c] :
% 0.30/0.46 ( ( times_a_c @ X51 @ X52 )
% 0.30/0.46 != ( differential_a_c @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(39)
% 0.30/0.46 thf(fact_35_trm_Odistinct_I37_J,axiom,
% 0.30/0.46 ! [X51: trm_sf_sz,X52: trm_sf_sz,X6: sz] :
% 0.30/0.46 ( ( times_sf_sz @ X51 @ X52 )
% 0.30/0.46 != ( diffVar_sz_sf @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(37)
% 0.30/0.46 thf(fact_36_trm_Odistinct_I37_J,axiom,
% 0.30/0.46 ! [X51: trm_a_c,X52: trm_a_c,X6: c] :
% 0.30/0.46 ( ( times_a_c @ X51 @ X52 )
% 0.30/0.46 != ( diffVar_c_a @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(37)
% 0.30/0.46 thf(fact_37_trm_Odistinct_I35_J,axiom,
% 0.30/0.46 ! [X41: trm_sf_sz,X42: trm_sf_sz,X7: trm_sf_sz] :
% 0.30/0.46 ( ( plus_sf_sz @ X41 @ X42 )
% 0.30/0.46 != ( differential_sf_sz @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(35)
% 0.30/0.46 thf(fact_38_trm_Odistinct_I35_J,axiom,
% 0.30/0.46 ! [X41: trm_a_c,X42: trm_a_c,X7: trm_a_c] :
% 0.30/0.46 ( ( plus_a_c @ X41 @ X42 )
% 0.30/0.46 != ( differential_a_c @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(35)
% 0.30/0.46 thf(fact_39_trm_Odistinct_I33_J,axiom,
% 0.30/0.46 ! [X41: trm_sf_sz,X42: trm_sf_sz,X6: sz] :
% 0.30/0.46 ( ( plus_sf_sz @ X41 @ X42 )
% 0.30/0.46 != ( diffVar_sz_sf @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(33)
% 0.30/0.46 thf(fact_40_trm_Odistinct_I33_J,axiom,
% 0.30/0.46 ! [X41: trm_a_c,X42: trm_a_c,X6: c] :
% 0.30/0.46 ( ( plus_a_c @ X41 @ X42 )
% 0.30/0.46 != ( diffVar_c_a @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(33)
% 0.30/0.46 thf(fact_41_trm_Odistinct_I31_J,axiom,
% 0.30/0.46 ! [X41: trm_sf_sz,X42: trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 0.30/0.46 ( ( plus_sf_sz @ X41 @ X42 )
% 0.30/0.46 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(31)
% 0.30/0.46 thf(fact_42_trm_Odistinct_I31_J,axiom,
% 0.30/0.46 ! [X41: trm_a_c,X42: trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 0.30/0.46 ( ( plus_a_c @ X41 @ X42 )
% 0.30/0.46 != ( times_a_c @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(31)
% 0.30/0.46 thf(fact_43_trm_Odistinct_I29_J,axiom,
% 0.30/0.46 ! [X31: sf,X32: sz > trm_sf_sz,X7: trm_sf_sz] :
% 0.30/0.46 ( ( function_sf_sz @ X31 @ X32 )
% 0.30/0.46 != ( differential_sf_sz @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(29)
% 0.30/0.46 thf(fact_44_trm_Odistinct_I29_J,axiom,
% 0.30/0.46 ! [X31: a,X32: c > trm_a_c,X7: trm_a_c] :
% 0.30/0.46 ( ( function_a_c @ X31 @ X32 )
% 0.30/0.46 != ( differential_a_c @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(29)
% 0.30/0.46 thf(fact_45_trm_Odistinct_I27_J,axiom,
% 0.30/0.46 ! [X31: a,X32: c > trm_a_c,X6: c] :
% 0.30/0.46 ( ( function_a_c @ X31 @ X32 )
% 0.30/0.46 != ( diffVar_c_a @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(27)
% 0.30/0.46 thf(fact_46_trm_Odistinct_I27_J,axiom,
% 0.30/0.46 ! [X31: sf,X32: sz > trm_sf_sz,X6: sz] :
% 0.30/0.46 ( ( function_sf_sz @ X31 @ X32 )
% 0.30/0.46 != ( diffVar_sz_sf @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(27)
% 0.30/0.46 thf(fact_47_trm_Odistinct_I25_J,axiom,
% 0.30/0.46 ! [X31: a,X32: c > trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 0.30/0.46 ( ( function_a_c @ X31 @ X32 )
% 0.30/0.46 != ( times_a_c @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(25)
% 0.30/0.46 thf(fact_48_trm_Odistinct_I25_J,axiom,
% 0.30/0.46 ! [X31: sf,X32: sz > trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 0.30/0.46 ( ( function_sf_sz @ X31 @ X32 )
% 0.30/0.46 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(25)
% 0.30/0.46 thf(fact_49_trm_Odistinct_I23_J,axiom,
% 0.30/0.46 ! [X31: a,X32: c > trm_a_c,X41: trm_a_c,X42: trm_a_c] :
% 0.30/0.46 ( ( function_a_c @ X31 @ X32 )
% 0.30/0.46 != ( plus_a_c @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(23)
% 0.30/0.46 thf(fact_50_trm_Odistinct_I23_J,axiom,
% 0.30/0.46 ! [X31: sf,X32: sz > trm_sf_sz,X41: trm_sf_sz,X42: trm_sf_sz] :
% 0.30/0.46 ( ( function_sf_sz @ X31 @ X32 )
% 0.30/0.46 != ( plus_sf_sz @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(23)
% 0.30/0.46 thf(fact_51_trm_Odistinct_I11_J,axiom,
% 0.30/0.46 ! [X1: sz,X7: trm_sf_sz] :
% 0.30/0.46 ( ( var_sz_sf @ X1 )
% 0.30/0.46 != ( differential_sf_sz @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(11)
% 0.30/0.46 thf(fact_52_trm_Odistinct_I11_J,axiom,
% 0.30/0.46 ! [X1: c,X7: trm_a_c] :
% 0.30/0.46 ( ( var_c_a @ X1 )
% 0.30/0.46 != ( differential_a_c @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(11)
% 0.30/0.46 thf(fact_53_trm_Odistinct_I9_J,axiom,
% 0.30/0.46 ! [X1: sz,X6: sz] :
% 0.30/0.46 ( ( var_sz_sf @ X1 )
% 0.30/0.46 != ( diffVar_sz_sf @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(9)
% 0.30/0.46 thf(fact_54_trm_Odistinct_I9_J,axiom,
% 0.30/0.46 ! [X1: c,X6: c] :
% 0.30/0.46 ( ( var_c_a @ X1 )
% 0.30/0.46 != ( diffVar_c_a @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(9)
% 0.30/0.46 thf(fact_55_trm_Odistinct_I7_J,axiom,
% 0.30/0.46 ! [X1: sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 0.30/0.46 ( ( var_sz_sf @ X1 )
% 0.30/0.46 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(7)
% 0.30/0.46 thf(fact_56_trm_Odistinct_I7_J,axiom,
% 0.30/0.46 ! [X1: c,X51: trm_a_c,X52: trm_a_c] :
% 0.30/0.46 ( ( var_c_a @ X1 )
% 0.30/0.46 != ( times_a_c @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(7)
% 0.30/0.46 thf(fact_57_trm_Odistinct_I5_J,axiom,
% 0.30/0.46 ! [X1: sz,X41: trm_sf_sz,X42: trm_sf_sz] :
% 0.30/0.46 ( ( var_sz_sf @ X1 )
% 0.30/0.46 != ( plus_sf_sz @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(5)
% 0.30/0.46 thf(fact_58_trm_Odistinct_I5_J,axiom,
% 0.30/0.46 ! [X1: c,X41: trm_a_c,X42: trm_a_c] :
% 0.30/0.46 ( ( var_c_a @ X1 )
% 0.30/0.46 != ( plus_a_c @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(5)
% 0.30/0.46 thf(fact_59_trm_Odistinct_I3_J,axiom,
% 0.30/0.46 ! [X1: c,X31: a,X32: c > trm_a_c] :
% 0.30/0.46 ( ( var_c_a @ X1 )
% 0.30/0.46 != ( function_a_c @ X31 @ X32 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(3)
% 0.30/0.46 thf(fact_60_trm_Odistinct_I3_J,axiom,
% 0.30/0.46 ! [X1: sz,X31: sf,X32: sz > trm_sf_sz] :
% 0.30/0.46 ( ( var_sz_sf @ X1 )
% 0.30/0.46 != ( function_sf_sz @ X31 @ X32 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(3)
% 0.30/0.46 thf(fact_61_dfree_Odfree__Fun,axiom,
% 0.30/0.46 ! [Args: c > trm_a_c,I: a] :
% 0.30/0.46 ( ! [I3: c] : ( dfree_a_c @ ( Args @ I3 ) )
% 0.30/0.46 => ( dfree_a_c @ ( function_a_c @ I @ Args ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree.dfree_Fun
% 0.30/0.46 thf(fact_62_dfree_Odfree__Fun,axiom,
% 0.30/0.46 ! [Args: sz > trm_sf_sz,I: sf] :
% 0.30/0.46 ( ! [I3: sz] : ( dfree_sf_sz @ ( Args @ I3 ) )
% 0.30/0.46 => ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree.dfree_Fun
% 0.30/0.46 thf(fact_63_dfree__Plus,axiom,
% 0.30/0.46 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 0.30/0.46 ( ( dfree_a_c @ Theta_1 )
% 0.30/0.46 => ( ( dfree_a_c @ Theta_2 )
% 0.30/0.46 => ( dfree_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Plus
% 0.30/0.46 thf(fact_64_dfree__Plus,axiom,
% 0.30/0.46 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 0.30/0.46 ( ( dfree_sf_sz @ Theta_1 )
% 0.30/0.46 => ( ( dfree_sf_sz @ Theta_2 )
% 0.30/0.46 => ( dfree_sf_sz @ ( plus_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Plus
% 0.30/0.46 thf(fact_65_dfree__Times,axiom,
% 0.30/0.46 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 0.30/0.46 ( ( dfree_a_c @ Theta_1 )
% 0.30/0.46 => ( ( dfree_a_c @ Theta_2 )
% 0.30/0.46 => ( dfree_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Times
% 0.30/0.46 thf(fact_66_dfree__Times,axiom,
% 0.30/0.46 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 0.30/0.46 ( ( dfree_sf_sz @ Theta_1 )
% 0.30/0.46 => ( ( dfree_sf_sz @ Theta_2 )
% 0.30/0.46 => ( dfree_sf_sz @ ( times_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Times
% 0.30/0.46 thf(fact_67_dfree__Var,axiom,
% 0.30/0.46 ! [I: sz] : ( dfree_sf_sz @ ( var_sz_sf @ I ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Var
% 0.30/0.46 thf(fact_68_dfree__Var,axiom,
% 0.30/0.46 ! [I: c] : ( dfree_a_c @ ( var_c_a @ I ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Var
% 0.30/0.46 thf(fact_69_agree__times1,axiom,
% 0.30/0.46 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.30/0.46 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 0.30/0.46 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_times1
% 0.30/0.46 thf(fact_70_agree__times1,axiom,
% 0.30/0.46 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.30/0.46 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 0.30/0.46 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_times1
% 0.30/0.46 thf(fact_71_agree__times2,axiom,
% 0.30/0.46 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.30/0.46 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 0.30/0.46 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_times2
% 0.30/0.46 thf(fact_72_agree__times2,axiom,
% 0.30/0.46 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.30/0.46 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 0.30/0.46 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_times2
% 0.30/0.46 thf(fact_73_agree__plus1,axiom,
% 0.30/0.46 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.30/0.46 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( plus_sf_sz @ T1 @ T2 ) ) )
% 0.30/0.46 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_plus1
% 0.30/0.46 thf(fact_74_agree__plus1,axiom,
% 0.30/0.46 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.30/0.46 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ T1 @ T2 ) ) )
% 0.30/0.46 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_plus1
% 0.30/0.46 thf(fact_75_agree__plus2,axiom,
% 0.30/0.46 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 0.30/0.46 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( plus_sf_sz @ T1 @ T2 ) ) )
% 0.30/0.46 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_plus2
% 0.30/0.46 thf(fact_76_agree__plus2,axiom,
% 0.30/0.46 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 0.30/0.46 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ T1 @ T2 ) ) )
% 0.30/0.46 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_plus2
% 0.30/0.46 thf(fact_77_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: produc999471430t_unit,P: produc999471430t_unit > $o] :
% 0.30/0.46 ( ( member235934813t_unit @ A @ ( collec377961627t_unit @ P ) )
% 0.30/0.46 = ( P @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_78_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: trm_sf_sz,P: trm_sf_sz > $o] :
% 0.30/0.46 ( ( member_trm_sf_sz @ A @ ( collect_trm_sf_sz @ P ) )
% 0.30/0.46 = ( P @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_79_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: trm_a_c,P: trm_a_c > $o] :
% 0.30/0.46 ( ( member_trm_a_c @ A @ ( collect_trm_a_c @ P ) )
% 0.30/0.46 = ( P @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_80_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: sf,P: sf > $o] :
% 0.30/0.46 ( ( member_sf @ A @ ( collect_sf @ P ) )
% 0.30/0.46 = ( P @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_81_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: a,P: a > $o] :
% 0.30/0.46 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.30/0.46 = ( P @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_82_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A2: set_Pr2041213564t_unit] :
% 0.30/0.46 ( ( collec377961627t_unit
% 0.30/0.46 @ ^ [X2: produc999471430t_unit] : ( member235934813t_unit @ X2 @ A2 ) )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_83_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A2: set_trm_sf_sz] :
% 0.30/0.46 ( ( collect_trm_sf_sz
% 0.30/0.46 @ ^ [X2: trm_sf_sz] : ( member_trm_sf_sz @ X2 @ A2 ) )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_84_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A2: set_trm_a_c] :
% 0.30/0.46 ( ( collect_trm_a_c
% 0.30/0.46 @ ^ [X2: trm_a_c] : ( member_trm_a_c @ X2 @ A2 ) )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_85_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A2: set_sf] :
% 0.30/0.46 ( ( collect_sf
% 0.30/0.46 @ ^ [X2: sf] : ( member_sf @ X2 @ A2 ) )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_86_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A2: set_a] :
% 0.30/0.46 ( ( collect_a
% 0.30/0.46 @ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_87_agree__func,axiom,
% 0.30/0.46 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,Var: sf,Args: sz > trm_sf_sz,I: sz] :
% 0.30/0.46 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( function_sf_sz @ Var @ Args ) ) )
% 0.30/0.46 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( Args @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_func
% 0.30/0.46 thf(fact_88_agree__func,axiom,
% 0.30/0.46 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Var: a,Args: c > trm_a_c,I: c] :
% 0.30/0.46 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( function_a_c @ Var @ Args ) ) )
% 0.30/0.46 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( Args @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % agree_func
% 0.30/0.46 thf(fact_89_prod_Oinject,axiom,
% 0.30/0.46 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz,Y1: list_f1238882004_sc_sz,Y2: list_f1238882004_sc_sz] :
% 0.30/0.46 ( ( ( produc1822718231_sc_sz @ X1 @ X22 )
% 0.30/0.46 = ( produc1822718231_sc_sz @ Y1 @ Y2 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X22 = Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_90_prod_Oinject,axiom,
% 0.30/0.46 ! [X1: finite1398487019real_c,X22: finite1398487019real_c,Y1: finite1398487019real_c,Y2: finite1398487019real_c] :
% 0.30/0.46 ( ( ( produc394644079real_c @ X1 @ X22 )
% 0.30/0.46 = ( produc394644079real_c @ Y1 @ Y2 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X22 = Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_91_prod_Oinject,axiom,
% 0.30/0.46 ! [X1: trm_sf_sz,X22: sz,Y1: trm_sf_sz,Y2: sz] :
% 0.30/0.46 ( ( ( produc792909658_sz_sz @ X1 @ X22 )
% 0.30/0.46 = ( produc792909658_sz_sz @ Y1 @ Y2 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X22 = Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_92_prod_Oinject,axiom,
% 0.30/0.46 ! [X1: produc866628903_sc_sz,X22: denota610675952t_unit,Y1: produc866628903_sc_sz,Y2: denota610675952t_unit] :
% 0.30/0.46 ( ( ( produc502616768t_unit @ X1 @ X22 )
% 0.30/0.46 = ( produc502616768t_unit @ Y1 @ Y2 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X22 = Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_93_prod_Oinject,axiom,
% 0.30/0.46 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz,Y1: denota610675952t_unit,Y2: produc866628903_sc_sz] :
% 0.30/0.46 ( ( ( produc789536734_sc_sz @ X1 @ X22 )
% 0.30/0.46 = ( produc789536734_sc_sz @ Y1 @ Y2 ) )
% 0.30/0.46 = ( ( X1 = Y1 )
% 0.30/0.46 & ( X22 = Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod.inject
% 0.30/0.46 thf(fact_94_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: list_f1238882004_sc_sz,B: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.30/0.46 ( ( ( produc1822718231_sc_sz @ A @ B )
% 0.30/0.46 = ( produc1822718231_sc_sz @ A3 @ B2 ) )
% 0.30/0.46 = ( ( A = A3 )
% 0.30/0.46 & ( B = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_95_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c,A3: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.30/0.46 ( ( ( produc394644079real_c @ A @ B )
% 0.30/0.46 = ( produc394644079real_c @ A3 @ B2 ) )
% 0.30/0.46 = ( ( A = A3 )
% 0.30/0.46 & ( B = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_96_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: trm_sf_sz,B: sz,A3: trm_sf_sz,B2: sz] :
% 0.30/0.46 ( ( ( produc792909658_sz_sz @ A @ B )
% 0.30/0.46 = ( produc792909658_sz_sz @ A3 @ B2 ) )
% 0.30/0.46 = ( ( A = A3 )
% 0.30/0.46 & ( B = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_97_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: produc866628903_sc_sz,B: denota610675952t_unit,A3: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 0.30/0.46 ( ( ( produc502616768t_unit @ A @ B )
% 0.30/0.46 = ( produc502616768t_unit @ A3 @ B2 ) )
% 0.30/0.46 = ( ( A = A3 )
% 0.30/0.46 & ( B = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_98_old_Oprod_Oinject,axiom,
% 0.30/0.46 ! [A: denota610675952t_unit,B: produc866628903_sc_sz,A3: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.30/0.46 ( ( ( produc789536734_sc_sz @ A @ B )
% 0.30/0.46 = ( produc789536734_sc_sz @ A3 @ B2 ) )
% 0.30/0.46 = ( ( A = A3 )
% 0.30/0.46 & ( B = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inject
% 0.30/0.46 thf(fact_99_trm_Oexhaust,axiom,
% 0.30/0.46 ! [Y: trm_sf_sz] :
% 0.30/0.46 ( ! [X12: sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( var_sz_sf @ X12 ) )
% 0.30/0.46 => ( ! [X23: real] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( const_sf_sz @ X23 ) )
% 0.30/0.46 => ( ! [X312: sf,X322: sz > trm_sf_sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( function_sf_sz @ X312 @ X322 ) )
% 0.30/0.46 => ( ! [X412: trm_sf_sz,X422: trm_sf_sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( plus_sf_sz @ X412 @ X422 ) )
% 0.30/0.46 => ( ! [X512: trm_sf_sz,X522: trm_sf_sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( times_sf_sz @ X512 @ X522 ) )
% 0.30/0.46 => ( ! [X62: sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( diffVar_sz_sf @ X62 ) )
% 0.30/0.46 => ~ ! [X72: trm_sf_sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( differential_sf_sz @ X72 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.exhaust
% 0.30/0.46 thf(fact_100_trm_Oexhaust,axiom,
% 0.30/0.46 ! [Y: trm_a_c] :
% 0.30/0.46 ( ! [X12: c] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( var_c_a @ X12 ) )
% 0.30/0.46 => ( ! [X23: real] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( const_a_c @ X23 ) )
% 0.30/0.46 => ( ! [X312: a,X322: c > trm_a_c] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( function_a_c @ X312 @ X322 ) )
% 0.30/0.46 => ( ! [X412: trm_a_c,X422: trm_a_c] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( plus_a_c @ X412 @ X422 ) )
% 0.30/0.46 => ( ! [X512: trm_a_c,X522: trm_a_c] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( times_a_c @ X512 @ X522 ) )
% 0.30/0.46 => ( ! [X62: c] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( diffVar_c_a @ X62 ) )
% 0.30/0.46 => ~ ! [X72: trm_a_c] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( differential_a_c @ X72 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.exhaust
% 0.30/0.46 thf(fact_101_prod__cases3,axiom,
% 0.30/0.46 ! [Y: produc1821101996_sc_sz] :
% 0.30/0.46 ~ ! [A4: denota610675952t_unit,B3: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B3 @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases3
% 0.30/0.46 thf(fact_102_trm_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X22: real,Y2: real] :
% 0.30/0.46 ( ( ( const_a_c @ X22 )
% 0.30/0.46 = ( const_a_c @ Y2 ) )
% 0.30/0.46 = ( X22 = Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(2)
% 0.30/0.46 thf(fact_103_trm_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X22: real,Y2: real] :
% 0.30/0.46 ( ( ( const_sf_sz @ X22 )
% 0.30/0.46 = ( const_sf_sz @ Y2 ) )
% 0.30/0.46 = ( X22 = Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.inject(2)
% 0.30/0.46 thf(fact_104_dfree__Const__simps,axiom,
% 0.30/0.46 ! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Const_simps
% 0.30/0.46 thf(fact_105_dfree__Const__simps,axiom,
% 0.30/0.46 ! [R: real] : ( dfree_sf_sz @ ( const_sf_sz @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Const_simps
% 0.30/0.46 thf(fact_106_dfree__Const,axiom,
% 0.30/0.46 ! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Const
% 0.30/0.46 thf(fact_107_dfree__Const,axiom,
% 0.30/0.46 ! [R: real] : ( dfree_sf_sz @ ( const_sf_sz @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree_Const
% 0.30/0.46 thf(fact_108_trm_Odistinct_I13_J,axiom,
% 0.30/0.46 ! [X22: real,X31: a,X32: c > trm_a_c] :
% 0.30/0.46 ( ( const_a_c @ X22 )
% 0.30/0.46 != ( function_a_c @ X31 @ X32 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(13)
% 0.30/0.46 thf(fact_109_trm_Odistinct_I13_J,axiom,
% 0.30/0.46 ! [X22: real,X31: sf,X32: sz > trm_sf_sz] :
% 0.30/0.46 ( ( const_sf_sz @ X22 )
% 0.30/0.46 != ( function_sf_sz @ X31 @ X32 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(13)
% 0.30/0.46 thf(fact_110_trm_Odistinct_I15_J,axiom,
% 0.30/0.46 ! [X22: real,X41: trm_a_c,X42: trm_a_c] :
% 0.30/0.46 ( ( const_a_c @ X22 )
% 0.30/0.46 != ( plus_a_c @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(15)
% 0.30/0.46 thf(fact_111_trm_Odistinct_I15_J,axiom,
% 0.30/0.46 ! [X22: real,X41: trm_sf_sz,X42: trm_sf_sz] :
% 0.30/0.46 ( ( const_sf_sz @ X22 )
% 0.30/0.46 != ( plus_sf_sz @ X41 @ X42 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(15)
% 0.30/0.46 thf(fact_112_trm_Odistinct_I17_J,axiom,
% 0.30/0.46 ! [X22: real,X51: trm_sf_sz,X52: trm_sf_sz] :
% 0.30/0.46 ( ( const_sf_sz @ X22 )
% 0.30/0.46 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(17)
% 0.30/0.46 thf(fact_113_trm_Odistinct_I17_J,axiom,
% 0.30/0.46 ! [X22: real,X51: trm_a_c,X52: trm_a_c] :
% 0.30/0.46 ( ( const_a_c @ X22 )
% 0.30/0.46 != ( times_a_c @ X51 @ X52 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(17)
% 0.30/0.46 thf(fact_114_trm_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X1: sz,X22: real] :
% 0.30/0.46 ( ( var_sz_sf @ X1 )
% 0.30/0.46 != ( const_sf_sz @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(1)
% 0.30/0.46 thf(fact_115_trm_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X1: c,X22: real] :
% 0.30/0.46 ( ( var_c_a @ X1 )
% 0.30/0.46 != ( const_a_c @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(1)
% 0.30/0.46 thf(fact_116_trm_Odistinct_I21_J,axiom,
% 0.30/0.46 ! [X22: real,X7: trm_sf_sz] :
% 0.30/0.46 ( ( const_sf_sz @ X22 )
% 0.30/0.46 != ( differential_sf_sz @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(21)
% 0.30/0.46 thf(fact_117_trm_Odistinct_I21_J,axiom,
% 0.30/0.46 ! [X22: real,X7: trm_a_c] :
% 0.30/0.46 ( ( const_a_c @ X22 )
% 0.30/0.46 != ( differential_a_c @ X7 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(21)
% 0.30/0.46 thf(fact_118_trm_Odistinct_I19_J,axiom,
% 0.30/0.46 ! [X22: real,X6: sz] :
% 0.30/0.46 ( ( const_sf_sz @ X22 )
% 0.30/0.46 != ( diffVar_sz_sf @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(19)
% 0.30/0.46 thf(fact_119_trm_Odistinct_I19_J,axiom,
% 0.30/0.46 ! [X22: real,X6: c] :
% 0.30/0.46 ( ( const_a_c @ X22 )
% 0.30/0.46 != ( diffVar_c_a @ X6 ) ) ).
% 0.30/0.46
% 0.30/0.46 % trm.distinct(19)
% 0.30/0.46 thf(fact_120_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [P: produc866628903_sc_sz > $o,Prod: produc866628903_sc_sz] :
% 0.30/0.46 ( ! [A4: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_121_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 0.30/0.46 ( ! [A4: finite1398487019real_c,B3: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_122_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [P: produc861709536_sz_sz > $o,Prod: produc861709536_sz_sz] :
% 0.30/0.46 ( ! [A4: trm_sf_sz,B3: sz] : ( P @ ( produc792909658_sz_sz @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_123_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [P: produc999471430t_unit > $o,Prod: produc999471430t_unit] :
% 0.30/0.46 ( ! [A4: produc866628903_sc_sz,B3: denota610675952t_unit] : ( P @ ( produc502616768t_unit @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_124_old_Oprod_Oinducts,axiom,
% 0.30/0.46 ! [P: produc1821101996_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 0.30/0.46 ( ! [A4: denota610675952t_unit,B3: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ Prod ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.inducts
% 0.30/0.46 thf(fact_125_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [Y: produc866628903_sc_sz] :
% 0.30/0.46 ~ ! [A4: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( produc1822718231_sc_sz @ A4 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_126_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [Y: produc190496183real_c] :
% 0.30/0.46 ~ ! [A4: finite1398487019real_c,B3: finite1398487019real_c] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( produc394644079real_c @ A4 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_127_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [Y: produc861709536_sz_sz] :
% 0.30/0.46 ~ ! [A4: trm_sf_sz,B3: sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( produc792909658_sz_sz @ A4 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_128_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [Y: produc999471430t_unit] :
% 0.30/0.46 ~ ! [A4: produc866628903_sc_sz,B3: denota610675952t_unit] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( produc502616768t_unit @ A4 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_129_old_Oprod_Oexhaust,axiom,
% 0.30/0.46 ! [Y: produc1821101996_sc_sz] :
% 0.30/0.46 ~ ! [A4: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( produc789536734_sc_sz @ A4 @ B3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.prod.exhaust
% 0.30/0.46 thf(fact_130_Pair__inject,axiom,
% 0.30/0.46 ! [A: list_f1238882004_sc_sz,B: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.30/0.46 ( ( ( produc1822718231_sc_sz @ A @ B )
% 0.30/0.46 = ( produc1822718231_sc_sz @ A3 @ B2 ) )
% 0.30/0.46 => ~ ( ( A = A3 )
% 0.30/0.46 => ( B != B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_131_Pair__inject,axiom,
% 0.30/0.46 ! [A: finite1398487019real_c,B: finite1398487019real_c,A3: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.30/0.46 ( ( ( produc394644079real_c @ A @ B )
% 0.30/0.46 = ( produc394644079real_c @ A3 @ B2 ) )
% 0.30/0.46 => ~ ( ( A = A3 )
% 0.30/0.46 => ( B != B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_132_Pair__inject,axiom,
% 0.30/0.46 ! [A: trm_sf_sz,B: sz,A3: trm_sf_sz,B2: sz] :
% 0.30/0.46 ( ( ( produc792909658_sz_sz @ A @ B )
% 0.30/0.46 = ( produc792909658_sz_sz @ A3 @ B2 ) )
% 0.30/0.46 => ~ ( ( A = A3 )
% 0.30/0.46 => ( B != B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_133_Pair__inject,axiom,
% 0.30/0.46 ! [A: produc866628903_sc_sz,B: denota610675952t_unit,A3: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 0.30/0.46 ( ( ( produc502616768t_unit @ A @ B )
% 0.30/0.46 = ( produc502616768t_unit @ A3 @ B2 ) )
% 0.30/0.46 => ~ ( ( A = A3 )
% 0.30/0.46 => ( B != B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_134_Pair__inject,axiom,
% 0.30/0.46 ! [A: denota610675952t_unit,B: produc866628903_sc_sz,A3: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.30/0.46 ( ( ( produc789536734_sc_sz @ A @ B )
% 0.30/0.46 = ( produc789536734_sc_sz @ A3 @ B2 ) )
% 0.30/0.46 => ~ ( ( A = A3 )
% 0.30/0.46 => ( B != B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Pair_inject
% 0.30/0.46 thf(fact_135_prod__cases,axiom,
% 0.30/0.46 ! [P: produc866628903_sc_sz > $o,P2: produc866628903_sc_sz] :
% 0.30/0.46 ( ! [A4: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_136_prod__cases,axiom,
% 0.30/0.46 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 0.30/0.46 ( ! [A4: finite1398487019real_c,B3: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_137_prod__cases,axiom,
% 0.30/0.46 ! [P: produc861709536_sz_sz > $o,P2: produc861709536_sz_sz] :
% 0.30/0.46 ( ! [A4: trm_sf_sz,B3: sz] : ( P @ ( produc792909658_sz_sz @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_138_prod__cases,axiom,
% 0.30/0.46 ! [P: produc999471430t_unit > $o,P2: produc999471430t_unit] :
% 0.30/0.46 ( ! [A4: produc866628903_sc_sz,B3: denota610675952t_unit] : ( P @ ( produc502616768t_unit @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_139_prod__cases,axiom,
% 0.30/0.46 ! [P: produc1821101996_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 0.30/0.46 ( ! [A4: denota610675952t_unit,B3: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B3 ) )
% 0.30/0.46 => ( P @ P2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_cases
% 0.30/0.46 thf(fact_140_surj__pair,axiom,
% 0.30/0.46 ! [P2: produc866628903_sc_sz] :
% 0.30/0.46 ? [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( produc1822718231_sc_sz @ X3 @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_141_surj__pair,axiom,
% 0.30/0.46 ! [P2: produc190496183real_c] :
% 0.30/0.46 ? [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( produc394644079real_c @ X3 @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_142_surj__pair,axiom,
% 0.30/0.46 ! [P2: produc861709536_sz_sz] :
% 0.30/0.46 ? [X3: trm_sf_sz,Y3: sz] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( produc792909658_sz_sz @ X3 @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_143_surj__pair,axiom,
% 0.30/0.46 ! [P2: produc999471430t_unit] :
% 0.30/0.46 ? [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( produc502616768t_unit @ X3 @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_144_surj__pair,axiom,
% 0.30/0.46 ! [P2: produc1821101996_sc_sz] :
% 0.30/0.46 ? [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.30/0.46 ( P2
% 0.30/0.46 = ( produc789536734_sc_sz @ X3 @ Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % surj_pair
% 0.30/0.46 thf(fact_145_dfree_Oinducts,axiom,
% 0.30/0.46 ! [X: trm_a_c,P: trm_a_c > $o] :
% 0.30/0.46 ( ( dfree_a_c @ X )
% 0.30/0.46 => ( ! [I3: c] : ( P @ ( var_c_a @ I3 ) )
% 0.30/0.46 => ( ! [R2: real] : ( P @ ( const_a_c @ R2 ) )
% 0.30/0.46 => ( ! [Args2: c > trm_a_c,I3: a] :
% 0.30/0.46 ( ! [Ia: c] : ( dfree_a_c @ ( Args2 @ Ia ) )
% 0.30/0.46 => ( ! [Ia: c] : ( P @ ( Args2 @ Ia ) )
% 0.30/0.46 => ( P @ ( function_a_c @ I3 @ Args2 ) ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 0.30/0.46 ( ( dfree_a_c @ Theta_12 )
% 0.30/0.46 => ( ( P @ Theta_12 )
% 0.30/0.46 => ( ( dfree_a_c @ Theta_22 )
% 0.30/0.46 => ( ( P @ Theta_22 )
% 0.30/0.46 => ( P @ ( plus_a_c @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 0.30/0.46 ( ( dfree_a_c @ Theta_12 )
% 0.30/0.46 => ( ( P @ Theta_12 )
% 0.30/0.46 => ( ( dfree_a_c @ Theta_22 )
% 0.30/0.46 => ( ( P @ Theta_22 )
% 0.30/0.46 => ( P @ ( times_a_c @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree.inducts
% 0.30/0.46 thf(fact_146_dfree_Oinducts,axiom,
% 0.30/0.46 ! [X: trm_sf_sz,P: trm_sf_sz > $o] :
% 0.30/0.46 ( ( dfree_sf_sz @ X )
% 0.30/0.46 => ( ! [I3: sz] : ( P @ ( var_sz_sf @ I3 ) )
% 0.30/0.46 => ( ! [R2: real] : ( P @ ( const_sf_sz @ R2 ) )
% 0.30/0.46 => ( ! [Args2: sz > trm_sf_sz,I3: sf] :
% 0.30/0.46 ( ! [Ia: sz] : ( dfree_sf_sz @ ( Args2 @ Ia ) )
% 0.30/0.46 => ( ! [Ia: sz] : ( P @ ( Args2 @ Ia ) )
% 0.30/0.46 => ( P @ ( function_sf_sz @ I3 @ Args2 ) ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 0.30/0.46 ( ( dfree_sf_sz @ Theta_12 )
% 0.30/0.46 => ( ( P @ Theta_12 )
% 0.30/0.46 => ( ( dfree_sf_sz @ Theta_22 )
% 0.30/0.46 => ( ( P @ Theta_22 )
% 0.30/0.46 => ( P @ ( plus_sf_sz @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 0.30/0.46 ( ( dfree_sf_sz @ Theta_12 )
% 0.30/0.46 => ( ( P @ Theta_12 )
% 0.30/0.46 => ( ( dfree_sf_sz @ Theta_22 )
% 0.30/0.46 => ( ( P @ Theta_22 )
% 0.30/0.46 => ( P @ ( times_sf_sz @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree.inducts
% 0.30/0.46 thf(fact_147_dfree_Osimps,axiom,
% 0.30/0.46 ( dfree_a_c
% 0.30/0.46 = ( ^ [A5: trm_a_c] :
% 0.30/0.46 ( ? [I4: c] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( var_c_a @ I4 ) )
% 0.30/0.46 | ? [R3: real] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( const_a_c @ R3 ) )
% 0.30/0.46 | ? [Args3: c > trm_a_c,I4: a] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( function_a_c @ I4 @ Args3 ) )
% 0.30/0.46 & ! [X2: c] : ( dfree_a_c @ ( Args3 @ X2 ) ) )
% 0.30/0.46 | ? [Theta_13: trm_a_c,Theta_23: trm_a_c] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( plus_a_c @ Theta_13 @ Theta_23 ) )
% 0.30/0.46 & ( dfree_a_c @ Theta_13 )
% 0.30/0.46 & ( dfree_a_c @ Theta_23 ) )
% 0.30/0.46 | ? [Theta_13: trm_a_c,Theta_23: trm_a_c] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( times_a_c @ Theta_13 @ Theta_23 ) )
% 0.30/0.46 & ( dfree_a_c @ Theta_13 )
% 0.30/0.46 & ( dfree_a_c @ Theta_23 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree.simps
% 0.30/0.46 thf(fact_148_dfree_Osimps,axiom,
% 0.30/0.46 ( dfree_sf_sz
% 0.30/0.46 = ( ^ [A5: trm_sf_sz] :
% 0.30/0.46 ( ? [I4: sz] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( var_sz_sf @ I4 ) )
% 0.30/0.46 | ? [R3: real] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( const_sf_sz @ R3 ) )
% 0.30/0.46 | ? [Args3: sz > trm_sf_sz,I4: sf] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( function_sf_sz @ I4 @ Args3 ) )
% 0.30/0.46 & ! [X2: sz] : ( dfree_sf_sz @ ( Args3 @ X2 ) ) )
% 0.30/0.46 | ? [Theta_13: trm_sf_sz,Theta_23: trm_sf_sz] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( plus_sf_sz @ Theta_13 @ Theta_23 ) )
% 0.30/0.46 & ( dfree_sf_sz @ Theta_13 )
% 0.30/0.46 & ( dfree_sf_sz @ Theta_23 ) )
% 0.30/0.46 | ? [Theta_13: trm_sf_sz,Theta_23: trm_sf_sz] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( times_sf_sz @ Theta_13 @ Theta_23 ) )
% 0.30/0.46 & ( dfree_sf_sz @ Theta_13 )
% 0.30/0.46 & ( dfree_sf_sz @ Theta_23 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree.simps
% 0.30/0.46 thf(fact_149_dfree_Ocases,axiom,
% 0.30/0.46 ! [A: trm_a_c] :
% 0.30/0.46 ( ( dfree_a_c @ A )
% 0.30/0.46 => ( ! [I3: c] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( var_c_a @ I3 ) )
% 0.30/0.46 => ( ! [R2: real] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( const_a_c @ R2 ) )
% 0.30/0.46 => ( ! [Args2: c > trm_a_c] :
% 0.30/0.46 ( ? [I3: a] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( function_a_c @ I3 @ Args2 ) )
% 0.30/0.46 => ~ ! [I5: c] : ( dfree_a_c @ ( Args2 @ I5 ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( plus_a_c @ Theta_12 @ Theta_22 ) )
% 0.30/0.46 => ( ( dfree_a_c @ Theta_12 )
% 0.30/0.46 => ~ ( dfree_a_c @ Theta_22 ) ) )
% 0.30/0.46 => ~ ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( times_a_c @ Theta_12 @ Theta_22 ) )
% 0.30/0.46 => ( ( dfree_a_c @ Theta_12 )
% 0.30/0.46 => ~ ( dfree_a_c @ Theta_22 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree.cases
% 0.30/0.46 thf(fact_150_dfree_Ocases,axiom,
% 0.30/0.46 ! [A: trm_sf_sz] :
% 0.30/0.46 ( ( dfree_sf_sz @ A )
% 0.30/0.46 => ( ! [I3: sz] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( var_sz_sf @ I3 ) )
% 0.30/0.46 => ( ! [R2: real] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( const_sf_sz @ R2 ) )
% 0.30/0.46 => ( ! [Args2: sz > trm_sf_sz] :
% 0.30/0.46 ( ? [I3: sf] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( function_sf_sz @ I3 @ Args2 ) )
% 0.30/0.46 => ~ ! [I5: sz] : ( dfree_sf_sz @ ( Args2 @ I5 ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( plus_sf_sz @ Theta_12 @ Theta_22 ) )
% 0.30/0.46 => ( ( dfree_sf_sz @ Theta_12 )
% 0.30/0.46 => ~ ( dfree_sf_sz @ Theta_22 ) ) )
% 0.30/0.46 => ~ ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( times_sf_sz @ Theta_12 @ Theta_22 ) )
% 0.30/0.46 => ( ( dfree_sf_sz @ Theta_12 )
% 0.30/0.46 => ~ ( dfree_sf_sz @ Theta_22 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dfree.cases
% 0.30/0.46 thf(fact_151_prod__induct3,axiom,
% 0.30/0.46 ! [P: produc1821101996_sc_sz > $o,X: produc1821101996_sc_sz] :
% 0.30/0.46 ( ! [A4: denota610675952t_unit,B3: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B3 @ C ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % prod_induct3
% 0.30/0.46 thf(fact_152_f0__def,axiom,
% 0.30/0.46 ( f0_sf_sz
% 0.30/0.46 = ( ^ [F: sf] : ( function_sf_sz @ F @ empty_sz_sf ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % f0_def
% 0.30/0.46 thf(fact_153_dsafe_Oinducts,axiom,
% 0.30/0.46 ! [X: trm_sf_sz,P: trm_sf_sz > $o] :
% 0.30/0.46 ( ( dsafe_sf_sz @ X )
% 0.30/0.46 => ( ! [I3: sz] : ( P @ ( var_sz_sf @ I3 ) )
% 0.30/0.46 => ( ! [R2: real] : ( P @ ( const_sf_sz @ R2 ) )
% 0.30/0.46 => ( ! [Args2: sz > trm_sf_sz,I3: sf] :
% 0.30/0.46 ( ! [Ia: sz] : ( dsafe_sf_sz @ ( Args2 @ Ia ) )
% 0.30/0.46 => ( ! [Ia: sz] : ( P @ ( Args2 @ Ia ) )
% 0.30/0.46 => ( P @ ( function_sf_sz @ I3 @ Args2 ) ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 0.30/0.46 ( ( dsafe_sf_sz @ Theta_12 )
% 0.30/0.46 => ( ( P @ Theta_12 )
% 0.30/0.46 => ( ( dsafe_sf_sz @ Theta_22 )
% 0.30/0.46 => ( ( P @ Theta_22 )
% 0.30/0.46 => ( P @ ( plus_sf_sz @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 0.30/0.46 ( ( dsafe_sf_sz @ Theta_12 )
% 0.30/0.46 => ( ( P @ Theta_12 )
% 0.30/0.46 => ( ( dsafe_sf_sz @ Theta_22 )
% 0.30/0.46 => ( ( P @ Theta_22 )
% 0.30/0.46 => ( P @ ( times_sf_sz @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 0.30/0.46 => ( ! [Theta: trm_sf_sz] :
% 0.30/0.46 ( ( dfree_sf_sz @ Theta )
% 0.30/0.46 => ( P @ ( differential_sf_sz @ Theta ) ) )
% 0.30/0.46 => ( ! [I3: sz] : ( P @ ( diffVar_sz_sf @ I3 ) )
% 0.30/0.46 => ( P @ X ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe.inducts
% 0.30/0.46 thf(fact_154_dsafe_Oinducts,axiom,
% 0.30/0.46 ! [X: trm_a_c,P: trm_a_c > $o] :
% 0.30/0.46 ( ( dsafe_a_c @ X )
% 0.30/0.46 => ( ! [I3: c] : ( P @ ( var_c_a @ I3 ) )
% 0.30/0.46 => ( ! [R2: real] : ( P @ ( const_a_c @ R2 ) )
% 0.30/0.46 => ( ! [Args2: c > trm_a_c,I3: a] :
% 0.30/0.46 ( ! [Ia: c] : ( dsafe_a_c @ ( Args2 @ Ia ) )
% 0.30/0.46 => ( ! [Ia: c] : ( P @ ( Args2 @ Ia ) )
% 0.30/0.46 => ( P @ ( function_a_c @ I3 @ Args2 ) ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 0.30/0.46 ( ( dsafe_a_c @ Theta_12 )
% 0.30/0.46 => ( ( P @ Theta_12 )
% 0.30/0.46 => ( ( dsafe_a_c @ Theta_22 )
% 0.30/0.46 => ( ( P @ Theta_22 )
% 0.30/0.46 => ( P @ ( plus_a_c @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 0.30/0.46 ( ( dsafe_a_c @ Theta_12 )
% 0.30/0.46 => ( ( P @ Theta_12 )
% 0.30/0.46 => ( ( dsafe_a_c @ Theta_22 )
% 0.30/0.46 => ( ( P @ Theta_22 )
% 0.30/0.46 => ( P @ ( times_a_c @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 0.30/0.46 => ( ! [Theta: trm_a_c] :
% 0.30/0.46 ( ( dfree_a_c @ Theta )
% 0.30/0.46 => ( P @ ( differential_a_c @ Theta ) ) )
% 0.30/0.46 => ( ! [I3: c] : ( P @ ( diffVar_c_a @ I3 ) )
% 0.30/0.46 => ( P @ X ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe.inducts
% 0.30/0.46 thf(fact_155_dsafe_Osimps,axiom,
% 0.30/0.46 ( dsafe_sf_sz
% 0.30/0.46 = ( ^ [A5: trm_sf_sz] :
% 0.30/0.46 ( ? [I4: sz] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( var_sz_sf @ I4 ) )
% 0.30/0.46 | ? [R3: real] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( const_sf_sz @ R3 ) )
% 0.30/0.46 | ? [Args3: sz > trm_sf_sz,I4: sf] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( function_sf_sz @ I4 @ Args3 ) )
% 0.30/0.46 & ! [X2: sz] : ( dsafe_sf_sz @ ( Args3 @ X2 ) ) )
% 0.30/0.46 | ? [Theta_13: trm_sf_sz,Theta_23: trm_sf_sz] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( plus_sf_sz @ Theta_13 @ Theta_23 ) )
% 0.30/0.46 & ( dsafe_sf_sz @ Theta_13 )
% 0.30/0.46 & ( dsafe_sf_sz @ Theta_23 ) )
% 0.30/0.46 | ? [Theta_13: trm_sf_sz,Theta_23: trm_sf_sz] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( times_sf_sz @ Theta_13 @ Theta_23 ) )
% 0.30/0.46 & ( dsafe_sf_sz @ Theta_13 )
% 0.30/0.46 & ( dsafe_sf_sz @ Theta_23 ) )
% 0.30/0.46 | ? [Theta2: trm_sf_sz] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( differential_sf_sz @ Theta2 ) )
% 0.30/0.46 & ( dfree_sf_sz @ Theta2 ) )
% 0.30/0.46 | ? [I4: sz] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( diffVar_sz_sf @ I4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe.simps
% 0.30/0.46 thf(fact_156_dsafe_Osimps,axiom,
% 0.30/0.46 ( dsafe_a_c
% 0.30/0.46 = ( ^ [A5: trm_a_c] :
% 0.30/0.46 ( ? [I4: c] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( var_c_a @ I4 ) )
% 0.30/0.46 | ? [R3: real] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( const_a_c @ R3 ) )
% 0.30/0.46 | ? [Args3: c > trm_a_c,I4: a] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( function_a_c @ I4 @ Args3 ) )
% 0.30/0.46 & ! [X2: c] : ( dsafe_a_c @ ( Args3 @ X2 ) ) )
% 0.30/0.46 | ? [Theta_13: trm_a_c,Theta_23: trm_a_c] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( plus_a_c @ Theta_13 @ Theta_23 ) )
% 0.30/0.46 & ( dsafe_a_c @ Theta_13 )
% 0.30/0.46 & ( dsafe_a_c @ Theta_23 ) )
% 0.30/0.46 | ? [Theta_13: trm_a_c,Theta_23: trm_a_c] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( times_a_c @ Theta_13 @ Theta_23 ) )
% 0.30/0.46 & ( dsafe_a_c @ Theta_13 )
% 0.30/0.46 & ( dsafe_a_c @ Theta_23 ) )
% 0.30/0.46 | ? [Theta2: trm_a_c] :
% 0.30/0.46 ( ( A5
% 0.30/0.46 = ( differential_a_c @ Theta2 ) )
% 0.30/0.46 & ( dfree_a_c @ Theta2 ) )
% 0.30/0.46 | ? [I4: c] :
% 0.30/0.46 ( A5
% 0.30/0.46 = ( diffVar_c_a @ I4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe.simps
% 0.30/0.46 thf(fact_157_dsafe_Ocases,axiom,
% 0.30/0.46 ! [A: trm_sf_sz] :
% 0.30/0.46 ( ( dsafe_sf_sz @ A )
% 0.30/0.46 => ( ! [I3: sz] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( var_sz_sf @ I3 ) )
% 0.30/0.46 => ( ! [R2: real] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( const_sf_sz @ R2 ) )
% 0.30/0.46 => ( ! [Args2: sz > trm_sf_sz] :
% 0.30/0.46 ( ? [I3: sf] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( function_sf_sz @ I3 @ Args2 ) )
% 0.30/0.46 => ~ ! [I5: sz] : ( dsafe_sf_sz @ ( Args2 @ I5 ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( plus_sf_sz @ Theta_12 @ Theta_22 ) )
% 0.30/0.46 => ( ( dsafe_sf_sz @ Theta_12 )
% 0.30/0.46 => ~ ( dsafe_sf_sz @ Theta_22 ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( times_sf_sz @ Theta_12 @ Theta_22 ) )
% 0.30/0.46 => ( ( dsafe_sf_sz @ Theta_12 )
% 0.30/0.46 => ~ ( dsafe_sf_sz @ Theta_22 ) ) )
% 0.30/0.46 => ( ! [Theta: trm_sf_sz] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( differential_sf_sz @ Theta ) )
% 0.30/0.46 => ~ ( dfree_sf_sz @ Theta ) )
% 0.30/0.46 => ~ ! [I3: sz] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( diffVar_sz_sf @ I3 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe.cases
% 0.30/0.46 thf(fact_158_dsafe_Ocases,axiom,
% 0.30/0.46 ! [A: trm_a_c] :
% 0.30/0.46 ( ( dsafe_a_c @ A )
% 0.30/0.46 => ( ! [I3: c] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( var_c_a @ I3 ) )
% 0.30/0.46 => ( ! [R2: real] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( const_a_c @ R2 ) )
% 0.30/0.46 => ( ! [Args2: c > trm_a_c] :
% 0.30/0.46 ( ? [I3: a] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( function_a_c @ I3 @ Args2 ) )
% 0.30/0.46 => ~ ! [I5: c] : ( dsafe_a_c @ ( Args2 @ I5 ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( plus_a_c @ Theta_12 @ Theta_22 ) )
% 0.30/0.46 => ( ( dsafe_a_c @ Theta_12 )
% 0.30/0.46 => ~ ( dsafe_a_c @ Theta_22 ) ) )
% 0.30/0.46 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( times_a_c @ Theta_12 @ Theta_22 ) )
% 0.30/0.46 => ( ( dsafe_a_c @ Theta_12 )
% 0.30/0.46 => ~ ( dsafe_a_c @ Theta_22 ) ) )
% 0.30/0.46 => ( ! [Theta: trm_a_c] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( differential_a_c @ Theta ) )
% 0.30/0.46 => ~ ( dfree_a_c @ Theta ) )
% 0.30/0.46 => ~ ! [I3: c] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( diffVar_c_a @ I3 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe.cases
% 0.30/0.46 thf(fact_159_strm_Oright__unique,axiom,
% 0.30/0.46 right_963419005_sf_sz @ freche1244000341_sf_sz ).
% 0.30/0.46
% 0.30/0.46 % strm.right_unique
% 0.30/0.46 thf(fact_160_strm_Oright__unique,axiom,
% 0.30/0.46 right_1933252621rm_a_c @ frechet_cr_strm_a_c ).
% 0.30/0.46
% 0.30/0.46 % strm.right_unique
% 0.30/0.46 thf(fact_161_dsafe__Const__simps,axiom,
% 0.30/0.46 ! [R: real] : ( dsafe_a_c @ ( const_a_c @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Const_simps
% 0.30/0.46 thf(fact_162_dsafe__Const__simps,axiom,
% 0.30/0.46 ! [R: real] : ( dsafe_sf_sz @ ( const_sf_sz @ R ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Const_simps
% 0.30/0.46 thf(fact_163_dsafe__Fun__simps,axiom,
% 0.30/0.46 ! [I: a,Args: c > trm_a_c] :
% 0.30/0.46 ( ( dsafe_a_c @ ( function_a_c @ I @ Args ) )
% 0.30/0.46 = ( ! [X2: c] : ( dsafe_a_c @ ( Args @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Fun_simps
% 0.30/0.46 thf(fact_164_dsafe__Fun__simps,axiom,
% 0.30/0.46 ! [I: sf,Args: sz > trm_sf_sz] :
% 0.30/0.46 ( ( dsafe_sf_sz @ ( function_sf_sz @ I @ Args ) )
% 0.30/0.46 = ( ! [X2: sz] : ( dsafe_sf_sz @ ( Args @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Fun_simps
% 0.30/0.46 thf(fact_165_dsafe__Plus__simps,axiom,
% 0.30/0.46 ! [A: trm_sf_sz,B: trm_sf_sz] :
% 0.30/0.46 ( ( dsafe_sf_sz @ ( plus_sf_sz @ A @ B ) )
% 0.30/0.46 = ( ( dsafe_sf_sz @ A )
% 0.30/0.46 & ( dsafe_sf_sz @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Plus_simps
% 0.30/0.46 thf(fact_166_dsafe__Plus__simps,axiom,
% 0.30/0.46 ! [A: trm_a_c,B: trm_a_c] :
% 0.30/0.46 ( ( dsafe_a_c @ ( plus_a_c @ A @ B ) )
% 0.30/0.46 = ( ( dsafe_a_c @ A )
% 0.30/0.46 & ( dsafe_a_c @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Plus_simps
% 0.30/0.46 thf(fact_167_dsafe__Times__simps,axiom,
% 0.30/0.46 ! [A: trm_sf_sz,B: trm_sf_sz] :
% 0.30/0.46 ( ( dsafe_sf_sz @ ( times_sf_sz @ A @ B ) )
% 0.30/0.46 = ( ( dsafe_sf_sz @ A )
% 0.30/0.46 & ( dsafe_sf_sz @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Times_simps
% 0.30/0.46 thf(fact_168_dsafe__Times__simps,axiom,
% 0.30/0.46 ! [A: trm_a_c,B: trm_a_c] :
% 0.30/0.46 ( ( dsafe_a_c @ ( times_a_c @ A @ B ) )
% 0.30/0.46 = ( ( dsafe_a_c @ A )
% 0.30/0.46 & ( dsafe_a_c @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Times_simps
% 0.30/0.46 thf(fact_169_dsafe__Var__simps,axiom,
% 0.30/0.46 ! [X: sz] : ( dsafe_sf_sz @ ( var_sz_sf @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Var_simps
% 0.30/0.46 thf(fact_170_dsafe__Var__simps,axiom,
% 0.30/0.46 ! [X: c] : ( dsafe_a_c @ ( var_c_a @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_Var_simps
% 0.30/0.46 thf(fact_171_dsafe__DiffVar__simps,axiom,
% 0.30/0.46 ! [X: sz] : ( dsafe_sf_sz @ ( diffVar_sz_sf @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % dsafe_DiffVar_simps
% 0.30/0.46 thf(fact_172_dsafe__DiffVar__simps,axiom,
% 0.30/0.47 ! [X: c] : ( dsafe_a_c @ ( diffVar_c_a @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_DiffVar_simps
% 0.30/0.47 thf(fact_173_dsafe__Diff__simps,axiom,
% 0.30/0.47 ! [A: trm_sf_sz] :
% 0.30/0.47 ( ( dsafe_sf_sz @ ( differential_sf_sz @ A ) )
% 0.30/0.47 = ( dfree_sf_sz @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Diff_simps
% 0.30/0.47 thf(fact_174_dsafe__Diff__simps,axiom,
% 0.30/0.47 ! [A: trm_a_c] :
% 0.30/0.47 ( ( dsafe_a_c @ ( differential_a_c @ A ) )
% 0.30/0.47 = ( dfree_a_c @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Diff_simps
% 0.30/0.47 thf(fact_175_dfree__is__dsafe,axiom,
% 0.30/0.47 ! [Theta3: trm_a_c] :
% 0.30/0.47 ( ( dfree_a_c @ Theta3 )
% 0.30/0.47 => ( dsafe_a_c @ Theta3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % dfree_is_dsafe
% 0.30/0.47 thf(fact_176_dfree__is__dsafe,axiom,
% 0.30/0.47 ! [Theta3: trm_sf_sz] :
% 0.30/0.47 ( ( dfree_sf_sz @ Theta3 )
% 0.30/0.47 => ( dsafe_sf_sz @ Theta3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % dfree_is_dsafe
% 0.30/0.47 thf(fact_177_dsafe__Const,axiom,
% 0.30/0.47 ! [R: real] : ( dsafe_a_c @ ( const_a_c @ R ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Const
% 0.30/0.47 thf(fact_178_dsafe__Const,axiom,
% 0.30/0.47 ! [R: real] : ( dsafe_sf_sz @ ( const_sf_sz @ R ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Const
% 0.30/0.47 thf(fact_179_dsafe__Fun,axiom,
% 0.30/0.47 ! [Args: c > trm_a_c,I: a] :
% 0.30/0.47 ( ! [I3: c] : ( dsafe_a_c @ ( Args @ I3 ) )
% 0.30/0.47 => ( dsafe_a_c @ ( function_a_c @ I @ Args ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Fun
% 0.30/0.47 thf(fact_180_dsafe__Fun,axiom,
% 0.30/0.47 ! [Args: sz > trm_sf_sz,I: sf] :
% 0.30/0.47 ( ! [I3: sz] : ( dsafe_sf_sz @ ( Args @ I3 ) )
% 0.30/0.47 => ( dsafe_sf_sz @ ( function_sf_sz @ I @ Args ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Fun
% 0.30/0.47 thf(fact_181_dsafe__Plus,axiom,
% 0.30/0.47 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 0.30/0.47 ( ( dsafe_sf_sz @ Theta_1 )
% 0.30/0.47 => ( ( dsafe_sf_sz @ Theta_2 )
% 0.30/0.47 => ( dsafe_sf_sz @ ( plus_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Plus
% 0.30/0.47 thf(fact_182_dsafe__Plus,axiom,
% 0.30/0.47 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 0.30/0.47 ( ( dsafe_a_c @ Theta_1 )
% 0.30/0.47 => ( ( dsafe_a_c @ Theta_2 )
% 0.30/0.47 => ( dsafe_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Plus
% 0.30/0.47 thf(fact_183_dsafe__Times,axiom,
% 0.30/0.47 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 0.30/0.47 ( ( dsafe_sf_sz @ Theta_1 )
% 0.30/0.47 => ( ( dsafe_sf_sz @ Theta_2 )
% 0.30/0.47 => ( dsafe_sf_sz @ ( times_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Times
% 0.30/0.47 thf(fact_184_dsafe__Times,axiom,
% 0.30/0.47 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 0.30/0.47 ( ( dsafe_a_c @ Theta_1 )
% 0.30/0.47 => ( ( dsafe_a_c @ Theta_2 )
% 0.30/0.47 => ( dsafe_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Times
% 0.30/0.47 thf(fact_185_dsafe__Var,axiom,
% 0.30/0.47 ! [I: sz] : ( dsafe_sf_sz @ ( var_sz_sf @ I ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Var
% 0.30/0.47 thf(fact_186_dsafe__Var,axiom,
% 0.30/0.47 ! [I: c] : ( dsafe_a_c @ ( var_c_a @ I ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Var
% 0.30/0.47 thf(fact_187_dsafe__DiffVar,axiom,
% 0.30/0.47 ! [I: sz] : ( dsafe_sf_sz @ ( diffVar_sz_sf @ I ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_DiffVar
% 0.30/0.47 thf(fact_188_dsafe__DiffVar,axiom,
% 0.30/0.47 ! [I: c] : ( dsafe_a_c @ ( diffVar_c_a @ I ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_DiffVar
% 0.30/0.47 thf(fact_189_dsafe__Diff,axiom,
% 0.30/0.47 ! [Theta3: trm_sf_sz] :
% 0.30/0.47 ( ( dfree_sf_sz @ Theta3 )
% 0.30/0.47 => ( dsafe_sf_sz @ ( differential_sf_sz @ Theta3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Diff
% 0.30/0.47 thf(fact_190_dsafe__Diff,axiom,
% 0.30/0.47 ! [Theta3: trm_a_c] :
% 0.30/0.47 ( ( dfree_a_c @ Theta3 )
% 0.30/0.47 => ( dsafe_a_c @ ( differential_a_c @ Theta3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dsafe_Diff
% 0.30/0.47 thf(fact_191_local_Oempty__def,axiom,
% 0.30/0.47 ( empty_c_a
% 0.30/0.47 = ( ^ [I4: c] : ( const_a_c @ zero_zero_real ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.empty_def
% 0.30/0.47 thf(fact_192_local_Oempty__def,axiom,
% 0.30/0.47 ( empty_sz_sf
% 0.30/0.47 = ( ^ [I4: sz] : ( const_sf_sz @ zero_zero_real ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.empty_def
% 0.30/0.47 thf(fact_193_ids_Of0__def,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,F2: sf] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ( ( f0_sf_sz @ F2 )
% 0.30/0.47 = ( function_sf_sz @ F2 @ empty_sz_sf ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.f0_def
% 0.30/0.47 thf(fact_194_dfree__Fun_OIH,axiom,
% 0.30/0.47 ! [I: c] :
% 0.30/0.47 ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( args @ I ) ) )
% 0.30/0.47 => ( ( denota229585092_a_b_c @ i @ ( args @ I ) @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
% 0.30/0.47 = ( denota229585092_a_b_c @ i @ ( args @ I ) @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dfree_Fun.IH
% 0.30/0.47 thf(fact_195_strm_Oleft__unique,axiom,
% 0.30/0.47 left_u638806404_sf_sz @ freche1244000341_sf_sz ).
% 0.30/0.47
% 0.30/0.47 % strm.left_unique
% 0.30/0.47 thf(fact_196_strm_Oleft__unique,axiom,
% 0.30/0.47 left_u968903956rm_a_c @ frechet_cr_strm_a_c ).
% 0.30/0.47
% 0.30/0.47 % strm.left_unique
% 0.30/0.47 thf(fact_197_trm_Oinduct,axiom,
% 0.30/0.47 ! [P: trm_sf_sz > $o,Trm: trm_sf_sz] :
% 0.30/0.47 ( ! [X3: sz] : ( P @ ( var_sz_sf @ X3 ) )
% 0.30/0.47 => ( ! [X3: real] : ( P @ ( const_sf_sz @ X3 ) )
% 0.30/0.47 => ( ! [X1a: sf,X2a: sz > trm_sf_sz] :
% 0.30/0.47 ( ! [X2aa: trm_sf_sz] :
% 0.30/0.47 ( ( member_trm_sf_sz @ X2aa @ ( image_sz_trm_sf_sz @ X2a @ top_top_set_sz ) )
% 0.30/0.47 => ( P @ X2aa ) )
% 0.30/0.47 => ( P @ ( function_sf_sz @ X1a @ X2a ) ) )
% 0.30/0.47 => ( ! [X1a: trm_sf_sz,X2a: trm_sf_sz] :
% 0.30/0.47 ( ( P @ X1a )
% 0.30/0.47 => ( ( P @ X2a )
% 0.30/0.47 => ( P @ ( plus_sf_sz @ X1a @ X2a ) ) ) )
% 0.30/0.47 => ( ! [X1a: trm_sf_sz,X2a: trm_sf_sz] :
% 0.30/0.47 ( ( P @ X1a )
% 0.30/0.47 => ( ( P @ X2a )
% 0.30/0.47 => ( P @ ( times_sf_sz @ X1a @ X2a ) ) ) )
% 0.30/0.47 => ( ! [X3: sz] : ( P @ ( diffVar_sz_sf @ X3 ) )
% 0.30/0.47 => ( ! [X3: trm_sf_sz] :
% 0.30/0.47 ( ( P @ X3 )
% 0.30/0.47 => ( P @ ( differential_sf_sz @ X3 ) ) )
% 0.30/0.47 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.induct
% 0.30/0.47 thf(fact_198_trm_Oinduct,axiom,
% 0.30/0.47 ! [P: trm_a_c > $o,Trm: trm_a_c] :
% 0.30/0.47 ( ! [X3: c] : ( P @ ( var_c_a @ X3 ) )
% 0.30/0.47 => ( ! [X3: real] : ( P @ ( const_a_c @ X3 ) )
% 0.30/0.47 => ( ! [X1a: a,X2a: c > trm_a_c] :
% 0.30/0.47 ( ! [X2aa: trm_a_c] :
% 0.30/0.47 ( ( member_trm_a_c @ X2aa @ ( image_c_trm_a_c @ X2a @ top_top_set_c ) )
% 0.30/0.47 => ( P @ X2aa ) )
% 0.30/0.47 => ( P @ ( function_a_c @ X1a @ X2a ) ) )
% 0.30/0.47 => ( ! [X1a: trm_a_c,X2a: trm_a_c] :
% 0.30/0.47 ( ( P @ X1a )
% 0.30/0.47 => ( ( P @ X2a )
% 0.30/0.47 => ( P @ ( plus_a_c @ X1a @ X2a ) ) ) )
% 0.30/0.47 => ( ! [X1a: trm_a_c,X2a: trm_a_c] :
% 0.30/0.47 ( ( P @ X1a )
% 0.30/0.47 => ( ( P @ X2a )
% 0.30/0.47 => ( P @ ( times_a_c @ X1a @ X2a ) ) ) )
% 0.30/0.47 => ( ! [X3: c] : ( P @ ( diffVar_c_a @ X3 ) )
% 0.30/0.47 => ( ! [X3: trm_a_c] :
% 0.30/0.47 ( ( P @ X3 )
% 0.30/0.47 => ( P @ ( differential_a_c @ X3 ) ) )
% 0.30/0.47 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.induct
% 0.30/0.47 thf(fact_199_agree__comm,axiom,
% 0.30/0.47 ! [A2: produc1149990247eal_sz,B4: produc1149990247eal_sz,V: set_Sum_sum_sz_sz] :
% 0.30/0.47 ( ( denota102713844ree_sz @ A2 @ B4 @ V )
% 0.30/0.47 => ( denota102713844ree_sz @ B4 @ A2 @ V ) ) ).
% 0.30/0.47
% 0.30/0.47 % agree_comm
% 0.30/0.47 thf(fact_200_agree__comm,axiom,
% 0.30/0.47 ! [A2: produc190496183real_c,B4: produc190496183real_c,V: set_Sum_sum_c_c] :
% 0.30/0.47 ( ( denota1997846518gree_c @ A2 @ B4 @ V )
% 0.30/0.47 => ( denota1997846518gree_c @ B4 @ A2 @ V ) ) ).
% 0.30/0.47
% 0.30/0.47 % agree_comm
% 0.30/0.47 thf(fact_201_prod_Ocollapse,axiom,
% 0.30/0.47 ! [Prod: produc866628903_sc_sz] :
% 0.30/0.47 ( ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) )
% 0.30/0.47 = Prod ) ).
% 0.30/0.47
% 0.30/0.47 % prod.collapse
% 0.30/0.47 thf(fact_202_prod_Ocollapse,axiom,
% 0.30/0.47 ! [Prod: produc861709536_sz_sz] :
% 0.30/0.47 ( ( produc792909658_sz_sz @ ( produc2069561454_sz_sz @ Prod ) @ ( produc181739436_sz_sz @ Prod ) )
% 0.30/0.47 = Prod ) ).
% 0.30/0.47
% 0.30/0.47 % prod.collapse
% 0.30/0.47 thf(fact_203_prod_Ocollapse,axiom,
% 0.30/0.47 ! [Prod: produc999471430t_unit] :
% 0.30/0.47 ( ( produc502616768t_unit @ ( produc1216682964t_unit @ Prod ) @ ( produc687319826t_unit @ Prod ) )
% 0.30/0.47 = Prod ) ).
% 0.30/0.47
% 0.30/0.47 % prod.collapse
% 0.30/0.47 thf(fact_204_prod_Ocollapse,axiom,
% 0.30/0.47 ! [Prod: produc1821101996_sc_sz] :
% 0.30/0.47 ( ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) )
% 0.30/0.47 = Prod ) ).
% 0.30/0.47
% 0.30/0.47 % prod.collapse
% 0.30/0.47 thf(fact_205_prod_Ocollapse,axiom,
% 0.30/0.47 ! [Prod: produc190496183real_c] :
% 0.30/0.47 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 0.30/0.47 = Prod ) ).
% 0.30/0.47
% 0.30/0.47 % prod.collapse
% 0.30/0.47 thf(fact_206_prod_Oexhaust__sel,axiom,
% 0.30/0.47 ! [Prod: produc866628903_sc_sz] :
% 0.30/0.47 ( Prod
% 0.30/0.47 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.exhaust_sel
% 0.30/0.47 thf(fact_207_prod_Oexhaust__sel,axiom,
% 0.30/0.47 ! [Prod: produc861709536_sz_sz] :
% 0.30/0.47 ( Prod
% 0.30/0.47 = ( produc792909658_sz_sz @ ( produc2069561454_sz_sz @ Prod ) @ ( produc181739436_sz_sz @ Prod ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.exhaust_sel
% 0.30/0.47 thf(fact_208_prod_Oexhaust__sel,axiom,
% 0.30/0.47 ! [Prod: produc999471430t_unit] :
% 0.30/0.47 ( Prod
% 0.30/0.47 = ( produc502616768t_unit @ ( produc1216682964t_unit @ Prod ) @ ( produc687319826t_unit @ Prod ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.exhaust_sel
% 0.30/0.47 thf(fact_209_prod_Oexhaust__sel,axiom,
% 0.30/0.47 ! [Prod: produc1821101996_sc_sz] :
% 0.30/0.47 ( Prod
% 0.30/0.47 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.exhaust_sel
% 0.30/0.47 thf(fact_210_prod_Oexhaust__sel,axiom,
% 0.30/0.47 ! [Prod: produc190496183real_c] :
% 0.30/0.47 ( Prod
% 0.30/0.47 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.exhaust_sel
% 0.30/0.47 thf(fact_211_surjective__pairing,axiom,
% 0.30/0.47 ! [T3: produc866628903_sc_sz] :
% 0.30/0.47 ( T3
% 0.30/0.47 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ T3 ) @ ( produc4753477_sc_sz @ T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % surjective_pairing
% 0.30/0.47 thf(fact_212_surjective__pairing,axiom,
% 0.30/0.47 ! [T3: produc861709536_sz_sz] :
% 0.30/0.47 ( T3
% 0.30/0.47 = ( produc792909658_sz_sz @ ( produc2069561454_sz_sz @ T3 ) @ ( produc181739436_sz_sz @ T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % surjective_pairing
% 0.30/0.47 thf(fact_213_surjective__pairing,axiom,
% 0.30/0.47 ! [T3: produc999471430t_unit] :
% 0.30/0.47 ( T3
% 0.30/0.47 = ( produc502616768t_unit @ ( produc1216682964t_unit @ T3 ) @ ( produc687319826t_unit @ T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % surjective_pairing
% 0.30/0.47 thf(fact_214_surjective__pairing,axiom,
% 0.30/0.47 ! [T3: produc1821101996_sc_sz] :
% 0.30/0.47 ( T3
% 0.30/0.47 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ T3 ) @ ( produc974239792_sc_sz @ T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % surjective_pairing
% 0.30/0.47 thf(fact_215_surjective__pairing,axiom,
% 0.30/0.47 ! [T3: produc190496183real_c] :
% 0.30/0.47 ( T3
% 0.30/0.47 = ( produc394644079real_c @ ( produc2010422875real_c @ T3 ) @ ( produc314122909real_c @ T3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % surjective_pairing
% 0.30/0.47 thf(fact_216_agree__UNIV__eq,axiom,
% 0.30/0.47 ! [Nu: produc1149990247eal_sz,Omega: produc1149990247eal_sz] :
% 0.30/0.47 ( ( denota102713844ree_sz @ Nu @ Omega @ top_to1246370329_sz_sz )
% 0.30/0.47 => ( Nu = Omega ) ) ).
% 0.30/0.47
% 0.30/0.47 % agree_UNIV_eq
% 0.30/0.47 thf(fact_217_agree__UNIV__eq,axiom,
% 0.30/0.47 ! [Nu: produc190496183real_c,Omega: produc190496183real_c] :
% 0.30/0.47 ( ( denota1997846518gree_c @ Nu @ Omega @ top_to1660572043um_c_c )
% 0.30/0.47 => ( Nu = Omega ) ) ).
% 0.30/0.47
% 0.30/0.47 % agree_UNIV_eq
% 0.30/0.47 thf(fact_218_Vagree__univ,axiom,
% 0.30/0.47 ! [A: finite824932053eal_sz,B: finite824932053eal_sz,C2: finite824932053eal_sz,D: finite824932053eal_sz] :
% 0.30/0.47 ( ( denota102713844ree_sz @ ( produc1308130519eal_sz @ A @ B ) @ ( produc1308130519eal_sz @ C2 @ D ) @ top_to1246370329_sz_sz )
% 0.30/0.47 => ( ( A = C2 )
% 0.30/0.47 & ( B = D ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_univ
% 0.30/0.47 thf(fact_219_Vagree__univ,axiom,
% 0.30/0.47 ! [A: finite1398487019real_c,B: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 0.30/0.47 ( ( denota1997846518gree_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C2 @ D ) @ top_to1660572043um_c_c )
% 0.30/0.47 => ( ( A = C2 )
% 0.30/0.47 & ( B = D ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Vagree_univ
% 0.30/0.47 thf(fact_220_ids_Oseq__sem_Ocases,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,X: produc1821101996_sc_sz] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 0.30/0.47 ( X
% 0.30/0.47 != ( produc789536734_sc_sz @ I2 @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.seq_sem.cases
% 0.30/0.47 thf(fact_221_ids_Oseq__sem_Oinduct,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P: denota610675952t_unit > produc866628903_sc_sz > $o,A0: denota610675952t_unit,A1: produc866628903_sc_sz] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ( ! [I2: denota610675952t_unit,X_1: produc866628903_sc_sz] : ( P @ I2 @ X_1 )
% 0.30/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.seq_sem.induct
% 0.30/0.47 thf(fact_222_frechet_Osimps_I5_J,axiom,
% 0.30/0.47 ! [I6: denota231621370t_unit,R: real,V2: finite1398487019real_c] :
% 0.30/0.47 ( ( denota229585092_a_b_c @ I6 @ ( const_a_c @ R ) @ V2 )
% 0.30/0.47 = ( ^ [V3: finite1398487019real_c] : zero_zero_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % frechet.simps(5)
% 0.30/0.47 thf(fact_223_prod__eqI,axiom,
% 0.30/0.47 ! [P2: produc1821101996_sc_sz,Q: produc1821101996_sc_sz] :
% 0.30/0.47 ( ( ( produc1503602930_sc_sz @ P2 )
% 0.30/0.47 = ( produc1503602930_sc_sz @ Q ) )
% 0.30/0.47 => ( ( ( produc974239792_sc_sz @ P2 )
% 0.30/0.47 = ( produc974239792_sc_sz @ Q ) )
% 0.30/0.47 => ( P2 = Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_eqI
% 0.30/0.47 thf(fact_224_prod__eqI,axiom,
% 0.30/0.47 ! [P2: produc999471430t_unit,Q: produc999471430t_unit] :
% 0.30/0.47 ( ( ( produc1216682964t_unit @ P2 )
% 0.30/0.47 = ( produc1216682964t_unit @ Q ) )
% 0.30/0.47 => ( ( ( produc687319826t_unit @ P2 )
% 0.30/0.47 = ( produc687319826t_unit @ Q ) )
% 0.30/0.47 => ( P2 = Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_eqI
% 0.30/0.47 thf(fact_225_prod__eqI,axiom,
% 0.30/0.47 ! [P2: produc190496183real_c,Q: produc190496183real_c] :
% 0.30/0.47 ( ( ( produc2010422875real_c @ P2 )
% 0.30/0.47 = ( produc2010422875real_c @ Q ) )
% 0.30/0.47 => ( ( ( produc314122909real_c @ P2 )
% 0.30/0.47 = ( produc314122909real_c @ Q ) )
% 0.30/0.47 => ( P2 = Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_eqI
% 0.30/0.47 thf(fact_226_prod_Oexpand,axiom,
% 0.30/0.47 ! [Prod: produc1821101996_sc_sz,Prod2: produc1821101996_sc_sz] :
% 0.30/0.47 ( ( ( ( produc1503602930_sc_sz @ Prod )
% 0.30/0.47 = ( produc1503602930_sc_sz @ Prod2 ) )
% 0.30/0.47 & ( ( produc974239792_sc_sz @ Prod )
% 0.30/0.47 = ( produc974239792_sc_sz @ Prod2 ) ) )
% 0.30/0.47 => ( Prod = Prod2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.expand
% 0.30/0.47 thf(fact_227_prod_Oexpand,axiom,
% 0.30/0.47 ! [Prod: produc999471430t_unit,Prod2: produc999471430t_unit] :
% 0.30/0.47 ( ( ( ( produc1216682964t_unit @ Prod )
% 0.30/0.47 = ( produc1216682964t_unit @ Prod2 ) )
% 0.30/0.47 & ( ( produc687319826t_unit @ Prod )
% 0.30/0.47 = ( produc687319826t_unit @ Prod2 ) ) )
% 0.30/0.47 => ( Prod = Prod2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.expand
% 0.30/0.47 thf(fact_228_prod_Oexpand,axiom,
% 0.30/0.47 ! [Prod: produc190496183real_c,Prod2: produc190496183real_c] :
% 0.30/0.47 ( ( ( ( produc2010422875real_c @ Prod )
% 0.30/0.47 = ( produc2010422875real_c @ Prod2 ) )
% 0.30/0.47 & ( ( produc314122909real_c @ Prod )
% 0.30/0.47 = ( produc314122909real_c @ Prod2 ) ) )
% 0.30/0.47 => ( Prod = Prod2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.expand
% 0.30/0.47 thf(fact_229_prod__eq__iff,axiom,
% 0.30/0.47 ( ( ^ [Y4: produc1821101996_sc_sz,Z: produc1821101996_sc_sz] : ( Y4 = Z ) )
% 0.30/0.47 = ( ^ [S2: produc1821101996_sc_sz,T4: produc1821101996_sc_sz] :
% 0.30/0.47 ( ( ( produc1503602930_sc_sz @ S2 )
% 0.30/0.47 = ( produc1503602930_sc_sz @ T4 ) )
% 0.30/0.47 & ( ( produc974239792_sc_sz @ S2 )
% 0.30/0.47 = ( produc974239792_sc_sz @ T4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_eq_iff
% 0.30/0.47 thf(fact_230_prod__eq__iff,axiom,
% 0.30/0.47 ( ( ^ [Y4: produc999471430t_unit,Z: produc999471430t_unit] : ( Y4 = Z ) )
% 0.30/0.47 = ( ^ [S2: produc999471430t_unit,T4: produc999471430t_unit] :
% 0.30/0.47 ( ( ( produc1216682964t_unit @ S2 )
% 0.30/0.47 = ( produc1216682964t_unit @ T4 ) )
% 0.30/0.47 & ( ( produc687319826t_unit @ S2 )
% 0.30/0.47 = ( produc687319826t_unit @ T4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_eq_iff
% 0.30/0.47 thf(fact_231_prod__eq__iff,axiom,
% 0.30/0.47 ( ( ^ [Y4: produc190496183real_c,Z: produc190496183real_c] : ( Y4 = Z ) )
% 0.30/0.47 = ( ^ [S2: produc190496183real_c,T4: produc190496183real_c] :
% 0.30/0.47 ( ( ( produc2010422875real_c @ S2 )
% 0.30/0.47 = ( produc2010422875real_c @ T4 ) )
% 0.30/0.47 & ( ( produc314122909real_c @ S2 )
% 0.30/0.47 = ( produc314122909real_c @ T4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_eq_iff
% 0.30/0.47 thf(fact_232_snd__conv,axiom,
% 0.30/0.47 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 0.30/0.47 ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 0.30/0.47 = X22 ) ).
% 0.30/0.47
% 0.30/0.47 % snd_conv
% 0.30/0.47 thf(fact_233_snd__conv,axiom,
% 0.30/0.47 ! [X1: trm_sf_sz,X22: sz] :
% 0.30/0.47 ( ( produc181739436_sz_sz @ ( produc792909658_sz_sz @ X1 @ X22 ) )
% 0.30/0.47 = X22 ) ).
% 0.30/0.47
% 0.30/0.47 % snd_conv
% 0.30/0.47 thf(fact_234_snd__conv,axiom,
% 0.30/0.47 ! [X1: produc866628903_sc_sz,X22: denota610675952t_unit] :
% 0.30/0.47 ( ( produc687319826t_unit @ ( produc502616768t_unit @ X1 @ X22 ) )
% 0.30/0.47 = X22 ) ).
% 0.30/0.47
% 0.30/0.47 % snd_conv
% 0.30/0.47 thf(fact_235_snd__conv,axiom,
% 0.30/0.47 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 0.30/0.47 ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 0.30/0.47 = X22 ) ).
% 0.30/0.47
% 0.30/0.47 % snd_conv
% 0.30/0.47 thf(fact_236_snd__conv,axiom,
% 0.30/0.47 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.30/0.47 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.30/0.47 = X22 ) ).
% 0.30/0.47
% 0.30/0.47 % snd_conv
% 0.30/0.47 thf(fact_237_snd__eqD,axiom,
% 0.30/0.47 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A: list_f1238882004_sc_sz] :
% 0.30/0.47 ( ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( Y = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % snd_eqD
% 0.30/0.47 thf(fact_238_snd__eqD,axiom,
% 0.30/0.47 ! [X: trm_sf_sz,Y: sz,A: sz] :
% 0.30/0.47 ( ( ( produc181739436_sz_sz @ ( produc792909658_sz_sz @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( Y = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % snd_eqD
% 0.30/0.47 thf(fact_239_snd__eqD,axiom,
% 0.30/0.47 ! [X: produc866628903_sc_sz,Y: denota610675952t_unit,A: denota610675952t_unit] :
% 0.30/0.47 ( ( ( produc687319826t_unit @ ( produc502616768t_unit @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( Y = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % snd_eqD
% 0.30/0.47 thf(fact_240_snd__eqD,axiom,
% 0.30/0.47 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A: produc866628903_sc_sz] :
% 0.30/0.47 ( ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( Y = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % snd_eqD
% 0.30/0.47 thf(fact_241_snd__eqD,axiom,
% 0.30/0.47 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 0.30/0.47 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( Y = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % snd_eqD
% 0.30/0.47 thf(fact_242_fst__conv,axiom,
% 0.30/0.47 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 0.30/0.47 ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 0.30/0.47 = X1 ) ).
% 0.30/0.47
% 0.30/0.47 % fst_conv
% 0.30/0.47 thf(fact_243_fst__conv,axiom,
% 0.30/0.47 ! [X1: trm_sf_sz,X22: sz] :
% 0.30/0.47 ( ( produc2069561454_sz_sz @ ( produc792909658_sz_sz @ X1 @ X22 ) )
% 0.30/0.47 = X1 ) ).
% 0.30/0.47
% 0.30/0.47 % fst_conv
% 0.30/0.47 thf(fact_244_fst__conv,axiom,
% 0.30/0.47 ! [X1: produc866628903_sc_sz,X22: denota610675952t_unit] :
% 0.30/0.47 ( ( produc1216682964t_unit @ ( produc502616768t_unit @ X1 @ X22 ) )
% 0.30/0.47 = X1 ) ).
% 0.30/0.47
% 0.30/0.47 % fst_conv
% 0.30/0.47 thf(fact_245_fst__conv,axiom,
% 0.30/0.47 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 0.30/0.47 ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 0.30/0.47 = X1 ) ).
% 0.30/0.47
% 0.30/0.47 % fst_conv
% 0.30/0.47 thf(fact_246_fst__conv,axiom,
% 0.30/0.47 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.30/0.47 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.30/0.47 = X1 ) ).
% 0.30/0.47
% 0.30/0.47 % fst_conv
% 0.30/0.47 thf(fact_247_fst__eqD,axiom,
% 0.30/0.47 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A: list_f1238882004_sc_sz] :
% 0.30/0.47 ( ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( X = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % fst_eqD
% 0.30/0.47 thf(fact_248_fst__eqD,axiom,
% 0.30/0.47 ! [X: trm_sf_sz,Y: sz,A: trm_sf_sz] :
% 0.30/0.47 ( ( ( produc2069561454_sz_sz @ ( produc792909658_sz_sz @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( X = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % fst_eqD
% 0.30/0.47 thf(fact_249_fst__eqD,axiom,
% 0.30/0.47 ! [X: produc866628903_sc_sz,Y: denota610675952t_unit,A: produc866628903_sc_sz] :
% 0.30/0.47 ( ( ( produc1216682964t_unit @ ( produc502616768t_unit @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( X = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % fst_eqD
% 0.30/0.47 thf(fact_250_fst__eqD,axiom,
% 0.30/0.47 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A: denota610675952t_unit] :
% 0.30/0.47 ( ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( X = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % fst_eqD
% 0.30/0.47 thf(fact_251_fst__eqD,axiom,
% 0.30/0.47 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 0.30/0.47 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.30/0.47 = A )
% 0.30/0.47 => ( X = A ) ) ).
% 0.30/0.47
% 0.30/0.47 % fst_eqD
% 0.30/0.47 thf(fact_252_ids_Oempty__def,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ( empty_c_a
% 0.30/0.47 = ( ^ [I4: c] : ( const_a_c @ zero_zero_real ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.empty_def
% 0.30/0.47 thf(fact_253_ids_Oempty__def,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ( empty_sz_sf
% 0.30/0.47 = ( ^ [I4: sz] : ( const_sf_sz @ zero_zero_real ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.empty_def
% 0.30/0.47 thf(fact_254_ids_Osingleton_Ocases,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,X: produc861709536_sz_sz] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ~ ! [T: trm_sf_sz,I3: sz] :
% 0.30/0.47 ( X
% 0.30/0.47 != ( produc792909658_sz_sz @ T @ I3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.singleton.cases
% 0.30/0.47 thf(fact_255_ids_OP__def,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P2: sc] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ( ( p_sc_sf_sz @ P2 )
% 0.30/0.47 = ( predic913887884_sf_sz @ P2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.P_def
% 0.30/0.47 thf(fact_256_agree__refl,axiom,
% 0.30/0.47 ! [Nu: produc1149990247eal_sz,A2: set_Sum_sum_sz_sz] : ( denota102713844ree_sz @ Nu @ Nu @ A2 ) ).
% 0.30/0.47
% 0.30/0.47 % agree_refl
% 0.30/0.47 thf(fact_257_agree__refl,axiom,
% 0.30/0.47 ! [Nu: produc190496183real_c,A2: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu @ Nu @ A2 ) ).
% 0.30/0.47
% 0.30/0.47 % agree_refl
% 0.30/0.47 thf(fact_258_ids_Ostrm_Odomain,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ( ( domain2047240575rm_a_c @ frechet_cr_strm_a_c )
% 0.30/0.47 = dfree_a_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.strm.domain
% 0.30/0.47 thf(fact_259_ids_Ostrm_Odomain,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ( ( domain512309999_sf_sz @ freche1244000341_sf_sz )
% 0.30/0.47 = dfree_sf_sz ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.strm.domain
% 0.30/0.47 thf(fact_260_snd__zero,axiom,
% 0.30/0.47 ( ( produc314122909real_c @ zero_z1506780526real_c )
% 0.30/0.47 = zero_z109254132real_c ) ).
% 0.30/0.47
% 0.30/0.47 % snd_zero
% 0.30/0.47 thf(fact_261_fst__zero,axiom,
% 0.30/0.47 ( ( produc2010422875real_c @ zero_z1506780526real_c )
% 0.30/0.47 = zero_z109254132real_c ) ).
% 0.30/0.47
% 0.30/0.47 % fst_zero
% 0.30/0.47 thf(fact_262_zero__prod__def,axiom,
% 0.30/0.47 ( zero_z659284464l_real
% 0.30/0.47 = ( produc705216881l_real @ zero_zero_real @ zero_zero_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_prod_def
% 0.30/0.47 thf(fact_263_zero__prod__def,axiom,
% 0.30/0.47 ( zero_z72018569real_c
% 0.30/0.47 = ( produc2134005810real_c @ zero_zero_real @ zero_z1506780526real_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_prod_def
% 0.30/0.47 thf(fact_264_zero__prod__def,axiom,
% 0.30/0.47 ( zero_z464587567real_c
% 0.30/0.47 = ( produc1327150128real_c @ zero_zero_real @ zero_z109254132real_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_prod_def
% 0.30/0.47 thf(fact_265_zero__prod__def,axiom,
% 0.30/0.47 ( zero_z1830236699c_real
% 0.30/0.47 = ( produc171591948c_real @ zero_z1506780526real_c @ zero_zero_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_prod_def
% 0.30/0.47 thf(fact_266_zero__prod__def,axiom,
% 0.30/0.47 ( zero_z993734942real_c
% 0.30/0.47 = ( produc1687028567real_c @ zero_z1506780526real_c @ zero_z1506780526real_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_prod_def
% 0.30/0.47 thf(fact_267_zero__prod__def,axiom,
% 0.30/0.47 ( zero_z440955354real_c
% 0.30/0.47 = ( produc116546123real_c @ zero_z1506780526real_c @ zero_z109254132real_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_prod_def
% 0.30/0.47 thf(fact_268_zero__prod__def,axiom,
% 0.30/0.47 ( zero_z1273814959c_real
% 0.30/0.47 = ( produc1715747632c_real @ zero_z109254132real_c @ zero_zero_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_prod_def
% 0.30/0.47 thf(fact_269_zero__prod__def,axiom,
% 0.30/0.47 ( zero_z735295626real_c
% 0.30/0.47 = ( produc1563404851real_c @ zero_z109254132real_c @ zero_z1506780526real_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_prod_def
% 0.30/0.47 thf(fact_270_zero__prod__def,axiom,
% 0.30/0.47 ( zero_z1506780526real_c
% 0.30/0.47 = ( produc394644079real_c @ zero_z109254132real_c @ zero_z109254132real_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % zero_prod_def
% 0.30/0.47 thf(fact_271_top__prod__def,axiom,
% 0.30/0.47 ( top_to543326711_set_c
% 0.30/0.47 = ( produc878845847_set_c @ top_top_set_c @ top_top_set_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_272_top__prod__def,axiom,
% 0.30/0.47 ( top_to1303770207set_sz
% 0.30/0.47 = ( produc2039118377set_sz @ top_top_set_c @ top_top_set_sz ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_273_top__prod__def,axiom,
% 0.30/0.47 ( top_to474099557_set_c
% 0.30/0.47 = ( produc760013927_set_c @ top_top_set_sz @ top_top_set_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_274_top__prod__def,axiom,
% 0.30/0.47 ( top_to1999610481set_sz
% 0.30/0.47 = ( produc2156889set_sz @ top_top_set_sz @ top_top_set_sz ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_275_top__prod__def,axiom,
% 0.30/0.47 ( top_to1128637210um_c_c
% 0.30/0.47 = ( produc1519884516um_c_c @ top_top_set_c @ top_to1660572043um_c_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_276_top__prod__def,axiom,
% 0.30/0.47 ( top_to1783191648real_c
% 0.30/0.47 = ( produc280329770real_c @ top_top_set_c @ top_to1642137041real_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_277_top__prod__def,axiom,
% 0.30/0.47 ( top_to1102260780um_c_c
% 0.30/0.47 = ( produc590684180um_c_c @ top_top_set_sz @ top_to1660572043um_c_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_278_top__prod__def,axiom,
% 0.30/0.47 ( top_to1102487922real_c
% 0.30/0.47 = ( produc1915663706real_c @ top_top_set_sz @ top_to1642137041real_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_279_top__prod__def,axiom,
% 0.30/0.47 ( top_to1309524330_set_c
% 0.30/0.47 = ( produc1767696108_set_c @ top_to1660572043um_c_c @ top_top_set_c ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_280_top__prod__def,axiom,
% 0.30/0.47 ( top_to1246597548set_sz
% 0.30/0.47 = ( produc1251379220set_sz @ top_to1660572043um_c_c @ top_top_set_sz ) ) ).
% 0.30/0.47
% 0.30/0.47 % top_prod_def
% 0.30/0.47 thf(fact_281_ids_Ostrm_Oright__unique,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ( right_963419005_sf_sz @ freche1244000341_sf_sz ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.strm.right_unique
% 0.30/0.47 thf(fact_282_directional__derivative__def,axiom,
% 0.30/0.47 ( denota2112424896_a_b_c
% 0.30/0.47 = ( ^ [I7: denota231621370t_unit,T4: trm_a_c,V4: produc190496183real_c] : ( denota229585092_a_b_c @ I7 @ T4 @ ( produc2010422875real_c @ V4 ) @ ( produc314122909real_c @ V4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % directional_derivative_def
% 0.30/0.47 thf(fact_283_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.30/0.47 ! [P: denota610675952t_unit > produc866628903_sc_sz > $o,X: denota610675952t_unit,Y: produc866628903_sc_sz,A: produc1821101996_sc_sz] :
% 0.30/0.47 ( ( P @ X @ Y )
% 0.30/0.47 => ( ( A
% 0.30/0.47 = ( produc789536734_sc_sz @ X @ Y ) )
% 0.30/0.47 => ( P @ ( produc1503602930_sc_sz @ A ) @ ( produc974239792_sc_sz @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.30/0.47 thf(fact_284_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.30/0.47 ! [P: finite1398487019real_c > finite1398487019real_c > $o,X: finite1398487019real_c,Y: finite1398487019real_c,A: produc190496183real_c] :
% 0.30/0.47 ( ( P @ X @ Y )
% 0.30/0.47 => ( ( A
% 0.30/0.47 = ( produc394644079real_c @ X @ Y ) )
% 0.30/0.47 => ( P @ ( produc2010422875real_c @ A ) @ ( produc314122909real_c @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % BNF_Greatest_Fixpoint.subst_Pair
% 0.30/0.47 thf(fact_285_conjI__realizer,axiom,
% 0.30/0.47 ! [P: denota610675952t_unit > $o,P2: denota610675952t_unit,Q2: produc866628903_sc_sz > $o,Q: produc866628903_sc_sz] :
% 0.30/0.47 ( ( P @ P2 )
% 0.30/0.47 => ( ( Q2 @ Q )
% 0.30/0.47 => ( ( P @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q ) ) )
% 0.30/0.47 & ( Q2 @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % conjI_realizer
% 0.30/0.47 thf(fact_286_conjI__realizer,axiom,
% 0.30/0.47 ! [P: finite1398487019real_c > $o,P2: finite1398487019real_c,Q2: finite1398487019real_c > $o,Q: finite1398487019real_c] :
% 0.30/0.47 ( ( P @ P2 )
% 0.30/0.47 => ( ( Q2 @ Q )
% 0.30/0.47 => ( ( P @ ( produc2010422875real_c @ ( produc394644079real_c @ P2 @ Q ) ) )
% 0.30/0.47 & ( Q2 @ ( produc314122909real_c @ ( produc394644079real_c @ P2 @ Q ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % conjI_realizer
% 0.30/0.47 thf(fact_287_exI__realizer,axiom,
% 0.30/0.47 ! [P: produc866628903_sc_sz > denota610675952t_unit > $o,Y: produc866628903_sc_sz,X: denota610675952t_unit] :
% 0.30/0.47 ( ( P @ Y @ X )
% 0.30/0.47 => ( P @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % exI_realizer
% 0.30/0.47 thf(fact_288_exI__realizer,axiom,
% 0.30/0.47 ! [P: finite1398487019real_c > finite1398487019real_c > $o,Y: finite1398487019real_c,X: finite1398487019real_c] :
% 0.30/0.47 ( ( P @ Y @ X )
% 0.30/0.47 => ( P @ ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) ) @ ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % exI_realizer
% 0.30/0.47 thf(fact_289_exE__realizer_H,axiom,
% 0.30/0.47 ! [P: finite1398487019real_c > finite1398487019real_c > $o,P2: produc190496183real_c] :
% 0.30/0.47 ( ( P @ ( produc314122909real_c @ P2 ) @ ( produc2010422875real_c @ P2 ) )
% 0.30/0.47 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.30/0.47 ~ ( P @ Y3 @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % exE_realizer'
% 0.30/0.47 thf(fact_290_sndI,axiom,
% 0.30/0.47 ! [X: produc1821101996_sc_sz,Y: denota610675952t_unit,Z2: produc866628903_sc_sz] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( produc789536734_sc_sz @ Y @ Z2 ) )
% 0.30/0.47 => ( ( produc974239792_sc_sz @ X )
% 0.30/0.47 = Z2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sndI
% 0.30/0.47 thf(fact_291_sndI,axiom,
% 0.30/0.47 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z2: finite1398487019real_c] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( produc394644079real_c @ Y @ Z2 ) )
% 0.30/0.47 => ( ( produc314122909real_c @ X )
% 0.30/0.47 = Z2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sndI
% 0.30/0.47 thf(fact_292_eq__snd__iff,axiom,
% 0.30/0.47 ! [B: produc866628903_sc_sz,P2: produc1821101996_sc_sz] :
% 0.30/0.47 ( ( B
% 0.30/0.47 = ( produc974239792_sc_sz @ P2 ) )
% 0.30/0.47 = ( ? [A5: denota610675952t_unit] :
% 0.30/0.47 ( P2
% 0.30/0.47 = ( produc789536734_sc_sz @ A5 @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_snd_iff
% 0.30/0.47 thf(fact_293_eq__snd__iff,axiom,
% 0.30/0.47 ! [B: finite1398487019real_c,P2: produc190496183real_c] :
% 0.30/0.47 ( ( B
% 0.30/0.47 = ( produc314122909real_c @ P2 ) )
% 0.30/0.47 = ( ? [A5: finite1398487019real_c] :
% 0.30/0.47 ( P2
% 0.30/0.47 = ( produc394644079real_c @ A5 @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_snd_iff
% 0.30/0.47 thf(fact_294_eq__fst__iff,axiom,
% 0.30/0.47 ! [A: denota610675952t_unit,P2: produc1821101996_sc_sz] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( produc1503602930_sc_sz @ P2 ) )
% 0.30/0.47 = ( ? [B5: produc866628903_sc_sz] :
% 0.30/0.47 ( P2
% 0.30/0.47 = ( produc789536734_sc_sz @ A @ B5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_fst_iff
% 0.30/0.47 thf(fact_295_eq__fst__iff,axiom,
% 0.30/0.47 ! [A: finite1398487019real_c,P2: produc190496183real_c] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( produc2010422875real_c @ P2 ) )
% 0.30/0.47 = ( ? [B5: finite1398487019real_c] :
% 0.30/0.47 ( P2
% 0.30/0.47 = ( produc394644079real_c @ A @ B5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_fst_iff
% 0.30/0.47 thf(fact_296_fstI,axiom,
% 0.30/0.47 ! [X: produc1821101996_sc_sz,Y: denota610675952t_unit,Z2: produc866628903_sc_sz] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( produc789536734_sc_sz @ Y @ Z2 ) )
% 0.30/0.47 => ( ( produc1503602930_sc_sz @ X )
% 0.30/0.47 = Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % fstI
% 0.30/0.47 thf(fact_297_fstI,axiom,
% 0.30/0.47 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z2: finite1398487019real_c] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( produc394644079real_c @ Y @ Z2 ) )
% 0.30/0.47 => ( ( produc2010422875real_c @ X )
% 0.30/0.47 = Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % fstI
% 0.30/0.47 thf(fact_298_range__snd,axiom,
% 0.30/0.47 ( ( image_14429021real_c @ produc314122909real_c @ top_to226056039real_c )
% 0.30/0.47 = top_to1642137041real_c ) ).
% 0.30/0.47
% 0.30/0.47 % range_snd
% 0.30/0.47 thf(fact_299_range__fst,axiom,
% 0.30/0.47 ( ( image_14429021real_c @ produc2010422875real_c @ top_to226056039real_c )
% 0.30/0.47 = top_to1642137041real_c ) ).
% 0.30/0.47
% 0.30/0.47 % range_fst
% 0.30/0.47 thf(fact_300_DomainpE,axiom,
% 0.30/0.47 ! [R: trm_a_c > frechet_strm_a_c > $o,A: trm_a_c] :
% 0.30/0.47 ( ( domain2047240575rm_a_c @ R @ A )
% 0.30/0.47 => ~ ! [B3: frechet_strm_a_c] :
% 0.30/0.47 ~ ( R @ A @ B3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % DomainpE
% 0.30/0.47 thf(fact_301_Domainp__iff,axiom,
% 0.30/0.47 ( domain2047240575rm_a_c
% 0.30/0.47 = ( ^ [T5: trm_a_c > frechet_strm_a_c > $o,X2: trm_a_c] :
% 0.30/0.47 ? [X4: frechet_strm_a_c] : ( T5 @ X2 @ X4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Domainp_iff
% 0.30/0.47 thf(fact_302_Domainp__refl,axiom,
% 0.30/0.47 domain2047240575rm_a_c = domain2047240575rm_a_c ).
% 0.30/0.47
% 0.30/0.47 % Domainp_refl
% 0.30/0.47 thf(fact_303_Domainp_Ocases,axiom,
% 0.30/0.47 ! [R: trm_a_c > frechet_strm_a_c > $o,A: trm_a_c] :
% 0.30/0.47 ( ( domain2047240575rm_a_c @ R @ A )
% 0.30/0.47 => ~ ! [B3: frechet_strm_a_c] :
% 0.30/0.47 ~ ( R @ A @ B3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Domainp.cases
% 0.30/0.47 thf(fact_304_Domainp_Osimps,axiom,
% 0.30/0.47 ( domain2047240575rm_a_c
% 0.30/0.47 = ( ^ [R3: trm_a_c > frechet_strm_a_c > $o,A5: trm_a_c] :
% 0.30/0.47 ? [B5: trm_a_c,C3: frechet_strm_a_c] :
% 0.30/0.47 ( ( A5 = B5 )
% 0.30/0.47 & ( R3 @ B5 @ C3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Domainp.simps
% 0.30/0.47 thf(fact_305_Domainp_ODomainI,axiom,
% 0.30/0.47 ! [R: trm_a_c > frechet_strm_a_c > $o,A: trm_a_c,B: frechet_strm_a_c] :
% 0.30/0.47 ( ( R @ A @ B )
% 0.30/0.47 => ( domain2047240575rm_a_c @ R @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % Domainp.DomainI
% 0.30/0.47 thf(fact_306_Domainp_Oinducts,axiom,
% 0.30/0.47 ! [R: trm_a_c > frechet_strm_a_c > $o,X: trm_a_c,P: trm_a_c > $o] :
% 0.30/0.47 ( ( domain2047240575rm_a_c @ R @ X )
% 0.30/0.47 => ( ! [A4: trm_a_c,B3: frechet_strm_a_c] :
% 0.30/0.47 ( ( R @ A4 @ B3 )
% 0.30/0.47 => ( P @ A4 ) )
% 0.30/0.47 => ( P @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Domainp.inducts
% 0.30/0.47 thf(fact_307_trm_Oset__cases,axiom,
% 0.30/0.47 ! [E: sf,A: trm_sf_sz] :
% 0.30/0.47 ( ( member_sf @ E @ ( set_trm_sf_sz2 @ A ) )
% 0.30/0.47 => ( ! [Z22: sz > trm_sf_sz] :
% 0.30/0.47 ( A
% 0.30/0.47 != ( function_sf_sz @ E @ Z22 ) )
% 0.30/0.47 => ( ! [Z1: sf,Z22: sz > trm_sf_sz] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( function_sf_sz @ Z1 @ Z22 ) )
% 0.30/0.47 => ! [X3: trm_sf_sz] :
% 0.30/0.47 ( ( member_trm_sf_sz @ X3 @ ( image_sz_trm_sf_sz @ Z22 @ top_top_set_sz ) )
% 0.30/0.47 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ X3 ) ) ) )
% 0.30/0.47 => ( ! [Z1: trm_sf_sz] :
% 0.30/0.47 ( ? [Z22: trm_sf_sz] :
% 0.30/0.47 ( A
% 0.30/0.47 = ( plus_sf_sz @ Z1 @ Z22 ) )
% 0.30/0.47 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z1 ) ) )
% 0.30/0.47 => ( ! [Z1: trm_sf_sz,Z22: trm_sf_sz] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( plus_sf_sz @ Z1 @ Z22 ) )
% 0.30/0.47 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z22 ) ) )
% 0.30/0.47 => ( ! [Z1: trm_sf_sz] :
% 0.30/0.47 ( ? [Z22: trm_sf_sz] :
% 0.30/0.47 ( A
% 0.30/0.47 = ( times_sf_sz @ Z1 @ Z22 ) )
% 0.30/0.47 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z1 ) ) )
% 0.30/0.47 => ( ! [Z1: trm_sf_sz,Z22: trm_sf_sz] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( times_sf_sz @ Z1 @ Z22 ) )
% 0.30/0.47 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z22 ) ) )
% 0.30/0.47 => ~ ! [Z3: trm_sf_sz] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( differential_sf_sz @ Z3 ) )
% 0.30/0.47 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z3 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.set_cases
% 0.30/0.47 thf(fact_308_trm_Oset__cases,axiom,
% 0.30/0.47 ! [E: a,A: trm_a_c] :
% 0.30/0.47 ( ( member_a @ E @ ( set_trm_a_c2 @ A ) )
% 0.30/0.47 => ( ! [Z22: c > trm_a_c] :
% 0.30/0.47 ( A
% 0.30/0.47 != ( function_a_c @ E @ Z22 ) )
% 0.30/0.47 => ( ! [Z1: a,Z22: c > trm_a_c] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( function_a_c @ Z1 @ Z22 ) )
% 0.30/0.47 => ! [X3: trm_a_c] :
% 0.30/0.47 ( ( member_trm_a_c @ X3 @ ( image_c_trm_a_c @ Z22 @ top_top_set_c ) )
% 0.30/0.47 => ~ ( member_a @ E @ ( set_trm_a_c2 @ X3 ) ) ) )
% 0.30/0.47 => ( ! [Z1: trm_a_c] :
% 0.30/0.47 ( ? [Z22: trm_a_c] :
% 0.30/0.47 ( A
% 0.30/0.47 = ( plus_a_c @ Z1 @ Z22 ) )
% 0.30/0.47 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z1 ) ) )
% 0.30/0.47 => ( ! [Z1: trm_a_c,Z22: trm_a_c] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( plus_a_c @ Z1 @ Z22 ) )
% 0.30/0.47 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z22 ) ) )
% 0.30/0.47 => ( ! [Z1: trm_a_c] :
% 0.30/0.47 ( ? [Z22: trm_a_c] :
% 0.30/0.47 ( A
% 0.30/0.47 = ( times_a_c @ Z1 @ Z22 ) )
% 0.30/0.47 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z1 ) ) )
% 0.30/0.47 => ( ! [Z1: trm_a_c,Z22: trm_a_c] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( times_a_c @ Z1 @ Z22 ) )
% 0.30/0.47 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z22 ) ) )
% 0.30/0.47 => ~ ! [Z3: trm_a_c] :
% 0.30/0.47 ( ( A
% 0.30/0.47 = ( differential_a_c @ Z3 ) )
% 0.30/0.47 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z3 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.set_cases
% 0.30/0.47 thf(fact_309_trm_Oset__intros_I1_J,axiom,
% 0.30/0.47 ! [X31: a,X32: c > trm_a_c] : ( member_a @ X31 @ ( set_trm_a_c2 @ ( function_a_c @ X31 @ X32 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.set_intros(1)
% 0.30/0.47 thf(fact_310_trm_Oset__intros_I1_J,axiom,
% 0.30/0.47 ! [X31: sf,X32: sz > trm_sf_sz] : ( member_sf @ X31 @ ( set_trm_sf_sz2 @ ( function_sf_sz @ X31 @ X32 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.set_intros(1)
% 0.30/0.47 thf(fact_311_trm_Osimps_I126_J,axiom,
% 0.30/0.47 ! [X7: trm_a_c] :
% 0.30/0.47 ( ( set_trm_a_c2 @ ( differential_a_c @ X7 ) )
% 0.30/0.47 = ( set_trm_a_c2 @ X7 ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.simps(126)
% 0.30/0.47 thf(fact_312_trm_Oset__intros_I7_J,axiom,
% 0.30/0.47 ! [Yf: a,X7: trm_a_c] :
% 0.30/0.47 ( ( member_a @ Yf @ ( set_trm_a_c2 @ X7 ) )
% 0.30/0.47 => ( member_a @ Yf @ ( set_trm_a_c2 @ ( differential_a_c @ X7 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.set_intros(7)
% 0.30/0.47 thf(fact_313_trm_Oset__intros_I2_J,axiom,
% 0.30/0.47 ! [Y: trm_a_c,X32: c > trm_a_c,Ya: a,X31: a] :
% 0.30/0.47 ( ( member_trm_a_c @ Y @ ( image_c_trm_a_c @ X32 @ top_top_set_c ) )
% 0.30/0.47 => ( ( member_a @ Ya @ ( set_trm_a_c2 @ Y ) )
% 0.30/0.47 => ( member_a @ Ya @ ( set_trm_a_c2 @ ( function_a_c @ X31 @ X32 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.set_intros(2)
% 0.30/0.47 thf(fact_314_trm_Oset__intros_I2_J,axiom,
% 0.30/0.47 ! [Y: trm_sf_sz,X32: sz > trm_sf_sz,Ya: sf,X31: sf] :
% 0.30/0.47 ( ( member_trm_sf_sz @ Y @ ( image_sz_trm_sf_sz @ X32 @ top_top_set_sz ) )
% 0.30/0.47 => ( ( member_sf @ Ya @ ( set_trm_sf_sz2 @ Y ) )
% 0.30/0.47 => ( member_sf @ Ya @ ( set_trm_sf_sz2 @ ( function_sf_sz @ X31 @ X32 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % trm.set_intros(2)
% 0.30/0.47 thf(fact_315_ids_Osingleton_Ocong,axiom,
% 0.30/0.47 singleton_sz_sf = singleton_sz_sf ).
% 0.30/0.47
% 0.30/0.47 % ids.singleton.cong
% 0.30/0.47 thf(fact_316_ids_Of1_Ocong,axiom,
% 0.30/0.47 f1_sz_sf = f1_sz_sf ).
% 0.30/0.47
% 0.30/0.47 % ids.f1.cong
% 0.30/0.47 thf(fact_317_singleton_Opelims,axiom,
% 0.30/0.47 ! [X: trm_sf_sz,Xa: sz,Y: trm_sf_sz] :
% 0.30/0.47 ( ( ( singleton_sz_sf @ vid1 @ X @ Xa )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( accp_P529224471_sz_sz @ singleton_rel_sf_sz @ ( produc792909658_sz_sz @ X @ Xa ) )
% 0.30/0.47 => ~ ( ( ( ( Xa = vid1 )
% 0.30/0.47 => ( Y = X ) )
% 0.30/0.47 & ( ( Xa != vid1 )
% 0.30/0.47 => ( Y
% 0.30/0.47 = ( const_sf_sz @ zero_zero_real ) ) ) )
% 0.30/0.47 => ~ ( accp_P529224471_sz_sz @ singleton_rel_sf_sz @ ( produc792909658_sz_sz @ X @ Xa ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton.pelims
% 0.30/0.47 thf(fact_318_f1__def,axiom,
% 0.30/0.47 ! [F2: sf,X: sz] :
% 0.30/0.47 ( ( f1_sz_sf @ vid1 @ F2 @ X )
% 0.30/0.47 = ( function_sf_sz @ F2 @ ( singleton_sz_sf @ vid1 @ ( var_sz_sf @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % f1_def
% 0.30/0.47 thf(fact_319_proj__sing1,axiom,
% 0.30/0.47 ! [Theta3: trm_sf_sz] :
% 0.30/0.47 ( ( singleton_sz_sf @ vid1 @ Theta3 @ vid1 )
% 0.30/0.47 = Theta3 ) ).
% 0.30/0.47
% 0.30/0.47 % proj_sing1
% 0.30/0.47 thf(fact_320_expand__singleton,axiom,
% 0.30/0.47 ! [T3: trm_sf_sz] :
% 0.30/0.47 ( ( singleton_sz_sf @ vid1 @ T3 )
% 0.30/0.47 = ( ^ [I4: sz] : ( if_trm_sf_sz @ ( I4 = vid1 ) @ T3 @ ( const_sf_sz @ zero_zero_real ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % expand_singleton
% 0.30/0.47 thf(fact_321_proj__sing2,axiom,
% 0.30/0.47 ! [Y: sz,Theta3: trm_sf_sz] :
% 0.30/0.47 ( ( vid1 != Y )
% 0.30/0.47 => ( ( singleton_sz_sf @ vid1 @ Theta3 @ Y )
% 0.30/0.47 = ( const_sf_sz @ zero_zero_real ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % proj_sing2
% 0.30/0.47 thf(fact_322_singleton_Oelims,axiom,
% 0.30/0.47 ! [X: trm_sf_sz,Xa: sz,Y: trm_sf_sz] :
% 0.30/0.47 ( ( ( singleton_sz_sf @ vid1 @ X @ Xa )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = vid1 )
% 0.30/0.47 => ( Y = X ) )
% 0.30/0.47 & ( ( Xa != vid1 )
% 0.30/0.47 => ( Y
% 0.30/0.47 = ( const_sf_sz @ zero_zero_real ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton.elims
% 0.30/0.47 thf(fact_323_singleton_Osimps,axiom,
% 0.30/0.47 ! [I: sz,T3: trm_sf_sz] :
% 0.30/0.47 ( ( ( I = vid1 )
% 0.30/0.47 => ( ( singleton_sz_sf @ vid1 @ T3 @ I )
% 0.30/0.47 = T3 ) )
% 0.30/0.47 & ( ( I != vid1 )
% 0.30/0.47 => ( ( singleton_sz_sf @ vid1 @ T3 @ I )
% 0.30/0.47 = ( const_sf_sz @ zero_zero_real ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton.simps
% 0.30/0.47 thf(fact_324_local_Oid__simps_I15_J,axiom,
% 0.30/0.47 vid3 != vid1 ).
% 0.30/0.47
% 0.30/0.47 % local.id_simps(15)
% 0.30/0.47 thf(fact_325_local_Oid__simps_I13_J,axiom,
% 0.30/0.47 vid2 != vid1 ).
% 0.30/0.47
% 0.30/0.47 % local.id_simps(13)
% 0.30/0.47 thf(fact_326_vne13,axiom,
% 0.30/0.47 vid1 != vid3 ).
% 0.30/0.47
% 0.30/0.47 % vne13
% 0.30/0.47 thf(fact_327_vne12,axiom,
% 0.30/0.47 vid1 != vid2 ).
% 0.30/0.47
% 0.30/0.47 % vne12
% 0.30/0.47 thf(fact_328_local_Oid__simps_I1_J,axiom,
% 0.30/0.47 vid1 != vid2 ).
% 0.30/0.47
% 0.30/0.47 % local.id_simps(1)
% 0.30/0.47 thf(fact_329_local_Oid__simps_I3_J,axiom,
% 0.30/0.47 vid1 != vid3 ).
% 0.30/0.47
% 0.30/0.47 % local.id_simps(3)
% 0.30/0.47 thf(fact_330_vne23,axiom,
% 0.30/0.47 vid2 != vid3 ).
% 0.30/0.47
% 0.30/0.47 % vne23
% 0.30/0.47 thf(fact_331_local_Oid__simps_I2_J,axiom,
% 0.30/0.47 vid2 != vid3 ).
% 0.30/0.47
% 0.30/0.47 % local.id_simps(2)
% 0.30/0.47 thf(fact_332_local_Oid__simps_I14_J,axiom,
% 0.30/0.47 vid3 != vid2 ).
% 0.30/0.47
% 0.30/0.47 % local.id_simps(14)
% 0.30/0.47 thf(fact_333_p1__def,axiom,
% 0.30/0.47 ! [P2: sz,X: sz] :
% 0.30/0.47 ( ( p1_sz_sf_sc @ vid1 @ P2 @ X )
% 0.30/0.47 = ( prop_sz_sf_sc @ P2 @ ( singleton_sz_sf @ vid1 @ ( var_sz_sf @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % p1_def
% 0.30/0.47 thf(fact_334_prod_Oswap__def,axiom,
% 0.30/0.47 ( produc245128480t_unit
% 0.30/0.47 = ( ^ [P3: produc999471430t_unit] : ( produc789536734_sc_sz @ ( produc687319826t_unit @ P3 ) @ ( produc1216682964t_unit @ P3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.swap_def
% 0.30/0.47 thf(fact_335_prod_Oswap__def,axiom,
% 0.30/0.47 ( produc704157711real_c
% 0.30/0.47 = ( ^ [P3: produc190496183real_c] : ( produc394644079real_c @ ( produc314122909real_c @ P3 ) @ ( produc2010422875real_c @ P3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod.swap_def
% 0.30/0.47 thf(fact_336_formula_Oinject_I2_J,axiom,
% 0.30/0.47 ! [X21: sz,X222: sz > trm_sf_sz,Y21: sz,Y22: sz > trm_sf_sz] :
% 0.30/0.47 ( ( ( prop_sz_sf_sc @ X21 @ X222 )
% 0.30/0.47 = ( prop_sz_sf_sc @ Y21 @ Y22 ) )
% 0.30/0.47 = ( ( X21 = Y21 )
% 0.30/0.47 & ( X222 = Y22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % formula.inject(2)
% 0.30/0.47 thf(fact_337_pair__in__swap__image,axiom,
% 0.30/0.47 ! [Y: produc866628903_sc_sz,X: denota610675952t_unit,A2: set_Pr1169339874_sc_sz] :
% 0.30/0.47 ( ( member235934813t_unit @ ( produc502616768t_unit @ Y @ X ) @ ( image_904562809t_unit @ produc532048446_sc_sz @ A2 ) )
% 0.30/0.47 = ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pair_in_swap_image
% 0.30/0.47 thf(fact_338_pair__in__swap__image,axiom,
% 0.30/0.47 ! [Y: denota610675952t_unit,X: produc866628903_sc_sz,A2: set_Pr2041213564t_unit] :
% 0.30/0.47 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ Y @ X ) @ ( image_1426741113_sc_sz @ produc245128480t_unit @ A2 ) )
% 0.30/0.47 = ( member235934813t_unit @ ( produc502616768t_unit @ X @ Y ) @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % pair_in_swap_image
% 0.30/0.47 thf(fact_339_swap__simp,axiom,
% 0.30/0.47 ! [X: produc866628903_sc_sz,Y: denota610675952t_unit] :
% 0.30/0.47 ( ( produc245128480t_unit @ ( produc502616768t_unit @ X @ Y ) )
% 0.30/0.47 = ( produc789536734_sc_sz @ Y @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % swap_simp
% 0.30/0.47 thf(fact_340_swap__simp,axiom,
% 0.30/0.47 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz] :
% 0.30/0.47 ( ( produc532048446_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.30/0.47 = ( produc502616768t_unit @ Y @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % swap_simp
% 0.30/0.47 thf(fact_341_snd__swap,axiom,
% 0.30/0.47 ! [X: produc190496183real_c] :
% 0.30/0.47 ( ( produc314122909real_c @ ( produc704157711real_c @ X ) )
% 0.30/0.47 = ( produc2010422875real_c @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % snd_swap
% 0.30/0.47 thf(fact_342_fst__swap,axiom,
% 0.30/0.47 ! [X: produc190496183real_c] :
% 0.30/0.47 ( ( produc2010422875real_c @ ( produc704157711real_c @ X ) )
% 0.30/0.47 = ( produc314122909real_c @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % fst_swap
% 0.30/0.47 thf(fact_343_ids_Op1_Ocong,axiom,
% 0.30/0.47 p1_sz_sf_sc = p1_sz_sf_sc ).
% 0.30/0.47
% 0.30/0.47 % ids.p1.cong
% 0.30/0.47 thf(fact_344_ids_Op1__def,axiom,
% 0.30/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P2: sz,X: sz] :
% 0.30/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.30/0.47 => ( ( p1_sz_sf_sc @ Vid1 @ P2 @ X )
% 0.30/0.47 = ( prop_sz_sf_sc @ P2 @ ( singleton_sz_sf @ Vid1 @ ( var_sz_sf @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ids.p1_def
% 0.30/0.47 thf(fact_345_formula_Oset__intros_I3_J,axiom,
% 0.30/0.47 ! [Yb: trm_sf_sz,X222: sz > trm_sf_sz,Yc: sf,X21: sz] :
% 0.30/0.47 ( ( member_trm_sf_sz @ Yb @ ( image_sz_trm_sf_sz @ X222 @ top_top_set_sz ) )
% 0.30/0.47 => ( ( member_sf @ Yc @ ( set_trm_sf_sz2 @ Yb ) )
% 0.30/0.47 => ( member_sf @ Yc @ ( set1_f989022726_sc_sz @ ( prop_sz_sf_sc @ X21 @ X222 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % formula.set_intros(3)
% 0.30/0.47 thf(fact_346_hpfree__ffree_Ointros_I10_J,axiom,
% 0.30/0.47 ! [Args: sz > trm_sf_sz,P2: sz] :
% 0.30/0.47 ( ! [Arg: trm_sf_sz] :
% 0.30/0.47 ( ( member_trm_sf_sz @ Arg @ ( image_sz_trm_sf_sz @ Args @ top_top_set_sz ) )
% 0.30/0.47 => ( dfree_sf_sz @ Arg ) )
% 0.30/0.47 => ( ffree_sf_sc_sz @ ( prop_sz_sf_sc @ P2 @ Args ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % hpfree_ffree.intros(10)
% 0.30/0.47 thf(fact_347_hpfree__ffree_Ointros_I15_J,axiom,
% 0.30/0.47 ! [P: sc] : ( ffree_sf_sc_sz @ ( predic913887884_sf_sz @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % hpfree_ffree.intros(15)
% 0.30/0.47 thf(fact_348_map__prod__simp,axiom,
% 0.30/0.47 ! [F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz,A: denota610675952t_unit,B: produc866628903_sc_sz] :
% 0.30/0.47 ( ( produc403791768_sc_sz @ F2 @ G @ ( produc789536734_sc_sz @ A @ B ) )
% 0.30/0.47 = ( produc789536734_sc_sz @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_prod_simp
% 0.30/0.47 thf(fact_349_fst__map__prod,axiom,
% 0.30/0.47 ! [F2: finite1398487019real_c > finite1398487019real_c,G: finite1398487019real_c > finite1398487019real_c,X: produc190496183real_c] :
% 0.30/0.47 ( ( produc2010422875real_c @ ( produc368345510real_c @ F2 @ G @ X ) )
% 0.30/0.47 = ( F2 @ ( produc2010422875real_c @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fst_map_prod
% 0.30/0.47 thf(fact_350_snd__map__prod,axiom,
% 0.30/0.47 ! [F2: finite1398487019real_c > finite1398487019real_c,G: finite1398487019real_c > finite1398487019real_c,X: produc190496183real_c] :
% 0.30/0.47 ( ( produc314122909real_c @ ( produc368345510real_c @ F2 @ G @ X ) )
% 0.30/0.47 = ( G @ ( produc314122909real_c @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % snd_map_prod
% 0.30/0.47 thf(fact_351_map__prod__imageI,axiom,
% 0.30/0.47 ! [A: denota610675952t_unit,B: produc866628903_sc_sz,R4: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz] :
% 0.30/0.47 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A @ B ) @ R4 )
% 0.30/0.47 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_1726193375_sc_sz @ ( produc403791768_sc_sz @ F2 @ G ) @ R4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_prod_imageI
% 0.30/0.47 thf(fact_352_prod__fun__imageE,axiom,
% 0.30/0.47 ! [C2: produc1821101996_sc_sz,F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz,R4: set_Pr1169339874_sc_sz] :
% 0.30/0.47 ( ( member1057565379_sc_sz @ C2 @ ( image_1726193375_sc_sz @ ( produc403791768_sc_sz @ F2 @ G ) @ R4 ) )
% 0.30/0.47 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.30/0.47 ( ( C2
% 0.30/0.47 = ( produc789536734_sc_sz @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 0.30/0.47 => ~ ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ R4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % prod_fun_imageE
% 0.30/0.47
% 0.30/0.47 % Helper facts (3)
% 0.30/0.47 thf(help_If_3_1_If_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_T,axiom,
% 0.30/0.47 ! [P: $o] :
% 0.30/0.47 ( ( P = $true )
% 0.30/0.47 | ( P = $false ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_2_1_If_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_T,axiom,
% 0.30/0.47 ! [X: trm_sf_sz,Y: trm_sf_sz] :
% 0.30/0.47 ( ( if_trm_sf_sz @ $false @ X @ Y )
% 0.30/0.47 = Y ) ).
% 0.30/0.47
% 0.30/0.47 thf(help_If_1_1_If_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_T,axiom,
% 0.30/0.47 ! [X: trm_sf_sz,Y: trm_sf_sz] :
% 0.30/0.47 ( ( if_trm_sf_sz @ $true @ X @ Y )
% 0.30/0.47 = X ) ).
% 0.30/0.47
% 0.30/0.47 % Conjectures (1)
% 0.30/0.47 thf(conj_0,conjecture,
% 0.30/0.47 dfree_a_c @ ( args @ i2 ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 2.76/1.44 ---- Embedded in THF ---
% 2.76/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.76/1.44 %%% Generated on Tue Feb 24 08:24:17 EST 2026
% 2.76/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 2.76/1.44 %%% Logic specification used:
% 2.76/1.44 %%% thf(spec, logic, $$dhol).
% 2.76/1.44
% 2.76/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ItXc5YzKVO/DTF2DTF27746.p
% See solution above
% 2.76/1.45 ------------------------
% 2.76/1.48 ---- Cleaned THF ---
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 produc640052711real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J_J,type,
% 2.76/1.48 set_Pr2041213564t_unit: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_J,type,
% 2.76/1.48 set_Pr1169339874_sc_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 2.76/1.48 produc999471430t_unit: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 2.76/1.48 produc1821101996_sc_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 produc1952288593real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 produc99145217real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 produc1295591296real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Real__Oreal_J,type,
% 2.76/1.48 produc906325778c_real: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 set_Pr1389752855real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 2.76/1.48 produc1149990247eal_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 produc190496183real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 2.76/1.48 produc866628903_sc_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 produc729314338real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 produc1299700144real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 produc1471603704real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Real__Oreal_J,type,
% 2.76/1.48 produc133347448c_real: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 2.76/1.48 denota610675952t_unit: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 2.76/1.48 produc44682460um_c_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 2.76/1.48 produc189019228set_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 2.76/1.48 produc621499498um_c_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_Itf__c_J_J,type,
% 2.76/1.48 produc802386618_set_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J,type,
% 2.76/1.48 denota231621370t_unit: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 set_Fi1407883041real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 2.76/1.48 produc2057661729set_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_Itf__c_J_J,type,
% 2.76/1.48 produc1631500469_set_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 2.76/1.48 produc313687471set_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_Itf__c_J_J,type,
% 2.76/1.48 produc756982951_set_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_Mtf__sz_J,type,
% 2.76/1.48 produc861709536_sz_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 2.76/1.48 finite824932053eal_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 finite1398487019real_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 2.76/1.48 list_f1238882004_sc_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 2.76/1.48 produc957004601l_real: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J,type,
% 2.76/1.48 frechet_strm_sf_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__sz_Mtf__sz_J_J,type,
% 2.76/1.48 set_Sum_sum_sz_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__c_J,type,
% 2.76/1.48 frechet_strm_a_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 2.76/1.48 set_Sum_sum_c_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_J,type,
% 2.76/1.48 set_trm_sf_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_It__Syntax__Otrm_Itf__a_Mtf__c_J_J,type,
% 2.76/1.48 set_trm_a_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J,type,
% 2.76/1.48 formula_sf_sc_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 2.76/1.48 trm_sf_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 2.76/1.48 trm_a_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_Itf__sz_J,type,
% 2.76/1.48 set_sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_Itf__sf_J,type,
% 2.76/1.48 set_sf: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_Itf__c_J,type,
% 2.76/1.48 set_c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.76/1.48 set_a: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_t__Real__Oreal,type,
% 2.76/1.48 real: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_tf__sz,type,
% 2.76/1.48 sz: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_tf__sf,type,
% 2.76/1.48 sf: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_tf__sc,type,
% 2.76/1.48 sc: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_tf__c,type,
% 2.76/1.48 c: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(ty_n_tf__a,type,
% 2.76/1.48 a: $tType ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Denotational__Semantics_OVagree_001tf__c,type,
% 2.76/1.48 denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Denotational__Semantics_OVagree_001tf__sz,type,
% 2.76/1.48 denota102713844ree_sz: produc1149990247eal_sz > produc1149990247eal_sz > set_Sum_sum_sz_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Denotational__Semantics_Odirectional__derivative_001tf__a_001tf__b_001tf__c,type,
% 2.76/1.48 denota2112424896_a_b_c: denota231621370t_unit > trm_a_c > produc190496183real_c > real ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Denotational__Semantics_Ofrechet_001tf__a_001tf__b_001tf__c,type,
% 2.76/1.48 denota229585092_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > finite1398487019real_c > real ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm_001tf__a_001tf__c,type,
% 2.76/1.48 frechet_cr_strm_a_c: trm_a_c > frechet_strm_a_c > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Frechet__Correctness_Oids_Ocr__strm_001tf__sf_001tf__sz,type,
% 2.76/1.48 freche1244000341_sf_sz: trm_sf_sz > frechet_strm_sf_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 zero_z109254132real_c: finite1398487019real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 zero_z1506780526real_c: produc190496183real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 zero_z735295626real_c: produc99145217real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Real__Oreal_J,type,
% 2.76/1.48 zero_z1273814959c_real: produc133347448c_real ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 zero_z440955354real_c: produc1952288593real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 zero_z993734942real_c: produc640052711real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Real__Oreal_J,type,
% 2.76/1.48 zero_z1830236699c_real: produc906325778c_real ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 zero_z464587567real_c: produc1471603704real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 zero_z72018569real_c: produc1295591296real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 2.76/1.48 zero_z659284464l_real: produc957004601l_real ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 2.76/1.48 zero_zero_real: real ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Ids_Oids_001tf__sz_001tf__sf_001tf__sc,type,
% 2.76/1.48 ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_If_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 2.76/1.48 if_trm_sf_sz: $o > trm_sf_sz > trm_sf_sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_Itf__c_J_J,type,
% 2.76/1.48 top_to1309524330_set_c: produc802386618_set_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 2.76/1.48 top_to1246597548set_sz: produc189019228set_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 top_to1783191648real_c: produc1299700144real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 2.76/1.48 top_to1128637210um_c_c: produc621499498um_c_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_Itf__c_J_J,type,
% 2.76/1.48 top_to543326711_set_c: produc756982951_set_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__c_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 2.76/1.48 top_to1303770207set_sz: produc313687471set_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 top_to1102487922real_c: produc729314338real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_J,type,
% 2.76/1.48 top_to1102260780um_c_c: produc44682460um_c_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_Itf__c_J_J,type,
% 2.76/1.48 top_to474099557_set_c: produc1631500469_set_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Oprod_It__Set__Oset_Itf__sz_J_Mt__Set__Oset_Itf__sz_J_J,type,
% 2.76/1.48 top_to1999610481set_sz: produc2057661729set_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 top_to1642137041real_c: set_Fi1407883041real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 2.76/1.48 top_to226056039real_c: set_Pr1389752855real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 2.76/1.48 top_to1660572043um_c_c: set_Sum_sum_c_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__sz_Mtf__sz_J_J,type,
% 2.76/1.48 top_to1246370329_sz_sz: set_Sum_sum_sz_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__c_J,type,
% 2.76/1.48 top_top_set_c: set_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__sz_J,type,
% 2.76/1.48 top_top_set_sz: set_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 2.76/1.48 produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 produc1563404851real_c: finite1398487019real_c > produc190496183real_c > produc99145217real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Real__Oreal,type,
% 2.76/1.48 produc1715747632c_real: finite1398487019real_c > real > produc133347448c_real ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J,type,
% 2.76/1.48 produc1308130519eal_sz: finite824932053eal_sz > finite824932053eal_sz > produc1149990247eal_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 2.76/1.48 produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 produc116546123real_c: produc190496183real_c > finite1398487019real_c > produc1952288593real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Real__Oreal,type,
% 2.76/1.48 produc171591948c_real: produc190496183real_c > real > produc906325778c_real ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 2.76/1.48 produc502616768t_unit: produc866628903_sc_sz > denota610675952t_unit > produc999471430t_unit ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 produc1327150128real_c: real > finite1398487019real_c > produc1471603704real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 produc2134005810real_c: real > produc190496183real_c > produc1295591296real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Real__Oreal_001t__Real__Oreal,type,
% 2.76/1.48 produc705216881l_real: real > real > produc957004601l_real ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_001t__Set__Oset_Itf__c_J,type,
% 2.76/1.48 produc1767696108_set_c: set_Sum_sum_c_c > set_c > produc802386618_set_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J_001t__Set__Oset_Itf__sz_J,type,
% 2.76/1.48 produc1251379220set_sz: set_Sum_sum_c_c > set_sz > produc189019228set_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c_J_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 produc280329770real_c: set_c > set_Fi1407883041real_c > produc1299700144real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c_J_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 2.76/1.48 produc1519884516um_c_c: set_c > set_Sum_sum_c_c > produc621499498um_c_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c_J_001t__Set__Oset_Itf__c_J,type,
% 2.76/1.48 produc878845847_set_c: set_c > set_c > produc756982951_set_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__c_J_001t__Set__Oset_Itf__sz_J,type,
% 2.76/1.48 produc2039118377set_sz: set_c > set_sz > produc313687471set_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__sz_J_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 2.76/1.48 produc1915663706real_c: set_sz > set_Fi1407883041real_c > produc729314338real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__sz_J_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 2.76/1.48 produc590684180um_c_c: set_sz > set_Sum_sum_c_c > produc44682460um_c_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__sz_J_001t__Set__Oset_Itf__c_J,type,
% 2.76/1.48 produc760013927_set_c: set_sz > set_c > produc1631500469_set_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__sz_J_001t__Set__Oset_Itf__sz_J,type,
% 2.76/1.48 produc2156889set_sz: set_sz > set_sz > produc2057661729set_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_OPair_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001tf__sz,type,
% 2.76/1.48 produc792909658_sz_sz: trm_sf_sz > sz > produc861709536_sz_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Omap__prod_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 2.76/1.48 produc403791768_sc_sz: ( denota610675952t_unit > denota610675952t_unit ) > ( produc866628903_sc_sz > produc866628903_sc_sz ) > produc1821101996_sc_sz > produc1821101996_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Omap__prod_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 produc368345510real_c: ( finite1398487019real_c > finite1398487019real_c ) > ( finite1398487019real_c > finite1398487019real_c ) > produc190496183real_c > produc190496183real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Ofst_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 2.76/1.48 produc1503602930_sc_sz: produc1821101996_sc_sz > denota610675952t_unit ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Ofst_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 produc2010422875real_c: produc190496183real_c > finite1398487019real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Ofst_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 2.76/1.48 produc548504323_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 2.76/1.48 produc1216682964t_unit: produc999471430t_unit > produc866628903_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Ofst_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001tf__sz,type,
% 2.76/1.48 produc2069561454_sz_sz: produc861709536_sz_sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Osnd_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 2.76/1.48 produc974239792_sc_sz: produc1821101996_sc_sz > produc866628903_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Osnd_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 produc314122909real_c: produc190496183real_c > finite1398487019real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Osnd_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 2.76/1.48 produc4753477_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 2.76/1.48 produc687319826t_unit: produc999471430t_unit > denota610675952t_unit ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Osnd_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001tf__sz,type,
% 2.76/1.48 produc181739436_sz_sz: produc861709536_sz_sz > sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Oswap_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 2.76/1.48 produc532048446_sc_sz: produc1821101996_sc_sz > produc999471430t_unit ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Oswap_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 produc704157711real_c: produc190496183real_c > produc190496183real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Product__Type_Oprod_Oswap_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 2.76/1.48 produc245128480t_unit: produc999471430t_unit > produc1821101996_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Relation_ODomainp_001t__Syntax__Otrm_Itf__a_Mtf__c_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__c_J,type,
% 2.76/1.48 domain2047240575rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > trm_a_c > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Relation_ODomainp_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J,type,
% 2.76/1.48 domain512309999_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > trm_sf_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 2.76/1.48 collec377961627t_unit: ( produc999471430t_unit > $o ) > set_Pr2041213564t_unit ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_OCollect_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 2.76/1.48 collect_trm_a_c: ( trm_a_c > $o ) > set_trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_OCollect_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 2.76/1.48 collect_trm_sf_sz: ( trm_sf_sz > $o ) > set_trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.76/1.48 collect_a: ( a > $o ) > set_a ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_OCollect_001tf__sf,type,
% 2.76/1.48 collect_sf: ( sf > $o ) > set_sf ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 2.76/1.48 image_1726193375_sc_sz: ( produc1821101996_sc_sz > produc1821101996_sc_sz ) > set_Pr1169339874_sc_sz > set_Pr1169339874_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 2.76/1.48 image_904562809t_unit: ( produc1821101996_sc_sz > produc999471430t_unit ) > set_Pr1169339874_sc_sz > set_Pr2041213564t_unit ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 2.76/1.48 image_14429021real_c: ( produc190496183real_c > finite1398487019real_c ) > set_Pr1389752855real_c > set_Fi1407883041real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 2.76/1.48 image_1426741113_sc_sz: ( produc999471430t_unit > produc1821101996_sc_sz ) > set_Pr2041213564t_unit > set_Pr1169339874_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_Oimage_001tf__c_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 2.76/1.48 image_c_trm_a_c: ( c > trm_a_c ) > set_c > set_trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Set_Oimage_001tf__sz_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 2.76/1.48 image_sz_trm_sf_sz: ( sz > trm_sf_sz ) > set_sz > set_trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Static__Semantics_OFVDiff_001tf__a_001tf__c,type,
% 2.76/1.48 static_FVDiff_a_c: trm_a_c > set_Sum_sum_c_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Static__Semantics_OFVDiff_001tf__sf_001tf__sz,type,
% 2.76/1.48 static_FVDiff_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_OPredicational_001tf__sc_001tf__sf_001tf__sz,type,
% 2.76/1.48 predic913887884_sf_sz: sc > formula_sf_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Odfree_001tf__a_001tf__c,type,
% 2.76/1.48 dfree_a_c: trm_a_c > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Odfree_001tf__sf_001tf__sz,type,
% 2.76/1.48 dfree_sf_sz: trm_sf_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Odsafe_001tf__a_001tf__c,type,
% 2.76/1.48 dsafe_a_c: trm_a_c > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Odsafe_001tf__sf_001tf__sz,type,
% 2.76/1.48 dsafe_sf_sz: trm_sf_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Offree_001tf__sf_001tf__sc_001tf__sz,type,
% 2.76/1.48 ffree_sf_sc_sz: formula_sf_sc_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oformula_OProp_001tf__sz_001tf__sf_001tf__sc,type,
% 2.76/1.48 prop_sz_sf_sc: sz > ( sz > trm_sf_sz ) > formula_sf_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oformula_Oset1__formula_001tf__sf_001tf__sc_001tf__sz,type,
% 2.76/1.48 set1_f989022726_sc_sz: formula_sf_sc_sz > set_sf ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oids_OP_001tf__sc_001tf__sf_001tf__sz,type,
% 2.76/1.48 p_sc_sf_sz: sc > formula_sf_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oids_Oempty_001tf__c_001tf__a,type,
% 2.76/1.48 empty_c_a: c > trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oids_Oempty_001tf__sz_001tf__sf,type,
% 2.76/1.48 empty_sz_sf: sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oids_Of0_001tf__sf_001tf__sz,type,
% 2.76/1.48 f0_sf_sz: sf > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oids_Of1_001tf__sz_001tf__sf,type,
% 2.76/1.48 f1_sz_sf: sz > sf > sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oids_Op1_001tf__sz_001tf__sf_001tf__sc,type,
% 2.76/1.48 p1_sz_sf_sc: sz > sz > sz > formula_sf_sc_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oids_Osingleton_001tf__sz_001tf__sf,type,
% 2.76/1.48 singleton_sz_sf: sz > trm_sf_sz > sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Oids_Osingleton__rel_001tf__sf_001tf__sz,type,
% 2.76/1.48 singleton_rel_sf_sz: produc861709536_sz_sz > produc861709536_sz_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OConst_001tf__a_001tf__c,type,
% 2.76/1.48 const_a_c: real > trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OConst_001tf__sf_001tf__sz,type,
% 2.76/1.48 const_sf_sz: real > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_ODiffVar_001tf__c_001tf__a,type,
% 2.76/1.48 diffVar_c_a: c > trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_ODiffVar_001tf__sz_001tf__sf,type,
% 2.76/1.48 diffVar_sz_sf: sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_ODifferential_001tf__a_001tf__c,type,
% 2.76/1.48 differential_a_c: trm_a_c > trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_ODifferential_001tf__sf_001tf__sz,type,
% 2.76/1.48 differential_sf_sz: trm_sf_sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OFunction_001tf__a_001tf__c,type,
% 2.76/1.48 function_a_c: a > ( c > trm_a_c ) > trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OFunction_001tf__sf_001tf__sz,type,
% 2.76/1.48 function_sf_sz: sf > ( sz > trm_sf_sz ) > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OPlus_001tf__a_001tf__c,type,
% 2.76/1.48 plus_a_c: trm_a_c > trm_a_c > trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OPlus_001tf__sf_001tf__sz,type,
% 2.76/1.48 plus_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OTimes_001tf__a_001tf__c,type,
% 2.76/1.48 times_a_c: trm_a_c > trm_a_c > trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OTimes_001tf__sf_001tf__sz,type,
% 2.76/1.48 times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OVar_001tf__c_001tf__a,type,
% 2.76/1.48 var_c_a: c > trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_OVar_001tf__sz_001tf__sf,type,
% 2.76/1.48 var_sz_sf: sz > trm_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_Oset__trm_001tf__a_001tf__c,type,
% 2.76/1.48 set_trm_a_c2: trm_a_c > set_a ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Syntax_Otrm_Oset__trm_001tf__sf_001tf__sz,type,
% 2.76/1.48 set_trm_sf_sz2: trm_sf_sz > set_sf ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Transfer_Oleft__unique_001t__Syntax__Otrm_Itf__a_Mtf__c_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__c_J,type,
% 2.76/1.48 left_u968903956rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Transfer_Oleft__unique_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J,type,
% 2.76/1.48 left_u638806404_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Transfer_Oright__unique_001t__Syntax__Otrm_Itf__a_Mtf__c_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__a_Mtf__c_J,type,
% 2.76/1.48 right_1933252621rm_a_c: ( trm_a_c > frechet_strm_a_c > $o ) > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Transfer_Oright__unique_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_001t__Frechet____Correctness__Oids__Ostrm_Itf__sf_Mtf__sz_J,type,
% 2.76/1.48 right_963419005_sf_sz: ( trm_sf_sz > frechet_strm_sf_sz > $o ) > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Syntax__Otrm_Itf__sf_Mtf__sz_J_Mtf__sz_J,type,
% 2.76/1.48 accp_P529224471_sz_sz: ( produc861709536_sz_sz > produc861709536_sz_sz > $o ) > produc861709536_sz_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_member_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 2.76/1.48 member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 2.76/1.48 member235934813t_unit: produc999471430t_unit > set_Pr2041213564t_unit > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_member_001t__Syntax__Otrm_Itf__a_Mtf__c_J,type,
% 2.76/1.48 member_trm_a_c: trm_a_c > set_trm_a_c > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_member_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J,type,
% 2.76/1.48 member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_member_001tf__a,type,
% 2.76/1.48 member_a: a > set_a > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_c_member_001tf__sf,type,
% 2.76/1.48 member_sf: sf > set_sf > $o ).
% 2.76/1.48
% 2.76/1.48 thf(sy_v_I,type,
% 2.76/1.48 i: denota231621370t_unit ).
% 2.76/1.48
% 2.76/1.48 thf(sy_v__092_060nu_062,type,
% 2.76/1.48 nu: produc190496183real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_v__092_060nu_062_H,type,
% 2.76/1.48 nu2: produc190496183real_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_v_args____,type,
% 2.76/1.48 args: c > trm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_v_i,type,
% 2.76/1.48 i2: c ).
% 2.76/1.48
% 2.76/1.48 thf(sy_v_var____,type,
% 2.76/1.48 var: a ).
% 2.76/1.48
% 2.76/1.48 thf(sy_v_vid1,type,
% 2.76/1.48 vid1: sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_v_vid2,type,
% 2.76/1.48 vid2: sz ).
% 2.76/1.48
% 2.76/1.48 thf(sy_v_vid3,type,
% 2.76/1.48 vid3: sz ).
% 2.76/1.48
% 2.76/1.48 thf(fact_0_free,axiom,
% 2.76/1.48 ! [I: c] : ( dfree_a_c @ ( args @ I ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_1_P__def,axiom,
% 2.76/1.48 p_sc_sf_sz = predic913887884_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(fact_2_strm_Odomain,axiom,
% 2.76/1.48 ( ( domain512309999_sf_sz @ freche1244000341_sf_sz )
% 2.76/1.48 = dfree_sf_sz ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_3_strm_Odomain,axiom,
% 2.76/1.48 ( ( domain2047240575rm_a_c @ frechet_cr_strm_a_c )
% 2.76/1.48 = dfree_a_c ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_4_dfree__DiffVar__simps,axiom,
% 2.76/1.48 ! [X: sz] :
% 2.76/1.48 ~ ( dfree_sf_sz @ ( diffVar_sz_sf @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_5_dfree__DiffVar__simps,axiom,
% 2.76/1.48 ! [X: c] :
% 2.76/1.48 ~ ( dfree_a_c @ ( diffVar_c_a @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_6_seq__sem_Ocases,axiom,
% 2.76/1.48 ! [X: produc1821101996_sc_sz] :
% 2.76/1.48 ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 2.76/1.48 ( X
% 2.76/1.48 != ( produc789536734_sc_sz @ I2 @ S ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_7_singleton_Ocases,axiom,
% 2.76/1.48 ! [X: produc861709536_sz_sz] :
% 2.76/1.48 ~ ! [T: trm_sf_sz,I3: sz] :
% 2.76/1.48 ( X
% 2.76/1.48 != ( produc792909658_sz_sz @ T @ I3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_8_dfree__Differential__simps,axiom,
% 2.76/1.48 ! [X: trm_sf_sz] :
% 2.76/1.48 ~ ( dfree_sf_sz @ ( differential_sf_sz @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_9_dfree__Differential__simps,axiom,
% 2.76/1.48 ! [X: trm_a_c] :
% 2.76/1.48 ~ ( dfree_a_c @ ( differential_a_c @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_10_dfree__Var__simps,axiom,
% 2.76/1.48 ! [X: c] : ( dfree_a_c @ ( var_c_a @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_11_dfree__Var__simps,axiom,
% 2.76/1.48 ! [X: sz] : ( dfree_sf_sz @ ( var_sz_sf @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_12_dfree__Times__simps,axiom,
% 2.76/1.48 ! [A: trm_a_c,B: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ ( times_a_c @ A @ B ) )
% 2.76/1.48 = ( ( dfree_a_c @ A )
% 2.76/1.48 & ( dfree_a_c @ B ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_13_dfree__Times__simps,axiom,
% 2.76/1.48 ! [A: trm_sf_sz,B: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ ( times_sf_sz @ A @ B ) )
% 2.76/1.48 = ( ( dfree_sf_sz @ A )
% 2.76/1.48 & ( dfree_sf_sz @ B ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_14_dfree__Plus__simps,axiom,
% 2.76/1.48 ! [A: trm_a_c,B: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ ( plus_a_c @ A @ B ) )
% 2.76/1.48 = ( ( dfree_a_c @ A )
% 2.76/1.48 & ( dfree_a_c @ B ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_15_dfree__Plus__simps,axiom,
% 2.76/1.48 ! [A: trm_sf_sz,B: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ ( plus_sf_sz @ A @ B ) )
% 2.76/1.48 = ( ( dfree_sf_sz @ A )
% 2.76/1.48 & ( dfree_sf_sz @ B ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_16_dfree__Fun_Oprems,axiom,
% 2.76/1.48 denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( function_a_c @ var @ args ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_17_trm_Oinject_I3_J,axiom,
% 2.76/1.48 ! [X31: a,X32: c > trm_a_c,Y31: a,Y32: c > trm_a_c] :
% 2.76/1.48 ( ( ( function_a_c @ X31 @ X32 )
% 2.76/1.48 = ( function_a_c @ Y31 @ Y32 ) )
% 2.76/1.48 = ( ( X31 = Y31 )
% 2.76/1.48 & ( X32 = Y32 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_18_trm_Oinject_I3_J,axiom,
% 2.76/1.48 ! [X31: sf,X32: sz > trm_sf_sz,Y31: sf,Y32: sz > trm_sf_sz] :
% 2.76/1.48 ( ( ( function_sf_sz @ X31 @ X32 )
% 2.76/1.48 = ( function_sf_sz @ Y31 @ Y32 ) )
% 2.76/1.48 = ( ( X31 = Y31 )
% 2.76/1.48 & ( X32 = Y32 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_19_trm_Oinject_I4_J,axiom,
% 2.76/1.48 ! [X41: trm_sf_sz,X42: trm_sf_sz,Y41: trm_sf_sz,Y42: trm_sf_sz] :
% 2.76/1.48 ( ( ( plus_sf_sz @ X41 @ X42 )
% 2.76/1.48 = ( plus_sf_sz @ Y41 @ Y42 ) )
% 2.76/1.48 = ( ( X41 = Y41 )
% 2.76/1.48 & ( X42 = Y42 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_20_trm_Oinject_I4_J,axiom,
% 2.76/1.48 ! [X41: trm_a_c,X42: trm_a_c,Y41: trm_a_c,Y42: trm_a_c] :
% 2.76/1.48 ( ( ( plus_a_c @ X41 @ X42 )
% 2.76/1.48 = ( plus_a_c @ Y41 @ Y42 ) )
% 2.76/1.48 = ( ( X41 = Y41 )
% 2.76/1.48 & ( X42 = Y42 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_21_trm_Oinject_I5_J,axiom,
% 2.76/1.48 ! [X51: trm_sf_sz,X52: trm_sf_sz,Y51: trm_sf_sz,Y52: trm_sf_sz] :
% 2.76/1.48 ( ( ( times_sf_sz @ X51 @ X52 )
% 2.76/1.48 = ( times_sf_sz @ Y51 @ Y52 ) )
% 2.76/1.48 = ( ( X51 = Y51 )
% 2.76/1.48 & ( X52 = Y52 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_22_trm_Oinject_I5_J,axiom,
% 2.76/1.48 ! [X51: trm_a_c,X52: trm_a_c,Y51: trm_a_c,Y52: trm_a_c] :
% 2.76/1.48 ( ( ( times_a_c @ X51 @ X52 )
% 2.76/1.48 = ( times_a_c @ Y51 @ Y52 ) )
% 2.76/1.48 = ( ( X51 = Y51 )
% 2.76/1.48 & ( X52 = Y52 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_23_trm_Oinject_I1_J,axiom,
% 2.76/1.48 ! [X1: sz,Y1: sz] :
% 2.76/1.48 ( ( ( var_sz_sf @ X1 )
% 2.76/1.48 = ( var_sz_sf @ Y1 ) )
% 2.76/1.48 = ( X1 = Y1 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_24_trm_Oinject_I1_J,axiom,
% 2.76/1.48 ! [X1: c,Y1: c] :
% 2.76/1.48 ( ( ( var_c_a @ X1 )
% 2.76/1.48 = ( var_c_a @ Y1 ) )
% 2.76/1.48 = ( X1 = Y1 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_25_trm_Oinject_I7_J,axiom,
% 2.76/1.48 ! [X7: trm_sf_sz,Y7: trm_sf_sz] :
% 2.76/1.48 ( ( ( differential_sf_sz @ X7 )
% 2.76/1.48 = ( differential_sf_sz @ Y7 ) )
% 2.76/1.48 = ( X7 = Y7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_26_trm_Oinject_I7_J,axiom,
% 2.76/1.48 ! [X7: trm_a_c,Y7: trm_a_c] :
% 2.76/1.48 ( ( ( differential_a_c @ X7 )
% 2.76/1.48 = ( differential_a_c @ Y7 ) )
% 2.76/1.48 = ( X7 = Y7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_27_trm_Oinject_I6_J,axiom,
% 2.76/1.48 ! [X6: sz,Y6: sz] :
% 2.76/1.48 ( ( ( diffVar_sz_sf @ X6 )
% 2.76/1.48 = ( diffVar_sz_sf @ Y6 ) )
% 2.76/1.48 = ( X6 = Y6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_28_trm_Oinject_I6_J,axiom,
% 2.76/1.48 ! [X6: c,Y6: c] :
% 2.76/1.48 ( ( ( diffVar_c_a @ X6 )
% 2.76/1.48 = ( diffVar_c_a @ Y6 ) )
% 2.76/1.48 = ( X6 = Y6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_29_dfree__Fun__simps,axiom,
% 2.76/1.48 ! [I: a,Args: c > trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ ( function_a_c @ I @ Args ) )
% 2.76/1.48 = ( ! [X2: c] : ( dfree_a_c @ ( Args @ X2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_30_dfree__Fun__simps,axiom,
% 2.76/1.48 ! [I: sf,Args: sz > trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) )
% 2.76/1.48 = ( ! [X2: sz] : ( dfree_sf_sz @ ( Args @ X2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_31_trm_Odistinct_I41_J,axiom,
% 2.76/1.48 ! [X6: sz,X7: trm_sf_sz] :
% 2.76/1.48 ( ( diffVar_sz_sf @ X6 )
% 2.76/1.48 != ( differential_sf_sz @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_32_trm_Odistinct_I41_J,axiom,
% 2.76/1.48 ! [X6: c,X7: trm_a_c] :
% 2.76/1.48 ( ( diffVar_c_a @ X6 )
% 2.76/1.48 != ( differential_a_c @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_33_trm_Odistinct_I39_J,axiom,
% 2.76/1.48 ! [X51: trm_sf_sz,X52: trm_sf_sz,X7: trm_sf_sz] :
% 2.76/1.48 ( ( times_sf_sz @ X51 @ X52 )
% 2.76/1.48 != ( differential_sf_sz @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_34_trm_Odistinct_I39_J,axiom,
% 2.76/1.48 ! [X51: trm_a_c,X52: trm_a_c,X7: trm_a_c] :
% 2.76/1.48 ( ( times_a_c @ X51 @ X52 )
% 2.76/1.48 != ( differential_a_c @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_35_trm_Odistinct_I37_J,axiom,
% 2.76/1.48 ! [X51: trm_sf_sz,X52: trm_sf_sz,X6: sz] :
% 2.76/1.48 ( ( times_sf_sz @ X51 @ X52 )
% 2.76/1.48 != ( diffVar_sz_sf @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_36_trm_Odistinct_I37_J,axiom,
% 2.76/1.48 ! [X51: trm_a_c,X52: trm_a_c,X6: c] :
% 2.76/1.48 ( ( times_a_c @ X51 @ X52 )
% 2.76/1.48 != ( diffVar_c_a @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_37_trm_Odistinct_I35_J,axiom,
% 2.76/1.48 ! [X41: trm_sf_sz,X42: trm_sf_sz,X7: trm_sf_sz] :
% 2.76/1.48 ( ( plus_sf_sz @ X41 @ X42 )
% 2.76/1.48 != ( differential_sf_sz @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_38_trm_Odistinct_I35_J,axiom,
% 2.76/1.48 ! [X41: trm_a_c,X42: trm_a_c,X7: trm_a_c] :
% 2.76/1.48 ( ( plus_a_c @ X41 @ X42 )
% 2.76/1.48 != ( differential_a_c @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_39_trm_Odistinct_I33_J,axiom,
% 2.76/1.48 ! [X41: trm_sf_sz,X42: trm_sf_sz,X6: sz] :
% 2.76/1.48 ( ( plus_sf_sz @ X41 @ X42 )
% 2.76/1.48 != ( diffVar_sz_sf @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_40_trm_Odistinct_I33_J,axiom,
% 2.76/1.48 ! [X41: trm_a_c,X42: trm_a_c,X6: c] :
% 2.76/1.48 ( ( plus_a_c @ X41 @ X42 )
% 2.76/1.48 != ( diffVar_c_a @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_41_trm_Odistinct_I31_J,axiom,
% 2.76/1.48 ! [X41: trm_sf_sz,X42: trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 2.76/1.48 ( ( plus_sf_sz @ X41 @ X42 )
% 2.76/1.48 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_42_trm_Odistinct_I31_J,axiom,
% 2.76/1.48 ! [X41: trm_a_c,X42: trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 2.76/1.48 ( ( plus_a_c @ X41 @ X42 )
% 2.76/1.48 != ( times_a_c @ X51 @ X52 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_43_trm_Odistinct_I29_J,axiom,
% 2.76/1.48 ! [X31: sf,X32: sz > trm_sf_sz,X7: trm_sf_sz] :
% 2.76/1.48 ( ( function_sf_sz @ X31 @ X32 )
% 2.76/1.48 != ( differential_sf_sz @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_44_trm_Odistinct_I29_J,axiom,
% 2.76/1.48 ! [X31: a,X32: c > trm_a_c,X7: trm_a_c] :
% 2.76/1.48 ( ( function_a_c @ X31 @ X32 )
% 2.76/1.48 != ( differential_a_c @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_45_trm_Odistinct_I27_J,axiom,
% 2.76/1.48 ! [X31: a,X32: c > trm_a_c,X6: c] :
% 2.76/1.48 ( ( function_a_c @ X31 @ X32 )
% 2.76/1.48 != ( diffVar_c_a @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_46_trm_Odistinct_I27_J,axiom,
% 2.76/1.48 ! [X31: sf,X32: sz > trm_sf_sz,X6: sz] :
% 2.76/1.48 ( ( function_sf_sz @ X31 @ X32 )
% 2.76/1.48 != ( diffVar_sz_sf @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_47_trm_Odistinct_I25_J,axiom,
% 2.76/1.48 ! [X31: a,X32: c > trm_a_c,X51: trm_a_c,X52: trm_a_c] :
% 2.76/1.48 ( ( function_a_c @ X31 @ X32 )
% 2.76/1.48 != ( times_a_c @ X51 @ X52 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_48_trm_Odistinct_I25_J,axiom,
% 2.76/1.48 ! [X31: sf,X32: sz > trm_sf_sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 2.76/1.48 ( ( function_sf_sz @ X31 @ X32 )
% 2.76/1.48 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_49_trm_Odistinct_I23_J,axiom,
% 2.76/1.48 ! [X31: a,X32: c > trm_a_c,X41: trm_a_c,X42: trm_a_c] :
% 2.76/1.48 ( ( function_a_c @ X31 @ X32 )
% 2.76/1.48 != ( plus_a_c @ X41 @ X42 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_50_trm_Odistinct_I23_J,axiom,
% 2.76/1.48 ! [X31: sf,X32: sz > trm_sf_sz,X41: trm_sf_sz,X42: trm_sf_sz] :
% 2.76/1.48 ( ( function_sf_sz @ X31 @ X32 )
% 2.76/1.48 != ( plus_sf_sz @ X41 @ X42 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_51_trm_Odistinct_I11_J,axiom,
% 2.76/1.48 ! [X1: sz,X7: trm_sf_sz] :
% 2.76/1.48 ( ( var_sz_sf @ X1 )
% 2.76/1.48 != ( differential_sf_sz @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_52_trm_Odistinct_I11_J,axiom,
% 2.76/1.48 ! [X1: c,X7: trm_a_c] :
% 2.76/1.48 ( ( var_c_a @ X1 )
% 2.76/1.48 != ( differential_a_c @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_53_trm_Odistinct_I9_J,axiom,
% 2.76/1.48 ! [X1: sz,X6: sz] :
% 2.76/1.48 ( ( var_sz_sf @ X1 )
% 2.76/1.48 != ( diffVar_sz_sf @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_54_trm_Odistinct_I9_J,axiom,
% 2.76/1.48 ! [X1: c,X6: c] :
% 2.76/1.48 ( ( var_c_a @ X1 )
% 2.76/1.48 != ( diffVar_c_a @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_55_trm_Odistinct_I7_J,axiom,
% 2.76/1.48 ! [X1: sz,X51: trm_sf_sz,X52: trm_sf_sz] :
% 2.76/1.48 ( ( var_sz_sf @ X1 )
% 2.76/1.48 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_56_trm_Odistinct_I7_J,axiom,
% 2.76/1.48 ! [X1: c,X51: trm_a_c,X52: trm_a_c] :
% 2.76/1.48 ( ( var_c_a @ X1 )
% 2.76/1.48 != ( times_a_c @ X51 @ X52 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_57_trm_Odistinct_I5_J,axiom,
% 2.76/1.48 ! [X1: sz,X41: trm_sf_sz,X42: trm_sf_sz] :
% 2.76/1.48 ( ( var_sz_sf @ X1 )
% 2.76/1.48 != ( plus_sf_sz @ X41 @ X42 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_58_trm_Odistinct_I5_J,axiom,
% 2.76/1.48 ! [X1: c,X41: trm_a_c,X42: trm_a_c] :
% 2.76/1.48 ( ( var_c_a @ X1 )
% 2.76/1.48 != ( plus_a_c @ X41 @ X42 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_59_trm_Odistinct_I3_J,axiom,
% 2.76/1.48 ! [X1: c,X31: a,X32: c > trm_a_c] :
% 2.76/1.48 ( ( var_c_a @ X1 )
% 2.76/1.48 != ( function_a_c @ X31 @ X32 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_60_trm_Odistinct_I3_J,axiom,
% 2.76/1.48 ! [X1: sz,X31: sf,X32: sz > trm_sf_sz] :
% 2.76/1.48 ( ( var_sz_sf @ X1 )
% 2.76/1.48 != ( function_sf_sz @ X31 @ X32 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_61_dfree_Odfree__Fun,axiom,
% 2.76/1.48 ! [Args: c > trm_a_c,I: a] :
% 2.76/1.48 ( ! [I3: c] : ( dfree_a_c @ ( Args @ I3 ) )
% 2.76/1.48 => ( dfree_a_c @ ( function_a_c @ I @ Args ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_62_dfree_Odfree__Fun,axiom,
% 2.76/1.48 ! [Args: sz > trm_sf_sz,I: sf] :
% 2.76/1.48 ( ! [I3: sz] : ( dfree_sf_sz @ ( Args @ I3 ) )
% 2.76/1.48 => ( dfree_sf_sz @ ( function_sf_sz @ I @ Args ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_63_dfree__Plus,axiom,
% 2.76/1.48 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ Theta_1 )
% 2.76/1.48 => ( ( dfree_a_c @ Theta_2 )
% 2.76/1.48 => ( dfree_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_64_dfree__Plus,axiom,
% 2.76/1.48 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ Theta_1 )
% 2.76/1.48 => ( ( dfree_sf_sz @ Theta_2 )
% 2.76/1.48 => ( dfree_sf_sz @ ( plus_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_65_dfree__Times,axiom,
% 2.76/1.48 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ Theta_1 )
% 2.76/1.48 => ( ( dfree_a_c @ Theta_2 )
% 2.76/1.48 => ( dfree_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_66_dfree__Times,axiom,
% 2.76/1.48 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ Theta_1 )
% 2.76/1.48 => ( ( dfree_sf_sz @ Theta_2 )
% 2.76/1.48 => ( dfree_sf_sz @ ( times_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_67_dfree__Var,axiom,
% 2.76/1.48 ! [I: sz] : ( dfree_sf_sz @ ( var_sz_sf @ I ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_68_dfree__Var,axiom,
% 2.76/1.48 ! [I: c] : ( dfree_a_c @ ( var_c_a @ I ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_69_agree__times1,axiom,
% 2.76/1.48 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 2.76/1.48 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 2.76/1.48 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T1 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_70_agree__times1,axiom,
% 2.76/1.48 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 2.76/1.48 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 2.76/1.48 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T1 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_71_agree__times2,axiom,
% 2.76/1.48 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 2.76/1.48 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( times_sf_sz @ T1 @ T2 ) ) )
% 2.76/1.48 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_72_agree__times2,axiom,
% 2.76/1.48 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 2.76/1.48 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( times_a_c @ T1 @ T2 ) ) )
% 2.76/1.48 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_73_agree__plus1,axiom,
% 2.76/1.48 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 2.76/1.48 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( plus_sf_sz @ T1 @ T2 ) ) )
% 2.76/1.48 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T1 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_74_agree__plus1,axiom,
% 2.76/1.48 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 2.76/1.48 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ T1 @ T2 ) ) )
% 2.76/1.48 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T1 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_75_agree__plus2,axiom,
% 2.76/1.48 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,T1: trm_sf_sz,T2: trm_sf_sz] :
% 2.76/1.48 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( plus_sf_sz @ T1 @ T2 ) ) )
% 2.76/1.48 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ T2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_76_agree__plus2,axiom,
% 2.76/1.48 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,T1: trm_a_c,T2: trm_a_c] :
% 2.76/1.48 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( plus_a_c @ T1 @ T2 ) ) )
% 2.76/1.48 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ T2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_77_mem__Collect__eq,axiom,
% 2.76/1.48 ! [A: produc999471430t_unit,P: produc999471430t_unit > $o] :
% 2.76/1.48 ( ( member235934813t_unit @ A @ ( collec377961627t_unit @ P ) )
% 2.76/1.48 = ( P @ A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_78_mem__Collect__eq,axiom,
% 2.76/1.48 ! [A: trm_sf_sz,P: trm_sf_sz > $o] :
% 2.76/1.48 ( ( member_trm_sf_sz @ A @ ( collect_trm_sf_sz @ P ) )
% 2.76/1.48 = ( P @ A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_79_mem__Collect__eq,axiom,
% 2.76/1.48 ! [A: trm_a_c,P: trm_a_c > $o] :
% 2.76/1.48 ( ( member_trm_a_c @ A @ ( collect_trm_a_c @ P ) )
% 2.76/1.48 = ( P @ A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_80_mem__Collect__eq,axiom,
% 2.76/1.48 ! [A: sf,P: sf > $o] :
% 2.76/1.48 ( ( member_sf @ A @ ( collect_sf @ P ) )
% 2.76/1.48 = ( P @ A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_81_mem__Collect__eq,axiom,
% 2.76/1.48 ! [A: a,P: a > $o] :
% 2.76/1.48 ( ( member_a @ A @ ( collect_a @ P ) )
% 2.76/1.48 = ( P @ A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_82_Collect__mem__eq,axiom,
% 2.76/1.48 ! [A2: set_Pr2041213564t_unit] :
% 2.76/1.48 ( ( collec377961627t_unit
% 2.76/1.48 @ ^ [X2: produc999471430t_unit] : ( member235934813t_unit @ X2 @ A2 ) )
% 2.76/1.48 = A2 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_83_Collect__mem__eq,axiom,
% 2.76/1.48 ! [A2: set_trm_sf_sz] :
% 2.76/1.48 ( ( collect_trm_sf_sz
% 2.76/1.48 @ ^ [X2: trm_sf_sz] : ( member_trm_sf_sz @ X2 @ A2 ) )
% 2.76/1.48 = A2 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_84_Collect__mem__eq,axiom,
% 2.76/1.48 ! [A2: set_trm_a_c] :
% 2.76/1.48 ( ( collect_trm_a_c
% 2.76/1.48 @ ^ [X2: trm_a_c] : ( member_trm_a_c @ X2 @ A2 ) )
% 2.76/1.48 = A2 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_85_Collect__mem__eq,axiom,
% 2.76/1.48 ! [A2: set_sf] :
% 2.76/1.48 ( ( collect_sf
% 2.76/1.48 @ ^ [X2: sf] : ( member_sf @ X2 @ A2 ) )
% 2.76/1.48 = A2 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_86_Collect__mem__eq,axiom,
% 2.76/1.48 ! [A2: set_a] :
% 2.76/1.48 ( ( collect_a
% 2.76/1.48 @ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
% 2.76/1.48 = A2 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_87_agree__func,axiom,
% 2.76/1.48 ! [Nu: produc1149990247eal_sz,Nu2: produc1149990247eal_sz,Var: sf,Args: sz > trm_sf_sz,I: sz] :
% 2.76/1.48 ( ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( function_sf_sz @ Var @ Args ) ) )
% 2.76/1.48 => ( denota102713844ree_sz @ Nu @ Nu2 @ ( static_FVDiff_sf_sz @ ( Args @ I ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_88_agree__func,axiom,
% 2.76/1.48 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Var: a,Args: c > trm_a_c,I: c] :
% 2.76/1.48 ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( function_a_c @ Var @ Args ) ) )
% 2.76/1.48 => ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVDiff_a_c @ ( Args @ I ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_89_prod_Oinject,axiom,
% 2.76/1.48 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz,Y1: list_f1238882004_sc_sz,Y2: list_f1238882004_sc_sz] :
% 2.76/1.48 ( ( ( produc1822718231_sc_sz @ X1 @ X22 )
% 2.76/1.48 = ( produc1822718231_sc_sz @ Y1 @ Y2 ) )
% 2.76/1.48 = ( ( X1 = Y1 )
% 2.76/1.48 & ( X22 = Y2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_90_prod_Oinject,axiom,
% 2.76/1.48 ! [X1: finite1398487019real_c,X22: finite1398487019real_c,Y1: finite1398487019real_c,Y2: finite1398487019real_c] :
% 2.76/1.48 ( ( ( produc394644079real_c @ X1 @ X22 )
% 2.76/1.48 = ( produc394644079real_c @ Y1 @ Y2 ) )
% 2.76/1.48 = ( ( X1 = Y1 )
% 2.76/1.48 & ( X22 = Y2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_91_prod_Oinject,axiom,
% 2.76/1.48 ! [X1: trm_sf_sz,X22: sz,Y1: trm_sf_sz,Y2: sz] :
% 2.76/1.48 ( ( ( produc792909658_sz_sz @ X1 @ X22 )
% 2.76/1.48 = ( produc792909658_sz_sz @ Y1 @ Y2 ) )
% 2.76/1.48 = ( ( X1 = Y1 )
% 2.76/1.48 & ( X22 = Y2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_92_prod_Oinject,axiom,
% 2.76/1.48 ! [X1: produc866628903_sc_sz,X22: denota610675952t_unit,Y1: produc866628903_sc_sz,Y2: denota610675952t_unit] :
% 2.76/1.48 ( ( ( produc502616768t_unit @ X1 @ X22 )
% 2.76/1.48 = ( produc502616768t_unit @ Y1 @ Y2 ) )
% 2.76/1.48 = ( ( X1 = Y1 )
% 2.76/1.48 & ( X22 = Y2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_93_prod_Oinject,axiom,
% 2.76/1.48 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz,Y1: denota610675952t_unit,Y2: produc866628903_sc_sz] :
% 2.76/1.48 ( ( ( produc789536734_sc_sz @ X1 @ X22 )
% 2.76/1.48 = ( produc789536734_sc_sz @ Y1 @ Y2 ) )
% 2.76/1.48 = ( ( X1 = Y1 )
% 2.76/1.48 & ( X22 = Y2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_94_old_Oprod_Oinject,axiom,
% 2.76/1.48 ! [A: list_f1238882004_sc_sz,B: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 2.76/1.48 ( ( ( produc1822718231_sc_sz @ A @ B )
% 2.76/1.48 = ( produc1822718231_sc_sz @ A3 @ B2 ) )
% 2.76/1.48 = ( ( A = A3 )
% 2.76/1.48 & ( B = B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_95_old_Oprod_Oinject,axiom,
% 2.76/1.48 ! [A: finite1398487019real_c,B: finite1398487019real_c,A3: finite1398487019real_c,B2: finite1398487019real_c] :
% 2.76/1.48 ( ( ( produc394644079real_c @ A @ B )
% 2.76/1.48 = ( produc394644079real_c @ A3 @ B2 ) )
% 2.76/1.48 = ( ( A = A3 )
% 2.76/1.48 & ( B = B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_96_old_Oprod_Oinject,axiom,
% 2.76/1.48 ! [A: trm_sf_sz,B: sz,A3: trm_sf_sz,B2: sz] :
% 2.76/1.48 ( ( ( produc792909658_sz_sz @ A @ B )
% 2.76/1.48 = ( produc792909658_sz_sz @ A3 @ B2 ) )
% 2.76/1.48 = ( ( A = A3 )
% 2.76/1.48 & ( B = B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_97_old_Oprod_Oinject,axiom,
% 2.76/1.48 ! [A: produc866628903_sc_sz,B: denota610675952t_unit,A3: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 2.76/1.48 ( ( ( produc502616768t_unit @ A @ B )
% 2.76/1.48 = ( produc502616768t_unit @ A3 @ B2 ) )
% 2.76/1.48 = ( ( A = A3 )
% 2.76/1.48 & ( B = B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_98_old_Oprod_Oinject,axiom,
% 2.76/1.48 ! [A: denota610675952t_unit,B: produc866628903_sc_sz,A3: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 2.76/1.48 ( ( ( produc789536734_sc_sz @ A @ B )
% 2.76/1.48 = ( produc789536734_sc_sz @ A3 @ B2 ) )
% 2.76/1.48 = ( ( A = A3 )
% 2.76/1.48 & ( B = B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_99_trm_Oexhaust,axiom,
% 2.76/1.48 ! [Y: trm_sf_sz] :
% 2.76/1.48 ( ! [X12: sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( var_sz_sf @ X12 ) )
% 2.76/1.48 => ( ! [X23: real] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( const_sf_sz @ X23 ) )
% 2.76/1.48 => ( ! [X312: sf,X322: sz > trm_sf_sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( function_sf_sz @ X312 @ X322 ) )
% 2.76/1.48 => ( ! [X412: trm_sf_sz,X422: trm_sf_sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( plus_sf_sz @ X412 @ X422 ) )
% 2.76/1.48 => ( ! [X512: trm_sf_sz,X522: trm_sf_sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( times_sf_sz @ X512 @ X522 ) )
% 2.76/1.48 => ( ! [X62: sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( diffVar_sz_sf @ X62 ) )
% 2.76/1.48 => ~ ! [X72: trm_sf_sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( differential_sf_sz @ X72 ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_100_trm_Oexhaust,axiom,
% 2.76/1.48 ! [Y: trm_a_c] :
% 2.76/1.48 ( ! [X12: c] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( var_c_a @ X12 ) )
% 2.76/1.48 => ( ! [X23: real] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( const_a_c @ X23 ) )
% 2.76/1.48 => ( ! [X312: a,X322: c > trm_a_c] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( function_a_c @ X312 @ X322 ) )
% 2.76/1.48 => ( ! [X412: trm_a_c,X422: trm_a_c] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( plus_a_c @ X412 @ X422 ) )
% 2.76/1.48 => ( ! [X512: trm_a_c,X522: trm_a_c] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( times_a_c @ X512 @ X522 ) )
% 2.76/1.48 => ( ! [X62: c] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( diffVar_c_a @ X62 ) )
% 2.76/1.48 => ~ ! [X72: trm_a_c] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( differential_a_c @ X72 ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_101_prod__cases3,axiom,
% 2.76/1.48 ! [Y: produc1821101996_sc_sz] :
% 2.76/1.48 ~ ! [A4: denota610675952t_unit,B3: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B3 @ C ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_102_trm_Oinject_I2_J,axiom,
% 2.76/1.48 ! [X22: real,Y2: real] :
% 2.76/1.48 ( ( ( const_a_c @ X22 )
% 2.76/1.48 = ( const_a_c @ Y2 ) )
% 2.76/1.48 = ( X22 = Y2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_103_trm_Oinject_I2_J,axiom,
% 2.76/1.48 ! [X22: real,Y2: real] :
% 2.76/1.48 ( ( ( const_sf_sz @ X22 )
% 2.76/1.48 = ( const_sf_sz @ Y2 ) )
% 2.76/1.48 = ( X22 = Y2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_104_dfree__Const__simps,axiom,
% 2.76/1.48 ! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_105_dfree__Const__simps,axiom,
% 2.76/1.48 ! [R: real] : ( dfree_sf_sz @ ( const_sf_sz @ R ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_106_dfree__Const,axiom,
% 2.76/1.48 ! [R: real] : ( dfree_a_c @ ( const_a_c @ R ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_107_dfree__Const,axiom,
% 2.76/1.48 ! [R: real] : ( dfree_sf_sz @ ( const_sf_sz @ R ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_108_trm_Odistinct_I13_J,axiom,
% 2.76/1.48 ! [X22: real,X31: a,X32: c > trm_a_c] :
% 2.76/1.48 ( ( const_a_c @ X22 )
% 2.76/1.48 != ( function_a_c @ X31 @ X32 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_109_trm_Odistinct_I13_J,axiom,
% 2.76/1.48 ! [X22: real,X31: sf,X32: sz > trm_sf_sz] :
% 2.76/1.48 ( ( const_sf_sz @ X22 )
% 2.76/1.48 != ( function_sf_sz @ X31 @ X32 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_110_trm_Odistinct_I15_J,axiom,
% 2.76/1.48 ! [X22: real,X41: trm_a_c,X42: trm_a_c] :
% 2.76/1.48 ( ( const_a_c @ X22 )
% 2.76/1.48 != ( plus_a_c @ X41 @ X42 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_111_trm_Odistinct_I15_J,axiom,
% 2.76/1.48 ! [X22: real,X41: trm_sf_sz,X42: trm_sf_sz] :
% 2.76/1.48 ( ( const_sf_sz @ X22 )
% 2.76/1.48 != ( plus_sf_sz @ X41 @ X42 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_112_trm_Odistinct_I17_J,axiom,
% 2.76/1.48 ! [X22: real,X51: trm_sf_sz,X52: trm_sf_sz] :
% 2.76/1.48 ( ( const_sf_sz @ X22 )
% 2.76/1.48 != ( times_sf_sz @ X51 @ X52 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_113_trm_Odistinct_I17_J,axiom,
% 2.76/1.48 ! [X22: real,X51: trm_a_c,X52: trm_a_c] :
% 2.76/1.48 ( ( const_a_c @ X22 )
% 2.76/1.48 != ( times_a_c @ X51 @ X52 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_114_trm_Odistinct_I1_J,axiom,
% 2.76/1.48 ! [X1: sz,X22: real] :
% 2.76/1.48 ( ( var_sz_sf @ X1 )
% 2.76/1.48 != ( const_sf_sz @ X22 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_115_trm_Odistinct_I1_J,axiom,
% 2.76/1.48 ! [X1: c,X22: real] :
% 2.76/1.48 ( ( var_c_a @ X1 )
% 2.76/1.48 != ( const_a_c @ X22 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_116_trm_Odistinct_I21_J,axiom,
% 2.76/1.48 ! [X22: real,X7: trm_sf_sz] :
% 2.76/1.48 ( ( const_sf_sz @ X22 )
% 2.76/1.48 != ( differential_sf_sz @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_117_trm_Odistinct_I21_J,axiom,
% 2.76/1.48 ! [X22: real,X7: trm_a_c] :
% 2.76/1.48 ( ( const_a_c @ X22 )
% 2.76/1.48 != ( differential_a_c @ X7 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_118_trm_Odistinct_I19_J,axiom,
% 2.76/1.48 ! [X22: real,X6: sz] :
% 2.76/1.48 ( ( const_sf_sz @ X22 )
% 2.76/1.48 != ( diffVar_sz_sf @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_119_trm_Odistinct_I19_J,axiom,
% 2.76/1.48 ! [X22: real,X6: c] :
% 2.76/1.48 ( ( const_a_c @ X22 )
% 2.76/1.48 != ( diffVar_c_a @ X6 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_120_old_Oprod_Oinducts,axiom,
% 2.76/1.48 ! [P: produc866628903_sc_sz > $o,Prod: produc866628903_sc_sz] :
% 2.76/1.48 ( ! [A4: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ Prod ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_121_old_Oprod_Oinducts,axiom,
% 2.76/1.48 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 2.76/1.48 ( ! [A4: finite1398487019real_c,B3: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ Prod ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_122_old_Oprod_Oinducts,axiom,
% 2.76/1.48 ! [P: produc861709536_sz_sz > $o,Prod: produc861709536_sz_sz] :
% 2.76/1.48 ( ! [A4: trm_sf_sz,B3: sz] : ( P @ ( produc792909658_sz_sz @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ Prod ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_123_old_Oprod_Oinducts,axiom,
% 2.76/1.48 ! [P: produc999471430t_unit > $o,Prod: produc999471430t_unit] :
% 2.76/1.48 ( ! [A4: produc866628903_sc_sz,B3: denota610675952t_unit] : ( P @ ( produc502616768t_unit @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ Prod ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_124_old_Oprod_Oinducts,axiom,
% 2.76/1.48 ! [P: produc1821101996_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 2.76/1.48 ( ! [A4: denota610675952t_unit,B3: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ Prod ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_125_old_Oprod_Oexhaust,axiom,
% 2.76/1.48 ! [Y: produc866628903_sc_sz] :
% 2.76/1.48 ~ ! [A4: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( produc1822718231_sc_sz @ A4 @ B3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_126_old_Oprod_Oexhaust,axiom,
% 2.76/1.48 ! [Y: produc190496183real_c] :
% 2.76/1.48 ~ ! [A4: finite1398487019real_c,B3: finite1398487019real_c] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( produc394644079real_c @ A4 @ B3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_127_old_Oprod_Oexhaust,axiom,
% 2.76/1.48 ! [Y: produc861709536_sz_sz] :
% 2.76/1.48 ~ ! [A4: trm_sf_sz,B3: sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( produc792909658_sz_sz @ A4 @ B3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_128_old_Oprod_Oexhaust,axiom,
% 2.76/1.48 ! [Y: produc999471430t_unit] :
% 2.76/1.48 ~ ! [A4: produc866628903_sc_sz,B3: denota610675952t_unit] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( produc502616768t_unit @ A4 @ B3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_129_old_Oprod_Oexhaust,axiom,
% 2.76/1.48 ! [Y: produc1821101996_sc_sz] :
% 2.76/1.48 ~ ! [A4: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 2.76/1.48 ( Y
% 2.76/1.48 != ( produc789536734_sc_sz @ A4 @ B3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_130_Pair__inject,axiom,
% 2.76/1.48 ! [A: list_f1238882004_sc_sz,B: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 2.76/1.48 ( ( ( produc1822718231_sc_sz @ A @ B )
% 2.76/1.48 = ( produc1822718231_sc_sz @ A3 @ B2 ) )
% 2.76/1.48 => ~ ( ( A = A3 )
% 2.76/1.48 => ( B != B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_131_Pair__inject,axiom,
% 2.76/1.48 ! [A: finite1398487019real_c,B: finite1398487019real_c,A3: finite1398487019real_c,B2: finite1398487019real_c] :
% 2.76/1.48 ( ( ( produc394644079real_c @ A @ B )
% 2.76/1.48 = ( produc394644079real_c @ A3 @ B2 ) )
% 2.76/1.48 => ~ ( ( A = A3 )
% 2.76/1.48 => ( B != B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_132_Pair__inject,axiom,
% 2.76/1.48 ! [A: trm_sf_sz,B: sz,A3: trm_sf_sz,B2: sz] :
% 2.76/1.48 ( ( ( produc792909658_sz_sz @ A @ B )
% 2.76/1.48 = ( produc792909658_sz_sz @ A3 @ B2 ) )
% 2.76/1.48 => ~ ( ( A = A3 )
% 2.76/1.48 => ( B != B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_133_Pair__inject,axiom,
% 2.76/1.48 ! [A: produc866628903_sc_sz,B: denota610675952t_unit,A3: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 2.76/1.48 ( ( ( produc502616768t_unit @ A @ B )
% 2.76/1.48 = ( produc502616768t_unit @ A3 @ B2 ) )
% 2.76/1.48 => ~ ( ( A = A3 )
% 2.76/1.48 => ( B != B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_134_Pair__inject,axiom,
% 2.76/1.48 ! [A: denota610675952t_unit,B: produc866628903_sc_sz,A3: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 2.76/1.48 ( ( ( produc789536734_sc_sz @ A @ B )
% 2.76/1.48 = ( produc789536734_sc_sz @ A3 @ B2 ) )
% 2.76/1.48 => ~ ( ( A = A3 )
% 2.76/1.48 => ( B != B2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_135_prod__cases,axiom,
% 2.76/1.48 ! [P: produc866628903_sc_sz > $o,P2: produc866628903_sc_sz] :
% 2.76/1.48 ( ! [A4: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ P2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_136_prod__cases,axiom,
% 2.76/1.48 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 2.76/1.48 ( ! [A4: finite1398487019real_c,B3: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ P2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_137_prod__cases,axiom,
% 2.76/1.48 ! [P: produc861709536_sz_sz > $o,P2: produc861709536_sz_sz] :
% 2.76/1.48 ( ! [A4: trm_sf_sz,B3: sz] : ( P @ ( produc792909658_sz_sz @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ P2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_138_prod__cases,axiom,
% 2.76/1.48 ! [P: produc999471430t_unit > $o,P2: produc999471430t_unit] :
% 2.76/1.48 ( ! [A4: produc866628903_sc_sz,B3: denota610675952t_unit] : ( P @ ( produc502616768t_unit @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ P2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_139_prod__cases,axiom,
% 2.76/1.48 ! [P: produc1821101996_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 2.76/1.48 ( ! [A4: denota610675952t_unit,B3: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B3 ) )
% 2.76/1.48 => ( P @ P2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_140_surj__pair,axiom,
% 2.76/1.48 ! [P2: produc866628903_sc_sz] :
% 2.76/1.48 ? [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 2.76/1.48 ( P2
% 2.76/1.48 = ( produc1822718231_sc_sz @ X3 @ Y3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_141_surj__pair,axiom,
% 2.76/1.48 ! [P2: produc190496183real_c] :
% 2.76/1.48 ? [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 2.76/1.48 ( P2
% 2.76/1.48 = ( produc394644079real_c @ X3 @ Y3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_142_surj__pair,axiom,
% 2.76/1.48 ! [P2: produc861709536_sz_sz] :
% 2.76/1.48 ? [X3: trm_sf_sz,Y3: sz] :
% 2.76/1.48 ( P2
% 2.76/1.48 = ( produc792909658_sz_sz @ X3 @ Y3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_143_surj__pair,axiom,
% 2.76/1.48 ! [P2: produc999471430t_unit] :
% 2.76/1.48 ? [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 2.76/1.48 ( P2
% 2.76/1.48 = ( produc502616768t_unit @ X3 @ Y3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_144_surj__pair,axiom,
% 2.76/1.48 ! [P2: produc1821101996_sc_sz] :
% 2.76/1.48 ? [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 2.76/1.48 ( P2
% 2.76/1.48 = ( produc789536734_sc_sz @ X3 @ Y3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_145_dfree_Oinducts,axiom,
% 2.76/1.48 ! [X: trm_a_c,P: trm_a_c > $o] :
% 2.76/1.48 ( ( dfree_a_c @ X )
% 2.76/1.48 => ( ! [I3: c] : ( P @ ( var_c_a @ I3 ) )
% 2.76/1.48 => ( ! [R2: real] : ( P @ ( const_a_c @ R2 ) )
% 2.76/1.48 => ( ! [Args2: c > trm_a_c,I3: a] :
% 2.76/1.48 ( ! [Ia: c] : ( dfree_a_c @ ( Args2 @ Ia ) )
% 2.76/1.48 => ( ! [Ia: c] : ( P @ ( Args2 @ Ia ) )
% 2.76/1.48 => ( P @ ( function_a_c @ I3 @ Args2 ) ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ Theta_12 )
% 2.76/1.48 => ( ( P @ Theta_12 )
% 2.76/1.48 => ( ( dfree_a_c @ Theta_22 )
% 2.76/1.48 => ( ( P @ Theta_22 )
% 2.76/1.48 => ( P @ ( plus_a_c @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ Theta_12 )
% 2.76/1.48 => ( ( P @ Theta_12 )
% 2.76/1.48 => ( ( dfree_a_c @ Theta_22 )
% 2.76/1.48 => ( ( P @ Theta_22 )
% 2.76/1.48 => ( P @ ( times_a_c @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 2.76/1.48 => ( P @ X ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_146_dfree_Oinducts,axiom,
% 2.76/1.48 ! [X: trm_sf_sz,P: trm_sf_sz > $o] :
% 2.76/1.48 ( ( dfree_sf_sz @ X )
% 2.76/1.48 => ( ! [I3: sz] : ( P @ ( var_sz_sf @ I3 ) )
% 2.76/1.48 => ( ! [R2: real] : ( P @ ( const_sf_sz @ R2 ) )
% 2.76/1.48 => ( ! [Args2: sz > trm_sf_sz,I3: sf] :
% 2.76/1.48 ( ! [Ia: sz] : ( dfree_sf_sz @ ( Args2 @ Ia ) )
% 2.76/1.48 => ( ! [Ia: sz] : ( P @ ( Args2 @ Ia ) )
% 2.76/1.48 => ( P @ ( function_sf_sz @ I3 @ Args2 ) ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ Theta_12 )
% 2.76/1.48 => ( ( P @ Theta_12 )
% 2.76/1.48 => ( ( dfree_sf_sz @ Theta_22 )
% 2.76/1.48 => ( ( P @ Theta_22 )
% 2.76/1.48 => ( P @ ( plus_sf_sz @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ Theta_12 )
% 2.76/1.48 => ( ( P @ Theta_12 )
% 2.76/1.48 => ( ( dfree_sf_sz @ Theta_22 )
% 2.76/1.48 => ( ( P @ Theta_22 )
% 2.76/1.48 => ( P @ ( times_sf_sz @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 2.76/1.48 => ( P @ X ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_147_dfree_Osimps,axiom,
% 2.76/1.48 ( dfree_a_c
% 2.76/1.48 = ( ^ [A5: trm_a_c] :
% 2.76/1.48 ( ? [I4: c] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( var_c_a @ I4 ) )
% 2.76/1.48 | ? [R3: real] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( const_a_c @ R3 ) )
% 2.76/1.48 | ? [Args3: c > trm_a_c,I4: a] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( function_a_c @ I4 @ Args3 ) )
% 2.76/1.48 & ! [X2: c] : ( dfree_a_c @ ( Args3 @ X2 ) ) )
% 2.76/1.48 | ? [Theta_13: trm_a_c,Theta_23: trm_a_c] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( plus_a_c @ Theta_13 @ Theta_23 ) )
% 2.76/1.48 & ( dfree_a_c @ Theta_13 )
% 2.76/1.48 & ( dfree_a_c @ Theta_23 ) )
% 2.76/1.48 | ? [Theta_13: trm_a_c,Theta_23: trm_a_c] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( times_a_c @ Theta_13 @ Theta_23 ) )
% 2.76/1.48 & ( dfree_a_c @ Theta_13 )
% 2.76/1.48 & ( dfree_a_c @ Theta_23 ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_148_dfree_Osimps,axiom,
% 2.76/1.48 ( dfree_sf_sz
% 2.76/1.48 = ( ^ [A5: trm_sf_sz] :
% 2.76/1.48 ( ? [I4: sz] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( var_sz_sf @ I4 ) )
% 2.76/1.48 | ? [R3: real] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( const_sf_sz @ R3 ) )
% 2.76/1.48 | ? [Args3: sz > trm_sf_sz,I4: sf] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( function_sf_sz @ I4 @ Args3 ) )
% 2.76/1.48 & ! [X2: sz] : ( dfree_sf_sz @ ( Args3 @ X2 ) ) )
% 2.76/1.48 | ? [Theta_13: trm_sf_sz,Theta_23: trm_sf_sz] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( plus_sf_sz @ Theta_13 @ Theta_23 ) )
% 2.76/1.48 & ( dfree_sf_sz @ Theta_13 )
% 2.76/1.48 & ( dfree_sf_sz @ Theta_23 ) )
% 2.76/1.48 | ? [Theta_13: trm_sf_sz,Theta_23: trm_sf_sz] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( times_sf_sz @ Theta_13 @ Theta_23 ) )
% 2.76/1.48 & ( dfree_sf_sz @ Theta_13 )
% 2.76/1.48 & ( dfree_sf_sz @ Theta_23 ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_149_dfree_Ocases,axiom,
% 2.76/1.48 ! [A: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ A )
% 2.76/1.48 => ( ! [I3: c] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( var_c_a @ I3 ) )
% 2.76/1.48 => ( ! [R2: real] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( const_a_c @ R2 ) )
% 2.76/1.48 => ( ! [Args2: c > trm_a_c] :
% 2.76/1.48 ( ? [I3: a] :
% 2.76/1.48 ( A
% 2.76/1.48 = ( function_a_c @ I3 @ Args2 ) )
% 2.76/1.48 => ~ ! [I5: c] : ( dfree_a_c @ ( Args2 @ I5 ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( plus_a_c @ Theta_12 @ Theta_22 ) )
% 2.76/1.48 => ( ( dfree_a_c @ Theta_12 )
% 2.76/1.48 => ~ ( dfree_a_c @ Theta_22 ) ) )
% 2.76/1.48 => ~ ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( times_a_c @ Theta_12 @ Theta_22 ) )
% 2.76/1.48 => ( ( dfree_a_c @ Theta_12 )
% 2.76/1.48 => ~ ( dfree_a_c @ Theta_22 ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_150_dfree_Ocases,axiom,
% 2.76/1.48 ! [A: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ A )
% 2.76/1.48 => ( ! [I3: sz] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( var_sz_sf @ I3 ) )
% 2.76/1.48 => ( ! [R2: real] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( const_sf_sz @ R2 ) )
% 2.76/1.48 => ( ! [Args2: sz > trm_sf_sz] :
% 2.76/1.48 ( ? [I3: sf] :
% 2.76/1.48 ( A
% 2.76/1.48 = ( function_sf_sz @ I3 @ Args2 ) )
% 2.76/1.48 => ~ ! [I5: sz] : ( dfree_sf_sz @ ( Args2 @ I5 ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( plus_sf_sz @ Theta_12 @ Theta_22 ) )
% 2.76/1.48 => ( ( dfree_sf_sz @ Theta_12 )
% 2.76/1.48 => ~ ( dfree_sf_sz @ Theta_22 ) ) )
% 2.76/1.48 => ~ ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( times_sf_sz @ Theta_12 @ Theta_22 ) )
% 2.76/1.48 => ( ( dfree_sf_sz @ Theta_12 )
% 2.76/1.48 => ~ ( dfree_sf_sz @ Theta_22 ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_151_prod__induct3,axiom,
% 2.76/1.48 ! [P: produc1821101996_sc_sz > $o,X: produc1821101996_sc_sz] :
% 2.76/1.48 ( ! [A4: denota610675952t_unit,B3: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B3 @ C ) ) )
% 2.76/1.48 => ( P @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_152_f0__def,axiom,
% 2.76/1.48 ( f0_sf_sz
% 2.76/1.48 = ( ^ [F: sf] : ( function_sf_sz @ F @ empty_sz_sf ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_153_dsafe_Oinducts,axiom,
% 2.76/1.48 ! [X: trm_sf_sz,P: trm_sf_sz > $o] :
% 2.76/1.48 ( ( dsafe_sf_sz @ X )
% 2.76/1.48 => ( ! [I3: sz] : ( P @ ( var_sz_sf @ I3 ) )
% 2.76/1.48 => ( ! [R2: real] : ( P @ ( const_sf_sz @ R2 ) )
% 2.76/1.48 => ( ! [Args2: sz > trm_sf_sz,I3: sf] :
% 2.76/1.48 ( ! [Ia: sz] : ( dsafe_sf_sz @ ( Args2 @ Ia ) )
% 2.76/1.48 => ( ! [Ia: sz] : ( P @ ( Args2 @ Ia ) )
% 2.76/1.48 => ( P @ ( function_sf_sz @ I3 @ Args2 ) ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 2.76/1.48 ( ( dsafe_sf_sz @ Theta_12 )
% 2.76/1.48 => ( ( P @ Theta_12 )
% 2.76/1.48 => ( ( dsafe_sf_sz @ Theta_22 )
% 2.76/1.48 => ( ( P @ Theta_22 )
% 2.76/1.48 => ( P @ ( plus_sf_sz @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 2.76/1.48 ( ( dsafe_sf_sz @ Theta_12 )
% 2.76/1.48 => ( ( P @ Theta_12 )
% 2.76/1.48 => ( ( dsafe_sf_sz @ Theta_22 )
% 2.76/1.48 => ( ( P @ Theta_22 )
% 2.76/1.48 => ( P @ ( times_sf_sz @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 2.76/1.48 => ( ! [Theta: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ Theta )
% 2.76/1.48 => ( P @ ( differential_sf_sz @ Theta ) ) )
% 2.76/1.48 => ( ! [I3: sz] : ( P @ ( diffVar_sz_sf @ I3 ) )
% 2.76/1.48 => ( P @ X ) ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_154_dsafe_Oinducts,axiom,
% 2.76/1.48 ! [X: trm_a_c,P: trm_a_c > $o] :
% 2.76/1.48 ( ( dsafe_a_c @ X )
% 2.76/1.48 => ( ! [I3: c] : ( P @ ( var_c_a @ I3 ) )
% 2.76/1.48 => ( ! [R2: real] : ( P @ ( const_a_c @ R2 ) )
% 2.76/1.48 => ( ! [Args2: c > trm_a_c,I3: a] :
% 2.76/1.48 ( ! [Ia: c] : ( dsafe_a_c @ ( Args2 @ Ia ) )
% 2.76/1.48 => ( ! [Ia: c] : ( P @ ( Args2 @ Ia ) )
% 2.76/1.48 => ( P @ ( function_a_c @ I3 @ Args2 ) ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 2.76/1.48 ( ( dsafe_a_c @ Theta_12 )
% 2.76/1.48 => ( ( P @ Theta_12 )
% 2.76/1.48 => ( ( dsafe_a_c @ Theta_22 )
% 2.76/1.48 => ( ( P @ Theta_22 )
% 2.76/1.48 => ( P @ ( plus_a_c @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 2.76/1.48 ( ( dsafe_a_c @ Theta_12 )
% 2.76/1.48 => ( ( P @ Theta_12 )
% 2.76/1.48 => ( ( dsafe_a_c @ Theta_22 )
% 2.76/1.48 => ( ( P @ Theta_22 )
% 2.76/1.48 => ( P @ ( times_a_c @ Theta_12 @ Theta_22 ) ) ) ) ) )
% 2.76/1.48 => ( ! [Theta: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ Theta )
% 2.76/1.48 => ( P @ ( differential_a_c @ Theta ) ) )
% 2.76/1.48 => ( ! [I3: c] : ( P @ ( diffVar_c_a @ I3 ) )
% 2.76/1.48 => ( P @ X ) ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_155_dsafe_Osimps,axiom,
% 2.76/1.48 ( dsafe_sf_sz
% 2.76/1.48 = ( ^ [A5: trm_sf_sz] :
% 2.76/1.48 ( ? [I4: sz] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( var_sz_sf @ I4 ) )
% 2.76/1.48 | ? [R3: real] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( const_sf_sz @ R3 ) )
% 2.76/1.48 | ? [Args3: sz > trm_sf_sz,I4: sf] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( function_sf_sz @ I4 @ Args3 ) )
% 2.76/1.48 & ! [X2: sz] : ( dsafe_sf_sz @ ( Args3 @ X2 ) ) )
% 2.76/1.48 | ? [Theta_13: trm_sf_sz,Theta_23: trm_sf_sz] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( plus_sf_sz @ Theta_13 @ Theta_23 ) )
% 2.76/1.48 & ( dsafe_sf_sz @ Theta_13 )
% 2.76/1.48 & ( dsafe_sf_sz @ Theta_23 ) )
% 2.76/1.48 | ? [Theta_13: trm_sf_sz,Theta_23: trm_sf_sz] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( times_sf_sz @ Theta_13 @ Theta_23 ) )
% 2.76/1.48 & ( dsafe_sf_sz @ Theta_13 )
% 2.76/1.48 & ( dsafe_sf_sz @ Theta_23 ) )
% 2.76/1.48 | ? [Theta2: trm_sf_sz] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( differential_sf_sz @ Theta2 ) )
% 2.76/1.48 & ( dfree_sf_sz @ Theta2 ) )
% 2.76/1.48 | ? [I4: sz] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( diffVar_sz_sf @ I4 ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_156_dsafe_Osimps,axiom,
% 2.76/1.48 ( dsafe_a_c
% 2.76/1.48 = ( ^ [A5: trm_a_c] :
% 2.76/1.48 ( ? [I4: c] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( var_c_a @ I4 ) )
% 2.76/1.48 | ? [R3: real] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( const_a_c @ R3 ) )
% 2.76/1.48 | ? [Args3: c > trm_a_c,I4: a] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( function_a_c @ I4 @ Args3 ) )
% 2.76/1.48 & ! [X2: c] : ( dsafe_a_c @ ( Args3 @ X2 ) ) )
% 2.76/1.48 | ? [Theta_13: trm_a_c,Theta_23: trm_a_c] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( plus_a_c @ Theta_13 @ Theta_23 ) )
% 2.76/1.48 & ( dsafe_a_c @ Theta_13 )
% 2.76/1.48 & ( dsafe_a_c @ Theta_23 ) )
% 2.76/1.48 | ? [Theta_13: trm_a_c,Theta_23: trm_a_c] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( times_a_c @ Theta_13 @ Theta_23 ) )
% 2.76/1.48 & ( dsafe_a_c @ Theta_13 )
% 2.76/1.48 & ( dsafe_a_c @ Theta_23 ) )
% 2.76/1.48 | ? [Theta2: trm_a_c] :
% 2.76/1.48 ( ( A5
% 2.76/1.48 = ( differential_a_c @ Theta2 ) )
% 2.76/1.48 & ( dfree_a_c @ Theta2 ) )
% 2.76/1.48 | ? [I4: c] :
% 2.76/1.48 ( A5
% 2.76/1.48 = ( diffVar_c_a @ I4 ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_157_dsafe_Ocases,axiom,
% 2.76/1.48 ! [A: trm_sf_sz] :
% 2.76/1.48 ( ( dsafe_sf_sz @ A )
% 2.76/1.48 => ( ! [I3: sz] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( var_sz_sf @ I3 ) )
% 2.76/1.48 => ( ! [R2: real] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( const_sf_sz @ R2 ) )
% 2.76/1.48 => ( ! [Args2: sz > trm_sf_sz] :
% 2.76/1.48 ( ? [I3: sf] :
% 2.76/1.48 ( A
% 2.76/1.48 = ( function_sf_sz @ I3 @ Args2 ) )
% 2.76/1.48 => ~ ! [I5: sz] : ( dsafe_sf_sz @ ( Args2 @ I5 ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( plus_sf_sz @ Theta_12 @ Theta_22 ) )
% 2.76/1.48 => ( ( dsafe_sf_sz @ Theta_12 )
% 2.76/1.48 => ~ ( dsafe_sf_sz @ Theta_22 ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_sf_sz,Theta_22: trm_sf_sz] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( times_sf_sz @ Theta_12 @ Theta_22 ) )
% 2.76/1.48 => ( ( dsafe_sf_sz @ Theta_12 )
% 2.76/1.48 => ~ ( dsafe_sf_sz @ Theta_22 ) ) )
% 2.76/1.48 => ( ! [Theta: trm_sf_sz] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( differential_sf_sz @ Theta ) )
% 2.76/1.48 => ~ ( dfree_sf_sz @ Theta ) )
% 2.76/1.48 => ~ ! [I3: sz] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( diffVar_sz_sf @ I3 ) ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_158_dsafe_Ocases,axiom,
% 2.76/1.48 ! [A: trm_a_c] :
% 2.76/1.48 ( ( dsafe_a_c @ A )
% 2.76/1.48 => ( ! [I3: c] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( var_c_a @ I3 ) )
% 2.76/1.48 => ( ! [R2: real] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( const_a_c @ R2 ) )
% 2.76/1.48 => ( ! [Args2: c > trm_a_c] :
% 2.76/1.48 ( ? [I3: a] :
% 2.76/1.48 ( A
% 2.76/1.48 = ( function_a_c @ I3 @ Args2 ) )
% 2.76/1.48 => ~ ! [I5: c] : ( dsafe_a_c @ ( Args2 @ I5 ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( plus_a_c @ Theta_12 @ Theta_22 ) )
% 2.76/1.48 => ( ( dsafe_a_c @ Theta_12 )
% 2.76/1.48 => ~ ( dsafe_a_c @ Theta_22 ) ) )
% 2.76/1.48 => ( ! [Theta_12: trm_a_c,Theta_22: trm_a_c] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( times_a_c @ Theta_12 @ Theta_22 ) )
% 2.76/1.48 => ( ( dsafe_a_c @ Theta_12 )
% 2.76/1.48 => ~ ( dsafe_a_c @ Theta_22 ) ) )
% 2.76/1.48 => ( ! [Theta: trm_a_c] :
% 2.76/1.48 ( ( A
% 2.76/1.48 = ( differential_a_c @ Theta ) )
% 2.76/1.48 => ~ ( dfree_a_c @ Theta ) )
% 2.76/1.48 => ~ ! [I3: c] :
% 2.76/1.48 ( A
% 2.76/1.48 != ( diffVar_c_a @ I3 ) ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_159_strm_Oright__unique,axiom,
% 2.76/1.48 right_963419005_sf_sz @ freche1244000341_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(fact_160_strm_Oright__unique,axiom,
% 2.76/1.48 right_1933252621rm_a_c @ frechet_cr_strm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(fact_161_dsafe__Const__simps,axiom,
% 2.76/1.48 ! [R: real] : ( dsafe_a_c @ ( const_a_c @ R ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_162_dsafe__Const__simps,axiom,
% 2.76/1.48 ! [R: real] : ( dsafe_sf_sz @ ( const_sf_sz @ R ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_163_dsafe__Fun__simps,axiom,
% 2.76/1.48 ! [I: a,Args: c > trm_a_c] :
% 2.76/1.48 ( ( dsafe_a_c @ ( function_a_c @ I @ Args ) )
% 2.76/1.48 = ( ! [X2: c] : ( dsafe_a_c @ ( Args @ X2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_164_dsafe__Fun__simps,axiom,
% 2.76/1.48 ! [I: sf,Args: sz > trm_sf_sz] :
% 2.76/1.48 ( ( dsafe_sf_sz @ ( function_sf_sz @ I @ Args ) )
% 2.76/1.48 = ( ! [X2: sz] : ( dsafe_sf_sz @ ( Args @ X2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_165_dsafe__Plus__simps,axiom,
% 2.76/1.48 ! [A: trm_sf_sz,B: trm_sf_sz] :
% 2.76/1.48 ( ( dsafe_sf_sz @ ( plus_sf_sz @ A @ B ) )
% 2.76/1.48 = ( ( dsafe_sf_sz @ A )
% 2.76/1.48 & ( dsafe_sf_sz @ B ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_166_dsafe__Plus__simps,axiom,
% 2.76/1.48 ! [A: trm_a_c,B: trm_a_c] :
% 2.76/1.48 ( ( dsafe_a_c @ ( plus_a_c @ A @ B ) )
% 2.76/1.48 = ( ( dsafe_a_c @ A )
% 2.76/1.48 & ( dsafe_a_c @ B ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_167_dsafe__Times__simps,axiom,
% 2.76/1.48 ! [A: trm_sf_sz,B: trm_sf_sz] :
% 2.76/1.48 ( ( dsafe_sf_sz @ ( times_sf_sz @ A @ B ) )
% 2.76/1.48 = ( ( dsafe_sf_sz @ A )
% 2.76/1.48 & ( dsafe_sf_sz @ B ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_168_dsafe__Times__simps,axiom,
% 2.76/1.48 ! [A: trm_a_c,B: trm_a_c] :
% 2.76/1.48 ( ( dsafe_a_c @ ( times_a_c @ A @ B ) )
% 2.76/1.48 = ( ( dsafe_a_c @ A )
% 2.76/1.48 & ( dsafe_a_c @ B ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_169_dsafe__Var__simps,axiom,
% 2.76/1.48 ! [X: sz] : ( dsafe_sf_sz @ ( var_sz_sf @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_170_dsafe__Var__simps,axiom,
% 2.76/1.48 ! [X: c] : ( dsafe_a_c @ ( var_c_a @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_171_dsafe__DiffVar__simps,axiom,
% 2.76/1.48 ! [X: sz] : ( dsafe_sf_sz @ ( diffVar_sz_sf @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_172_dsafe__DiffVar__simps,axiom,
% 2.76/1.48 ! [X: c] : ( dsafe_a_c @ ( diffVar_c_a @ X ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_173_dsafe__Diff__simps,axiom,
% 2.76/1.48 ! [A: trm_sf_sz] :
% 2.76/1.48 ( ( dsafe_sf_sz @ ( differential_sf_sz @ A ) )
% 2.76/1.48 = ( dfree_sf_sz @ A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_174_dsafe__Diff__simps,axiom,
% 2.76/1.48 ! [A: trm_a_c] :
% 2.76/1.48 ( ( dsafe_a_c @ ( differential_a_c @ A ) )
% 2.76/1.48 = ( dfree_a_c @ A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_175_dfree__is__dsafe,axiom,
% 2.76/1.48 ! [Theta3: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ Theta3 )
% 2.76/1.48 => ( dsafe_a_c @ Theta3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_176_dfree__is__dsafe,axiom,
% 2.76/1.48 ! [Theta3: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ Theta3 )
% 2.76/1.48 => ( dsafe_sf_sz @ Theta3 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_177_dsafe__Const,axiom,
% 2.76/1.48 ! [R: real] : ( dsafe_a_c @ ( const_a_c @ R ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_178_dsafe__Const,axiom,
% 2.76/1.48 ! [R: real] : ( dsafe_sf_sz @ ( const_sf_sz @ R ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_179_dsafe__Fun,axiom,
% 2.76/1.48 ! [Args: c > trm_a_c,I: a] :
% 2.76/1.48 ( ! [I3: c] : ( dsafe_a_c @ ( Args @ I3 ) )
% 2.76/1.48 => ( dsafe_a_c @ ( function_a_c @ I @ Args ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_180_dsafe__Fun,axiom,
% 2.76/1.48 ! [Args: sz > trm_sf_sz,I: sf] :
% 2.76/1.48 ( ! [I3: sz] : ( dsafe_sf_sz @ ( Args @ I3 ) )
% 2.76/1.48 => ( dsafe_sf_sz @ ( function_sf_sz @ I @ Args ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_181_dsafe__Plus,axiom,
% 2.76/1.48 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 2.76/1.48 ( ( dsafe_sf_sz @ Theta_1 )
% 2.76/1.48 => ( ( dsafe_sf_sz @ Theta_2 )
% 2.76/1.48 => ( dsafe_sf_sz @ ( plus_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_182_dsafe__Plus,axiom,
% 2.76/1.48 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 2.76/1.48 ( ( dsafe_a_c @ Theta_1 )
% 2.76/1.48 => ( ( dsafe_a_c @ Theta_2 )
% 2.76/1.48 => ( dsafe_a_c @ ( plus_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_183_dsafe__Times,axiom,
% 2.76/1.48 ! [Theta_1: trm_sf_sz,Theta_2: trm_sf_sz] :
% 2.76/1.48 ( ( dsafe_sf_sz @ Theta_1 )
% 2.76/1.48 => ( ( dsafe_sf_sz @ Theta_2 )
% 2.76/1.48 => ( dsafe_sf_sz @ ( times_sf_sz @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_184_dsafe__Times,axiom,
% 2.76/1.48 ! [Theta_1: trm_a_c,Theta_2: trm_a_c] :
% 2.76/1.48 ( ( dsafe_a_c @ Theta_1 )
% 2.76/1.48 => ( ( dsafe_a_c @ Theta_2 )
% 2.76/1.48 => ( dsafe_a_c @ ( times_a_c @ Theta_1 @ Theta_2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_185_dsafe__Var,axiom,
% 2.76/1.48 ! [I: sz] : ( dsafe_sf_sz @ ( var_sz_sf @ I ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_186_dsafe__Var,axiom,
% 2.76/1.48 ! [I: c] : ( dsafe_a_c @ ( var_c_a @ I ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_187_dsafe__DiffVar,axiom,
% 2.76/1.48 ! [I: sz] : ( dsafe_sf_sz @ ( diffVar_sz_sf @ I ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_188_dsafe__DiffVar,axiom,
% 2.76/1.48 ! [I: c] : ( dsafe_a_c @ ( diffVar_c_a @ I ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_189_dsafe__Diff,axiom,
% 2.76/1.48 ! [Theta3: trm_sf_sz] :
% 2.76/1.48 ( ( dfree_sf_sz @ Theta3 )
% 2.76/1.48 => ( dsafe_sf_sz @ ( differential_sf_sz @ Theta3 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_190_dsafe__Diff,axiom,
% 2.76/1.48 ! [Theta3: trm_a_c] :
% 2.76/1.48 ( ( dfree_a_c @ Theta3 )
% 2.76/1.48 => ( dsafe_a_c @ ( differential_a_c @ Theta3 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_191_local_Oempty__def,axiom,
% 2.76/1.48 ( empty_c_a
% 2.76/1.48 = ( ^ [I4: c] : ( const_a_c @ zero_zero_real ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_192_local_Oempty__def,axiom,
% 2.76/1.48 ( empty_sz_sf
% 2.76/1.48 = ( ^ [I4: sz] : ( const_sf_sz @ zero_zero_real ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_193_ids_Of0__def,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,F2: sf] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ( ( f0_sf_sz @ F2 )
% 2.76/1.48 = ( function_sf_sz @ F2 @ empty_sz_sf ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_194_dfree__Fun_OIH,axiom,
% 2.76/1.48 ! [I: c] :
% 2.76/1.48 ( ( denota1997846518gree_c @ nu @ nu2 @ ( static_FVDiff_a_c @ ( args @ I ) ) )
% 2.76/1.48 => ( ( denota229585092_a_b_c @ i @ ( args @ I ) @ ( produc2010422875real_c @ nu ) @ ( produc314122909real_c @ nu ) )
% 2.76/1.48 = ( denota229585092_a_b_c @ i @ ( args @ I ) @ ( produc2010422875real_c @ nu2 ) @ ( produc314122909real_c @ nu2 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_195_strm_Oleft__unique,axiom,
% 2.76/1.48 left_u638806404_sf_sz @ freche1244000341_sf_sz ).
% 2.76/1.48
% 2.76/1.48 thf(fact_196_strm_Oleft__unique,axiom,
% 2.76/1.48 left_u968903956rm_a_c @ frechet_cr_strm_a_c ).
% 2.76/1.48
% 2.76/1.48 thf(fact_197_trm_Oinduct,axiom,
% 2.76/1.48 ! [P: trm_sf_sz > $o,Trm: trm_sf_sz] :
% 2.76/1.48 ( ! [X3: sz] : ( P @ ( var_sz_sf @ X3 ) )
% 2.76/1.48 => ( ! [X3: real] : ( P @ ( const_sf_sz @ X3 ) )
% 2.76/1.48 => ( ! [X1a: sf,X2a: sz > trm_sf_sz] :
% 2.76/1.48 ( ! [X2aa: trm_sf_sz] :
% 2.76/1.48 ( ( member_trm_sf_sz @ X2aa @ ( image_sz_trm_sf_sz @ X2a @ top_top_set_sz ) )
% 2.76/1.48 => ( P @ X2aa ) )
% 2.76/1.48 => ( P @ ( function_sf_sz @ X1a @ X2a ) ) )
% 2.76/1.48 => ( ! [X1a: trm_sf_sz,X2a: trm_sf_sz] :
% 2.76/1.48 ( ( P @ X1a )
% 2.76/1.48 => ( ( P @ X2a )
% 2.76/1.48 => ( P @ ( plus_sf_sz @ X1a @ X2a ) ) ) )
% 2.76/1.48 => ( ! [X1a: trm_sf_sz,X2a: trm_sf_sz] :
% 2.76/1.48 ( ( P @ X1a )
% 2.76/1.48 => ( ( P @ X2a )
% 2.76/1.48 => ( P @ ( times_sf_sz @ X1a @ X2a ) ) ) )
% 2.76/1.48 => ( ! [X3: sz] : ( P @ ( diffVar_sz_sf @ X3 ) )
% 2.76/1.48 => ( ! [X3: trm_sf_sz] :
% 2.76/1.48 ( ( P @ X3 )
% 2.76/1.48 => ( P @ ( differential_sf_sz @ X3 ) ) )
% 2.76/1.48 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_198_trm_Oinduct,axiom,
% 2.76/1.48 ! [P: trm_a_c > $o,Trm: trm_a_c] :
% 2.76/1.48 ( ! [X3: c] : ( P @ ( var_c_a @ X3 ) )
% 2.76/1.48 => ( ! [X3: real] : ( P @ ( const_a_c @ X3 ) )
% 2.76/1.48 => ( ! [X1a: a,X2a: c > trm_a_c] :
% 2.76/1.48 ( ! [X2aa: trm_a_c] :
% 2.76/1.48 ( ( member_trm_a_c @ X2aa @ ( image_c_trm_a_c @ X2a @ top_top_set_c ) )
% 2.76/1.48 => ( P @ X2aa ) )
% 2.76/1.48 => ( P @ ( function_a_c @ X1a @ X2a ) ) )
% 2.76/1.48 => ( ! [X1a: trm_a_c,X2a: trm_a_c] :
% 2.76/1.48 ( ( P @ X1a )
% 2.76/1.48 => ( ( P @ X2a )
% 2.76/1.48 => ( P @ ( plus_a_c @ X1a @ X2a ) ) ) )
% 2.76/1.48 => ( ! [X1a: trm_a_c,X2a: trm_a_c] :
% 2.76/1.48 ( ( P @ X1a )
% 2.76/1.48 => ( ( P @ X2a )
% 2.76/1.48 => ( P @ ( times_a_c @ X1a @ X2a ) ) ) )
% 2.76/1.48 => ( ! [X3: c] : ( P @ ( diffVar_c_a @ X3 ) )
% 2.76/1.48 => ( ! [X3: trm_a_c] :
% 2.76/1.48 ( ( P @ X3 )
% 2.76/1.48 => ( P @ ( differential_a_c @ X3 ) ) )
% 2.76/1.48 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_199_agree__comm,axiom,
% 2.76/1.48 ! [A2: produc1149990247eal_sz,B4: produc1149990247eal_sz,V: set_Sum_sum_sz_sz] :
% 2.76/1.48 ( ( denota102713844ree_sz @ A2 @ B4 @ V )
% 2.76/1.48 => ( denota102713844ree_sz @ B4 @ A2 @ V ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_200_agree__comm,axiom,
% 2.76/1.48 ! [A2: produc190496183real_c,B4: produc190496183real_c,V: set_Sum_sum_c_c] :
% 2.76/1.48 ( ( denota1997846518gree_c @ A2 @ B4 @ V )
% 2.76/1.48 => ( denota1997846518gree_c @ B4 @ A2 @ V ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_201_prod_Ocollapse,axiom,
% 2.76/1.48 ! [Prod: produc866628903_sc_sz] :
% 2.76/1.48 ( ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) )
% 2.76/1.48 = Prod ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_202_prod_Ocollapse,axiom,
% 2.76/1.48 ! [Prod: produc861709536_sz_sz] :
% 2.76/1.48 ( ( produc792909658_sz_sz @ ( produc2069561454_sz_sz @ Prod ) @ ( produc181739436_sz_sz @ Prod ) )
% 2.76/1.48 = Prod ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_203_prod_Ocollapse,axiom,
% 2.76/1.48 ! [Prod: produc999471430t_unit] :
% 2.76/1.48 ( ( produc502616768t_unit @ ( produc1216682964t_unit @ Prod ) @ ( produc687319826t_unit @ Prod ) )
% 2.76/1.48 = Prod ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_204_prod_Ocollapse,axiom,
% 2.76/1.48 ! [Prod: produc1821101996_sc_sz] :
% 2.76/1.48 ( ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) )
% 2.76/1.48 = Prod ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_205_prod_Ocollapse,axiom,
% 2.76/1.48 ! [Prod: produc190496183real_c] :
% 2.76/1.48 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 2.76/1.48 = Prod ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_206_prod_Oexhaust__sel,axiom,
% 2.76/1.48 ! [Prod: produc866628903_sc_sz] :
% 2.76/1.48 ( Prod
% 2.76/1.48 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ Prod ) @ ( produc4753477_sc_sz @ Prod ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_207_prod_Oexhaust__sel,axiom,
% 2.76/1.48 ! [Prod: produc861709536_sz_sz] :
% 2.76/1.48 ( Prod
% 2.76/1.48 = ( produc792909658_sz_sz @ ( produc2069561454_sz_sz @ Prod ) @ ( produc181739436_sz_sz @ Prod ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_208_prod_Oexhaust__sel,axiom,
% 2.76/1.48 ! [Prod: produc999471430t_unit] :
% 2.76/1.48 ( Prod
% 2.76/1.48 = ( produc502616768t_unit @ ( produc1216682964t_unit @ Prod ) @ ( produc687319826t_unit @ Prod ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_209_prod_Oexhaust__sel,axiom,
% 2.76/1.48 ! [Prod: produc1821101996_sc_sz] :
% 2.76/1.48 ( Prod
% 2.76/1.48 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ Prod ) @ ( produc974239792_sc_sz @ Prod ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_210_prod_Oexhaust__sel,axiom,
% 2.76/1.48 ! [Prod: produc190496183real_c] :
% 2.76/1.48 ( Prod
% 2.76/1.48 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_211_surjective__pairing,axiom,
% 2.76/1.48 ! [T3: produc866628903_sc_sz] :
% 2.76/1.48 ( T3
% 2.76/1.48 = ( produc1822718231_sc_sz @ ( produc548504323_sc_sz @ T3 ) @ ( produc4753477_sc_sz @ T3 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_212_surjective__pairing,axiom,
% 2.76/1.48 ! [T3: produc861709536_sz_sz] :
% 2.76/1.48 ( T3
% 2.76/1.48 = ( produc792909658_sz_sz @ ( produc2069561454_sz_sz @ T3 ) @ ( produc181739436_sz_sz @ T3 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_213_surjective__pairing,axiom,
% 2.76/1.48 ! [T3: produc999471430t_unit] :
% 2.76/1.48 ( T3
% 2.76/1.48 = ( produc502616768t_unit @ ( produc1216682964t_unit @ T3 ) @ ( produc687319826t_unit @ T3 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_214_surjective__pairing,axiom,
% 2.76/1.48 ! [T3: produc1821101996_sc_sz] :
% 2.76/1.48 ( T3
% 2.76/1.48 = ( produc789536734_sc_sz @ ( produc1503602930_sc_sz @ T3 ) @ ( produc974239792_sc_sz @ T3 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_215_surjective__pairing,axiom,
% 2.76/1.48 ! [T3: produc190496183real_c] :
% 2.76/1.48 ( T3
% 2.76/1.48 = ( produc394644079real_c @ ( produc2010422875real_c @ T3 ) @ ( produc314122909real_c @ T3 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_216_agree__UNIV__eq,axiom,
% 2.76/1.48 ! [Nu: produc1149990247eal_sz,Omega: produc1149990247eal_sz] :
% 2.76/1.48 ( ( denota102713844ree_sz @ Nu @ Omega @ top_to1246370329_sz_sz )
% 2.76/1.48 => ( Nu = Omega ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_217_agree__UNIV__eq,axiom,
% 2.76/1.48 ! [Nu: produc190496183real_c,Omega: produc190496183real_c] :
% 2.76/1.48 ( ( denota1997846518gree_c @ Nu @ Omega @ top_to1660572043um_c_c )
% 2.76/1.48 => ( Nu = Omega ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_218_Vagree__univ,axiom,
% 2.76/1.48 ! [A: finite824932053eal_sz,B: finite824932053eal_sz,C2: finite824932053eal_sz,D: finite824932053eal_sz] :
% 2.76/1.48 ( ( denota102713844ree_sz @ ( produc1308130519eal_sz @ A @ B ) @ ( produc1308130519eal_sz @ C2 @ D ) @ top_to1246370329_sz_sz )
% 2.76/1.48 => ( ( A = C2 )
% 2.76/1.48 & ( B = D ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_219_Vagree__univ,axiom,
% 2.76/1.48 ! [A: finite1398487019real_c,B: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 2.76/1.48 ( ( denota1997846518gree_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C2 @ D ) @ top_to1660572043um_c_c )
% 2.76/1.48 => ( ( A = C2 )
% 2.76/1.48 & ( B = D ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_220_ids_Oseq__sem_Ocases,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,X: produc1821101996_sc_sz] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ~ ! [I2: denota610675952t_unit,S: produc866628903_sc_sz] :
% 2.76/1.48 ( X
% 2.76/1.48 != ( produc789536734_sc_sz @ I2 @ S ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_221_ids_Oseq__sem_Oinduct,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P: denota610675952t_unit > produc866628903_sc_sz > $o,A0: denota610675952t_unit,A1: produc866628903_sc_sz] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ( ! [I2: denota610675952t_unit,X_1: produc866628903_sc_sz] : ( P @ I2 @ X_1 )
% 2.76/1.48 => ( P @ A0 @ A1 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_222_frechet_Osimps_I5_J,axiom,
% 2.76/1.48 ! [I6: denota231621370t_unit,R: real,V2: finite1398487019real_c] :
% 2.76/1.48 ( ( denota229585092_a_b_c @ I6 @ ( const_a_c @ R ) @ V2 )
% 2.76/1.48 = ( ^ [V3: finite1398487019real_c] : zero_zero_real ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_223_prod__eqI,axiom,
% 2.76/1.48 ! [P2: produc1821101996_sc_sz,Q: produc1821101996_sc_sz] :
% 2.76/1.48 ( ( ( produc1503602930_sc_sz @ P2 )
% 2.76/1.48 = ( produc1503602930_sc_sz @ Q ) )
% 2.76/1.48 => ( ( ( produc974239792_sc_sz @ P2 )
% 2.76/1.48 = ( produc974239792_sc_sz @ Q ) )
% 2.76/1.48 => ( P2 = Q ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_224_prod__eqI,axiom,
% 2.76/1.48 ! [P2: produc999471430t_unit,Q: produc999471430t_unit] :
% 2.76/1.48 ( ( ( produc1216682964t_unit @ P2 )
% 2.76/1.48 = ( produc1216682964t_unit @ Q ) )
% 2.76/1.48 => ( ( ( produc687319826t_unit @ P2 )
% 2.76/1.48 = ( produc687319826t_unit @ Q ) )
% 2.76/1.48 => ( P2 = Q ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_225_prod__eqI,axiom,
% 2.76/1.48 ! [P2: produc190496183real_c,Q: produc190496183real_c] :
% 2.76/1.48 ( ( ( produc2010422875real_c @ P2 )
% 2.76/1.48 = ( produc2010422875real_c @ Q ) )
% 2.76/1.48 => ( ( ( produc314122909real_c @ P2 )
% 2.76/1.48 = ( produc314122909real_c @ Q ) )
% 2.76/1.48 => ( P2 = Q ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_226_prod_Oexpand,axiom,
% 2.76/1.48 ! [Prod: produc1821101996_sc_sz,Prod2: produc1821101996_sc_sz] :
% 2.76/1.48 ( ( ( ( produc1503602930_sc_sz @ Prod )
% 2.76/1.48 = ( produc1503602930_sc_sz @ Prod2 ) )
% 2.76/1.48 & ( ( produc974239792_sc_sz @ Prod )
% 2.76/1.48 = ( produc974239792_sc_sz @ Prod2 ) ) )
% 2.76/1.48 => ( Prod = Prod2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_227_prod_Oexpand,axiom,
% 2.76/1.48 ! [Prod: produc999471430t_unit,Prod2: produc999471430t_unit] :
% 2.76/1.48 ( ( ( ( produc1216682964t_unit @ Prod )
% 2.76/1.48 = ( produc1216682964t_unit @ Prod2 ) )
% 2.76/1.48 & ( ( produc687319826t_unit @ Prod )
% 2.76/1.48 = ( produc687319826t_unit @ Prod2 ) ) )
% 2.76/1.48 => ( Prod = Prod2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_228_prod_Oexpand,axiom,
% 2.76/1.48 ! [Prod: produc190496183real_c,Prod2: produc190496183real_c] :
% 2.76/1.48 ( ( ( ( produc2010422875real_c @ Prod )
% 2.76/1.48 = ( produc2010422875real_c @ Prod2 ) )
% 2.76/1.48 & ( ( produc314122909real_c @ Prod )
% 2.76/1.48 = ( produc314122909real_c @ Prod2 ) ) )
% 2.76/1.48 => ( Prod = Prod2 ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_229_prod__eq__iff,axiom,
% 2.76/1.48 ( ( ^ [Y4: produc1821101996_sc_sz,Z: produc1821101996_sc_sz] : ( Y4 = Z ) )
% 2.76/1.48 = ( ^ [S2: produc1821101996_sc_sz,T4: produc1821101996_sc_sz] :
% 2.76/1.48 ( ( ( produc1503602930_sc_sz @ S2 )
% 2.76/1.48 = ( produc1503602930_sc_sz @ T4 ) )
% 2.76/1.48 & ( ( produc974239792_sc_sz @ S2 )
% 2.76/1.48 = ( produc974239792_sc_sz @ T4 ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_230_prod__eq__iff,axiom,
% 2.76/1.48 ( ( ^ [Y4: produc999471430t_unit,Z: produc999471430t_unit] : ( Y4 = Z ) )
% 2.76/1.48 = ( ^ [S2: produc999471430t_unit,T4: produc999471430t_unit] :
% 2.76/1.48 ( ( ( produc1216682964t_unit @ S2 )
% 2.76/1.48 = ( produc1216682964t_unit @ T4 ) )
% 2.76/1.48 & ( ( produc687319826t_unit @ S2 )
% 2.76/1.48 = ( produc687319826t_unit @ T4 ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_231_prod__eq__iff,axiom,
% 2.76/1.48 ( ( ^ [Y4: produc190496183real_c,Z: produc190496183real_c] : ( Y4 = Z ) )
% 2.76/1.48 = ( ^ [S2: produc190496183real_c,T4: produc190496183real_c] :
% 2.76/1.48 ( ( ( produc2010422875real_c @ S2 )
% 2.76/1.48 = ( produc2010422875real_c @ T4 ) )
% 2.76/1.48 & ( ( produc314122909real_c @ S2 )
% 2.76/1.48 = ( produc314122909real_c @ T4 ) ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_232_snd__conv,axiom,
% 2.76/1.48 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 2.76/1.48 ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 2.76/1.48 = X22 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_233_snd__conv,axiom,
% 2.76/1.48 ! [X1: trm_sf_sz,X22: sz] :
% 2.76/1.48 ( ( produc181739436_sz_sz @ ( produc792909658_sz_sz @ X1 @ X22 ) )
% 2.76/1.48 = X22 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_234_snd__conv,axiom,
% 2.76/1.48 ! [X1: produc866628903_sc_sz,X22: denota610675952t_unit] :
% 2.76/1.48 ( ( produc687319826t_unit @ ( produc502616768t_unit @ X1 @ X22 ) )
% 2.76/1.48 = X22 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_235_snd__conv,axiom,
% 2.76/1.48 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 2.76/1.48 ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 2.76/1.48 = X22 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_236_snd__conv,axiom,
% 2.76/1.48 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 2.76/1.48 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 2.76/1.48 = X22 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_237_snd__eqD,axiom,
% 2.76/1.48 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A: list_f1238882004_sc_sz] :
% 2.76/1.48 ( ( ( produc4753477_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( Y = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_238_snd__eqD,axiom,
% 2.76/1.48 ! [X: trm_sf_sz,Y: sz,A: sz] :
% 2.76/1.48 ( ( ( produc181739436_sz_sz @ ( produc792909658_sz_sz @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( Y = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_239_snd__eqD,axiom,
% 2.76/1.48 ! [X: produc866628903_sc_sz,Y: denota610675952t_unit,A: denota610675952t_unit] :
% 2.76/1.48 ( ( ( produc687319826t_unit @ ( produc502616768t_unit @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( Y = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_240_snd__eqD,axiom,
% 2.76/1.48 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A: produc866628903_sc_sz] :
% 2.76/1.48 ( ( ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( Y = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_241_snd__eqD,axiom,
% 2.76/1.48 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 2.76/1.48 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( Y = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_242_fst__conv,axiom,
% 2.76/1.48 ! [X1: list_f1238882004_sc_sz,X22: list_f1238882004_sc_sz] :
% 2.76/1.48 ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X1 @ X22 ) )
% 2.76/1.48 = X1 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_243_fst__conv,axiom,
% 2.76/1.48 ! [X1: trm_sf_sz,X22: sz] :
% 2.76/1.48 ( ( produc2069561454_sz_sz @ ( produc792909658_sz_sz @ X1 @ X22 ) )
% 2.76/1.48 = X1 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_244_fst__conv,axiom,
% 2.76/1.48 ! [X1: produc866628903_sc_sz,X22: denota610675952t_unit] :
% 2.76/1.48 ( ( produc1216682964t_unit @ ( produc502616768t_unit @ X1 @ X22 ) )
% 2.76/1.48 = X1 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_245_fst__conv,axiom,
% 2.76/1.48 ! [X1: denota610675952t_unit,X22: produc866628903_sc_sz] :
% 2.76/1.48 ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X1 @ X22 ) )
% 2.76/1.48 = X1 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_246_fst__conv,axiom,
% 2.76/1.48 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 2.76/1.48 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 2.76/1.48 = X1 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_247_fst__eqD,axiom,
% 2.76/1.48 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz,A: list_f1238882004_sc_sz] :
% 2.76/1.48 ( ( ( produc548504323_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( X = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_248_fst__eqD,axiom,
% 2.76/1.48 ! [X: trm_sf_sz,Y: sz,A: trm_sf_sz] :
% 2.76/1.48 ( ( ( produc2069561454_sz_sz @ ( produc792909658_sz_sz @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( X = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_249_fst__eqD,axiom,
% 2.76/1.48 ! [X: produc866628903_sc_sz,Y: denota610675952t_unit,A: produc866628903_sc_sz] :
% 2.76/1.48 ( ( ( produc1216682964t_unit @ ( produc502616768t_unit @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( X = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_250_fst__eqD,axiom,
% 2.76/1.48 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A: denota610675952t_unit] :
% 2.76/1.48 ( ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( X = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_251_fst__eqD,axiom,
% 2.76/1.48 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 2.76/1.48 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 2.76/1.48 = A )
% 2.76/1.48 => ( X = A ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_252_ids_Oempty__def,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ( empty_c_a
% 2.76/1.48 = ( ^ [I4: c] : ( const_a_c @ zero_zero_real ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_253_ids_Oempty__def,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ( empty_sz_sf
% 2.76/1.48 = ( ^ [I4: sz] : ( const_sf_sz @ zero_zero_real ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_254_ids_Osingleton_Ocases,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,X: produc861709536_sz_sz] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ~ ! [T: trm_sf_sz,I3: sz] :
% 2.76/1.48 ( X
% 2.76/1.48 != ( produc792909658_sz_sz @ T @ I3 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_255_ids_OP__def,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P2: sc] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ( ( p_sc_sf_sz @ P2 )
% 2.76/1.48 = ( predic913887884_sf_sz @ P2 ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_256_agree__refl,axiom,
% 2.76/1.48 ! [Nu: produc1149990247eal_sz,A2: set_Sum_sum_sz_sz] : ( denota102713844ree_sz @ Nu @ Nu @ A2 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_257_agree__refl,axiom,
% 2.76/1.48 ! [Nu: produc190496183real_c,A2: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu @ Nu @ A2 ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_258_ids_Ostrm_Odomain,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ( ( domain2047240575rm_a_c @ frechet_cr_strm_a_c )
% 2.76/1.48 = dfree_a_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_259_ids_Ostrm_Odomain,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ( ( domain512309999_sf_sz @ freche1244000341_sf_sz )
% 2.76/1.48 = dfree_sf_sz ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_260_snd__zero,axiom,
% 2.76/1.48 ( ( produc314122909real_c @ zero_z1506780526real_c )
% 2.76/1.48 = zero_z109254132real_c ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_261_fst__zero,axiom,
% 2.76/1.48 ( ( produc2010422875real_c @ zero_z1506780526real_c )
% 2.76/1.48 = zero_z109254132real_c ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_262_zero__prod__def,axiom,
% 2.76/1.48 ( zero_z659284464l_real
% 2.76/1.48 = ( produc705216881l_real @ zero_zero_real @ zero_zero_real ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_263_zero__prod__def,axiom,
% 2.76/1.48 ( zero_z72018569real_c
% 2.76/1.48 = ( produc2134005810real_c @ zero_zero_real @ zero_z1506780526real_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_264_zero__prod__def,axiom,
% 2.76/1.48 ( zero_z464587567real_c
% 2.76/1.48 = ( produc1327150128real_c @ zero_zero_real @ zero_z109254132real_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_265_zero__prod__def,axiom,
% 2.76/1.48 ( zero_z1830236699c_real
% 2.76/1.48 = ( produc171591948c_real @ zero_z1506780526real_c @ zero_zero_real ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_266_zero__prod__def,axiom,
% 2.76/1.48 ( zero_z993734942real_c
% 2.76/1.48 = ( produc1687028567real_c @ zero_z1506780526real_c @ zero_z1506780526real_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_267_zero__prod__def,axiom,
% 2.76/1.48 ( zero_z440955354real_c
% 2.76/1.48 = ( produc116546123real_c @ zero_z1506780526real_c @ zero_z109254132real_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_268_zero__prod__def,axiom,
% 2.76/1.48 ( zero_z1273814959c_real
% 2.76/1.48 = ( produc1715747632c_real @ zero_z109254132real_c @ zero_zero_real ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_269_zero__prod__def,axiom,
% 2.76/1.48 ( zero_z735295626real_c
% 2.76/1.48 = ( produc1563404851real_c @ zero_z109254132real_c @ zero_z1506780526real_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_270_zero__prod__def,axiom,
% 2.76/1.48 ( zero_z1506780526real_c
% 2.76/1.48 = ( produc394644079real_c @ zero_z109254132real_c @ zero_z109254132real_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_271_top__prod__def,axiom,
% 2.76/1.48 ( top_to543326711_set_c
% 2.76/1.48 = ( produc878845847_set_c @ top_top_set_c @ top_top_set_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_272_top__prod__def,axiom,
% 2.76/1.48 ( top_to1303770207set_sz
% 2.76/1.48 = ( produc2039118377set_sz @ top_top_set_c @ top_top_set_sz ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_273_top__prod__def,axiom,
% 2.76/1.48 ( top_to474099557_set_c
% 2.76/1.48 = ( produc760013927_set_c @ top_top_set_sz @ top_top_set_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_274_top__prod__def,axiom,
% 2.76/1.48 ( top_to1999610481set_sz
% 2.76/1.48 = ( produc2156889set_sz @ top_top_set_sz @ top_top_set_sz ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_275_top__prod__def,axiom,
% 2.76/1.48 ( top_to1128637210um_c_c
% 2.76/1.48 = ( produc1519884516um_c_c @ top_top_set_c @ top_to1660572043um_c_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_276_top__prod__def,axiom,
% 2.76/1.48 ( top_to1783191648real_c
% 2.76/1.48 = ( produc280329770real_c @ top_top_set_c @ top_to1642137041real_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_277_top__prod__def,axiom,
% 2.76/1.48 ( top_to1102260780um_c_c
% 2.76/1.48 = ( produc590684180um_c_c @ top_top_set_sz @ top_to1660572043um_c_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_278_top__prod__def,axiom,
% 2.76/1.48 ( top_to1102487922real_c
% 2.76/1.48 = ( produc1915663706real_c @ top_top_set_sz @ top_to1642137041real_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_279_top__prod__def,axiom,
% 2.76/1.48 ( top_to1309524330_set_c
% 2.76/1.48 = ( produc1767696108_set_c @ top_to1660572043um_c_c @ top_top_set_c ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_280_top__prod__def,axiom,
% 2.76/1.48 ( top_to1246597548set_sz
% 2.76/1.48 = ( produc1251379220set_sz @ top_to1660572043um_c_c @ top_top_set_sz ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_281_ids_Ostrm_Oright__unique,axiom,
% 2.76/1.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 2.76/1.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.48 => ( right_963419005_sf_sz @ freche1244000341_sf_sz ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_282_directional__derivative__def,axiom,
% 2.76/1.48 ( denota2112424896_a_b_c
% 2.76/1.48 = ( ^ [I7: denota231621370t_unit,T4: trm_a_c,V4: produc190496183real_c] : ( denota229585092_a_b_c @ I7 @ T4 @ ( produc2010422875real_c @ V4 ) @ ( produc314122909real_c @ V4 ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_283_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 2.76/1.48 ! [P: denota610675952t_unit > produc866628903_sc_sz > $o,X: denota610675952t_unit,Y: produc866628903_sc_sz,A: produc1821101996_sc_sz] :
% 2.76/1.48 ( ( P @ X @ Y )
% 2.76/1.48 => ( ( A
% 2.76/1.48 = ( produc789536734_sc_sz @ X @ Y ) )
% 2.76/1.48 => ( P @ ( produc1503602930_sc_sz @ A ) @ ( produc974239792_sc_sz @ A ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_284_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 2.76/1.48 ! [P: finite1398487019real_c > finite1398487019real_c > $o,X: finite1398487019real_c,Y: finite1398487019real_c,A: produc190496183real_c] :
% 2.76/1.48 ( ( P @ X @ Y )
% 2.76/1.48 => ( ( A
% 2.76/1.48 = ( produc394644079real_c @ X @ Y ) )
% 2.76/1.48 => ( P @ ( produc2010422875real_c @ A ) @ ( produc314122909real_c @ A ) ) ) ) ).
% 2.76/1.48
% 2.76/1.48 thf(fact_285_conjI__realizer,axiom,
% 2.76/1.48 ! [P: denota610675952t_unit > $o,P2: denota610675952t_unit,Q2: produc866628903_sc_sz > $o,Q: produc866628903_sc_sz] :
% 2.76/1.49 ( ( P @ P2 )
% 2.76/1.49 => ( ( Q2 @ Q )
% 2.76/1.49 => ( ( P @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q ) ) )
% 2.76/1.49 & ( Q2 @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ P2 @ Q ) ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_286_conjI__realizer,axiom,
% 2.76/1.49 ! [P: finite1398487019real_c > $o,P2: finite1398487019real_c,Q2: finite1398487019real_c > $o,Q: finite1398487019real_c] :
% 2.76/1.49 ( ( P @ P2 )
% 2.76/1.49 => ( ( Q2 @ Q )
% 2.76/1.49 => ( ( P @ ( produc2010422875real_c @ ( produc394644079real_c @ P2 @ Q ) ) )
% 2.76/1.49 & ( Q2 @ ( produc314122909real_c @ ( produc394644079real_c @ P2 @ Q ) ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_287_exI__realizer,axiom,
% 2.76/1.49 ! [P: produc866628903_sc_sz > denota610675952t_unit > $o,Y: produc866628903_sc_sz,X: denota610675952t_unit] :
% 2.76/1.49 ( ( P @ Y @ X )
% 2.76/1.49 => ( P @ ( produc974239792_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) @ ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_288_exI__realizer,axiom,
% 2.76/1.49 ! [P: finite1398487019real_c > finite1398487019real_c > $o,Y: finite1398487019real_c,X: finite1398487019real_c] :
% 2.76/1.49 ( ( P @ Y @ X )
% 2.76/1.49 => ( P @ ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) ) @ ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_289_exE__realizer_H,axiom,
% 2.76/1.49 ! [P: finite1398487019real_c > finite1398487019real_c > $o,P2: produc190496183real_c] :
% 2.76/1.49 ( ( P @ ( produc314122909real_c @ P2 ) @ ( produc2010422875real_c @ P2 ) )
% 2.76/1.49 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 2.76/1.49 ~ ( P @ Y3 @ X3 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_290_sndI,axiom,
% 2.76/1.49 ! [X: produc1821101996_sc_sz,Y: denota610675952t_unit,Z2: produc866628903_sc_sz] :
% 2.76/1.49 ( ( X
% 2.76/1.49 = ( produc789536734_sc_sz @ Y @ Z2 ) )
% 2.76/1.49 => ( ( produc974239792_sc_sz @ X )
% 2.76/1.49 = Z2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_291_sndI,axiom,
% 2.76/1.49 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z2: finite1398487019real_c] :
% 2.76/1.49 ( ( X
% 2.76/1.49 = ( produc394644079real_c @ Y @ Z2 ) )
% 2.76/1.49 => ( ( produc314122909real_c @ X )
% 2.76/1.49 = Z2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_292_eq__snd__iff,axiom,
% 2.76/1.49 ! [B: produc866628903_sc_sz,P2: produc1821101996_sc_sz] :
% 2.76/1.49 ( ( B
% 2.76/1.49 = ( produc974239792_sc_sz @ P2 ) )
% 2.76/1.49 = ( ? [A5: denota610675952t_unit] :
% 2.76/1.49 ( P2
% 2.76/1.49 = ( produc789536734_sc_sz @ A5 @ B ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_293_eq__snd__iff,axiom,
% 2.76/1.49 ! [B: finite1398487019real_c,P2: produc190496183real_c] :
% 2.76/1.49 ( ( B
% 2.76/1.49 = ( produc314122909real_c @ P2 ) )
% 2.76/1.49 = ( ? [A5: finite1398487019real_c] :
% 2.76/1.49 ( P2
% 2.76/1.49 = ( produc394644079real_c @ A5 @ B ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_294_eq__fst__iff,axiom,
% 2.76/1.49 ! [A: denota610675952t_unit,P2: produc1821101996_sc_sz] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( produc1503602930_sc_sz @ P2 ) )
% 2.76/1.49 = ( ? [B5: produc866628903_sc_sz] :
% 2.76/1.49 ( P2
% 2.76/1.49 = ( produc789536734_sc_sz @ A @ B5 ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_295_eq__fst__iff,axiom,
% 2.76/1.49 ! [A: finite1398487019real_c,P2: produc190496183real_c] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( produc2010422875real_c @ P2 ) )
% 2.76/1.49 = ( ? [B5: finite1398487019real_c] :
% 2.76/1.49 ( P2
% 2.76/1.49 = ( produc394644079real_c @ A @ B5 ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_296_fstI,axiom,
% 2.76/1.49 ! [X: produc1821101996_sc_sz,Y: denota610675952t_unit,Z2: produc866628903_sc_sz] :
% 2.76/1.49 ( ( X
% 2.76/1.49 = ( produc789536734_sc_sz @ Y @ Z2 ) )
% 2.76/1.49 => ( ( produc1503602930_sc_sz @ X )
% 2.76/1.49 = Y ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_297_fstI,axiom,
% 2.76/1.49 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z2: finite1398487019real_c] :
% 2.76/1.49 ( ( X
% 2.76/1.49 = ( produc394644079real_c @ Y @ Z2 ) )
% 2.76/1.49 => ( ( produc2010422875real_c @ X )
% 2.76/1.49 = Y ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_298_range__snd,axiom,
% 2.76/1.49 ( ( image_14429021real_c @ produc314122909real_c @ top_to226056039real_c )
% 2.76/1.49 = top_to1642137041real_c ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_299_range__fst,axiom,
% 2.76/1.49 ( ( image_14429021real_c @ produc2010422875real_c @ top_to226056039real_c )
% 2.76/1.49 = top_to1642137041real_c ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_300_DomainpE,axiom,
% 2.76/1.49 ! [R: trm_a_c > frechet_strm_a_c > $o,A: trm_a_c] :
% 2.76/1.49 ( ( domain2047240575rm_a_c @ R @ A )
% 2.76/1.49 => ~ ! [B3: frechet_strm_a_c] :
% 2.76/1.49 ~ ( R @ A @ B3 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_301_Domainp__iff,axiom,
% 2.76/1.49 ( domain2047240575rm_a_c
% 2.76/1.49 = ( ^ [T5: trm_a_c > frechet_strm_a_c > $o,X2: trm_a_c] :
% 2.76/1.49 ? [X4: frechet_strm_a_c] : ( T5 @ X2 @ X4 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_302_Domainp__refl,axiom,
% 2.76/1.49 domain2047240575rm_a_c = domain2047240575rm_a_c ).
% 2.76/1.49
% 2.76/1.49 thf(fact_303_Domainp_Ocases,axiom,
% 2.76/1.49 ! [R: trm_a_c > frechet_strm_a_c > $o,A: trm_a_c] :
% 2.76/1.49 ( ( domain2047240575rm_a_c @ R @ A )
% 2.76/1.49 => ~ ! [B3: frechet_strm_a_c] :
% 2.76/1.49 ~ ( R @ A @ B3 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_304_Domainp_Osimps,axiom,
% 2.76/1.49 ( domain2047240575rm_a_c
% 2.76/1.49 = ( ^ [R3: trm_a_c > frechet_strm_a_c > $o,A5: trm_a_c] :
% 2.76/1.49 ? [B5: trm_a_c,C3: frechet_strm_a_c] :
% 2.76/1.49 ( ( A5 = B5 )
% 2.76/1.49 & ( R3 @ B5 @ C3 ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_305_Domainp_ODomainI,axiom,
% 2.76/1.49 ! [R: trm_a_c > frechet_strm_a_c > $o,A: trm_a_c,B: frechet_strm_a_c] :
% 2.76/1.49 ( ( R @ A @ B )
% 2.76/1.49 => ( domain2047240575rm_a_c @ R @ A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_306_Domainp_Oinducts,axiom,
% 2.76/1.49 ! [R: trm_a_c > frechet_strm_a_c > $o,X: trm_a_c,P: trm_a_c > $o] :
% 2.76/1.49 ( ( domain2047240575rm_a_c @ R @ X )
% 2.76/1.49 => ( ! [A4: trm_a_c,B3: frechet_strm_a_c] :
% 2.76/1.49 ( ( R @ A4 @ B3 )
% 2.76/1.49 => ( P @ A4 ) )
% 2.76/1.49 => ( P @ X ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_307_trm_Oset__cases,axiom,
% 2.76/1.49 ! [E: sf,A: trm_sf_sz] :
% 2.76/1.49 ( ( member_sf @ E @ ( set_trm_sf_sz2 @ A ) )
% 2.76/1.49 => ( ! [Z22: sz > trm_sf_sz] :
% 2.76/1.49 ( A
% 2.76/1.49 != ( function_sf_sz @ E @ Z22 ) )
% 2.76/1.49 => ( ! [Z1: sf,Z22: sz > trm_sf_sz] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( function_sf_sz @ Z1 @ Z22 ) )
% 2.76/1.49 => ! [X3: trm_sf_sz] :
% 2.76/1.49 ( ( member_trm_sf_sz @ X3 @ ( image_sz_trm_sf_sz @ Z22 @ top_top_set_sz ) )
% 2.76/1.49 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ X3 ) ) ) )
% 2.76/1.49 => ( ! [Z1: trm_sf_sz] :
% 2.76/1.49 ( ? [Z22: trm_sf_sz] :
% 2.76/1.49 ( A
% 2.76/1.49 = ( plus_sf_sz @ Z1 @ Z22 ) )
% 2.76/1.49 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z1 ) ) )
% 2.76/1.49 => ( ! [Z1: trm_sf_sz,Z22: trm_sf_sz] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( plus_sf_sz @ Z1 @ Z22 ) )
% 2.76/1.49 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z22 ) ) )
% 2.76/1.49 => ( ! [Z1: trm_sf_sz] :
% 2.76/1.49 ( ? [Z22: trm_sf_sz] :
% 2.76/1.49 ( A
% 2.76/1.49 = ( times_sf_sz @ Z1 @ Z22 ) )
% 2.76/1.49 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z1 ) ) )
% 2.76/1.49 => ( ! [Z1: trm_sf_sz,Z22: trm_sf_sz] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( times_sf_sz @ Z1 @ Z22 ) )
% 2.76/1.49 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z22 ) ) )
% 2.76/1.49 => ~ ! [Z3: trm_sf_sz] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( differential_sf_sz @ Z3 ) )
% 2.76/1.49 => ~ ( member_sf @ E @ ( set_trm_sf_sz2 @ Z3 ) ) ) ) ) ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_308_trm_Oset__cases,axiom,
% 2.76/1.49 ! [E: a,A: trm_a_c] :
% 2.76/1.49 ( ( member_a @ E @ ( set_trm_a_c2 @ A ) )
% 2.76/1.49 => ( ! [Z22: c > trm_a_c] :
% 2.76/1.49 ( A
% 2.76/1.49 != ( function_a_c @ E @ Z22 ) )
% 2.76/1.49 => ( ! [Z1: a,Z22: c > trm_a_c] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( function_a_c @ Z1 @ Z22 ) )
% 2.76/1.49 => ! [X3: trm_a_c] :
% 2.76/1.49 ( ( member_trm_a_c @ X3 @ ( image_c_trm_a_c @ Z22 @ top_top_set_c ) )
% 2.76/1.49 => ~ ( member_a @ E @ ( set_trm_a_c2 @ X3 ) ) ) )
% 2.76/1.49 => ( ! [Z1: trm_a_c] :
% 2.76/1.49 ( ? [Z22: trm_a_c] :
% 2.76/1.49 ( A
% 2.76/1.49 = ( plus_a_c @ Z1 @ Z22 ) )
% 2.76/1.49 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z1 ) ) )
% 2.76/1.49 => ( ! [Z1: trm_a_c,Z22: trm_a_c] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( plus_a_c @ Z1 @ Z22 ) )
% 2.76/1.49 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z22 ) ) )
% 2.76/1.49 => ( ! [Z1: trm_a_c] :
% 2.76/1.49 ( ? [Z22: trm_a_c] :
% 2.76/1.49 ( A
% 2.76/1.49 = ( times_a_c @ Z1 @ Z22 ) )
% 2.76/1.49 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z1 ) ) )
% 2.76/1.49 => ( ! [Z1: trm_a_c,Z22: trm_a_c] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( times_a_c @ Z1 @ Z22 ) )
% 2.76/1.49 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z22 ) ) )
% 2.76/1.49 => ~ ! [Z3: trm_a_c] :
% 2.76/1.49 ( ( A
% 2.76/1.49 = ( differential_a_c @ Z3 ) )
% 2.76/1.49 => ~ ( member_a @ E @ ( set_trm_a_c2 @ Z3 ) ) ) ) ) ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_309_trm_Oset__intros_I1_J,axiom,
% 2.76/1.49 ! [X31: a,X32: c > trm_a_c] : ( member_a @ X31 @ ( set_trm_a_c2 @ ( function_a_c @ X31 @ X32 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_310_trm_Oset__intros_I1_J,axiom,
% 2.76/1.49 ! [X31: sf,X32: sz > trm_sf_sz] : ( member_sf @ X31 @ ( set_trm_sf_sz2 @ ( function_sf_sz @ X31 @ X32 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_311_trm_Osimps_I126_J,axiom,
% 2.76/1.49 ! [X7: trm_a_c] :
% 2.76/1.49 ( ( set_trm_a_c2 @ ( differential_a_c @ X7 ) )
% 2.76/1.49 = ( set_trm_a_c2 @ X7 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_312_trm_Oset__intros_I7_J,axiom,
% 2.76/1.49 ! [Yf: a,X7: trm_a_c] :
% 2.76/1.49 ( ( member_a @ Yf @ ( set_trm_a_c2 @ X7 ) )
% 2.76/1.49 => ( member_a @ Yf @ ( set_trm_a_c2 @ ( differential_a_c @ X7 ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_313_trm_Oset__intros_I2_J,axiom,
% 2.76/1.49 ! [Y: trm_a_c,X32: c > trm_a_c,Ya: a,X31: a] :
% 2.76/1.49 ( ( member_trm_a_c @ Y @ ( image_c_trm_a_c @ X32 @ top_top_set_c ) )
% 2.76/1.49 => ( ( member_a @ Ya @ ( set_trm_a_c2 @ Y ) )
% 2.76/1.49 => ( member_a @ Ya @ ( set_trm_a_c2 @ ( function_a_c @ X31 @ X32 ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_314_trm_Oset__intros_I2_J,axiom,
% 2.76/1.49 ! [Y: trm_sf_sz,X32: sz > trm_sf_sz,Ya: sf,X31: sf] :
% 2.76/1.49 ( ( member_trm_sf_sz @ Y @ ( image_sz_trm_sf_sz @ X32 @ top_top_set_sz ) )
% 2.76/1.49 => ( ( member_sf @ Ya @ ( set_trm_sf_sz2 @ Y ) )
% 2.76/1.49 => ( member_sf @ Ya @ ( set_trm_sf_sz2 @ ( function_sf_sz @ X31 @ X32 ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_315_ids_Osingleton_Ocong,axiom,
% 2.76/1.49 singleton_sz_sf = singleton_sz_sf ).
% 2.76/1.49
% 2.76/1.49 thf(fact_316_ids_Of1_Ocong,axiom,
% 2.76/1.49 f1_sz_sf = f1_sz_sf ).
% 2.76/1.49
% 2.76/1.49 thf(fact_317_singleton_Opelims,axiom,
% 2.76/1.49 ! [X: trm_sf_sz,Xa: sz,Y: trm_sf_sz] :
% 2.76/1.49 ( ( ( singleton_sz_sf @ vid1 @ X @ Xa )
% 2.76/1.49 = Y )
% 2.76/1.49 => ( ( accp_P529224471_sz_sz @ singleton_rel_sf_sz @ ( produc792909658_sz_sz @ X @ Xa ) )
% 2.76/1.49 => ~ ( ( ( ( Xa = vid1 )
% 2.76/1.49 => ( Y = X ) )
% 2.76/1.49 & ( ( Xa != vid1 )
% 2.76/1.49 => ( Y
% 2.76/1.49 = ( const_sf_sz @ zero_zero_real ) ) ) )
% 2.76/1.49 => ~ ( accp_P529224471_sz_sz @ singleton_rel_sf_sz @ ( produc792909658_sz_sz @ X @ Xa ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_318_f1__def,axiom,
% 2.76/1.49 ! [F2: sf,X: sz] :
% 2.76/1.49 ( ( f1_sz_sf @ vid1 @ F2 @ X )
% 2.76/1.49 = ( function_sf_sz @ F2 @ ( singleton_sz_sf @ vid1 @ ( var_sz_sf @ X ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_319_proj__sing1,axiom,
% 2.76/1.49 ! [Theta3: trm_sf_sz] :
% 2.76/1.49 ( ( singleton_sz_sf @ vid1 @ Theta3 @ vid1 )
% 2.76/1.49 = Theta3 ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_320_expand__singleton,axiom,
% 2.76/1.49 ! [T3: trm_sf_sz] :
% 2.76/1.49 ( ( singleton_sz_sf @ vid1 @ T3 )
% 2.76/1.49 = ( ^ [I4: sz] : ( if_trm_sf_sz @ ( I4 = vid1 ) @ T3 @ ( const_sf_sz @ zero_zero_real ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_321_proj__sing2,axiom,
% 2.76/1.49 ! [Y: sz,Theta3: trm_sf_sz] :
% 2.76/1.49 ( ( vid1 != Y )
% 2.76/1.49 => ( ( singleton_sz_sf @ vid1 @ Theta3 @ Y )
% 2.76/1.49 = ( const_sf_sz @ zero_zero_real ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_322_singleton_Oelims,axiom,
% 2.76/1.49 ! [X: trm_sf_sz,Xa: sz,Y: trm_sf_sz] :
% 2.76/1.49 ( ( ( singleton_sz_sf @ vid1 @ X @ Xa )
% 2.76/1.49 = Y )
% 2.76/1.49 => ( ( ( Xa = vid1 )
% 2.76/1.49 => ( Y = X ) )
% 2.76/1.49 & ( ( Xa != vid1 )
% 2.76/1.49 => ( Y
% 2.76/1.49 = ( const_sf_sz @ zero_zero_real ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_323_singleton_Osimps,axiom,
% 2.76/1.49 ! [I: sz,T3: trm_sf_sz] :
% 2.76/1.49 ( ( ( I = vid1 )
% 2.76/1.49 => ( ( singleton_sz_sf @ vid1 @ T3 @ I )
% 2.76/1.49 = T3 ) )
% 2.76/1.49 & ( ( I != vid1 )
% 2.76/1.49 => ( ( singleton_sz_sf @ vid1 @ T3 @ I )
% 2.76/1.49 = ( const_sf_sz @ zero_zero_real ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_324_local_Oid__simps_I15_J,axiom,
% 2.76/1.49 vid3 != vid1 ).
% 2.76/1.49
% 2.76/1.49 thf(fact_325_local_Oid__simps_I13_J,axiom,
% 2.76/1.49 vid2 != vid1 ).
% 2.76/1.49
% 2.76/1.49 thf(fact_326_vne13,axiom,
% 2.76/1.49 vid1 != vid3 ).
% 2.76/1.49
% 2.76/1.49 thf(fact_327_vne12,axiom,
% 2.76/1.49 vid1 != vid2 ).
% 2.76/1.49
% 2.76/1.49 thf(fact_328_local_Oid__simps_I1_J,axiom,
% 2.76/1.49 vid1 != vid2 ).
% 2.76/1.49
% 2.76/1.49 thf(fact_329_local_Oid__simps_I3_J,axiom,
% 2.76/1.49 vid1 != vid3 ).
% 2.76/1.49
% 2.76/1.49 thf(fact_330_vne23,axiom,
% 2.76/1.49 vid2 != vid3 ).
% 2.76/1.49
% 2.76/1.49 thf(fact_331_local_Oid__simps_I2_J,axiom,
% 2.76/1.49 vid2 != vid3 ).
% 2.76/1.49
% 2.76/1.49 thf(fact_332_local_Oid__simps_I14_J,axiom,
% 2.76/1.49 vid3 != vid2 ).
% 2.76/1.49
% 2.76/1.49 thf(fact_333_p1__def,axiom,
% 2.76/1.49 ! [P2: sz,X: sz] :
% 2.76/1.49 ( ( p1_sz_sf_sc @ vid1 @ P2 @ X )
% 2.76/1.49 = ( prop_sz_sf_sc @ P2 @ ( singleton_sz_sf @ vid1 @ ( var_sz_sf @ X ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_334_prod_Oswap__def,axiom,
% 2.76/1.49 ( produc245128480t_unit
% 2.76/1.49 = ( ^ [P3: produc999471430t_unit] : ( produc789536734_sc_sz @ ( produc687319826t_unit @ P3 ) @ ( produc1216682964t_unit @ P3 ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_335_prod_Oswap__def,axiom,
% 2.76/1.49 ( produc704157711real_c
% 2.76/1.49 = ( ^ [P3: produc190496183real_c] : ( produc394644079real_c @ ( produc314122909real_c @ P3 ) @ ( produc2010422875real_c @ P3 ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_336_formula_Oinject_I2_J,axiom,
% 2.76/1.49 ! [X21: sz,X222: sz > trm_sf_sz,Y21: sz,Y22: sz > trm_sf_sz] :
% 2.76/1.49 ( ( ( prop_sz_sf_sc @ X21 @ X222 )
% 2.76/1.49 = ( prop_sz_sf_sc @ Y21 @ Y22 ) )
% 2.76/1.49 = ( ( X21 = Y21 )
% 2.76/1.49 & ( X222 = Y22 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_337_pair__in__swap__image,axiom,
% 2.76/1.49 ! [Y: produc866628903_sc_sz,X: denota610675952t_unit,A2: set_Pr1169339874_sc_sz] :
% 2.76/1.49 ( ( member235934813t_unit @ ( produc502616768t_unit @ Y @ X ) @ ( image_904562809t_unit @ produc532048446_sc_sz @ A2 ) )
% 2.76/1.49 = ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) @ A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_338_pair__in__swap__image,axiom,
% 2.76/1.49 ! [Y: denota610675952t_unit,X: produc866628903_sc_sz,A2: set_Pr2041213564t_unit] :
% 2.76/1.49 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ Y @ X ) @ ( image_1426741113_sc_sz @ produc245128480t_unit @ A2 ) )
% 2.76/1.49 = ( member235934813t_unit @ ( produc502616768t_unit @ X @ Y ) @ A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_339_swap__simp,axiom,
% 2.76/1.49 ! [X: produc866628903_sc_sz,Y: denota610675952t_unit] :
% 2.76/1.49 ( ( produc245128480t_unit @ ( produc502616768t_unit @ X @ Y ) )
% 2.76/1.49 = ( produc789536734_sc_sz @ Y @ X ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_340_swap__simp,axiom,
% 2.76/1.49 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz] :
% 2.76/1.49 ( ( produc532048446_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 2.76/1.49 = ( produc502616768t_unit @ Y @ X ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_341_snd__swap,axiom,
% 2.76/1.49 ! [X: produc190496183real_c] :
% 2.76/1.49 ( ( produc314122909real_c @ ( produc704157711real_c @ X ) )
% 2.76/1.49 = ( produc2010422875real_c @ X ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_342_fst__swap,axiom,
% 2.76/1.49 ! [X: produc190496183real_c] :
% 2.76/1.49 ( ( produc2010422875real_c @ ( produc704157711real_c @ X ) )
% 2.76/1.49 = ( produc314122909real_c @ X ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_343_ids_Op1_Ocong,axiom,
% 2.76/1.49 p1_sz_sf_sc = p1_sz_sf_sc ).
% 2.76/1.49
% 2.76/1.49 thf(fact_344_ids_Op1__def,axiom,
% 2.76/1.49 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P2: sz,X: sz] :
% 2.76/1.49 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 2.76/1.49 => ( ( p1_sz_sf_sc @ Vid1 @ P2 @ X )
% 2.76/1.49 = ( prop_sz_sf_sc @ P2 @ ( singleton_sz_sf @ Vid1 @ ( var_sz_sf @ X ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_345_formula_Oset__intros_I3_J,axiom,
% 2.76/1.49 ! [Yb: trm_sf_sz,X222: sz > trm_sf_sz,Yc: sf,X21: sz] :
% 2.76/1.49 ( ( member_trm_sf_sz @ Yb @ ( image_sz_trm_sf_sz @ X222 @ top_top_set_sz ) )
% 2.76/1.49 => ( ( member_sf @ Yc @ ( set_trm_sf_sz2 @ Yb ) )
% 2.76/1.49 => ( member_sf @ Yc @ ( set1_f989022726_sc_sz @ ( prop_sz_sf_sc @ X21 @ X222 ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_346_hpfree__ffree_Ointros_I10_J,axiom,
% 2.76/1.49 ! [Args: sz > trm_sf_sz,P2: sz] :
% 2.76/1.49 ( ! [Arg: trm_sf_sz] :
% 2.76/1.49 ( ( member_trm_sf_sz @ Arg @ ( image_sz_trm_sf_sz @ Args @ top_top_set_sz ) )
% 2.76/1.49 => ( dfree_sf_sz @ Arg ) )
% 2.76/1.49 => ( ffree_sf_sc_sz @ ( prop_sz_sf_sc @ P2 @ Args ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_347_hpfree__ffree_Ointros_I15_J,axiom,
% 2.76/1.49 ! [P: sc] : ( ffree_sf_sc_sz @ ( predic913887884_sf_sz @ P ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_348_map__prod__simp,axiom,
% 2.76/1.49 ! [F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz,A: denota610675952t_unit,B: produc866628903_sc_sz] :
% 2.76/1.49 ( ( produc403791768_sc_sz @ F2 @ G @ ( produc789536734_sc_sz @ A @ B ) )
% 2.76/1.49 = ( produc789536734_sc_sz @ ( F2 @ A ) @ ( G @ B ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_349_fst__map__prod,axiom,
% 2.76/1.49 ! [F2: finite1398487019real_c > finite1398487019real_c,G: finite1398487019real_c > finite1398487019real_c,X: produc190496183real_c] :
% 2.76/1.49 ( ( produc2010422875real_c @ ( produc368345510real_c @ F2 @ G @ X ) )
% 2.76/1.49 = ( F2 @ ( produc2010422875real_c @ X ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_350_snd__map__prod,axiom,
% 2.76/1.49 ! [F2: finite1398487019real_c > finite1398487019real_c,G: finite1398487019real_c > finite1398487019real_c,X: produc190496183real_c] :
% 2.76/1.49 ( ( produc314122909real_c @ ( produc368345510real_c @ F2 @ G @ X ) )
% 2.76/1.49 = ( G @ ( produc314122909real_c @ X ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_351_map__prod__imageI,axiom,
% 2.76/1.49 ! [A: denota610675952t_unit,B: produc866628903_sc_sz,R4: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz] :
% 2.76/1.49 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A @ B ) @ R4 )
% 2.76/1.49 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_1726193375_sc_sz @ ( produc403791768_sc_sz @ F2 @ G ) @ R4 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_352_prod__fun__imageE,axiom,
% 2.76/1.49 ! [C2: produc1821101996_sc_sz,F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz,R4: set_Pr1169339874_sc_sz] :
% 2.76/1.49 ( ( member1057565379_sc_sz @ C2 @ ( image_1726193375_sc_sz @ ( produc403791768_sc_sz @ F2 @ G ) @ R4 ) )
% 2.76/1.49 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 2.76/1.49 ( ( C2
% 2.76/1.49 = ( produc789536734_sc_sz @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 2.76/1.49 => ~ ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ R4 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(help_If_3_1_If_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_T,axiom,
% 2.76/1.49 ! [P: $o] :
% 2.76/1.49 ( ( P = $true )
% 2.76/1.49 | ( P = $false ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(help_If_2_1_If_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_T,axiom,
% 2.76/1.49 ! [X: trm_sf_sz,Y: trm_sf_sz] :
% 2.76/1.49 ( ( if_trm_sf_sz @ $false @ X @ Y )
% 2.76/1.49 = Y ) ).
% 2.76/1.49
% 2.76/1.49 thf(help_If_1_1_If_001t__Syntax__Otrm_Itf__sf_Mtf__sz_J_T,axiom,
% 2.76/1.49 ! [X: trm_sf_sz,Y: trm_sf_sz] :
% 2.76/1.49 ( ( if_trm_sf_sz @ $true @ X @ Y )
% 2.76/1.49 = X ) ).
% 2.76/1.49
% 2.76/1.49 thf(conj_0,conjecture,
% 2.76/1.49 dfree_a_c @ ( args @ i2 ) ).
% 2.76/1.49 ------------------------
% 2.90/1.51 % (27941)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_27746 for (2999ds/27Mi)
% 2.90/1.51 % (27943)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_27746 for (2999ds/2Mi)
% 2.90/1.51 % (27944)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_27746 for (2999ds/275Mi)
% 2.90/1.51 % (27940)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_27746 for (2999ds/4Mi)
% 2.90/1.51 % (27945)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27746 for (2999ds/18Mi)
% 2.90/1.51 % (27939)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27746 for (2999ds/183Mi)
% 2.90/1.51 % (27943)Instruction limit reached!
% 2.90/1.51 % (27943)------------------------------
% 2.90/1.51 % (27943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.51 % (27943)Termination reason: Unknown
% 2.90/1.51 % (27943)Termination phase: shuffling
% 2.90/1.51
% 2.90/1.51 % (27943)Memory used [KB]: 1535
% 2.90/1.51 % (27943)Time elapsed: 0.003 s
% 2.90/1.51 % (27943)Instructions burned: 5 (million)
% 2.90/1.51 % (27943)------------------------------
% 2.90/1.51 % (27943)------------------------------
% 2.90/1.51 % (27940)Instruction limit reached!
% 2.90/1.51 % (27940)------------------------------
% 2.90/1.51 % (27940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.51 % (27940)Termination reason: Unknown
% 2.90/1.51 % (27940)Termination phase: shuffling
% 2.90/1.51
% 2.90/1.51 % (27940)Memory used [KB]: 1535
% 2.90/1.51 % (27940)Time elapsed: 0.003 s
% 2.90/1.51 % (27940)Instructions burned: 4 (million)
% 2.90/1.51 % (27940)------------------------------
% 2.90/1.51 % (27940)------------------------------
% 2.90/1.51 % (27945)Instruction limit reached!
% 2.90/1.51 % (27945)------------------------------
% 2.90/1.51 % (27945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.51 % (27945)Termination reason: Unknown
% 2.90/1.51 % (27945)Termination phase: shuffling
% 2.90/1.51
% 2.90/1.51 % (27945)Memory used [KB]: 2046
% 2.90/1.51 % (27945)Time elapsed: 0.008 s
% 2.90/1.51 % (27945)Instructions burned: 19 (million)
% 2.90/1.51 % (27945)------------------------------
% 2.90/1.51 % (27945)------------------------------
% 2.90/1.51 % (27942)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27746 for (2999ds/2Mi)
% 2.90/1.52 % (27941)Instruction limit reached!
% 2.90/1.52 % (27941)------------------------------
% 2.90/1.52 % (27941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.52 % (27941)Termination reason: Unknown
% 2.90/1.52 % (27941)Termination phase: Property scanning
% 2.90/1.52
% 2.90/1.52 % (27941)Memory used [KB]: 2046
% 2.90/1.52 % (27941)Time elapsed: 0.011 s
% 2.90/1.52 % (27941)Instructions burned: 30 (million)
% 2.90/1.52 % (27941)------------------------------
% 2.90/1.52 % (27941)------------------------------
% 2.90/1.52 % (27942)Instruction limit reached!
% 2.90/1.52 % (27942)------------------------------
% 2.90/1.52 % (27942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.52 % (27942)Termination reason: Unknown
% 2.90/1.52 % (27942)Termination phase: shuffling
% 2.90/1.52
% 2.90/1.52 % (27942)Memory used [KB]: 1535
% 2.90/1.52 % (27942)Time elapsed: 0.003 s
% 2.90/1.52 % (27942)Instructions burned: 2 (million)
% 2.90/1.52 % (27942)------------------------------
% 2.90/1.52 % (27942)------------------------------
% 2.90/1.52 % (27946)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27746 for (2999ds/3Mi)
% 2.90/1.52 % (27944)First to succeed.
% 2.90/1.52 % (27947)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_27746 for (2999ds/37Mi)
% 2.90/1.52 % (27946)Instruction limit reached!
% 2.90/1.52 % (27946)------------------------------
% 2.90/1.52 % (27946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.52 % (27946)Termination reason: Unknown
% 2.90/1.52 % (27946)Termination phase: shuffling
% 2.90/1.52
% 2.90/1.52 % (27946)Memory used [KB]: 1535
% 2.90/1.52 % (27946)Time elapsed: 0.003 s
% 2.90/1.52 % (27946)Instructions burned: 4 (million)
% 2.90/1.52 % (27946)------------------------------
% 2.90/1.52 % (27946)------------------------------
% 2.90/1.52 % (27944)Refutation found. Thanks to Tanya!
% 2.90/1.52 % SZS status Theorem for DTF2THF_27746
% 2.90/1.52 % SZS output start Proof for DTF2THF_27746
% 2.90/1.52 thf(type_def_5, type, produc190496183real_c: $tType).
% 2.90/1.52 thf(type_def_6, type, set_Sum_sum_c_c: $tType).
% 2.90/1.52 thf(type_def_8, type, produc1149990247eal_sz: $tType).
% 2.90/1.52 thf(type_def_9, type, set_Sum_sum_sz_sz: $tType).
% 2.90/1.52 thf(type_def_10, type, denota231621370t_unit: $tType).
% 2.90/1.52 thf(type_def_11, type, trm_a_c: $tType).
% 2.90/1.52 thf(type_def_12, type, real: $tType).
% 2.90/1.52 thf(type_def_13, type, finite1398487019real_c: $tType).
% 2.90/1.52 thf(type_def_14, type, frechet_strm_a_c: $tType).
% 2.90/1.52 thf(type_def_15, type, trm_sf_sz: $tType).
% 2.90/1.52 thf(type_def_16, type, frechet_strm_sf_sz: $tType).
% 2.90/1.52 thf(type_def_17, type, produc99145217real_c: $tType).
% 2.90/1.52 thf(type_def_18, type, produc133347448c_real: $tType).
% 2.90/1.52 thf(type_def_19, type, produc1952288593real_c: $tType).
% 2.90/1.52 thf(type_def_20, type, produc640052711real_c: $tType).
% 2.90/1.52 thf(type_def_21, type, produc906325778c_real: $tType).
% 2.90/1.52 thf(type_def_22, type, produc1471603704real_c: $tType).
% 2.90/1.52 thf(type_def_23, type, produc1295591296real_c: $tType).
% 2.90/1.52 thf(type_def_24, type, produc957004601l_real: $tType).
% 2.90/1.52 thf(type_def_25, type, sz: $tType).
% 2.90/1.52 thf(type_def_26, type, sf: $tType).
% 2.90/1.52 thf(type_def_27, type, sc: $tType).
% 2.90/1.52 thf(type_def_28, type, produc802386618_set_c: $tType).
% 2.90/1.52 thf(type_def_29, type, produc189019228set_sz: $tType).
% 2.90/1.52 thf(type_def_30, type, produc1299700144real_c: $tType).
% 2.90/1.52 thf(type_def_31, type, produc621499498um_c_c: $tType).
% 2.90/1.52 thf(type_def_32, type, produc756982951_set_c: $tType).
% 2.90/1.52 thf(type_def_33, type, produc313687471set_sz: $tType).
% 2.90/1.52 thf(type_def_34, type, produc729314338real_c: $tType).
% 2.90/1.52 thf(type_def_35, type, produc44682460um_c_c: $tType).
% 2.90/1.52 thf(type_def_36, type, produc1631500469_set_c: $tType).
% 2.90/1.52 thf(type_def_37, type, produc2057661729set_sz: $tType).
% 2.90/1.52 thf(type_def_38, type, set_Fi1407883041real_c: $tType).
% 2.90/1.52 thf(type_def_39, type, set_Pr1389752855real_c: $tType).
% 2.90/1.52 thf(type_def_40, type, set_c: $tType).
% 2.90/1.52 thf(type_def_41, type, set_sz: $tType).
% 2.90/1.52 thf(type_def_42, type, denota610675952t_unit: $tType).
% 2.90/1.52 thf(type_def_43, type, produc866628903_sc_sz: $tType).
% 2.90/1.52 thf(type_def_44, type, produc1821101996_sc_sz: $tType).
% 2.90/1.52 thf(type_def_45, type, finite824932053eal_sz: $tType).
% 2.90/1.52 thf(type_def_46, type, list_f1238882004_sc_sz: $tType).
% 2.90/1.52 thf(type_def_47, type, produc999471430t_unit: $tType).
% 2.90/1.52 thf(type_def_48, type, produc861709536_sz_sz: $tType).
% 2.90/1.52 thf(type_def_49, type, set_Pr2041213564t_unit: $tType).
% 2.90/1.52 thf(type_def_50, type, set_trm_a_c: $tType).
% 2.90/1.52 thf(type_def_51, type, set_trm_sf_sz: $tType).
% 2.90/1.52 thf(type_def_52, type, a: $tType).
% 2.90/1.52 thf(type_def_53, type, set_a: $tType).
% 2.90/1.52 thf(type_def_54, type, set_sf: $tType).
% 2.90/1.52 thf(type_def_55, type, set_Pr1169339874_sc_sz: $tType).
% 2.90/1.52 thf(type_def_56, type, c: $tType).
% 2.90/1.52 thf(type_def_57, type, formula_sf_sc_sz: $tType).
% 2.90/1.52 thf(func_def_0, type, produc640052711real_c: $tType).
% 2.90/1.52 thf(func_def_1, type, set_Pr2041213564t_unit: $tType).
% 2.90/1.52 thf(func_def_2, type, set_Pr1169339874_sc_sz: $tType).
% 2.90/1.52 thf(func_def_3, type, produc999471430t_unit: $tType).
% 2.90/1.52 thf(func_def_4, type, produc1821101996_sc_sz: $tType).
% 2.90/1.52 thf(func_def_5, type, produc1952288593real_c: $tType).
% 2.90/1.52 thf(func_def_6, type, produc99145217real_c: $tType).
% 2.90/1.52 thf(func_def_7, type, produc1295591296real_c: $tType).
% 2.90/1.52 thf(func_def_8, type, produc906325778c_real: $tType).
% 2.90/1.52 thf(func_def_9, type, set_Pr1389752855real_c: $tType).
% 2.90/1.52 thf(func_def_10, type, produc1149990247eal_sz: $tType).
% 2.90/1.52 thf(func_def_11, type, produc190496183real_c: $tType).
% 2.90/1.52 thf(func_def_12, type, produc866628903_sc_sz: $tType).
% 2.90/1.52 thf(func_def_13, type, produc729314338real_c: $tType).
% 2.90/1.52 thf(func_def_14, type, produc1299700144real_c: $tType).
% 2.90/1.52 thf(func_def_15, type, produc1471603704real_c: $tType).
% 2.90/1.52 thf(func_def_16, type, produc133347448c_real: $tType).
% 2.90/1.52 thf(func_def_17, type, denota610675952t_unit: $tType).
% 2.90/1.52 thf(func_def_18, type, produc44682460um_c_c: $tType).
% 2.90/1.52 thf(func_def_19, type, produc189019228set_sz: $tType).
% 2.90/1.52 thf(func_def_20, type, produc621499498um_c_c: $tType).
% 2.90/1.52 thf(func_def_21, type, produc802386618_set_c: $tType).
% 2.90/1.52 thf(func_def_22, type, denota231621370t_unit: $tType).
% 2.90/1.52 thf(func_def_23, type, set_Fi1407883041real_c: $tType).
% 2.90/1.52 thf(func_def_24, type, produc2057661729set_sz: $tType).
% 2.90/1.52 thf(func_def_25, type, produc1631500469_set_c: $tType).
% 2.90/1.52 thf(func_def_26, type, produc313687471set_sz: $tType).
% 2.90/1.52 thf(func_def_27, type, produc756982951_set_c: $tType).
% 2.90/1.52 thf(func_def_28, type, produc861709536_sz_sz: $tType).
% 2.90/1.52 thf(func_def_29, type, finite824932053eal_sz: $tType).
% 2.90/1.52 thf(func_def_30, type, finite1398487019real_c: $tType).
% 2.90/1.52 thf(func_def_31, type, list_f1238882004_sc_sz: $tType).
% 2.90/1.52 thf(func_def_32, type, produc957004601l_real: $tType).
% 2.90/1.52 thf(func_def_33, type, frechet_strm_sf_sz: $tType).
% 2.90/1.52 thf(func_def_34, type, set_Sum_sum_sz_sz: $tType).
% 2.90/1.52 thf(func_def_35, type, frechet_strm_a_c: $tType).
% 2.90/1.52 thf(func_def_36, type, set_Sum_sum_c_c: $tType).
% 2.90/1.52 thf(func_def_37, type, set_trm_sf_sz: $tType).
% 2.90/1.52 thf(func_def_38, type, set_trm_a_c: $tType).
% 2.90/1.52 thf(func_def_39, type, formula_sf_sc_sz: $tType).
% 2.90/1.52 thf(func_def_40, type, trm_sf_sz: $tType).
% 2.90/1.52 thf(func_def_41, type, trm_a_c: $tType).
% 2.90/1.52 thf(func_def_42, type, set_sz: $tType).
% 2.90/1.52 thf(func_def_43, type, set_sf: $tType).
% 2.90/1.52 thf(func_def_44, type, set_c: $tType).
% 2.90/1.52 thf(func_def_45, type, set_a: $tType).
% 2.90/1.52 thf(func_def_46, type, real: $tType).
% 2.90/1.52 thf(func_def_47, type, sz: $tType).
% 2.90/1.52 thf(func_def_48, type, sf: $tType).
% 2.90/1.52 thf(func_def_49, type, sc: $tType).
% 2.90/1.52 thf(func_def_50, type, c: $tType).
% 2.90/1.52 thf(func_def_51, type, a: $tType).
% 2.90/1.52 thf(func_def_52, type, denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o).
% 2.90/1.52 thf(func_def_53, type, denota102713844ree_sz: produc1149990247eal_sz > produc1149990247eal_sz > set_Sum_sum_sz_sz > $o).
% 2.90/1.52 thf(func_def_54, type, denota2112424896_a_b_c: denota231621370t_unit > trm_a_c > produc190496183real_c > real).
% 2.90/1.52 thf(func_def_55, type, denota229585092_a_b_c: denota231621370t_unit > trm_a_c > finite1398487019real_c > finite1398487019real_c > real).
% 2.90/1.52 thf(func_def_56, type, frechet_cr_strm_a_c: trm_a_c > frechet_strm_a_c > $o).
% 2.90/1.52 thf(func_def_57, type, freche1244000341_sf_sz: trm_sf_sz > frechet_strm_sf_sz > $o).
% 2.90/1.52 thf(func_def_58, type, zero_z109254132real_c: finite1398487019real_c).
% 2.90/1.52 thf(func_def_59, type, zero_z1506780526real_c: produc190496183real_c).
% 2.90/1.52 thf(func_def_60, type, zero_z735295626real_c: produc99145217real_c).
% 2.90/1.52 thf(func_def_61, type, zero_z1273814959c_real: produc133347448c_real).
% 2.90/1.52 thf(func_def_62, type, zero_z440955354real_c: produc1952288593real_c).
% 2.90/1.52 thf(func_def_63, type, zero_z993734942real_c: produc640052711real_c).
% 2.90/1.52 thf(func_def_64, type, zero_z1830236699c_real: produc906325778c_real).
% 2.90/1.52 thf(func_def_65, type, zero_z464587567real_c: produc1471603704real_c).
% 2.90/1.52 thf(func_def_66, type, zero_z72018569real_c: produc1295591296real_c).
% 2.90/1.52 thf(func_def_67, type, zero_z659284464l_real: produc957004601l_real).
% 2.90/1.52 thf(func_def_68, type, zero_zero_real: real).
% 2.90/1.52 thf(func_def_69, type, ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o).
% 2.90/1.52 thf(func_def_70, type, if_trm_sf_sz: $o > trm_sf_sz > trm_sf_sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_71, type, top_to1309524330_set_c: produc802386618_set_c).
% 2.90/1.52 thf(func_def_72, type, top_to1246597548set_sz: produc189019228set_sz).
% 2.90/1.52 thf(func_def_73, type, top_to1783191648real_c: produc1299700144real_c).
% 2.90/1.52 thf(func_def_74, type, top_to1128637210um_c_c: produc621499498um_c_c).
% 2.90/1.52 thf(func_def_75, type, top_to543326711_set_c: produc756982951_set_c).
% 2.90/1.52 thf(func_def_76, type, top_to1303770207set_sz: produc313687471set_sz).
% 2.90/1.52 thf(func_def_77, type, top_to1102487922real_c: produc729314338real_c).
% 2.90/1.52 thf(func_def_78, type, top_to1102260780um_c_c: produc44682460um_c_c).
% 2.90/1.52 thf(func_def_79, type, top_to474099557_set_c: produc1631500469_set_c).
% 2.90/1.52 thf(func_def_80, type, top_to1999610481set_sz: produc2057661729set_sz).
% 2.90/1.52 thf(func_def_81, type, top_to1642137041real_c: set_Fi1407883041real_c).
% 2.90/1.52 thf(func_def_82, type, top_to226056039real_c: set_Pr1389752855real_c).
% 2.90/1.52 thf(func_def_83, type, top_to1660572043um_c_c: set_Sum_sum_c_c).
% 2.90/1.52 thf(func_def_84, type, top_to1246370329_sz_sz: set_Sum_sum_sz_sz).
% 2.90/1.52 thf(func_def_85, type, top_top_set_c: set_c).
% 2.90/1.52 thf(func_def_86, type, top_top_set_sz: set_sz).
% 2.90/1.52 thf(func_def_87, type, produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz).
% 2.90/1.52 thf(func_def_88, type, produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c).
% 2.90/1.52 thf(func_def_89, type, produc1563404851real_c: finite1398487019real_c > produc190496183real_c > produc99145217real_c).
% 2.90/1.52 thf(func_def_90, type, produc1715747632c_real: finite1398487019real_c > real > produc133347448c_real).
% 2.90/1.52 thf(func_def_91, type, produc1308130519eal_sz: finite824932053eal_sz > finite824932053eal_sz > produc1149990247eal_sz).
% 2.90/1.52 thf(func_def_92, type, produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz).
% 2.90/1.52 thf(func_def_93, type, produc116546123real_c: produc190496183real_c > finite1398487019real_c > produc1952288593real_c).
% 2.90/1.52 thf(func_def_94, type, produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c).
% 2.90/1.52 thf(func_def_95, type, produc171591948c_real: produc190496183real_c > real > produc906325778c_real).
% 2.90/1.52 thf(func_def_96, type, produc502616768t_unit: produc866628903_sc_sz > denota610675952t_unit > produc999471430t_unit).
% 2.90/1.52 thf(func_def_97, type, produc1327150128real_c: real > finite1398487019real_c > produc1471603704real_c).
% 2.90/1.52 thf(func_def_98, type, produc2134005810real_c: real > produc190496183real_c > produc1295591296real_c).
% 2.90/1.52 thf(func_def_99, type, produc705216881l_real: real > real > produc957004601l_real).
% 2.90/1.52 thf(func_def_100, type, produc1767696108_set_c: set_Sum_sum_c_c > set_c > produc802386618_set_c).
% 2.90/1.52 thf(func_def_101, type, produc1251379220set_sz: set_Sum_sum_c_c > set_sz > produc189019228set_sz).
% 2.90/1.52 thf(func_def_102, type, produc280329770real_c: set_c > set_Fi1407883041real_c > produc1299700144real_c).
% 2.90/1.52 thf(func_def_103, type, produc1519884516um_c_c: set_c > set_Sum_sum_c_c > produc621499498um_c_c).
% 2.90/1.52 thf(func_def_104, type, produc878845847_set_c: set_c > set_c > produc756982951_set_c).
% 2.90/1.52 thf(func_def_105, type, produc2039118377set_sz: set_c > set_sz > produc313687471set_sz).
% 2.90/1.52 thf(func_def_106, type, produc1915663706real_c: set_sz > set_Fi1407883041real_c > produc729314338real_c).
% 2.90/1.52 thf(func_def_107, type, produc590684180um_c_c: set_sz > set_Sum_sum_c_c > produc44682460um_c_c).
% 2.90/1.52 thf(func_def_108, type, produc760013927_set_c: set_sz > set_c > produc1631500469_set_c).
% 2.90/1.52 thf(func_def_109, type, produc2156889set_sz: set_sz > set_sz > produc2057661729set_sz).
% 2.90/1.52 thf(func_def_110, type, produc792909658_sz_sz: trm_sf_sz > sz > produc861709536_sz_sz).
% 2.90/1.52 thf(func_def_111, type, produc403791768_sc_sz: (denota610675952t_unit > denota610675952t_unit) > (produc866628903_sc_sz > produc866628903_sc_sz) > produc1821101996_sc_sz > produc1821101996_sc_sz).
% 2.90/1.52 thf(func_def_112, type, produc368345510real_c: (finite1398487019real_c > finite1398487019real_c) > (finite1398487019real_c > finite1398487019real_c) > produc190496183real_c > produc190496183real_c).
% 2.90/1.52 thf(func_def_113, type, produc1503602930_sc_sz: produc1821101996_sc_sz > denota610675952t_unit).
% 2.90/1.52 thf(func_def_114, type, produc2010422875real_c: produc190496183real_c > finite1398487019real_c).
% 2.90/1.52 thf(func_def_115, type, produc548504323_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz).
% 2.90/1.52 thf(func_def_116, type, produc1216682964t_unit: produc999471430t_unit > produc866628903_sc_sz).
% 2.90/1.52 thf(func_def_117, type, produc2069561454_sz_sz: produc861709536_sz_sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_118, type, produc974239792_sc_sz: produc1821101996_sc_sz > produc866628903_sc_sz).
% 2.90/1.52 thf(func_def_119, type, produc314122909real_c: produc190496183real_c > finite1398487019real_c).
% 2.90/1.52 thf(func_def_120, type, produc4753477_sc_sz: produc866628903_sc_sz > list_f1238882004_sc_sz).
% 2.90/1.52 thf(func_def_121, type, produc687319826t_unit: produc999471430t_unit > denota610675952t_unit).
% 2.90/1.52 thf(func_def_122, type, produc181739436_sz_sz: produc861709536_sz_sz > sz).
% 2.90/1.52 thf(func_def_123, type, produc532048446_sc_sz: produc1821101996_sc_sz > produc999471430t_unit).
% 2.90/1.52 thf(func_def_124, type, produc704157711real_c: produc190496183real_c > produc190496183real_c).
% 2.90/1.52 thf(func_def_125, type, produc245128480t_unit: produc999471430t_unit > produc1821101996_sc_sz).
% 2.90/1.52 thf(func_def_126, type, domain2047240575rm_a_c: (trm_a_c > frechet_strm_a_c > $o) > trm_a_c > $o).
% 2.90/1.52 thf(func_def_127, type, domain512309999_sf_sz: (trm_sf_sz > frechet_strm_sf_sz > $o) > trm_sf_sz > $o).
% 2.90/1.52 thf(func_def_128, type, collec377961627t_unit: (produc999471430t_unit > $o) > set_Pr2041213564t_unit).
% 2.90/1.52 thf(func_def_129, type, collect_trm_a_c: (trm_a_c > $o) > set_trm_a_c).
% 2.90/1.52 thf(func_def_130, type, collect_trm_sf_sz: (trm_sf_sz > $o) > set_trm_sf_sz).
% 2.90/1.52 thf(func_def_131, type, collect_a: (a > $o) > set_a).
% 2.90/1.52 thf(func_def_132, type, collect_sf: (sf > $o) > set_sf).
% 2.90/1.52 thf(func_def_133, type, image_1726193375_sc_sz: (produc1821101996_sc_sz > produc1821101996_sc_sz) > set_Pr1169339874_sc_sz > set_Pr1169339874_sc_sz).
% 2.90/1.52 thf(func_def_134, type, image_904562809t_unit: (produc1821101996_sc_sz > produc999471430t_unit) > set_Pr1169339874_sc_sz > set_Pr2041213564t_unit).
% 2.90/1.52 thf(func_def_135, type, image_14429021real_c: (produc190496183real_c > finite1398487019real_c) > set_Pr1389752855real_c > set_Fi1407883041real_c).
% 2.90/1.52 thf(func_def_136, type, image_1426741113_sc_sz: (produc999471430t_unit > produc1821101996_sc_sz) > set_Pr2041213564t_unit > set_Pr1169339874_sc_sz).
% 2.90/1.52 thf(func_def_137, type, image_c_trm_a_c: (c > trm_a_c) > set_c > set_trm_a_c).
% 2.90/1.52 thf(func_def_138, type, image_sz_trm_sf_sz: (sz > trm_sf_sz) > set_sz > set_trm_sf_sz).
% 2.90/1.52 thf(func_def_139, type, static_FVDiff_a_c: trm_a_c > set_Sum_sum_c_c).
% 2.90/1.52 thf(func_def_140, type, static_FVDiff_sf_sz: trm_sf_sz > set_Sum_sum_sz_sz).
% 2.90/1.52 thf(func_def_141, type, predic913887884_sf_sz: sc > formula_sf_sc_sz).
% 2.90/1.52 thf(func_def_142, type, dfree_a_c: trm_a_c > $o).
% 2.90/1.52 thf(func_def_143, type, dfree_sf_sz: trm_sf_sz > $o).
% 2.90/1.52 thf(func_def_144, type, dsafe_a_c: trm_a_c > $o).
% 2.90/1.52 thf(func_def_145, type, dsafe_sf_sz: trm_sf_sz > $o).
% 2.90/1.52 thf(func_def_146, type, ffree_sf_sc_sz: formula_sf_sc_sz > $o).
% 2.90/1.52 thf(func_def_147, type, prop_sz_sf_sc: sz > (sz > trm_sf_sz) > formula_sf_sc_sz).
% 2.90/1.52 thf(func_def_148, type, set1_f989022726_sc_sz: formula_sf_sc_sz > set_sf).
% 2.90/1.52 thf(func_def_149, type, p_sc_sf_sz: sc > formula_sf_sc_sz).
% 2.90/1.52 thf(func_def_150, type, empty_c_a: c > trm_a_c).
% 2.90/1.52 thf(func_def_151, type, empty_sz_sf: sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_152, type, f0_sf_sz: sf > trm_sf_sz).
% 2.90/1.52 thf(func_def_153, type, f1_sz_sf: sz > sf > sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_154, type, p1_sz_sf_sc: sz > sz > sz > formula_sf_sc_sz).
% 2.90/1.52 thf(func_def_155, type, singleton_sz_sf: sz > trm_sf_sz > sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_156, type, singleton_rel_sf_sz: produc861709536_sz_sz > produc861709536_sz_sz > $o).
% 2.90/1.52 thf(func_def_157, type, const_a_c: real > trm_a_c).
% 2.90/1.52 thf(func_def_158, type, const_sf_sz: real > trm_sf_sz).
% 2.90/1.52 thf(func_def_159, type, diffVar_c_a: c > trm_a_c).
% 2.90/1.52 thf(func_def_160, type, diffVar_sz_sf: sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_161, type, differential_a_c: trm_a_c > trm_a_c).
% 2.90/1.52 thf(func_def_162, type, differential_sf_sz: trm_sf_sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_163, type, function_a_c: a > (c > trm_a_c) > trm_a_c).
% 2.90/1.52 thf(func_def_164, type, function_sf_sz: sf > (sz > trm_sf_sz) > trm_sf_sz).
% 2.90/1.52 thf(func_def_165, type, plus_a_c: trm_a_c > trm_a_c > trm_a_c).
% 2.90/1.52 thf(func_def_166, type, plus_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_167, type, times_a_c: trm_a_c > trm_a_c > trm_a_c).
% 2.90/1.52 thf(func_def_168, type, times_sf_sz: trm_sf_sz > trm_sf_sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_169, type, var_c_a: c > trm_a_c).
% 2.90/1.52 thf(func_def_170, type, var_sz_sf: sz > trm_sf_sz).
% 2.90/1.52 thf(func_def_171, type, set_trm_a_c2: trm_a_c > set_a).
% 2.90/1.52 thf(func_def_172, type, set_trm_sf_sz2: trm_sf_sz > set_sf).
% 2.90/1.52 thf(func_def_173, type, left_u968903956rm_a_c: (trm_a_c > frechet_strm_a_c > $o) > $o).
% 2.90/1.52 thf(func_def_174, type, left_u638806404_sf_sz: (trm_sf_sz > frechet_strm_sf_sz > $o) > $o).
% 2.90/1.52 thf(func_def_175, type, right_1933252621rm_a_c: (trm_a_c > frechet_strm_a_c > $o) > $o).
% 2.90/1.52 thf(func_def_176, type, right_963419005_sf_sz: (trm_sf_sz > frechet_strm_sf_sz > $o) > $o).
% 2.90/1.52 thf(func_def_177, type, accp_P529224471_sz_sz: (produc861709536_sz_sz > produc861709536_sz_sz > $o) > produc861709536_sz_sz > $o).
% 2.90/1.52 thf(func_def_178, type, member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o).
% 2.90/1.52 thf(func_def_179, type, member235934813t_unit: produc999471430t_unit > set_Pr2041213564t_unit > $o).
% 2.90/1.52 thf(func_def_180, type, member_trm_a_c: trm_a_c > set_trm_a_c > $o).
% 2.90/1.52 thf(func_def_181, type, member_trm_sf_sz: trm_sf_sz > set_trm_sf_sz > $o).
% 2.90/1.52 thf(func_def_182, type, member_a: a > set_a > $o).
% 2.90/1.52 thf(func_def_183, type, member_sf: sf > set_sf > $o).
% 2.90/1.52 thf(func_def_184, type, i: denota231621370t_unit).
% 2.90/1.52 thf(func_def_185, type, nu: produc190496183real_c).
% 2.90/1.52 thf(func_def_186, type, nu2: produc190496183real_c).
% 2.90/1.52 thf(func_def_187, type, args: c > trm_a_c).
% 2.90/1.52 thf(func_def_188, type, i2: c).
% 2.90/1.52 thf(func_def_189, type, var: a).
% 2.90/1.52 thf(func_def_190, type, vid1: sz).
% 2.90/1.52 thf(func_def_191, type, vid2: sz).
% 2.90/1.52 thf(func_def_192, type, vid3: sz).
% 2.90/1.52 thf(f743,plain,(
% 2.90/1.52 $false),
% 2.90/1.52 inference(subsumption_resolution,[status(thm)],[f740,f739])).
% 2.90/1.52 thf(f739,plain,(
% 2.90/1.52 ( ! [X0 : c] : (((dfree_a_c @ (args @ X0)) = $true)) )),
% 2.90/1.52 inference(cnf_transformation,[status(thm)],[f705])).
% 2.90/1.52 thf(f705,plain,(
% 2.90/1.52 ! [X0 : c] : ((dfree_a_c @ (args @ X0)) = $true)),
% 2.90/1.52 inference(fool_elimination,[status(thm)],[f704])).
% 2.90/1.52 thf(f704,plain,(
% 2.90/1.52 ! [X0 : c] : (dfree_a_c @ (args @ X0))),
% 2.90/1.52 inference(rectify,[status(thm)],[f1])).
% 2.90/1.52 thf(f1,axiom,(
% 2.90/1.52 ! [X0 : c] : (dfree_a_c @ (args @ X0))),
% 2.90/1.52 file('/export/starexec/sandbox/tmp/tmp.ItXc5YzKVO/DTF2THF_27746.p',fact_0_free)).
% 2.90/1.52 thf(f740,plain,(
% 2.90/1.52 ((dfree_a_c @ (args @ i2)) != $true)),
% 2.90/1.52 inference(cnf_transformation,[status(thm)],[f736])).
% 2.90/1.52 thf(f736,plain,(
% 2.90/1.52 ((dfree_a_c @ (args @ i2)) != $true)),
% 2.90/1.52 inference(flattening,[status(thm)],[f607])).
% 2.90/1.52 thf(f607,plain,(
% 2.90/1.52 ~((dfree_a_c @ (args @ i2)) = $true)),
% 2.90/1.52 inference(fool_elimination,[status(thm)],[f606])).
% 2.90/1.52 thf(f606,plain,(
% 2.90/1.52 ~(dfree_a_c @ (args @ i2))),
% 2.90/1.52 inference(rectify,[status(thm)],[f358])).
% 2.90/1.52 thf(f358,negated_conjecture,(
% 2.90/1.52 ~(dfree_a_c @ (args @ i2))),
% 2.90/1.52 inference(negated_conjecture,[status(cth)],[f357])).
% 2.90/1.52 thf(f357,conjecture,(
% 2.90/1.52 (dfree_a_c @ (args @ i2))),
% 2.90/1.52 file('/export/starexec/sandbox/tmp/tmp.ItXc5YzKVO/DTF2THF_27746.p',conj_0)).
% 2.90/1.52 % SZS output end Proof for DTF2THF_27746
% 2.90/1.52 % (27944)------------------------------
% 2.90/1.52 % (27944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.52 % (27944)Termination reason: Refutation
% 2.90/1.52
% 2.90/1.52 % (27944)Memory used [KB]: 6524
% 2.90/1.52 % (27944)Time elapsed: 0.014 s
% 2.90/1.52 % (27944)Instructions burned: 37 (million)
% 2.90/1.52 % (27944)------------------------------
% 2.90/1.52 % (27944)------------------------------
% 2.90/1.52 % (27938)Success in time 0.032 s
%------------------------------------------------------------------------------