%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP046^1 : 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 : n025.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 08:55:07 AM UTC 2026
% Result : Theorem 3.12s 1.78s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 88 ( 15 ~; 3 |; 0 &; 67 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 36 ( 35 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 324 ( 321 usr; 31 con; 0-7 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
l: $tType ).
thf(type_def_6,type,
option_val_r_l_v: $tType ).
thf(type_def_8,type,
const: $tType ).
thf(type_def_9,type,
produc1156025366_r_l_v: $tType ).
thf(type_def_10,type,
set_l: $tType ).
thf(type_def_11,type,
expr_r_l_v: $tType ).
thf(type_def_12,type,
val_r_l_v: $tType ).
thf(type_def_13,type,
cntxt_r_l_v: $tType ).
thf(type_def_14,type,
r: $tType ).
thf(type_def_15,type,
v: $tType ).
thf(type_def_16,type,
option1457017436_r_l_v: $tType ).
thf(type_def_17,type,
set_Pr1409704485_r_l_v: $tType ).
thf(type_def_18,type,
set_option_l: $tType ).
thf(type_def_19,type,
set_option_r: $tType ).
thf(type_def_20,type,
set_Product_prod_l_l: $tType ).
thf(type_def_21,type,
set_Product_prod_l_r: $tType ).
thf(type_def_22,type,
set_Product_prod_r_l: $tType ).
thf(type_def_23,type,
set_Product_prod_r_r: $tType ).
thf(type_def_24,type,
set_set_set_l: $tType ).
thf(type_def_25,type,
set_set_set_r: $tType ).
thf(type_def_26,type,
set_set_Sum_sum_l_l: $tType ).
thf(type_def_27,type,
set_set_Sum_sum_l_r: $tType ).
thf(type_def_28,type,
set_set_Sum_sum_r_l: $tType ).
thf(type_def_29,type,
set_set_l: $tType ).
thf(type_def_30,type,
set_set_r: $tType ).
thf(type_def_31,type,
set_Sum_sum_l_l: $tType ).
thf(type_def_32,type,
set_Sum_sum_l_r: $tType ).
thf(type_def_33,type,
set_Sum_sum_r_l: $tType ).
thf(type_def_34,type,
set_Sum_sum_r_r: $tType ).
thf(type_def_35,type,
set_r: $tType ).
thf(type_def_36,type,
produc1389397445_r_l_v: $tType ).
thf(type_def_37,type,
produc1164766533_r_l_v: $tType ).
thf(type_def_38,type,
sum_sum_l_l: $tType ).
thf(type_def_39,type,
sum_sum_l_r: $tType ).
thf(type_def_40,type,
sum_sum_r_l: $tType ).
thf(func_def_0,type,
set_Pr1409704485_r_l_v: $tType ).
thf(func_def_1,type,
produc1389397445_r_l_v: $tType ).
thf(func_def_2,type,
option1457017436_r_l_v: $tType ).
thf(func_def_3,type,
produc1156025366_r_l_v: $tType ).
thf(func_def_4,type,
produc1164766533_r_l_v: $tType ).
thf(func_def_5,type,
set_set_Sum_sum_r_l: $tType ).
thf(func_def_6,type,
set_set_Sum_sum_l_r: $tType ).
thf(func_def_7,type,
set_set_Sum_sum_l_l: $tType ).
thf(func_def_8,type,
option_val_r_l_v: $tType ).
thf(func_def_9,type,
set_Product_prod_r_r: $tType ).
thf(func_def_10,type,
set_Product_prod_r_l: $tType ).
thf(func_def_11,type,
set_Product_prod_l_r: $tType ).
thf(func_def_12,type,
set_Product_prod_l_l: $tType ).
thf(func_def_13,type,
set_set_set_r: $tType ).
thf(func_def_14,type,
set_set_set_l: $tType ).
thf(func_def_15,type,
set_Sum_sum_r_r: $tType ).
thf(func_def_16,type,
set_Sum_sum_r_l: $tType ).
thf(func_def_17,type,
set_Sum_sum_l_r: $tType ).
thf(func_def_18,type,
set_Sum_sum_l_l: $tType ).
thf(func_def_19,type,
set_option_r: $tType ).
thf(func_def_20,type,
set_option_l: $tType ).
thf(func_def_21,type,
cntxt_r_l_v: $tType ).
thf(func_def_22,type,
set_set_r: $tType ).
thf(func_def_23,type,
set_set_l: $tType ).
thf(func_def_24,type,
expr_r_l_v: $tType ).
thf(func_def_25,type,
sum_sum_r_l: $tType ).
thf(func_def_26,type,
sum_sum_l_r: $tType ).
thf(func_def_27,type,
sum_sum_l_l: $tType ).
thf(func_def_28,type,
val_r_l_v: $tType ).
thf(func_def_29,type,
set_r: $tType ).
thf(func_def_30,type,
set_l: $tType ).
thf(func_def_31,type,
const: $tType ).
thf(func_def_32,type,
v: $tType ).
thf(func_def_33,type,
r: $tType ).
thf(func_def_34,type,
l: $tType ).
thf(func_def_35,type,
combine_l_val_r_l_v: ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_36,type,
f: const ).
thf(func_def_37,type,
t: const ).
thf(func_def_38,type,
unit: const ).
thf(func_def_39,type,
doms_l_r_v: produc1156025366_r_l_v > set_l ).
thf(func_def_40,type,
assign_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v ).
thf(func_def_41,type,
ite_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v > expr_r_l_v ).
thf(func_def_42,type,
read_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_43,type,
ref_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_44,type,
rfork_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_45,type,
rjoin_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_46,type,
vE_r_l_v: val_r_l_v > expr_r_l_v ).
thf(func_def_47,type,
plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).
thf(func_def_48,type,
cV_r_l_v: const > val_r_l_v ).
thf(func_def_49,type,
loc_l_r_v: l > val_r_l_v ).
thf(func_def_50,type,
rid_r_l_v: r > val_r_l_v ).
thf(func_def_51,type,
execution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > expr_r_l_v > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_52,type,
induct1670415253_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( ( r > option1457017436_r_l_v ) > $o ) > $o ).
thf(func_def_53,type,
maxima311842975_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > expr_r_l_v > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_54,type,
reachable_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_55,type,
steps_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > set_Pr1409704485_r_l_v ).
thf(func_def_56,type,
terminates_in_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > expr_r_l_v > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_57,type,
finite2114249848tion_l: set_option_l > $o ).
thf(func_def_58,type,
finite16335230tion_r: set_option_r > $o ).
thf(func_def_59,type,
finite1853159534_r_l_v: set_Pr1409704485_r_l_v > $o ).
thf(func_def_60,type,
finite785973648od_l_l: set_Product_prod_l_l > $o ).
thf(func_def_61,type,
finite835542678od_l_r: set_Product_prod_l_r > $o ).
thf(func_def_62,type,
finite1457622794od_r_l: set_Product_prod_r_l > $o ).
thf(func_def_63,type,
finite1507191824od_r_r: set_Product_prod_r_r > $o ).
thf(func_def_64,type,
finite1256628466_set_l: set_set_set_l > $o ).
thf(func_def_65,type,
finite1651563256_set_r: set_set_set_r > $o ).
thf(func_def_66,type,
finite88277554um_l_l: set_set_Sum_sum_l_l > $o ).
thf(func_def_67,type,
finite483212344um_l_r: set_set_Sum_sum_l_r > $o ).
thf(func_def_68,type,
finite1407742636um_r_l: set_set_Sum_sum_r_l > $o ).
thf(func_def_69,type,
finite_finite_set_l: set_set_l > $o ).
thf(func_def_70,type,
finite_finite_set_r: set_set_r > $o ).
thf(func_def_71,type,
finite1541484284um_l_l: set_Sum_sum_l_l > $o ).
thf(func_def_72,type,
finite1591053314um_l_r: set_Sum_sum_l_r > $o ).
thf(func_def_73,type,
finite65649782um_r_l: set_Sum_sum_r_l > $o ).
thf(func_def_74,type,
finite115218812um_r_r: set_Sum_sum_r_r > $o ).
thf(func_def_75,type,
finite_finite_l: set_l > $o ).
thf(func_def_76,type,
finite_finite_r: set_r > $o ).
thf(func_def_77,type,
fun_up1835647912_r_l_v: ( l > option_val_r_l_v ) > l > option_val_r_l_v > l > option_val_r_l_v ).
thf(func_def_78,type,
fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).
thf(func_def_79,type,
if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v ).
thf(func_def_80,type,
if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v ).
thf(func_def_81,type,
dom_Pr939617279_r_l_v: ( produc1389397445_r_l_v > option_val_r_l_v ) > set_Pr1409704485_r_l_v ).
thf(func_def_82,type,
dom_Pr1162080227_r_l_v: ( produc1389397445_r_l_v > option1457017436_r_l_v ) > set_Pr1409704485_r_l_v ).
thf(func_def_83,type,
dom_l_val_r_l_v: ( l > option_val_r_l_v ) > set_l ).
thf(func_def_84,type,
dom_l_45837855_r_l_v: ( l > option1457017436_r_l_v ) > set_l ).
thf(func_def_85,type,
dom_r_val_r_l_v: ( r > option_val_r_l_v ) > set_r ).
thf(func_def_86,type,
dom_r_259548057_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
thf(func_def_87,type,
lID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_l ).
thf(func_def_88,type,
lID_L_l_r_v: produc1156025366_r_l_v > set_l ).
thf(func_def_89,type,
rID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
thf(func_def_90,type,
rID_L_l_r_v: produc1156025366_r_l_v > set_r ).
thf(func_def_91,type,
domain87684397_l_r_v: produc1156025366_r_l_v > $o ).
thf(func_def_92,type,
domain1547879849_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_93,type,
revision_step_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_94,type,
revisi1291188644_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_95,type,
subsum148050133_r_l_v: r > r > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_96,type,
subsum680764357_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_97,type,
none_val_r_l_v: option_val_r_l_v ).
thf(func_def_98,type,
none_P277133687_r_l_v: option1457017436_r_l_v ).
thf(func_def_99,type,
some_val_r_l_v: val_r_l_v > option_val_r_l_v ).
thf(func_def_100,type,
some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).
thf(func_def_101,type,
the_val_r_l_v: option_val_r_l_v > val_r_l_v ).
thf(func_def_102,type,
ord_le2116509289_set_l: set_set_l > set_set_l > $o ).
thf(func_def_103,type,
ord_le363960431_set_r: set_set_r > set_set_r > $o ).
thf(func_def_104,type,
ord_le1122554619um_l_l: set_Sum_sum_l_l > set_Sum_sum_l_l > $o ).
thf(func_def_105,type,
ord_le1517489409um_l_r: set_Sum_sum_l_r > set_Sum_sum_l_r > $o ).
thf(func_def_106,type,
ord_le294536053um_r_l: set_Sum_sum_r_l > set_Sum_sum_r_l > $o ).
thf(func_def_107,type,
ord_less_eq_set_l: set_l > set_l > $o ).
thf(func_def_108,type,
ord_less_eq_set_r: set_r > set_r > $o ).
thf(func_def_109,type,
top_top_set_option_l: set_option_l ).
thf(func_def_110,type,
top_top_set_option_r: set_option_r ).
thf(func_def_111,type,
top_to1238153077_r_l_v: set_Pr1409704485_r_l_v ).
thf(func_def_112,type,
top_to320296343od_l_l: set_Product_prod_l_l ).
thf(func_def_113,type,
top_to715231133od_l_r: set_Product_prod_l_r ).
thf(func_def_114,type,
top_to1639761425od_r_l: set_Product_prod_r_l ).
thf(func_def_115,type,
top_to2034696215od_r_r: set_Product_prod_r_r ).
thf(func_def_116,type,
top_top_set_set_l: set_set_l ).
thf(func_def_117,type,
top_top_set_set_r: set_set_r ).
thf(func_def_118,type,
top_to1010946379um_l_l: set_Sum_sum_l_l ).
thf(func_def_119,type,
top_to1405881169um_l_r: set_Sum_sum_l_r ).
thf(func_def_120,type,
top_to182927813um_r_l: set_Sum_sum_r_l ).
thf(func_def_121,type,
top_to577862603um_r_r: set_Sum_sum_r_r ).
thf(func_def_122,type,
top_top_set_l: set_l ).
thf(func_def_123,type,
top_top_set_r: set_r ).
thf(func_def_124,type,
produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).
thf(func_def_125,type,
produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).
thf(func_def_126,type,
produc1175464189_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > produc1389397445_r_l_v ).
thf(func_def_127,type,
eq_states_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_128,type,
collec1978425008_r_l_v: ( produc1389397445_r_l_v > $o ) > set_Pr1409704485_r_l_v ).
thf(func_def_129,type,
collect_set_set_l: ( set_set_l > $o ) > set_set_set_l ).
thf(func_def_130,type,
collect_set_set_r: ( set_set_r > $o ) > set_set_set_r ).
thf(func_def_131,type,
collec1593187440um_l_l: ( set_Sum_sum_l_l > $o ) > set_set_Sum_sum_l_l ).
thf(func_def_132,type,
collec1988122230um_l_r: ( set_Sum_sum_l_r > $o ) > set_set_Sum_sum_l_r ).
thf(func_def_133,type,
collec765168874um_r_l: ( set_Sum_sum_r_l > $o ) > set_set_Sum_sum_r_l ).
thf(func_def_134,type,
collect_set_l: ( set_l > $o ) > set_set_l ).
thf(func_def_135,type,
collect_set_r: ( set_r > $o ) > set_set_r ).
thf(func_def_136,type,
collect_Sum_sum_l_l: ( sum_sum_l_l > $o ) > set_Sum_sum_l_l ).
thf(func_def_137,type,
collect_Sum_sum_l_r: ( sum_sum_l_r > $o ) > set_Sum_sum_l_r ).
thf(func_def_138,type,
collect_Sum_sum_r_l: ( sum_sum_r_l > $o ) > set_Sum_sum_r_l ).
thf(func_def_139,type,
collect_l: ( l > $o ) > set_l ).
thf(func_def_140,type,
collect_r: ( r > $o ) > set_r ).
thf(func_def_141,type,
substitution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > $o ).
thf(func_def_142,type,
transi1323086383_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v ).
thf(func_def_143,type,
member1522896238_r_l_v: produc1389397445_r_l_v > set_Pr1409704485_r_l_v > $o ).
thf(func_def_144,type,
member_set_l: set_l > set_set_l > $o ).
thf(func_def_145,type,
member_set_r: set_r > set_set_r > $o ).
thf(func_def_146,type,
member_l: l > set_l > $o ).
thf(func_def_147,type,
member_r: r > set_r > $o ).
thf(func_def_148,type,
e: cntxt_r_l_v ).
thf(func_def_149,type,
e2: cntxt_r_l_v ).
thf(func_def_150,type,
sigma: l > option_val_r_l_v ).
thf(func_def_151,type,
sigma2: l > option_val_r_l_v ).
thf(func_def_152,type,
tau: l > option_val_r_l_v ).
thf(func_def_153,type,
tau2: l > option_val_r_l_v ).
thf(func_def_154,type,
e3: expr_r_l_v ).
thf(func_def_155,type,
e4: expr_r_l_v ).
thf(func_def_156,type,
left_forkee: r ).
thf(func_def_157,type,
r2: r ).
thf(func_def_158,type,
r3: r ).
thf(func_def_159,type,
right_forkee: r ).
thf(func_def_160,type,
s_1: r > option1457017436_r_l_v ).
thf(func_def_161,type,
s_2: r > option1457017436_r_l_v ).
thf(func_def_162,type,
s_22: r > option1457017436_r_l_v ).
thf(func_def_163,type,
subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
thf(func_def_179,type,
sP0: ( option_val_r_l_v > option_val_r_l_v > $o ) > option_val_r_l_v > option_val_r_l_v > $o ).
thf(func_def_180,type,
sP1: ( option1457017436_r_l_v > option_val_r_l_v > $o ) > option_val_r_l_v > option1457017436_r_l_v > $o ).
thf(func_def_181,type,
sP2: ( option1457017436_r_l_v > option1457017436_r_l_v > $o ) > option1457017436_r_l_v > option1457017436_r_l_v > $o ).
thf(func_def_182,type,
sP3: ( option_val_r_l_v > option1457017436_r_l_v > $o ) > option_val_r_l_v > option1457017436_r_l_v > $o ).
thf(func_def_183,type,
sP4: r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_184,type,
sP5: r > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_185,type,
sK6: ( option_val_r_l_v > option_val_r_l_v > $o ) > option_val_r_l_v > option_val_r_l_v > val_r_l_v ).
thf(func_def_186,type,
sK7: ( option_val_r_l_v > option_val_r_l_v > $o ) > option_val_r_l_v > option_val_r_l_v > val_r_l_v ).
thf(func_def_187,type,
sK8: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_188,type,
sK9: ( r > option1457017436_r_l_v ) > produc1156025366_r_l_v ).
thf(func_def_189,type,
sK10: ( option1457017436_r_l_v > option_val_r_l_v > $o ) > option_val_r_l_v > option1457017436_r_l_v > val_r_l_v ).
thf(func_def_190,type,
sK11: ( option1457017436_r_l_v > option_val_r_l_v > $o ) > option_val_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_191,type,
sK12: ( option1457017436_r_l_v > option1457017436_r_l_v > $o ) > option1457017436_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_192,type,
sK13: ( option1457017436_r_l_v > option1457017436_r_l_v > $o ) > option1457017436_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_193,type,
sK14: option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_194,type,
sK15: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > r > option1457017436_r_l_v ).
thf(func_def_195,type,
sK16: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > r > option1457017436_r_l_v ).
thf(func_def_196,type,
sK17: ( r > $o ) > r ).
thf(func_def_197,type,
sK18: produc1389397445_r_l_v > ( produc1389397445_r_l_v > option_val_r_l_v ) > val_r_l_v ).
thf(func_def_198,type,
sK19: set_l > l ).
thf(func_def_199,type,
sK20: set_l > set_set_l > set_l ).
thf(func_def_200,type,
sK21: ( r > option_val_r_l_v ) > r ).
thf(func_def_201,type,
sK22: ( r > option1457017436_r_l_v ) > cntxt_r_l_v > expr_r_l_v > r > ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > ( r > option1457017436_r_l_v ) > r ).
thf(func_def_202,type,
sK23: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_203,type,
sK24: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_204,type,
sK25: option_val_r_l_v > val_r_l_v ).
thf(func_def_205,type,
sK26: option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_206,type,
sK27: set_l > set_set_l > set_l ).
thf(func_def_207,type,
sK28: ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r ).
thf(func_def_208,type,
sK29: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_209,type,
sK30: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_210,type,
sK31: ( option_val_r_l_v > option1457017436_r_l_v > $o ) > option_val_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_211,type,
sK32: ( option_val_r_l_v > option1457017436_r_l_v > $o ) > option_val_r_l_v > option1457017436_r_l_v > val_r_l_v ).
thf(func_def_212,type,
sK33: ( option1457017436_r_l_v > $o ) > produc1156025366_r_l_v ).
thf(func_def_213,type,
sK34: expr_r_l_v > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_214,type,
sK35: ( produc1389397445_r_l_v > $o ) > ( produc1389397445_r_l_v > $o ) > produc1389397445_r_l_v ).
thf(func_def_215,type,
sK36: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r ).
thf(func_def_216,type,
sK37: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_217,type,
sK38: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_218,type,
sK39: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_219,type,
sK40: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_220,type,
sK41: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_221,type,
sK42: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_222,type,
sK43: ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_223,type,
sK44: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_224,type,
sK45: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_225,type,
sK46: set_Pr1409704485_r_l_v > set_l > ( produc1389397445_r_l_v > l > $o ) > produc1389397445_r_l_v ).
thf(func_def_226,type,
sK47: set_Pr1409704485_r_l_v > set_l > ( produc1389397445_r_l_v > l > $o ) > l ).
thf(func_def_227,type,
sK48: r > ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_228,type,
sK49: r > ( r > option1457017436_r_l_v ) > cntxt_r_l_v ).
thf(func_def_229,type,
sK50: r > ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_230,type,
sK51: r > ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_231,type,
sK52: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_232,type,
sK53: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_233,type,
sK54: ( l > r > $o ) > set_l > set_r > r ).
thf(func_def_234,type,
sK55: ( l > r > $o ) > set_l > set_r > l ).
thf(func_def_235,type,
sK56: r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_236,type,
sK57: r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_237,type,
sK58: ( r > option1457017436_r_l_v ) > l ).
thf(func_def_238,type,
sK59: ( r > option1457017436_r_l_v ) > l ).
thf(func_def_239,type,
sK60: ( l > option_val_r_l_v ) > l ).
thf(func_def_240,type,
sK61: ( l > option1457017436_r_l_v ) > l > produc1156025366_r_l_v ).
thf(func_def_241,type,
sK62: r > ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_242,type,
sK63: r > ( r > option1457017436_r_l_v ) > cntxt_r_l_v ).
thf(func_def_243,type,
sK64: r > ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_244,type,
sK65: r > ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_245,type,
sK66: r > ( r > option1457017436_r_l_v ) > produc1156025366_r_l_v ).
thf(func_def_246,type,
sK67: r > ( r > option1457017436_r_l_v ) > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_247,type,
sK68: r > ( r > option1457017436_r_l_v ) > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_248,type,
sK69: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_249,type,
sK70: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_250,type,
sK71: ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_251,type,
sK72: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_252,type,
sK73: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_253,type,
sK74: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_254,type,
sK75: ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_255,type,
sK76: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_256,type,
sK77: set_set_r > set_r > set_r ).
thf(func_def_257,type,
sK78: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_258,type,
sK79: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_259,type,
sK80: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_260,type,
sK81: ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_261,type,
sK82: ( set_r > $o ) > ( set_r > $o ) > set_r ).
thf(func_def_262,type,
sK83: set_Pr1409704485_r_l_v > produc1389397445_r_l_v ).
thf(func_def_263,type,
sK84: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_264,type,
sK85: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_265,type,
sK86: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_266,type,
sK87: ( l > option_val_r_l_v ) > ( r > option1457017436_r_l_v ) > cntxt_r_l_v > ( l > option_val_r_l_v ) > ( r > option1457017436_r_l_v ) > r > val_r_l_v > l ).
thf(func_def_267,type,
sK88: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_268,type,
sK89: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_269,type,
sK90: ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_270,type,
sK91: ( option_val_r_l_v > $o ) > val_r_l_v ).
thf(func_def_271,type,
sK92: r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_272,type,
sK93: r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_273,type,
sK94: ( r > l > $o ) > set_l > set_r > l ).
thf(func_def_274,type,
sK95: ( r > l > $o ) > set_l > set_r > r ).
thf(func_def_275,type,
sK96: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > r > option1457017436_r_l_v ).
thf(func_def_276,type,
sK97: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > r > option1457017436_r_l_v ).
thf(func_def_277,type,
sK98: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_278,type,
sK99: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_279,type,
sK100: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_280,type,
sK101: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_281,type,
sK102: ( r > option1457017436_r_l_v ) > r > val_r_l_v ).
thf(func_def_282,type,
sK103: ( r > option1457017436_r_l_v ) > r > cntxt_r_l_v ).
thf(func_def_283,type,
sK104: ( set_l > $o ) > ( set_l > $o ) > set_l ).
thf(func_def_284,type,
sK105: r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_285,type,
sK106: r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_286,type,
sK107: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_287,type,
sK108: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_288,type,
sK109: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_289,type,
sK110: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_290,type,
sK111: ( r > option1457017436_r_l_v ) > r > expr_r_l_v ).
thf(func_def_291,type,
sK112: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_292,type,
sK113: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_293,type,
sK114: ( r > option1457017436_r_l_v ) > r > cntxt_r_l_v ).
thf(func_def_294,type,
sK115: ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_295,type,
sK116: ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_296,type,
sK117: ( l > l > $o ) > set_l > set_l > l ).
thf(func_def_297,type,
sK118: ( l > l > $o ) > set_l > set_l > l ).
thf(func_def_298,type,
sK119: val_r_l_v > cntxt_r_l_v > r > ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > l ).
thf(func_def_299,type,
sK120: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_300,type,
sK121: ( r > option1457017436_r_l_v ) > r > cntxt_r_l_v ).
thf(func_def_301,type,
sK122: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_302,type,
sK123: ( r > option1457017436_r_l_v ) > r > val_r_l_v ).
thf(func_def_303,type,
sK124: ( produc1389397445_r_l_v > option1457017436_r_l_v ) > produc1389397445_r_l_v > produc1156025366_r_l_v ).
thf(func_def_304,type,
sK125: r > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_305,type,
sK126: r > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_306,type,
sK127: ( r > option1457017436_r_l_v ) > r > cntxt_r_l_v ).
thf(func_def_307,type,
sK128: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_308,type,
sK129: ( r > option1457017436_r_l_v ) > r > expr_r_l_v ).
thf(func_def_309,type,
sK130: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_310,type,
sK131: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_311,type,
sK132: option1457017436_r_l_v > ( ( r > option1457017436_r_l_v ) > $o ) > r > option1457017436_r_l_v ).
thf(func_def_312,type,
sK133: option1457017436_r_l_v > ( ( r > option1457017436_r_l_v ) > $o ) > r ).
thf(func_def_313,type,
sK134: option1457017436_r_l_v > ( ( r > option1457017436_r_l_v ) > $o ) > option1457017436_r_l_v ).
thf(func_def_314,type,
sK135: r > ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_315,type,
sK136: r > ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_316,type,
sK137: r > ( r > option1457017436_r_l_v ) > val_r_l_v ).
thf(func_def_317,type,
sK138: r > ( r > option1457017436_r_l_v ) > cntxt_r_l_v ).
thf(func_def_318,type,
sK139: produc1156025366_r_l_v > expr_r_l_v ).
thf(func_def_319,type,
sK140: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_320,type,
sK141: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_321,type,
sK142: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_322,type,
sK143: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_323,type,
sK144: ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_324,type,
sK145: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_325,type,
sK146: ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_326,type,
sK147: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_327,type,
sK148: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_328,type,
sK149: ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_329,type,
sK150: r > ( r > option_val_r_l_v ) > val_r_l_v ).
thf(func_def_330,type,
sK151: ( r > option1457017436_r_l_v ) > cntxt_r_l_v > ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > ( r > option1457017436_r_l_v ) > expr_r_l_v > r > r ).
thf(func_def_331,type,
sK152: r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_332,type,
sK153: r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_333,type,
sK154: option_val_r_l_v > ( ( l > option_val_r_l_v ) > $o ) > option_val_r_l_v ).
thf(func_def_334,type,
sK155: option_val_r_l_v > ( ( l > option_val_r_l_v ) > $o ) > l > option_val_r_l_v ).
thf(func_def_335,type,
sK156: option_val_r_l_v > ( ( l > option_val_r_l_v ) > $o ) > l ).
thf(func_def_336,type,
sK157: option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_337,type,
sK158: ( r > option1457017436_r_l_v ) > expr_r_l_v > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_338,type,
sK159: set_set_r > set_r > set_r ).
thf(func_def_339,type,
sK160: ( r > option1457017436_r_l_v ) > r > cntxt_r_l_v ).
thf(func_def_340,type,
sK161: ( r > option1457017436_r_l_v ) > r > val_r_l_v ).
thf(func_def_341,type,
sK162: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_342,type,
sK163: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_343,type,
sK164: option_val_r_l_v > val_r_l_v ).
thf(func_def_344,type,
sK165: r > r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_345,type,
sK166: r > r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_346,type,
sK167: ( l > $o ) > l ).
thf(func_def_347,type,
sK168: ( r > option1457017436_r_l_v ) > l > produc1156025366_r_l_v ).
thf(func_def_348,type,
sK169: ( r > option1457017436_r_l_v ) > l > r ).
thf(func_def_349,type,
sK170: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_350,type,
sK171: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_351,type,
sK172: ( l > option1457017436_r_l_v ) > l ).
thf(func_def_352,type,
sK173: ( l > $o ) > ( l > $o ) > l ).
thf(func_def_353,type,
sK174: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_354,type,
sK175: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_355,type,
sK176: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_356,type,
sK177: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_357,type,
sK178: ( produc1156025366_r_l_v > $o ) > expr_r_l_v ).
thf(func_def_358,type,
sK179: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_359,type,
sK180: r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_360,type,
sK181: r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_361,type,
sK182: ( produc1389397445_r_l_v > r > $o ) > set_Pr1409704485_r_l_v > set_r > produc1389397445_r_l_v ).
thf(func_def_362,type,
sK183: ( produc1389397445_r_l_v > r > $o ) > set_Pr1409704485_r_l_v > set_r > r ).
thf(func_def_363,type,
sK184: set_r > r ).
thf(func_def_364,type,
sK185: option_val_r_l_v > val_r_l_v ).
thf(func_def_365,type,
sK186: l > ( l > option_val_r_l_v ) > val_r_l_v ).
thf(func_def_366,type,
sK187: ( r > $o ) > ( r > $o ) > r ).
thf(func_def_367,type,
sK188: set_r > set_r > ( r > r > $o ) > r ).
thf(func_def_368,type,
sK189: set_r > set_r > ( r > r > $o ) > r ).
thf(func_def_370,type,
ph191:
!>[X0: $tType] : X0 ).
thf(func_def_371,type,
sK192: r ).
thf(f2588,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2580]) ).
thf(f2580,plain,
( ( s_1 @ r3 )
!= ( s_1 @ r3 ) ),
inference(superposition,[status(thm)],[f2427,f1829]) ).
thf(f1829,plain,
( ( s_1 @ r3 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma2 @ ( produc1834103605_r_l_v @ tau2 @ ( plug_r_l_v @ e2 @ ( rfork_r_l_v @ e4 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( s_1 @ r3 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma2 @ ( produc1834103605_r_l_v @ tau2 @ ( plug_r_l_v @ e2 @ ( rfork_r_l_v @ e4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a64ubDLv2V/DTF2THF_3281.p',fact_6_local_Ofork_I2_J) ).
thf(f2427,plain,
! [X0: produc1156025366_r_l_v] :
( ( s_1 @ r3 )
!= ( some_P1807977723_r_l_v @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f2425]) ).
thf(f2425,plain,
! [X0: produc1156025366_r_l_v] :
( ( $true != $true )
| ( ( s_1 @ r3 )
!= ( some_P1807977723_r_l_v @ X0 ) ) ),
inference(superposition,[status(thm)],[f2422,f2159]) ).
thf(f2159,plain,
! [X2: r,X0: r > option1457017436_r_l_v,X1: produc1156025366_r_l_v] :
( ( $true
= ( member_r @ X2 @ ( rID_G_r_l_v @ X0 ) ) )
| ( ( some_P1807977723_r_l_v @ X1 )
!= ( X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f1067]) ).
thf(f1067,plain,
! [X0: r > option1457017436_r_l_v,X1: produc1156025366_r_l_v,X2: r] :
( ( ( some_P1807977723_r_l_v @ X1 )
!= ( X0 @ X2 ) )
| ( $true
= ( member_r @ X2 @ ( rID_G_r_l_v @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f506]) ).
thf(f506,plain,
! [X0: r > option1457017436_r_l_v,X1: produc1156025366_r_l_v,X2: r] :
( ( ( some_P1807977723_r_l_v @ X1 )
= ( X0 @ X2 ) )
=> ( $true
= ( member_r @ X2 @ ( rID_G_r_l_v @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f505]) ).
thf(f505,plain,
! [X0: r > option1457017436_r_l_v,X1: produc1156025366_r_l_v,X2: r] :
( ( ( some_P1807977723_r_l_v @ X1 )
= ( X0 @ X2 ) )
=> ( member_r @ X2 @ ( rID_G_r_l_v @ X0 ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,axiom,
! [X2: r > option1457017436_r_l_v,X24: produc1156025366_r_l_v,X1: r] :
( ( ( X2 @ X1 )
= ( some_P1807977723_r_l_v @ X24 ) )
=> ( member_r @ X1 @ ( rID_G_r_l_v @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a64ubDLv2V/DTF2THF_3281.p',fact_24_RID_092_060_094sub_062GI_I1_J) ).
thf(f2422,plain,
( $true
!= ( member_r @ r3 @ ( rID_G_r_l_v @ s_1 ) ) ),
inference(superposition,[status(thm)],[f2067,f1948]) ).
thf(f1948,plain,
right_forkee = r3,
inference(cnf_transformation,[status(thm)],[f953]) ).
thf(f953,plain,
right_forkee = r3,
inference(flattening,[status(thm)],[f359]) ).
thf(f359,negated_conjecture,
~ ( ( right_forkee != r3 ) ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f358,conjecture,
right_forkee != r3,
file('/export/starexec/sandbox/tmp/tmp.a64ubDLv2V/DTF2THF_3281.p',conj_0) ).
thf(f2067,plain,
( ( member_r @ right_forkee @ ( rID_G_r_l_v @ s_1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f922]) ).
thf(f922,plain,
( ( member_r @ right_forkee @ ( rID_G_r_l_v @ s_1 ) )
!= $true ),
inference(flattening,[status(thm)],[f366]) ).
thf(f366,plain,
( ( member_r @ right_forkee @ ( rID_G_r_l_v @ s_1 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f365]) ).
thf(f365,plain,
~ ( member_r @ right_forkee @ ( rID_G_r_l_v @ s_1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ( member_r @ right_forkee @ ( rID_G_r_l_v @ s_1 ) ),
file('/export/starexec/sandbox/tmp/tmp.a64ubDLv2V/DTF2THF_3281.p',fact_0_local_Ofork_I3_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP046^1 : 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
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:24:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : ITP046^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.47 % Domain : Interactive Theorem Proving
% 0.30/0.47 % Problem : Sledgehammer Determinacy problem prob_599__3354110_1
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Des21]
% 0.30/0.47 % Names : Determinacy/prob_599__3354110_1 [Des21]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.30/0.47 % Syntax : Number of formulae : 522 ( 135 unt; 164 typ; 0 def)
% 0.30/0.47 % Number of atoms : 1192 ( 510 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 13 ( 3 avg)
% 0.30/0.47 % Number of connectives : 4899 ( 166 ~; 69 |; 115 &;4020 @)
% 0.30/0.47 % ( 0 <=>; 529 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 35 ( 8 avg)
% 0.30/0.47 % Number of types : 36 ( 35 usr)
% 0.30/0.47 % Number of type conns : 1017 (1017 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 132 ( 129 usr; 30 con; 0-4 aty)
% 0.30/0.47 % Number of variables : 1423 ( 107 ^;1215 !; 101 ?;1423 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:14.777
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % Could-be-implicit typings (35)
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_M_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_J_J,type,
% 0.30/0.47 set_Pr1409704485_r_l_v: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_M_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_J,type,
% 0.30/0.47 produc1389397445_r_l_v: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 0.30/0.47 option1457017436_r_l_v: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 0.30/0.47 produc1156025366_r_l_v: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.30/0.47 produc1164766533_r_l_v: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J_J,type,
% 0.30/0.47 set_set_Sum_sum_r_l: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J_J,type,
% 0.30/0.47 set_set_Sum_sum_l_r: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J_J,type,
% 0.30/0.47 set_set_Sum_sum_l_l: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.30/0.47 option_val_r_l_v: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__r_J_J,type,
% 0.30/0.47 set_Product_prod_r_r: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__l_J_J,type,
% 0.30/0.47 set_Product_prod_r_l: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__r_J_J,type,
% 0.30/0.47 set_Product_prod_l_r: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__l_J_J,type,
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% 0.30/0.47 e: cntxt_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v__092_060E_062_H____,type,
% 0.30/0.47 e2: cntxt_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v__092_060sigma_062,type,
% 0.30/0.47 sigma: l > option_val_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v__092_060sigma_062_H____,type,
% 0.30/0.47 sigma2: l > option_val_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v__092_060tau_062,type,
% 0.30/0.47 tau: l > option_val_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v__092_060tau_062_H____,type,
% 0.30/0.47 tau2: l > option_val_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_e,type,
% 0.30/0.47 e3: expr_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_e_H____,type,
% 0.30/0.47 e4: expr_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_left__forkee,type,
% 0.30/0.47 left_forkee: r ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_r,type,
% 0.30/0.47 r2: r ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_r_H,type,
% 0.30/0.47 r3: r ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_right__forkee____,type,
% 0.30/0.47 right_forkee: r ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_s_092_060_094sub_0621,type,
% 0.30/0.47 s_1: r > option1457017436_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_s_092_060_094sub_0622,type,
% 0.30/0.47 s_2: r > option1457017436_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_s_092_060_094sub_0622_H,type,
% 0.30/0.47 s_22: r > option1457017436_r_l_v ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_subst,type,
% 0.30/0.47 subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
% 0.30/0.47
% 0.30/0.47 % Relevant facts (352)
% 0.30/0.47 thf(fact_0_local_Ofork_I3_J,axiom,
% 0.30/0.47 ~ ( member_r @ right_forkee @ ( rID_G_r_l_v @ s_1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.fork(3)
% 0.30/0.47 thf(fact_1_side,axiom,
% 0.30/0.47 ~ ( member_r @ left_forkee @ ( rID_G_r_l_v @ s_1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % side
% 0.30/0.47 thf(fact_2_neq,axiom,
% 0.30/0.47 r2 != r3 ).
% 0.30/0.47
% 0.30/0.47 % neq
% 0.30/0.47 thf(fact_3__092_060open_062r_H_A_092_060noteq_062_Aleft__forkee_092_060close_062,axiom,
% 0.30/0.47 r3 != left_forkee ).
% 0.30/0.47
% 0.30/0.47 % \<open>r' \<noteq> left_forkee\<close>
% 0.30/0.47 thf(fact_4_r_H__unchanged__left,axiom,
% 0.30/0.47 ( ( s_2 @ r3 )
% 0.30/0.47 = ( s_1 @ r3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % r'_unchanged_left
% 0.30/0.47 thf(fact_5__092_060open_062r_A_092_060noteq_062_Aright__forkee_092_060close_062,axiom,
% 0.30/0.47 r2 != right_forkee ).
% 0.30/0.47
% 0.30/0.47 % \<open>r \<noteq> right_forkee\<close>
% 0.30/0.47 thf(fact_6_local_Ofork_I2_J,axiom,
% 0.30/0.47 ( ( s_1 @ r3 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma2 @ ( produc1834103605_r_l_v @ tau2 @ ( plug_r_l_v @ e2 @ ( rfork_r_l_v @ e4 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.fork(2)
% 0.30/0.47 thf(fact_7_right,axiom,
% 0.30/0.47 revision_step_r_l_v @ subst @ r3 @ s_1 @ s_22 ).
% 0.30/0.47
% 0.30/0.47 % right
% 0.30/0.47 thf(fact_8_local_Ofork_I1_J,axiom,
% 0.30/0.47 ( s_22
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma2 @ ( produc1834103605_r_l_v @ tau2 @ ( plug_r_l_v @ e2 @ ( vE_r_l_v @ ( rid_r_l_v @ right_forkee ) ) ) ) ) ) ) @ right_forkee
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma2 @ tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ e4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local.fork(1)
% 0.30/0.47 thf(fact_9__092_060open_062r_A_092_060noteq_062_Aleft__forkee_092_060close_062,axiom,
% 0.30/0.47 r2 != left_forkee ).
% 0.30/0.47
% 0.30/0.47 % \<open>r \<noteq> left_forkee\<close>
% 0.30/0.47 thf(fact_10_r__unchanged__right,axiom,
% 0.30/0.47 ( ( s_22 @ r2 )
% 0.30/0.47 = ( s_1 @ r2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % r_unchanged_right
% 0.30/0.47 thf(fact_11_reach,axiom,
% 0.30/0.47 reachable_r_l_v @ subst @ s_1 ).
% 0.30/0.47
% 0.30/0.47 % reach
% 0.30/0.47 thf(fact_12_left__step,axiom,
% 0.30/0.47 revision_step_r_l_v @ subst @ r2 @ s_1 @ s_2 ).
% 0.30/0.47
% 0.30/0.47 % left_step
% 0.30/0.47 thf(fact_13_only__fork__introduces__rids_H,axiom,
% 0.30/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 0.30/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v] :
% 0.30/0.47 ( ( S @ R )
% 0.30/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E2 ) ) ) ) ) )
% 0.30/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % only_fork_introduces_rids'
% 0.30/0.47 thf(fact_14_revision__step_Ofork,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.30/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ( revision_step_r_l_v @ subst @ R @ S
% 0.30/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step.fork
% 0.30/0.47 thf(fact_15_fork__pseudodeterministic,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 = ( ? [R3: r] :
% 0.30/0.47 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
% 0.30/0.47 & ( S2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fork_pseudodeterministic
% 0.30/0.47 thf(fact_16_substitution__axioms,axiom,
% 0.30/0.47 substitution_r_l_v @ subst ).
% 0.30/0.47
% 0.30/0.47 % substitution_axioms
% 0.30/0.47 thf(fact_17_revision__step__relaxed_Ofork,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.30/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 0.30/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step_relaxed.fork
% 0.30/0.47 thf(fact_18_local__and__fork__commute,axiom,
% 0.30/0.47 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
% 0.30/0.47 ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.30/0.47 => ( ( S_22
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) ) )
% 0.30/0.47 => ( ( ( S_2 @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.30/0.47 => ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S_22
% 0.30/0.47 @ ( fun_up709272714_r_l_v
% 0.30/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) )
% 0.30/0.47 @ R
% 0.30/0.47 @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ( ( R != R4 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local_and_fork_commute
% 0.30/0.47 thf(fact_19_s_092_060_094sub_0622,axiom,
% 0.30/0.47 ( s_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ left_forkee ) ) ) ) ) ) ) @ left_forkee
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ e3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % s\<^sub>2
% 0.30/0.47 thf(fact_20_restrictions__inwards,axiom,
% 0.30/0.47 ! [X2: r,X3: r,F: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( X2 != X3 )
% 0.30/0.47 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X2 @ ( some_P1807977723_r_l_v @ Y ) ) @ X3 @ none_P277133687_r_l_v )
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X3 @ none_P277133687_r_l_v ) @ X2 @ ( some_P1807977723_r_l_v @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % restrictions_inwards
% 0.30/0.47 thf(fact_21_restrictions__inwards,axiom,
% 0.30/0.47 ! [X2: l,X3: l,F: l > option_val_r_l_v,Y: val_r_l_v] :
% 0.30/0.47 ( ( X2 != X3 )
% 0.30/0.47 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X2 @ ( some_val_r_l_v @ Y ) ) @ X3 @ none_val_r_l_v )
% 0.30/0.47 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X3 @ none_val_r_l_v ) @ X2 @ ( some_val_r_l_v @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % restrictions_inwards
% 0.30/0.47 thf(fact_22_empty__upd__none,axiom,
% 0.30/0.47 ! [X2: l] :
% 0.30/0.47 ( ( fun_up1835647912_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ X2
% 0.30/0.47 @ none_val_r_l_v )
% 0.30/0.47 = ( ^ [X: l] : none_val_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_upd_none
% 0.30/0.47 thf(fact_23_empty__upd__none,axiom,
% 0.30/0.47 ! [X2: r] :
% 0.30/0.47 ( ( fun_up709272714_r_l_v
% 0.30/0.47 @ ^ [X: r] : none_P277133687_r_l_v
% 0.30/0.47 @ X2
% 0.30/0.47 @ none_P277133687_r_l_v )
% 0.30/0.47 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_upd_none
% 0.30/0.47 thf(fact_24_RID_092_060_094sub_062GI_I1_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,V: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ V ) )
% 0.30/0.47 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RID\<^sub>GI(1)
% 0.30/0.47 thf(fact_25_not__None__eq,axiom,
% 0.30/0.47 ! [X2: option1457017436_r_l_v] :
% 0.30/0.47 ( ( X2 != none_P277133687_r_l_v )
% 0.30/0.47 = ( ? [Y2: produc1156025366_r_l_v] :
% 0.30/0.47 ( X2
% 0.30/0.47 = ( some_P1807977723_r_l_v @ Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_None_eq
% 0.30/0.47 thf(fact_26_not__None__eq,axiom,
% 0.30/0.47 ! [X2: option_val_r_l_v] :
% 0.30/0.47 ( ( X2 != none_val_r_l_v )
% 0.30/0.47 = ( ? [Y2: val_r_l_v] :
% 0.30/0.47 ( X2
% 0.30/0.47 = ( some_val_r_l_v @ Y2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_None_eq
% 0.30/0.47 thf(fact_27_not__Some__eq,axiom,
% 0.30/0.47 ! [X2: option1457017436_r_l_v] :
% 0.30/0.47 ( ( ! [Y2: produc1156025366_r_l_v] :
% 0.30/0.47 ( X2
% 0.30/0.47 != ( some_P1807977723_r_l_v @ Y2 ) ) )
% 0.30/0.47 = ( X2 = none_P277133687_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_Some_eq
% 0.30/0.47 thf(fact_28_not__Some__eq,axiom,
% 0.30/0.47 ! [X2: option_val_r_l_v] :
% 0.30/0.47 ( ( ! [Y2: val_r_l_v] :
% 0.30/0.47 ( X2
% 0.30/0.47 != ( some_val_r_l_v @ Y2 ) ) )
% 0.30/0.47 = ( X2 = none_val_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_Some_eq
% 0.30/0.47 thf(fact_29_s_092_060_094sub_0621__r,axiom,
% 0.30/0.47 ( ( s_1 @ r2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e3 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % s\<^sub>1_r
% 0.30/0.47 thf(fact_30_local__steps__commute,axiom,
% 0.30/0.47 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.30/0.47 => ( ( S_22
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local_steps_commute
% 0.30/0.47 thf(fact_31_only__fork__introduces__rids,axiom,
% 0.30/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v] :
% 0.30/0.47 ( ( S @ R )
% 0.30/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E2 ) ) ) ) ) )
% 0.30/0.47 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % only_fork_introduces_rids
% 0.30/0.47 thf(fact_32_local__determinism,axiom,
% 0.30/0.47 ! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_22 )
% 0.30/0.47 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local_determinism
% 0.30/0.47 thf(fact_33_SLC__sym,axiom,
% 0.30/0.47 ! [R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_33 )
% 0.30/0.47 | ( S_2 = S_33 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_34 )
% 0.30/0.47 | ( S_22 = S_34 ) ) )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_3 )
% 0.30/0.47 | ( S_22 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_32 )
% 0.30/0.47 | ( S_2 = S_32 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % SLC_sym
% 0.30/0.47 thf(fact_34_SLC__commute,axiom,
% 0.30/0.47 ! [S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( S_35 = S_36 )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 0.30/0.47 => ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 0.30/0.47 | ( S_2 = S_35 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 0.30/0.47 | ( S_22 = S_36 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % SLC_commute
% 0.30/0.47 thf(fact_35_reachability__closed__under__execution__step,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % reachability_closed_under_execution_step
% 0.30/0.47 thf(fact_36_option_Oinject,axiom,
% 0.30/0.47 ! [X22: produc1156025366_r_l_v,Y22: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( ( some_P1807977723_r_l_v @ X22 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ Y22 ) )
% 0.30/0.47 = ( X22 = Y22 ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.inject
% 0.30/0.47 thf(fact_37_option_Oinject,axiom,
% 0.30/0.47 ! [X22: val_r_l_v,Y22: val_r_l_v] :
% 0.30/0.47 ( ( ( some_val_r_l_v @ X22 )
% 0.30/0.47 = ( some_val_r_l_v @ Y22 ) )
% 0.30/0.47 = ( X22 = Y22 ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.inject
% 0.30/0.47 thf(fact_38_transition__relations__equivalent,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 = ( revisi1291188644_r_l_v @ subst @ R @ S @ S2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % transition_relations_equivalent
% 0.30/0.47 thf(fact_39_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 0.30/0.47 ! [R2: r,S: r > option1457017436_r_l_v,R: r] :
% 0.30/0.47 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.30/0.47 => ( member_r @ R2 @ ( rID_G_r_l_v @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_restricted_global_in_unrestricted_global(1)
% 0.30/0.47 thf(fact_40_in__restricted__global__in__updated__global_I1_J,axiom,
% 0.30/0.47 ! [R2: r,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.30/0.47 => ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_restricted_global_in_updated_global(1)
% 0.30/0.47 thf(fact_41_reachable__def,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.47 = ( ? [E5: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ subst @ E5 @ S3 @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % reachable_def
% 0.30/0.47 thf(fact_42_substitution_Olocal__determinism,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_22 )
% 0.30/0.47 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.local_determinism
% 0.30/0.47 thf(fact_43_substitution_OSLC__commute,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( S_35 = S_36 )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 0.30/0.47 => ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 0.30/0.47 | ( S_2 = S_35 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 0.30/0.47 | ( S_22 = S_36 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.SLC_commute
% 0.30/0.47 thf(fact_44_substitution_OSLC__sym,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_33 )
% 0.30/0.47 | ( S_2 = S_33 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_34 )
% 0.30/0.47 | ( S_22 = S_34 ) ) )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_3 )
% 0.30/0.47 | ( S_22 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_32 )
% 0.30/0.47 | ( S_2 = S_32 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.SLC_sym
% 0.30/0.47 thf(fact_45_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r] : ( ord_less_eq_set_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) @ ( rID_G_r_l_v @ S ) ) ).
% 0.30/0.47
% 0.30/0.47 % ID_restricted_global_subset_unrestricted(2)
% 0.30/0.47 thf(fact_46_substitution_Olocal__steps__commute,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.30/0.47 => ( ( S_22
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.local_steps_commute
% 0.30/0.47 thf(fact_47_substitution_Olocal__and__fork__commute,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.30/0.47 => ( ( S_22
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) ) )
% 0.30/0.47 => ( ( ( S_2 @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.30/0.47 => ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_22
% 0.30/0.47 @ ( fun_up709272714_r_l_v
% 0.30/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) )
% 0.30/0.47 @ R
% 0.30/0.47 @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ( ( R != R4 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.local_and_fork_commute
% 0.30/0.47 thf(fact_48_combine__options__cases,axiom,
% 0.30/0.47 ! [X2: option1457017436_r_l_v,P: option1457017436_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( X2 = none_P277133687_r_l_v )
% 0.30/0.47 => ( P @ X2 @ Y ) )
% 0.30/0.47 => ( ( ( Y = none_P277133687_r_l_v )
% 0.30/0.47 => ( P @ X2 @ Y ) )
% 0.30/0.47 => ( ! [A: produc1156025366_r_l_v,B: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( some_P1807977723_r_l_v @ A ) )
% 0.30/0.47 => ( ( Y
% 0.30/0.47 = ( some_P1807977723_r_l_v @ B ) )
% 0.30/0.47 => ( P @ X2 @ Y ) ) )
% 0.30/0.47 => ( P @ X2 @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % combine_options_cases
% 0.30/0.47 thf(fact_49_combine__options__cases,axiom,
% 0.30/0.47 ! [X2: option1457017436_r_l_v,P: option1457017436_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 0.30/0.47 ( ( ( X2 = none_P277133687_r_l_v )
% 0.30/0.47 => ( P @ X2 @ Y ) )
% 0.30/0.47 => ( ( ( Y = none_val_r_l_v )
% 0.30/0.47 => ( P @ X2 @ Y ) )
% 0.30/0.47 => ( ! [A: produc1156025366_r_l_v,B: val_r_l_v] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( some_P1807977723_r_l_v @ A ) )
% 0.30/0.47 => ( ( Y
% 0.30/0.47 = ( some_val_r_l_v @ B ) )
% 0.30/0.47 => ( P @ X2 @ Y ) ) )
% 0.30/0.47 => ( P @ X2 @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % combine_options_cases
% 0.30/0.47 thf(fact_50_combine__options__cases,axiom,
% 0.30/0.47 ! [X2: option_val_r_l_v,P: option_val_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( X2 = none_val_r_l_v )
% 0.30/0.47 => ( P @ X2 @ Y ) )
% 0.30/0.47 => ( ( ( Y = none_P277133687_r_l_v )
% 0.30/0.47 => ( P @ X2 @ Y ) )
% 0.30/0.47 => ( ! [A: val_r_l_v,B: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( some_val_r_l_v @ A ) )
% 0.30/0.47 => ( ( Y
% 0.30/0.47 = ( some_P1807977723_r_l_v @ B ) )
% 0.30/0.47 => ( P @ X2 @ Y ) ) )
% 0.30/0.47 => ( P @ X2 @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % combine_options_cases
% 0.30/0.47 thf(fact_51_combine__options__cases,axiom,
% 0.30/0.47 ! [X2: option_val_r_l_v,P: option_val_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 0.30/0.47 ( ( ( X2 = none_val_r_l_v )
% 0.30/0.47 => ( P @ X2 @ Y ) )
% 0.30/0.47 => ( ( ( Y = none_val_r_l_v )
% 0.30/0.47 => ( P @ X2 @ Y ) )
% 0.30/0.47 => ( ! [A: val_r_l_v,B: val_r_l_v] :
% 0.30/0.47 ( ( X2
% 0.30/0.47 = ( some_val_r_l_v @ A ) )
% 0.30/0.47 => ( ( Y
% 0.30/0.47 = ( some_val_r_l_v @ B ) )
% 0.30/0.47 => ( P @ X2 @ Y ) ) )
% 0.30/0.47 => ( P @ X2 @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % combine_options_cases
% 0.30/0.47 thf(fact_52_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A2: set_l,P: set_l > $o] :
% 0.30/0.47 ( ( member_set_l @ A2 @ ( collect_set_l @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_53_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A2: set_r,P: set_r > $o] :
% 0.30/0.47 ( ( member_set_r @ A2 @ ( collect_set_r @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_54_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A2: r,P: r > $o] :
% 0.30/0.47 ( ( member_r @ A2 @ ( collect_r @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_55_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A2: l,P: l > $o] :
% 0.30/0.47 ( ( member_l @ A2 @ ( collect_l @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_56_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A2: produc1389397445_r_l_v,P: produc1389397445_r_l_v > $o] :
% 0.30/0.47 ( ( member1522896238_r_l_v @ A2 @ ( collec1978425008_r_l_v @ P ) )
% 0.30/0.47 = ( P @ A2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_57_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A3: set_set_l] :
% 0.30/0.47 ( ( collect_set_l
% 0.30/0.47 @ ^ [X: set_l] : ( member_set_l @ X @ A3 ) )
% 0.30/0.47 = A3 ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_58_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A3: set_set_r] :
% 0.30/0.47 ( ( collect_set_r
% 0.30/0.47 @ ^ [X: set_r] : ( member_set_r @ X @ A3 ) )
% 0.30/0.47 = A3 ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_59_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A3: set_r] :
% 0.30/0.47 ( ( collect_r
% 0.30/0.47 @ ^ [X: r] : ( member_r @ X @ A3 ) )
% 0.30/0.47 = A3 ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_60_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A3: set_l] :
% 0.30/0.47 ( ( collect_l
% 0.30/0.47 @ ^ [X: l] : ( member_l @ X @ A3 ) )
% 0.30/0.47 = A3 ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_61_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A3: set_Pr1409704485_r_l_v] :
% 0.30/0.47 ( ( collec1978425008_r_l_v
% 0.30/0.47 @ ^ [X: produc1389397445_r_l_v] : ( member1522896238_r_l_v @ X @ A3 ) )
% 0.30/0.47 = A3 ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_62_Collect__cong,axiom,
% 0.30/0.47 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 0.30/0.47 ( ! [X4: produc1389397445_r_l_v] :
% 0.30/0.47 ( ( P @ X4 )
% 0.30/0.47 = ( Q @ X4 ) )
% 0.30/0.47 => ( ( collec1978425008_r_l_v @ P )
% 0.30/0.47 = ( collec1978425008_r_l_v @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_cong
% 0.30/0.47 thf(fact_63_Collect__cong,axiom,
% 0.30/0.47 ! [P: l > $o,Q: l > $o] :
% 0.30/0.47 ( ! [X4: l] :
% 0.30/0.47 ( ( P @ X4 )
% 0.30/0.47 = ( Q @ X4 ) )
% 0.30/0.47 => ( ( collect_l @ P )
% 0.30/0.47 = ( collect_l @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_cong
% 0.30/0.47 thf(fact_64_Collect__cong,axiom,
% 0.30/0.47 ! [P: r > $o,Q: r > $o] :
% 0.30/0.47 ( ! [X4: r] :
% 0.30/0.47 ( ( P @ X4 )
% 0.30/0.47 = ( Q @ X4 ) )
% 0.30/0.47 => ( ( collect_r @ P )
% 0.30/0.47 = ( collect_r @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_cong
% 0.30/0.47 thf(fact_65_Collect__cong,axiom,
% 0.30/0.47 ! [P: set_l > $o,Q: set_l > $o] :
% 0.30/0.47 ( ! [X4: set_l] :
% 0.30/0.47 ( ( P @ X4 )
% 0.30/0.47 = ( Q @ X4 ) )
% 0.30/0.47 => ( ( collect_set_l @ P )
% 0.30/0.47 = ( collect_set_l @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_cong
% 0.30/0.47 thf(fact_66_Collect__cong,axiom,
% 0.30/0.47 ! [P: set_r > $o,Q: set_r > $o] :
% 0.30/0.47 ( ! [X4: set_r] :
% 0.30/0.47 ( ( P @ X4 )
% 0.30/0.47 = ( Q @ X4 ) )
% 0.30/0.47 => ( ( collect_set_r @ P )
% 0.30/0.47 = ( collect_set_r @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_cong
% 0.30/0.47 thf(fact_67_split__option__all,axiom,
% 0.30/0.47 ( ( ^ [P2: option1457017436_r_l_v > $o] :
% 0.30/0.47 ! [X5: option1457017436_r_l_v] : ( P2 @ X5 ) )
% 0.30/0.47 = ( ^ [P3: option1457017436_r_l_v > $o] :
% 0.30/0.47 ( ( P3 @ none_P277133687_r_l_v )
% 0.30/0.47 & ! [X: produc1156025366_r_l_v] : ( P3 @ ( some_P1807977723_r_l_v @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_option_all
% 0.30/0.47 thf(fact_68_split__option__all,axiom,
% 0.30/0.47 ( ( ^ [P2: option_val_r_l_v > $o] :
% 0.30/0.47 ! [X5: option_val_r_l_v] : ( P2 @ X5 ) )
% 0.30/0.47 = ( ^ [P3: option_val_r_l_v > $o] :
% 0.30/0.47 ( ( P3 @ none_val_r_l_v )
% 0.30/0.47 & ! [X: val_r_l_v] : ( P3 @ ( some_val_r_l_v @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_option_all
% 0.30/0.47 thf(fact_69_split__option__ex,axiom,
% 0.30/0.47 ( ( ^ [P2: option1457017436_r_l_v > $o] :
% 0.30/0.47 ? [X5: option1457017436_r_l_v] : ( P2 @ X5 ) )
% 0.30/0.47 = ( ^ [P3: option1457017436_r_l_v > $o] :
% 0.30/0.47 ( ( P3 @ none_P277133687_r_l_v )
% 0.30/0.47 | ? [X: produc1156025366_r_l_v] : ( P3 @ ( some_P1807977723_r_l_v @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_option_ex
% 0.30/0.47 thf(fact_70_split__option__ex,axiom,
% 0.30/0.47 ( ( ^ [P2: option_val_r_l_v > $o] :
% 0.30/0.47 ? [X5: option_val_r_l_v] : ( P2 @ X5 ) )
% 0.30/0.47 = ( ^ [P3: option_val_r_l_v > $o] :
% 0.30/0.47 ( ( P3 @ none_val_r_l_v )
% 0.30/0.47 | ? [X: val_r_l_v] : ( P3 @ ( some_val_r_l_v @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_option_ex
% 0.30/0.47 thf(fact_71_option_Oinducts,axiom,
% 0.30/0.47 ! [P: option1457017436_r_l_v > $o,Option: option1457017436_r_l_v] :
% 0.30/0.47 ( ( P @ none_P277133687_r_l_v )
% 0.30/0.47 => ( ! [X4: produc1156025366_r_l_v] : ( P @ ( some_P1807977723_r_l_v @ X4 ) )
% 0.30/0.47 => ( P @ Option ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.inducts
% 0.30/0.47 thf(fact_72_option_Oinducts,axiom,
% 0.30/0.47 ! [P: option_val_r_l_v > $o,Option: option_val_r_l_v] :
% 0.30/0.47 ( ( P @ none_val_r_l_v )
% 0.30/0.47 => ( ! [X4: val_r_l_v] : ( P @ ( some_val_r_l_v @ X4 ) )
% 0.30/0.47 => ( P @ Option ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.inducts
% 0.30/0.47 thf(fact_73_option_Oexhaust,axiom,
% 0.30/0.47 ! [Y: option1457017436_r_l_v] :
% 0.30/0.47 ( ( Y != none_P277133687_r_l_v )
% 0.30/0.47 => ~ ! [X23: produc1156025366_r_l_v] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( some_P1807977723_r_l_v @ X23 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.exhaust
% 0.30/0.47 thf(fact_74_option_Oexhaust,axiom,
% 0.30/0.47 ! [Y: option_val_r_l_v] :
% 0.30/0.47 ( ( Y != none_val_r_l_v )
% 0.30/0.47 => ~ ! [X23: val_r_l_v] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( some_val_r_l_v @ X23 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.exhaust
% 0.30/0.47 thf(fact_75_option_OdiscI,axiom,
% 0.30/0.47 ! [Option: option1457017436_r_l_v,X22: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( Option
% 0.30/0.47 = ( some_P1807977723_r_l_v @ X22 ) )
% 0.30/0.47 => ( Option != none_P277133687_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.discI
% 0.30/0.47 thf(fact_76_option_OdiscI,axiom,
% 0.30/0.47 ! [Option: option_val_r_l_v,X22: val_r_l_v] :
% 0.30/0.47 ( ( Option
% 0.30/0.47 = ( some_val_r_l_v @ X22 ) )
% 0.30/0.47 => ( Option != none_val_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.discI
% 0.30/0.47 thf(fact_77_option_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [X22: produc1156025366_r_l_v] :
% 0.30/0.47 ( none_P277133687_r_l_v
% 0.30/0.47 != ( some_P1807977723_r_l_v @ X22 ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.distinct(1)
% 0.30/0.47 thf(fact_78_option_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [X22: val_r_l_v] :
% 0.30/0.47 ( none_val_r_l_v
% 0.30/0.47 != ( some_val_r_l_v @ X22 ) ) ).
% 0.30/0.47
% 0.30/0.47 % option.distinct(1)
% 0.30/0.47 thf(fact_79_map__upd__Some__unfold,axiom,
% 0.30/0.47 ! [M: r > option1457017436_r_l_v,A2: r,B2: produc1156025366_r_l_v,X2: r,Y: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( ( fun_up709272714_r_l_v @ M @ A2 @ ( some_P1807977723_r_l_v @ B2 ) @ X2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ Y ) )
% 0.30/0.47 = ( ( ( X2 = A2 )
% 0.30/0.47 & ( B2 = Y ) )
% 0.30/0.47 | ( ( X2 != A2 )
% 0.30/0.47 & ( ( M @ X2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_upd_Some_unfold
% 0.30/0.47 thf(fact_80_map__upd__Some__unfold,axiom,
% 0.30/0.47 ! [M: l > option_val_r_l_v,A2: l,B2: val_r_l_v,X2: l,Y: val_r_l_v] :
% 0.30/0.47 ( ( ( fun_up1835647912_r_l_v @ M @ A2 @ ( some_val_r_l_v @ B2 ) @ X2 )
% 0.30/0.47 = ( some_val_r_l_v @ Y ) )
% 0.30/0.47 = ( ( ( X2 = A2 )
% 0.30/0.47 & ( B2 = Y ) )
% 0.30/0.47 | ( ( X2 != A2 )
% 0.30/0.47 & ( ( M @ X2 )
% 0.30/0.47 = ( some_val_r_l_v @ Y ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_upd_Some_unfold
% 0.30/0.47 thf(fact_81_map__upd__triv,axiom,
% 0.30/0.47 ! [T: r > option1457017436_r_l_v,K: r,X2: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( ( T @ K )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ X2 ) )
% 0.30/0.47 => ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X2 ) )
% 0.30/0.47 = T ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_upd_triv
% 0.30/0.47 thf(fact_82_map__upd__triv,axiom,
% 0.30/0.47 ! [T: l > option_val_r_l_v,K: l,X2: val_r_l_v] :
% 0.30/0.47 ( ( ( T @ K )
% 0.30/0.47 = ( some_val_r_l_v @ X2 ) )
% 0.30/0.47 => ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X2 ) )
% 0.30/0.47 = T ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_upd_triv
% 0.30/0.47 thf(fact_83_map__upd__eqD1,axiom,
% 0.30/0.47 ! [M: r > option1457017436_r_l_v,A2: r,X2: produc1156025366_r_l_v,N: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( ( fun_up709272714_r_l_v @ M @ A2 @ ( some_P1807977723_r_l_v @ X2 ) )
% 0.30/0.47 = ( fun_up709272714_r_l_v @ N @ A2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.30/0.47 => ( X2 = Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_upd_eqD1
% 0.30/0.47 thf(fact_84_map__upd__eqD1,axiom,
% 0.30/0.47 ! [M: l > option_val_r_l_v,A2: l,X2: val_r_l_v,N: l > option_val_r_l_v,Y: val_r_l_v] :
% 0.30/0.47 ( ( ( fun_up1835647912_r_l_v @ M @ A2 @ ( some_val_r_l_v @ X2 ) )
% 0.30/0.47 = ( fun_up1835647912_r_l_v @ N @ A2 @ ( some_val_r_l_v @ Y ) ) )
% 0.30/0.47 => ( X2 = Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_upd_eqD1
% 0.30/0.47 thf(fact_85_map__upd__nonempty,axiom,
% 0.30/0.47 ! [T: r > option1457017436_r_l_v,K: r,X2: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X2 ) )
% 0.30/0.47 != ( ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_upd_nonempty
% 0.30/0.47 thf(fact_86_map__upd__nonempty,axiom,
% 0.30/0.47 ! [T: l > option_val_r_l_v,K: l,X2: val_r_l_v] :
% 0.30/0.47 ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X2 ) )
% 0.30/0.47 != ( ^ [X: l] : none_val_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_upd_nonempty
% 0.30/0.47 thf(fact_87_substitution_Ofork__pseudodeterministic,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 = ( ? [R3: r] :
% 0.30/0.47 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
% 0.30/0.47 & ( S2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.fork_pseudodeterministic
% 0.30/0.47 thf(fact_88_inductive__invariant__is__execution__invariant,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 0.30/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.47 => ( ( induct1670415253_r_l_v @ subst @ P )
% 0.30/0.47 => ( P @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inductive_invariant_is_execution_invariant
% 0.30/0.47 thf(fact_89_substitution_Orevision__step__relaxed_Ofork,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.30/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 0.30/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step_relaxed.fork
% 0.30/0.47 thf(fact_90_substitution_Orevision__step_Ofork,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.30/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ( revision_step_r_l_v @ Subst @ R @ S
% 0.30/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 0.30/0.47 @ ( some_P1807977723_r_l_v
% 0.30/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.30/0.47 @ ( produc1834103605_r_l_v
% 0.30/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.30/0.47 @ E4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step.fork
% 0.30/0.47 thf(fact_91_substitution_Oonly__fork__introduces__rids,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v] :
% 0.30/0.47 ( ( S @ R )
% 0.30/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E2 ) ) ) ) ) )
% 0.30/0.47 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.only_fork_introduces_rids
% 0.30/0.47 thf(fact_92_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.47 => ( domain1547879849_r_l_v @ S ) ) ).
% 0.30/0.47
% 0.30/0.47 % reachable_imp_\<S>\<^sub>G
% 0.30/0.47 thf(fact_93_substitution_Oonly__fork__introduces__rids_H,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v] :
% 0.30/0.47 ( ( S @ R )
% 0.30/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E2 ) ) ) ) ) )
% 0.30/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.only_fork_introduces_rids'
% 0.30/0.47 thf(fact_94_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.30/0.47 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( S_1 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( ^ [X: r] : none_P277133687_r_l_v ) )
% 0.30/0.47 => ( ( ( S_1 @ R4 )
% 0.30/0.47 = none_P277133687_r_l_v )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % SLC_join\<^sub>\<epsilon>
% 0.30/0.47 thf(fact_95_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = none_P277133687_r_l_v )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 0.30/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step_relaxed.join\<^sub>\<epsilon>
% 0.30/0.47 thf(fact_96_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = none_P277133687_r_l_v )
% 0.30/0.47 => ( revision_step_r_l_v @ subst @ R @ S
% 0.30/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step.join\<^sub>\<epsilon>
% 0.30/0.47 thf(fact_97_domains__subsume__globally__def,axiom,
% 0.30/0.47 ( domain1547879849_r_l_v
% 0.30/0.47 = ( ^ [S4: r > option1457017436_r_l_v] :
% 0.30/0.47 ! [R5: r,Ls2: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( ( S4 @ R5 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 0.30/0.47 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % domains_subsume_globally_def
% 0.30/0.47 thf(fact_98_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = none_P277133687_r_l_v )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 = ( S2
% 0.30/0.47 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rjoin\<^sub>\<epsilon>_deterministic
% 0.30/0.47 thf(fact_99_substitution_Orevision__step_Ocong,axiom,
% 0.30/0.47 revision_step_r_l_v = revision_step_r_l_v ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step.cong
% 0.30/0.47 thf(fact_100_substitution_Orevision__step__relaxed_Ocong,axiom,
% 0.30/0.47 revisi1291188644_r_l_v = revisi1291188644_r_l_v ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step_relaxed.cong
% 0.30/0.47 thf(fact_101_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = none_P277133687_r_l_v )
% 0.30/0.47 => ( revision_step_r_l_v @ Subst @ R @ S
% 0.30/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step.join\<^sub>\<epsilon>
% 0.30/0.47 thf(fact_102_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = none_P277133687_r_l_v )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 0.30/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step_relaxed.join\<^sub>\<epsilon>
% 0.30/0.47 thf(fact_103_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = none_P277133687_r_l_v )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 = ( S2
% 0.30/0.47 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.rjoin\<^sub>\<epsilon>_deterministic
% 0.30/0.47 thf(fact_104_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S_1 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( ^ [X: r] : none_P277133687_r_l_v ) )
% 0.30/0.47 => ( ( ( S_1 @ R4 )
% 0.30/0.47 = none_P277133687_r_l_v )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.SLC_join\<^sub>\<epsilon>
% 0.30/0.47 thf(fact_105_nice__ind__inv__is__inductive__invariant,axiom,
% 0.30/0.47 ( induct1670415253_r_l_v @ subst
% 0.30/0.47 @ ^ [S4: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( domain1547879849_r_l_v @ S4 )
% 0.30/0.47 & ( subsum680764357_r_l_v @ S4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % nice_ind_inv_is_inductive_invariant
% 0.30/0.47 thf(fact_106_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.30/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.30/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.30/0.47 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.30/0.47 thf(fact_107_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.30/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.30/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.30/0.47 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.30/0.47 thf(fact_108_substitution_Odomains__subsume__globallyI,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ! [R6: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E2: expr_r_l_v] :
% 0.30/0.47 ( ( ( S @ R6 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) )
% 0.30/0.47 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) )
% 0.30/0.47 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.domains_subsume_globallyI
% 0.30/0.47 thf(fact_109_substitution_Otransition__relations__equivalent,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 = ( revisi1291188644_r_l_v @ Subst @ R @ S @ S2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.transition_relations_equivalent
% 0.30/0.47 thf(fact_110_domains__subsume__globallyI,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ! [R6: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E2: expr_r_l_v] :
% 0.30/0.47 ( ( ( S @ R6 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) )
% 0.30/0.47 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) )
% 0.30/0.47 => ( domain1547879849_r_l_v @ S ) ) ).
% 0.30/0.47
% 0.30/0.47 % domains_subsume_globallyI
% 0.30/0.47 thf(fact_111_substitution_Oreachable__def,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.30/0.47 = ( ? [E5: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ Subst @ E5 @ S3 @ S ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.reachable_def
% 0.30/0.47 thf(fact_112_substitution_Oreachable_Ocong,axiom,
% 0.30/0.47 reachable_r_l_v = reachable_r_l_v ).
% 0.30/0.47
% 0.30/0.47 % substitution.reachable.cong
% 0.30/0.47 thf(fact_113_substitution_Oinductive__invariant_Ocong,axiom,
% 0.30/0.47 induct1670415253_r_l_v = induct1670415253_r_l_v ).
% 0.30/0.47
% 0.30/0.47 % substitution.inductive_invariant.cong
% 0.30/0.47 thf(fact_114_substitution_Oexecution_Ocong,axiom,
% 0.30/0.47 execution_r_l_v = execution_r_l_v ).
% 0.30/0.47
% 0.30/0.47 % substitution.execution.cong
% 0.30/0.47 thf(fact_115_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( induct1670415253_r_l_v @ Subst
% 0.30/0.47 @ ^ [S4: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( domain1547879849_r_l_v @ S4 )
% 0.30/0.47 & ( subsum680764357_r_l_v @ S4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.nice_ind_inv_is_inductive_invariant
% 0.30/0.47 thf(fact_116_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.30/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.30/0.47 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.30/0.47 thf(fact_117_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.30/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.30/0.47 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.30/0.47 thf(fact_118_substitution_Odomains__subsume__globally__def,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.30/0.47 = ( ! [R5: r,Ls2: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( ( S @ R5 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 0.30/0.47 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.domains_subsume_globally_def
% 0.30/0.47 thf(fact_119_substitution_Oreachability__closed__under__execution__step,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 => ( reachable_r_l_v @ Subst @ S2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.reachability_closed_under_execution_step
% 0.30/0.47 thf(fact_120_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.30/0.47 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.reachable_imp_\<S>\<^sub>G
% 0.30/0.47 thf(fact_121_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.30/0.47 => ( ( induct1670415253_r_l_v @ Subst @ P )
% 0.30/0.47 => ( P @ S ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.inductive_invariant_is_execution_invariant
% 0.30/0.47 thf(fact_122_substitution_Osubsumes__accessible__globallyI,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ! [R_1: r,Sigma_1: l > option_val_r_l_v,Tau_1: l > option_val_r_l_v,E_1: expr_r_l_v,R_2: r,Sigma_2: l > option_val_r_l_v,Tau_2: l > option_val_r_l_v,E_2: expr_r_l_v] :
% 0.30/0.47 ( ( ( S @ R_1 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 0.30/0.47 => ( ( ( S @ R_2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 0.30/0.47 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 0.30/0.47 => ( subsum680764357_r_l_v @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.subsumes_accessible_globallyI
% 0.30/0.47 thf(fact_123_join__and__local__commute,axiom,
% 0.30/0.47 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.30/0.47 ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.30/0.47 => ( ( S_22
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ( ( R2 != R4 )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.30/0.47 => ( ( ( S_22 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S_22 @ R4 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % join_and_local_commute
% 0.30/0.47 thf(fact_124_SLC__join,axiom,
% 0.30/0.47 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( S_1 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.30/0.47 => ( ( ( S_1 @ R4 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % SLC_join
% 0.30/0.47 thf(fact_125_revision__step__relaxed_Ojoin,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step_relaxed.join
% 0.30/0.47 thf(fact_126_reachable__imp__identifiers__finite_I1_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % reachable_imp_identifiers_finite(1)
% 0.30/0.47 thf(fact_127_revision__step_Ojoin,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step.join
% 0.30/0.47 thf(fact_128_empty__map__finite_I3_J,axiom,
% 0.30/0.47 ( finite_finite_r
% 0.30/0.47 @ ( rID_G_r_l_v
% 0.30/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_map_finite(3)
% 0.30/0.47 thf(fact_129_rid__inf,axiom,
% 0.30/0.47 ~ ( finite_finite_r @ top_top_set_r ) ).
% 0.30/0.47
% 0.30/0.47 % rid_inf
% 0.30/0.47 thf(fact_130_RID_092_060_094sub_062G__finite__invariant,axiom,
% 0.30/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RID\<^sub>G_finite_invariant
% 0.30/0.47 thf(fact_131_finite__state__imp__restriction__finite_I1_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r] :
% 0.30/0.47 ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_state_imp_restriction_finite(1)
% 0.30/0.47 thf(fact_132_subsumes__accessible__globallyI,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ! [R_1: r,Sigma_1: l > option_val_r_l_v,Tau_1: l > option_val_r_l_v,E_1: expr_r_l_v,R_2: r,Sigma_2: l > option_val_r_l_v,Tau_2: l > option_val_r_l_v,E_2: expr_r_l_v] :
% 0.30/0.47 ( ( ( S @ R_1 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 0.30/0.47 => ( ( ( S @ R_2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 0.30/0.47 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 0.30/0.47 => ( subsum680764357_r_l_v @ S ) ) ).
% 0.30/0.47
% 0.30/0.47 % subsumes_accessible_globallyI
% 0.30/0.47 thf(fact_133_rjoin__deterministic,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 = ( S2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rjoin_deterministic
% 0.30/0.47 thf(fact_134_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.RID\<^sub>G_finite_invariant
% 0.30/0.47 thf(fact_135_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.30/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.reachable_imp_identifiers_finite(1)
% 0.30/0.47 thf(fact_136_substitution_Oempty__map__finite_I3_J,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( finite_finite_r
% 0.30/0.47 @ ( rID_G_r_l_v
% 0.30/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.empty_map_finite(3)
% 0.30/0.47 thf(fact_137_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.30/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.finite_state_imp_restriction_finite(1)
% 0.30/0.47 thf(fact_138_substitution_Orevision__step_Ojoin,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step.join
% 0.30/0.47 thf(fact_139_substitution_Orjoin__deterministic,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 = ( S2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.rjoin_deterministic
% 0.30/0.47 thf(fact_140_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step_relaxed.join
% 0.30/0.47 thf(fact_141_substitution_OSLC__join,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S_1 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.30/0.47 => ( ( ( S_1 @ R4 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.SLC_join
% 0.30/0.47 thf(fact_142_substitution_Ojoin__and__local__commute,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.30/0.47 => ( ( S_22
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ( ( R2 != R4 )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.30/0.47 => ( ( ( S_22 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.30/0.47 => ( ( ( S_22 @ R4 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.join_and_local_commute
% 0.30/0.47 thf(fact_143_finite__Collect__subsets,axiom,
% 0.30/0.47 ! [A3: set_Sum_sum_r_l] :
% 0.30/0.47 ( ( finite65649782um_r_l @ A3 )
% 0.30/0.47 => ( finite1407742636um_r_l
% 0.30/0.47 @ ( collec765168874um_r_l
% 0.30/0.47 @ ^ [B3: set_Sum_sum_r_l] : ( ord_le294536053um_r_l @ B3 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_subsets
% 0.30/0.47 thf(fact_144_finite__Collect__subsets,axiom,
% 0.30/0.47 ! [A3: set_Sum_sum_l_r] :
% 0.30/0.47 ( ( finite1591053314um_l_r @ A3 )
% 0.30/0.47 => ( finite483212344um_l_r
% 0.30/0.47 @ ( collec1988122230um_l_r
% 0.30/0.47 @ ^ [B3: set_Sum_sum_l_r] : ( ord_le1517489409um_l_r @ B3 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_subsets
% 0.30/0.47 thf(fact_145_finite__Collect__subsets,axiom,
% 0.30/0.47 ! [A3: set_Sum_sum_l_l] :
% 0.30/0.47 ( ( finite1541484284um_l_l @ A3 )
% 0.30/0.47 => ( finite88277554um_l_l
% 0.30/0.47 @ ( collec1593187440um_l_l
% 0.30/0.47 @ ^ [B3: set_Sum_sum_l_l] : ( ord_le1122554619um_l_l @ B3 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_subsets
% 0.30/0.47 thf(fact_146_finite__Collect__subsets,axiom,
% 0.30/0.47 ! [A3: set_set_r] :
% 0.30/0.47 ( ( finite_finite_set_r @ A3 )
% 0.30/0.47 => ( finite1651563256_set_r
% 0.30/0.47 @ ( collect_set_set_r
% 0.30/0.47 @ ^ [B3: set_set_r] : ( ord_le363960431_set_r @ B3 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_subsets
% 0.30/0.47 thf(fact_147_finite__Collect__subsets,axiom,
% 0.30/0.47 ! [A3: set_set_l] :
% 0.30/0.47 ( ( finite_finite_set_l @ A3 )
% 0.30/0.47 => ( finite1256628466_set_l
% 0.30/0.47 @ ( collect_set_set_l
% 0.30/0.47 @ ^ [B3: set_set_l] : ( ord_le2116509289_set_l @ B3 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_subsets
% 0.30/0.47 thf(fact_148_finite__Collect__subsets,axiom,
% 0.30/0.47 ! [A3: set_r] :
% 0.30/0.47 ( ( finite_finite_r @ A3 )
% 0.30/0.47 => ( finite_finite_set_r
% 0.30/0.47 @ ( collect_set_r
% 0.30/0.47 @ ^ [B3: set_r] : ( ord_less_eq_set_r @ B3 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_subsets
% 0.30/0.47 thf(fact_149_finite__Collect__subsets,axiom,
% 0.30/0.47 ! [A3: set_l] :
% 0.30/0.47 ( ( finite_finite_l @ A3 )
% 0.30/0.47 => ( finite_finite_set_l
% 0.30/0.47 @ ( collect_set_l
% 0.30/0.47 @ ^ [B3: set_l] : ( ord_less_eq_set_l @ B3 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_subsets
% 0.30/0.47 thf(fact_150_reachable__imp__identifiers__available_I1_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 => ? [R6: r] :
% 0.30/0.47 ~ ( member_r @ R6 @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % reachable_imp_identifiers_available(1)
% 0.30/0.47 thf(fact_151_finite__Collect__conjI,axiom,
% 0.30/0.47 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 0.30/0.47 ( ( ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ P ) )
% 0.30/0.47 | ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ Q ) ) )
% 0.30/0.47 => ( finite1853159534_r_l_v
% 0.30/0.47 @ ( collec1978425008_r_l_v
% 0.30/0.47 @ ^ [X: produc1389397445_r_l_v] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_conjI
% 0.30/0.47 thf(fact_152_finite__Collect__conjI,axiom,
% 0.30/0.47 ! [P: sum_sum_r_l > $o,Q: sum_sum_r_l > $o] :
% 0.30/0.47 ( ( ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ P ) )
% 0.30/0.47 | ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ Q ) ) )
% 0.30/0.47 => ( finite65649782um_r_l
% 0.30/0.47 @ ( collect_Sum_sum_r_l
% 0.30/0.47 @ ^ [X: sum_sum_r_l] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_conjI
% 0.30/0.47 thf(fact_153_finite__Collect__conjI,axiom,
% 0.30/0.47 ! [P: sum_sum_l_r > $o,Q: sum_sum_l_r > $o] :
% 0.30/0.47 ( ( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
% 0.30/0.47 | ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ Q ) ) )
% 0.30/0.47 => ( finite1591053314um_l_r
% 0.30/0.47 @ ( collect_Sum_sum_l_r
% 0.30/0.47 @ ^ [X: sum_sum_l_r] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_conjI
% 0.30/0.47 thf(fact_154_finite__Collect__conjI,axiom,
% 0.30/0.47 ! [P: sum_sum_l_l > $o,Q: sum_sum_l_l > $o] :
% 0.30/0.47 ( ( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
% 0.30/0.47 | ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ Q ) ) )
% 0.30/0.47 => ( finite1541484284um_l_l
% 0.30/0.47 @ ( collect_Sum_sum_l_l
% 0.30/0.47 @ ^ [X: sum_sum_l_l] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_conjI
% 0.30/0.47 thf(fact_155_finite__Collect__conjI,axiom,
% 0.30/0.47 ! [P: set_r > $o,Q: set_r > $o] :
% 0.30/0.47 ( ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 0.30/0.47 | ( finite_finite_set_r @ ( collect_set_r @ Q ) ) )
% 0.30/0.47 => ( finite_finite_set_r
% 0.30/0.47 @ ( collect_set_r
% 0.30/0.47 @ ^ [X: set_r] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_conjI
% 0.30/0.47 thf(fact_156_finite__Collect__conjI,axiom,
% 0.30/0.47 ! [P: set_l > $o,Q: set_l > $o] :
% 0.30/0.47 ( ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 0.30/0.47 | ( finite_finite_set_l @ ( collect_set_l @ Q ) ) )
% 0.30/0.47 => ( finite_finite_set_l
% 0.30/0.47 @ ( collect_set_l
% 0.30/0.47 @ ^ [X: set_l] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_conjI
% 0.30/0.47 thf(fact_157_finite__Collect__conjI,axiom,
% 0.30/0.47 ! [P: r > $o,Q: r > $o] :
% 0.30/0.47 ( ( ( finite_finite_r @ ( collect_r @ P ) )
% 0.30/0.47 | ( finite_finite_r @ ( collect_r @ Q ) ) )
% 0.30/0.47 => ( finite_finite_r
% 0.30/0.47 @ ( collect_r
% 0.30/0.47 @ ^ [X: r] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_conjI
% 0.30/0.47 thf(fact_158_finite__Collect__conjI,axiom,
% 0.30/0.47 ! [P: l > $o,Q: l > $o] :
% 0.30/0.47 ( ( ( finite_finite_l @ ( collect_l @ P ) )
% 0.30/0.47 | ( finite_finite_l @ ( collect_l @ Q ) ) )
% 0.30/0.47 => ( finite_finite_l
% 0.30/0.47 @ ( collect_l
% 0.30/0.47 @ ^ [X: l] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_conjI
% 0.30/0.47 thf(fact_159_finite__Collect__disjI,axiom,
% 0.30/0.47 ! [P: sum_sum_l_r > $o,Q: sum_sum_l_r > $o] :
% 0.30/0.47 ( ( finite1591053314um_l_r
% 0.30/0.47 @ ( collect_Sum_sum_l_r
% 0.30/0.47 @ ^ [X: sum_sum_l_r] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 | ( Q @ X ) ) ) )
% 0.30/0.47 = ( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
% 0.30/0.47 & ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ Q ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_disjI
% 0.30/0.47 thf(fact_160_finite__Collect__disjI,axiom,
% 0.30/0.47 ! [P: sum_sum_l_l > $o,Q: sum_sum_l_l > $o] :
% 0.30/0.47 ( ( finite1541484284um_l_l
% 0.30/0.47 @ ( collect_Sum_sum_l_l
% 0.30/0.47 @ ^ [X: sum_sum_l_l] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 | ( Q @ X ) ) ) )
% 0.30/0.47 = ( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
% 0.30/0.47 & ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ Q ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_disjI
% 0.30/0.47 thf(fact_161_finite__Collect__disjI,axiom,
% 0.30/0.47 ! [P: set_r > $o,Q: set_r > $o] :
% 0.30/0.47 ( ( finite_finite_set_r
% 0.30/0.47 @ ( collect_set_r
% 0.30/0.47 @ ^ [X: set_r] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 | ( Q @ X ) ) ) )
% 0.30/0.47 = ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 0.30/0.47 & ( finite_finite_set_r @ ( collect_set_r @ Q ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_disjI
% 0.30/0.47 thf(fact_162_finite__Collect__disjI,axiom,
% 0.30/0.47 ! [P: set_l > $o,Q: set_l > $o] :
% 0.30/0.47 ( ( finite_finite_set_l
% 0.30/0.47 @ ( collect_set_l
% 0.30/0.47 @ ^ [X: set_l] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 | ( Q @ X ) ) ) )
% 0.30/0.47 = ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 0.30/0.47 & ( finite_finite_set_l @ ( collect_set_l @ Q ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_disjI
% 0.30/0.47 thf(fact_163_finite__Collect__disjI,axiom,
% 0.30/0.47 ! [P: r > $o,Q: r > $o] :
% 0.30/0.47 ( ( finite_finite_r
% 0.30/0.47 @ ( collect_r
% 0.30/0.47 @ ^ [X: r] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 | ( Q @ X ) ) ) )
% 0.30/0.47 = ( ( finite_finite_r @ ( collect_r @ P ) )
% 0.30/0.47 & ( finite_finite_r @ ( collect_r @ Q ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_disjI
% 0.30/0.47 thf(fact_164_finite__Collect__disjI,axiom,
% 0.30/0.47 ! [P: l > $o,Q: l > $o] :
% 0.30/0.47 ( ( finite_finite_l
% 0.30/0.47 @ ( collect_l
% 0.30/0.47 @ ^ [X: l] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 | ( Q @ X ) ) ) )
% 0.30/0.47 = ( ( finite_finite_l @ ( collect_l @ P ) )
% 0.30/0.47 & ( finite_finite_l @ ( collect_l @ Q ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_disjI
% 0.30/0.47 thf(fact_165_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.30/0.47 ( ( ( S @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.30/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % local_state_of_finite_restricted_global_state_is_finite(1)
% 0.30/0.47 thf(fact_166_finite__option__UNIV,axiom,
% 0.30/0.47 ( ( finite16335230tion_r @ top_top_set_option_r )
% 0.30/0.47 = ( finite_finite_r @ top_top_set_r ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_option_UNIV
% 0.30/0.47 thf(fact_167_finite__option__UNIV,axiom,
% 0.30/0.47 ( ( finite2114249848tion_l @ top_top_set_option_l )
% 0.30/0.47 = ( finite_finite_l @ top_top_set_l ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_option_UNIV
% 0.30/0.47 thf(fact_168_finite__Plus__UNIV__iff,axiom,
% 0.30/0.47 ( ( finite115218812um_r_r @ top_to577862603um_r_r )
% 0.30/0.47 = ( ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Plus_UNIV_iff
% 0.30/0.47 thf(fact_169_finite__Plus__UNIV__iff,axiom,
% 0.30/0.47 ( ( finite65649782um_r_l @ top_to182927813um_r_l )
% 0.30/0.47 = ( ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Plus_UNIV_iff
% 0.30/0.47 thf(fact_170_finite__Plus__UNIV__iff,axiom,
% 0.30/0.47 ( ( finite1591053314um_l_r @ top_to1405881169um_l_r )
% 0.30/0.47 = ( ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Plus_UNIV_iff
% 0.30/0.47 thf(fact_171_finite__Plus__UNIV__iff,axiom,
% 0.30/0.47 ( ( finite1541484284um_l_l @ top_to1010946379um_l_l )
% 0.30/0.47 = ( ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Plus_UNIV_iff
% 0.30/0.47 thf(fact_172_finite__Collect__not,axiom,
% 0.30/0.47 ! [P: r > $o] :
% 0.30/0.47 ( ( finite_finite_r @ ( collect_r @ P ) )
% 0.30/0.47 => ( ( finite_finite_r
% 0.30/0.47 @ ( collect_r
% 0.30/0.47 @ ^ [X: r] :
% 0.30/0.47 ~ ( P @ X ) ) )
% 0.30/0.47 = ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_not
% 0.30/0.47 thf(fact_173_finite__Collect__not,axiom,
% 0.30/0.47 ! [P: l > $o] :
% 0.30/0.47 ( ( finite_finite_l @ ( collect_l @ P ) )
% 0.30/0.47 => ( ( finite_finite_l
% 0.30/0.47 @ ( collect_l
% 0.30/0.47 @ ^ [X: l] :
% 0.30/0.47 ~ ( P @ X ) ) )
% 0.30/0.47 = ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Collect_not
% 0.30/0.47 thf(fact_174_RID_092_060_094sub_062GI_I2_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.30/0.47 ( ( ( S @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.30/0.47 => ( ( member_r @ R @ ( rID_L_l_r_v @ Ls ) )
% 0.30/0.47 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RID\<^sub>GI(2)
% 0.30/0.47 thf(fact_175_Finite__Set_Ofinite__set,axiom,
% 0.30/0.47 ( ( finite_finite_set_r @ top_top_set_set_r )
% 0.30/0.47 = ( finite_finite_r @ top_top_set_r ) ) ).
% 0.30/0.47
% 0.30/0.47 % Finite_Set.finite_set
% 0.30/0.47 thf(fact_176_Finite__Set_Ofinite__set,axiom,
% 0.30/0.47 ( ( finite_finite_set_l @ top_top_set_set_l )
% 0.30/0.47 = ( finite_finite_l @ top_top_set_l ) ) ).
% 0.30/0.47
% 0.30/0.47 % Finite_Set.finite_set
% 0.30/0.47 thf(fact_177_finite__prod,axiom,
% 0.30/0.47 ( ( finite1507191824od_r_r @ top_to2034696215od_r_r )
% 0.30/0.47 = ( ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_prod
% 0.30/0.47 thf(fact_178_finite__prod,axiom,
% 0.30/0.47 ( ( finite1457622794od_r_l @ top_to1639761425od_r_l )
% 0.30/0.47 = ( ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_prod
% 0.30/0.47 thf(fact_179_finite__prod,axiom,
% 0.30/0.47 ( ( finite835542678od_l_r @ top_to715231133od_l_r )
% 0.30/0.47 = ( ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_prod
% 0.30/0.47 thf(fact_180_finite__prod,axiom,
% 0.30/0.47 ( ( finite785973648od_l_l @ top_to320296343od_l_l )
% 0.30/0.47 = ( ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_prod
% 0.30/0.47 thf(fact_181_ex__new__if__finite,axiom,
% 0.30/0.47 ! [A3: set_Pr1409704485_r_l_v] :
% 0.30/0.47 ( ~ ( finite1853159534_r_l_v @ top_to1238153077_r_l_v )
% 0.30/0.47 => ( ( finite1853159534_r_l_v @ A3 )
% 0.30/0.47 => ? [A: produc1389397445_r_l_v] :
% 0.30/0.47 ~ ( member1522896238_r_l_v @ A @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ex_new_if_finite
% 0.30/0.47 thf(fact_182_ex__new__if__finite,axiom,
% 0.30/0.47 ! [A3: set_r] :
% 0.30/0.47 ( ~ ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 => ( ( finite_finite_r @ A3 )
% 0.30/0.47 => ? [A: r] :
% 0.30/0.47 ~ ( member_r @ A @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ex_new_if_finite
% 0.30/0.47 thf(fact_183_ex__new__if__finite,axiom,
% 0.30/0.47 ! [A3: set_l] :
% 0.30/0.47 ( ~ ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 => ( ( finite_finite_l @ A3 )
% 0.30/0.47 => ? [A: l] :
% 0.30/0.47 ~ ( member_l @ A @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ex_new_if_finite
% 0.30/0.47 thf(fact_184_finite__Prod__UNIV,axiom,
% 0.30/0.47 ( ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 => ( ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 => ( finite1507191824od_r_r @ top_to2034696215od_r_r ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Prod_UNIV
% 0.30/0.47 thf(fact_185_finite__Prod__UNIV,axiom,
% 0.30/0.47 ( ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 => ( ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 => ( finite1457622794od_r_l @ top_to1639761425od_r_l ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Prod_UNIV
% 0.30/0.47 thf(fact_186_finite__Prod__UNIV,axiom,
% 0.30/0.47 ( ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 => ( ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 => ( finite835542678od_l_r @ top_to715231133od_l_r ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Prod_UNIV
% 0.30/0.47 thf(fact_187_finite__Prod__UNIV,axiom,
% 0.30/0.47 ( ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 => ( ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 => ( finite785973648od_l_l @ top_to320296343od_l_l ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_Prod_UNIV
% 0.30/0.47 thf(fact_188_pigeonhole__infinite__rel,axiom,
% 0.30/0.47 ! [A3: set_Pr1409704485_r_l_v,B4: set_r,R7: produc1389397445_r_l_v > r > $o] :
% 0.30/0.47 ( ~ ( finite1853159534_r_l_v @ A3 )
% 0.30/0.47 => ( ( finite_finite_r @ B4 )
% 0.30/0.47 => ( ! [X4: produc1389397445_r_l_v] :
% 0.30/0.47 ( ( member1522896238_r_l_v @ X4 @ A3 )
% 0.30/0.47 => ? [Xa: r] :
% 0.30/0.47 ( ( member_r @ Xa @ B4 )
% 0.30/0.47 & ( R7 @ X4 @ Xa ) ) )
% 0.30/0.47 => ? [X4: r] :
% 0.30/0.47 ( ( member_r @ X4 @ B4 )
% 0.30/0.47 & ~ ( finite1853159534_r_l_v
% 0.30/0.47 @ ( collec1978425008_r_l_v
% 0.30/0.47 @ ^ [A4: produc1389397445_r_l_v] :
% 0.30/0.47 ( ( member1522896238_r_l_v @ A4 @ A3 )
% 0.30/0.47 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pigeonhole_infinite_rel
% 0.30/0.47 thf(fact_189_pigeonhole__infinite__rel,axiom,
% 0.30/0.47 ! [A3: set_Pr1409704485_r_l_v,B4: set_l,R7: produc1389397445_r_l_v > l > $o] :
% 0.30/0.47 ( ~ ( finite1853159534_r_l_v @ A3 )
% 0.30/0.47 => ( ( finite_finite_l @ B4 )
% 0.30/0.47 => ( ! [X4: produc1389397445_r_l_v] :
% 0.30/0.47 ( ( member1522896238_r_l_v @ X4 @ A3 )
% 0.30/0.47 => ? [Xa: l] :
% 0.30/0.47 ( ( member_l @ Xa @ B4 )
% 0.30/0.47 & ( R7 @ X4 @ Xa ) ) )
% 0.30/0.47 => ? [X4: l] :
% 0.30/0.47 ( ( member_l @ X4 @ B4 )
% 0.30/0.47 & ~ ( finite1853159534_r_l_v
% 0.30/0.47 @ ( collec1978425008_r_l_v
% 0.30/0.47 @ ^ [A4: produc1389397445_r_l_v] :
% 0.30/0.47 ( ( member1522896238_r_l_v @ A4 @ A3 )
% 0.30/0.47 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pigeonhole_infinite_rel
% 0.30/0.47 thf(fact_190_pigeonhole__infinite__rel,axiom,
% 0.30/0.47 ! [A3: set_r,B4: set_r,R7: r > r > $o] :
% 0.30/0.47 ( ~ ( finite_finite_r @ A3 )
% 0.30/0.47 => ( ( finite_finite_r @ B4 )
% 0.30/0.47 => ( ! [X4: r] :
% 0.30/0.47 ( ( member_r @ X4 @ A3 )
% 0.30/0.47 => ? [Xa: r] :
% 0.30/0.47 ( ( member_r @ Xa @ B4 )
% 0.30/0.47 & ( R7 @ X4 @ Xa ) ) )
% 0.30/0.47 => ? [X4: r] :
% 0.30/0.47 ( ( member_r @ X4 @ B4 )
% 0.30/0.47 & ~ ( finite_finite_r
% 0.30/0.47 @ ( collect_r
% 0.30/0.47 @ ^ [A4: r] :
% 0.30/0.47 ( ( member_r @ A4 @ A3 )
% 0.30/0.47 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pigeonhole_infinite_rel
% 0.30/0.47 thf(fact_191_pigeonhole__infinite__rel,axiom,
% 0.30/0.47 ! [A3: set_r,B4: set_l,R7: r > l > $o] :
% 0.30/0.47 ( ~ ( finite_finite_r @ A3 )
% 0.30/0.47 => ( ( finite_finite_l @ B4 )
% 0.30/0.47 => ( ! [X4: r] :
% 0.30/0.47 ( ( member_r @ X4 @ A3 )
% 0.30/0.47 => ? [Xa: l] :
% 0.30/0.47 ( ( member_l @ Xa @ B4 )
% 0.30/0.47 & ( R7 @ X4 @ Xa ) ) )
% 0.30/0.47 => ? [X4: l] :
% 0.30/0.47 ( ( member_l @ X4 @ B4 )
% 0.30/0.47 & ~ ( finite_finite_r
% 0.30/0.47 @ ( collect_r
% 0.30/0.47 @ ^ [A4: r] :
% 0.30/0.47 ( ( member_r @ A4 @ A3 )
% 0.30/0.47 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pigeonhole_infinite_rel
% 0.30/0.47 thf(fact_192_pigeonhole__infinite__rel,axiom,
% 0.30/0.47 ! [A3: set_l,B4: set_r,R7: l > r > $o] :
% 0.30/0.47 ( ~ ( finite_finite_l @ A3 )
% 0.30/0.47 => ( ( finite_finite_r @ B4 )
% 0.30/0.47 => ( ! [X4: l] :
% 0.30/0.47 ( ( member_l @ X4 @ A3 )
% 0.30/0.47 => ? [Xa: r] :
% 0.30/0.47 ( ( member_r @ Xa @ B4 )
% 0.30/0.47 & ( R7 @ X4 @ Xa ) ) )
% 0.30/0.47 => ? [X4: r] :
% 0.30/0.47 ( ( member_r @ X4 @ B4 )
% 0.30/0.47 & ~ ( finite_finite_l
% 0.30/0.47 @ ( collect_l
% 0.30/0.47 @ ^ [A4: l] :
% 0.30/0.47 ( ( member_l @ A4 @ A3 )
% 0.30/0.47 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pigeonhole_infinite_rel
% 0.30/0.47 thf(fact_193_pigeonhole__infinite__rel,axiom,
% 0.30/0.47 ! [A3: set_l,B4: set_l,R7: l > l > $o] :
% 0.30/0.47 ( ~ ( finite_finite_l @ A3 )
% 0.30/0.47 => ( ( finite_finite_l @ B4 )
% 0.30/0.47 => ( ! [X4: l] :
% 0.30/0.47 ( ( member_l @ X4 @ A3 )
% 0.30/0.47 => ? [Xa: l] :
% 0.30/0.47 ( ( member_l @ Xa @ B4 )
% 0.30/0.47 & ( R7 @ X4 @ Xa ) ) )
% 0.30/0.47 => ? [X4: l] :
% 0.30/0.47 ( ( member_l @ X4 @ B4 )
% 0.30/0.47 & ~ ( finite_finite_l
% 0.30/0.47 @ ( collect_l
% 0.30/0.47 @ ^ [A4: l] :
% 0.30/0.47 ( ( member_l @ A4 @ A3 )
% 0.30/0.47 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pigeonhole_infinite_rel
% 0.30/0.47 thf(fact_194_not__finite__existsD,axiom,
% 0.30/0.47 ! [P: r > $o] :
% 0.30/0.47 ( ~ ( finite_finite_r @ ( collect_r @ P ) )
% 0.30/0.47 => ? [X_1: r] : ( P @ X_1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_finite_existsD
% 0.30/0.47 thf(fact_195_not__finite__existsD,axiom,
% 0.30/0.47 ! [P: l > $o] :
% 0.30/0.47 ( ~ ( finite_finite_l @ ( collect_l @ P ) )
% 0.30/0.47 => ? [X_1: l] : ( P @ X_1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_finite_existsD
% 0.30/0.47 thf(fact_196_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.30/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.30/0.47 => ? [R6: r] :
% 0.30/0.47 ~ ( member_r @ R6 @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.reachable_imp_identifiers_available(1)
% 0.30/0.47 thf(fact_197_finite__has__minimal2,axiom,
% 0.30/0.47 ! [A3: set_set_r,A2: set_r] :
% 0.30/0.47 ( ( finite_finite_set_r @ A3 )
% 0.30/0.47 => ( ( member_set_r @ A2 @ A3 )
% 0.30/0.47 => ? [X4: set_r] :
% 0.30/0.47 ( ( member_set_r @ X4 @ A3 )
% 0.30/0.47 & ( ord_less_eq_set_r @ X4 @ A2 )
% 0.30/0.47 & ! [Xa: set_r] :
% 0.30/0.47 ( ( member_set_r @ Xa @ A3 )
% 0.30/0.47 => ( ( ord_less_eq_set_r @ Xa @ X4 )
% 0.30/0.47 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_has_minimal2
% 0.30/0.47 thf(fact_198_finite__has__minimal2,axiom,
% 0.30/0.47 ! [A3: set_set_l,A2: set_l] :
% 0.30/0.47 ( ( finite_finite_set_l @ A3 )
% 0.30/0.47 => ( ( member_set_l @ A2 @ A3 )
% 0.30/0.47 => ? [X4: set_l] :
% 0.30/0.47 ( ( member_set_l @ X4 @ A3 )
% 0.30/0.47 & ( ord_less_eq_set_l @ X4 @ A2 )
% 0.30/0.47 & ! [Xa: set_l] :
% 0.30/0.47 ( ( member_set_l @ Xa @ A3 )
% 0.30/0.47 => ( ( ord_less_eq_set_l @ Xa @ X4 )
% 0.30/0.47 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_has_minimal2
% 0.30/0.47 thf(fact_199_finite__has__maximal2,axiom,
% 0.30/0.47 ! [A3: set_set_r,A2: set_r] :
% 0.30/0.47 ( ( finite_finite_set_r @ A3 )
% 0.30/0.47 => ( ( member_set_r @ A2 @ A3 )
% 0.30/0.47 => ? [X4: set_r] :
% 0.30/0.47 ( ( member_set_r @ X4 @ A3 )
% 0.30/0.47 & ( ord_less_eq_set_r @ A2 @ X4 )
% 0.30/0.47 & ! [Xa: set_r] :
% 0.30/0.47 ( ( member_set_r @ Xa @ A3 )
% 0.30/0.47 => ( ( ord_less_eq_set_r @ X4 @ Xa )
% 0.30/0.47 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_has_maximal2
% 0.30/0.47 thf(fact_200_finite__has__maximal2,axiom,
% 0.30/0.47 ! [A3: set_set_l,A2: set_l] :
% 0.30/0.47 ( ( finite_finite_set_l @ A3 )
% 0.30/0.47 => ( ( member_set_l @ A2 @ A3 )
% 0.30/0.47 => ? [X4: set_l] :
% 0.30/0.47 ( ( member_set_l @ X4 @ A3 )
% 0.30/0.47 & ( ord_less_eq_set_l @ A2 @ X4 )
% 0.30/0.47 & ! [Xa: set_l] :
% 0.30/0.47 ( ( member_set_l @ Xa @ A3 )
% 0.30/0.47 => ( ( ord_less_eq_set_l @ X4 @ Xa )
% 0.30/0.47 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_has_maximal2
% 0.30/0.47 thf(fact_201_finite__subset,axiom,
% 0.30/0.47 ! [A3: set_r,B4: set_r] :
% 0.30/0.47 ( ( ord_less_eq_set_r @ A3 @ B4 )
% 0.30/0.47 => ( ( finite_finite_r @ B4 )
% 0.30/0.47 => ( finite_finite_r @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_subset
% 0.30/0.47 thf(fact_202_finite__subset,axiom,
% 0.30/0.47 ! [A3: set_l,B4: set_l] :
% 0.30/0.47 ( ( ord_less_eq_set_l @ A3 @ B4 )
% 0.30/0.47 => ( ( finite_finite_l @ B4 )
% 0.30/0.47 => ( finite_finite_l @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_subset
% 0.30/0.47 thf(fact_203_infinite__super,axiom,
% 0.30/0.47 ! [S5: set_r,T2: set_r] :
% 0.30/0.47 ( ( ord_less_eq_set_r @ S5 @ T2 )
% 0.30/0.47 => ( ~ ( finite_finite_r @ S5 )
% 0.30/0.47 => ~ ( finite_finite_r @ T2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % infinite_super
% 0.30/0.47 thf(fact_204_infinite__super,axiom,
% 0.30/0.47 ! [S5: set_l,T2: set_l] :
% 0.30/0.47 ( ( ord_less_eq_set_l @ S5 @ T2 )
% 0.30/0.47 => ( ~ ( finite_finite_l @ S5 )
% 0.30/0.47 => ~ ( finite_finite_l @ T2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % infinite_super
% 0.30/0.47 thf(fact_205_rev__finite__subset,axiom,
% 0.30/0.47 ! [B4: set_r,A3: set_r] :
% 0.30/0.47 ( ( finite_finite_r @ B4 )
% 0.30/0.47 => ( ( ord_less_eq_set_r @ A3 @ B4 )
% 0.30/0.47 => ( finite_finite_r @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rev_finite_subset
% 0.30/0.47 thf(fact_206_rev__finite__subset,axiom,
% 0.30/0.47 ! [B4: set_l,A3: set_l] :
% 0.30/0.47 ( ( finite_finite_l @ B4 )
% 0.30/0.47 => ( ( ord_less_eq_set_l @ A3 @ B4 )
% 0.30/0.47 => ( finite_finite_l @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % rev_finite_subset
% 0.30/0.47 thf(fact_207_finite__update__induct,axiom,
% 0.30/0.47 ! [F: r > option1457017436_r_l_v,C: option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 0.30/0.47 ( ( finite_finite_r
% 0.30/0.47 @ ( collect_r
% 0.30/0.47 @ ^ [A4: r] :
% 0.30/0.47 ( ( F @ A4 )
% 0.30/0.47 != C ) ) )
% 0.30/0.47 => ( ( P
% 0.30/0.47 @ ^ [A4: r] : C )
% 0.30/0.47 => ( ! [A: r,B: option1457017436_r_l_v,F2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( finite_finite_r
% 0.30/0.47 @ ( collect_r
% 0.30/0.47 @ ^ [C2: r] :
% 0.30/0.47 ( ( F2 @ C2 )
% 0.30/0.47 != C ) ) )
% 0.30/0.47 => ( ( ( F2 @ A )
% 0.30/0.47 = C )
% 0.30/0.47 => ( ( B != C )
% 0.30/0.47 => ( ( P @ F2 )
% 0.30/0.47 => ( P @ ( fun_up709272714_r_l_v @ F2 @ A @ B ) ) ) ) ) )
% 0.30/0.47 => ( P @ F ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_update_induct
% 0.30/0.47 thf(fact_208_finite__update__induct,axiom,
% 0.30/0.47 ! [F: l > option_val_r_l_v,C: option_val_r_l_v,P: ( l > option_val_r_l_v ) > $o] :
% 0.30/0.47 ( ( finite_finite_l
% 0.30/0.47 @ ( collect_l
% 0.30/0.47 @ ^ [A4: l] :
% 0.30/0.47 ( ( F @ A4 )
% 0.30/0.47 != C ) ) )
% 0.30/0.47 => ( ( P
% 0.30/0.47 @ ^ [A4: l] : C )
% 0.30/0.47 => ( ! [A: l,B: option_val_r_l_v,F2: l > option_val_r_l_v] :
% 0.30/0.47 ( ( finite_finite_l
% 0.30/0.47 @ ( collect_l
% 0.30/0.47 @ ^ [C2: l] :
% 0.30/0.47 ( ( F2 @ C2 )
% 0.30/0.47 != C ) ) )
% 0.30/0.47 => ( ( ( F2 @ A )
% 0.30/0.47 = C )
% 0.30/0.47 => ( ( B != C )
% 0.30/0.47 => ( ( P @ F2 )
% 0.30/0.47 => ( P @ ( fun_up1835647912_r_l_v @ F2 @ A @ B ) ) ) ) ) )
% 0.30/0.47 => ( P @ F ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_update_induct
% 0.30/0.47 thf(fact_209_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R2 )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.30/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.local_state_of_finite_restricted_global_state_is_finite(1)
% 0.30/0.47 thf(fact_210_SLC__ifTrue,axiom,
% 0.30/0.47 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( S_1 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % SLC_ifTrue
% 0.30/0.47 thf(fact_211_SLC__ifFalse,axiom,
% 0.30/0.47 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( S_1 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % SLC_ifFalse
% 0.30/0.47 thf(fact_212_expr_Oinject_I7_J,axiom,
% 0.30/0.47 ! [X7: expr_r_l_v,Y7: expr_r_l_v] :
% 0.30/0.47 ( ( ( rfork_r_l_v @ X7 )
% 0.30/0.47 = ( rfork_r_l_v @ Y7 ) )
% 0.30/0.47 = ( X7 = Y7 ) ) ).
% 0.30/0.47
% 0.30/0.47 % expr.inject(7)
% 0.30/0.47 thf(fact_213_val_Oinject_I4_J,axiom,
% 0.30/0.47 ! [X42: r,Y4: r] :
% 0.30/0.47 ( ( ( rid_r_l_v @ X42 )
% 0.30/0.47 = ( rid_r_l_v @ Y4 ) )
% 0.30/0.47 = ( X42 = Y4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % val.inject(4)
% 0.30/0.47 thf(fact_214_expr_Oinject_I1_J,axiom,
% 0.30/0.47 ! [X1: val_r_l_v,Y1: val_r_l_v] :
% 0.30/0.47 ( ( ( vE_r_l_v @ X1 )
% 0.30/0.47 = ( vE_r_l_v @ Y1 ) )
% 0.30/0.47 = ( X1 = Y1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % expr.inject(1)
% 0.30/0.47 thf(fact_215_injective__cntxt,axiom,
% 0.30/0.47 ! [E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.30/0.47 ( ( ( plug_r_l_v @ E3 @ E1 )
% 0.30/0.47 = ( plug_r_l_v @ E3 @ E22 ) )
% 0.30/0.47 = ( E1 = E22 ) ) ).
% 0.30/0.47
% 0.30/0.47 % injective_cntxt
% 0.30/0.47 thf(fact_216_val_Oinject_I1_J,axiom,
% 0.30/0.47 ! [X1: const,Y1: const] :
% 0.30/0.47 ( ( ( cV_r_l_v @ X1 )
% 0.30/0.47 = ( cV_r_l_v @ Y1 ) )
% 0.30/0.47 = ( X1 = Y1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % val.inject(1)
% 0.30/0.47 thf(fact_217_expr_Oinject_I8_J,axiom,
% 0.30/0.47 ! [X8: expr_r_l_v,Y8: expr_r_l_v] :
% 0.30/0.47 ( ( ( rjoin_r_l_v @ X8 )
% 0.30/0.47 = ( rjoin_r_l_v @ Y8 ) )
% 0.30/0.47 = ( X8 = Y8 ) ) ).
% 0.30/0.47
% 0.30/0.47 % expr.inject(8)
% 0.30/0.47 thf(fact_218_revision__step_OifFalse,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step.ifFalse
% 0.30/0.47 thf(fact_219_revision__step_OifTrue,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step.ifTrue
% 0.30/0.47 thf(fact_220_revision__step__relaxed_OifFalse,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step_relaxed.ifFalse
% 0.30/0.47 thf(fact_221_revision__step__relaxed_OifTrue,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % revision_step_relaxed.ifTrue
% 0.30/0.47 thf(fact_222_ifFalse__deterministic,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 = ( S2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ifFalse_deterministic
% 0.30/0.47 thf(fact_223_ifTrue__deterministic,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 = ( S2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ifTrue_deterministic
% 0.30/0.47 thf(fact_224_expr_Odistinct_I35_J,axiom,
% 0.30/0.47 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X8: expr_r_l_v] :
% 0.30/0.47 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 0.30/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.30/0.47
% 0.30/0.47 % expr.distinct(35)
% 0.30/0.47 thf(fact_225_expr_Odistinct_I33_J,axiom,
% 0.30/0.47 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X7: expr_r_l_v] :
% 0.30/0.47 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 0.30/0.47 != ( rfork_r_l_v @ X7 ) ) ).
% 0.30/0.47
% 0.30/0.47 % expr.distinct(33)
% 0.30/0.47 thf(fact_226_expr_Odistinct_I3_J,axiom,
% 0.30/0.47 ! [X1: val_r_l_v,X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v] :
% 0.30/0.47 ( ( vE_r_l_v @ X1 )
% 0.30/0.47 != ( ite_r_l_v @ X31 @ X32 @ X33 ) ) ).
% 0.30/0.47
% 0.30/0.47 % expr.distinct(3)
% 0.30/0.47 thf(fact_227_const_Oexhaust,axiom,
% 0.30/0.47 ! [Y: const] :
% 0.30/0.47 ( ( Y != unit )
% 0.30/0.47 => ( ( Y != f )
% 0.30/0.47 => ( Y = t ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % const.exhaust
% 0.30/0.47 thf(fact_228_const_Oinduct,axiom,
% 0.30/0.47 ! [P: const > $o,Const: const] :
% 0.30/0.47 ( ( P @ unit )
% 0.30/0.47 => ( ( P @ f )
% 0.30/0.47 => ( ( P @ t )
% 0.30/0.47 => ( P @ Const ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % const.induct
% 0.30/0.47 thf(fact_229_const_Odistinct_I1_J,axiom,
% 0.30/0.47 unit != f ).
% 0.30/0.47
% 0.30/0.47 % const.distinct(1)
% 0.30/0.47 thf(fact_230_const_Odistinct_I3_J,axiom,
% 0.30/0.47 unit != t ).
% 0.30/0.47
% 0.30/0.47 % const.distinct(3)
% 0.30/0.47 thf(fact_231_substitution_Orevision__step_OifTrue,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step.ifTrue
% 0.30/0.47 thf(fact_232_substitution_Orevision__step_OifFalse,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step.ifFalse
% 0.30/0.47 thf(fact_233_substitution_OifTrue__deterministic,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 = ( S2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.ifTrue_deterministic
% 0.30/0.47 thf(fact_234_substitution_OifFalse__deterministic,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 = ( S2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.ifFalse_deterministic
% 0.30/0.47 thf(fact_235_substitution_Orevision__step__relaxed_OifTrue,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step_relaxed.ifTrue
% 0.30/0.47 thf(fact_236_substitution_Orevision__step__relaxed_OifFalse,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.revision_step_relaxed.ifFalse
% 0.30/0.47 thf(fact_237_substitution_OSLC__ifTrue,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S_1 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.SLC_ifTrue
% 0.30/0.47 thf(fact_238_substitution_OSLC__ifFalse,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( ( S_1 @ R )
% 0.30/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( S_2
% 0.30/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.30/0.47 => ( ( R != R2 )
% 0.30/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.30/0.47 | ( S_2 = S_3 ) )
% 0.30/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.30/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.SLC_ifFalse
% 0.30/0.47 thf(fact_239_LID__local__store_Ocases,axiom,
% 0.30/0.47 ! [X2: produc1156025366_r_l_v] :
% 0.30/0.47 ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E2: expr_r_l_v] :
% 0.30/0.47 ( X2
% 0.30/0.47 != ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % LID_local_store.cases
% 0.30/0.47 thf(fact_240_LID__local__store_Oinduct,axiom,
% 0.30/0.47 ! [P: produc1156025366_r_l_v > $o,A0: produc1156025366_r_l_v] :
% 0.30/0.47 ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E2: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) )
% 0.30/0.47 => ( P @ A0 ) ) ).
% 0.30/0.47
% 0.30/0.47 % LID_local_store.induct
% 0.30/0.47 thf(fact_241_expr_Odistinct_I13_J,axiom,
% 0.30/0.47 ! [X1: val_r_l_v,X8: expr_r_l_v] :
% 0.30/0.47 ( ( vE_r_l_v @ X1 )
% 0.30/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.30/0.47
% 0.30/0.47 % expr.distinct(13)
% 0.30/0.47 thf(fact_242_expr_Odistinct_I11_J,axiom,
% 0.30/0.47 ! [X1: val_r_l_v,X7: expr_r_l_v] :
% 0.30/0.47 ( ( vE_r_l_v @ X1 )
% 0.30/0.47 != ( rfork_r_l_v @ X7 ) ) ).
% 0.30/0.47
% 0.30/0.47 % expr.distinct(11)
% 0.30/0.47 thf(fact_243_combine_Oelims,axiom,
% 0.30/0.47 ! [X2: l > option_val_r_l_v,Xa2: l > option_val_r_l_v,Xb: l,Y: option_val_r_l_v] :
% 0.30/0.47 ( ( ( combine_l_val_r_l_v @ X2 @ Xa2 @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( ( Xa2 @ Xb )
% 0.30/0.47 = none_val_r_l_v )
% 0.30/0.47 => ( Y
% 0.30/0.47 = ( X2 @ Xb ) ) )
% 0.30/0.47 & ( ( ( Xa2 @ Xb )
% 0.30/0.47 != none_val_r_l_v )
% 0.30/0.47 => ( Y
% 0.30/0.47 = ( Xa2 @ Xb ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % combine.elims
% 0.30/0.47 thf(fact_244_combine_Osimps,axiom,
% 0.30/0.47 ( combine_l_val_r_l_v
% 0.30/0.47 = ( ^ [F3: l > option_val_r_l_v,G: l > option_val_r_l_v,X: l] :
% 0.30/0.47 ( if_option_val_r_l_v
% 0.30/0.47 @ ( ( G @ X )
% 0.30/0.47 = none_val_r_l_v )
% 0.30/0.47 @ ( F3 @ X )
% 0.30/0.47 @ ( G @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % combine.simps
% 0.30/0.47 thf(fact_245_val_Odistinct_I5_J,axiom,
% 0.30/0.47 ! [X1: const,X42: r] :
% 0.30/0.47 ( ( cV_r_l_v @ X1 )
% 0.30/0.47 != ( rid_r_l_v @ X42 ) ) ).
% 0.30/0.47
% 0.30/0.47 % val.distinct(5)
% 0.30/0.47 thf(fact_246_expr_Odistinct_I55_J,axiom,
% 0.30/0.47 ! [X7: expr_r_l_v,X8: expr_r_l_v] :
% 0.30/0.47 ( ( rfork_r_l_v @ X7 )
% 0.30/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.30/0.47
% 0.30/0.47 % expr.distinct(55)
% 0.30/0.47 thf(fact_247_empty__map__finite_I4_J,axiom,
% 0.30/0.47 ( finite_finite_l
% 0.30/0.47 @ ( lID_G_r_l_v
% 0.30/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_map_finite(4)
% 0.30/0.47 thf(fact_248_fun__upd__upd,axiom,
% 0.30/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 0.30/0.47 ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X2 @ Y ) @ X2 @ Z )
% 0.30/0.47 = ( fun_up709272714_r_l_v @ F @ X2 @ Z ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_upd
% 0.30/0.47 thf(fact_249_fun__upd__upd,axiom,
% 0.30/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v,Z: option_val_r_l_v] :
% 0.30/0.47 ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X2 @ Y ) @ X2 @ Z )
% 0.30/0.47 = ( fun_up1835647912_r_l_v @ F @ X2 @ Z ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_upd
% 0.30/0.47 thf(fact_250_fun__upd__triv,axiom,
% 0.30/0.47 ! [F: r > option1457017436_r_l_v,X2: r] :
% 0.30/0.47 ( ( fun_up709272714_r_l_v @ F @ X2 @ ( F @ X2 ) )
% 0.30/0.47 = F ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_triv
% 0.30/0.47 thf(fact_251_fun__upd__triv,axiom,
% 0.30/0.47 ! [F: l > option_val_r_l_v,X2: l] :
% 0.30/0.47 ( ( fun_up1835647912_r_l_v @ F @ X2 @ ( F @ X2 ) )
% 0.30/0.47 = F ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_triv
% 0.30/0.47 thf(fact_252_RID_092_060_094sub_062L__finite__invariant,axiom,
% 0.30/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.47 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.30/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % RID\<^sub>L_finite_invariant
% 0.30/0.47 thf(fact_253_reachable__imp__identifiers__finite_I2_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % reachable_imp_identifiers_finite(2)
% 0.30/0.47 thf(fact_254_reachable__imp__identifiers__available_I2_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.47 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.30/0.47 => ? [L: l] :
% 0.30/0.47 ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % reachable_imp_identifiers_available(2)
% 0.30/0.47 thf(fact_255_fun__upd__apply,axiom,
% 0.30/0.47 ( fun_up709272714_r_l_v
% 0.30/0.47 = ( ^ [F3: r > option1457017436_r_l_v,X: r,Y2: option1457017436_r_l_v,Z2: r] : ( if_opt1153928738_r_l_v @ ( Z2 = X ) @ Y2 @ ( F3 @ Z2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_apply
% 0.30/0.47 thf(fact_256_fun__upd__apply,axiom,
% 0.30/0.47 ( fun_up1835647912_r_l_v
% 0.30/0.47 = ( ^ [F3: l > option_val_r_l_v,X: l,Y2: option_val_r_l_v,Z2: l] : ( if_option_val_r_l_v @ ( Z2 = X ) @ Y2 @ ( F3 @ Z2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_apply
% 0.30/0.47 thf(fact_257_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 0.30/0.47 ! [L2: l,S: r > option1457017436_r_l_v,R: r] :
% 0.30/0.47 ( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.30/0.47 => ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_restricted_global_in_unrestricted_global(2)
% 0.30/0.47 thf(fact_258_finite__state__imp__restriction__finite_I2_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r] :
% 0.30/0.47 ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.30/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % finite_state_imp_restriction_finite(2)
% 0.30/0.47 thf(fact_259_in__restricted__global__in__updated__global_I2_J,axiom,
% 0.30/0.47 ! [L2: l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 0.30/0.47 ( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.30/0.47 => ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % in_restricted_global_in_updated_global(2)
% 0.30/0.47 thf(fact_260_fun__upd__idem__iff,axiom,
% 0.30/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 0.30/0.47 = F )
% 0.30/0.47 = ( ( F @ X2 )
% 0.30/0.47 = Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_idem_iff
% 0.30/0.47 thf(fact_261_fun__upd__idem__iff,axiom,
% 0.30/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 0.30/0.47 ( ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 0.30/0.47 = F )
% 0.30/0.47 = ( ( F @ X2 )
% 0.30/0.47 = Y ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_idem_iff
% 0.30/0.47 thf(fact_262_fun__upd__twist,axiom,
% 0.30/0.47 ! [A2: r,C: r,M: r > option1457017436_r_l_v,B2: option1457017436_r_l_v,D: option1457017436_r_l_v] :
% 0.30/0.47 ( ( A2 != C )
% 0.30/0.47 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ A2 @ B2 ) @ C @ D )
% 0.30/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ C @ D ) @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_twist
% 0.30/0.47 thf(fact_263_fun__upd__twist,axiom,
% 0.30/0.47 ! [A2: l,C: l,M: l > option_val_r_l_v,B2: option_val_r_l_v,D: option_val_r_l_v] :
% 0.30/0.47 ( ( A2 != C )
% 0.30/0.47 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ A2 @ B2 ) @ C @ D )
% 0.30/0.47 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ C @ D ) @ A2 @ B2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_twist
% 0.30/0.47 thf(fact_264_fun__upd__other,axiom,
% 0.30/0.47 ! [Z: r,X2: r,F: r > option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 0.30/0.47 ( ( Z != X2 )
% 0.30/0.47 => ( ( fun_up709272714_r_l_v @ F @ X2 @ Y @ Z )
% 0.30/0.47 = ( F @ Z ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_other
% 0.30/0.47 thf(fact_265_fun__upd__other,axiom,
% 0.30/0.47 ! [Z: l,X2: l,F: l > option_val_r_l_v,Y: option_val_r_l_v] :
% 0.30/0.47 ( ( Z != X2 )
% 0.30/0.47 => ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y @ Z )
% 0.30/0.47 = ( F @ Z ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_other
% 0.30/0.47 thf(fact_266_fun__upd__same,axiom,
% 0.30/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 0.30/0.47 ( ( fun_up709272714_r_l_v @ F @ X2 @ Y @ X2 )
% 0.30/0.47 = Y ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_same
% 0.30/0.47 thf(fact_267_fun__upd__same,axiom,
% 0.30/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 0.30/0.47 ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y @ X2 )
% 0.30/0.47 = Y ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_same
% 0.30/0.47 thf(fact_268_fun__upd__idem,axiom,
% 0.30/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( F @ X2 )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 0.30/0.47 = F ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_idem
% 0.30/0.47 thf(fact_269_fun__upd__idem,axiom,
% 0.30/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 0.30/0.47 ( ( ( F @ X2 )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 0.30/0.47 = F ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_idem
% 0.30/0.47 thf(fact_270_fun__upd__eqD,axiom,
% 0.30/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v,G2: r > option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 0.30/0.47 ( ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 0.30/0.47 = ( fun_up709272714_r_l_v @ G2 @ X2 @ Z ) )
% 0.30/0.47 => ( Y = Z ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_eqD
% 0.30/0.47 thf(fact_271_fun__upd__eqD,axiom,
% 0.30/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v,G2: l > option_val_r_l_v,Z: option_val_r_l_v] :
% 0.30/0.47 ( ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 0.30/0.47 = ( fun_up1835647912_r_l_v @ G2 @ X2 @ Z ) )
% 0.30/0.47 => ( Y = Z ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_eqD
% 0.30/0.47 thf(fact_272_fun__upd__def,axiom,
% 0.30/0.47 ( fun_up709272714_r_l_v
% 0.30/0.47 = ( ^ [F3: r > option1457017436_r_l_v,A4: r,B5: option1457017436_r_l_v,X: r] : ( if_opt1153928738_r_l_v @ ( X = A4 ) @ B5 @ ( F3 @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_def
% 0.30/0.47 thf(fact_273_fun__upd__def,axiom,
% 0.30/0.47 ( fun_up1835647912_r_l_v
% 0.30/0.47 = ( ^ [F3: l > option_val_r_l_v,A4: l,B5: option_val_r_l_v,X: l] : ( if_option_val_r_l_v @ ( X = A4 ) @ B5 @ ( F3 @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_upd_def
% 0.30/0.47 thf(fact_274_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.47 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.30/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.RID\<^sub>L_finite_invariant
% 0.30/0.47 thf(fact_275_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 0.30/0.47 ! [S: r > option1457017436_r_l_v,R: r] : ( ord_less_eq_set_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) @ ( lID_G_r_l_v @ S ) ) ).
% 0.30/0.47
% 0.30/0.47 % ID_restricted_global_subset_unrestricted(1)
% 0.30/0.47 thf(fact_276_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.30/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.reachable_imp_identifiers_finite(2)
% 0.30/0.47 thf(fact_277_substitution_Oempty__map__finite_I4_J,axiom,
% 0.30/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 0.30/0.47 ( ( substitution_r_l_v @ Subst )
% 0.30/0.47 => ( finite_finite_l
% 0.30/0.47 @ ( lID_G_r_l_v
% 0.30/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % substitution.empty_map_finite(4)
% 0.30/0.47 thf(fact_278_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.30/0.48 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.finite_state_imp_restriction_finite(2)
% 0.30/0.48 thf(fact_279_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( reachable_r_l_v @ Subst @ S )
% 0.30/0.48 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.30/0.48 => ? [L: l] :
% 0.30/0.48 ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.reachable_imp_identifiers_available(2)
% 0.30/0.48 thf(fact_280_only__new__introduces__lids_H,axiom,
% 0.30/0.48 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,L2: l] :
% 0.30/0.48 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.48 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V2: val_r_l_v] :
% 0.30/0.48 ( ( S @ R )
% 0.30/0.48 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.30/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 0.30/0.48 => ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % only_new_introduces_lids'
% 0.30/0.48 thf(fact_281_valid__stepE,axiom,
% 0.30/0.48 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ subst ) )
% 0.30/0.48 => ? [R6: r] : ( revision_step_r_l_v @ subst @ R6 @ S @ S2 ) ) ).
% 0.30/0.48
% 0.30/0.48 % valid_stepE
% 0.30/0.48 thf(fact_282_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.30/0.48 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.30/0.48 ( ( ( S @ R2 )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.30/0.48 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.30/0.48 => ( ( R != R2 )
% 0.30/0.48 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % local_state_of_finite_restricted_global_state_is_finite(2)
% 0.30/0.48 thf(fact_283_LID_092_060_094sub_062GI,axiom,
% 0.30/0.48 ! [S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v,L2: l] :
% 0.30/0.48 ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.30/0.48 => ( ( member_l @ L2 @ ( lID_L_l_r_v @ Ls ) )
% 0.30/0.48 => ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % LID\<^sub>GI
% 0.30/0.48 thf(fact_284_valid__stepI,axiom,
% 0.30/0.48 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.48 => ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ subst ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % valid_stepI
% 0.30/0.48 thf(fact_285_maximal__execution__def,axiom,
% 0.30/0.48 ! [E4: expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( maxima311842975_r_l_v @ subst @ E4 @ S @ S2 )
% 0.30/0.48 = ( ( execution_r_l_v @ subst @ E4 @ S @ S2 )
% 0.30/0.48 & ~ ? [S6: r > option1457017436_r_l_v] : ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S2 @ S6 ) @ ( steps_r_l_v @ subst ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % maximal_execution_def
% 0.30/0.48 thf(fact_286_only__new__introduces__lids,axiom,
% 0.30/0.48 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.48 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V2: val_r_l_v] :
% 0.30/0.48 ( ( S @ R )
% 0.30/0.48 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.30/0.48 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % only_new_introduces_lids
% 0.30/0.48 thf(fact_287_substitution_Osteps_Ocong,axiom,
% 0.30/0.48 steps_r_l_v = steps_r_l_v ).
% 0.30/0.48
% 0.30/0.48 % substitution.steps.cong
% 0.30/0.48 thf(fact_288_expr_Odistinct_I5_J,axiom,
% 0.30/0.48 ! [X1: val_r_l_v,X42: expr_r_l_v] :
% 0.30/0.48 ( ( vE_r_l_v @ X1 )
% 0.30/0.48 != ( ref_r_l_v @ X42 ) ) ).
% 0.30/0.48
% 0.30/0.48 % expr.distinct(5)
% 0.30/0.48 thf(fact_289_expr_Odistinct_I41_J,axiom,
% 0.30/0.48 ! [X42: expr_r_l_v,X7: expr_r_l_v] :
% 0.30/0.48 ( ( ref_r_l_v @ X42 )
% 0.30/0.48 != ( rfork_r_l_v @ X7 ) ) ).
% 0.30/0.48
% 0.30/0.48 % expr.distinct(41)
% 0.30/0.48 thf(fact_290_expr_Odistinct_I43_J,axiom,
% 0.30/0.48 ! [X42: expr_r_l_v,X8: expr_r_l_v] :
% 0.30/0.48 ( ( ref_r_l_v @ X42 )
% 0.30/0.48 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.30/0.48
% 0.30/0.48 % expr.distinct(43)
% 0.30/0.48 thf(fact_291_LID_092_060_094sub_062GE,axiom,
% 0.30/0.48 ! [L2: l,S: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 0.30/0.48 => ~ ! [R6: r,Ls3: produc1156025366_r_l_v] :
% 0.30/0.48 ( ( ( S @ R6 )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ Ls3 ) )
% 0.30/0.48 => ~ ( member_l @ L2 @ ( lID_L_l_r_v @ Ls3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % LID\<^sub>GE
% 0.30/0.48 thf(fact_292_substitution_Ovalid__stepE,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ Subst ) )
% 0.30/0.48 => ? [R6: r] : ( revision_step_r_l_v @ Subst @ R6 @ S @ S2 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.valid_stepE
% 0.30/0.48 thf(fact_293_substitution_Ovalid__stepI,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.48 => ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ Subst ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.valid_stepI
% 0.30/0.48 thf(fact_294_substitution_Oonly__new__introduces__lids_H,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,L2: l] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.48 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V2: val_r_l_v] :
% 0.30/0.48 ( ( S @ R )
% 0.30/0.48 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.30/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 0.30/0.48 => ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.only_new_introduces_lids'
% 0.30/0.48 thf(fact_295_substitution_Oonly__new__introduces__lids,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.48 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V2: val_r_l_v] :
% 0.30/0.48 ( ( S @ R )
% 0.30/0.48 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.30/0.48 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.only_new_introduces_lids
% 0.30/0.48 thf(fact_296_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( ( S @ R2 )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.30/0.48 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.30/0.48 => ( ( R != R2 )
% 0.30/0.48 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.local_state_of_finite_restricted_global_state_is_finite(2)
% 0.30/0.48 thf(fact_297_domains__subsume__def,axiom,
% 0.30/0.48 ( domain87684397_l_r_v
% 0.30/0.48 = ( ^ [Ls2: produc1156025366_r_l_v] : ( ord_less_eq_set_l @ ( lID_L_l_r_v @ Ls2 ) @ ( doms_l_r_v @ Ls2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domains_subsume_def
% 0.30/0.48 thf(fact_298_SLC__new,axiom,
% 0.30/0.48 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( ( S_1 @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( S_2
% 0.30/0.48 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 0.30/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
% 0.30/0.48 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.30/0.48 => ( ( R != R2 )
% 0.30/0.48 => ( ( reachable_r_l_v @ subst @ S_1 )
% 0.30/0.48 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.30/0.48 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.48 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.48 | ( S_2 = S_3 ) )
% 0.30/0.48 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.48 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % SLC_new
% 0.30/0.48 thf(fact_299_terminates__in__def,axiom,
% 0.30/0.48 ! [E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( terminates_in_r_l_v @ subst @ E4 @ S2 )
% 0.30/0.48 = ( ? [S4: r > option1457017436_r_l_v] : ( maxima311842975_r_l_v @ subst @ E4 @ S4 @ S2 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % terminates_in_def
% 0.30/0.48 thf(fact_300_revision__step_Onew,axiom,
% 0.30/0.48 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,L2: l] :
% 0.30/0.48 ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 0.30/0.48 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % revision_step.new
% 0.30/0.48 thf(fact_301_new__pseudodeterministic,axiom,
% 0.30/0.48 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.48 = ( ? [L3: l] :
% 0.30/0.48 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 0.30/0.48 & ( S2
% 0.30/0.48 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % new_pseudodeterministic
% 0.30/0.48 thf(fact_302_val_Odistinct_I3_J,axiom,
% 0.30/0.48 ! [X1: const,X34: l] :
% 0.30/0.48 ( ( cV_r_l_v @ X1 )
% 0.30/0.48 != ( loc_l_r_v @ X34 ) ) ).
% 0.30/0.48
% 0.30/0.48 % val.distinct(3)
% 0.30/0.48 thf(fact_303_val_Odistinct_I15_J,axiom,
% 0.30/0.48 ! [X34: l,X42: r] :
% 0.30/0.48 ( ( loc_l_r_v @ X34 )
% 0.30/0.48 != ( rid_r_l_v @ X42 ) ) ).
% 0.30/0.48
% 0.30/0.48 % val.distinct(15)
% 0.30/0.48 thf(fact_304_substitution_Omaximal__execution_Ocong,axiom,
% 0.30/0.48 maxima311842975_r_l_v = maxima311842975_r_l_v ).
% 0.30/0.48
% 0.30/0.48 % substitution.maximal_execution.cong
% 0.30/0.48 thf(fact_305_substitution_Odomains__subsume__def,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Ls: produc1156025366_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( domain87684397_l_r_v @ Ls )
% 0.30/0.48 = ( ord_less_eq_set_l @ ( lID_L_l_r_v @ Ls ) @ ( doms_l_r_v @ Ls ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.domains_subsume_def
% 0.30/0.48 thf(fact_306_substitution_Onew__pseudodeterministic,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.48 = ( ? [L3: l] :
% 0.30/0.48 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 0.30/0.48 & ( S2
% 0.30/0.48 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.new_pseudodeterministic
% 0.30/0.48 thf(fact_307_substitution_Orevision__step_Onew,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,L2: l] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 0.30/0.48 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.revision_step.new
% 0.30/0.48 thf(fact_308_substitution_Omaximal__execution__def,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,E4: expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( maxima311842975_r_l_v @ Subst @ E4 @ S @ S2 )
% 0.30/0.48 = ( ( execution_r_l_v @ Subst @ E4 @ S @ S2 )
% 0.30/0.48 & ~ ? [S6: r > option1457017436_r_l_v] : ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S2 @ S6 ) @ ( steps_r_l_v @ Subst ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.maximal_execution_def
% 0.30/0.48 thf(fact_309_substitution_OSLC__new,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( ( S_1 @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( S_2
% 0.30/0.48 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 0.30/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
% 0.30/0.48 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.30/0.48 => ( ( R != R2 )
% 0.30/0.48 => ( ( reachable_r_l_v @ Subst @ S_1 )
% 0.30/0.48 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.30/0.48 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.48 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.30/0.48 | ( S_2 = S_3 ) )
% 0.30/0.48 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.30/0.48 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.SLC_new
% 0.30/0.48 thf(fact_310_revision__step__relaxed_Oset,axiom,
% 0.30/0.48 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v] :
% 0.30/0.48 ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % revision_step_relaxed.set
% 0.30/0.48 thf(fact_311_substitution_Orevision__step__relaxed_Oset,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.revision_step_relaxed.set
% 0.30/0.48 thf(fact_312_substitution_Oterminates__in_Ocong,axiom,
% 0.30/0.48 terminates_in_r_l_v = terminates_in_r_l_v ).
% 0.30/0.48
% 0.30/0.48 % substitution.terminates_in.cong
% 0.30/0.48 thf(fact_313_expr_Odistinct_I9_J,axiom,
% 0.30/0.48 ! [X1: val_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 0.30/0.48 ( ( vE_r_l_v @ X1 )
% 0.30/0.48 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 0.30/0.48
% 0.30/0.48 % expr.distinct(9)
% 0.30/0.48 thf(fact_314_expr_Odistinct_I51_J,axiom,
% 0.30/0.48 ! [X61: expr_r_l_v,X62: expr_r_l_v,X7: expr_r_l_v] :
% 0.30/0.48 ( ( assign_r_l_v @ X61 @ X62 )
% 0.30/0.48 != ( rfork_r_l_v @ X7 ) ) ).
% 0.30/0.48
% 0.30/0.48 % expr.distinct(51)
% 0.30/0.48 thf(fact_315_expr_Odistinct_I53_J,axiom,
% 0.30/0.48 ! [X61: expr_r_l_v,X62: expr_r_l_v,X8: expr_r_l_v] :
% 0.30/0.48 ( ( assign_r_l_v @ X61 @ X62 )
% 0.30/0.48 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.30/0.48
% 0.30/0.48 % expr.distinct(53)
% 0.30/0.48 thf(fact_316_substitution_Oterminates__in__def,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( terminates_in_r_l_v @ Subst @ E4 @ S2 )
% 0.30/0.48 = ( ? [S4: r > option1457017436_r_l_v] : ( maxima311842975_r_l_v @ Subst @ E4 @ S4 @ S2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.terminates_in_def
% 0.30/0.48 thf(fact_317_SLC__set,axiom,
% 0.30/0.48 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( ( S_1 @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( S_2
% 0.30/0.48 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) )
% 0.30/0.48 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 0.30/0.48 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.30/0.48 => ( ( R != R2 )
% 0.30/0.48 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.48 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.48 | ( S_2 = S_3 ) )
% 0.30/0.48 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.48 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % SLC_set
% 0.30/0.48 thf(fact_318_revision__step_Oset,axiom,
% 0.30/0.48 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v] :
% 0.30/0.48 ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 0.30/0.48 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % revision_step.set
% 0.30/0.48 thf(fact_319_dom__const,axiom,
% 0.30/0.48 ! [F: r > produc1156025366_r_l_v] :
% 0.30/0.48 ( ( dom_r_259548057_r_l_v
% 0.30/0.48 @ ^ [X: r] : ( some_P1807977723_r_l_v @ ( F @ X ) ) )
% 0.30/0.48 = top_top_set_r ) ).
% 0.30/0.48
% 0.30/0.48 % dom_const
% 0.30/0.48 thf(fact_320_dom__const,axiom,
% 0.30/0.48 ! [F: r > val_r_l_v] :
% 0.30/0.48 ( ( dom_r_val_r_l_v
% 0.30/0.48 @ ^ [X: r] : ( some_val_r_l_v @ ( F @ X ) ) )
% 0.30/0.48 = top_top_set_r ) ).
% 0.30/0.48
% 0.30/0.48 % dom_const
% 0.30/0.48 thf(fact_321_dom__const,axiom,
% 0.30/0.48 ! [F: l > produc1156025366_r_l_v] :
% 0.30/0.48 ( ( dom_l_45837855_r_l_v
% 0.30/0.48 @ ^ [X: l] : ( some_P1807977723_r_l_v @ ( F @ X ) ) )
% 0.30/0.48 = top_top_set_l ) ).
% 0.30/0.48
% 0.30/0.48 % dom_const
% 0.30/0.48 thf(fact_322_dom__const,axiom,
% 0.30/0.48 ! [F: l > val_r_l_v] :
% 0.30/0.48 ( ( dom_l_val_r_l_v
% 0.30/0.48 @ ^ [X: l] : ( some_val_r_l_v @ ( F @ X ) ) )
% 0.30/0.48 = top_top_set_l ) ).
% 0.30/0.48
% 0.30/0.48 % dom_const
% 0.30/0.48 thf(fact_323_set__deterministic,axiom,
% 0.30/0.48 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.30/0.48 = ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 0.30/0.48 & ( S2
% 0.30/0.48 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % set_deterministic
% 0.30/0.48 thf(fact_324_domD,axiom,
% 0.30/0.48 ! [A2: r,M: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( member_r @ A2 @ ( dom_r_259548057_r_l_v @ M ) )
% 0.30/0.48 => ? [B: produc1156025366_r_l_v] :
% 0.30/0.48 ( ( M @ A2 )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domD
% 0.30/0.48 thf(fact_325_domD,axiom,
% 0.30/0.48 ! [A2: l,M: l > option1457017436_r_l_v] :
% 0.30/0.48 ( ( member_l @ A2 @ ( dom_l_45837855_r_l_v @ M ) )
% 0.30/0.48 => ? [B: produc1156025366_r_l_v] :
% 0.30/0.48 ( ( M @ A2 )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domD
% 0.30/0.48 thf(fact_326_domD,axiom,
% 0.30/0.48 ! [A2: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option1457017436_r_l_v] :
% 0.30/0.48 ( ( member1522896238_r_l_v @ A2 @ ( dom_Pr1162080227_r_l_v @ M ) )
% 0.30/0.48 => ? [B: produc1156025366_r_l_v] :
% 0.30/0.48 ( ( M @ A2 )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domD
% 0.30/0.48 thf(fact_327_domD,axiom,
% 0.30/0.48 ! [A2: r,M: r > option_val_r_l_v] :
% 0.30/0.48 ( ( member_r @ A2 @ ( dom_r_val_r_l_v @ M ) )
% 0.30/0.48 => ? [B: val_r_l_v] :
% 0.30/0.48 ( ( M @ A2 )
% 0.30/0.48 = ( some_val_r_l_v @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domD
% 0.30/0.48 thf(fact_328_domD,axiom,
% 0.30/0.48 ! [A2: l,M: l > option_val_r_l_v] :
% 0.30/0.48 ( ( member_l @ A2 @ ( dom_l_val_r_l_v @ M ) )
% 0.30/0.48 => ? [B: val_r_l_v] :
% 0.30/0.48 ( ( M @ A2 )
% 0.30/0.48 = ( some_val_r_l_v @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domD
% 0.30/0.48 thf(fact_329_domD,axiom,
% 0.30/0.48 ! [A2: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option_val_r_l_v] :
% 0.30/0.48 ( ( member1522896238_r_l_v @ A2 @ ( dom_Pr939617279_r_l_v @ M ) )
% 0.30/0.48 => ? [B: val_r_l_v] :
% 0.30/0.48 ( ( M @ A2 )
% 0.30/0.48 = ( some_val_r_l_v @ B ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domD
% 0.30/0.48 thf(fact_330_domI,axiom,
% 0.30/0.48 ! [M: r > option1457017436_r_l_v,A2: r,B2: produc1156025366_r_l_v] :
% 0.30/0.48 ( ( ( M @ A2 )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ B2 ) )
% 0.30/0.48 => ( member_r @ A2 @ ( dom_r_259548057_r_l_v @ M ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domI
% 0.30/0.48 thf(fact_331_domI,axiom,
% 0.30/0.48 ! [M: l > option1457017436_r_l_v,A2: l,B2: produc1156025366_r_l_v] :
% 0.30/0.48 ( ( ( M @ A2 )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ B2 ) )
% 0.30/0.48 => ( member_l @ A2 @ ( dom_l_45837855_r_l_v @ M ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domI
% 0.30/0.48 thf(fact_332_domI,axiom,
% 0.30/0.48 ! [M: produc1389397445_r_l_v > option1457017436_r_l_v,A2: produc1389397445_r_l_v,B2: produc1156025366_r_l_v] :
% 0.30/0.48 ( ( ( M @ A2 )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ B2 ) )
% 0.30/0.48 => ( member1522896238_r_l_v @ A2 @ ( dom_Pr1162080227_r_l_v @ M ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domI
% 0.30/0.48 thf(fact_333_domI,axiom,
% 0.30/0.48 ! [M: r > option_val_r_l_v,A2: r,B2: val_r_l_v] :
% 0.30/0.48 ( ( ( M @ A2 )
% 0.30/0.48 = ( some_val_r_l_v @ B2 ) )
% 0.30/0.48 => ( member_r @ A2 @ ( dom_r_val_r_l_v @ M ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domI
% 0.30/0.48 thf(fact_334_domI,axiom,
% 0.30/0.48 ! [M: l > option_val_r_l_v,A2: l,B2: val_r_l_v] :
% 0.30/0.48 ( ( ( M @ A2 )
% 0.30/0.48 = ( some_val_r_l_v @ B2 ) )
% 0.30/0.48 => ( member_l @ A2 @ ( dom_l_val_r_l_v @ M ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domI
% 0.30/0.48 thf(fact_335_domI,axiom,
% 0.30/0.48 ! [M: produc1389397445_r_l_v > option_val_r_l_v,A2: produc1389397445_r_l_v,B2: val_r_l_v] :
% 0.30/0.48 ( ( ( M @ A2 )
% 0.30/0.48 = ( some_val_r_l_v @ B2 ) )
% 0.30/0.48 => ( member1522896238_r_l_v @ A2 @ ( dom_Pr939617279_r_l_v @ M ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % domI
% 0.30/0.48 thf(fact_336_finite__map__freshness,axiom,
% 0.30/0.48 ! [F: r > option_val_r_l_v] :
% 0.30/0.48 ( ( finite_finite_r @ ( dom_r_val_r_l_v @ F ) )
% 0.30/0.48 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.30/0.48 => ? [X4: r] :
% 0.30/0.48 ( ( F @ X4 )
% 0.30/0.48 = none_val_r_l_v ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % finite_map_freshness
% 0.30/0.48 thf(fact_337_finite__map__freshness,axiom,
% 0.30/0.48 ! [F: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( finite_finite_r @ ( dom_r_259548057_r_l_v @ F ) )
% 0.30/0.48 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.30/0.48 => ? [X4: r] :
% 0.30/0.48 ( ( F @ X4 )
% 0.30/0.48 = none_P277133687_r_l_v ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % finite_map_freshness
% 0.30/0.48 thf(fact_338_finite__map__freshness,axiom,
% 0.30/0.48 ! [F: l > option_val_r_l_v] :
% 0.30/0.48 ( ( finite_finite_l @ ( dom_l_val_r_l_v @ F ) )
% 0.30/0.48 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.30/0.48 => ? [X4: l] :
% 0.30/0.48 ( ( F @ X4 )
% 0.30/0.48 = none_val_r_l_v ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % finite_map_freshness
% 0.30/0.48 thf(fact_339_finite__map__freshness,axiom,
% 0.30/0.48 ! [F: l > option1457017436_r_l_v] :
% 0.30/0.48 ( ( finite_finite_l @ ( dom_l_45837855_r_l_v @ F ) )
% 0.30/0.48 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.30/0.48 => ? [X4: l] :
% 0.30/0.48 ( ( F @ X4 )
% 0.30/0.48 = none_P277133687_r_l_v ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % finite_map_freshness
% 0.30/0.48 thf(fact_340_dom__def,axiom,
% 0.30/0.48 ( dom_l_val_r_l_v
% 0.30/0.48 = ( ^ [M2: l > option_val_r_l_v] :
% 0.30/0.48 ( collect_l
% 0.30/0.48 @ ^ [A4: l] :
% 0.30/0.48 ( ( M2 @ A4 )
% 0.30/0.48 != none_val_r_l_v ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % dom_def
% 0.30/0.48 thf(fact_341_domIff,axiom,
% 0.30/0.48 ! [A2: r,M: r > option_val_r_l_v] :
% 0.30/0.48 ( ( member_r @ A2 @ ( dom_r_val_r_l_v @ M ) )
% 0.30/0.48 = ( ( M @ A2 )
% 0.30/0.48 != none_val_r_l_v ) ) ).
% 0.30/0.48
% 0.30/0.48 % domIff
% 0.30/0.48 thf(fact_342_domIff,axiom,
% 0.30/0.48 ! [A2: l,M: l > option_val_r_l_v] :
% 0.30/0.48 ( ( member_l @ A2 @ ( dom_l_val_r_l_v @ M ) )
% 0.30/0.48 = ( ( M @ A2 )
% 0.30/0.48 != none_val_r_l_v ) ) ).
% 0.30/0.48
% 0.30/0.48 % domIff
% 0.30/0.48 thf(fact_343_domIff,axiom,
% 0.30/0.48 ! [A2: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option_val_r_l_v] :
% 0.30/0.48 ( ( member1522896238_r_l_v @ A2 @ ( dom_Pr939617279_r_l_v @ M ) )
% 0.30/0.48 = ( ( M @ A2 )
% 0.30/0.48 != none_val_r_l_v ) ) ).
% 0.30/0.48
% 0.30/0.48 % domIff
% 0.30/0.48 thf(fact_344_domIff,axiom,
% 0.30/0.48 ! [A2: r,M: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( member_r @ A2 @ ( dom_r_259548057_r_l_v @ M ) )
% 0.30/0.48 = ( ( M @ A2 )
% 0.30/0.48 != none_P277133687_r_l_v ) ) ).
% 0.30/0.48
% 0.30/0.48 % domIff
% 0.30/0.48 thf(fact_345_domIff,axiom,
% 0.30/0.48 ! [A2: l,M: l > option1457017436_r_l_v] :
% 0.30/0.48 ( ( member_l @ A2 @ ( dom_l_45837855_r_l_v @ M ) )
% 0.30/0.48 = ( ( M @ A2 )
% 0.30/0.48 != none_P277133687_r_l_v ) ) ).
% 0.30/0.48
% 0.30/0.48 % domIff
% 0.30/0.48 thf(fact_346_domIff,axiom,
% 0.30/0.48 ! [A2: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option1457017436_r_l_v] :
% 0.30/0.48 ( ( member1522896238_r_l_v @ A2 @ ( dom_Pr1162080227_r_l_v @ M ) )
% 0.30/0.48 = ( ( M @ A2 )
% 0.30/0.48 != none_P277133687_r_l_v ) ) ).
% 0.30/0.48
% 0.30/0.48 % domIff
% 0.30/0.48 thf(fact_347_substitution_Oset__deterministic,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.30/0.48 = ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 0.30/0.48 & ( S2
% 0.30/0.48 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.set_deterministic
% 0.30/0.48 thf(fact_348_substitution_Orevision__step_Oset,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( ( S @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 0.30/0.48 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.revision_step.set
% 0.30/0.48 thf(fact_349_substitution_OSLC__set,axiom,
% 0.30/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( substitution_r_l_v @ Subst )
% 0.30/0.48 => ( ( ( S_1 @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.30/0.48 => ( ( S_2
% 0.30/0.48 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) )
% 0.30/0.48 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 0.30/0.48 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.30/0.48 => ( ( R != R2 )
% 0.30/0.48 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.48 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.30/0.48 | ( S_2 = S_3 ) )
% 0.30/0.48 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.30/0.48 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % substitution.SLC_set
% 0.30/0.48 thf(fact_350_reachability__closed__under__execution,axiom,
% 0.30/0.48 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( reachable_r_l_v @ subst @ S )
% 0.30/0.48 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( transi1323086383_r_l_v @ ( steps_r_l_v @ subst ) ) )
% 0.30/0.48 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % reachability_closed_under_execution
% 0.30/0.48 thf(fact_351_SLC__get,axiom,
% 0.30/0.48 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( ( S_1 @ R )
% 0.30/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 0.30/0.48 => ( ( S_2
% 0.30/0.48 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 @ L2 ) ) ) ) ) ) ) ) )
% 0.30/0.48 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 0.30/0.48 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.30/0.48 => ( ( R != R2 )
% 0.30/0.48 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.30/0.48 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.30/0.48 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.30/0.48 | ( S_2 = S_3 ) )
% 0.30/0.48 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.30/0.48 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % SLC_get
% 0.30/0.48
% 0.30/0.48 % Helper facts (5)
% 0.30/0.48 thf(help_If_2_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 0.30/0.48 ! [X2: option_val_r_l_v,Y: option_val_r_l_v] :
% 0.30/0.48 ( ( if_option_val_r_l_v @ $false @ X2 @ Y )
% 0.30/0.48 = Y ) ).
% 0.30/0.48
% 0.30/0.48 thf(help_If_1_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 0.30/0.48 ! [X2: option_val_r_l_v,Y: option_val_r_l_v] :
% 0.30/0.48 ( ( if_option_val_r_l_v @ $true @ X2 @ Y )
% 0.30/0.48 = X2 ) ).
% 0.30/0.48
% 0.30/0.48 thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 0.30/0.48 ! [P: $o] :
% 0.30/0.48 ( ( P = $true )
% 0.30/0.48 | ( P = $false ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 0.30/0.48 ! [X2: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 0.30/0.48 ( ( if_opt1153928738_r_l_v @ $false @ X2 @ Y )
% 0.30/0.48 = Y ) ).
% 0.30/0.48
% 0.30/0.48 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 0.30/0.48 ! [X2: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 0.30/0.48 ( ( if_opt1153928738_r_l_v @ $true @ X2 @ Y )
% 0.30/0.48 = X2 ) ).
% 0.30/0.48
% 0.30/0.48 % Conjectures (1)
% 0.30/0.48 thf(conj_0,conjecture,
% 0.30/0.48 r3 != right_forkee ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 2.97/1.54 ---- Embedded in THF ---
% 2.97/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.97/1.54 %%% Generated on Tue Feb 24 08:24:43 EST 2026
% 2.97/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.97/1.54 %%% Logic specification used:
% 2.97/1.54 %%% thf(spec, logic, $$dhol).
% 2.97/1.54
% 2.97/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.a64ubDLv2V/DTF2DTF3281.p
% See solution above
% 2.97/1.54 ------------------------
% 2.97/1.58 ---- Cleaned THF ---
% 2.97/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_M_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_J_J,type,
% 2.97/1.58 set_Pr1409704485_r_l_v: $tType ).
% 2.97/1.58
% 2.97/1.58 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_M_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_J,type,
% 2.97/1.58 produc1389397445_r_l_v: $tType ).
% 2.97/1.58
% 2.97/1.58 thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 2.97/1.58 option1457017436_r_l_v: $tType ).
% 2.97/1.58
% 2.97/1.58 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 2.97/1.58 produc1156025366_r_l_v: $tType ).
% 2.97/1.58
% 2.97/1.58 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 2.97/1.58 produc1164766533_r_l_v: $tType ).
% 2.97/1.58
% 2.97/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J_J,type,
% 2.97/1.58 set_set_Sum_sum_r_l: $tType ).
% 2.97/1.58
% 2.97/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J_J,type,
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% 2.97/1.58 transi1323086383_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_c_member_001t__Product____Type__Oprod_I_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_M_062_Itf__r_Mt__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J_J,type,
% 2.97/1.58 member1522896238_r_l_v: produc1389397445_r_l_v > set_Pr1409704485_r_l_v > $o ).
% 2.97/1.58
% 2.97/1.58 thf(sy_c_member_001t__Set__Oset_Itf__l_J,type,
% 2.97/1.58 member_set_l: set_l > set_set_l > $o ).
% 2.97/1.58
% 2.97/1.58 thf(sy_c_member_001t__Set__Oset_Itf__r_J,type,
% 2.97/1.58 member_set_r: set_r > set_set_r > $o ).
% 2.97/1.58
% 2.97/1.58 thf(sy_c_member_001tf__l,type,
% 2.97/1.58 member_l: l > set_l > $o ).
% 2.97/1.58
% 2.97/1.58 thf(sy_c_member_001tf__r,type,
% 2.97/1.58 member_r: r > set_r > $o ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v__092_060E_062,type,
% 2.97/1.58 e: cntxt_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v__092_060E_062_H____,type,
% 2.97/1.58 e2: cntxt_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v__092_060sigma_062,type,
% 2.97/1.58 sigma: l > option_val_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v__092_060sigma_062_H____,type,
% 2.97/1.58 sigma2: l > option_val_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v__092_060tau_062,type,
% 2.97/1.58 tau: l > option_val_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v__092_060tau_062_H____,type,
% 2.97/1.58 tau2: l > option_val_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_e,type,
% 2.97/1.58 e3: expr_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_e_H____,type,
% 2.97/1.58 e4: expr_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_left__forkee,type,
% 2.97/1.58 left_forkee: r ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_r,type,
% 2.97/1.58 r2: r ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_r_H,type,
% 2.97/1.58 r3: r ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_right__forkee____,type,
% 2.97/1.58 right_forkee: r ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_s_092_060_094sub_0621,type,
% 2.97/1.58 s_1: r > option1457017436_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_s_092_060_094sub_0622,type,
% 2.97/1.58 s_2: r > option1457017436_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_s_092_060_094sub_0622_H,type,
% 2.97/1.58 s_22: r > option1457017436_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(sy_v_subst,type,
% 2.97/1.58 subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(fact_0_local_Ofork_I3_J,axiom,
% 2.97/1.58 ~ ( member_r @ right_forkee @ ( rID_G_r_l_v @ s_1 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_1_side,axiom,
% 2.97/1.58 ~ ( member_r @ left_forkee @ ( rID_G_r_l_v @ s_1 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_2_neq,axiom,
% 2.97/1.58 r2 != r3 ).
% 2.97/1.58
% 2.97/1.58 thf(fact_3__092_060open_062r_H_A_092_060noteq_062_Aleft__forkee_092_060close_062,axiom,
% 2.97/1.58 r3 != left_forkee ).
% 2.97/1.58
% 2.97/1.58 thf(fact_4_r_H__unchanged__left,axiom,
% 2.97/1.58 ( ( s_2 @ r3 )
% 2.97/1.58 = ( s_1 @ r3 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_5__092_060open_062r_A_092_060noteq_062_Aright__forkee_092_060close_062,axiom,
% 2.97/1.58 r2 != right_forkee ).
% 2.97/1.58
% 2.97/1.58 thf(fact_6_local_Ofork_I2_J,axiom,
% 2.97/1.58 ( ( s_1 @ r3 )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma2 @ ( produc1834103605_r_l_v @ tau2 @ ( plug_r_l_v @ e2 @ ( rfork_r_l_v @ e4 ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_7_right,axiom,
% 2.97/1.58 revision_step_r_l_v @ subst @ r3 @ s_1 @ s_22 ).
% 2.97/1.58
% 2.97/1.58 thf(fact_8_local_Ofork_I1_J,axiom,
% 2.97/1.58 ( s_22
% 2.97/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma2 @ ( produc1834103605_r_l_v @ tau2 @ ( plug_r_l_v @ e2 @ ( vE_r_l_v @ ( rid_r_l_v @ right_forkee ) ) ) ) ) ) ) @ right_forkee
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma2 @ tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ e4 ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_9__092_060open_062r_A_092_060noteq_062_Aleft__forkee_092_060close_062,axiom,
% 2.97/1.58 r2 != left_forkee ).
% 2.97/1.58
% 2.97/1.58 thf(fact_10_r__unchanged__right,axiom,
% 2.97/1.58 ( ( s_22 @ r2 )
% 2.97/1.58 = ( s_1 @ r2 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_11_reach,axiom,
% 2.97/1.58 reachable_r_l_v @ subst @ s_1 ).
% 2.97/1.58
% 2.97/1.58 thf(fact_12_left__step,axiom,
% 2.97/1.58 revision_step_r_l_v @ subst @ r2 @ s_1 @ s_2 ).
% 2.97/1.58
% 2.97/1.58 thf(fact_13_only__fork__introduces__rids_H,axiom,
% 2.97/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 2.97/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.58 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v] :
% 2.97/1.58 ( ( S @ R )
% 2.97/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E2 ) ) ) ) ) )
% 2.97/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 2.97/1.58 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_14_revision__step_Ofork,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 2.97/1.58 ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 2.97/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 2.97/1.58 => ( revision_step_r_l_v @ subst @ R @ S
% 2.97/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_15_fork__pseudodeterministic,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.58 = ( ? [R3: r] :
% 2.97/1.58 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
% 2.97/1.58 & ( S2
% 2.97/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_16_substitution__axioms,axiom,
% 2.97/1.58 substitution_r_l_v @ subst ).
% 2.97/1.58
% 2.97/1.58 thf(fact_17_revision__step__relaxed_Ofork,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 2.97/1.58 ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 2.97/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 2.97/1.58 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 2.97/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_18_local__and__fork__commute,axiom,
% 2.97/1.58 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
% 2.97/1.58 ( ( S_2
% 2.97/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 2.97/1.58 => ( ( S_22
% 2.97/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) ) )
% 2.97/1.58 => ( ( ( S_2 @ R2 )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 2.97/1.58 => ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S_22
% 2.97/1.58 @ ( fun_up709272714_r_l_v
% 2.97/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) )
% 2.97/1.58 @ R
% 2.97/1.58 @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 2.97/1.58 => ( ( R != R2 )
% 2.97/1.58 => ( ( R != R4 )
% 2.97/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.58 | ( S_2 = S_3 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_19_s_092_060_094sub_0622,axiom,
% 2.97/1.58 ( s_2
% 2.97/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ left_forkee ) ) ) ) ) ) ) @ left_forkee
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ e3 ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_20_restrictions__inwards,axiom,
% 2.97/1.58 ! [X2: r,X3: r,F: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( X2 != X3 )
% 2.97/1.58 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X2 @ ( some_P1807977723_r_l_v @ Y ) ) @ X3 @ none_P277133687_r_l_v )
% 2.97/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X3 @ none_P277133687_r_l_v ) @ X2 @ ( some_P1807977723_r_l_v @ Y ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_21_restrictions__inwards,axiom,
% 2.97/1.58 ! [X2: l,X3: l,F: l > option_val_r_l_v,Y: val_r_l_v] :
% 2.97/1.58 ( ( X2 != X3 )
% 2.97/1.58 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X2 @ ( some_val_r_l_v @ Y ) ) @ X3 @ none_val_r_l_v )
% 2.97/1.58 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X3 @ none_val_r_l_v ) @ X2 @ ( some_val_r_l_v @ Y ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_22_empty__upd__none,axiom,
% 2.97/1.58 ! [X2: l] :
% 2.97/1.58 ( ( fun_up1835647912_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ X2
% 2.97/1.58 @ none_val_r_l_v )
% 2.97/1.58 = ( ^ [X: l] : none_val_r_l_v ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_23_empty__upd__none,axiom,
% 2.97/1.58 ! [X2: r] :
% 2.97/1.58 ( ( fun_up709272714_r_l_v
% 2.97/1.58 @ ^ [X: r] : none_P277133687_r_l_v
% 2.97/1.58 @ X2
% 2.97/1.58 @ none_P277133687_r_l_v )
% 2.97/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_24_RID_092_060_094sub_062GI_I1_J,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r,V: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ V ) )
% 2.97/1.58 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_25_not__None__eq,axiom,
% 2.97/1.58 ! [X2: option1457017436_r_l_v] :
% 2.97/1.58 ( ( X2 != none_P277133687_r_l_v )
% 2.97/1.58 = ( ? [Y2: produc1156025366_r_l_v] :
% 2.97/1.58 ( X2
% 2.97/1.58 = ( some_P1807977723_r_l_v @ Y2 ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_26_not__None__eq,axiom,
% 2.97/1.58 ! [X2: option_val_r_l_v] :
% 2.97/1.58 ( ( X2 != none_val_r_l_v )
% 2.97/1.58 = ( ? [Y2: val_r_l_v] :
% 2.97/1.58 ( X2
% 2.97/1.58 = ( some_val_r_l_v @ Y2 ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_27_not__Some__eq,axiom,
% 2.97/1.58 ! [X2: option1457017436_r_l_v] :
% 2.97/1.58 ( ( ! [Y2: produc1156025366_r_l_v] :
% 2.97/1.58 ( X2
% 2.97/1.58 != ( some_P1807977723_r_l_v @ Y2 ) ) )
% 2.97/1.58 = ( X2 = none_P277133687_r_l_v ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_28_not__Some__eq,axiom,
% 2.97/1.58 ! [X2: option_val_r_l_v] :
% 2.97/1.58 ( ( ! [Y2: val_r_l_v] :
% 2.97/1.58 ( X2
% 2.97/1.58 != ( some_val_r_l_v @ Y2 ) ) )
% 2.97/1.58 = ( X2 = none_val_r_l_v ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_29_s_092_060_094sub_0621__r,axiom,
% 2.97/1.58 ( ( s_1 @ r2 )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e3 ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_30_local__steps__commute,axiom,
% 2.97/1.58 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( S_2
% 2.97/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 2.97/1.58 => ( ( S_22
% 2.97/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 2.97/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.58 | ( S_2 = S_3 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_31_only__fork__introduces__rids,axiom,
% 2.97/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.58 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v] :
% 2.97/1.58 ( ( S @ R )
% 2.97/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E2 ) ) ) ) ) )
% 2.97/1.58 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_32_local__determinism,axiom,
% 2.97/1.58 ! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_22 )
% 2.97/1.58 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_33_SLC__sym,axiom,
% 2.97/1.58 ! [R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_33 )
% 2.97/1.58 | ( S_2 = S_33 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_34 )
% 2.97/1.58 | ( S_22 = S_34 ) ) )
% 2.97/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_3 )
% 2.97/1.58 | ( S_22 = S_3 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_32 )
% 2.97/1.58 | ( S_2 = S_32 ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_34_SLC__commute,axiom,
% 2.97/1.58 ! [S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( S_35 = S_36 )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 2.97/1.58 => ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 2.97/1.58 | ( S_2 = S_35 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 2.97/1.58 | ( S_22 = S_36 ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_35_reachability__closed__under__execution__step,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.58 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_36_option_Oinject,axiom,
% 2.97/1.58 ! [X22: produc1156025366_r_l_v,Y22: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( ( some_P1807977723_r_l_v @ X22 )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ Y22 ) )
% 2.97/1.58 = ( X22 = Y22 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_37_option_Oinject,axiom,
% 2.97/1.58 ! [X22: val_r_l_v,Y22: val_r_l_v] :
% 2.97/1.58 ( ( ( some_val_r_l_v @ X22 )
% 2.97/1.58 = ( some_val_r_l_v @ Y22 ) )
% 2.97/1.58 = ( X22 = Y22 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_38_transition__relations__equivalent,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.58 = ( revisi1291188644_r_l_v @ subst @ R @ S @ S2 ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_39_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 2.97/1.58 ! [R2: r,S: r > option1457017436_r_l_v,R: r] :
% 2.97/1.58 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 2.97/1.58 => ( member_r @ R2 @ ( rID_G_r_l_v @ S ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_40_in__restricted__global__in__updated__global_I1_J,axiom,
% 2.97/1.58 ! [R2: r,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 2.97/1.58 => ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_41_reachable__def,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.58 = ( ? [E5: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ subst @ E5 @ S3 @ S ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_42_substitution_Olocal__determinism,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_22 )
% 2.97/1.58 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_43_substitution_OSLC__commute,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( S_35 = S_36 )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 2.97/1.58 => ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 2.97/1.58 | ( S_2 = S_35 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 2.97/1.58 | ( S_22 = S_36 ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_44_substitution_OSLC__sym,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_33 )
% 2.97/1.58 | ( S_2 = S_33 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_34 )
% 2.97/1.58 | ( S_22 = S_34 ) ) )
% 2.97/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_3 )
% 2.97/1.58 | ( S_22 = S_3 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_32 )
% 2.97/1.58 | ( S_2 = S_32 ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_45_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r] : ( ord_less_eq_set_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) @ ( rID_G_r_l_v @ S ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_46_substitution_Olocal__steps__commute,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( S_2
% 2.97/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 2.97/1.58 => ( ( S_22
% 2.97/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 2.97/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 2.97/1.58 | ( S_2 = S_3 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 2.97/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_47_substitution_Olocal__and__fork__commute,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( S_2
% 2.97/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 2.97/1.58 => ( ( S_22
% 2.97/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) ) )
% 2.97/1.58 => ( ( ( S_2 @ R2 )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 2.97/1.58 => ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S_22
% 2.97/1.58 @ ( fun_up709272714_r_l_v
% 2.97/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) )
% 2.97/1.58 @ R
% 2.97/1.58 @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 2.97/1.58 => ( ( R != R2 )
% 2.97/1.58 => ( ( R != R4 )
% 2.97/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 2.97/1.58 | ( S_2 = S_3 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 2.97/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_48_combine__options__cases,axiom,
% 2.97/1.58 ! [X2: option1457017436_r_l_v,P: option1457017436_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 2.97/1.58 ( ( ( X2 = none_P277133687_r_l_v )
% 2.97/1.58 => ( P @ X2 @ Y ) )
% 2.97/1.58 => ( ( ( Y = none_P277133687_r_l_v )
% 2.97/1.58 => ( P @ X2 @ Y ) )
% 2.97/1.58 => ( ! [A: produc1156025366_r_l_v,B: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( X2
% 2.97/1.58 = ( some_P1807977723_r_l_v @ A ) )
% 2.97/1.58 => ( ( Y
% 2.97/1.58 = ( some_P1807977723_r_l_v @ B ) )
% 2.97/1.58 => ( P @ X2 @ Y ) ) )
% 2.97/1.58 => ( P @ X2 @ Y ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_49_combine__options__cases,axiom,
% 2.97/1.58 ! [X2: option1457017436_r_l_v,P: option1457017436_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 2.97/1.58 ( ( ( X2 = none_P277133687_r_l_v )
% 2.97/1.58 => ( P @ X2 @ Y ) )
% 2.97/1.58 => ( ( ( Y = none_val_r_l_v )
% 2.97/1.58 => ( P @ X2 @ Y ) )
% 2.97/1.58 => ( ! [A: produc1156025366_r_l_v,B: val_r_l_v] :
% 2.97/1.58 ( ( X2
% 2.97/1.58 = ( some_P1807977723_r_l_v @ A ) )
% 2.97/1.58 => ( ( Y
% 2.97/1.58 = ( some_val_r_l_v @ B ) )
% 2.97/1.58 => ( P @ X2 @ Y ) ) )
% 2.97/1.58 => ( P @ X2 @ Y ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_50_combine__options__cases,axiom,
% 2.97/1.58 ! [X2: option_val_r_l_v,P: option_val_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 2.97/1.58 ( ( ( X2 = none_val_r_l_v )
% 2.97/1.58 => ( P @ X2 @ Y ) )
% 2.97/1.58 => ( ( ( Y = none_P277133687_r_l_v )
% 2.97/1.58 => ( P @ X2 @ Y ) )
% 2.97/1.58 => ( ! [A: val_r_l_v,B: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( X2
% 2.97/1.58 = ( some_val_r_l_v @ A ) )
% 2.97/1.58 => ( ( Y
% 2.97/1.58 = ( some_P1807977723_r_l_v @ B ) )
% 2.97/1.58 => ( P @ X2 @ Y ) ) )
% 2.97/1.58 => ( P @ X2 @ Y ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_51_combine__options__cases,axiom,
% 2.97/1.58 ! [X2: option_val_r_l_v,P: option_val_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 2.97/1.58 ( ( ( X2 = none_val_r_l_v )
% 2.97/1.58 => ( P @ X2 @ Y ) )
% 2.97/1.58 => ( ( ( Y = none_val_r_l_v )
% 2.97/1.58 => ( P @ X2 @ Y ) )
% 2.97/1.58 => ( ! [A: val_r_l_v,B: val_r_l_v] :
% 2.97/1.58 ( ( X2
% 2.97/1.58 = ( some_val_r_l_v @ A ) )
% 2.97/1.58 => ( ( Y
% 2.97/1.58 = ( some_val_r_l_v @ B ) )
% 2.97/1.58 => ( P @ X2 @ Y ) ) )
% 2.97/1.58 => ( P @ X2 @ Y ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_52_mem__Collect__eq,axiom,
% 2.97/1.58 ! [A2: set_l,P: set_l > $o] :
% 2.97/1.58 ( ( member_set_l @ A2 @ ( collect_set_l @ P ) )
% 2.97/1.58 = ( P @ A2 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_53_mem__Collect__eq,axiom,
% 2.97/1.58 ! [A2: set_r,P: set_r > $o] :
% 2.97/1.58 ( ( member_set_r @ A2 @ ( collect_set_r @ P ) )
% 2.97/1.58 = ( P @ A2 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_54_mem__Collect__eq,axiom,
% 2.97/1.58 ! [A2: r,P: r > $o] :
% 2.97/1.58 ( ( member_r @ A2 @ ( collect_r @ P ) )
% 2.97/1.58 = ( P @ A2 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_55_mem__Collect__eq,axiom,
% 2.97/1.58 ! [A2: l,P: l > $o] :
% 2.97/1.58 ( ( member_l @ A2 @ ( collect_l @ P ) )
% 2.97/1.58 = ( P @ A2 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_56_mem__Collect__eq,axiom,
% 2.97/1.58 ! [A2: produc1389397445_r_l_v,P: produc1389397445_r_l_v > $o] :
% 2.97/1.58 ( ( member1522896238_r_l_v @ A2 @ ( collec1978425008_r_l_v @ P ) )
% 2.97/1.58 = ( P @ A2 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_57_Collect__mem__eq,axiom,
% 2.97/1.58 ! [A3: set_set_l] :
% 2.97/1.58 ( ( collect_set_l
% 2.97/1.58 @ ^ [X: set_l] : ( member_set_l @ X @ A3 ) )
% 2.97/1.58 = A3 ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_58_Collect__mem__eq,axiom,
% 2.97/1.58 ! [A3: set_set_r] :
% 2.97/1.58 ( ( collect_set_r
% 2.97/1.58 @ ^ [X: set_r] : ( member_set_r @ X @ A3 ) )
% 2.97/1.58 = A3 ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_59_Collect__mem__eq,axiom,
% 2.97/1.58 ! [A3: set_r] :
% 2.97/1.58 ( ( collect_r
% 2.97/1.58 @ ^ [X: r] : ( member_r @ X @ A3 ) )
% 2.97/1.58 = A3 ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_60_Collect__mem__eq,axiom,
% 2.97/1.58 ! [A3: set_l] :
% 2.97/1.58 ( ( collect_l
% 2.97/1.58 @ ^ [X: l] : ( member_l @ X @ A3 ) )
% 2.97/1.58 = A3 ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_61_Collect__mem__eq,axiom,
% 2.97/1.58 ! [A3: set_Pr1409704485_r_l_v] :
% 2.97/1.58 ( ( collec1978425008_r_l_v
% 2.97/1.58 @ ^ [X: produc1389397445_r_l_v] : ( member1522896238_r_l_v @ X @ A3 ) )
% 2.97/1.58 = A3 ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_62_Collect__cong,axiom,
% 2.97/1.58 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 2.97/1.58 ( ! [X4: produc1389397445_r_l_v] :
% 2.97/1.58 ( ( P @ X4 )
% 2.97/1.58 = ( Q @ X4 ) )
% 2.97/1.58 => ( ( collec1978425008_r_l_v @ P )
% 2.97/1.58 = ( collec1978425008_r_l_v @ Q ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_63_Collect__cong,axiom,
% 2.97/1.58 ! [P: l > $o,Q: l > $o] :
% 2.97/1.58 ( ! [X4: l] :
% 2.97/1.58 ( ( P @ X4 )
% 2.97/1.58 = ( Q @ X4 ) )
% 2.97/1.58 => ( ( collect_l @ P )
% 2.97/1.58 = ( collect_l @ Q ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_64_Collect__cong,axiom,
% 2.97/1.58 ! [P: r > $o,Q: r > $o] :
% 2.97/1.58 ( ! [X4: r] :
% 2.97/1.58 ( ( P @ X4 )
% 2.97/1.58 = ( Q @ X4 ) )
% 2.97/1.58 => ( ( collect_r @ P )
% 2.97/1.58 = ( collect_r @ Q ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_65_Collect__cong,axiom,
% 2.97/1.58 ! [P: set_l > $o,Q: set_l > $o] :
% 2.97/1.58 ( ! [X4: set_l] :
% 2.97/1.58 ( ( P @ X4 )
% 2.97/1.58 = ( Q @ X4 ) )
% 2.97/1.58 => ( ( collect_set_l @ P )
% 2.97/1.58 = ( collect_set_l @ Q ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_66_Collect__cong,axiom,
% 2.97/1.58 ! [P: set_r > $o,Q: set_r > $o] :
% 2.97/1.58 ( ! [X4: set_r] :
% 2.97/1.58 ( ( P @ X4 )
% 2.97/1.58 = ( Q @ X4 ) )
% 2.97/1.58 => ( ( collect_set_r @ P )
% 2.97/1.58 = ( collect_set_r @ Q ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_67_split__option__all,axiom,
% 2.97/1.58 ( ( ^ [P2: option1457017436_r_l_v > $o] :
% 2.97/1.58 ! [X5: option1457017436_r_l_v] : ( P2 @ X5 ) )
% 2.97/1.58 = ( ^ [P3: option1457017436_r_l_v > $o] :
% 2.97/1.58 ( ( P3 @ none_P277133687_r_l_v )
% 2.97/1.58 & ! [X: produc1156025366_r_l_v] : ( P3 @ ( some_P1807977723_r_l_v @ X ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_68_split__option__all,axiom,
% 2.97/1.58 ( ( ^ [P2: option_val_r_l_v > $o] :
% 2.97/1.58 ! [X5: option_val_r_l_v] : ( P2 @ X5 ) )
% 2.97/1.58 = ( ^ [P3: option_val_r_l_v > $o] :
% 2.97/1.58 ( ( P3 @ none_val_r_l_v )
% 2.97/1.58 & ! [X: val_r_l_v] : ( P3 @ ( some_val_r_l_v @ X ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_69_split__option__ex,axiom,
% 2.97/1.58 ( ( ^ [P2: option1457017436_r_l_v > $o] :
% 2.97/1.58 ? [X5: option1457017436_r_l_v] : ( P2 @ X5 ) )
% 2.97/1.58 = ( ^ [P3: option1457017436_r_l_v > $o] :
% 2.97/1.58 ( ( P3 @ none_P277133687_r_l_v )
% 2.97/1.58 | ? [X: produc1156025366_r_l_v] : ( P3 @ ( some_P1807977723_r_l_v @ X ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_70_split__option__ex,axiom,
% 2.97/1.58 ( ( ^ [P2: option_val_r_l_v > $o] :
% 2.97/1.58 ? [X5: option_val_r_l_v] : ( P2 @ X5 ) )
% 2.97/1.58 = ( ^ [P3: option_val_r_l_v > $o] :
% 2.97/1.58 ( ( P3 @ none_val_r_l_v )
% 2.97/1.58 | ? [X: val_r_l_v] : ( P3 @ ( some_val_r_l_v @ X ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_71_option_Oinducts,axiom,
% 2.97/1.58 ! [P: option1457017436_r_l_v > $o,Option: option1457017436_r_l_v] :
% 2.97/1.58 ( ( P @ none_P277133687_r_l_v )
% 2.97/1.58 => ( ! [X4: produc1156025366_r_l_v] : ( P @ ( some_P1807977723_r_l_v @ X4 ) )
% 2.97/1.58 => ( P @ Option ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_72_option_Oinducts,axiom,
% 2.97/1.58 ! [P: option_val_r_l_v > $o,Option: option_val_r_l_v] :
% 2.97/1.58 ( ( P @ none_val_r_l_v )
% 2.97/1.58 => ( ! [X4: val_r_l_v] : ( P @ ( some_val_r_l_v @ X4 ) )
% 2.97/1.58 => ( P @ Option ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_73_option_Oexhaust,axiom,
% 2.97/1.58 ! [Y: option1457017436_r_l_v] :
% 2.97/1.58 ( ( Y != none_P277133687_r_l_v )
% 2.97/1.58 => ~ ! [X23: produc1156025366_r_l_v] :
% 2.97/1.58 ( Y
% 2.97/1.58 != ( some_P1807977723_r_l_v @ X23 ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_74_option_Oexhaust,axiom,
% 2.97/1.58 ! [Y: option_val_r_l_v] :
% 2.97/1.58 ( ( Y != none_val_r_l_v )
% 2.97/1.58 => ~ ! [X23: val_r_l_v] :
% 2.97/1.58 ( Y
% 2.97/1.58 != ( some_val_r_l_v @ X23 ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_75_option_OdiscI,axiom,
% 2.97/1.58 ! [Option: option1457017436_r_l_v,X22: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( Option
% 2.97/1.58 = ( some_P1807977723_r_l_v @ X22 ) )
% 2.97/1.58 => ( Option != none_P277133687_r_l_v ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_76_option_OdiscI,axiom,
% 2.97/1.58 ! [Option: option_val_r_l_v,X22: val_r_l_v] :
% 2.97/1.58 ( ( Option
% 2.97/1.58 = ( some_val_r_l_v @ X22 ) )
% 2.97/1.58 => ( Option != none_val_r_l_v ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_77_option_Odistinct_I1_J,axiom,
% 2.97/1.58 ! [X22: produc1156025366_r_l_v] :
% 2.97/1.58 ( none_P277133687_r_l_v
% 2.97/1.58 != ( some_P1807977723_r_l_v @ X22 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_78_option_Odistinct_I1_J,axiom,
% 2.97/1.58 ! [X22: val_r_l_v] :
% 2.97/1.58 ( none_val_r_l_v
% 2.97/1.58 != ( some_val_r_l_v @ X22 ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_79_map__upd__Some__unfold,axiom,
% 2.97/1.58 ! [M: r > option1457017436_r_l_v,A2: r,B2: produc1156025366_r_l_v,X2: r,Y: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( ( fun_up709272714_r_l_v @ M @ A2 @ ( some_P1807977723_r_l_v @ B2 ) @ X2 )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ Y ) )
% 2.97/1.58 = ( ( ( X2 = A2 )
% 2.97/1.58 & ( B2 = Y ) )
% 2.97/1.58 | ( ( X2 != A2 )
% 2.97/1.58 & ( ( M @ X2 )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ Y ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_80_map__upd__Some__unfold,axiom,
% 2.97/1.58 ! [M: l > option_val_r_l_v,A2: l,B2: val_r_l_v,X2: l,Y: val_r_l_v] :
% 2.97/1.58 ( ( ( fun_up1835647912_r_l_v @ M @ A2 @ ( some_val_r_l_v @ B2 ) @ X2 )
% 2.97/1.58 = ( some_val_r_l_v @ Y ) )
% 2.97/1.58 = ( ( ( X2 = A2 )
% 2.97/1.58 & ( B2 = Y ) )
% 2.97/1.58 | ( ( X2 != A2 )
% 2.97/1.58 & ( ( M @ X2 )
% 2.97/1.58 = ( some_val_r_l_v @ Y ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_81_map__upd__triv,axiom,
% 2.97/1.58 ! [T: r > option1457017436_r_l_v,K: r,X2: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( ( T @ K )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ X2 ) )
% 2.97/1.58 => ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X2 ) )
% 2.97/1.58 = T ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_82_map__upd__triv,axiom,
% 2.97/1.58 ! [T: l > option_val_r_l_v,K: l,X2: val_r_l_v] :
% 2.97/1.58 ( ( ( T @ K )
% 2.97/1.58 = ( some_val_r_l_v @ X2 ) )
% 2.97/1.58 => ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X2 ) )
% 2.97/1.58 = T ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_83_map__upd__eqD1,axiom,
% 2.97/1.58 ! [M: r > option1457017436_r_l_v,A2: r,X2: produc1156025366_r_l_v,N: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( ( fun_up709272714_r_l_v @ M @ A2 @ ( some_P1807977723_r_l_v @ X2 ) )
% 2.97/1.58 = ( fun_up709272714_r_l_v @ N @ A2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 2.97/1.58 => ( X2 = Y ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_84_map__upd__eqD1,axiom,
% 2.97/1.58 ! [M: l > option_val_r_l_v,A2: l,X2: val_r_l_v,N: l > option_val_r_l_v,Y: val_r_l_v] :
% 2.97/1.58 ( ( ( fun_up1835647912_r_l_v @ M @ A2 @ ( some_val_r_l_v @ X2 ) )
% 2.97/1.58 = ( fun_up1835647912_r_l_v @ N @ A2 @ ( some_val_r_l_v @ Y ) ) )
% 2.97/1.58 => ( X2 = Y ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_85_map__upd__nonempty,axiom,
% 2.97/1.58 ! [T: r > option1457017436_r_l_v,K: r,X2: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X2 ) )
% 2.97/1.58 != ( ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_86_map__upd__nonempty,axiom,
% 2.97/1.58 ! [T: l > option_val_r_l_v,K: l,X2: val_r_l_v] :
% 2.97/1.58 ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X2 ) )
% 2.97/1.58 != ( ^ [X: l] : none_val_r_l_v ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_87_substitution_Ofork__pseudodeterministic,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.58 = ( ? [R3: r] :
% 2.97/1.58 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
% 2.97/1.58 & ( S2
% 2.97/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_88_inductive__invariant__is__execution__invariant,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 2.97/1.58 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.58 => ( ( induct1670415253_r_l_v @ subst @ P )
% 2.97/1.58 => ( P @ S ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_89_substitution_Orevision__step__relaxed_Ofork,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 2.97/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 2.97/1.58 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 2.97/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_90_substitution_Orevision__step_Ofork,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 2.97/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 2.97/1.58 => ( revision_step_r_l_v @ Subst @ R @ S
% 2.97/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 2.97/1.58 @ ( some_P1807977723_r_l_v
% 2.97/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 2.97/1.58 @ ( produc1834103605_r_l_v
% 2.97/1.58 @ ^ [X: l] : none_val_r_l_v
% 2.97/1.58 @ E4 ) ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_91_substitution_Oonly__fork__introduces__rids,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.58 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v] :
% 2.97/1.58 ( ( S @ R )
% 2.97/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E2 ) ) ) ) ) )
% 2.97/1.58 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_92_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.58 => ( domain1547879849_r_l_v @ S ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_93_substitution_Oonly__fork__introduces__rids_H,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.58 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v] :
% 2.97/1.58 ( ( S @ R )
% 2.97/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E2 ) ) ) ) ) )
% 2.97/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 2.97/1.58 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_94_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 2.97/1.58 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( ( S_1 @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 2.97/1.58 => ( ( S_2
% 2.97/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) )
% 2.97/1.58 => ( ( ( S_1 @ R4 )
% 2.97/1.58 = none_P277133687_r_l_v )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 2.97/1.58 => ( ( R != R2 )
% 2.97/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.58 | ( S_2 = S_3 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_95_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r] :
% 2.97/1.58 ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.58 => ( ( ( S @ R2 )
% 2.97/1.58 = none_P277133687_r_l_v )
% 2.97/1.58 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 2.97/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_96_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r] :
% 2.97/1.58 ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.58 => ( ( ( S @ R2 )
% 2.97/1.58 = none_P277133687_r_l_v )
% 2.97/1.58 => ( revision_step_r_l_v @ subst @ R @ S
% 2.97/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_97_domains__subsume__globally__def,axiom,
% 2.97/1.58 ( domain1547879849_r_l_v
% 2.97/1.58 = ( ^ [S4: r > option1457017436_r_l_v] :
% 2.97/1.58 ! [R5: r,Ls2: produc1156025366_r_l_v] :
% 2.97/1.58 ( ( ( S4 @ R5 )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 2.97/1.58 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_98_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 2.97/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.58 => ( ( ( S @ R2 )
% 2.97/1.58 = none_P277133687_r_l_v )
% 2.97/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.58 = ( S2
% 2.97/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_99_substitution_Orevision__step_Ocong,axiom,
% 2.97/1.58 revision_step_r_l_v = revision_step_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(fact_100_substitution_Orevision__step__relaxed_Ocong,axiom,
% 2.97/1.58 revisi1291188644_r_l_v = revisi1291188644_r_l_v ).
% 2.97/1.58
% 2.97/1.58 thf(fact_101_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.58 => ( ( ( S @ R2 )
% 2.97/1.58 = none_P277133687_r_l_v )
% 2.97/1.58 => ( revision_step_r_l_v @ Subst @ R @ S
% 2.97/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_102_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.58 => ( ( ( S @ R2 )
% 2.97/1.58 = none_P277133687_r_l_v )
% 2.97/1.58 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 2.97/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_103_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( ( S @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.58 => ( ( ( S @ R2 )
% 2.97/1.58 = none_P277133687_r_l_v )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.58 = ( S2
% 2.97/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_104_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 2.97/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( substitution_r_l_v @ Subst )
% 2.97/1.58 => ( ( ( S_1 @ R )
% 2.97/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 2.97/1.58 => ( ( S_2
% 2.97/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) )
% 2.97/1.58 => ( ( ( S_1 @ R4 )
% 2.97/1.58 = none_P277133687_r_l_v )
% 2.97/1.58 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 2.97/1.58 => ( ( R != R2 )
% 2.97/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 2.97/1.58 | ( S_2 = S_3 ) )
% 2.97/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 2.97/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 2.97/1.58
% 2.97/1.58 thf(fact_105_nice__ind__inv__is__inductive__invariant,axiom,
% 2.97/1.58 ( induct1670415253_r_l_v @ subst
% 2.97/1.59 @ ^ [S4: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( domain1547879849_r_l_v @ S4 )
% 2.97/1.59 & ( subsum680764357_r_l_v @ S4 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_106_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 2.97/1.59 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 => ( ( domain1547879849_r_l_v @ S )
% 2.97/1.59 => ( ( subsum680764357_r_l_v @ S )
% 2.97/1.59 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_107_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 2.97/1.59 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 => ( ( domain1547879849_r_l_v @ S )
% 2.97/1.59 => ( ( subsum680764357_r_l_v @ S )
% 2.97/1.59 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_108_substitution_Odomains__subsume__globallyI,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ! [R6: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E2: expr_r_l_v] :
% 2.97/1.59 ( ( ( S @ R6 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) )
% 2.97/1.59 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) )
% 2.97/1.59 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_109_substitution_Otransition__relations__equivalent,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 = ( revisi1291188644_r_l_v @ Subst @ R @ S @ S2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_110_domains__subsume__globallyI,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ! [R6: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E2: expr_r_l_v] :
% 2.97/1.59 ( ( ( S @ R6 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) )
% 2.97/1.59 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) )
% 2.97/1.59 => ( domain1547879849_r_l_v @ S ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_111_substitution_Oreachable__def,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S )
% 2.97/1.59 = ( ? [E5: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ Subst @ E5 @ S3 @ S ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_112_substitution_Oreachable_Ocong,axiom,
% 2.97/1.59 reachable_r_l_v = reachable_r_l_v ).
% 2.97/1.59
% 2.97/1.59 thf(fact_113_substitution_Oinductive__invariant_Ocong,axiom,
% 2.97/1.59 induct1670415253_r_l_v = induct1670415253_r_l_v ).
% 2.97/1.59
% 2.97/1.59 thf(fact_114_substitution_Oexecution_Ocong,axiom,
% 2.97/1.59 execution_r_l_v = execution_r_l_v ).
% 2.97/1.59
% 2.97/1.59 thf(fact_115_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( induct1670415253_r_l_v @ Subst
% 2.97/1.59 @ ^ [S4: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( domain1547879849_r_l_v @ S4 )
% 2.97/1.59 & ( subsum680764357_r_l_v @ S4 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_116_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 => ( ( domain1547879849_r_l_v @ S )
% 2.97/1.59 => ( ( subsum680764357_r_l_v @ S )
% 2.97/1.59 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_117_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 => ( ( domain1547879849_r_l_v @ S )
% 2.97/1.59 => ( ( subsum680764357_r_l_v @ S )
% 2.97/1.59 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_118_substitution_Odomains__subsume__globally__def,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( domain1547879849_r_l_v @ S )
% 2.97/1.59 = ( ! [R5: r,Ls2: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( ( S @ R5 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 2.97/1.59 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_119_substitution_Oreachability__closed__under__execution__step,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 => ( reachable_r_l_v @ Subst @ S2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_120_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S )
% 2.97/1.59 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_121_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S )
% 2.97/1.59 => ( ( induct1670415253_r_l_v @ Subst @ P )
% 2.97/1.59 => ( P @ S ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_122_substitution_Osubsumes__accessible__globallyI,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ! [R_1: r,Sigma_1: l > option_val_r_l_v,Tau_1: l > option_val_r_l_v,E_1: expr_r_l_v,R_2: r,Sigma_2: l > option_val_r_l_v,Tau_2: l > option_val_r_l_v,E_2: expr_r_l_v] :
% 2.97/1.59 ( ( ( S @ R_1 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 2.97/1.59 => ( ( ( S @ R_2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 2.97/1.59 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 2.97/1.59 => ( subsum680764357_r_l_v @ S ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_123_join__and__local__commute,axiom,
% 2.97/1.59 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
% 2.97/1.59 ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 2.97/1.59 => ( ( S_22
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ( ( R2 != R4 )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 2.97/1.59 => ( ( ( S_22 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( ( S_22 @ R4 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_124_SLC__join,axiom,
% 2.97/1.59 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 2.97/1.59 => ( ( ( S_1 @ R4 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_125_revision__step__relaxed_Ojoin,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_126_reachable__imp__identifiers__finite_I1_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.59 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_127_revision__step_Ojoin,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_128_empty__map__finite_I3_J,axiom,
% 2.97/1.59 ( finite_finite_r
% 2.97/1.59 @ ( rID_G_r_l_v
% 2.97/1.59 @ ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_129_rid__inf,axiom,
% 2.97/1.59 ~ ( finite_finite_r @ top_top_set_r ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_130_RID_092_060_094sub_062G__finite__invariant,axiom,
% 2.97/1.59 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 2.97/1.59 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_131_finite__state__imp__restriction__finite_I1_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r] :
% 2.97/1.59 ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 2.97/1.59 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_132_subsumes__accessible__globallyI,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ! [R_1: r,Sigma_1: l > option_val_r_l_v,Tau_1: l > option_val_r_l_v,E_1: expr_r_l_v,R_2: r,Sigma_2: l > option_val_r_l_v,Tau_2: l > option_val_r_l_v,E_2: expr_r_l_v] :
% 2.97/1.59 ( ( ( S @ R_1 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 2.97/1.59 => ( ( ( S @ R_2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 2.97/1.59 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 2.97/1.59 => ( subsum680764357_r_l_v @ S ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_133_rjoin__deterministic,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 = ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_134_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 2.97/1.59 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_135_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S )
% 2.97/1.59 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_136_substitution_Oempty__map__finite_I3_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( finite_finite_r
% 2.97/1.59 @ ( rID_G_r_l_v
% 2.97/1.59 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_137_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 2.97/1.59 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_138_substitution_Orevision__step_Ojoin,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_139_substitution_Orjoin__deterministic,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 = ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_140_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_141_substitution_OSLC__join,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 2.97/1.59 => ( ( ( S_1 @ R4 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_142_substitution_Ojoin__and__local__commute,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E3: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 2.97/1.59 => ( ( S_22
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ( ( R2 != R4 )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 2.97/1.59 => ( ( ( S_22 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( ( S_22 @ R4 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_143_finite__Collect__subsets,axiom,
% 2.97/1.59 ! [A3: set_Sum_sum_r_l] :
% 2.97/1.59 ( ( finite65649782um_r_l @ A3 )
% 2.97/1.59 => ( finite1407742636um_r_l
% 2.97/1.59 @ ( collec765168874um_r_l
% 2.97/1.59 @ ^ [B3: set_Sum_sum_r_l] : ( ord_le294536053um_r_l @ B3 @ A3 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_144_finite__Collect__subsets,axiom,
% 2.97/1.59 ! [A3: set_Sum_sum_l_r] :
% 2.97/1.59 ( ( finite1591053314um_l_r @ A3 )
% 2.97/1.59 => ( finite483212344um_l_r
% 2.97/1.59 @ ( collec1988122230um_l_r
% 2.97/1.59 @ ^ [B3: set_Sum_sum_l_r] : ( ord_le1517489409um_l_r @ B3 @ A3 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_145_finite__Collect__subsets,axiom,
% 2.97/1.59 ! [A3: set_Sum_sum_l_l] :
% 2.97/1.59 ( ( finite1541484284um_l_l @ A3 )
% 2.97/1.59 => ( finite88277554um_l_l
% 2.97/1.59 @ ( collec1593187440um_l_l
% 2.97/1.59 @ ^ [B3: set_Sum_sum_l_l] : ( ord_le1122554619um_l_l @ B3 @ A3 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_146_finite__Collect__subsets,axiom,
% 2.97/1.59 ! [A3: set_set_r] :
% 2.97/1.59 ( ( finite_finite_set_r @ A3 )
% 2.97/1.59 => ( finite1651563256_set_r
% 2.97/1.59 @ ( collect_set_set_r
% 2.97/1.59 @ ^ [B3: set_set_r] : ( ord_le363960431_set_r @ B3 @ A3 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_147_finite__Collect__subsets,axiom,
% 2.97/1.59 ! [A3: set_set_l] :
% 2.97/1.59 ( ( finite_finite_set_l @ A3 )
% 2.97/1.59 => ( finite1256628466_set_l
% 2.97/1.59 @ ( collect_set_set_l
% 2.97/1.59 @ ^ [B3: set_set_l] : ( ord_le2116509289_set_l @ B3 @ A3 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_148_finite__Collect__subsets,axiom,
% 2.97/1.59 ! [A3: set_r] :
% 2.97/1.59 ( ( finite_finite_r @ A3 )
% 2.97/1.59 => ( finite_finite_set_r
% 2.97/1.59 @ ( collect_set_r
% 2.97/1.59 @ ^ [B3: set_r] : ( ord_less_eq_set_r @ B3 @ A3 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_149_finite__Collect__subsets,axiom,
% 2.97/1.59 ! [A3: set_l] :
% 2.97/1.59 ( ( finite_finite_l @ A3 )
% 2.97/1.59 => ( finite_finite_set_l
% 2.97/1.59 @ ( collect_set_l
% 2.97/1.59 @ ^ [B3: set_l] : ( ord_less_eq_set_l @ B3 @ A3 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_150_reachable__imp__identifiers__available_I1_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.59 => ( ~ ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 => ? [R6: r] :
% 2.97/1.59 ~ ( member_r @ R6 @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_151_finite__Collect__conjI,axiom,
% 2.97/1.59 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 2.97/1.59 ( ( ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ P ) )
% 2.97/1.59 | ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ Q ) ) )
% 2.97/1.59 => ( finite1853159534_r_l_v
% 2.97/1.59 @ ( collec1978425008_r_l_v
% 2.97/1.59 @ ^ [X: produc1389397445_r_l_v] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 & ( Q @ X ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_152_finite__Collect__conjI,axiom,
% 2.97/1.59 ! [P: sum_sum_r_l > $o,Q: sum_sum_r_l > $o] :
% 2.97/1.59 ( ( ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ P ) )
% 2.97/1.59 | ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ Q ) ) )
% 2.97/1.59 => ( finite65649782um_r_l
% 2.97/1.59 @ ( collect_Sum_sum_r_l
% 2.97/1.59 @ ^ [X: sum_sum_r_l] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 & ( Q @ X ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_153_finite__Collect__conjI,axiom,
% 2.97/1.59 ! [P: sum_sum_l_r > $o,Q: sum_sum_l_r > $o] :
% 2.97/1.59 ( ( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
% 2.97/1.59 | ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ Q ) ) )
% 2.97/1.59 => ( finite1591053314um_l_r
% 2.97/1.59 @ ( collect_Sum_sum_l_r
% 2.97/1.59 @ ^ [X: sum_sum_l_r] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 & ( Q @ X ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_154_finite__Collect__conjI,axiom,
% 2.97/1.59 ! [P: sum_sum_l_l > $o,Q: sum_sum_l_l > $o] :
% 2.97/1.59 ( ( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
% 2.97/1.59 | ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ Q ) ) )
% 2.97/1.59 => ( finite1541484284um_l_l
% 2.97/1.59 @ ( collect_Sum_sum_l_l
% 2.97/1.59 @ ^ [X: sum_sum_l_l] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 & ( Q @ X ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_155_finite__Collect__conjI,axiom,
% 2.97/1.59 ! [P: set_r > $o,Q: set_r > $o] :
% 2.97/1.59 ( ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 2.97/1.59 | ( finite_finite_set_r @ ( collect_set_r @ Q ) ) )
% 2.97/1.59 => ( finite_finite_set_r
% 2.97/1.59 @ ( collect_set_r
% 2.97/1.59 @ ^ [X: set_r] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 & ( Q @ X ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_156_finite__Collect__conjI,axiom,
% 2.97/1.59 ! [P: set_l > $o,Q: set_l > $o] :
% 2.97/1.59 ( ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 2.97/1.59 | ( finite_finite_set_l @ ( collect_set_l @ Q ) ) )
% 2.97/1.59 => ( finite_finite_set_l
% 2.97/1.59 @ ( collect_set_l
% 2.97/1.59 @ ^ [X: set_l] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 & ( Q @ X ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_157_finite__Collect__conjI,axiom,
% 2.97/1.59 ! [P: r > $o,Q: r > $o] :
% 2.97/1.59 ( ( ( finite_finite_r @ ( collect_r @ P ) )
% 2.97/1.59 | ( finite_finite_r @ ( collect_r @ Q ) ) )
% 2.97/1.59 => ( finite_finite_r
% 2.97/1.59 @ ( collect_r
% 2.97/1.59 @ ^ [X: r] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 & ( Q @ X ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_158_finite__Collect__conjI,axiom,
% 2.97/1.59 ! [P: l > $o,Q: l > $o] :
% 2.97/1.59 ( ( ( finite_finite_l @ ( collect_l @ P ) )
% 2.97/1.59 | ( finite_finite_l @ ( collect_l @ Q ) ) )
% 2.97/1.59 => ( finite_finite_l
% 2.97/1.59 @ ( collect_l
% 2.97/1.59 @ ^ [X: l] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 & ( Q @ X ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_159_finite__Collect__disjI,axiom,
% 2.97/1.59 ! [P: sum_sum_l_r > $o,Q: sum_sum_l_r > $o] :
% 2.97/1.59 ( ( finite1591053314um_l_r
% 2.97/1.59 @ ( collect_Sum_sum_l_r
% 2.97/1.59 @ ^ [X: sum_sum_l_r] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 | ( Q @ X ) ) ) )
% 2.97/1.59 = ( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
% 2.97/1.59 & ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ Q ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_160_finite__Collect__disjI,axiom,
% 2.97/1.59 ! [P: sum_sum_l_l > $o,Q: sum_sum_l_l > $o] :
% 2.97/1.59 ( ( finite1541484284um_l_l
% 2.97/1.59 @ ( collect_Sum_sum_l_l
% 2.97/1.59 @ ^ [X: sum_sum_l_l] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 | ( Q @ X ) ) ) )
% 2.97/1.59 = ( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
% 2.97/1.59 & ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ Q ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_161_finite__Collect__disjI,axiom,
% 2.97/1.59 ! [P: set_r > $o,Q: set_r > $o] :
% 2.97/1.59 ( ( finite_finite_set_r
% 2.97/1.59 @ ( collect_set_r
% 2.97/1.59 @ ^ [X: set_r] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 | ( Q @ X ) ) ) )
% 2.97/1.59 = ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 2.97/1.59 & ( finite_finite_set_r @ ( collect_set_r @ Q ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_162_finite__Collect__disjI,axiom,
% 2.97/1.59 ! [P: set_l > $o,Q: set_l > $o] :
% 2.97/1.59 ( ( finite_finite_set_l
% 2.97/1.59 @ ( collect_set_l
% 2.97/1.59 @ ^ [X: set_l] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 | ( Q @ X ) ) ) )
% 2.97/1.59 = ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 2.97/1.59 & ( finite_finite_set_l @ ( collect_set_l @ Q ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_163_finite__Collect__disjI,axiom,
% 2.97/1.59 ! [P: r > $o,Q: r > $o] :
% 2.97/1.59 ( ( finite_finite_r
% 2.97/1.59 @ ( collect_r
% 2.97/1.59 @ ^ [X: r] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 | ( Q @ X ) ) ) )
% 2.97/1.59 = ( ( finite_finite_r @ ( collect_r @ P ) )
% 2.97/1.59 & ( finite_finite_r @ ( collect_r @ Q ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_164_finite__Collect__disjI,axiom,
% 2.97/1.59 ! [P: l > $o,Q: l > $o] :
% 2.97/1.59 ( ( finite_finite_l
% 2.97/1.59 @ ( collect_l
% 2.97/1.59 @ ^ [X: l] :
% 2.97/1.59 ( ( P @ X )
% 2.97/1.59 | ( Q @ X ) ) ) )
% 2.97/1.59 = ( ( finite_finite_l @ ( collect_l @ P ) )
% 2.97/1.59 & ( finite_finite_l @ ( collect_l @ Q ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_165_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 2.97/1.59 ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ Ls ) )
% 2.97/1.59 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_166_finite__option__UNIV,axiom,
% 2.97/1.59 ( ( finite16335230tion_r @ top_top_set_option_r )
% 2.97/1.59 = ( finite_finite_r @ top_top_set_r ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_167_finite__option__UNIV,axiom,
% 2.97/1.59 ( ( finite2114249848tion_l @ top_top_set_option_l )
% 2.97/1.59 = ( finite_finite_l @ top_top_set_l ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_168_finite__Plus__UNIV__iff,axiom,
% 2.97/1.59 ( ( finite115218812um_r_r @ top_to577862603um_r_r )
% 2.97/1.59 = ( ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_169_finite__Plus__UNIV__iff,axiom,
% 2.97/1.59 ( ( finite65649782um_r_l @ top_to182927813um_r_l )
% 2.97/1.59 = ( ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_170_finite__Plus__UNIV__iff,axiom,
% 2.97/1.59 ( ( finite1591053314um_l_r @ top_to1405881169um_l_r )
% 2.97/1.59 = ( ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_171_finite__Plus__UNIV__iff,axiom,
% 2.97/1.59 ( ( finite1541484284um_l_l @ top_to1010946379um_l_l )
% 2.97/1.59 = ( ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_172_finite__Collect__not,axiom,
% 2.97/1.59 ! [P: r > $o] :
% 2.97/1.59 ( ( finite_finite_r @ ( collect_r @ P ) )
% 2.97/1.59 => ( ( finite_finite_r
% 2.97/1.59 @ ( collect_r
% 2.97/1.59 @ ^ [X: r] :
% 2.97/1.59 ~ ( P @ X ) ) )
% 2.97/1.59 = ( finite_finite_r @ top_top_set_r ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_173_finite__Collect__not,axiom,
% 2.97/1.59 ! [P: l > $o] :
% 2.97/1.59 ( ( finite_finite_l @ ( collect_l @ P ) )
% 2.97/1.59 => ( ( finite_finite_l
% 2.97/1.59 @ ( collect_l
% 2.97/1.59 @ ^ [X: l] :
% 2.97/1.59 ~ ( P @ X ) ) )
% 2.97/1.59 = ( finite_finite_l @ top_top_set_l ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_174_RID_092_060_094sub_062GI_I2_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 2.97/1.59 ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ Ls ) )
% 2.97/1.59 => ( ( member_r @ R @ ( rID_L_l_r_v @ Ls ) )
% 2.97/1.59 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_175_Finite__Set_Ofinite__set,axiom,
% 2.97/1.59 ( ( finite_finite_set_r @ top_top_set_set_r )
% 2.97/1.59 = ( finite_finite_r @ top_top_set_r ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_176_Finite__Set_Ofinite__set,axiom,
% 2.97/1.59 ( ( finite_finite_set_l @ top_top_set_set_l )
% 2.97/1.59 = ( finite_finite_l @ top_top_set_l ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_177_finite__prod,axiom,
% 2.97/1.59 ( ( finite1507191824od_r_r @ top_to2034696215od_r_r )
% 2.97/1.59 = ( ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_178_finite__prod,axiom,
% 2.97/1.59 ( ( finite1457622794od_r_l @ top_to1639761425od_r_l )
% 2.97/1.59 = ( ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_179_finite__prod,axiom,
% 2.97/1.59 ( ( finite835542678od_l_r @ top_to715231133od_l_r )
% 2.97/1.59 = ( ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_180_finite__prod,axiom,
% 2.97/1.59 ( ( finite785973648od_l_l @ top_to320296343od_l_l )
% 2.97/1.59 = ( ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_181_ex__new__if__finite,axiom,
% 2.97/1.59 ! [A3: set_Pr1409704485_r_l_v] :
% 2.97/1.59 ( ~ ( finite1853159534_r_l_v @ top_to1238153077_r_l_v )
% 2.97/1.59 => ( ( finite1853159534_r_l_v @ A3 )
% 2.97/1.59 => ? [A: produc1389397445_r_l_v] :
% 2.97/1.59 ~ ( member1522896238_r_l_v @ A @ A3 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_182_ex__new__if__finite,axiom,
% 2.97/1.59 ! [A3: set_r] :
% 2.97/1.59 ( ~ ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 => ( ( finite_finite_r @ A3 )
% 2.97/1.59 => ? [A: r] :
% 2.97/1.59 ~ ( member_r @ A @ A3 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_183_ex__new__if__finite,axiom,
% 2.97/1.59 ! [A3: set_l] :
% 2.97/1.59 ( ~ ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ( ( finite_finite_l @ A3 )
% 2.97/1.59 => ? [A: l] :
% 2.97/1.59 ~ ( member_l @ A @ A3 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_184_finite__Prod__UNIV,axiom,
% 2.97/1.59 ( ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 => ( ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 => ( finite1507191824od_r_r @ top_to2034696215od_r_r ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_185_finite__Prod__UNIV,axiom,
% 2.97/1.59 ( ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 => ( ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ( finite1457622794od_r_l @ top_to1639761425od_r_l ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_186_finite__Prod__UNIV,axiom,
% 2.97/1.59 ( ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ( ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 => ( finite835542678od_l_r @ top_to715231133od_l_r ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_187_finite__Prod__UNIV,axiom,
% 2.97/1.59 ( ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ( ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ( finite785973648od_l_l @ top_to320296343od_l_l ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_188_pigeonhole__infinite__rel,axiom,
% 2.97/1.59 ! [A3: set_Pr1409704485_r_l_v,B4: set_r,R7: produc1389397445_r_l_v > r > $o] :
% 2.97/1.59 ( ~ ( finite1853159534_r_l_v @ A3 )
% 2.97/1.59 => ( ( finite_finite_r @ B4 )
% 2.97/1.59 => ( ! [X4: produc1389397445_r_l_v] :
% 2.97/1.59 ( ( member1522896238_r_l_v @ X4 @ A3 )
% 2.97/1.59 => ? [Xa: r] :
% 2.97/1.59 ( ( member_r @ Xa @ B4 )
% 2.97/1.59 & ( R7 @ X4 @ Xa ) ) )
% 2.97/1.59 => ? [X4: r] :
% 2.97/1.59 ( ( member_r @ X4 @ B4 )
% 2.97/1.59 & ~ ( finite1853159534_r_l_v
% 2.97/1.59 @ ( collec1978425008_r_l_v
% 2.97/1.59 @ ^ [A4: produc1389397445_r_l_v] :
% 2.97/1.59 ( ( member1522896238_r_l_v @ A4 @ A3 )
% 2.97/1.59 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_189_pigeonhole__infinite__rel,axiom,
% 2.97/1.59 ! [A3: set_Pr1409704485_r_l_v,B4: set_l,R7: produc1389397445_r_l_v > l > $o] :
% 2.97/1.59 ( ~ ( finite1853159534_r_l_v @ A3 )
% 2.97/1.59 => ( ( finite_finite_l @ B4 )
% 2.97/1.59 => ( ! [X4: produc1389397445_r_l_v] :
% 2.97/1.59 ( ( member1522896238_r_l_v @ X4 @ A3 )
% 2.97/1.59 => ? [Xa: l] :
% 2.97/1.59 ( ( member_l @ Xa @ B4 )
% 2.97/1.59 & ( R7 @ X4 @ Xa ) ) )
% 2.97/1.59 => ? [X4: l] :
% 2.97/1.59 ( ( member_l @ X4 @ B4 )
% 2.97/1.59 & ~ ( finite1853159534_r_l_v
% 2.97/1.59 @ ( collec1978425008_r_l_v
% 2.97/1.59 @ ^ [A4: produc1389397445_r_l_v] :
% 2.97/1.59 ( ( member1522896238_r_l_v @ A4 @ A3 )
% 2.97/1.59 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_190_pigeonhole__infinite__rel,axiom,
% 2.97/1.59 ! [A3: set_r,B4: set_r,R7: r > r > $o] :
% 2.97/1.59 ( ~ ( finite_finite_r @ A3 )
% 2.97/1.59 => ( ( finite_finite_r @ B4 )
% 2.97/1.59 => ( ! [X4: r] :
% 2.97/1.59 ( ( member_r @ X4 @ A3 )
% 2.97/1.59 => ? [Xa: r] :
% 2.97/1.59 ( ( member_r @ Xa @ B4 )
% 2.97/1.59 & ( R7 @ X4 @ Xa ) ) )
% 2.97/1.59 => ? [X4: r] :
% 2.97/1.59 ( ( member_r @ X4 @ B4 )
% 2.97/1.59 & ~ ( finite_finite_r
% 2.97/1.59 @ ( collect_r
% 2.97/1.59 @ ^ [A4: r] :
% 2.97/1.59 ( ( member_r @ A4 @ A3 )
% 2.97/1.59 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_191_pigeonhole__infinite__rel,axiom,
% 2.97/1.59 ! [A3: set_r,B4: set_l,R7: r > l > $o] :
% 2.97/1.59 ( ~ ( finite_finite_r @ A3 )
% 2.97/1.59 => ( ( finite_finite_l @ B4 )
% 2.97/1.59 => ( ! [X4: r] :
% 2.97/1.59 ( ( member_r @ X4 @ A3 )
% 2.97/1.59 => ? [Xa: l] :
% 2.97/1.59 ( ( member_l @ Xa @ B4 )
% 2.97/1.59 & ( R7 @ X4 @ Xa ) ) )
% 2.97/1.59 => ? [X4: l] :
% 2.97/1.59 ( ( member_l @ X4 @ B4 )
% 2.97/1.59 & ~ ( finite_finite_r
% 2.97/1.59 @ ( collect_r
% 2.97/1.59 @ ^ [A4: r] :
% 2.97/1.59 ( ( member_r @ A4 @ A3 )
% 2.97/1.59 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_192_pigeonhole__infinite__rel,axiom,
% 2.97/1.59 ! [A3: set_l,B4: set_r,R7: l > r > $o] :
% 2.97/1.59 ( ~ ( finite_finite_l @ A3 )
% 2.97/1.59 => ( ( finite_finite_r @ B4 )
% 2.97/1.59 => ( ! [X4: l] :
% 2.97/1.59 ( ( member_l @ X4 @ A3 )
% 2.97/1.59 => ? [Xa: r] :
% 2.97/1.59 ( ( member_r @ Xa @ B4 )
% 2.97/1.59 & ( R7 @ X4 @ Xa ) ) )
% 2.97/1.59 => ? [X4: r] :
% 2.97/1.59 ( ( member_r @ X4 @ B4 )
% 2.97/1.59 & ~ ( finite_finite_l
% 2.97/1.59 @ ( collect_l
% 2.97/1.59 @ ^ [A4: l] :
% 2.97/1.59 ( ( member_l @ A4 @ A3 )
% 2.97/1.59 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_193_pigeonhole__infinite__rel,axiom,
% 2.97/1.59 ! [A3: set_l,B4: set_l,R7: l > l > $o] :
% 2.97/1.59 ( ~ ( finite_finite_l @ A3 )
% 2.97/1.59 => ( ( finite_finite_l @ B4 )
% 2.97/1.59 => ( ! [X4: l] :
% 2.97/1.59 ( ( member_l @ X4 @ A3 )
% 2.97/1.59 => ? [Xa: l] :
% 2.97/1.59 ( ( member_l @ Xa @ B4 )
% 2.97/1.59 & ( R7 @ X4 @ Xa ) ) )
% 2.97/1.59 => ? [X4: l] :
% 2.97/1.59 ( ( member_l @ X4 @ B4 )
% 2.97/1.59 & ~ ( finite_finite_l
% 2.97/1.59 @ ( collect_l
% 2.97/1.59 @ ^ [A4: l] :
% 2.97/1.59 ( ( member_l @ A4 @ A3 )
% 2.97/1.59 & ( R7 @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_194_not__finite__existsD,axiom,
% 2.97/1.59 ! [P: r > $o] :
% 2.97/1.59 ( ~ ( finite_finite_r @ ( collect_r @ P ) )
% 2.97/1.59 => ? [X_1: r] : ( P @ X_1 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_195_not__finite__existsD,axiom,
% 2.97/1.59 ! [P: l > $o] :
% 2.97/1.59 ( ~ ( finite_finite_l @ ( collect_l @ P ) )
% 2.97/1.59 => ? [X_1: l] : ( P @ X_1 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_196_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S )
% 2.97/1.59 => ( ~ ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 => ? [R6: r] :
% 2.97/1.59 ~ ( member_r @ R6 @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_197_finite__has__minimal2,axiom,
% 2.97/1.59 ! [A3: set_set_r,A2: set_r] :
% 2.97/1.59 ( ( finite_finite_set_r @ A3 )
% 2.97/1.59 => ( ( member_set_r @ A2 @ A3 )
% 2.97/1.59 => ? [X4: set_r] :
% 2.97/1.59 ( ( member_set_r @ X4 @ A3 )
% 2.97/1.59 & ( ord_less_eq_set_r @ X4 @ A2 )
% 2.97/1.59 & ! [Xa: set_r] :
% 2.97/1.59 ( ( member_set_r @ Xa @ A3 )
% 2.97/1.59 => ( ( ord_less_eq_set_r @ Xa @ X4 )
% 2.97/1.59 => ( X4 = Xa ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_198_finite__has__minimal2,axiom,
% 2.97/1.59 ! [A3: set_set_l,A2: set_l] :
% 2.97/1.59 ( ( finite_finite_set_l @ A3 )
% 2.97/1.59 => ( ( member_set_l @ A2 @ A3 )
% 2.97/1.59 => ? [X4: set_l] :
% 2.97/1.59 ( ( member_set_l @ X4 @ A3 )
% 2.97/1.59 & ( ord_less_eq_set_l @ X4 @ A2 )
% 2.97/1.59 & ! [Xa: set_l] :
% 2.97/1.59 ( ( member_set_l @ Xa @ A3 )
% 2.97/1.59 => ( ( ord_less_eq_set_l @ Xa @ X4 )
% 2.97/1.59 => ( X4 = Xa ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_199_finite__has__maximal2,axiom,
% 2.97/1.59 ! [A3: set_set_r,A2: set_r] :
% 2.97/1.59 ( ( finite_finite_set_r @ A3 )
% 2.97/1.59 => ( ( member_set_r @ A2 @ A3 )
% 2.97/1.59 => ? [X4: set_r] :
% 2.97/1.59 ( ( member_set_r @ X4 @ A3 )
% 2.97/1.59 & ( ord_less_eq_set_r @ A2 @ X4 )
% 2.97/1.59 & ! [Xa: set_r] :
% 2.97/1.59 ( ( member_set_r @ Xa @ A3 )
% 2.97/1.59 => ( ( ord_less_eq_set_r @ X4 @ Xa )
% 2.97/1.59 => ( X4 = Xa ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_200_finite__has__maximal2,axiom,
% 2.97/1.59 ! [A3: set_set_l,A2: set_l] :
% 2.97/1.59 ( ( finite_finite_set_l @ A3 )
% 2.97/1.59 => ( ( member_set_l @ A2 @ A3 )
% 2.97/1.59 => ? [X4: set_l] :
% 2.97/1.59 ( ( member_set_l @ X4 @ A3 )
% 2.97/1.59 & ( ord_less_eq_set_l @ A2 @ X4 )
% 2.97/1.59 & ! [Xa: set_l] :
% 2.97/1.59 ( ( member_set_l @ Xa @ A3 )
% 2.97/1.59 => ( ( ord_less_eq_set_l @ X4 @ Xa )
% 2.97/1.59 => ( X4 = Xa ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_201_finite__subset,axiom,
% 2.97/1.59 ! [A3: set_r,B4: set_r] :
% 2.97/1.59 ( ( ord_less_eq_set_r @ A3 @ B4 )
% 2.97/1.59 => ( ( finite_finite_r @ B4 )
% 2.97/1.59 => ( finite_finite_r @ A3 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_202_finite__subset,axiom,
% 2.97/1.59 ! [A3: set_l,B4: set_l] :
% 2.97/1.59 ( ( ord_less_eq_set_l @ A3 @ B4 )
% 2.97/1.59 => ( ( finite_finite_l @ B4 )
% 2.97/1.59 => ( finite_finite_l @ A3 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_203_infinite__super,axiom,
% 2.97/1.59 ! [S5: set_r,T2: set_r] :
% 2.97/1.59 ( ( ord_less_eq_set_r @ S5 @ T2 )
% 2.97/1.59 => ( ~ ( finite_finite_r @ S5 )
% 2.97/1.59 => ~ ( finite_finite_r @ T2 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_204_infinite__super,axiom,
% 2.97/1.59 ! [S5: set_l,T2: set_l] :
% 2.97/1.59 ( ( ord_less_eq_set_l @ S5 @ T2 )
% 2.97/1.59 => ( ~ ( finite_finite_l @ S5 )
% 2.97/1.59 => ~ ( finite_finite_l @ T2 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_205_rev__finite__subset,axiom,
% 2.97/1.59 ! [B4: set_r,A3: set_r] :
% 2.97/1.59 ( ( finite_finite_r @ B4 )
% 2.97/1.59 => ( ( ord_less_eq_set_r @ A3 @ B4 )
% 2.97/1.59 => ( finite_finite_r @ A3 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_206_rev__finite__subset,axiom,
% 2.97/1.59 ! [B4: set_l,A3: set_l] :
% 2.97/1.59 ( ( finite_finite_l @ B4 )
% 2.97/1.59 => ( ( ord_less_eq_set_l @ A3 @ B4 )
% 2.97/1.59 => ( finite_finite_l @ A3 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_207_finite__update__induct,axiom,
% 2.97/1.59 ! [F: r > option1457017436_r_l_v,C: option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 2.97/1.59 ( ( finite_finite_r
% 2.97/1.59 @ ( collect_r
% 2.97/1.59 @ ^ [A4: r] :
% 2.97/1.59 ( ( F @ A4 )
% 2.97/1.59 != C ) ) )
% 2.97/1.59 => ( ( P
% 2.97/1.59 @ ^ [A4: r] : C )
% 2.97/1.59 => ( ! [A: r,B: option1457017436_r_l_v,F2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( finite_finite_r
% 2.97/1.59 @ ( collect_r
% 2.97/1.59 @ ^ [C2: r] :
% 2.97/1.59 ( ( F2 @ C2 )
% 2.97/1.59 != C ) ) )
% 2.97/1.59 => ( ( ( F2 @ A )
% 2.97/1.59 = C )
% 2.97/1.59 => ( ( B != C )
% 2.97/1.59 => ( ( P @ F2 )
% 2.97/1.59 => ( P @ ( fun_up709272714_r_l_v @ F2 @ A @ B ) ) ) ) ) )
% 2.97/1.59 => ( P @ F ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_208_finite__update__induct,axiom,
% 2.97/1.59 ! [F: l > option_val_r_l_v,C: option_val_r_l_v,P: ( l > option_val_r_l_v ) > $o] :
% 2.97/1.59 ( ( finite_finite_l
% 2.97/1.59 @ ( collect_l
% 2.97/1.59 @ ^ [A4: l] :
% 2.97/1.59 ( ( F @ A4 )
% 2.97/1.59 != C ) ) )
% 2.97/1.59 => ( ( P
% 2.97/1.59 @ ^ [A4: l] : C )
% 2.97/1.59 => ( ! [A: l,B: option_val_r_l_v,F2: l > option_val_r_l_v] :
% 2.97/1.59 ( ( finite_finite_l
% 2.97/1.59 @ ( collect_l
% 2.97/1.59 @ ^ [C2: l] :
% 2.97/1.59 ( ( F2 @ C2 )
% 2.97/1.59 != C ) ) )
% 2.97/1.59 => ( ( ( F2 @ A )
% 2.97/1.59 = C )
% 2.97/1.59 => ( ( B != C )
% 2.97/1.59 => ( ( P @ F2 )
% 2.97/1.59 => ( P @ ( fun_up1835647912_r_l_v @ F2 @ A @ B ) ) ) ) ) )
% 2.97/1.59 => ( P @ F ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_209_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ Ls ) )
% 2.97/1.59 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_210_SLC__ifTrue,axiom,
% 2.97/1.59 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_211_SLC__ifFalse,axiom,
% 2.97/1.59 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_212_expr_Oinject_I7_J,axiom,
% 2.97/1.59 ! [X7: expr_r_l_v,Y7: expr_r_l_v] :
% 2.97/1.59 ( ( ( rfork_r_l_v @ X7 )
% 2.97/1.59 = ( rfork_r_l_v @ Y7 ) )
% 2.97/1.59 = ( X7 = Y7 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_213_val_Oinject_I4_J,axiom,
% 2.97/1.59 ! [X42: r,Y4: r] :
% 2.97/1.59 ( ( ( rid_r_l_v @ X42 )
% 2.97/1.59 = ( rid_r_l_v @ Y4 ) )
% 2.97/1.59 = ( X42 = Y4 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_214_expr_Oinject_I1_J,axiom,
% 2.97/1.59 ! [X1: val_r_l_v,Y1: val_r_l_v] :
% 2.97/1.59 ( ( ( vE_r_l_v @ X1 )
% 2.97/1.59 = ( vE_r_l_v @ Y1 ) )
% 2.97/1.59 = ( X1 = Y1 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_215_injective__cntxt,axiom,
% 2.97/1.59 ! [E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 2.97/1.59 ( ( ( plug_r_l_v @ E3 @ E1 )
% 2.97/1.59 = ( plug_r_l_v @ E3 @ E22 ) )
% 2.97/1.59 = ( E1 = E22 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_216_val_Oinject_I1_J,axiom,
% 2.97/1.59 ! [X1: const,Y1: const] :
% 2.97/1.59 ( ( ( cV_r_l_v @ X1 )
% 2.97/1.59 = ( cV_r_l_v @ Y1 ) )
% 2.97/1.59 = ( X1 = Y1 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_217_expr_Oinject_I8_J,axiom,
% 2.97/1.59 ! [X8: expr_r_l_v,Y8: expr_r_l_v] :
% 2.97/1.59 ( ( ( rjoin_r_l_v @ X8 )
% 2.97/1.59 = ( rjoin_r_l_v @ Y8 ) )
% 2.97/1.59 = ( X8 = Y8 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_218_revision__step_OifFalse,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_219_revision__step_OifTrue,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_220_revision__step__relaxed_OifFalse,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_221_revision__step__relaxed_OifTrue,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_222_ifFalse__deterministic,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 = ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_223_ifTrue__deterministic,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 = ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_224_expr_Odistinct_I35_J,axiom,
% 2.97/1.59 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X8: expr_r_l_v] :
% 2.97/1.59 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 2.97/1.59 != ( rjoin_r_l_v @ X8 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_225_expr_Odistinct_I33_J,axiom,
% 2.97/1.59 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X7: expr_r_l_v] :
% 2.97/1.59 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 2.97/1.59 != ( rfork_r_l_v @ X7 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_226_expr_Odistinct_I3_J,axiom,
% 2.97/1.59 ! [X1: val_r_l_v,X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v] :
% 2.97/1.59 ( ( vE_r_l_v @ X1 )
% 2.97/1.59 != ( ite_r_l_v @ X31 @ X32 @ X33 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_227_const_Oexhaust,axiom,
% 2.97/1.59 ! [Y: const] :
% 2.97/1.59 ( ( Y != unit )
% 2.97/1.59 => ( ( Y != f )
% 2.97/1.59 => ( Y = t ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_228_const_Oinduct,axiom,
% 2.97/1.59 ! [P: const > $o,Const: const] :
% 2.97/1.59 ( ( P @ unit )
% 2.97/1.59 => ( ( P @ f )
% 2.97/1.59 => ( ( P @ t )
% 2.97/1.59 => ( P @ Const ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_229_const_Odistinct_I1_J,axiom,
% 2.97/1.59 unit != f ).
% 2.97/1.59
% 2.97/1.59 thf(fact_230_const_Odistinct_I3_J,axiom,
% 2.97/1.59 unit != t ).
% 2.97/1.59
% 2.97/1.59 thf(fact_231_substitution_Orevision__step_OifTrue,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_232_substitution_Orevision__step_OifFalse,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_233_substitution_OifTrue__deterministic,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 = ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_234_substitution_OifFalse__deterministic,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 = ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_235_substitution_Orevision__step__relaxed_OifTrue,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_236_substitution_Orevision__step__relaxed_OifFalse,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_237_substitution_OSLC__ifTrue,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E1 ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_238_substitution_OSLC__ifFalse,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ E22 ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_239_LID__local__store_Ocases,axiom,
% 2.97/1.59 ! [X2: produc1156025366_r_l_v] :
% 2.97/1.59 ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E2: expr_r_l_v] :
% 2.97/1.59 ( X2
% 2.97/1.59 != ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_240_LID__local__store_Oinduct,axiom,
% 2.97/1.59 ! [P: produc1156025366_r_l_v > $o,A0: produc1156025366_r_l_v] :
% 2.97/1.59 ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E2: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E2 ) ) )
% 2.97/1.59 => ( P @ A0 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_241_expr_Odistinct_I13_J,axiom,
% 2.97/1.59 ! [X1: val_r_l_v,X8: expr_r_l_v] :
% 2.97/1.59 ( ( vE_r_l_v @ X1 )
% 2.97/1.59 != ( rjoin_r_l_v @ X8 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_242_expr_Odistinct_I11_J,axiom,
% 2.97/1.59 ! [X1: val_r_l_v,X7: expr_r_l_v] :
% 2.97/1.59 ( ( vE_r_l_v @ X1 )
% 2.97/1.59 != ( rfork_r_l_v @ X7 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_243_combine_Oelims,axiom,
% 2.97/1.59 ! [X2: l > option_val_r_l_v,Xa2: l > option_val_r_l_v,Xb: l,Y: option_val_r_l_v] :
% 2.97/1.59 ( ( ( combine_l_val_r_l_v @ X2 @ Xa2 @ Xb )
% 2.97/1.59 = Y )
% 2.97/1.59 => ( ( ( ( Xa2 @ Xb )
% 2.97/1.59 = none_val_r_l_v )
% 2.97/1.59 => ( Y
% 2.97/1.59 = ( X2 @ Xb ) ) )
% 2.97/1.59 & ( ( ( Xa2 @ Xb )
% 2.97/1.59 != none_val_r_l_v )
% 2.97/1.59 => ( Y
% 2.97/1.59 = ( Xa2 @ Xb ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_244_combine_Osimps,axiom,
% 2.97/1.59 ( combine_l_val_r_l_v
% 2.97/1.59 = ( ^ [F3: l > option_val_r_l_v,G: l > option_val_r_l_v,X: l] :
% 2.97/1.59 ( if_option_val_r_l_v
% 2.97/1.59 @ ( ( G @ X )
% 2.97/1.59 = none_val_r_l_v )
% 2.97/1.59 @ ( F3 @ X )
% 2.97/1.59 @ ( G @ X ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_245_val_Odistinct_I5_J,axiom,
% 2.97/1.59 ! [X1: const,X42: r] :
% 2.97/1.59 ( ( cV_r_l_v @ X1 )
% 2.97/1.59 != ( rid_r_l_v @ X42 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_246_expr_Odistinct_I55_J,axiom,
% 2.97/1.59 ! [X7: expr_r_l_v,X8: expr_r_l_v] :
% 2.97/1.59 ( ( rfork_r_l_v @ X7 )
% 2.97/1.59 != ( rjoin_r_l_v @ X8 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_247_empty__map__finite_I4_J,axiom,
% 2.97/1.59 ( finite_finite_l
% 2.97/1.59 @ ( lID_G_r_l_v
% 2.97/1.59 @ ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_248_fun__upd__upd,axiom,
% 2.97/1.59 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 2.97/1.59 ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X2 @ Y ) @ X2 @ Z )
% 2.97/1.59 = ( fun_up709272714_r_l_v @ F @ X2 @ Z ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_249_fun__upd__upd,axiom,
% 2.97/1.59 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v,Z: option_val_r_l_v] :
% 2.97/1.59 ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X2 @ Y ) @ X2 @ Z )
% 2.97/1.59 = ( fun_up1835647912_r_l_v @ F @ X2 @ Z ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_250_fun__upd__triv,axiom,
% 2.97/1.59 ! [F: r > option1457017436_r_l_v,X2: r] :
% 2.97/1.59 ( ( fun_up709272714_r_l_v @ F @ X2 @ ( F @ X2 ) )
% 2.97/1.59 = F ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_251_fun__upd__triv,axiom,
% 2.97/1.59 ! [F: l > option_val_r_l_v,X2: l] :
% 2.97/1.59 ( ( fun_up1835647912_r_l_v @ F @ X2 @ ( F @ X2 ) )
% 2.97/1.59 = F ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_252_RID_092_060_094sub_062L__finite__invariant,axiom,
% 2.97/1.59 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_253_reachable__imp__identifiers__finite_I2_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.59 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_254_reachable__imp__identifiers__available_I2_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.59 => ( ~ ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ? [L: l] :
% 2.97/1.59 ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_255_fun__upd__apply,axiom,
% 2.97/1.59 ( fun_up709272714_r_l_v
% 2.97/1.59 = ( ^ [F3: r > option1457017436_r_l_v,X: r,Y2: option1457017436_r_l_v,Z2: r] : ( if_opt1153928738_r_l_v @ ( Z2 = X ) @ Y2 @ ( F3 @ Z2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_256_fun__upd__apply,axiom,
% 2.97/1.59 ( fun_up1835647912_r_l_v
% 2.97/1.59 = ( ^ [F3: l > option_val_r_l_v,X: l,Y2: option_val_r_l_v,Z2: l] : ( if_option_val_r_l_v @ ( Z2 = X ) @ Y2 @ ( F3 @ Z2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_257_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 2.97/1.59 ! [L2: l,S: r > option1457017436_r_l_v,R: r] :
% 2.97/1.59 ( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 2.97/1.59 => ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_258_finite__state__imp__restriction__finite_I2_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r] :
% 2.97/1.59 ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_259_in__restricted__global__in__updated__global_I2_J,axiom,
% 2.97/1.59 ! [L2: l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 2.97/1.59 => ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_260_fun__upd__idem__iff,axiom,
% 2.97/1.59 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 2.97/1.59 = F )
% 2.97/1.59 = ( ( F @ X2 )
% 2.97/1.59 = Y ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_261_fun__upd__idem__iff,axiom,
% 2.97/1.59 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 2.97/1.59 ( ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 2.97/1.59 = F )
% 2.97/1.59 = ( ( F @ X2 )
% 2.97/1.59 = Y ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_262_fun__upd__twist,axiom,
% 2.97/1.59 ! [A2: r,C: r,M: r > option1457017436_r_l_v,B2: option1457017436_r_l_v,D: option1457017436_r_l_v] :
% 2.97/1.59 ( ( A2 != C )
% 2.97/1.59 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ A2 @ B2 ) @ C @ D )
% 2.97/1.59 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ C @ D ) @ A2 @ B2 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_263_fun__upd__twist,axiom,
% 2.97/1.59 ! [A2: l,C: l,M: l > option_val_r_l_v,B2: option_val_r_l_v,D: option_val_r_l_v] :
% 2.97/1.59 ( ( A2 != C )
% 2.97/1.59 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ A2 @ B2 ) @ C @ D )
% 2.97/1.59 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ C @ D ) @ A2 @ B2 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_264_fun__upd__other,axiom,
% 2.97/1.59 ! [Z: r,X2: r,F: r > option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 2.97/1.59 ( ( Z != X2 )
% 2.97/1.59 => ( ( fun_up709272714_r_l_v @ F @ X2 @ Y @ Z )
% 2.97/1.59 = ( F @ Z ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_265_fun__upd__other,axiom,
% 2.97/1.59 ! [Z: l,X2: l,F: l > option_val_r_l_v,Y: option_val_r_l_v] :
% 2.97/1.59 ( ( Z != X2 )
% 2.97/1.59 => ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y @ Z )
% 2.97/1.59 = ( F @ Z ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_266_fun__upd__same,axiom,
% 2.97/1.59 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 2.97/1.59 ( ( fun_up709272714_r_l_v @ F @ X2 @ Y @ X2 )
% 2.97/1.59 = Y ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_267_fun__upd__same,axiom,
% 2.97/1.59 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 2.97/1.59 ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y @ X2 )
% 2.97/1.59 = Y ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_268_fun__upd__idem,axiom,
% 2.97/1.59 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( F @ X2 )
% 2.97/1.59 = Y )
% 2.97/1.59 => ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 2.97/1.59 = F ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_269_fun__upd__idem,axiom,
% 2.97/1.59 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 2.97/1.59 ( ( ( F @ X2 )
% 2.97/1.59 = Y )
% 2.97/1.59 => ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 2.97/1.59 = F ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_270_fun__upd__eqD,axiom,
% 2.97/1.59 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v,G2: r > option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 2.97/1.59 = ( fun_up709272714_r_l_v @ G2 @ X2 @ Z ) )
% 2.97/1.59 => ( Y = Z ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_271_fun__upd__eqD,axiom,
% 2.97/1.59 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v,G2: l > option_val_r_l_v,Z: option_val_r_l_v] :
% 2.97/1.59 ( ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 2.97/1.59 = ( fun_up1835647912_r_l_v @ G2 @ X2 @ Z ) )
% 2.97/1.59 => ( Y = Z ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_272_fun__upd__def,axiom,
% 2.97/1.59 ( fun_up709272714_r_l_v
% 2.97/1.59 = ( ^ [F3: r > option1457017436_r_l_v,A4: r,B5: option1457017436_r_l_v,X: r] : ( if_opt1153928738_r_l_v @ ( X = A4 ) @ B5 @ ( F3 @ X ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_273_fun__upd__def,axiom,
% 2.97/1.59 ( fun_up1835647912_r_l_v
% 2.97/1.59 = ( ^ [F3: l > option_val_r_l_v,A4: l,B5: option_val_r_l_v,X: l] : ( if_option_val_r_l_v @ ( X = A4 ) @ B5 @ ( F3 @ X ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_274_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_275_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r] : ( ord_less_eq_set_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) @ ( lID_G_r_l_v @ S ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_276_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S )
% 2.97/1.59 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_277_substitution_Oempty__map__finite_I4_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( finite_finite_l
% 2.97/1.59 @ ( lID_G_r_l_v
% 2.97/1.59 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_278_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_279_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S )
% 2.97/1.59 => ( ~ ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ? [L: l] :
% 2.97/1.59 ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_280_only__new__introduces__lids_H,axiom,
% 2.97/1.59 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,L2: l] :
% 2.97/1.59 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V2: val_r_l_v] :
% 2.97/1.59 ( ( S @ R )
% 2.97/1.59 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 2.97/1.59 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 => ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_281_valid__stepE,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ subst ) )
% 2.97/1.59 => ? [R6: r] : ( revision_step_r_l_v @ subst @ R6 @ S @ S2 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_282_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 2.97/1.59 ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ Ls ) )
% 2.97/1.59 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_283_LID_092_060_094sub_062GI,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v,L2: l] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ Ls ) )
% 2.97/1.59 => ( ( member_l @ L2 @ ( lID_L_l_r_v @ Ls ) )
% 2.97/1.59 => ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_284_valid__stepI,axiom,
% 2.97/1.59 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 => ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ subst ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_285_maximal__execution__def,axiom,
% 2.97/1.59 ! [E4: expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( maxima311842975_r_l_v @ subst @ E4 @ S @ S2 )
% 2.97/1.59 = ( ( execution_r_l_v @ subst @ E4 @ S @ S2 )
% 2.97/1.59 & ~ ? [S6: r > option1457017436_r_l_v] : ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S2 @ S6 ) @ ( steps_r_l_v @ subst ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_286_only__new__introduces__lids,axiom,
% 2.97/1.59 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V2: val_r_l_v] :
% 2.97/1.59 ( ( S @ R )
% 2.97/1.59 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 2.97/1.59 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_287_substitution_Osteps_Ocong,axiom,
% 2.97/1.59 steps_r_l_v = steps_r_l_v ).
% 2.97/1.59
% 2.97/1.59 thf(fact_288_expr_Odistinct_I5_J,axiom,
% 2.97/1.59 ! [X1: val_r_l_v,X42: expr_r_l_v] :
% 2.97/1.59 ( ( vE_r_l_v @ X1 )
% 2.97/1.59 != ( ref_r_l_v @ X42 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_289_expr_Odistinct_I41_J,axiom,
% 2.97/1.59 ! [X42: expr_r_l_v,X7: expr_r_l_v] :
% 2.97/1.59 ( ( ref_r_l_v @ X42 )
% 2.97/1.59 != ( rfork_r_l_v @ X7 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_290_expr_Odistinct_I43_J,axiom,
% 2.97/1.59 ! [X42: expr_r_l_v,X8: expr_r_l_v] :
% 2.97/1.59 ( ( ref_r_l_v @ X42 )
% 2.97/1.59 != ( rjoin_r_l_v @ X8 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_291_LID_092_060_094sub_062GE,axiom,
% 2.97/1.59 ! [L2: l,S: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 => ~ ! [R6: r,Ls3: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( ( S @ R6 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ Ls3 ) )
% 2.97/1.59 => ~ ( member_l @ L2 @ ( lID_L_l_r_v @ Ls3 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_292_substitution_Ovalid__stepE,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ Subst ) )
% 2.97/1.59 => ? [R6: r] : ( revision_step_r_l_v @ Subst @ R6 @ S @ S2 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_293_substitution_Ovalid__stepI,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 => ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ Subst ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_294_substitution_Oonly__new__introduces__lids_H,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,L2: l] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V2: val_r_l_v] :
% 2.97/1.59 ( ( S @ R )
% 2.97/1.59 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 2.97/1.59 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 => ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_295_substitution_Oonly__new__introduces__lids,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V2: val_r_l_v] :
% 2.97/1.59 ( ( S @ R )
% 2.97/1.59 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 2.97/1.59 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_296_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ Ls ) )
% 2.97/1.59 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_297_domains__subsume__def,axiom,
% 2.97/1.59 ( domain87684397_l_r_v
% 2.97/1.59 = ( ^ [Ls2: produc1156025366_r_l_v] : ( ord_less_eq_set_l @ ( lID_L_l_r_v @ Ls2 ) @ ( doms_l_r_v @ Ls2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_298_SLC__new,axiom,
% 2.97/1.59 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ( ( reachable_r_l_v @ subst @ S_1 )
% 2.97/1.59 => ( ~ ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_299_terminates__in__def,axiom,
% 2.97/1.59 ! [E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( terminates_in_r_l_v @ subst @ E4 @ S2 )
% 2.97/1.59 = ( ? [S4: r > option1457017436_r_l_v] : ( maxima311842975_r_l_v @ subst @ E4 @ S4 @ S2 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_300_revision__step_Onew,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,L2: l] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_301_new__pseudodeterministic,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 = ( ? [L3: l] :
% 2.97/1.59 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 & ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_302_val_Odistinct_I3_J,axiom,
% 2.97/1.59 ! [X1: const,X34: l] :
% 2.97/1.59 ( ( cV_r_l_v @ X1 )
% 2.97/1.59 != ( loc_l_r_v @ X34 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_303_val_Odistinct_I15_J,axiom,
% 2.97/1.59 ! [X34: l,X42: r] :
% 2.97/1.59 ( ( loc_l_r_v @ X34 )
% 2.97/1.59 != ( rid_r_l_v @ X42 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_304_substitution_Omaximal__execution_Ocong,axiom,
% 2.97/1.59 maxima311842975_r_l_v = maxima311842975_r_l_v ).
% 2.97/1.59
% 2.97/1.59 thf(fact_305_substitution_Odomains__subsume__def,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Ls: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( domain87684397_l_r_v @ Ls )
% 2.97/1.59 = ( ord_less_eq_set_l @ ( lID_L_l_r_v @ Ls ) @ ( doms_l_r_v @ Ls ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_306_substitution_Onew__pseudodeterministic,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 = ( ? [L3: l] :
% 2.97/1.59 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 & ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_307_substitution_Orevision__step_Onew,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,L2: l] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 2.97/1.59 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_308_substitution_Omaximal__execution__def,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,E4: expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( maxima311842975_r_l_v @ Subst @ E4 @ S @ S2 )
% 2.97/1.59 = ( ( execution_r_l_v @ Subst @ E4 @ S @ S2 )
% 2.97/1.59 & ~ ? [S6: r > option1457017436_r_l_v] : ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S2 @ S6 ) @ ( steps_r_l_v @ Subst ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_309_substitution_OSLC__new,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ( ( reachable_r_l_v @ Subst @ S_1 )
% 2.97/1.59 => ( ~ ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_310_revision__step__relaxed_Oset,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_311_substitution_Orevision__step__relaxed_Oset,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_312_substitution_Oterminates__in_Ocong,axiom,
% 2.97/1.59 terminates_in_r_l_v = terminates_in_r_l_v ).
% 2.97/1.59
% 2.97/1.59 thf(fact_313_expr_Odistinct_I9_J,axiom,
% 2.97/1.59 ! [X1: val_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 2.97/1.59 ( ( vE_r_l_v @ X1 )
% 2.97/1.59 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_314_expr_Odistinct_I51_J,axiom,
% 2.97/1.59 ! [X61: expr_r_l_v,X62: expr_r_l_v,X7: expr_r_l_v] :
% 2.97/1.59 ( ( assign_r_l_v @ X61 @ X62 )
% 2.97/1.59 != ( rfork_r_l_v @ X7 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_315_expr_Odistinct_I53_J,axiom,
% 2.97/1.59 ! [X61: expr_r_l_v,X62: expr_r_l_v,X8: expr_r_l_v] :
% 2.97/1.59 ( ( assign_r_l_v @ X61 @ X62 )
% 2.97/1.59 != ( rjoin_r_l_v @ X8 ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_316_substitution_Oterminates__in__def,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( terminates_in_r_l_v @ Subst @ E4 @ S2 )
% 2.97/1.59 = ( ? [S4: r > option1457017436_r_l_v] : ( maxima311842975_r_l_v @ Subst @ E4 @ S4 @ S2 ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_317_SLC__set,axiom,
% 2.97/1.59 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_318_revision__step_Oset,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 2.97/1.59 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_319_dom__const,axiom,
% 2.97/1.59 ! [F: r > produc1156025366_r_l_v] :
% 2.97/1.59 ( ( dom_r_259548057_r_l_v
% 2.97/1.59 @ ^ [X: r] : ( some_P1807977723_r_l_v @ ( F @ X ) ) )
% 2.97/1.59 = top_top_set_r ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_320_dom__const,axiom,
% 2.97/1.59 ! [F: r > val_r_l_v] :
% 2.97/1.59 ( ( dom_r_val_r_l_v
% 2.97/1.59 @ ^ [X: r] : ( some_val_r_l_v @ ( F @ X ) ) )
% 2.97/1.59 = top_top_set_r ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_321_dom__const,axiom,
% 2.97/1.59 ! [F: l > produc1156025366_r_l_v] :
% 2.97/1.59 ( ( dom_l_45837855_r_l_v
% 2.97/1.59 @ ^ [X: l] : ( some_P1807977723_r_l_v @ ( F @ X ) ) )
% 2.97/1.59 = top_top_set_l ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_322_dom__const,axiom,
% 2.97/1.59 ! [F: l > val_r_l_v] :
% 2.97/1.59 ( ( dom_l_val_r_l_v
% 2.97/1.59 @ ^ [X: l] : ( some_val_r_l_v @ ( F @ X ) ) )
% 2.97/1.59 = top_top_set_l ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_323_set__deterministic,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 2.97/1.59 = ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 2.97/1.59 & ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_324_domD,axiom,
% 2.97/1.59 ! [A2: r,M: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( member_r @ A2 @ ( dom_r_259548057_r_l_v @ M ) )
% 2.97/1.59 => ? [B: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( M @ A2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ B ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_325_domD,axiom,
% 2.97/1.59 ! [A2: l,M: l > option1457017436_r_l_v] :
% 2.97/1.59 ( ( member_l @ A2 @ ( dom_l_45837855_r_l_v @ M ) )
% 2.97/1.59 => ? [B: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( M @ A2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ B ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_326_domD,axiom,
% 2.97/1.59 ! [A2: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option1457017436_r_l_v] :
% 2.97/1.59 ( ( member1522896238_r_l_v @ A2 @ ( dom_Pr1162080227_r_l_v @ M ) )
% 2.97/1.59 => ? [B: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( M @ A2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ B ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_327_domD,axiom,
% 2.97/1.59 ! [A2: r,M: r > option_val_r_l_v] :
% 2.97/1.59 ( ( member_r @ A2 @ ( dom_r_val_r_l_v @ M ) )
% 2.97/1.59 => ? [B: val_r_l_v] :
% 2.97/1.59 ( ( M @ A2 )
% 2.97/1.59 = ( some_val_r_l_v @ B ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_328_domD,axiom,
% 2.97/1.59 ! [A2: l,M: l > option_val_r_l_v] :
% 2.97/1.59 ( ( member_l @ A2 @ ( dom_l_val_r_l_v @ M ) )
% 2.97/1.59 => ? [B: val_r_l_v] :
% 2.97/1.59 ( ( M @ A2 )
% 2.97/1.59 = ( some_val_r_l_v @ B ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_329_domD,axiom,
% 2.97/1.59 ! [A2: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option_val_r_l_v] :
% 2.97/1.59 ( ( member1522896238_r_l_v @ A2 @ ( dom_Pr939617279_r_l_v @ M ) )
% 2.97/1.59 => ? [B: val_r_l_v] :
% 2.97/1.59 ( ( M @ A2 )
% 2.97/1.59 = ( some_val_r_l_v @ B ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_330_domI,axiom,
% 2.97/1.59 ! [M: r > option1457017436_r_l_v,A2: r,B2: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( ( M @ A2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ B2 ) )
% 2.97/1.59 => ( member_r @ A2 @ ( dom_r_259548057_r_l_v @ M ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_331_domI,axiom,
% 2.97/1.59 ! [M: l > option1457017436_r_l_v,A2: l,B2: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( ( M @ A2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ B2 ) )
% 2.97/1.59 => ( member_l @ A2 @ ( dom_l_45837855_r_l_v @ M ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_332_domI,axiom,
% 2.97/1.59 ! [M: produc1389397445_r_l_v > option1457017436_r_l_v,A2: produc1389397445_r_l_v,B2: produc1156025366_r_l_v] :
% 2.97/1.59 ( ( ( M @ A2 )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ B2 ) )
% 2.97/1.59 => ( member1522896238_r_l_v @ A2 @ ( dom_Pr1162080227_r_l_v @ M ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_333_domI,axiom,
% 2.97/1.59 ! [M: r > option_val_r_l_v,A2: r,B2: val_r_l_v] :
% 2.97/1.59 ( ( ( M @ A2 )
% 2.97/1.59 = ( some_val_r_l_v @ B2 ) )
% 2.97/1.59 => ( member_r @ A2 @ ( dom_r_val_r_l_v @ M ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_334_domI,axiom,
% 2.97/1.59 ! [M: l > option_val_r_l_v,A2: l,B2: val_r_l_v] :
% 2.97/1.59 ( ( ( M @ A2 )
% 2.97/1.59 = ( some_val_r_l_v @ B2 ) )
% 2.97/1.59 => ( member_l @ A2 @ ( dom_l_val_r_l_v @ M ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_335_domI,axiom,
% 2.97/1.59 ! [M: produc1389397445_r_l_v > option_val_r_l_v,A2: produc1389397445_r_l_v,B2: val_r_l_v] :
% 2.97/1.59 ( ( ( M @ A2 )
% 2.97/1.59 = ( some_val_r_l_v @ B2 ) )
% 2.97/1.59 => ( member1522896238_r_l_v @ A2 @ ( dom_Pr939617279_r_l_v @ M ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_336_finite__map__freshness,axiom,
% 2.97/1.59 ! [F: r > option_val_r_l_v] :
% 2.97/1.59 ( ( finite_finite_r @ ( dom_r_val_r_l_v @ F ) )
% 2.97/1.59 => ( ~ ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 => ? [X4: r] :
% 2.97/1.59 ( ( F @ X4 )
% 2.97/1.59 = none_val_r_l_v ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_337_finite__map__freshness,axiom,
% 2.97/1.59 ! [F: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( finite_finite_r @ ( dom_r_259548057_r_l_v @ F ) )
% 2.97/1.59 => ( ~ ( finite_finite_r @ top_top_set_r )
% 2.97/1.59 => ? [X4: r] :
% 2.97/1.59 ( ( F @ X4 )
% 2.97/1.59 = none_P277133687_r_l_v ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_338_finite__map__freshness,axiom,
% 2.97/1.59 ! [F: l > option_val_r_l_v] :
% 2.97/1.59 ( ( finite_finite_l @ ( dom_l_val_r_l_v @ F ) )
% 2.97/1.59 => ( ~ ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ? [X4: l] :
% 2.97/1.59 ( ( F @ X4 )
% 2.97/1.59 = none_val_r_l_v ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_339_finite__map__freshness,axiom,
% 2.97/1.59 ! [F: l > option1457017436_r_l_v] :
% 2.97/1.59 ( ( finite_finite_l @ ( dom_l_45837855_r_l_v @ F ) )
% 2.97/1.59 => ( ~ ( finite_finite_l @ top_top_set_l )
% 2.97/1.59 => ? [X4: l] :
% 2.97/1.59 ( ( F @ X4 )
% 2.97/1.59 = none_P277133687_r_l_v ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_340_dom__def,axiom,
% 2.97/1.59 ( dom_l_val_r_l_v
% 2.97/1.59 = ( ^ [M2: l > option_val_r_l_v] :
% 2.97/1.59 ( collect_l
% 2.97/1.59 @ ^ [A4: l] :
% 2.97/1.59 ( ( M2 @ A4 )
% 2.97/1.59 != none_val_r_l_v ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_341_domIff,axiom,
% 2.97/1.59 ! [A2: r,M: r > option_val_r_l_v] :
% 2.97/1.59 ( ( member_r @ A2 @ ( dom_r_val_r_l_v @ M ) )
% 2.97/1.59 = ( ( M @ A2 )
% 2.97/1.59 != none_val_r_l_v ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_342_domIff,axiom,
% 2.97/1.59 ! [A2: l,M: l > option_val_r_l_v] :
% 2.97/1.59 ( ( member_l @ A2 @ ( dom_l_val_r_l_v @ M ) )
% 2.97/1.59 = ( ( M @ A2 )
% 2.97/1.59 != none_val_r_l_v ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_343_domIff,axiom,
% 2.97/1.59 ! [A2: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option_val_r_l_v] :
% 2.97/1.59 ( ( member1522896238_r_l_v @ A2 @ ( dom_Pr939617279_r_l_v @ M ) )
% 2.97/1.59 = ( ( M @ A2 )
% 2.97/1.59 != none_val_r_l_v ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_344_domIff,axiom,
% 2.97/1.59 ! [A2: r,M: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( member_r @ A2 @ ( dom_r_259548057_r_l_v @ M ) )
% 2.97/1.59 = ( ( M @ A2 )
% 2.97/1.59 != none_P277133687_r_l_v ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_345_domIff,axiom,
% 2.97/1.59 ! [A2: l,M: l > option1457017436_r_l_v] :
% 2.97/1.59 ( ( member_l @ A2 @ ( dom_l_45837855_r_l_v @ M ) )
% 2.97/1.59 = ( ( M @ A2 )
% 2.97/1.59 != none_P277133687_r_l_v ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_346_domIff,axiom,
% 2.97/1.59 ! [A2: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option1457017436_r_l_v] :
% 2.97/1.59 ( ( member1522896238_r_l_v @ A2 @ ( dom_Pr1162080227_r_l_v @ M ) )
% 2.97/1.59 = ( ( M @ A2 )
% 2.97/1.59 != none_P277133687_r_l_v ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_347_substitution_Oset__deterministic,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 2.97/1.59 = ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 2.97/1.59 & ( S2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_348_substitution_Orevision__step_Oset,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 2.97/1.59 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_349_substitution_OSLC__set,axiom,
% 2.97/1.59 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,V: val_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( substitution_r_l_v @ Subst )
% 2.97/1.59 => ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_350_reachability__closed__under__execution,axiom,
% 2.97/1.59 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( reachable_r_l_v @ subst @ S )
% 2.97/1.59 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( transi1323086383_r_l_v @ ( steps_r_l_v @ subst ) ) )
% 2.97/1.59 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(fact_351_SLC__get,axiom,
% 2.97/1.59 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,L2: l,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( ( S_1 @ R )
% 2.97/1.59 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( S_2
% 2.97/1.59 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 @ L2 ) ) ) ) ) ) ) ) )
% 2.97/1.59 => ( ( member_l @ L2 @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 ) ) )
% 2.97/1.59 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 2.97/1.59 => ( ( R != R2 )
% 2.97/1.59 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 2.97/1.59 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 2.97/1.59 | ( S_2 = S_3 ) )
% 2.97/1.59 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 2.97/1.59 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(help_If_2_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 2.97/1.59 ! [X2: option_val_r_l_v,Y: option_val_r_l_v] :
% 2.97/1.59 ( ( if_option_val_r_l_v @ $false @ X2 @ Y )
% 2.97/1.59 = Y ) ).
% 2.97/1.59
% 2.97/1.59 thf(help_If_1_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 2.97/1.59 ! [X2: option_val_r_l_v,Y: option_val_r_l_v] :
% 2.97/1.59 ( ( if_option_val_r_l_v @ $true @ X2 @ Y )
% 2.97/1.59 = X2 ) ).
% 2.97/1.59
% 2.97/1.59 thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 2.97/1.59 ! [P: $o] :
% 2.97/1.59 ( ( P = $true )
% 2.97/1.59 | ( P = $false ) ) ).
% 2.97/1.59
% 2.97/1.59 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 2.97/1.59 ! [X2: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 2.97/1.59 ( ( if_opt1153928738_r_l_v @ $false @ X2 @ Y )
% 2.97/1.59 = Y ) ).
% 2.97/1.59
% 2.97/1.59 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 2.97/1.59 ! [X2: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 2.97/1.59 ( ( if_opt1153928738_r_l_v @ $true @ X2 @ Y )
% 2.97/1.59 = X2 ) ).
% 2.97/1.59
% 2.97/1.59 thf(conj_0,conjecture,
% 2.97/1.59 r3 != right_forkee ).
% 2.97/1.59 ------------------------
% 3.12/1.62 % (3384)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/2Mi)
% 3.12/1.62 % (3381)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/183Mi)
% 3.12/1.62 % (3387)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/18Mi)
% 3.12/1.62 % (3384)Instruction limit reached!
% 3.12/1.62 % (3384)------------------------------
% 3.12/1.62 % (3384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.62 % (3384)Termination reason: Unknown
% 3.12/1.62 % (3384)Termination phase: shuffling
% 3.12/1.62
% 3.12/1.62 % (3384)Memory used [KB]: 1535
% 3.12/1.62 % (3383)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_3281 for (2999ds/27Mi)
% 3.12/1.62 % (3384)Time elapsed: 0.002 s
% 3.12/1.62 % (3384)Instructions burned: 2 (million)
% 3.12/1.62 % (3384)------------------------------
% 3.12/1.62 % (3384)------------------------------
% 3.12/1.62 % (3382)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_3281 for (2999ds/4Mi)
% 3.12/1.62 % (3387)Instruction limit reached!
% 3.12/1.62 % (3387)------------------------------
% 3.12/1.62 % (3387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.62 % (3387)Termination reason: Unknown
% 3.12/1.62 % (3387)Termination phase: shuffling
% 3.12/1.62
% 3.12/1.62 % (3387)Memory used [KB]: 1918
% 3.12/1.62 % (3387)Time elapsed: 0.007 s
% 3.12/1.62 % (3387)Instructions burned: 18 (million)
% 3.12/1.62 % (3387)------------------------------
% 3.12/1.62 % (3387)------------------------------
% 3.12/1.62 % (3382)Instruction limit reached!
% 3.12/1.62 % (3382)------------------------------
% 3.12/1.62 % (3382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.62 % (3382)Termination reason: Unknown
% 3.12/1.62 % (3382)Termination phase: shuffling
% 3.12/1.62
% 3.12/1.62 % (3382)Memory used [KB]: 1663
% 3.12/1.62 % (3382)Time elapsed: 0.004 s
% 3.12/1.62 % (3382)Instructions burned: 4 (million)
% 3.12/1.62 % (3382)------------------------------
% 3.12/1.62 % (3382)------------------------------
% 3.12/1.63 % (3385)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_3281 for (2999ds/2Mi)
% 3.12/1.63 % (3386)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_3281 for (2999ds/275Mi)
% 3.12/1.63 % (3385)Instruction limit reached!
% 3.12/1.63 % (3385)------------------------------
% 3.12/1.63 % (3385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.63 % (3385)Termination reason: Unknown
% 3.12/1.63 % (3385)Termination phase: shuffling
% 3.12/1.63
% 3.12/1.63 % (3385)Memory used [KB]: 1535
% 3.12/1.63 % (3385)Time elapsed: 0.004 s
% 3.12/1.63 % (3385)Instructions burned: 3 (million)
% 3.12/1.63 % (3385)------------------------------
% 3.12/1.63 % (3385)------------------------------
% 3.12/1.63 % (3388)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/3Mi)
% 3.12/1.63 % (3383)Instruction limit reached!
% 3.12/1.63 % (3383)------------------------------
% 3.12/1.63 % (3383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.63 % (3383)Termination reason: Unknown
% 3.12/1.63 % (3383)Termination phase: shuffling
% 3.12/1.63
% 3.12/1.63 % (3383)Memory used [KB]: 2046
% 3.12/1.63 % (3383)Time elapsed: 0.011 s
% 3.12/1.63 % (3383)Instructions burned: 28 (million)
% 3.12/1.63 % (3383)------------------------------
% 3.12/1.63 % (3383)------------------------------
% 3.12/1.63 % (3388)Instruction limit reached!
% 3.12/1.63 % (3388)------------------------------
% 3.12/1.63 % (3388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.63 % (3388)Termination reason: Unknown
% 3.12/1.63 % (3388)Termination phase: shuffling
% 3.12/1.63
% 3.12/1.63 % (3388)Memory used [KB]: 1535
% 3.12/1.63 % (3388)Time elapsed: 0.002 s
% 3.12/1.63 % (3388)Instructions burned: 3 (million)
% 3.12/1.63 % (3388)------------------------------
% 3.12/1.63 % (3388)------------------------------
% 3.12/1.63 % (3389)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_3281 for (2999ds/37Mi)
% 3.12/1.64 % (3392)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/1041Mi)
% 3.12/1.64 % (3390)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/15Mi)
% 3.12/1.64 % (3389)Instruction limit reached!
% 3.12/1.64 % (3389)------------------------------
% 3.12/1.64 % (3389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.64 % (3389)Termination reason: Unknown
% 3.12/1.64 % (3389)Termination phase: shuffling
% 3.12/1.64
% 3.12/1.64 % (3389)Memory used [KB]: 2302
% 3.12/1.64 % (3389)Time elapsed: 0.012 s
% 3.12/1.64 % (3389)Instructions burned: 40 (million)
% 3.12/1.64 % (3389)------------------------------
% 3.12/1.64 % (3389)------------------------------
% 3.12/1.64 % (3391)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/3Mi)
% 3.12/1.65 % (3393)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/7Mi)
% 3.12/1.65 % (3391)Instruction limit reached!
% 3.12/1.65 % (3391)------------------------------
% 3.12/1.65 % (3391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.65 % (3391)Termination reason: Unknown
% 3.12/1.65 % (3391)Termination phase: shuffling
% 3.12/1.65
% 3.12/1.65 % (3391)Memory used [KB]: 1535
% 3.12/1.65 % (3391)Time elapsed: 0.004 s
% 3.12/1.65 % (3391)Instructions burned: 3 (million)
% 3.12/1.65 % (3391)------------------------------
% 3.12/1.65 % (3391)------------------------------
% 3.12/1.65 % (3390)Instruction limit reached!
% 3.12/1.65 % (3390)------------------------------
% 3.12/1.65 % (3390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.65 % (3390)Termination reason: Unknown
% 3.12/1.65 % (3390)Termination phase: shuffling
% 3.12/1.65
% 3.12/1.65 % (3390)Memory used [KB]: 1918
% 3.12/1.65 % (3390)Time elapsed: 0.009 s
% 3.12/1.65 % (3390)Instructions burned: 17 (million)
% 3.12/1.65 % (3390)------------------------------
% 3.12/1.65 % (3390)------------------------------
% 3.12/1.65 % (3393)Instruction limit reached!
% 3.12/1.65 % (3393)------------------------------
% 3.12/1.65 % (3393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.65 % (3393)Termination reason: Unknown
% 3.12/1.65 % (3393)Termination phase: shuffling
% 3.12/1.65
% 3.12/1.65 % (3393)Memory used [KB]: 1663
% 3.12/1.65 % (3393)Time elapsed: 0.006 s
% 3.12/1.65 % (3393)Instructions burned: 8 (million)
% 3.12/1.65 % (3393)------------------------------
% 3.12/1.65 % (3393)------------------------------
% 3.12/1.65 % (3394)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/16Mi)
% 3.12/1.66 % (3394)Instruction limit reached!
% 3.12/1.66 % (3394)------------------------------
% 3.12/1.66 % (3394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.66 % (3394)Termination reason: Unknown
% 3.12/1.66 % (3394)Termination phase: shuffling
% 3.12/1.66
% 3.12/1.66 % (3394)Memory used [KB]: 1918
% 3.12/1.66 % (3394)Time elapsed: 0.007 s
% 3.12/1.66 % (3394)Instructions burned: 18 (million)
% 3.12/1.66 % (3394)------------------------------
% 3.12/1.66 % (3394)------------------------------
% 3.12/1.66 % (3396)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/3Mi)
% 3.12/1.66 % (3397)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/7Mi)
% 3.12/1.66 % (3396)Instruction limit reached!
% 3.12/1.66 % (3396)------------------------------
% 3.12/1.66 % (3396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.66 % (3396)Termination reason: Unknown
% 3.12/1.66 % (3396)Termination phase: shuffling
% 3.12/1.66
% 3.12/1.66 % (3396)Memory used [KB]: 1663
% 3.12/1.66 % (3396)Time elapsed: 0.003 s
% 3.12/1.66 % (3396)Instructions burned: 4 (million)
% 3.12/1.66 % (3396)------------------------------
% 3.12/1.66 % (3396)------------------------------
% 3.12/1.66 % (3397)Instruction limit reached!
% 3.12/1.66 % (3397)------------------------------
% 3.12/1.66 % (3397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.66 % (3397)Termination reason: Unknown
% 3.12/1.66 % (3397)Termination phase: shuffling
% 3.12/1.66
% 3.12/1.66 % (3397)Memory used [KB]: 1663
% 3.12/1.66 % (3397)Time elapsed: 0.004 s
% 3.12/1.66 % (3397)Instructions burned: 9 (million)
% 3.12/1.66 % (3397)------------------------------
% 3.12/1.66 % (3397)------------------------------
% 3.12/1.66 % (3395)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/3Mi)
% 3.12/1.67 % (3395)Instruction limit reached!
% 3.12/1.67 % (3395)------------------------------
% 3.12/1.67 % (3395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.67 % (3395)Termination reason: Unknown
% 3.12/1.67 % (3395)Termination phase: shuffling
% 3.12/1.67
% 3.12/1.67 % (3395)Memory used [KB]: 1535
% 3.12/1.67 % (3395)Time elapsed: 0.004 s
% 3.12/1.67 % (3395)Instructions burned: 3 (million)
% 3.12/1.67 % (3395)------------------------------
% 3.12/1.67 % (3395)------------------------------
% 3.12/1.67 % (3398)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/3Mi)
% 3.12/1.67 % (3381)Instruction limit reached!
% 3.12/1.67 % (3381)------------------------------
% 3.12/1.67 % (3381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.67 % (3381)Termination reason: Unknown
% 3.12/1.67 % (3381)Termination phase: Property scanning
% 3.12/1.67
% 3.12/1.67 % (3381)Memory used [KB]: 3198
% 3.12/1.67 % (3381)Time elapsed: 0.053 s
% 3.12/1.67 % (3381)Instructions burned: 185 (million)
% 3.12/1.67 % (3381)------------------------------
% 3.12/1.67 % (3381)------------------------------
% 3.12/1.67 % (3398)Instruction limit reached!
% 3.12/1.67 % (3398)------------------------------
% 3.12/1.67 % (3398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.67 % (3398)Termination reason: Unknown
% 3.12/1.67 % (3398)Termination phase: shuffling
% 3.12/1.67
% 3.12/1.67 % (3398)Memory used [KB]: 1663
% 3.12/1.67 % (3398)Time elapsed: 0.002 s
% 3.12/1.67 % (3398)Instructions burned: 3 (million)
% 3.12/1.67 % (3398)------------------------------
% 3.12/1.67 % (3398)------------------------------
% 3.12/1.67 % (3399)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/4Mi)
% 3.12/1.67 % (3400)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/18Mi)
% 3.12/1.67 % (3399)Instruction limit reached!
% 3.12/1.67 % (3399)------------------------------
% 3.12/1.67 % (3399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.67 % (3399)Termination reason: Unknown
% 3.12/1.67 % (3399)Termination phase: shuffling
% 3.12/1.67
% 3.12/1.67 % (3399)Memory used [KB]: 1663
% 3.12/1.67 % (3399)Time elapsed: 0.004 s
% 3.12/1.67 % (3399)Instructions burned: 6 (million)
% 3.12/1.67 % (3399)------------------------------
% 3.12/1.67 % (3399)------------------------------
% 3.12/1.68 % (3402)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/6Mi)
% 3.12/1.68 % (3400)Instruction limit reached!
% 3.12/1.68 % (3400)------------------------------
% 3.12/1.68 % (3400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.68 % (3400)Termination reason: Unknown
% 3.12/1.68 % (3403)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/902Mi)
% 3.12/1.68 % (3400)Termination phase: shuffling
% 3.12/1.68
% 3.12/1.68 % (3400)Memory used [KB]: 1918
% 3.12/1.68 % (3400)Time elapsed: 0.007 s
% 3.12/1.68 % (3400)Instructions burned: 19 (million)
% 3.12/1.68 % (3400)------------------------------
% 3.12/1.68 % (3400)------------------------------
% 3.12/1.68 % (3402)Instruction limit reached!
% 3.12/1.68 % (3402)------------------------------
% 3.12/1.68 % (3402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.68 % (3402)Termination reason: Unknown
% 3.12/1.68 % (3402)Termination phase: shuffling
% 3.12/1.68
% 3.12/1.68 % (3402)Memory used [KB]: 1663
% 3.12/1.68 % (3402)Time elapsed: 0.003 s
% 3.12/1.68 % (3402)Instructions burned: 6 (million)
% 3.12/1.68 % (3402)------------------------------
% 3.12/1.68 % (3402)------------------------------
% 3.12/1.68 % (3386)Refutation not found, incomplete strategy
% 3.12/1.68 % (3386)------------------------------
% 3.12/1.68 % (3386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.68 % (3386)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.68
% 3.12/1.68
% 3.12/1.68 % (3386)Memory used [KB]: 7036
% 3.12/1.68 % (3386)Time elapsed: 0.058 s
% 3.12/1.68 % (3386)Instructions burned: 96 (million)
% 3.12/1.68 % (3386)------------------------------
% 3.12/1.68 % (3386)------------------------------
% 3.12/1.68 % (3401)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/710Mi)
% 3.12/1.68 % (3404)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/21Mi)
% 3.12/1.69 % (3405)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/5Mi)
% 3.12/1.69 % (3406)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/6Mi)
% 3.12/1.69 % (3405)Instruction limit reached!
% 3.12/1.69 % (3405)------------------------------
% 3.12/1.69 % (3405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.69 % (3405)Termination reason: Unknown
% 3.12/1.69 % (3405)Termination phase: shuffling
% 3.12/1.69
% 3.12/1.69 % (3405)Memory used [KB]: 1791
% 3.12/1.69 % (3405)Time elapsed: 0.003 s
% 3.12/1.69 % (3405)Instructions burned: 7 (million)
% 3.12/1.69 % (3405)------------------------------
% 3.12/1.69 % (3405)------------------------------
% 3.12/1.69 % (3406)Instruction limit reached!
% 3.12/1.69 % (3406)------------------------------
% 3.12/1.69 % (3406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.69 % (3406)Termination reason: Unknown
% 3.12/1.69 % (3406)Termination phase: shuffling
% 3.12/1.69
% 3.12/1.69 % (3406)Memory used [KB]: 1663
% 3.12/1.69 % (3406)Time elapsed: 0.003 s
% 3.12/1.69 % (3406)Instructions burned: 6 (million)
% 3.12/1.69 % (3406)------------------------------
% 3.12/1.69 % (3406)------------------------------
% 3.12/1.69 % (3404)Instruction limit reached!
% 3.12/1.69 % (3404)------------------------------
% 3.12/1.69 % (3404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.69 % (3404)Termination reason: Unknown
% 3.12/1.69 % (3404)Termination phase: shuffling
% 3.12/1.69
% 3.12/1.69 % (3404)Memory used [KB]: 1918
% 3.12/1.69 % (3404)Time elapsed: 0.010 s
% 3.12/1.69 % (3404)Instructions burned: 23 (million)
% 3.12/1.69 % (3404)------------------------------
% 3.12/1.69 % (3404)------------------------------
% 3.12/1.70 % (3408)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/779Mi)
% 3.12/1.70 % (3407)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/377Mi)
% 3.12/1.70 % (3409)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/19Mi)
% 3.12/1.70 % (3410)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/879Mi)
% 3.12/1.71 % (3409)Instruction limit reached!
% 3.12/1.71 % (3409)------------------------------
% 3.12/1.71 % (3409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.71 % (3409)Termination reason: Unknown
% 3.12/1.71 % (3409)Termination phase: shuffling
% 3.12/1.71
% 3.12/1.71 % (3409)Memory used [KB]: 2046
% 3.12/1.71 % (3409)Time elapsed: 0.007 s
% 3.12/1.71 % (3409)Instructions burned: 21 (million)
% 3.12/1.71 % (3409)------------------------------
% 3.12/1.71 % (3409)------------------------------
% 3.12/1.72 % (3411)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3281 for (2999ds/17Mi)
% 3.12/1.72 % (3411)Instruction limit reached!
% 3.12/1.72 % (3411)------------------------------
% 3.12/1.72 % (3411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.72 % (3411)Termination reason: Unknown
% 3.12/1.72 % (3411)Termination phase: shuffling
% 3.12/1.72
% 3.12/1.72 % (3411)Memory used [KB]: 1918
% 3.12/1.72 % (3411)Time elapsed: 0.007 s
% 3.12/1.72 % (3411)Instructions burned: 17 (million)
% 3.12/1.72 % (3411)------------------------------
% 3.12/1.72 % (3411)------------------------------
% 3.12/1.73 % (3412)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3281 for (2998ds/3Mi)
% 3.12/1.73 % (3412)Instruction limit reached!
% 3.12/1.73 % (3412)------------------------------
% 3.12/1.73 % (3412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.73 % (3412)Termination reason: Unknown
% 3.12/1.73 % (3412)Termination phase: shuffling
% 3.12/1.73
% 3.12/1.73 % (3412)Memory used [KB]: 1663
% 3.12/1.73 % (3412)Time elapsed: 0.003 s
% 3.12/1.73 % (3412)Instructions burned: 5 (million)
% 3.12/1.73 % (3412)------------------------------
% 3.12/1.73 % (3412)------------------------------
% 3.12/1.74 % (3401)Refutation not found, incomplete strategy
% 3.12/1.74 % (3401)------------------------------
% 3.12/1.74 % (3401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.74 % (3410)Refutation not found, incomplete strategy
% 3.12/1.74 % (3410)------------------------------
% 3.12/1.74 % (3410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.74 % (3401)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.74
% 3.12/1.74
% 3.12/1.74 % (3401)Memory used [KB]: 7036
% 3.12/1.74 % (3401)Time elapsed: 0.056 s
% 3.12/1.74 % (3401)Instructions burned: 96 (million)
% 3.12/1.74 % (3401)------------------------------
% 3.12/1.74 % (3401)------------------------------
% 3.12/1.74 % (3410)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.74
% 3.12/1.74
% 3.12/1.74 % (3410)Memory used [KB]: 7036
% 3.12/1.74 % (3410)Time elapsed: 0.037 s
% 3.12/1.74 % (3410)Instructions burned: 106 (million)
% 3.12/1.74 % (3410)------------------------------
% 3.12/1.74 % (3410)------------------------------
% 3.12/1.74 % (3413)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3281 for (2998ds/30Mi)
% 3.12/1.75 % (3414)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3281 for (2998ds/127Mi)
% 3.12/1.75 % (3415)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3281 for (2998ds/100Mi)
% 3.12/1.75 % (3413)Instruction limit reached!
% 3.12/1.75 % (3413)------------------------------
% 3.12/1.75 % (3413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.75 % (3413)Termination reason: Unknown
% 3.12/1.75 % (3413)Termination phase: shuffling
% 3.12/1.75
% 3.12/1.75 % (3413)Memory used [KB]: 2046
% 3.12/1.75 % (3413)Time elapsed: 0.011 s
% 3.12/1.75 % (3413)Instructions burned: 32 (million)
% 3.12/1.75 % (3413)------------------------------
% 3.12/1.75 % (3413)------------------------------
% 3.12/1.76 % (3416)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_3281 for (2998ds/3Mi)
% 3.12/1.76 % (3416)Instruction limit reached!
% 3.12/1.76 % (3416)------------------------------
% 3.12/1.76 % (3416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.76 % (3416)Termination reason: Unknown
% 3.12/1.76 % (3416)Termination phase: shuffling
% 3.12/1.76
% 3.12/1.76 % (3416)Memory used [KB]: 1663
% 3.12/1.76 % (3416)Time elapsed: 0.003 s
% 3.12/1.76 % (3416)Instructions burned: 6 (million)
% 3.12/1.76 % (3416)------------------------------
% 3.12/1.76 % (3416)------------------------------
% 3.12/1.77 % (3417)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_3281 for (2998ds/20Mi)
% 3.12/1.78 % (3403)First to succeed.
% 3.12/1.78 % (3417)Instruction limit reached!
% 3.12/1.78 % (3417)------------------------------
% 3.12/1.78 % (3417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.78 % (3417)Termination reason: Unknown
% 3.12/1.78 % (3417)Termination phase: shuffling
% 3.12/1.78
% 3.12/1.78 % (3417)Memory used [KB]: 1918
% 3.12/1.78 % (3417)Time elapsed: 0.008 s
% 3.12/1.78 % (3417)Instructions burned: 21 (million)
% 3.12/1.78 % (3417)------------------------------
% 3.12/1.78 % (3417)------------------------------
% 3.12/1.78 % (3415)Instruction limit reached!
% 3.12/1.78 % (3415)------------------------------
% 3.12/1.78 % (3415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.78 % (3415)Termination reason: Unknown
% 3.12/1.78 % (3415)Termination phase: Property scanning
% 3.12/1.78
% 3.12/1.78 % (3415)Memory used [KB]: 3198
% 3.12/1.78 % (3415)Time elapsed: 0.031 s
% 3.12/1.78 % (3415)Instructions burned: 101 (million)
% 3.12/1.78 % (3415)------------------------------
% 3.12/1.78 % (3415)------------------------------
% 3.12/1.78 % (3403)Refutation found. Thanks to Tanya!
% 3.12/1.78 % SZS status Theorem for DTF2THF_3281
% 3.12/1.78 % SZS output start Proof for DTF2THF_3281
% 3.12/1.78 thf(type_def_5, type, l: $tType).
% 3.12/1.78 thf(type_def_6, type, option_val_r_l_v: $tType).
% 3.12/1.78 thf(type_def_8, type, const: $tType).
% 3.12/1.78 thf(type_def_9, type, produc1156025366_r_l_v: $tType).
% 3.12/1.78 thf(type_def_10, type, set_l: $tType).
% 3.12/1.78 thf(type_def_11, type, expr_r_l_v: $tType).
% 3.12/1.78 thf(type_def_12, type, val_r_l_v: $tType).
% 3.12/1.78 thf(type_def_13, type, cntxt_r_l_v: $tType).
% 3.12/1.78 thf(type_def_14, type, r: $tType).
% 3.12/1.78 thf(type_def_15, type, v: $tType).
% 3.12/1.78 thf(type_def_16, type, option1457017436_r_l_v: $tType).
% 3.12/1.78 thf(type_def_17, type, set_Pr1409704485_r_l_v: $tType).
% 3.12/1.78 thf(type_def_18, type, set_option_l: $tType).
% 3.12/1.78 thf(type_def_19, type, set_option_r: $tType).
% 3.12/1.78 thf(type_def_20, type, set_Product_prod_l_l: $tType).
% 3.12/1.78 thf(type_def_21, type, set_Product_prod_l_r: $tType).
% 3.12/1.78 thf(type_def_22, type, set_Product_prod_r_l: $tType).
% 3.12/1.78 thf(type_def_23, type, set_Product_prod_r_r: $tType).
% 3.12/1.78 thf(type_def_24, type, set_set_set_l: $tType).
% 3.12/1.78 thf(type_def_25, type, set_set_set_r: $tType).
% 3.12/1.78 thf(type_def_26, type, set_set_Sum_sum_l_l: $tType).
% 3.12/1.78 thf(type_def_27, type, set_set_Sum_sum_l_r: $tType).
% 3.12/1.78 thf(type_def_28, type, set_set_Sum_sum_r_l: $tType).
% 3.12/1.78 thf(type_def_29, type, set_set_l: $tType).
% 3.12/1.78 thf(type_def_30, type, set_set_r: $tType).
% 3.12/1.78 thf(type_def_31, type, set_Sum_sum_l_l: $tType).
% 3.12/1.78 thf(type_def_32, type, set_Sum_sum_l_r: $tType).
% 3.12/1.78 thf(type_def_33, type, set_Sum_sum_r_l: $tType).
% 3.12/1.78 thf(type_def_34, type, set_Sum_sum_r_r: $tType).
% 3.12/1.78 thf(type_def_35, type, set_r: $tType).
% 3.12/1.78 thf(type_def_36, type, produc1389397445_r_l_v: $tType).
% 3.12/1.78 thf(type_def_37, type, produc1164766533_r_l_v: $tType).
% 3.12/1.78 thf(type_def_38, type, sum_sum_l_l: $tType).
% 3.12/1.78 thf(type_def_39, type, sum_sum_l_r: $tType).
% 3.12/1.78 thf(type_def_40, type, sum_sum_r_l: $tType).
% 3.12/1.78 thf(func_def_0, type, set_Pr1409704485_r_l_v: $tType).
% 3.12/1.78 thf(func_def_1, type, produc1389397445_r_l_v: $tType).
% 3.12/1.78 thf(func_def_2, type, option1457017436_r_l_v: $tType).
% 3.12/1.78 thf(func_def_3, type, produc1156025366_r_l_v: $tType).
% 3.12/1.78 thf(func_def_4, type, produc1164766533_r_l_v: $tType).
% 3.12/1.78 thf(func_def_5, type, set_set_Sum_sum_r_l: $tType).
% 3.12/1.78 thf(func_def_6, type, set_set_Sum_sum_l_r: $tType).
% 3.12/1.78 thf(func_def_7, type, set_set_Sum_sum_l_l: $tType).
% 3.12/1.78 thf(func_def_8, type, option_val_r_l_v: $tType).
% 3.12/1.78 thf(func_def_9, type, set_Product_prod_r_r: $tType).
% 3.12/1.78 thf(func_def_10, type, set_Product_prod_r_l: $tType).
% 3.12/1.78 thf(func_def_11, type, set_Product_prod_l_r: $tType).
% 3.12/1.78 thf(func_def_12, type, set_Product_prod_l_l: $tType).
% 3.12/1.78 thf(func_def_13, type, set_set_set_r: $tType).
% 3.12/1.78 thf(func_def_14, type, set_set_set_l: $tType).
% 3.12/1.78 thf(func_def_15, type, set_Sum_sum_r_r: $tType).
% 3.12/1.78 thf(func_def_16, type, set_Sum_sum_r_l: $tType).
% 3.12/1.78 thf(func_def_17, type, set_Sum_sum_l_r: $tType).
% 3.12/1.78 thf(func_def_18, type, set_Sum_sum_l_l: $tType).
% 3.12/1.78 thf(func_def_19, type, set_option_r: $tType).
% 3.12/1.78 thf(func_def_20, type, set_option_l: $tType).
% 3.12/1.78 thf(func_def_21, type, cntxt_r_l_v: $tType).
% 3.12/1.78 thf(func_def_22, type, set_set_r: $tType).
% 3.12/1.78 thf(func_def_23, type, set_set_l: $tType).
% 3.12/1.78 thf(func_def_24, type, expr_r_l_v: $tType).
% 3.12/1.78 thf(func_def_25, type, sum_sum_r_l: $tType).
% 3.12/1.78 thf(func_def_26, type, sum_sum_l_r: $tType).
% 3.12/1.78 thf(func_def_27, type, sum_sum_l_l: $tType).
% 3.12/1.78 thf(func_def_28, type, val_r_l_v: $tType).
% 3.12/1.78 thf(func_def_29, type, set_r: $tType).
% 3.12/1.78 thf(func_def_30, type, set_l: $tType).
% 3.12/1.78 thf(func_def_31, type, const: $tType).
% 3.12/1.78 thf(func_def_32, type, v: $tType).
% 3.12/1.78 thf(func_def_33, type, r: $tType).
% 3.12/1.78 thf(func_def_34, type, l: $tType).
% 3.12/1.78 thf(func_def_35, type, combine_l_val_r_l_v: (l > option_val_r_l_v) > (l > option_val_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_36, type, f: const).
% 3.12/1.78 thf(func_def_37, type, t: const).
% 3.12/1.78 thf(func_def_38, type, unit: const).
% 3.12/1.78 thf(func_def_39, type, doms_l_r_v: produc1156025366_r_l_v > set_l).
% 3.12/1.78 thf(func_def_40, type, assign_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_41, type, ite_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_42, type, read_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_43, type, ref_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_44, type, rfork_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_45, type, rjoin_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_46, type, vE_r_l_v: val_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_47, type, plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_48, type, cV_r_l_v: const > val_r_l_v).
% 3.12/1.78 thf(func_def_49, type, loc_l_r_v: l > val_r_l_v).
% 3.12/1.78 thf(func_def_50, type, rid_r_l_v: r > val_r_l_v).
% 3.12/1.78 thf(func_def_51, type, execution_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > expr_r_l_v > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_52, type, induct1670415253_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > ((r > option1457017436_r_l_v) > $o) > $o).
% 3.12/1.78 thf(func_def_53, type, maxima311842975_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > expr_r_l_v > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_54, type, reachable_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_55, type, steps_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > set_Pr1409704485_r_l_v).
% 3.12/1.78 thf(func_def_56, type, terminates_in_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > expr_r_l_v > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_57, type, finite2114249848tion_l: set_option_l > $o).
% 3.12/1.78 thf(func_def_58, type, finite16335230tion_r: set_option_r > $o).
% 3.12/1.78 thf(func_def_59, type, finite1853159534_r_l_v: set_Pr1409704485_r_l_v > $o).
% 3.12/1.78 thf(func_def_60, type, finite785973648od_l_l: set_Product_prod_l_l > $o).
% 3.12/1.78 thf(func_def_61, type, finite835542678od_l_r: set_Product_prod_l_r > $o).
% 3.12/1.78 thf(func_def_62, type, finite1457622794od_r_l: set_Product_prod_r_l > $o).
% 3.12/1.78 thf(func_def_63, type, finite1507191824od_r_r: set_Product_prod_r_r > $o).
% 3.12/1.78 thf(func_def_64, type, finite1256628466_set_l: set_set_set_l > $o).
% 3.12/1.78 thf(func_def_65, type, finite1651563256_set_r: set_set_set_r > $o).
% 3.12/1.78 thf(func_def_66, type, finite88277554um_l_l: set_set_Sum_sum_l_l > $o).
% 3.12/1.78 thf(func_def_67, type, finite483212344um_l_r: set_set_Sum_sum_l_r > $o).
% 3.12/1.78 thf(func_def_68, type, finite1407742636um_r_l: set_set_Sum_sum_r_l > $o).
% 3.12/1.78 thf(func_def_69, type, finite_finite_set_l: set_set_l > $o).
% 3.12/1.78 thf(func_def_70, type, finite_finite_set_r: set_set_r > $o).
% 3.12/1.78 thf(func_def_71, type, finite1541484284um_l_l: set_Sum_sum_l_l > $o).
% 3.12/1.78 thf(func_def_72, type, finite1591053314um_l_r: set_Sum_sum_l_r > $o).
% 3.12/1.78 thf(func_def_73, type, finite65649782um_r_l: set_Sum_sum_r_l > $o).
% 3.12/1.78 thf(func_def_74, type, finite115218812um_r_r: set_Sum_sum_r_r > $o).
% 3.12/1.78 thf(func_def_75, type, finite_finite_l: set_l > $o).
% 3.12/1.78 thf(func_def_76, type, finite_finite_r: set_r > $o).
% 3.12/1.78 thf(func_def_77, type, fun_up1835647912_r_l_v: (l > option_val_r_l_v) > l > option_val_r_l_v > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_78, type, fun_up709272714_r_l_v: (r > option1457017436_r_l_v) > r > option1457017436_r_l_v > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_79, type, if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v).
% 3.12/1.78 thf(func_def_80, type, if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_81, type, dom_Pr939617279_r_l_v: (produc1389397445_r_l_v > option_val_r_l_v) > set_Pr1409704485_r_l_v).
% 3.12/1.78 thf(func_def_82, type, dom_Pr1162080227_r_l_v: (produc1389397445_r_l_v > option1457017436_r_l_v) > set_Pr1409704485_r_l_v).
% 3.12/1.78 thf(func_def_83, type, dom_l_val_r_l_v: (l > option_val_r_l_v) > set_l).
% 3.12/1.78 thf(func_def_84, type, dom_l_45837855_r_l_v: (l > option1457017436_r_l_v) > set_l).
% 3.12/1.78 thf(func_def_85, type, dom_r_val_r_l_v: (r > option_val_r_l_v) > set_r).
% 3.12/1.78 thf(func_def_86, type, dom_r_259548057_r_l_v: (r > option1457017436_r_l_v) > set_r).
% 3.12/1.78 thf(func_def_87, type, lID_G_r_l_v: (r > option1457017436_r_l_v) > set_l).
% 3.12/1.78 thf(func_def_88, type, lID_L_l_r_v: produc1156025366_r_l_v > set_l).
% 3.12/1.78 thf(func_def_89, type, rID_G_r_l_v: (r > option1457017436_r_l_v) > set_r).
% 3.12/1.78 thf(func_def_90, type, rID_L_l_r_v: produc1156025366_r_l_v > set_r).
% 3.12/1.78 thf(func_def_91, type, domain87684397_l_r_v: produc1156025366_r_l_v > $o).
% 3.12/1.78 thf(func_def_92, type, domain1547879849_r_l_v: (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_93, type, revision_step_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_94, type, revisi1291188644_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_95, type, subsum148050133_r_l_v: r > r > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_96, type, subsum680764357_r_l_v: (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_97, type, none_val_r_l_v: option_val_r_l_v).
% 3.12/1.78 thf(func_def_98, type, none_P277133687_r_l_v: option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_99, type, some_val_r_l_v: val_r_l_v > option_val_r_l_v).
% 3.12/1.78 thf(func_def_100, type, some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_101, type, the_val_r_l_v: option_val_r_l_v > val_r_l_v).
% 3.12/1.78 thf(func_def_102, type, ord_le2116509289_set_l: set_set_l > set_set_l > $o).
% 3.12/1.78 thf(func_def_103, type, ord_le363960431_set_r: set_set_r > set_set_r > $o).
% 3.12/1.78 thf(func_def_104, type, ord_le1122554619um_l_l: set_Sum_sum_l_l > set_Sum_sum_l_l > $o).
% 3.12/1.78 thf(func_def_105, type, ord_le1517489409um_l_r: set_Sum_sum_l_r > set_Sum_sum_l_r > $o).
% 3.12/1.78 thf(func_def_106, type, ord_le294536053um_r_l: set_Sum_sum_r_l > set_Sum_sum_r_l > $o).
% 3.12/1.78 thf(func_def_107, type, ord_less_eq_set_l: set_l > set_l > $o).
% 3.12/1.78 thf(func_def_108, type, ord_less_eq_set_r: set_r > set_r > $o).
% 3.12/1.78 thf(func_def_109, type, top_top_set_option_l: set_option_l).
% 3.12/1.78 thf(func_def_110, type, top_top_set_option_r: set_option_r).
% 3.12/1.78 thf(func_def_111, type, top_to1238153077_r_l_v: set_Pr1409704485_r_l_v).
% 3.12/1.78 thf(func_def_112, type, top_to320296343od_l_l: set_Product_prod_l_l).
% 3.12/1.78 thf(func_def_113, type, top_to715231133od_l_r: set_Product_prod_l_r).
% 3.12/1.78 thf(func_def_114, type, top_to1639761425od_r_l: set_Product_prod_r_l).
% 3.12/1.78 thf(func_def_115, type, top_to2034696215od_r_r: set_Product_prod_r_r).
% 3.12/1.78 thf(func_def_116, type, top_top_set_set_l: set_set_l).
% 3.12/1.78 thf(func_def_117, type, top_top_set_set_r: set_set_r).
% 3.12/1.78 thf(func_def_118, type, top_to1010946379um_l_l: set_Sum_sum_l_l).
% 3.12/1.78 thf(func_def_119, type, top_to1405881169um_l_r: set_Sum_sum_l_r).
% 3.12/1.78 thf(func_def_120, type, top_to182927813um_r_l: set_Sum_sum_r_l).
% 3.12/1.78 thf(func_def_121, type, top_to577862603um_r_r: set_Sum_sum_r_r).
% 3.12/1.78 thf(func_def_122, type, top_top_set_l: set_l).
% 3.12/1.78 thf(func_def_123, type, top_top_set_r: set_r).
% 3.12/1.78 thf(func_def_124, type, produc1834103605_r_l_v: (l > option_val_r_l_v) > expr_r_l_v > produc1164766533_r_l_v).
% 3.12/1.78 thf(func_def_125, type, produc297528454_r_l_v: (l > option_val_r_l_v) > produc1164766533_r_l_v > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_126, type, produc1175464189_r_l_v: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > produc1389397445_r_l_v).
% 3.12/1.78 thf(func_def_127, type, eq_states_r_l_v: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_128, type, collec1978425008_r_l_v: (produc1389397445_r_l_v > $o) > set_Pr1409704485_r_l_v).
% 3.12/1.78 thf(func_def_129, type, collect_set_set_l: (set_set_l > $o) > set_set_set_l).
% 3.12/1.78 thf(func_def_130, type, collect_set_set_r: (set_set_r > $o) > set_set_set_r).
% 3.12/1.78 thf(func_def_131, type, collec1593187440um_l_l: (set_Sum_sum_l_l > $o) > set_set_Sum_sum_l_l).
% 3.12/1.78 thf(func_def_132, type, collec1988122230um_l_r: (set_Sum_sum_l_r > $o) > set_set_Sum_sum_l_r).
% 3.12/1.78 thf(func_def_133, type, collec765168874um_r_l: (set_Sum_sum_r_l > $o) > set_set_Sum_sum_r_l).
% 3.12/1.78 thf(func_def_134, type, collect_set_l: (set_l > $o) > set_set_l).
% 3.12/1.78 thf(func_def_135, type, collect_set_r: (set_r > $o) > set_set_r).
% 3.12/1.78 thf(func_def_136, type, collect_Sum_sum_l_l: (sum_sum_l_l > $o) > set_Sum_sum_l_l).
% 3.12/1.78 thf(func_def_137, type, collect_Sum_sum_l_r: (sum_sum_l_r > $o) > set_Sum_sum_l_r).
% 3.12/1.78 thf(func_def_138, type, collect_Sum_sum_r_l: (sum_sum_r_l > $o) > set_Sum_sum_r_l).
% 3.12/1.78 thf(func_def_139, type, collect_l: (l > $o) > set_l).
% 3.12/1.78 thf(func_def_140, type, collect_r: (r > $o) > set_r).
% 3.12/1.78 thf(func_def_141, type, substitution_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > $o).
% 3.12/1.78 thf(func_def_142, type, transi1323086383_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v).
% 3.12/1.78 thf(func_def_143, type, member1522896238_r_l_v: produc1389397445_r_l_v > set_Pr1409704485_r_l_v > $o).
% 3.12/1.78 thf(func_def_144, type, member_set_l: set_l > set_set_l > $o).
% 3.12/1.78 thf(func_def_145, type, member_set_r: set_r > set_set_r > $o).
% 3.12/1.78 thf(func_def_146, type, member_l: l > set_l > $o).
% 3.12/1.78 thf(func_def_147, type, member_r: r > set_r > $o).
% 3.12/1.78 thf(func_def_148, type, e: cntxt_r_l_v).
% 3.12/1.78 thf(func_def_149, type, e2: cntxt_r_l_v).
% 3.12/1.78 thf(func_def_150, type, sigma: l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_151, type, sigma2: l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_152, type, tau: l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_153, type, tau2: l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_154, type, e3: expr_r_l_v).
% 3.12/1.78 thf(func_def_155, type, e4: expr_r_l_v).
% 3.12/1.78 thf(func_def_156, type, left_forkee: r).
% 3.12/1.78 thf(func_def_157, type, r2: r).
% 3.12/1.78 thf(func_def_158, type, r3: r).
% 3.12/1.78 thf(func_def_159, type, right_forkee: r).
% 3.12/1.78 thf(func_def_160, type, s_1: r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_161, type, s_2: r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_162, type, s_22: r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_163, type, subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_179, type, sP0: (option_val_r_l_v > option_val_r_l_v > $o) > option_val_r_l_v > option_val_r_l_v > $o).
% 3.12/1.78 thf(func_def_180, type, sP1: (option1457017436_r_l_v > option_val_r_l_v > $o) > option_val_r_l_v > option1457017436_r_l_v > $o).
% 3.12/1.78 thf(func_def_181, type, sP2: (option1457017436_r_l_v > option1457017436_r_l_v > $o) > option1457017436_r_l_v > option1457017436_r_l_v > $o).
% 3.12/1.78 thf(func_def_182, type, sP3: (option_val_r_l_v > option1457017436_r_l_v > $o) > option_val_r_l_v > option1457017436_r_l_v > $o).
% 3.12/1.78 thf(func_def_183, type, sP4: r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_184, type, sP5: r > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > $o).
% 3.12/1.78 thf(func_def_185, type, sK6: (option_val_r_l_v > option_val_r_l_v > $o) > option_val_r_l_v > option_val_r_l_v > val_r_l_v).
% 3.12/1.78 thf(func_def_186, type, sK7: (option_val_r_l_v > option_val_r_l_v > $o) > option_val_r_l_v > option_val_r_l_v > val_r_l_v).
% 3.12/1.78 thf(func_def_187, type, sK8: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_188, type, sK9: (r > option1457017436_r_l_v) > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_189, type, sK10: (option1457017436_r_l_v > option_val_r_l_v > $o) > option_val_r_l_v > option1457017436_r_l_v > val_r_l_v).
% 3.12/1.78 thf(func_def_190, type, sK11: (option1457017436_r_l_v > option_val_r_l_v > $o) > option_val_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_191, type, sK12: (option1457017436_r_l_v > option1457017436_r_l_v > $o) > option1457017436_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_192, type, sK13: (option1457017436_r_l_v > option1457017436_r_l_v > $o) > option1457017436_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_193, type, sK14: option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_194, type, sK15: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_195, type, sK16: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_196, type, sK17: (r > $o) > r).
% 3.12/1.78 thf(func_def_197, type, sK18: produc1389397445_r_l_v > (produc1389397445_r_l_v > option_val_r_l_v) > val_r_l_v).
% 3.12/1.78 thf(func_def_198, type, sK19: set_l > l).
% 3.12/1.78 thf(func_def_199, type, sK20: set_l > set_set_l > set_l).
% 3.12/1.78 thf(func_def_200, type, sK21: (r > option_val_r_l_v) > r).
% 3.12/1.78 thf(func_def_201, type, sK22: (r > option1457017436_r_l_v) > cntxt_r_l_v > expr_r_l_v > r > (l > option_val_r_l_v) > (l > option_val_r_l_v) > (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_202, type, sK23: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_203, type, sK24: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_204, type, sK25: option_val_r_l_v > val_r_l_v).
% 3.12/1.78 thf(func_def_205, type, sK26: option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_206, type, sK27: set_l > set_set_l > set_l).
% 3.12/1.78 thf(func_def_207, type, sK28: (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_208, type, sK29: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_209, type, sK30: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_210, type, sK31: (option_val_r_l_v > option1457017436_r_l_v > $o) > option_val_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_211, type, sK32: (option_val_r_l_v > option1457017436_r_l_v > $o) > option_val_r_l_v > option1457017436_r_l_v > val_r_l_v).
% 3.12/1.78 thf(func_def_212, type, sK33: (option1457017436_r_l_v > $o) > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_213, type, sK34: expr_r_l_v > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_214, type, sK35: (produc1389397445_r_l_v > $o) > (produc1389397445_r_l_v > $o) > produc1389397445_r_l_v).
% 3.12/1.78 thf(func_def_215, type, sK36: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_216, type, sK37: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_217, type, sK38: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_218, type, sK39: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_219, type, sK40: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_220, type, sK41: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_221, type, sK42: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_222, type, sK43: (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_223, type, sK44: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_224, type, sK45: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_225, type, sK46: set_Pr1409704485_r_l_v > set_l > (produc1389397445_r_l_v > l > $o) > produc1389397445_r_l_v).
% 3.12/1.78 thf(func_def_226, type, sK47: set_Pr1409704485_r_l_v > set_l > (produc1389397445_r_l_v > l > $o) > l).
% 3.12/1.78 thf(func_def_227, type, sK48: r > (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_228, type, sK49: r > (r > option1457017436_r_l_v) > cntxt_r_l_v).
% 3.12/1.78 thf(func_def_229, type, sK50: r > (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_230, type, sK51: r > (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_231, type, sK52: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_232, type, sK53: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_233, type, sK54: (l > r > $o) > set_l > set_r > r).
% 3.12/1.78 thf(func_def_234, type, sK55: (l > r > $o) > set_l > set_r > l).
% 3.12/1.78 thf(func_def_235, type, sK56: r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_236, type, sK57: r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_237, type, sK58: (r > option1457017436_r_l_v) > l).
% 3.12/1.78 thf(func_def_238, type, sK59: (r > option1457017436_r_l_v) > l).
% 3.12/1.78 thf(func_def_239, type, sK60: (l > option_val_r_l_v) > l).
% 3.12/1.78 thf(func_def_240, type, sK61: (l > option1457017436_r_l_v) > l > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_241, type, sK62: r > (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_242, type, sK63: r > (r > option1457017436_r_l_v) > cntxt_r_l_v).
% 3.12/1.78 thf(func_def_243, type, sK64: r > (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_244, type, sK65: r > (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_245, type, sK66: r > (r > option1457017436_r_l_v) > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_246, type, sK67: r > (r > option1457017436_r_l_v) > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_247, type, sK68: r > (r > option1457017436_r_l_v) > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_248, type, sK69: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_249, type, sK70: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_250, type, sK71: (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_251, type, sK72: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_252, type, sK73: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_253, type, sK74: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_254, type, sK75: (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_255, type, sK76: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_256, type, sK77: set_set_r > set_r > set_r).
% 3.12/1.78 thf(func_def_257, type, sK78: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_258, type, sK79: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_259, type, sK80: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_260, type, sK81: (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_261, type, sK82: (set_r > $o) > (set_r > $o) > set_r).
% 3.12/1.78 thf(func_def_262, type, sK83: set_Pr1409704485_r_l_v > produc1389397445_r_l_v).
% 3.12/1.78 thf(func_def_263, type, sK84: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_264, type, sK85: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_265, type, sK86: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_266, type, sK87: (l > option_val_r_l_v) > (r > option1457017436_r_l_v) > cntxt_r_l_v > (l > option_val_r_l_v) > (r > option1457017436_r_l_v) > r > val_r_l_v > l).
% 3.12/1.78 thf(func_def_267, type, sK88: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_268, type, sK89: (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_269, type, sK90: (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_270, type, sK91: (option_val_r_l_v > $o) > val_r_l_v).
% 3.12/1.78 thf(func_def_271, type, sK92: r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_272, type, sK93: r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_273, type, sK94: (r > l > $o) > set_l > set_r > l).
% 3.12/1.78 thf(func_def_274, type, sK95: (r > l > $o) > set_l > set_r > r).
% 3.12/1.78 thf(func_def_275, type, sK96: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_276, type, sK97: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_277, type, sK98: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_278, type, sK99: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_279, type, sK100: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_280, type, sK101: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_281, type, sK102: (r > option1457017436_r_l_v) > r > val_r_l_v).
% 3.12/1.78 thf(func_def_282, type, sK103: (r > option1457017436_r_l_v) > r > cntxt_r_l_v).
% 3.12/1.78 thf(func_def_283, type, sK104: (set_l > $o) > (set_l > $o) > set_l).
% 3.12/1.78 thf(func_def_284, type, sK105: r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_285, type, sK106: r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_286, type, sK107: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_287, type, sK108: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_288, type, sK109: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_289, type, sK110: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_290, type, sK111: (r > option1457017436_r_l_v) > r > expr_r_l_v).
% 3.12/1.78 thf(func_def_291, type, sK112: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_292, type, sK113: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_293, type, sK114: (r > option1457017436_r_l_v) > r > cntxt_r_l_v).
% 3.12/1.78 thf(func_def_294, type, sK115: (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_295, type, sK116: (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_296, type, sK117: (l > l > $o) > set_l > set_l > l).
% 3.12/1.78 thf(func_def_297, type, sK118: (l > l > $o) > set_l > set_l > l).
% 3.12/1.78 thf(func_def_298, type, sK119: val_r_l_v > cntxt_r_l_v > r > (l > option_val_r_l_v) > (l > option_val_r_l_v) > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > l).
% 3.12/1.78 thf(func_def_299, type, sK120: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_300, type, sK121: (r > option1457017436_r_l_v) > r > cntxt_r_l_v).
% 3.12/1.78 thf(func_def_301, type, sK122: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_302, type, sK123: (r > option1457017436_r_l_v) > r > val_r_l_v).
% 3.12/1.78 thf(func_def_303, type, sK124: (produc1389397445_r_l_v > option1457017436_r_l_v) > produc1389397445_r_l_v > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_304, type, sK125: r > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_305, type, sK126: r > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_306, type, sK127: (r > option1457017436_r_l_v) > r > cntxt_r_l_v).
% 3.12/1.78 thf(func_def_307, type, sK128: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_308, type, sK129: (r > option1457017436_r_l_v) > r > expr_r_l_v).
% 3.12/1.78 thf(func_def_309, type, sK130: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_310, type, sK131: (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_311, type, sK132: option1457017436_r_l_v > ((r > option1457017436_r_l_v) > $o) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_312, type, sK133: option1457017436_r_l_v > ((r > option1457017436_r_l_v) > $o) > r).
% 3.12/1.78 thf(func_def_313, type, sK134: option1457017436_r_l_v > ((r > option1457017436_r_l_v) > $o) > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_314, type, sK135: r > (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_315, type, sK136: r > (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_316, type, sK137: r > (r > option1457017436_r_l_v) > val_r_l_v).
% 3.12/1.78 thf(func_def_317, type, sK138: r > (r > option1457017436_r_l_v) > cntxt_r_l_v).
% 3.12/1.78 thf(func_def_318, type, sK139: produc1156025366_r_l_v > expr_r_l_v).
% 3.12/1.78 thf(func_def_319, type, sK140: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_320, type, sK141: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_321, type, sK142: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_322, type, sK143: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_323, type, sK144: (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_324, type, sK145: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_325, type, sK146: (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.12/1.78 thf(func_def_326, type, sK147: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_327, type, sK148: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_328, type, sK149: (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_329, type, sK150: r > (r > option_val_r_l_v) > val_r_l_v).
% 3.12/1.78 thf(func_def_330, type, sK151: (r > option1457017436_r_l_v) > cntxt_r_l_v > (l > option_val_r_l_v) > (l > option_val_r_l_v) > (r > option1457017436_r_l_v) > expr_r_l_v > r > r).
% 3.12/1.78 thf(func_def_331, type, sK152: r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_332, type, sK153: r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_333, type, sK154: option_val_r_l_v > ((l > option_val_r_l_v) > $o) > option_val_r_l_v).
% 3.12/1.78 thf(func_def_334, type, sK155: option_val_r_l_v > ((l > option_val_r_l_v) > $o) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_335, type, sK156: option_val_r_l_v > ((l > option_val_r_l_v) > $o) > l).
% 3.12/1.78 thf(func_def_336, type, sK157: option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_337, type, sK158: (r > option1457017436_r_l_v) > expr_r_l_v > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_338, type, sK159: set_set_r > set_r > set_r).
% 3.12/1.78 thf(func_def_339, type, sK160: (r > option1457017436_r_l_v) > r > cntxt_r_l_v).
% 3.12/1.78 thf(func_def_340, type, sK161: (r > option1457017436_r_l_v) > r > val_r_l_v).
% 3.12/1.78 thf(func_def_341, type, sK162: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_342, type, sK163: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_343, type, sK164: option_val_r_l_v > val_r_l_v).
% 3.12/1.78 thf(func_def_344, type, sK165: r > r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_345, type, sK166: r > r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_346, type, sK167: (l > $o) > l).
% 3.12/1.78 thf(func_def_347, type, sK168: (r > option1457017436_r_l_v) > l > produc1156025366_r_l_v).
% 3.12/1.78 thf(func_def_348, type, sK169: (r > option1457017436_r_l_v) > l > r).
% 3.12/1.78 thf(func_def_349, type, sK170: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_350, type, sK171: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_351, type, sK172: (l > option1457017436_r_l_v) > l).
% 3.12/1.78 thf(func_def_352, type, sK173: (l > $o) > (l > $o) > l).
% 3.12/1.78 thf(func_def_353, type, sK174: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_354, type, sK175: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_355, type, sK176: (r > option1457017436_r_l_v) > r).
% 3.12/1.78 thf(func_def_356, type, sK177: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_357, type, sK178: (produc1156025366_r_l_v > $o) > expr_r_l_v).
% 3.12/1.78 thf(func_def_358, type, sK179: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.12/1.78 thf(func_def_359, type, sK180: r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_360, type, sK181: r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.12/1.78 thf(func_def_361, type, sK182: (produc1389397445_r_l_v > r > $o) > set_Pr1409704485_r_l_v > set_r > produc1389397445_r_l_v).
% 3.12/1.78 thf(func_def_362, type, sK183: (produc1389397445_r_l_v > r > $o) > set_Pr1409704485_r_l_v > set_r > r).
% 3.12/1.78 thf(func_def_363, type, sK184: set_r > r).
% 3.12/1.78 thf(func_def_364, type, sK185: option_val_r_l_v > val_r_l_v).
% 3.12/1.78 thf(func_def_365, type, sK186: l > (l > option_val_r_l_v) > val_r_l_v).
% 3.12/1.78 thf(func_def_366, type, sK187: (r > $o) > (r > $o) > r).
% 3.12/1.78 thf(func_def_367, type, sK188: set_r > set_r > (r > r > $o) > r).
% 3.12/1.78 thf(func_def_368, type, sK189: set_r > set_r > (r > r > $o) > r).
% 3.12/1.78 thf(func_def_370, type, ph191: !>[X0: $tType]:(X0)).
% 3.12/1.78 thf(func_def_371, type, sK192: r).
% 3.12/1.78 thf(f2588,plain,(
% 3.12/1.78 $false),
% 3.12/1.78 inference(trivial_inequality_removal,[status(thm)],[f2580])).
% 3.12/1.78 thf(f2580,plain,(
% 3.12/1.78 ((s_1 @ r3) != (s_1 @ r3))),
% 3.12/1.78 inference(superposition,[status(thm)],[f2427,f1829])).
% 3.12/1.78 thf(f1829,plain,(
% 3.12/1.78 ((s_1 @ r3) = (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ sigma2 @ (produc1834103605_r_l_v @ tau2 @ (plug_r_l_v @ e2 @ (rfork_r_l_v @ e4))))))),
% 3.12/1.78 inference(cnf_transformation,[status(thm)],[f7])).
% 3.12/1.78 thf(f7,axiom,(
% 3.12/1.78 ((s_1 @ r3) = (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ sigma2 @ (produc1834103605_r_l_v @ tau2 @ (plug_r_l_v @ e2 @ (rfork_r_l_v @ e4))))))),
% 3.12/1.78 file('/export/starexec/sandbox/tmp/tmp.a64ubDLv2V/DTF2THF_3281.p',fact_6_local_Ofork_I2_J)).
% 3.12/1.78 thf(f2427,plain,(
% 3.12/1.78 ( ! [X0 : produc1156025366_r_l_v] : (((s_1 @ r3) != (some_P1807977723_r_l_v @ X0))) )),
% 3.12/1.78 inference(trivial_inequality_removal,[status(thm)],[f2425])).
% 3.12/1.78 thf(f2425,plain,(
% 3.12/1.78 ( ! [X0 : produc1156025366_r_l_v] : (($true != $true) | ((s_1 @ r3) != (some_P1807977723_r_l_v @ X0))) )),
% 3.12/1.78 inference(superposition,[status(thm)],[f2422,f2159])).
% 3.12/1.78 thf(f2159,plain,(
% 3.12/1.78 ( ! [X2 : r,X0 : r > option1457017436_r_l_v,X1 : produc1156025366_r_l_v] : (($true = (member_r @ X2 @ (rID_G_r_l_v @ X0))) | ((some_P1807977723_r_l_v @ X1) != (X0 @ X2))) )),
% 3.12/1.78 inference(cnf_transformation,[status(thm)],[f1067])).
% 3.12/1.78 thf(f1067,plain,(
% 3.12/1.78 ! [X0 : r > option1457017436_r_l_v,X1 : produc1156025366_r_l_v,X2 : r] : (((some_P1807977723_r_l_v @ X1) != (X0 @ X2)) | ($true = (member_r @ X2 @ (rID_G_r_l_v @ X0))))),
% 3.12/1.78 inference(ennf_transformation,[status(thm)],[f506])).
% 3.12/1.78 thf(f506,plain,(
% 3.12/1.78 ! [X0 : r > option1457017436_r_l_v,X1 : produc1156025366_r_l_v,X2 : r] : (((some_P1807977723_r_l_v @ X1) = (X0 @ X2)) => ($true = (member_r @ X2 @ (rID_G_r_l_v @ X0))))),
% 3.12/1.78 inference(fool_elimination,[status(thm)],[f505])).
% 3.12/1.78 thf(f505,plain,(
% 3.12/1.78 ! [X0 : r > option1457017436_r_l_v,X1 : produc1156025366_r_l_v,X2 : r] : (((some_P1807977723_r_l_v @ X1) = (X0 @ X2)) => (member_r @ X2 @ (rID_G_r_l_v @ X0)))),
% 3.12/1.78 inference(rectify,[status(thm)],[f25])).
% 3.12/1.78 thf(f25,axiom,(
% 3.12/1.78 ! [X2 : r > option1457017436_r_l_v,X24 : produc1156025366_r_l_v,X1 : r] : (((X2 @ X1) = (some_P1807977723_r_l_v @ X24)) => (member_r @ X1 @ (rID_G_r_l_v @ X2)))),
% 3.12/1.78 file('/export/starexec/sandbox/tmp/tmp.a64ubDLv2V/DTF2THF_3281.p',fact_24_RID_092_060_094sub_062GI_I1_J)).
% 3.12/1.78 thf(f2422,plain,(
% 3.12/1.78 ($true != (member_r @ r3 @ (rID_G_r_l_v @ s_1)))),
% 3.12/1.78 inference(superposition,[status(thm)],[f2067,f1948])).
% 3.12/1.78 thf(f1948,plain,(
% 3.12/1.78 (right_forkee = r3)),
% 3.12/1.78 inference(cnf_transformation,[status(thm)],[f953])).
% 3.12/1.78 thf(f953,plain,(
% 3.12/1.78 (right_forkee = r3)),
% 3.12/1.78 inference(flattening,[status(thm)],[f359])).
% 3.12/1.78 thf(f359,negated_conjecture,(
% 3.12/1.78 ~(right_forkee != r3)),
% 3.12/1.78 inference(negated_conjecture,[status(cth)],[f358])).
% 3.12/1.78 thf(f358,conjecture,(
% 3.12/1.78 (right_forkee != r3)),
% 3.12/1.78 file('/export/starexec/sandbox/tmp/tmp.a64ubDLv2V/DTF2THF_3281.p',conj_0)).
% 3.12/1.78 thf(f2067,plain,(
% 3.12/1.78 ((member_r @ right_forkee @ (rID_G_r_l_v @ s_1)) != $true)),
% 3.12/1.78 inference(cnf_transformation,[status(thm)],[f922])).
% 3.12/1.78 thf(f922,plain,(
% 3.12/1.78 ((member_r @ right_forkee @ (rID_G_r_l_v @ s_1)) != $true)),
% 3.12/1.78 inference(flattening,[status(thm)],[f366])).
% 3.12/1.78 thf(f366,plain,(
% 3.12/1.78 ~((member_r @ right_forkee @ (rID_G_r_l_v @ s_1)) = $true)),
% 3.12/1.78 inference(fool_elimination,[status(thm)],[f365])).
% 3.12/1.78 thf(f365,plain,(
% 3.12/1.78 ~(member_r @ right_forkee @ (rID_G_r_l_v @ s_1))),
% 3.12/1.78 inference(rectify,[status(thm)],[f1])).
% 3.12/1.78 thf(f1,axiom,(
% 3.12/1.78 ~(member_r @ right_forkee @ (rID_G_r_l_v @ s_1))),
% 3.12/1.78 file('/export/starexec/sandbox/tmp/tmp.a64ubDLv2V/DTF2THF_3281.p',fact_0_local_Ofork_I3_J)).
% 3.12/1.78 % SZS output end Proof for DTF2THF_3281
% 3.12/1.78 % (3403)------------------------------
% 3.12/1.78 % (3403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.78 % (3403)Termination reason: Refutation
% 3.12/1.78
% 3.12/1.78 % (3403)Memory used [KB]: 8699
% 3.12/1.78 % (3403)Time elapsed: 0.104 s
% 3.12/1.78 % (3403)Instructions burned: 362 (million)
% 3.12/1.78 % (3403)------------------------------
% 3.12/1.78 % (3403)------------------------------
% 3.12/1.78 % (3380)Success in time 0.188 s
%------------------------------------------------------------------------------