%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP141^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:52 AM UTC 2026
% Result : Theorem 2.92s 2.01s
% Output : Refutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 26
% Syntax : Number of formulae : 177 ( 6 unt; 0 typ; 14 def)
% Number of atoms : 1814 ( 567 equ; 0 cnn)
% Maximal formula atoms : 21 ( 10 avg)
% Number of connectives : 2433 ( 362 ~; 398 |; 145 &;1450 @)
% ( 14 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 21 ( 20 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 301 ( 297 usr; 38 con; 0-5 aty)
% ( 0 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 403 ( 96 ^; 256 !; 51 ?; 403 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_7,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_8,type,
set_nat: $tType ).
thf(type_def_9,type,
set_Pr795498619_state: $tType ).
thf(type_def_10,type,
state: $tType ).
thf(type_def_11,type,
set_state: $tType ).
thf(type_def_12,type,
set_Pr1702239303tate_o: $tType ).
thf(type_def_13,type,
produc696469763tate_o: $tType ).
thf(type_def_14,type,
set_Pr1590995257tate_o: $tType ).
thf(type_def_15,type,
set_Pr1490359111at_nat: $tType ).
thf(type_def_16,type,
product_prod_nat_nat: $tType ).
thf(type_def_17,type,
set_Pr778812871_state: $tType ).
thf(type_def_18,type,
produc1115495963_state: $tType ).
thf(type_def_19,type,
a: $tType ).
thf(type_def_20,type,
produc204914599tate_o: $tType ).
thf(type_def_21,type,
com: $tType ).
thf(type_def_22,type,
set_Pr1740974983tate_o: $tType ).
thf(type_def_23,type,
produc1307154919tate_o: $tType ).
thf(type_def_24,type,
produc842455143at_nat: $tType ).
thf(type_def_25,type,
produc1390548711_state: $tType ).
thf(func_def_0,type,
set_Pr1702239303tate_o: $tType ).
thf(func_def_1,type,
produc1307154919tate_o: $tType ).
thf(func_def_2,type,
set_Pr1590995257tate_o: $tType ).
thf(func_def_3,type,
set_Pr778812871_state: $tType ).
thf(func_def_4,type,
produc696469763tate_o: $tType ).
thf(func_def_5,type,
set_Pr1490359111at_nat: $tType ).
thf(func_def_6,type,
produc1390548711_state: $tType ).
thf(func_def_7,type,
produc842455143at_nat: $tType ).
thf(func_def_8,type,
set_Pr1740974983tate_o: $tType ).
thf(func_def_9,type,
produc204914599tate_o: $tType ).
thf(func_def_10,type,
set_Pr795498619_state: $tType ).
thf(func_def_11,type,
set_Pr1986765409at_nat: $tType ).
thf(func_def_12,type,
produc1115495963_state: $tType ).
thf(func_def_13,type,
product_prod_nat_nat: $tType ).
thf(func_def_14,type,
set_state: $tType ).
thf(func_def_15,type,
set_nat: $tType ).
thf(func_def_16,type,
state: $tType ).
thf(func_def_17,type,
com: $tType ).
thf(func_def_18,type,
nat: $tType ).
thf(func_def_19,type,
a: $tType ).
thf(func_def_20,type,
suc: nat > nat ).
thf(func_def_21,type,
order_aboveS_nat: set_Pr1986765409at_nat > nat > set_nat ).
thf(func_def_22,type,
order_aboveS_state: set_Pr795498619_state > state > set_state ).
thf(func_def_23,type,
order_1121016664tate_o: set_Pr1702239303tate_o > produc696469763tate_o > set_Pr1590995257tate_o ).
thf(func_def_24,type,
order_665764460at_nat: set_Pr1490359111at_nat > product_prod_nat_nat > set_Pr1986765409at_nat ).
thf(func_def_25,type,
order_2027321734_state: set_Pr778812871_state > produc1115495963_state > set_Pr795498619_state ).
thf(func_def_26,type,
order_130026331on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_27,type,
order_286167592_state: set_state > set_Pr795498619_state > $o ).
thf(func_def_28,type,
order_50454158tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o ).
thf(func_def_29,type,
order_721919926at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_30,type,
order_178668240_state: set_Pr795498619_state > set_Pr778812871_state > $o ).
thf(func_def_31,type,
bot_bo2130564770te_o_o: ( a > state > $o ) > produc204914599tate_o > $o ).
thf(func_def_32,type,
bot_bot_nat_nat_o: nat > nat > $o ).
thf(func_def_33,type,
bot_bo935656620te_o_o: com > ( a > state > $o ) > $o ).
thf(func_def_34,type,
bot_bo51534648tate_o: state > state > $o ).
thf(func_def_35,type,
bot_bo250281208te_o_o: produc696469763tate_o > $o ).
thf(func_def_36,type,
bot_bo513358416_nat_o: product_prod_nat_nat > $o ).
thf(func_def_37,type,
bot_bo446391478tate_o: produc1115495963_state > $o ).
thf(func_def_38,type,
bot_bot_set_nat: set_nat ).
thf(func_def_39,type,
bot_bot_set_state: set_state ).
thf(func_def_40,type,
bot_bo170732493tate_o: set_Pr1590995257tate_o ).
thf(func_def_41,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(func_def_42,type,
bot_bo1692783091tate_o: set_Pr1740974983tate_o ).
thf(func_def_43,type,
bot_bo1625160935_state: set_Pr795498619_state ).
thf(func_def_44,type,
bot_bo1714653363tate_o: set_Pr1702239303tate_o ).
thf(func_def_45,type,
bot_bo34127283at_nat: set_Pr1490359111at_nat ).
thf(func_def_46,type,
bot_bo1331673139_state: set_Pr778812871_state ).
thf(func_def_47,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_48,type,
pHoare382919414oare_a: set_Pr1590995257tate_o > ( a > state > $o ) > com > ( a > state > $o ) > $o ).
thf(func_def_49,type,
hoare_a: set_Pr1590995257tate_o > ( a > state > $o ) > com > ( a > state > $o ) > $o ).
thf(func_def_50,type,
body: com ).
thf(func_def_51,type,
call: com ).
thf(func_def_52,type,
semi: com > com > com ).
thf(func_def_53,type,
while: ( state > $o ) > com > com ).
thf(func_def_54,type,
exec: state > com > state > $o ).
thf(func_def_55,type,
execn: state > com > nat > state > $o ).
thf(func_def_56,type,
termi: com > state > $o ).
thf(func_def_57,type,
produc33908149tate_o: ( a > state > $o ) > produc204914599tate_o > produc696469763tate_o ).
thf(func_def_58,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_59,type,
produc1948644831tate_o: com > ( a > state > $o ) > produc204914599tate_o ).
thf(func_def_60,type,
produc64584659_state: state > state > produc1115495963_state ).
thf(func_def_61,type,
produc1684562079tate_o: produc696469763tate_o > produc696469763tate_o > produc1307154919tate_o ).
thf(func_def_62,type,
produc1168807639at_nat: product_prod_nat_nat > product_prod_nat_nat > produc842455143at_nat ).
thf(func_def_63,type,
produc1964772951_state: produc1115495963_state > produc1115495963_state > produc1390548711_state ).
thf(func_def_64,type,
produc385877620_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_65,type,
produc938968666tate_o: ( state > state > $o ) > produc1115495963_state > $o ).
thf(func_def_66,type,
produc1271576886te_o_o: ( ( a > state > $o ) > produc204914599tate_o > $o ) > produc696469763tate_o > $o ).
thf(func_def_67,type,
produc949581770_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_68,type,
produc1610543495tate_o: ( nat > nat > set_Pr1590995257tate_o ) > product_prod_nat_nat > set_Pr1590995257tate_o ).
thf(func_def_69,type,
produc1915186323at_nat: ( nat > nat > set_Pr1986765409at_nat ) > product_prod_nat_nat > set_Pr1986765409at_nat ).
thf(func_def_70,type,
produc1654445_state: ( nat > nat > set_Pr795498619_state ) > product_prod_nat_nat > set_Pr795498619_state ).
thf(func_def_71,type,
produc281270436te_o_o: ( com > ( a > state > $o ) > $o ) > produc204914599tate_o > $o ).
thf(func_def_72,type,
produc789892016tate_o: ( state > state > $o ) > produc1115495963_state > $o ).
thf(func_def_73,type,
irrefl_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_74,type,
refl_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_75,type,
refl_on_state: set_state > set_Pr795498619_state > $o ).
thf(func_def_76,type,
refl_o489021252tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o ).
thf(func_def_77,type,
refl_o1619599232at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_78,type,
refl_o1438232218_state: set_Pr795498619_state > set_Pr778812871_state > $o ).
thf(func_def_79,type,
total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_80,type,
total_on_state: set_state > set_Pr795498619_state > $o ).
thf(func_def_81,type,
total_795385983tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o ).
thf(func_def_82,type,
total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_83,type,
total_1316653983_state: set_Pr795498619_state > set_Pr778812871_state > $o ).
thf(func_def_84,type,
trans_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_85,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_86,type,
collect_state: ( state > $o ) > set_state ).
thf(func_def_87,type,
collec1499596504tate_o: ( produc696469763tate_o > $o ) > set_Pr1590995257tate_o ).
thf(func_def_88,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_89,type,
collec496201222_state: ( produc1115495963_state > $o ) > set_Pr795498619_state ).
thf(func_def_90,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_91,type,
insert_state: state > set_state > set_state ).
thf(func_def_92,type,
insert2053719859tate_o: produc696469763tate_o > set_Pr1590995257tate_o > set_Pr1590995257tate_o ).
thf(func_def_93,type,
insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_94,type,
insert311944171_state: produc1115495963_state > set_Pr795498619_state > set_Pr795498619_state ).
thf(func_def_95,type,
insert1597128631tate_o: produc1307154919tate_o > set_Pr1702239303tate_o > set_Pr1702239303tate_o ).
thf(func_def_96,type,
insert584009271at_nat: produc842455143at_nat > set_Pr1490359111at_nat > set_Pr1490359111at_nat ).
thf(func_def_97,type,
insert1616594103_state: produc1390548711_state > set_Pr778812871_state > set_Pr778812871_state ).
thf(func_def_98,type,
is_emp807847857tate_o: set_Pr1590995257tate_o > $o ).
thf(func_def_99,type,
is_emp825011411at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_100,type,
is_emp1062983149_state: set_Pr795498619_state > $o ).
thf(func_def_101,type,
is_sin1547905295tate_o: set_Pr1590995257tate_o > $o ).
thf(func_def_102,type,
is_sin1352690165at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_103,type,
is_sin1132515087_state: set_Pr795498619_state > $o ).
thf(func_def_104,type,
the_el1569055182tate_o: set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_105,type,
the_el1949240438at_nat: set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_106,type,
the_el1967402896_state: set_Pr795498619_state > produc1115495963_state ).
thf(func_def_107,type,
less_than: set_Pr1986765409at_nat ).
thf(func_def_108,type,
measure_nat: ( nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_109,type,
measure_state: ( state > nat ) > set_Pr795498619_state ).
thf(func_def_110,type,
pred_nat: set_Pr1986765409at_nat ).
thf(func_def_111,type,
wf_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_112,type,
wf_state: set_Pr795498619_state > $o ).
thf(func_def_113,type,
wf_Pro309705690tate_o: set_Pr1702239303tate_o > $o ).
thf(func_def_114,type,
wf_Pro745352042at_nat: set_Pr1490359111at_nat > $o ).
thf(func_def_115,type,
wf_Pro1783588484_state: set_Pr778812871_state > $o ).
thf(func_def_116,type,
member_nat: nat > set_nat > $o ).
thf(func_def_117,type,
member_state: state > set_state > $o ).
thf(func_def_118,type,
member1838112666tate_o: produc696469763tate_o > set_Pr1590995257tate_o > $o ).
thf(func_def_119,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_120,type,
member221067728tate_o: produc204914599tate_o > set_Pr1740974983tate_o > $o ).
thf(func_def_121,type,
member1389040324_state: produc1115495963_state > set_Pr795498619_state > $o ).
thf(func_def_122,type,
member1629320336tate_o: produc1307154919tate_o > set_Pr1702239303tate_o > $o ).
thf(func_def_123,type,
member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_124,type,
member768948240_state: produc1390548711_state > set_Pr778812871_state > $o ).
thf(func_def_125,type,
pa: a > state > $o ).
thf(func_def_126,type,
qa: a > state > $o ).
thf(func_def_127,type,
r: set_Pr795498619_state ).
thf(func_def_128,type,
x: state ).
thf(func_def_144,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_145,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_147,type,
sP3: state > $o ).
thf(func_def_148,type,
sK4: set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_149,type,
sK5: set_Pr1986765409at_nat > set_nat > nat ).
thf(func_def_150,type,
sK6: set_Pr1986765409at_nat > set_nat > nat ).
thf(func_def_151,type,
sK7: set_Pr1986765409at_nat > ( nat > $o ) > nat ).
thf(func_def_152,type,
sK8: produc1115495963_state > set_Pr795498619_state > set_Pr795498619_state ).
thf(func_def_153,type,
sK9: produc696469763tate_o > set_Pr1590995257tate_o > set_Pr1590995257tate_o ).
thf(func_def_154,type,
sK10: ( state > state > $o ) > ( state > state > $o ) > produc1115495963_state > state ).
thf(func_def_155,type,
sK11: ( state > state > $o ) > ( state > state > $o ) > produc1115495963_state > state ).
thf(func_def_156,type,
sK12: state > com > com > state ).
thf(func_def_157,type,
sK13: set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_158,type,
sK14: set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_159,type,
sK15: ( nat > nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_160,type,
sK16: ( nat > nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_161,type,
sK17: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_162,type,
sK18: state > ( state > $o ) > com > state ).
thf(func_def_163,type,
sK19: produc1115495963_state > ( state > state > $o ) > state ).
thf(func_def_164,type,
sK20: produc1115495963_state > ( state > state > $o ) > state ).
thf(func_def_165,type,
sK21: ( produc696469763tate_o > $o ) > a > state > $o ).
thf(func_def_166,type,
sK22: ( produc696469763tate_o > $o ) > produc204914599tate_o ).
thf(func_def_167,type,
sK23: ( ( a > state > $o ) > produc204914599tate_o > $o ) > produc696469763tate_o > produc204914599tate_o ).
thf(func_def_168,type,
sK24: ( ( a > state > $o ) > produc204914599tate_o > $o ) > produc696469763tate_o > a > state > $o ).
thf(func_def_169,type,
sK25: set_Pr795498619_state > state > $o ).
thf(func_def_170,type,
sK26: set_Pr795498619_state > state ).
thf(func_def_171,type,
sK27: state > set_Pr795498619_state > state ).
thf(func_def_172,type,
sK28: ( a > state > $o ) > ( a > state > $o ) > state ).
thf(func_def_173,type,
sK29: ( a > state > $o ) > ( a > state > $o ) > a ).
thf(func_def_174,type,
sK30: set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_175,type,
sK31: ( produc696469763tate_o > $o ) > ( produc696469763tate_o > $o ) > produc696469763tate_o ).
thf(func_def_176,type,
sK32: set_Pr795498619_state > set_Pr778812871_state > produc1115495963_state ).
thf(func_def_177,type,
sK33: produc1115495963_state > state ).
thf(func_def_178,type,
sK34: produc1115495963_state > state ).
thf(func_def_179,type,
sK35: produc696469763tate_o > produc204914599tate_o ).
thf(func_def_180,type,
sK36: produc696469763tate_o > a > state > $o ).
thf(func_def_181,type,
sK37: set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_182,type,
sK38: set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_183,type,
sK39: set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_184,type,
sK40: produc204914599tate_o > a > state > $o ).
thf(func_def_185,type,
sK41: produc204914599tate_o > com ).
thf(func_def_186,type,
sK42: com > nat > ( state > $o ) > ( state > $o ) > state ).
thf(func_def_187,type,
sK43: com > nat > ( state > $o ) > ( state > $o ) > state ).
thf(func_def_188,type,
sK44: set_Pr795498619_state > produc1115495963_state ).
thf(func_def_189,type,
sK45: set_Pr795498619_state > produc1115495963_state ).
thf(func_def_190,type,
sK46: ( produc1115495963_state > $o ) > ( produc1115495963_state > $o ) > produc1115495963_state ).
thf(func_def_191,type,
sK47: produc204914599tate_o > a > state > $o ).
thf(func_def_192,type,
sK48: produc204914599tate_o > com ).
thf(func_def_193,type,
sK49: ( state > $o ) > set_Pr795498619_state > state ).
thf(func_def_194,type,
sK50: set_Pr1986765409at_nat > nat ).
thf(func_def_195,type,
sK51: set_Pr1986765409at_nat > set_nat ).
thf(func_def_196,type,
sK52: nat > set_Pr1986765409at_nat > nat ).
thf(func_def_197,type,
sK53: ( produc1115495963_state > $o ) > ( state > state > $o ) > state ).
thf(func_def_198,type,
sK54: ( produc1115495963_state > $o ) > ( state > state > $o ) > state ).
thf(func_def_199,type,
sK55: produc204914599tate_o > ( com > ( a > state > $o ) > $o ) > com ).
thf(func_def_200,type,
sK56: produc204914599tate_o > ( com > ( a > state > $o ) > $o ) > a > state > $o ).
thf(func_def_201,type,
sK57: ( nat > nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_202,type,
sK58: ( nat > nat > $o ) > product_prod_nat_nat > nat ).
thf(func_def_203,type,
sK59: product_prod_nat_nat > nat ).
thf(func_def_204,type,
sK60: product_prod_nat_nat > nat ).
thf(func_def_205,type,
sK61: set_Pr795498619_state > produc1115495963_state ).
thf(func_def_206,type,
sK62: ( produc696469763tate_o > $o ) > a > state > $o ).
thf(func_def_207,type,
sK63: ( produc696469763tate_o > $o ) > produc204914599tate_o ).
thf(func_def_208,type,
sK64: ( produc1115495963_state > $o ) > state ).
thf(func_def_209,type,
sK65: ( produc1115495963_state > $o ) > state ).
thf(func_def_210,type,
sK66: ( state > state > $o ) > produc1115495963_state > state ).
thf(func_def_211,type,
sK67: ( state > state > $o ) > produc1115495963_state > state ).
thf(func_def_212,type,
sK68: ( produc204914599tate_o > $o ) > a > state > $o ).
thf(func_def_213,type,
sK69: ( produc204914599tate_o > $o ) > com ).
thf(func_def_214,type,
sK70: produc696469763tate_o > a > state > $o ).
thf(func_def_215,type,
sK71: produc696469763tate_o > a > state > $o ).
thf(func_def_216,type,
sK72: produc696469763tate_o > com ).
thf(func_def_217,type,
sK73: set_Pr795498619_state > set_state ).
thf(func_def_218,type,
sK74: set_Pr795498619_state > state ).
thf(func_def_219,type,
sK75: state > set_Pr795498619_state > state ).
thf(func_def_220,type,
sK76: set_Pr778812871_state > set_Pr795498619_state > produc1115495963_state ).
thf(func_def_221,type,
sK77: set_Pr1702239303tate_o > set_Pr1590995257tate_o ).
thf(func_def_222,type,
sK78: set_Pr1702239303tate_o > produc696469763tate_o ).
thf(func_def_223,type,
sK79: produc696469763tate_o > set_Pr1702239303tate_o > produc696469763tate_o ).
thf(func_def_224,type,
sK80: product_prod_nat_nat > product_prod_nat_nat > ( nat > nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_225,type,
sK81: product_prod_nat_nat > product_prod_nat_nat > ( nat > nat > set_Pr1986765409at_nat ) > nat ).
thf(func_def_226,type,
sK82: ( nat > $o ) > set_Pr1986765409at_nat > nat ).
thf(func_def_227,type,
sK83: ( a > state > $o ) > ( a > state > $o ) > set_Pr795498619_state > state ).
thf(func_def_228,type,
sK84: ( produc204914599tate_o > $o ) > com ).
thf(func_def_229,type,
sK85: ( produc204914599tate_o > $o ) > a > state > $o ).
thf(func_def_230,type,
sK86: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_231,type,
sK87: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_232,type,
sK88: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_233,type,
sK89: ( a > state > $o ) > ( a > state > $o ) > state ).
thf(func_def_234,type,
sK90: ( a > state > $o ) > ( a > state > $o ) > a ).
thf(func_def_235,type,
sK91: ( a > state > $o ) > ( a > state > $o ) > ( a > state > $o ) > ( a > state > $o ) > state ).
thf(func_def_236,type,
sK92: ( a > state > $o ) > ( a > state > $o ) > ( a > state > $o ) > ( a > state > $o ) > state ).
thf(func_def_237,type,
sK93: ( a > state > $o ) > ( a > state > $o ) > ( a > state > $o ) > ( a > state > $o ) > a ).
thf(func_def_238,type,
sK94: ( produc1115495963_state > $o ) > state ).
thf(func_def_239,type,
sK95: ( produc1115495963_state > $o ) > state ).
thf(func_def_240,type,
sK96: ( com > ( a > state > $o ) > $o ) > produc204914599tate_o > com ).
thf(func_def_241,type,
sK97: ( com > ( a > state > $o ) > $o ) > produc204914599tate_o > a > state > $o ).
thf(func_def_242,type,
sK98: ( ( a > state > $o ) > produc204914599tate_o > $o ) > produc696469763tate_o > produc204914599tate_o ).
thf(func_def_243,type,
sK99: ( ( a > state > $o ) > produc204914599tate_o > $o ) > produc696469763tate_o > a > state > $o ).
thf(func_def_244,type,
sK100: set_Pr795498619_state > set_Pr778812871_state > produc1115495963_state ).
thf(func_def_245,type,
sK101: set_Pr795498619_state > set_Pr778812871_state > produc1115495963_state ).
thf(func_def_246,type,
sK102: set_Pr1986765409at_nat > set_Pr1490359111at_nat > product_prod_nat_nat ).
thf(func_def_247,type,
sK103: set_state > set_Pr795498619_state > state ).
thf(func_def_248,type,
sK104: set_Pr1702239303tate_o > set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_249,type,
sK105: set_Pr1702239303tate_o > set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_250,type,
sK106: set_Pr1702239303tate_o > set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_251,type,
sK107: set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_252,type,
sK108: product_prod_nat_nat > produc696469763tate_o > ( nat > nat > set_Pr1590995257tate_o ) > nat ).
thf(func_def_253,type,
sK109: product_prod_nat_nat > produc696469763tate_o > ( nat > nat > set_Pr1590995257tate_o ) > nat ).
thf(func_def_254,type,
sK110: set_Pr1702239303tate_o > set_Pr1590995257tate_o > produc696469763tate_o ).
thf(func_def_255,type,
sK111: set_Pr1490359111at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_256,type,
sK112: ( produc696469763tate_o > $o ) > com ).
thf(func_def_257,type,
sK113: ( produc696469763tate_o > $o ) > a > state > $o ).
thf(func_def_258,type,
sK114: ( produc696469763tate_o > $o ) > a > state > $o ).
thf(func_def_259,type,
sK115: produc696469763tate_o > a > state > $o ).
thf(func_def_260,type,
sK116: produc696469763tate_o > produc204914599tate_o ).
thf(func_def_261,type,
sK117: set_Pr778812871_state > set_Pr795498619_state ).
thf(func_def_262,type,
sK118: set_Pr778812871_state > produc1115495963_state ).
thf(func_def_263,type,
sK119: produc1115495963_state > set_Pr778812871_state > produc1115495963_state ).
thf(func_def_264,type,
sK120: set_Pr1986765409at_nat > nat ).
thf(func_def_265,type,
sK121: set_Pr1986765409at_nat > nat > $o ).
thf(func_def_266,type,
sK122: nat > set_Pr1986765409at_nat > nat ).
thf(func_def_267,type,
sK123: set_Pr795498619_state > produc1115495963_state > set_Pr795498619_state ).
thf(func_def_268,type,
sK124: set_Pr795498619_state > produc1115495963_state ).
thf(func_def_269,type,
sK125: ( state > state > $o ) > produc1115495963_state > ( $o > $o ) > state ).
thf(func_def_270,type,
sK126: ( state > state > $o ) > produc1115495963_state > ( $o > $o ) > state ).
thf(func_def_271,type,
sK127: ( state > $o ) > ( nat > state ) > nat ).
thf(func_def_272,type,
sK128: com > ( nat > state ) > nat ).
thf(func_def_273,type,
sK129: product_prod_nat_nat > ( nat > nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_274,type,
sK130: product_prod_nat_nat > ( nat > nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_275,type,
sK131: set_Pr1490359111at_nat > product_prod_nat_nat ).
thf(func_def_276,type,
sK132: set_Pr1490359111at_nat > set_Pr1986765409at_nat ).
thf(func_def_277,type,
sK133: product_prod_nat_nat > set_Pr1490359111at_nat > product_prod_nat_nat ).
thf(func_def_278,type,
sK134: product_prod_nat_nat > ( $o > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_279,type,
sK135: product_prod_nat_nat > ( $o > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_280,type,
sK136: ( nat > state ) > ( state > $o ) > nat ).
thf(func_def_281,type,
sK137: com > ( nat > state ) > nat ).
thf(func_def_282,type,
sK138: ( a > state > $o ) > ( state > $o ) > set_Pr795498619_state > com > set_Pr1590995257tate_o > state ).
thf(func_def_283,type,
sK139: state ).
thf(func_def_284,type,
sK140: state ).
thf(func_def_285,type,
sK141: a ).
thf(func_def_286,type,
sK142: state ).
thf(func_def_287,type,
sK143: a ).
thf(func_def_288,type,
sK144: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat ).
thf(func_def_289,type,
sK145: set_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_290,type,
sK146: product_prod_nat_nat > nat ).
thf(func_def_291,type,
sK147: product_prod_nat_nat > nat ).
thf(func_def_292,type,
sK148: produc1115495963_state > state ).
thf(func_def_293,type,
sK149: produc1115495963_state > state ).
thf(func_def_294,type,
sK150: ( state > $o ) > set_Pr795498619_state > state ).
thf(func_def_295,type,
sK151: ( state > $o ) > nat > com > ( state > $o ) > state ).
thf(func_def_296,type,
sK152: ( state > $o ) > nat > com > ( state > $o ) > state ).
thf(func_def_297,type,
sK153: set_Pr1490359111at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_298,type,
sK154: set_Pr1490359111at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(func_def_299,type,
sK155: ( product_prod_nat_nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_300,type,
sK156: ( product_prod_nat_nat > $o ) > ( nat > nat > $o ) > nat ).
thf(func_def_301,type,
sK157: set_state > set_Pr795498619_state > state ).
thf(func_def_302,type,
sK158: set_nat > set_Pr1986765409at_nat > nat ).
thf(func_def_303,type,
sK159: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_304,type,
sK160: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_305,type,
sK161: state > state ).
thf(func_def_306,type,
sK162: state > state ).
thf(func_def_307,type,
sK163: state > a ).
thf(func_def_308,type,
sK164: state > a ).
thf(func_def_309,type,
sK165: state > state ).
thf(func_def_310,type,
sK166: ( nat > nat > set_Pr795498619_state ) > product_prod_nat_nat > produc1115495963_state > nat ).
thf(func_def_311,type,
sK167: ( nat > nat > set_Pr795498619_state ) > product_prod_nat_nat > produc1115495963_state > nat ).
thf(func_def_312,type,
sK168: set_Pr795498619_state > set_state > state ).
thf(func_def_313,type,
sK169: set_Pr795498619_state > set_state > state ).
thf(func_def_314,type,
sK170: ( a > state > $o ) > ( a > state > $o ) > a ).
thf(func_def_315,type,
sK171: ( a > state > $o ) > ( a > state > $o ) > state ).
thf(func_def_316,type,
sK172: set_Pr1590995257tate_o > produc696469763tate_o > set_Pr1590995257tate_o ).
thf(func_def_318,type,
ph174:
!>[X0: $tType] : X0 ).
thf(f3155,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2646,f2651,f2656,f2746,f2774,f2782,f2784,f2785,f2854,f2862,f2867,f2908,f3065,f3075,f3149,f3154]) ).
thf(f3154,plain,
( spl173_8
| spl173_5
| spl173_10
| ~ spl173_28 ),
inference(avatar_split_clause,[status(thm)],[f3153,f3073,f2684,f2664,f2677]) ).
thf(f2677,definition,
( spl173_8
<=> ! [X0: a] :
( ( pa @ X0 @ x )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_8])],[avatar_definition]) ).
thf(f2664,definition,
( spl173_5
<=> ( ( sP3 @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_5])],[avatar_definition]) ).
thf(f2684,definition,
( spl173_10
<=> ( ( termi @ body @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_10])],[avatar_definition]) ).
thf(f3073,definition,
( spl173_28
<=> ! [X0: a] :
( ( pa @ X0 @ ( sK165 @ x ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_28])],[avatar_definition]) ).
thf(f3153,plain,
( ! [X0: a] :
( ( pa @ X0 @ x )
!= $true )
| spl173_5
| spl173_10
| ~ spl173_28 ),
inference(subsumption_resolution,[status(thm)],[f3152,f2685]) ).
thf(f2685,plain,
( ( ( termi @ body @ x )
!= $true )
| spl173_10 ),
inference(avatar_component_clause,[status(thm)],[f2684]) ).
thf(f3152,plain,
( ! [X0: a] :
( ( ( pa @ X0 @ x )
!= $true )
| ( ( termi @ body @ x )
= $true ) )
| spl173_5
| ~ spl173_28 ),
inference(subsumption_resolution,[status(thm)],[f3151,f2666]) ).
thf(f2666,plain,
( ( ( sP3 @ x )
!= $true )
| spl173_5 ),
inference(avatar_component_clause,[status(thm)],[f2664]) ).
thf(f3151,plain,
( ! [X0: a] :
( ( ( sP3 @ x )
= $true )
| ( ( pa @ X0 @ x )
!= $true )
| ( ( termi @ body @ x )
= $true ) )
| ~ spl173_28 ),
inference(trivial_inequality_removal,[status(thm)],[f3150]) ).
thf(f3150,plain,
( ! [X0: a] :
( ( ( sP3 @ x )
= $true )
| ( ( termi @ body @ x )
= $true )
| ( $true != $true )
| ( ( pa @ X0 @ x )
!= $true ) )
| ~ spl173_28 ),
inference(superposition,[status(thm)],[f3074,f2431]) ).
thf(f2431,plain,
! [X6: state,X7: a] :
( ( ( pa @ ( sK164 @ X6 ) @ ( sK165 @ X6 ) )
= $true )
| ( ( pa @ X7 @ X6 )
!= $true )
| ( ( termi @ body @ X6 )
= $true )
| ( ( sP3 @ X6 )
= $true ) ),
inference(equality_resolution,[status(thm)],[f2078]) ).
thf(f2078,plain,
! [X0: state,X6: state,X7: a] :
( ( ( pa @ ( sK164 @ X0 ) @ ( sK165 @ X0 ) )
= $true )
| ( ( sP3 @ X0 )
= $true )
| ( ( termi @ body @ X6 )
= $true )
| ( X0 != X6 )
| ( ( pa @ X7 @ X6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
thf(f1602,plain,
! [X0: state] :
( ( ( ( ( termi @ body @ ( sK165 @ X0 ) )
!= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ X0 ) @ X0 ) @ r )
= $true )
& ( ( pa @ ( sK164 @ X0 ) @ ( sK165 @ X0 ) )
= $true ) )
| ( ( sP3 @ X0 )
= $true )
| ( ! [X3: state,X4: state] :
( ! [X5: a] :
( ( ( pa @ X5 @ X4 )
!= $true )
| ( X0 != X4 )
| ( ( qa @ X5 @ X3 )
= $true ) )
| ( ( exec @ X4 @ body @ X3 )
!= $true ) )
& ! [X6: state,X7: a] :
( ( ( termi @ body @ X6 )
= $true )
| ( X0 != X6 )
| ( ( pa @ X7 @ X6 )
!= $true ) ) ) )
& ( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [Y0: a,Y1: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y1 @ X0 ) @ r )
& ( pa @ Y0 @ Y1 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y0: a,Y1: state] :
( ( pa @ Y0 @ Y1 )
& ( X0 = Y1 ) )
@ body
@ qa )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164,sK165])],[f1600,f1601]) ).
thf(f1601,plain,
! [X0: state] :
( ? [X1: a,X2: state] :
( ( ( termi @ body @ X2 )
!= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ X2 @ X0 ) @ r )
= $true )
& ( ( pa @ X1 @ X2 )
= $true ) )
=> ( ( ( termi @ body @ ( sK165 @ X0 ) )
!= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ X0 ) @ X0 ) @ r )
= $true )
& ( ( pa @ ( sK164 @ X0 ) @ ( sK165 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1600,plain,
! [X0: state] :
( ( ? [X1: a,X2: state] :
( ( ( termi @ body @ X2 )
!= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ X2 @ X0 ) @ r )
= $true )
& ( ( pa @ X1 @ X2 )
= $true ) )
| ( ( sP3 @ X0 )
= $true )
| ( ! [X3: state,X4: state] :
( ! [X5: a] :
( ( ( pa @ X5 @ X4 )
!= $true )
| ( X0 != X4 )
| ( ( qa @ X5 @ X3 )
= $true ) )
| ( ( exec @ X4 @ body @ X3 )
!= $true ) )
& ! [X6: state,X7: a] :
( ( ( termi @ body @ X6 )
= $true )
| ( X0 != X6 )
| ( ( pa @ X7 @ X6 )
!= $true ) ) ) )
& ( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [Y0: a,Y1: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y1 @ X0 ) @ r )
& ( pa @ Y0 @ Y1 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y0: a,Y1: state] :
( ( pa @ Y0 @ Y1 )
& ( X0 = Y1 ) )
@ body
@ qa )
= $true ) ),
inference(rectify,[status(thm)],[f1401]) ).
thf(f1401,plain,
! [X0: state] :
( ( ? [X4: a,X5: state] :
( ( ( termi @ body @ X5 )
!= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ X5 @ X0 ) @ r )
= $true )
& ( ( pa @ X4 @ X5 )
= $true ) )
| ( ( sP3 @ X0 )
= $true )
| ( ! [X8: state,X9: state] :
( ! [X10: a] :
( ( ( pa @ X10 @ X9 )
!= $true )
| ( X0 != X9 )
| ( ( qa @ X10 @ X8 )
= $true ) )
| ( ( exec @ X9 @ body @ X8 )
!= $true ) )
& ! [X6: state,X7: a] :
( ( ( termi @ body @ X6 )
= $true )
| ( X0 != X6 )
| ( ( pa @ X7 @ X6 )
!= $true ) ) ) )
& ( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [Y0: a,Y1: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y1 @ X0 ) @ r )
& ( pa @ Y0 @ Y1 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y0: a,Y1: state] :
( ( pa @ Y0 @ Y1 )
& ( X0 = Y1 ) )
@ body
@ qa )
= $true ) ),
inference(definition_folding,[status(thm)],[f1393,f1400]) ).
thf(f1400,plain,
! [X0: state] :
( ? [X1: state,X2: state] :
( ? [X3: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ X1 @ X0 ) @ r )
= $true )
& ( ( qa @ X3 @ X2 )
!= $true )
& ( ( pa @ X3 @ X1 )
= $true ) )
& ( ( exec @ X1 @ body @ X2 )
= $true ) )
| ( ( sP3 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f1393,plain,
! [X0: state] :
( ( ? [X4: a,X5: state] :
( ( ( termi @ body @ X5 )
!= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ X5 @ X0 ) @ r )
= $true )
& ( ( pa @ X4 @ X5 )
= $true ) )
| ? [X1: state,X2: state] :
( ? [X3: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ X1 @ X0 ) @ r )
= $true )
& ( ( qa @ X3 @ X2 )
!= $true )
& ( ( pa @ X3 @ X1 )
= $true ) )
& ( ( exec @ X1 @ body @ X2 )
= $true ) )
| ( ! [X8: state,X9: state] :
( ! [X10: a] :
( ( ( pa @ X10 @ X9 )
!= $true )
| ( X0 != X9 )
| ( ( qa @ X10 @ X8 )
= $true ) )
| ( ( exec @ X9 @ body @ X8 )
!= $true ) )
& ! [X6: state,X7: a] :
( ( ( termi @ body @ X6 )
= $true )
| ( X0 != X6 )
| ( ( pa @ X7 @ X6 )
!= $true ) ) ) )
& ( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [Y0: a,Y1: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y1 @ X0 ) @ r )
& ( pa @ Y0 @ Y1 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y0: a,Y1: state] :
( ( pa @ Y0 @ Y1 )
& ( X0 = Y1 ) )
@ body
@ qa )
= $true ) ),
inference(flattening,[status(thm)],[f1392]) ).
thf(f1392,plain,
! [X0: state] :
( ( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [Y0: a,Y1: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y1 @ X0 ) @ r )
& ( pa @ Y0 @ Y1 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y0: a,Y1: state] :
( ( pa @ Y0 @ Y1 )
& ( X0 = Y1 ) )
@ body
@ qa )
= $true )
& ( ( ! [X8: state,X9: state] :
( ! [X10: a] :
( ( ( qa @ X10 @ X8 )
= $true )
| ( ( pa @ X10 @ X9 )
!= $true )
| ( X0 != X9 ) )
| ( ( exec @ X9 @ body @ X8 )
!= $true ) )
& ! [X6: state,X7: a] :
( ( ( termi @ body @ X6 )
= $true )
| ( ( pa @ X7 @ X6 )
!= $true )
| ( X0 != X6 ) ) )
| ? [X4: a,X5: state] :
( ( ( termi @ body @ X5 )
!= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ X5 @ X0 ) @ r )
= $true )
& ( ( pa @ X4 @ X5 )
= $true ) )
| ? [X1: state,X2: state] :
( ? [X3: a] :
( ( ( qa @ X3 @ X2 )
!= $true )
& ( ( pa @ X3 @ X1 )
= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ X1 @ X0 ) @ r )
= $true ) )
& ( ( exec @ X1 @ body @ X2 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f1111]) ).
thf(f1111,plain,
! [X0: state] :
( ( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [Y0: a,Y1: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y1 @ X0 ) @ r )
& ( pa @ Y0 @ Y1 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y0: a,Y1: state] :
( ( pa @ Y0 @ Y1 )
& ( X0 = Y1 ) )
@ body
@ qa )
= $true )
& ( ( ! [X4: a,X5: state] :
( ( ( ( member1389040324_state @ ( produc64584659_state @ X5 @ X0 ) @ r )
= $true )
& ( ( pa @ X4 @ X5 )
= $true ) )
=> ( ( termi @ body @ X5 )
= $true ) )
& ! [X1: state,X2: state] :
( ( ( exec @ X1 @ body @ X2 )
= $true )
=> ! [X3: a] :
( ( ( ( pa @ X3 @ X1 )
= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ X1 @ X0 ) @ r )
= $true ) )
=> ( ( qa @ X3 @ X2 )
= $true ) ) ) )
=> ( ! [X8: state,X9: state] :
( ( ( exec @ X9 @ body @ X8 )
= $true )
=> ! [X10: a] :
( ( ( ( pa @ X10 @ X9 )
= $true )
& ( X0 = X9 ) )
=> ( ( qa @ X10 @ X8 )
= $true ) ) )
& ! [X6: state,X7: a] :
( ( ( ( pa @ X7 @ X6 )
= $true )
& ( X0 = X6 ) )
=> ( ( termi @ body @ X6 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f634]) ).
thf(f634,plain,
! [X0: state] :
( ( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [Y0: a,Y1: state] :
( ( member1389040324_state @ ( produc64584659_state @ Y1 @ X0 ) @ r )
& ( pa @ Y0 @ Y1 ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [Y0: a,Y1: state] :
( ( pa @ Y0 @ Y1 )
& ( X0 = Y1 ) )
@ body
@ qa )
= $true )
& ( ( ! [X5: state,X6: state] :
( ( $true
= ( exec @ X5 @ body @ X6 ) )
=> ! [X7: a] :
( ( ( ( pa @ X7 @ X5 )
= $true )
& ( ( member1389040324_state @ ( produc64584659_state @ X5 @ X0 ) @ r )
= $true ) )
=> ( ( qa @ X7 @ X6 )
= $true ) ) )
& ! [X8: a,X9: state] :
( ( ( ( member1389040324_state @ ( produc64584659_state @ X9 @ X0 ) @ r )
= $true )
& ( ( pa @ X8 @ X9 )
= $true ) )
=> ( ( termi @ body @ X9 )
= $true ) ) )
=> ( ! [X10: state,X11: a] :
( ( ( ( pa @ X11 @ X10 )
= $true )
& ( X0 = X10 ) )
=> ( $true
= ( termi @ body @ X10 ) ) )
& ! [X12: state,X13: state] :
( ( $true
= ( exec @ X13 @ body @ X12 ) )
=> ! [X14: a] :
( ( ( X0 = X13 )
& ( ( pa @ X14 @ X13 )
= $true ) )
=> ( $true
= ( qa @ X14 @ X12 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f633]) ).
thf(f633,plain,
! [X0: state] :
( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [X1: a,X2: state] :
( ( pa @ X1 @ X2 )
& ( member1389040324_state @ ( produc64584659_state @ X2 @ X0 ) @ r ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [X3: a,X4: state] :
( ( X0 = X4 )
& ( pa @ X3 @ X4 ) )
@ body
@ qa )
& ( ( ! [X5: state,X6: state] :
( ( exec @ X5 @ body @ X6 )
=> ! [X7: a] :
( ( ( pa @ X7 @ X5 )
& ( member1389040324_state @ ( produc64584659_state @ X5 @ X0 ) @ r ) )
=> ( qa @ X7 @ X6 ) ) )
& ! [X8: a,X9: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ X9 @ X0 ) @ r )
& ( pa @ X8 @ X9 ) )
=> ( termi @ body @ X9 ) ) )
=> ( ! [X10: state,X11: a] :
( ( ( pa @ X11 @ X10 )
& ( X0 = X10 ) )
=> ( termi @ body @ X10 ) )
& ! [X12: state,X13: state] :
( ( exec @ X13 @ body @ X12 )
=> ! [X14: a] :
( ( ( X0 = X13 )
& ( pa @ X14 @ X13 ) )
=> ( qa @ X14 @ X12 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f355]) ).
thf(f355,axiom,
! [X91: state] :
( ( pHoare382919414oare_a
@ ( insert2053719859tate_o
@ ( produc33908149tate_o
@ ^ [X18: a,X19: state] :
( ( pa @ X18 @ X19 )
& ( member1389040324_state @ ( produc64584659_state @ X19 @ X91 ) @ r ) )
@ ( produc1948644831tate_o @ call @ qa ) )
@ bot_bo170732493tate_o )
@ ^ [X18: a,X19: state] :
( ( X19 = X91 )
& ( pa @ X18 @ X19 ) )
@ body
@ qa )
& ( ( ! [X6: state,X8: state] :
( ( exec @ X6 @ body @ X8 )
=> ! [X5: a] :
( ( ( pa @ X5 @ X6 )
& ( member1389040324_state @ ( produc64584659_state @ X6 @ X91 ) @ r ) )
=> ( qa @ X5 @ X8 ) ) )
& ! [X5: a,X6: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ X6 @ X91 ) @ r )
& ( pa @ X5 @ X6 ) )
=> ( termi @ body @ X6 ) ) )
=> ( ! [X92: state,X9: a] :
( ( ( pa @ X9 @ X92 )
& ( X91 = X92 ) )
=> ( termi @ body @ X92 ) )
& ! [X93: state,X92: state] :
( ( exec @ X92 @ body @ X93 )
=> ! [X9: a] :
( ( ( X91 = X92 )
& ( pa @ X9 @ X92 ) )
=> ( qa @ X9 @ X93 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H5mA5wl1hp/DTF2THF_16650.p',conj_0) ).
thf(f3074,plain,
( ! [X0: a] :
( ( pa @ X0 @ ( sK165 @ x ) )
!= $true )
| ~ spl173_28 ),
inference(avatar_component_clause,[status(thm)],[f3073]) ).
thf(f3149,plain,
( spl173_8
| spl173_5
| spl173_10
| ~ spl173_16 ),
inference(avatar_split_clause,[status(thm)],[f3148,f2771,f2684,f2664,f2677]) ).
thf(f2771,definition,
( spl173_16
<=> ( ( termi @ body @ ( sK165 @ x ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_16])],[avatar_definition]) ).
thf(f3148,plain,
( ! [X0: a] :
( ( pa @ X0 @ x )
!= $true )
| spl173_5
| spl173_10
| ~ spl173_16 ),
inference(subsumption_resolution,[status(thm)],[f3147,f2666]) ).
thf(f3147,plain,
( ! [X0: a] :
( ( ( sP3 @ x )
= $true )
| ( ( pa @ X0 @ x )
!= $true ) )
| spl173_10
| ~ spl173_16 ),
inference(subsumption_resolution,[status(thm)],[f3146,f2685]) ).
thf(f3146,plain,
( ! [X0: a] :
( ( ( termi @ body @ x )
= $true )
| ( ( pa @ X0 @ x )
!= $true )
| ( ( sP3 @ x )
= $true ) )
| ~ spl173_16 ),
inference(trivial_inequality_removal,[status(thm)],[f3145]) ).
thf(f3145,plain,
( ! [X0: a] :
( ( ( termi @ body @ x )
= $true )
| ( $true != $true )
| ( ( pa @ X0 @ x )
!= $true )
| ( ( sP3 @ x )
= $true ) )
| ~ spl173_16 ),
inference(superposition,[status(thm)],[f2427,f2772]) ).
thf(f2772,plain,
( ( ( termi @ body @ ( sK165 @ x ) )
= $true )
| ~ spl173_16 ),
inference(avatar_component_clause,[status(thm)],[f2771]) ).
thf(f2427,plain,
! [X6: state,X7: a] :
( ( ( termi @ body @ ( sK165 @ X6 ) )
!= $true )
| ( ( pa @ X7 @ X6 )
!= $true )
| ( ( termi @ body @ X6 )
= $true )
| ( ( sP3 @ X6 )
= $true ) ),
inference(equality_resolution,[status(thm)],[f2082]) ).
thf(f2082,plain,
! [X0: state,X6: state,X7: a] :
( ( ( termi @ body @ ( sK165 @ X0 ) )
!= $true )
| ( ( sP3 @ X0 )
= $true )
| ( ( termi @ body @ X6 )
= $true )
| ( X0 != X6 )
| ( ( pa @ X7 @ X6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
thf(f3075,plain,
( spl173_10
| spl173_16
| spl173_28
| spl173_8
| spl173_5 ),
inference(avatar_split_clause,[status(thm)],[f3071,f2664,f2677,f3073,f2771,f2684]) ).
thf(f3071,plain,
( ! [X0: a,X1: a] :
( ( ( pa @ X0 @ ( sK165 @ x ) )
!= $true )
| ( ( pa @ X1 @ x )
!= $true )
| ( ( termi @ body @ ( sK165 @ x ) )
= $true )
| ( ( termi @ body @ x )
= $true ) )
| spl173_5 ),
inference(subsumption_resolution,[status(thm)],[f2696,f2666]) ).
thf(f2696,plain,
! [X0: a,X1: a] :
( ( ( termi @ body @ ( sK165 @ x ) )
= $true )
| ( ( pa @ X0 @ ( sK165 @ x ) )
!= $true )
| ( ( termi @ body @ x )
= $true )
| ( ( sP3 @ x )
= $true )
| ( ( pa @ X1 @ x )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2688]) ).
thf(f2688,plain,
! [X0: a,X1: a] :
( ( ( termi @ body @ ( sK165 @ x ) )
= $true )
| ( ( pa @ X1 @ x )
!= $true )
| ( $true != $true )
| ( ( pa @ X0 @ ( sK165 @ x ) )
!= $true )
| ( ( termi @ body @ x )
= $true )
| ( ( sP3 @ x )
= $true ) ),
inference(superposition,[status(thm)],[f2419,f2429]) ).
thf(f2429,plain,
! [X6: state,X7: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ X6 ) @ X6 ) @ r )
= $true )
| ( ( termi @ body @ X6 )
= $true )
| ( ( sP3 @ X6 )
= $true )
| ( ( pa @ X7 @ X6 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f2080]) ).
thf(f2080,plain,
! [X0: state,X6: state,X7: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( sP3 @ X0 )
= $true )
| ( ( termi @ body @ X6 )
= $true )
| ( X0 != X6 )
| ( ( pa @ X7 @ X6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
thf(f2419,plain,
! [X4: a,X5: state] :
( ( $true
!= ( member1389040324_state @ ( produc64584659_state @ X5 @ x ) @ r ) )
| ( ( termi @ body @ X5 )
= $true )
| ( ( pa @ X4 @ X5 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f1769]) ).
thf(f1769,plain,
! [X0: state,X4: a,X5: state] :
( ( ( pa @ X4 @ X5 )
!= $true )
| ( X0 != X5 )
| ( ( termi @ body @ X5 )
= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ X0 @ x ) @ r )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1381]) ).
thf(f1381,plain,
! [X0: state] :
( ( ! [X1: state,X2: state] :
( ( ( exec @ X1 @ body @ X2 )
!= $true )
| ! [X3: a] :
( ( ( pa @ X3 @ X1 )
!= $true )
| ( ( qa @ X3 @ X2 )
= $true )
| ( X0 != X1 ) ) )
& ! [X4: a,X5: state] :
( ( ( pa @ X4 @ X5 )
!= $true )
| ( X0 != X5 )
| ( ( termi @ body @ X5 )
= $true ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ X0 @ x ) @ r )
!= $true ) ),
inference(flattening,[status(thm)],[f1380]) ).
thf(f1380,plain,
! [X0: state] :
( ( ! [X4: a,X5: state] :
( ( ( termi @ body @ X5 )
= $true )
| ( ( pa @ X4 @ X5 )
!= $true )
| ( X0 != X5 ) )
& ! [X1: state,X2: state] :
( ! [X3: a] :
( ( ( qa @ X3 @ X2 )
= $true )
| ( ( pa @ X3 @ X1 )
!= $true )
| ( X0 != X1 ) )
| ( ( exec @ X1 @ body @ X2 )
!= $true ) ) )
| ( ( member1389040324_state @ ( produc64584659_state @ X0 @ x ) @ r )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f890]) ).
thf(f890,plain,
! [X0: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ X0 @ x ) @ r )
= $true )
=> ( ! [X4: a,X5: state] :
( ( ( ( pa @ X4 @ X5 )
= $true )
& ( X0 = X5 ) )
=> ( ( termi @ body @ X5 )
= $true ) )
& ! [X1: state,X2: state] :
( ( ( exec @ X1 @ body @ X2 )
= $true )
=> ! [X3: a] :
( ( ( ( pa @ X3 @ X1 )
= $true )
& ( X0 = X1 ) )
=> ( ( qa @ X3 @ X2 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f889]) ).
thf(f889,plain,
! [X0: state] :
( ( member1389040324_state @ ( produc64584659_state @ X0 @ x ) @ r )
=> ( ! [X1: state,X2: state] :
( ( exec @ X1 @ body @ X2 )
=> ! [X3: a] :
( ( ( pa @ X3 @ X1 )
& ( X0 = X1 ) )
=> ( qa @ X3 @ X2 ) ) )
& ! [X4: a,X5: state] :
( ( ( pa @ X4 @ X5 )
& ( X0 = X5 ) )
=> ( termi @ body @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f356]) ).
thf(f356,axiom,
! [X34: state] :
( ( member1389040324_state @ ( produc64584659_state @ X34 @ x ) @ r )
=> ( ! [X92: state,X93: state] :
( ( exec @ X92 @ body @ X93 )
=> ! [X9: a] :
( ( ( pa @ X9 @ X92 )
& ( X34 = X92 ) )
=> ( qa @ X9 @ X93 ) ) )
& ! [X9: a,X92: state] :
( ( ( pa @ X9 @ X92 )
& ( X34 = X92 ) )
=> ( termi @ body @ X92 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H5mA5wl1hp/DTF2THF_16650.p',conj_1) ).
thf(f3065,plain,
( ~ spl173_1
| ~ spl173_15
| spl173_16
| ~ spl173_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f3064]) ).
thf(f3064,plain,
( $false
| ~ spl173_1
| ~ spl173_15
| spl173_16
| ~ spl173_22 ),
inference(trivial_inequality_removal,[status(thm)],[f3062]) ).
thf(f3062,plain,
( ( $true != $true )
| ~ spl173_1
| ~ spl173_15
| spl173_16
| ~ spl173_22 ),
inference(superposition,[status(thm)],[f3060,f2911]) ).
thf(f2911,plain,
( ( ( pa @ ( sK164 @ x ) @ ( sK165 @ x ) )
= $true )
| ~ spl173_1
| ~ spl173_15 ),
inference(subsumption_resolution,[status(thm)],[f2910,f2641]) ).
thf(f2641,plain,
( ( sP2 = $true )
| ~ spl173_1 ),
inference(avatar_component_clause,[status(thm)],[f2639]) ).
thf(f2639,definition,
( spl173_1
<=> ( sP2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl173_1])],[avatar_definition]) ).
thf(f2910,plain,
( ( ( pa @ ( sK164 @ x ) @ ( sK165 @ x ) )
= $true )
| ( sP2 != $true )
| ~ spl173_15 ),
inference(superposition,[status(thm)],[f2765,f2004]) ).
thf(f2004,plain,
( ( x = sK140 )
| ( sP2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1570]) ).
thf(f1570,plain,
( ( ( ( exec @ sK140 @ body @ sK139 )
= $true )
& ( ( qa @ sK141 @ sK139 )
!= $true )
& ( ( pa @ sK141 @ sK140 )
= $true )
& ( x = sK140 ) )
| ( sP2 != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK139,sK140,sK141])],[f1567,f1569,f1568]) ).
thf(f1568,plain,
( ? [X0: state,X1: state] :
( ( ( exec @ X1 @ body @ X0 )
= $true )
& ? [X2: a] :
( ( ( qa @ X2 @ X0 )
!= $true )
& ( ( pa @ X2 @ X1 )
= $true )
& ( x = X1 ) ) )
=> ( ( ( exec @ sK140 @ body @ sK139 )
= $true )
& ? [X2: a] :
( ( ( qa @ X2 @ sK139 )
!= $true )
& ( ( pa @ X2 @ sK140 )
= $true )
& ( x = sK140 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1569,plain,
( ? [X2: a] :
( ( ( qa @ X2 @ sK139 )
!= $true )
& ( ( pa @ X2 @ sK140 )
= $true )
& ( x = sK140 ) )
=> ( ( ( qa @ sK141 @ sK139 )
!= $true )
& ( ( pa @ sK141 @ sK140 )
= $true )
& ( x = sK140 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1567,plain,
( ? [X0: state,X1: state] :
( ( ( exec @ X1 @ body @ X0 )
= $true )
& ? [X2: a] :
( ( ( qa @ X2 @ X0 )
!= $true )
& ( ( pa @ X2 @ X1 )
= $true )
& ( x = X1 ) ) )
| ( sP2 != $true ) ),
inference(nnf_transformation,[status(thm)],[f1398]) ).
thf(f1398,plain,
( ? [X0: state,X1: state] :
( ( ( exec @ X1 @ body @ X0 )
= $true )
& ? [X2: a] :
( ( ( qa @ X2 @ X0 )
!= $true )
& ( ( pa @ X2 @ X1 )
= $true )
& ( x = X1 ) ) )
| ( sP2 != $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f2765,plain,
( ( ( pa @ ( sK164 @ sK140 ) @ ( sK165 @ sK140 ) )
= $true )
| ~ spl173_15 ),
inference(avatar_component_clause,[status(thm)],[f2763]) ).
thf(f2763,definition,
( spl173_15
<=> ( ( pa @ ( sK164 @ sK140 ) @ ( sK165 @ sK140 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_15])],[avatar_definition]) ).
thf(f3060,plain,
( ! [X0: a] :
( ( pa @ X0 @ ( sK165 @ x ) )
!= $true )
| ~ spl173_1
| spl173_16
| ~ spl173_22 ),
inference(subsumption_resolution,[status(thm)],[f3055,f2773]) ).
thf(f2773,plain,
( ( ( termi @ body @ ( sK165 @ x ) )
!= $true )
| spl173_16 ),
inference(avatar_component_clause,[status(thm)],[f2771]) ).
thf(f3055,plain,
( ! [X0: a] :
( ( ( pa @ X0 @ ( sK165 @ x ) )
!= $true )
| ( ( termi @ body @ ( sK165 @ x ) )
= $true ) )
| ~ spl173_1
| ~ spl173_22 ),
inference(trivial_inequality_removal,[status(thm)],[f3050]) ).
thf(f3050,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( pa @ X0 @ ( sK165 @ x ) )
!= $true )
| ( ( termi @ body @ ( sK165 @ x ) )
= $true ) )
| ~ spl173_1
| ~ spl173_22 ),
inference(superposition,[status(thm)],[f2419,f2921]) ).
thf(f2921,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ x ) @ x ) @ r )
= $true )
| ~ spl173_1
| ~ spl173_22 ),
inference(subsumption_resolution,[status(thm)],[f2912,f2641]) ).
thf(f2912,plain,
( ( sP2 != $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ x ) @ x ) @ r )
= $true )
| ~ spl173_22 ),
inference(superposition,[status(thm)],[f2861,f2004]) ).
thf(f2861,plain,
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ sK140 ) @ sK140 ) @ r )
= $true )
| ~ spl173_22 ),
inference(avatar_component_clause,[status(thm)],[f2859]) ).
thf(f2859,definition,
( spl173_22
<=> ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ sK140 ) @ sK140 ) @ r )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_22])],[avatar_definition]) ).
thf(f2908,plain,
~ spl173_5,
inference(avatar_contradiction_clause,[status(thm)],[f2907]) ).
thf(f2907,plain,
( $false
| ~ spl173_5 ),
inference(subsumption_resolution,[status(thm)],[f2906,f2665]) ).
thf(f2665,plain,
( ( ( sP3 @ x )
= $true )
| ~ spl173_5 ),
inference(avatar_component_clause,[status(thm)],[f2664]) ).
thf(f2906,plain,
( ( ( sP3 @ x )
!= $true )
| ~ spl173_5 ),
inference(trivial_inequality_removal,[status(thm)],[f2905]) ).
thf(f2905,plain,
( ( ( sP3 @ x )
!= $true )
| ( $true != $true )
| ~ spl173_5 ),
inference(superposition,[status(thm)],[f2904,f2074]) ).
thf(f2074,plain,
! [X0: state] :
( ( ( pa @ ( sK163 @ X0 ) @ ( sK161 @ X0 ) )
= $true )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1599]) ).
thf(f1599,plain,
! [X0: state] :
( ( ( ( member1389040324_state @ ( produc64584659_state @ ( sK161 @ X0 ) @ X0 ) @ r )
= $true )
& ( ( qa @ ( sK163 @ X0 ) @ ( sK162 @ X0 ) )
!= $true )
& ( ( pa @ ( sK163 @ X0 ) @ ( sK161 @ X0 ) )
= $true )
& ( ( exec @ ( sK161 @ X0 ) @ body @ ( sK162 @ X0 ) )
= $true ) )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161,sK162,sK163])],[f1596,f1598,f1597]) ).
thf(f1597,plain,
! [X0: state] :
( ? [X1: state,X2: state] :
( ? [X3: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ X1 @ X0 ) @ r )
= $true )
& ( ( qa @ X3 @ X2 )
!= $true )
& ( ( pa @ X3 @ X1 )
= $true ) )
& ( ( exec @ X1 @ body @ X2 )
= $true ) )
=> ( ? [X3: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK161 @ X0 ) @ X0 ) @ r )
= $true )
& ( ( qa @ X3 @ ( sK162 @ X0 ) )
!= $true )
& ( ( pa @ X3 @ ( sK161 @ X0 ) )
= $true ) )
& ( ( exec @ ( sK161 @ X0 ) @ body @ ( sK162 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1598,plain,
! [X0: state] :
( ? [X3: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK161 @ X0 ) @ X0 ) @ r )
= $true )
& ( ( qa @ X3 @ ( sK162 @ X0 ) )
!= $true )
& ( ( pa @ X3 @ ( sK161 @ X0 ) )
= $true ) )
=> ( ( ( member1389040324_state @ ( produc64584659_state @ ( sK161 @ X0 ) @ X0 ) @ r )
= $true )
& ( ( qa @ ( sK163 @ X0 ) @ ( sK162 @ X0 ) )
!= $true )
& ( ( pa @ ( sK163 @ X0 ) @ ( sK161 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1596,plain,
! [X0: state] :
( ? [X1: state,X2: state] :
( ? [X3: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ X1 @ X0 ) @ r )
= $true )
& ( ( qa @ X3 @ X2 )
!= $true )
& ( ( pa @ X3 @ X1 )
= $true ) )
& ( ( exec @ X1 @ body @ X2 )
= $true ) )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f1400]) ).
thf(f2904,plain,
( ( ( pa @ ( sK163 @ x ) @ ( sK161 @ x ) )
!= $true )
| ~ spl173_5 ),
inference(subsumption_resolution,[status(thm)],[f2903,f2665]) ).
thf(f2903,plain,
( ( ( pa @ ( sK163 @ x ) @ ( sK161 @ x ) )
!= $true )
| ( ( sP3 @ x )
!= $true )
| ~ spl173_5 ),
inference(trivial_inequality_removal,[status(thm)],[f2902]) ).
thf(f2902,plain,
( ( ( pa @ ( sK163 @ x ) @ ( sK161 @ x ) )
!= $true )
| ( $true != $true )
| ( ( sP3 @ x )
!= $true )
| ~ spl173_5 ),
inference(superposition,[status(thm)],[f2075,f2901]) ).
thf(f2901,plain,
( ! [X0: a] :
( ( ( qa @ X0 @ ( sK162 @ x ) )
= $true )
| ( ( pa @ X0 @ ( sK161 @ x ) )
!= $true ) )
| ~ spl173_5 ),
inference(subsumption_resolution,[status(thm)],[f2900,f2665]) ).
thf(f2900,plain,
! [X0: a] :
( ( ( pa @ X0 @ ( sK161 @ x ) )
!= $true )
| ( ( qa @ X0 @ ( sK162 @ x ) )
= $true )
| ( ( sP3 @ x )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2899]) ).
thf(f2899,plain,
! [X0: a] :
( ( ( pa @ X0 @ ( sK161 @ x ) )
!= $true )
| ( $true != $true )
| ( ( sP3 @ x )
!= $true )
| ( ( qa @ X0 @ ( sK162 @ x ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f2898]) ).
thf(f2898,plain,
! [X0: a] :
( ( ( qa @ X0 @ ( sK162 @ x ) )
= $true )
| ( ( pa @ X0 @ ( sK161 @ x ) )
!= $true )
| ( $true != $true )
| ( ( sP3 @ x )
!= $true )
| ( ( sP3 @ x )
!= $true ) ),
inference(superposition,[status(thm)],[f2708,f2076]) ).
thf(f2076,plain,
! [X0: state] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK161 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1599]) ).
thf(f2708,plain,
! [X0: state,X1: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK161 @ X0 ) @ x ) @ r )
!= $true )
| ( ( sP3 @ X0 )
!= $true )
| ( ( qa @ X1 @ ( sK162 @ X0 ) )
= $true )
| ( ( pa @ X1 @ ( sK161 @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2700]) ).
thf(f2700,plain,
! [X0: state,X1: a] :
( ( ( sP3 @ X0 )
!= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK161 @ X0 ) @ x ) @ r )
!= $true )
| ( ( pa @ X1 @ ( sK161 @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( qa @ X1 @ ( sK162 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f2633,f2555]) ).
thf(f2555,plain,
! [X0: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ ( sK161 @ X0 ) @ body @ Y0 @ ( sK162 @ X0 ) ) )
= $true )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2390]) ).
thf(f2390,plain,
! [X0: state] :
( ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ ( sK161 @ X0 )
@ body
@ ( sK162 @ X0 ) )
= $true )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2073,f1657]) ).
thf(f1657,plain,
( exec
= ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f622]) ).
thf(f622,plain,
( exec
= ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f621]) ).
thf(f621,plain,
( exec
= ( ^ [X0: state,X1: com,X2: state] :
? [X3: nat] : ( execn @ X0 @ X1 @ X3 @ X2 ) ) ),
inference(rectify,[status(thm)],[f342]) ).
thf(f342,axiom,
( exec
= ( ^ [X19: state,X80: com,X62: state] :
? [X79: nat] : ( execn @ X19 @ X80 @ X79 @ X62 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H5mA5wl1hp/DTF2THF_16650.p',fact_341_exec__iff__execn) ).
thf(f2073,plain,
! [X0: state] :
( ( ( exec @ ( sK161 @ X0 ) @ body @ ( sK162 @ X0 ) )
= $true )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1599]) ).
thf(f2633,plain,
! [X2: state,X3: a,X1: state] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X1 @ body @ Y0 @ X2 ) )
!= $true )
| ( ( qa @ X3 @ X2 )
= $true )
| ( ( pa @ X3 @ X1 )
!= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2418]) ).
thf(f2418,plain,
! [X2: state,X3: a,X1: state] :
( ( ( pa @ X3 @ X1 )
!= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ X1 @ x ) @ r )
!= $true )
| ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ X1
@ body
@ X2 )
!= $true )
| ( ( qa @ X3 @ X2 )
= $true ) ),
inference(equality_resolution,[status(thm)],[f2212]) ).
thf(f2212,plain,
! [X2: state,X3: a,X0: state,X1: state] :
( ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ X1
@ body
@ X2 )
!= $true )
| ( ( pa @ X3 @ X1 )
!= $true )
| ( ( qa @ X3 @ X2 )
= $true )
| ( X0 != X1 )
| ( ( member1389040324_state @ ( produc64584659_state @ X0 @ x ) @ r )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f1770,f1657]) ).
thf(f1770,plain,
! [X2: state,X3: a,X0: state,X1: state] :
( ( ( exec @ X1 @ body @ X2 )
!= $true )
| ( ( pa @ X3 @ X1 )
!= $true )
| ( ( qa @ X3 @ X2 )
= $true )
| ( X0 != X1 )
| ( ( member1389040324_state @ ( produc64584659_state @ X0 @ x ) @ r )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1381]) ).
thf(f2075,plain,
! [X0: state] :
( ( ( qa @ ( sK163 @ X0 ) @ ( sK162 @ X0 ) )
!= $true )
| ( ( sP3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1599]) ).
thf(f2867,plain,
( spl173_5
| ~ spl173_1
| ~ spl173_13 ),
inference(avatar_split_clause,[status(thm)],[f2864,f2739,f2639,f2664]) ).
thf(f2739,definition,
( spl173_13
<=> ( ( sP3 @ sK140 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_13])],[avatar_definition]) ).
thf(f2864,plain,
( ( ( sP3 @ x )
= $true )
| ~ spl173_1
| ~ spl173_13 ),
inference(subsumption_resolution,[status(thm)],[f2863,f2641]) ).
thf(f2863,plain,
( ( sP2 != $true )
| ( ( sP3 @ x )
= $true )
| ~ spl173_13 ),
inference(superposition,[status(thm)],[f2741,f2004]) ).
thf(f2741,plain,
( ( ( sP3 @ sK140 )
= $true )
| ~ spl173_13 ),
inference(avatar_component_clause,[status(thm)],[f2739]) ).
thf(f2862,plain,
( spl173_12
| spl173_13
| spl173_22
| ~ spl173_1 ),
inference(avatar_split_clause,[status(thm)],[f2857,f2639,f2859,f2739,f2719]) ).
thf(f2719,definition,
( spl173_12
<=> ! [X0: a] :
( ( ( qa @ X0 @ sK139 )
= $true )
| ( ( pa @ X0 @ sK140 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl173_12])],[avatar_definition]) ).
thf(f2857,plain,
( ! [X0: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ sK140 ) @ sK140 ) @ r )
= $true )
| ( ( pa @ X0 @ sK140 )
!= $true )
| ( ( sP3 @ sK140 )
= $true )
| ( ( qa @ X0 @ sK139 )
= $true ) )
| ~ spl173_1 ),
inference(subsumption_resolution,[status(thm)],[f2791,f2641]) ).
thf(f2791,plain,
! [X0: a] :
( ( ( qa @ X0 @ sK139 )
= $true )
| ( ( sP3 @ sK140 )
= $true )
| ( ( pa @ X0 @ sK140 )
!= $true )
| ( sP2 != $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ sK140 ) @ sK140 ) @ r )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2789]) ).
thf(f2789,plain,
! [X0: a] :
( ( ( sP3 @ sK140 )
= $true )
| ( sP2 != $true )
| ( $true != $true )
| ( ( qa @ X0 @ sK139 )
= $true )
| ( ( pa @ X0 @ sK140 )
!= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ sK140 ) @ sK140 ) @ r )
= $true ) ),
inference(superposition,[status(thm)],[f2637,f2564]) ).
thf(f2564,plain,
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ sK140 @ body @ Y0 @ sK139 ) )
= $true )
| ( sP2 != $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2356]) ).
thf(f2356,plain,
( ( sP2 != $true )
| ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ sK140
@ body
@ sK139 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f2007,f1657]) ).
thf(f2007,plain,
( ( ( exec @ sK140 @ body @ sK139 )
= $true )
| ( sP2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1570]) ).
thf(f2637,plain,
! [X3: state,X4: state,X5: a] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X4 @ body @ Y0 @ X3 ) )
!= $true )
| ( ( sP3 @ X4 )
= $true )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true )
| ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ X4 ) @ X4 ) @ r )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2428]) ).
thf(f2428,plain,
! [X3: state,X4: state,X5: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ X4 ) @ X4 ) @ r )
= $true )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ X4
@ body
@ X3 )
!= $true )
| ( ( sP3 @ X4 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f2392]) ).
thf(f2392,plain,
! [X3: state,X0: state,X4: state,X5: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( sP3 @ X0 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true )
| ( X0 != X4 )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ X4
@ body
@ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2081,f1657]) ).
thf(f2081,plain,
! [X3: state,X0: state,X4: state,X5: a] :
( ( ( member1389040324_state @ ( produc64584659_state @ ( sK165 @ X0 ) @ X0 ) @ r )
= $true )
| ( ( sP3 @ X0 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true )
| ( X0 != X4 )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( exec @ X4 @ body @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
thf(f2854,plain,
( ~ spl173_1
| ~ spl173_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f2853]) ).
thf(f2853,plain,
( $false
| ~ spl173_1
| ~ spl173_12 ),
inference(subsumption_resolution,[status(thm)],[f2852,f2641]) ).
thf(f2852,plain,
( ( sP2 != $true )
| ~ spl173_1
| ~ spl173_12 ),
inference(trivial_inequality_removal,[status(thm)],[f2851]) ).
thf(f2851,plain,
( ( $true != $true )
| ( sP2 != $true )
| ~ spl173_1
| ~ spl173_12 ),
inference(superposition,[status(thm)],[f2846,f2005]) ).
thf(f2005,plain,
( ( ( pa @ sK141 @ sK140 )
= $true )
| ( sP2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1570]) ).
thf(f2846,plain,
( ( ( pa @ sK141 @ sK140 )
!= $true )
| ~ spl173_1
| ~ spl173_12 ),
inference(subsumption_resolution,[status(thm)],[f2845,f2641]) ).
thf(f2845,plain,
( ( ( pa @ sK141 @ sK140 )
!= $true )
| ( sP2 != $true )
| ~ spl173_12 ),
inference(trivial_inequality_removal,[status(thm)],[f2844]) ).
thf(f2844,plain,
( ( ( pa @ sK141 @ sK140 )
!= $true )
| ( sP2 != $true )
| ( $true != $true )
| ~ spl173_12 ),
inference(superposition,[status(thm)],[f2006,f2720]) ).
thf(f2720,plain,
( ! [X0: a] :
( ( ( qa @ X0 @ sK139 )
= $true )
| ( ( pa @ X0 @ sK140 )
!= $true ) )
| ~ spl173_12 ),
inference(avatar_component_clause,[status(thm)],[f2719]) ).
thf(f2006,plain,
( ( ( qa @ sK141 @ sK139 )
!= $true )
| ( sP2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1570]) ).
thf(f2785,plain,
( ~ spl173_1
| spl173_13
| spl173_12
| spl173_15 ),
inference(avatar_split_clause,[status(thm)],[f2760,f2763,f2719,f2739,f2639]) ).
thf(f2760,plain,
! [X0: a] :
( ( sP2 != $true )
| ( ( pa @ X0 @ sK140 )
!= $true )
| ( ( qa @ X0 @ sK139 )
= $true )
| ( ( pa @ ( sK164 @ sK140 ) @ ( sK165 @ sK140 ) )
= $true )
| ( ( sP3 @ sK140 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2753]) ).
thf(f2753,plain,
! [X0: a] :
( ( sP2 != $true )
| ( ( qa @ X0 @ sK139 )
= $true )
| ( ( sP3 @ sK140 )
= $true )
| ( ( pa @ ( sK164 @ sK140 ) @ ( sK165 @ sK140 ) )
= $true )
| ( ( pa @ X0 @ sK140 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2634,f2564]) ).
thf(f2634,plain,
! [X3: state,X4: state,X5: a] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X4 @ body @ Y0 @ X3 ) )
!= $true )
| ( ( sP3 @ X4 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true )
| ( ( pa @ ( sK164 @ X4 ) @ ( sK165 @ X4 ) )
= $true )
| ( ( qa @ X5 @ X3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2430]) ).
thf(f2430,plain,
! [X3: state,X4: state,X5: a] :
( ( ( pa @ X5 @ X4 )
!= $true )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( pa @ ( sK164 @ X4 ) @ ( sK165 @ X4 ) )
= $true )
| ( ( sP3 @ X4 )
= $true )
| ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ X4
@ body
@ X3 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f2393]) ).
thf(f2393,plain,
! [X3: state,X0: state,X4: state,X5: a] :
( ( ( pa @ ( sK164 @ X0 ) @ ( sK165 @ X0 ) )
= $true )
| ( ( sP3 @ X0 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true )
| ( X0 != X4 )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ X4
@ body
@ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2079,f1657]) ).
thf(f2079,plain,
! [X3: state,X0: state,X4: state,X5: a] :
( ( ( pa @ ( sK164 @ X0 ) @ ( sK165 @ X0 ) )
= $true )
| ( ( sP3 @ X0 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true )
| ( X0 != X4 )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( exec @ X4 @ body @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
thf(f2784,plain,
( ~ spl173_2
| ~ spl173_3
| ~ spl173_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f2783]) ).
thf(f2783,plain,
( $false
| ~ spl173_2
| ~ spl173_3
| ~ spl173_8 ),
inference(subsumption_resolution,[status(thm)],[f2781,f2678]) ).
thf(f2678,plain,
( ! [X0: a] :
( ( pa @ X0 @ x )
!= $true )
| ~ spl173_8 ),
inference(avatar_component_clause,[status(thm)],[f2677]) ).
thf(f2781,plain,
( ( ( pa @ sK143 @ x )
= $true )
| ~ spl173_2
| ~ spl173_3 ),
inference(superposition,[status(thm)],[f2650,f2645]) ).
thf(f2645,plain,
( ( x = sK142 )
| ~ spl173_2 ),
inference(avatar_component_clause,[status(thm)],[f2643]) ).
thf(f2643,definition,
( spl173_2
<=> ( x = sK142 ) ),
introduced(definition,[new_symbols(naming,[spl173_2])],[avatar_definition]) ).
thf(f2650,plain,
( ( ( pa @ sK143 @ sK142 )
= $true )
| ~ spl173_3 ),
inference(avatar_component_clause,[status(thm)],[f2648]) ).
thf(f2648,definition,
( spl173_3
<=> ( ( pa @ sK143 @ sK142 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_3])],[avatar_definition]) ).
thf(f2782,plain,
( ~ spl173_10
| ~ spl173_2
| spl173_4 ),
inference(avatar_split_clause,[status(thm)],[f2780,f2653,f2643,f2684]) ).
thf(f2653,definition,
( spl173_4
<=> ( ( termi @ body @ sK142 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_4])],[avatar_definition]) ).
thf(f2780,plain,
( ( ( termi @ body @ x )
!= $true )
| ~ spl173_2
| spl173_4 ),
inference(superposition,[status(thm)],[f2655,f2645]) ).
thf(f2655,plain,
( ( ( termi @ body @ sK142 )
!= $true )
| spl173_4 ),
inference(avatar_component_clause,[status(thm)],[f2653]) ).
thf(f2774,plain,
( ~ spl173_16
| ~ spl173_1
| spl173_14 ),
inference(avatar_split_clause,[status(thm)],[f2748,f2743,f2639,f2771]) ).
thf(f2743,definition,
( spl173_14
<=> ( ( termi @ body @ ( sK165 @ sK140 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl173_14])],[avatar_definition]) ).
thf(f2748,plain,
( ( sP2 != $true )
| ( ( termi @ body @ ( sK165 @ x ) )
!= $true )
| spl173_14 ),
inference(superposition,[status(thm)],[f2745,f2004]) ).
thf(f2745,plain,
( ( ( termi @ body @ ( sK165 @ sK140 ) )
!= $true )
| spl173_14 ),
inference(avatar_component_clause,[status(thm)],[f2743]) ).
thf(f2746,plain,
( spl173_13
| spl173_12
| ~ spl173_14
| ~ spl173_1 ),
inference(avatar_split_clause,[status(thm)],[f2737,f2639,f2743,f2719,f2739]) ).
thf(f2737,plain,
( ! [X0: a] :
( ( ( sP3 @ sK140 )
= $true )
| ( ( qa @ X0 @ sK139 )
= $true )
| ( ( pa @ X0 @ sK140 )
!= $true )
| ( ( termi @ body @ ( sK165 @ sK140 ) )
!= $true ) )
| ~ spl173_1 ),
inference(subsumption_resolution,[status(thm)],[f2730,f2641]) ).
thf(f2730,plain,
! [X0: a] :
( ( ( sP3 @ sK140 )
= $true )
| ( ( termi @ body @ ( sK165 @ sK140 ) )
!= $true )
| ( ( qa @ X0 @ sK139 )
= $true )
| ( ( pa @ X0 @ sK140 )
!= $true )
| ( sP2 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2727]) ).
thf(f2727,plain,
! [X0: a] :
( ( ( sP3 @ sK140 )
= $true )
| ( ( termi @ body @ ( sK165 @ sK140 ) )
!= $true )
| ( sP2 != $true )
| ( ( qa @ X0 @ sK139 )
= $true )
| ( $true != $true )
| ( ( pa @ X0 @ sK140 )
!= $true ) ),
inference(superposition,[status(thm)],[f2635,f2564]) ).
thf(f2635,plain,
! [X3: state,X4: state,X5: a] :
( ( ( ?? @ nat
@ ^ [Y0: nat] : ( execn @ X4 @ body @ Y0 @ X3 ) )
!= $true )
| ( $true
!= ( termi @ body @ ( sK165 @ X4 ) ) )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true )
| ( ( sP3 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2426]) ).
thf(f2426,plain,
! [X3: state,X4: state,X5: a] :
( ( ( qa @ X5 @ X3 )
= $true )
| ( $true
!= ( termi @ body @ ( sK165 @ X4 ) ) )
| ( ( sP3 @ X4 )
= $true )
| ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ X4
@ body
@ X3 )
!= $true )
| ( ( pa @ X5 @ X4 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f2391]) ).
thf(f2391,plain,
! [X3: state,X0: state,X4: state,X5: a] :
( ( ( termi @ body @ ( sK165 @ X0 ) )
!= $true )
| ( ( sP3 @ X0 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true )
| ( X0 != X4 )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( ^ [Y0: state,Y1: com,Y2: state] :
( ?? @ nat
@ ^ [Y3: nat] : ( execn @ Y0 @ Y1 @ Y3 @ Y2 ) )
@ X4
@ body
@ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2083,f1657]) ).
thf(f2083,plain,
! [X3: state,X0: state,X4: state,X5: a] :
( ( ( termi @ body @ ( sK165 @ X0 ) )
!= $true )
| ( ( sP3 @ X0 )
= $true )
| ( ( pa @ X5 @ X4 )
!= $true )
| ( X0 != X4 )
| ( ( qa @ X5 @ X3 )
= $true )
| ( ( exec @ X4 @ body @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
thf(f2656,plain,
( spl173_1
| ~ spl173_4 ),
inference(avatar_split_clause,[status(thm)],[f2009,f2653,f2639]) ).
thf(f2009,plain,
( ( ( termi @ body @ sK142 )
!= $true )
| ( sP2 = $true ) ),
inference(cnf_transformation,[status(thm)],[f1573]) ).
thf(f1573,plain,
( ( ( ( pa @ sK143 @ sK142 )
= $true )
& ( ( termi @ body @ sK142 )
!= $true )
& ( x = sK142 ) )
| ( sP2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK142,sK143])],[f1571,f1572]) ).
thf(f1572,plain,
( ? [X0: state,X1: a] :
( ( ( pa @ X1 @ X0 )
= $true )
& ( ( termi @ body @ X0 )
!= $true )
& ( x = X0 ) )
=> ( ( ( pa @ sK143 @ sK142 )
= $true )
& ( ( termi @ body @ sK142 )
!= $true )
& ( x = sK142 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1571,plain,
( ? [X0: state,X1: a] :
( ( ( pa @ X1 @ X0 )
= $true )
& ( ( termi @ body @ X0 )
!= $true )
& ( x = X0 ) )
| ( sP2 = $true ) ),
inference(rectify,[status(thm)],[f1399]) ).
thf(f1399,plain,
( ? [X3: state,X4: a] :
( ( ( pa @ X4 @ X3 )
= $true )
& ( ( termi @ body @ X3 )
!= $true )
& ( x = X3 ) )
| ( sP2 = $true ) ),
inference(definition_folding,[status(thm)],[f1240,f1398]) ).
thf(f1240,plain,
( ? [X3: state,X4: a] :
( ( ( pa @ X4 @ X3 )
= $true )
& ( ( termi @ body @ X3 )
!= $true )
& ( x = X3 ) )
| ? [X0: state,X1: state] :
( ( ( exec @ X1 @ body @ X0 )
= $true )
& ? [X2: a] :
( ( ( qa @ X2 @ X0 )
!= $true )
& ( ( pa @ X2 @ X1 )
= $true )
& ( x = X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f1109]) ).
thf(f1109,plain,
~ ( ! [X0: state,X1: state] :
( ! [X2: a] :
( ( ( qa @ X2 @ X0 )
= $true )
| ( ( pa @ X2 @ X1 )
!= $true )
| ( x != X1 ) )
| ( ( exec @ X1 @ body @ X0 )
!= $true ) )
& ! [X3: state,X4: a] :
( ( x != X3 )
| ( ( termi @ body @ X3 )
= $true )
| ( ( pa @ X4 @ X3 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f609]) ).
thf(f609,plain,
~ ( ! [X0: state,X1: state] :
( ( ( exec @ X1 @ body @ X0 )
!= $true )
| ! [X2: a] :
( ( x != X1 )
| ( ( qa @ X2 @ X0 )
= $true )
| ( ( pa @ X2 @ X1 )
!= $true ) ) )
& ! [X3: state,X4: a] :
( ( ( pa @ X4 @ X3 )
!= $true )
| ( x != X3 )
| ( ( termi @ body @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f608]) ).
thf(f608,plain,
~ ( ! [X0: state,X1: state] :
( ~ ( exec @ X1 @ body @ X0 )
| ! [X2: a] :
( ( x != X1 )
| ( qa @ X2 @ X0 )
| ~ ( pa @ X2 @ X1 ) ) )
& ! [X3: state,X4: a] :
( ~ ( pa @ X4 @ X3 )
| ( x != X3 )
| ( termi @ body @ X3 ) ) ),
inference(rectify,[status(thm)],[f358]) ).
thf(f358,negated_conjecture,
~ ( ! [X8: state,X6: state] :
( ~ ( exec @ X6 @ body @ X8 )
| ! [X5: a] :
( ( x != X6 )
| ( qa @ X5 @ X8 )
| ~ ( pa @ X5 @ X6 ) ) )
& ! [X6: state,X5: a] :
( ~ ( pa @ X5 @ X6 )
| ( x != X6 )
| ( termi @ body @ X6 ) ) ),
inference(negated_conjecture,[status(cth)],[f357]) ).
thf(f357,conjecture,
( ! [X8: state,X6: state] :
( ~ ( exec @ X6 @ body @ X8 )
| ! [X5: a] :
( ( x != X6 )
| ( qa @ X5 @ X8 )
| ~ ( pa @ X5 @ X6 ) ) )
& ! [X6: state,X5: a] :
( ~ ( pa @ X5 @ X6 )
| ( x != X6 )
| ( termi @ body @ X6 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H5mA5wl1hp/DTF2THF_16650.p',conj_2) ).
thf(f2651,plain,
( spl173_1
| spl173_3 ),
inference(avatar_split_clause,[status(thm)],[f2010,f2648,f2639]) ).
thf(f2010,plain,
( ( sP2 = $true )
| ( ( pa @ sK143 @ sK142 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1573]) ).
thf(f2646,plain,
( spl173_1
| spl173_2 ),
inference(avatar_split_clause,[status(thm)],[f2008,f2643,f2639]) ).
thf(f2008,plain,
( ( sP2 = $true )
| ( x = sK142 ) ),
inference(cnf_transformation,[status(thm)],[f1573]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP141^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:26:11 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ITP141^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46 % Domain : Interactive Theorem Proving
% 0.31/0.46 % Problem : Sledgehammer PHoareTotal problem prob_135__3259094_1
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Des21]
% 0.31/0.46 % Names : PHoareTotal/prob_135__3259094_1 [Des21]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0
% 0.31/0.46 % Syntax : Number of formulae : 486 ( 197 unt; 129 typ; 0 def)
% 0.31/0.46 % Number of atoms : 965 ( 395 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 21 ( 2 avg)
% 0.31/0.46 % Number of connectives : 2845 ( 189 ~; 21 |; 103 &;2146 @)
% 0.31/0.46 % ( 0 <=>; 386 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 22 ( 7 avg)
% 0.31/0.46 % Number of types : 21 ( 20 usr)
% 0.31/0.46 % Number of type conns : 488 ( 488 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 112 ( 109 usr; 17 con; 0-4 aty)
% 0.31/0.46 % Number of variables : 1075 ( 140 ^; 895 !; 40 ?;1075 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:35.907
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % Could-be-implicit typings (20)
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J_J,type,
% 0.31/0.46 set_Pr1702239303tate_o: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J,type,
% 0.31/0.46 produc1307154919tate_o: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J,type,
% 0.31/0.46 set_Pr1590995257tate_o: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J_J,type,
% 0.31/0.46 set_Pr778812871_state: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 0.31/0.46 produc696469763tate_o: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.31/0.46 set_Pr1490359111at_nat: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46 produc1390548711_state: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.31/0.46 produc842455143at_nat: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 0.31/0.46 set_Pr1740974983tate_o: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J,type,
% 0.31/0.46 produc204914599tate_o: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46 set_Pr795498619_state: $tType ).
% 0.31/0.46
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% 0.31/0.46 trans_nat: set_Pr1986765409at_nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.31/0.46 collect_nat: ( nat > $o ) > set_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__PLang__Ostate,type,
% 0.31/0.46 collect_state: ( state > $o ) > set_state ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 0.31/0.46 collec1499596504tate_o: ( produc696469763tate_o > $o ) > set_Pr1590995257tate_o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/0.46 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.31/0.46 collec496201222_state: ( produc1115495963_state > $o ) > set_Pr795498619_state ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 0.31/0.46 insert_nat: nat > set_nat > set_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__PLang__Ostate,type,
% 0.31/0.46 insert_state: state > set_state > set_state ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 0.31/0.46 insert2053719859tate_o: produc696469763tate_o > set_Pr1590995257tate_o > set_Pr1590995257tate_o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/0.46 insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.31/0.46 insert311944171_state: produc1115495963_state > set_Pr795498619_state > set_Pr795498619_state ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J,type,
% 0.31/0.46 insert1597128631tate_o: produc1307154919tate_o > set_Pr1702239303tate_o > set_Pr1702239303tate_o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.31/0.46 insert584009271at_nat: produc842455143at_nat > set_Pr1490359111at_nat > set_Pr1490359111at_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46 insert1616594103_state: produc1390548711_state > set_Pr778812871_state > set_Pr778812871_state ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__empty_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 0.31/0.46 is_emp807847857tate_o: set_Pr1590995257tate_o > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__empty_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/0.46 is_emp825011411at_nat: set_Pr1986765409at_nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__empty_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.31/0.46 is_emp1062983149_state: set_Pr795498619_state > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 0.31/0.46 is_sin1547905295tate_o: set_Pr1590995257tate_o > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/0.46 is_sin1352690165at_nat: set_Pr1986765409at_nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.31/0.46 is_sin1132515087_state: set_Pr795498619_state > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 0.31/0.46 the_el1569055182tate_o: set_Pr1590995257tate_o > produc696469763tate_o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/0.46 the_el1949240438at_nat: set_Pr1986765409at_nat > product_prod_nat_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.31/0.46 the_el1967402896_state: set_Pr795498619_state > produc1115495963_state ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Oless__than,type,
% 0.31/0.46 less_than: set_Pr1986765409at_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Omeasure_001t__Nat__Onat,type,
% 0.31/0.46 measure_nat: ( nat > nat ) > set_Pr1986765409at_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Omeasure_001t__PLang__Ostate,type,
% 0.31/0.46 measure_state: ( state > nat ) > set_Pr795498619_state ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Opred__nat,type,
% 0.31/0.46 pred_nat: set_Pr1986765409at_nat ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 0.31/0.46 wf_nat: set_Pr1986765409at_nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Owf_001t__PLang__Ostate,type,
% 0.31/0.46 wf_state: set_Pr795498619_state > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 0.31/0.46 wf_Pro309705690tate_o: set_Pr1702239303tate_o > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/0.46 wf_Pro745352042at_nat: set_Pr1490359111at_nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.31/0.46 wf_Pro1783588484_state: set_Pr778812871_state > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Nat__Onat,type,
% 0.31/0.46 member_nat: nat > set_nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__PLang__Ostate,type,
% 0.31/0.46 member_state: state > set_state > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 0.31/0.46 member1838112666tate_o: produc696469763tate_o > set_Pr1590995257tate_o > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.31/0.46 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J,type,
% 0.31/0.46 member221067728tate_o: produc204914599tate_o > set_Pr1740974983tate_o > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 0.31/0.46 member1389040324_state: produc1115495963_state > set_Pr795498619_state > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J,type,
% 0.31/0.46 member1629320336tate_o: produc1307154919tate_o > set_Pr1702239303tate_o > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.31/0.46 member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J,type,
% 0.31/0.46 member768948240_state: produc1390548711_state > set_Pr778812871_state > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_Pa,type,
% 0.31/0.46 pa: a > state > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_Qa,type,
% 0.31/0.46 qa: a > state > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_r,type,
% 0.31/0.46 r: set_Pr795498619_state ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_x,type,
% 0.31/0.46 x: state ).
% 0.31/0.46
% 0.31/0.46 % Relevant facts (354)
% 0.31/0.46 thf(fact_0_thoare_OAsm,axiom,
% 0.31/0.46 ! [P: a > state > $o,Q: a > state > $o] : ( pHoare382919414oare_a @ ( insert2053719859tate_o @ ( produc33908149tate_o @ P @ ( produc1948644831tate_o @ call @ Q ) ) @ bot_bo170732493tate_o ) @ P @ call @ Q ) ).
% 0.31/0.46
% 0.31/0.46 % thoare.Asm
% 0.31/0.46 thf(fact_1_weaken__post,axiom,
% 0.31/0.46 ! [C: set_Pr1590995257tate_o,P: a > state > $o,C2: com,Q: a > state > $o,Q2: a > state > $o] :
% 0.31/0.46 ( ( pHoare382919414oare_a @ C @ P @ C2 @ Q )
% 0.31/0.46 => ( ! [Z: a,S: state] :
% 0.31/0.46 ( ( Q @ Z @ S )
% 0.31/0.46 => ( Q2 @ Z @ S ) )
% 0.31/0.46 => ( pHoare382919414oare_a @ C @ P @ C2 @ Q2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % weaken_post
% 0.31/0.46 thf(fact_2_thoare_OConseq,axiom,
% 0.31/0.46 ! [C: set_Pr1590995257tate_o,P2: a > state > $o,C2: com,Q2: a > state > $o,P: a > state > $o,Q: a > state > $o] :
% 0.31/0.46 ( ( pHoare382919414oare_a @ C @ P2 @ C2 @ Q2 )
% 0.31/0.46 => ( ( ! [S: state,T: state] :
% 0.31/0.46 ( ! [Z2: a] :
% 0.31/0.46 ( ( P2 @ Z2 @ S )
% 0.31/0.46 => ( Q2 @ Z2 @ T ) )
% 0.31/0.46 => ! [Z: a] :
% 0.31/0.46 ( ( P @ Z @ S )
% 0.31/0.46 => ( Q @ Z @ T ) ) )
% 0.31/0.46 & ! [S: state] :
% 0.31/0.46 ( ? [Z: a] : ( P @ Z @ S )
% 0.31/0.46 => ? [Z2: a] : ( P2 @ Z2 @ S ) ) )
% 0.31/0.46 => ( pHoare382919414oare_a @ C @ P @ C2 @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % thoare.Conseq
% 0.31/0.46 thf(fact_3_PHoareTotal__Mirabelle__ynemugpbor_Ostrengthen__pre,axiom,
% 0.31/0.46 ! [P2: a > state > $o,P: a > state > $o,C: set_Pr1590995257tate_o,C2: com,Q: a > state > $o] :
% 0.31/0.46 ( ! [Z: a,S: state] :
% 0.31/0.46 ( ( P2 @ Z @ S )
% 0.31/0.46 => ( P @ Z @ S ) )
% 0.31/0.46 => ( ( pHoare382919414oare_a @ C @ P @ C2 @ Q )
% 0.31/0.46 => ( pHoare382919414oare_a @ C @ P2 @ C2 @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % PHoareTotal_Mirabelle_ynemugpbor.strengthen_pre
% 0.31/0.46 thf(fact_4_singleton__conv,axiom,
% 0.31/0.46 ! [A: produc1115495963_state] :
% 0.31/0.46 ( ( collec496201222_state
% 0.31/0.46 @ ^ [X: produc1115495963_state] : ( X = A ) )
% 0.31/0.46 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_conv
% 0.31/0.46 thf(fact_5_singleton__conv,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat] :
% 0.31/0.46 ( ( collec7649004at_nat
% 0.31/0.46 @ ^ [X: product_prod_nat_nat] : ( X = A ) )
% 0.31/0.46 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_conv
% 0.31/0.46 thf(fact_6_singleton__conv,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o] :
% 0.31/0.46 ( ( collec1499596504tate_o
% 0.31/0.46 @ ^ [X: produc696469763tate_o] : ( X = A ) )
% 0.31/0.46 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_conv
% 0.31/0.46 thf(fact_7_singleton__conv2,axiom,
% 0.31/0.46 ! [A: produc1115495963_state] :
% 0.31/0.46 ( ( collec496201222_state
% 0.31/0.46 @ ( ^ [Y: produc1115495963_state,Z3: produc1115495963_state] : ( Y = Z3 )
% 0.31/0.46 @ A ) )
% 0.31/0.46 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_conv2
% 0.31/0.46 thf(fact_8_singleton__conv2,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat] :
% 0.31/0.46 ( ( collec7649004at_nat
% 0.31/0.46 @ ( ^ [Y: product_prod_nat_nat,Z3: product_prod_nat_nat] : ( Y = Z3 )
% 0.31/0.46 @ A ) )
% 0.31/0.46 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_conv2
% 0.31/0.46 thf(fact_9_singleton__conv2,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o] :
% 0.31/0.46 ( ( collec1499596504tate_o
% 0.31/0.46 @ ( ^ [Y: produc696469763tate_o,Z3: produc696469763tate_o] : ( Y = Z3 )
% 0.31/0.46 @ A ) )
% 0.31/0.46 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_conv2
% 0.31/0.46 thf(fact_10_singletonI,axiom,
% 0.31/0.46 ! [A: produc1115495963_state] : ( member1389040324_state @ A @ ( insert311944171_state @ A @ bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonI
% 0.31/0.46 thf(fact_11_singletonI,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonI
% 0.31/0.46 thf(fact_12_singletonI,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o] : ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonI
% 0.31/0.46 thf(fact_13_termi_Ointros_I7_J,axiom,
% 0.31/0.46 ! [S2: state] :
% 0.31/0.46 ( ( termi @ body @ S2 )
% 0.31/0.46 => ( termi @ call @ S2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % termi.intros(7)
% 0.31/0.46 thf(fact_14_exec_Ointros_I7_J,axiom,
% 0.31/0.46 ! [S2: state,T2: state] :
% 0.31/0.46 ( ( exec @ S2 @ body @ T2 )
% 0.31/0.46 => ( exec @ S2 @ call @ T2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % exec.intros(7)
% 0.31/0.46 thf(fact_15_thoare_OCall,axiom,
% 0.31/0.46 ! [R: set_Pr795498619_state,P: a > state > $o,Q: a > state > $o] :
% 0.31/0.46 ( ( wf_state @ R )
% 0.31/0.46 => ( ! [S3: state] :
% 0.31/0.46 ( pHoare382919414oare_a
% 0.31/0.46 @ ( insert2053719859tate_o
% 0.31/0.46 @ ( produc33908149tate_o
% 0.31/0.46 @ ^ [Z4: a,S4: state] :
% 0.31/0.46 ( ( P @ Z4 @ S4 )
% 0.31/0.46 & ( member1389040324_state @ ( produc64584659_state @ S4 @ S3 ) @ R ) )
% 0.31/0.46 @ ( produc1948644831tate_o @ call @ Q ) )
% 0.31/0.46 @ bot_bo170732493tate_o )
% 0.31/0.46 @ ^ [Z4: a,S4: state] :
% 0.31/0.46 ( ( P @ Z4 @ S4 )
% 0.31/0.46 & ( S4 = S3 ) )
% 0.31/0.46 @ body
% 0.31/0.46 @ Q )
% 0.31/0.46 => ( pHoare382919414oare_a @ bot_bo170732493tate_o @ P @ call @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % thoare.Call
% 0.31/0.46 thf(fact_16_insertCI,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,B: set_Pr795498619_state,B2: produc1115495963_state] :
% 0.31/0.46 ( ( ~ ( member1389040324_state @ A @ B )
% 0.31/0.46 => ( A = B2 ) )
% 0.31/0.46 => ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertCI
% 0.31/0.46 thf(fact_17_insertCI,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,B2: product_prod_nat_nat] :
% 0.31/0.46 ( ( ~ ( member701585322at_nat @ A @ B )
% 0.31/0.46 => ( A = B2 ) )
% 0.31/0.46 => ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertCI
% 0.31/0.46 thf(fact_18_insertCI,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,B: set_Pr1590995257tate_o,B2: produc696469763tate_o] :
% 0.31/0.46 ( ( ~ ( member1838112666tate_o @ A @ B )
% 0.31/0.46 => ( A = B2 ) )
% 0.31/0.46 => ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertCI
% 0.31/0.46 thf(fact_19_insert__iff,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,B2: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ A2 ) )
% 0.31/0.46 = ( ( A = B2 )
% 0.31/0.46 | ( member1389040324_state @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_iff
% 0.31/0.46 thf(fact_20_insert__iff,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ A2 ) )
% 0.31/0.46 = ( ( A = B2 )
% 0.31/0.46 | ( member701585322at_nat @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_iff
% 0.31/0.46 thf(fact_21_insert__iff,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,B2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ A2 ) )
% 0.31/0.46 = ( ( A = B2 )
% 0.31/0.46 | ( member1838112666tate_o @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_iff
% 0.31/0.46 thf(fact_22_insert__absorb2,axiom,
% 0.31/0.46 ! [X2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( insert2053719859tate_o @ X2 @ ( insert2053719859tate_o @ X2 @ A2 ) )
% 0.31/0.46 = ( insert2053719859tate_o @ X2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_absorb2
% 0.31/0.46 thf(fact_23_insert__absorb2,axiom,
% 0.31/0.46 ! [X2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( insert271595217at_nat @ X2 @ ( insert271595217at_nat @ X2 @ A2 ) )
% 0.31/0.46 = ( insert271595217at_nat @ X2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_absorb2
% 0.31/0.46 thf(fact_24_insert__absorb2,axiom,
% 0.31/0.46 ! [X2: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( insert311944171_state @ X2 @ ( insert311944171_state @ X2 @ A2 ) )
% 0.31/0.46 = ( insert311944171_state @ X2 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_absorb2
% 0.31/0.46 thf(fact_25_hoare_OCall,axiom,
% 0.31/0.46 ! [P: a > state > $o,Q: a > state > $o] :
% 0.31/0.46 ( ( hoare_a @ ( insert2053719859tate_o @ ( produc33908149tate_o @ P @ ( produc1948644831tate_o @ call @ Q ) ) @ bot_bo170732493tate_o ) @ P @ body @ Q )
% 0.31/0.46 => ( hoare_a @ bot_bo170732493tate_o @ P @ call @ Q ) ) ).
% 0.31/0.46
% 0.31/0.46 % hoare.Call
% 0.31/0.46 thf(fact_26_empty__iff,axiom,
% 0.31/0.46 ! [C2: produc696469763tate_o] :
% 0.31/0.46 ~ ( member1838112666tate_o @ C2 @ bot_bo170732493tate_o ) ).
% 0.31/0.46
% 0.31/0.46 % empty_iff
% 0.31/0.46 thf(fact_27_empty__iff,axiom,
% 0.31/0.46 ! [C2: product_prod_nat_nat] :
% 0.31/0.46 ~ ( member701585322at_nat @ C2 @ bot_bo2130386637at_nat ) ).
% 0.31/0.46
% 0.31/0.46 % empty_iff
% 0.31/0.46 thf(fact_28_empty__iff,axiom,
% 0.31/0.46 ! [C2: produc1115495963_state] :
% 0.31/0.46 ~ ( member1389040324_state @ C2 @ bot_bo1625160935_state ) ).
% 0.31/0.46
% 0.31/0.46 % empty_iff
% 0.31/0.46 thf(fact_29_all__not__in__conv,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( ! [X: produc696469763tate_o] :
% 0.31/0.46 ~ ( member1838112666tate_o @ X @ A2 ) )
% 0.31/0.46 = ( A2 = bot_bo170732493tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % all_not_in_conv
% 0.31/0.46 thf(fact_30_all__not__in__conv,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( ! [X: product_prod_nat_nat] :
% 0.31/0.46 ~ ( member701585322at_nat @ X @ A2 ) )
% 0.31/0.46 = ( A2 = bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % all_not_in_conv
% 0.31/0.46 thf(fact_31_all__not__in__conv,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( ! [X: produc1115495963_state] :
% 0.31/0.46 ~ ( member1389040324_state @ X @ A2 ) )
% 0.31/0.46 = ( A2 = bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % all_not_in_conv
% 0.31/0.46 thf(fact_32_empty__Collect__eq,axiom,
% 0.31/0.46 ! [P: produc696469763tate_o > $o] :
% 0.31/0.46 ( ( bot_bo170732493tate_o
% 0.31/0.46 = ( collec1499596504tate_o @ P ) )
% 0.31/0.46 = ( ! [X: produc696469763tate_o] :
% 0.31/0.46 ~ ( P @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_Collect_eq
% 0.31/0.46 thf(fact_33_empty__Collect__eq,axiom,
% 0.31/0.46 ! [P: product_prod_nat_nat > $o] :
% 0.31/0.46 ( ( bot_bo2130386637at_nat
% 0.31/0.46 = ( collec7649004at_nat @ P ) )
% 0.31/0.46 = ( ! [X: product_prod_nat_nat] :
% 0.31/0.46 ~ ( P @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_Collect_eq
% 0.31/0.46 thf(fact_34_empty__Collect__eq,axiom,
% 0.31/0.46 ! [P: produc1115495963_state > $o] :
% 0.31/0.46 ( ( bot_bo1625160935_state
% 0.31/0.46 = ( collec496201222_state @ P ) )
% 0.31/0.46 = ( ! [X: produc1115495963_state] :
% 0.31/0.46 ~ ( P @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_Collect_eq
% 0.31/0.46 thf(fact_35_Collect__empty__eq,axiom,
% 0.31/0.46 ! [P: produc696469763tate_o > $o] :
% 0.31/0.46 ( ( ( collec1499596504tate_o @ P )
% 0.31/0.46 = bot_bo170732493tate_o )
% 0.31/0.46 = ( ! [X: produc696469763tate_o] :
% 0.31/0.46 ~ ( P @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_empty_eq
% 0.31/0.46 thf(fact_36_Collect__empty__eq,axiom,
% 0.31/0.46 ! [P: product_prod_nat_nat > $o] :
% 0.31/0.46 ( ( ( collec7649004at_nat @ P )
% 0.31/0.46 = bot_bo2130386637at_nat )
% 0.31/0.46 = ( ! [X: product_prod_nat_nat] :
% 0.31/0.46 ~ ( P @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_empty_eq
% 0.31/0.46 thf(fact_37_Collect__empty__eq,axiom,
% 0.31/0.46 ! [P: produc1115495963_state > $o] :
% 0.31/0.46 ( ( ( collec496201222_state @ P )
% 0.31/0.46 = bot_bo1625160935_state )
% 0.31/0.46 = ( ! [X: produc1115495963_state] :
% 0.31/0.46 ~ ( P @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_empty_eq
% 0.31/0.46 thf(fact_38_ex__in__conv,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( ? [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ A2 ) )
% 0.31/0.46 = ( A2 != bot_bo170732493tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % ex_in_conv
% 0.31/0.46 thf(fact_39_ex__in__conv,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( ? [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ A2 ) )
% 0.31/0.46 = ( A2 != bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % ex_in_conv
% 0.31/0.46 thf(fact_40_ex__in__conv,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( ? [X: produc1115495963_state] : ( member1389040324_state @ X @ A2 ) )
% 0.31/0.46 = ( A2 != bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % ex_in_conv
% 0.31/0.46 thf(fact_41_equals0I,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ! [Y2: produc696469763tate_o] :
% 0.31/0.46 ~ ( member1838112666tate_o @ Y2 @ A2 )
% 0.31/0.46 => ( A2 = bot_bo170732493tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % equals0I
% 0.31/0.46 thf(fact_42_equals0I,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ! [Y2: product_prod_nat_nat] :
% 0.31/0.46 ~ ( member701585322at_nat @ Y2 @ A2 )
% 0.31/0.46 => ( A2 = bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % equals0I
% 0.31/0.46 thf(fact_43_equals0I,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state] :
% 0.31/0.46 ( ! [Y2: produc1115495963_state] :
% 0.31/0.46 ~ ( member1389040324_state @ Y2 @ A2 )
% 0.31/0.46 => ( A2 = bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % equals0I
% 0.31/0.46 thf(fact_44_equals0D,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o,A: produc696469763tate_o] :
% 0.31/0.46 ( ( A2 = bot_bo170732493tate_o )
% 0.31/0.46 => ~ ( member1838112666tate_o @ A @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % equals0D
% 0.31/0.46 thf(fact_45_equals0D,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat,A: product_prod_nat_nat] :
% 0.31/0.46 ( ( A2 = bot_bo2130386637at_nat )
% 0.31/0.46 => ~ ( member701585322at_nat @ A @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % equals0D
% 0.31/0.46 thf(fact_46_equals0D,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state,A: produc1115495963_state] :
% 0.31/0.46 ( ( A2 = bot_bo1625160935_state )
% 0.31/0.46 => ~ ( member1389040324_state @ A @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % equals0D
% 0.31/0.46 thf(fact_47_emptyE,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o] :
% 0.31/0.46 ~ ( member1838112666tate_o @ A @ bot_bo170732493tate_o ) ).
% 0.31/0.46
% 0.31/0.46 % emptyE
% 0.31/0.46 thf(fact_48_emptyE,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat] :
% 0.31/0.46 ~ ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ).
% 0.31/0.46
% 0.31/0.46 % emptyE
% 0.31/0.46 thf(fact_49_emptyE,axiom,
% 0.31/0.46 ! [A: produc1115495963_state] :
% 0.31/0.46 ~ ( member1389040324_state @ A @ bot_bo1625160935_state ) ).
% 0.31/0.46
% 0.31/0.46 % emptyE
% 0.31/0.46 thf(fact_50_mk__disjoint__insert,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( member1389040324_state @ A @ A2 )
% 0.31/0.46 => ? [B3: set_Pr795498619_state] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert311944171_state @ A @ B3 ) )
% 0.31/0.46 & ~ ( member1389040324_state @ A @ B3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % mk_disjoint_insert
% 0.31/0.46 thf(fact_51_mk__disjoint__insert,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ A @ A2 )
% 0.31/0.46 => ? [B3: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert271595217at_nat @ A @ B3 ) )
% 0.31/0.46 & ~ ( member701585322at_nat @ A @ B3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % mk_disjoint_insert
% 0.31/0.46 thf(fact_52_mk__disjoint__insert,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ A @ A2 )
% 0.31/0.46 => ? [B3: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert2053719859tate_o @ A @ B3 ) )
% 0.31/0.46 & ~ ( member1838112666tate_o @ A @ B3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % mk_disjoint_insert
% 0.31/0.46 thf(fact_53_insert__commute,axiom,
% 0.31/0.46 ! [X2: produc696469763tate_o,Y3: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( insert2053719859tate_o @ X2 @ ( insert2053719859tate_o @ Y3 @ A2 ) )
% 0.31/0.46 = ( insert2053719859tate_o @ Y3 @ ( insert2053719859tate_o @ X2 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_commute
% 0.31/0.46 thf(fact_54_insert__commute,axiom,
% 0.31/0.46 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( insert271595217at_nat @ X2 @ ( insert271595217at_nat @ Y3 @ A2 ) )
% 0.31/0.46 = ( insert271595217at_nat @ Y3 @ ( insert271595217at_nat @ X2 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_commute
% 0.31/0.46 thf(fact_55_insert__commute,axiom,
% 0.31/0.46 ! [X2: produc1115495963_state,Y3: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( insert311944171_state @ X2 @ ( insert311944171_state @ Y3 @ A2 ) )
% 0.31/0.46 = ( insert311944171_state @ Y3 @ ( insert311944171_state @ X2 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_commute
% 0.31/0.46 thf(fact_56_insert__eq__iff,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,A2: set_Pr795498619_state,B2: produc1115495963_state,B: set_Pr795498619_state] :
% 0.31/0.46 ( ~ ( member1389040324_state @ A @ A2 )
% 0.31/0.46 => ( ~ ( member1389040324_state @ B2 @ B )
% 0.31/0.46 => ( ( ( insert311944171_state @ A @ A2 )
% 0.31/0.46 = ( insert311944171_state @ B2 @ B ) )
% 0.31/0.46 = ( ( ( A = B2 )
% 0.31/0.46 => ( A2 = B ) )
% 0.31/0.46 & ( ( A != B2 )
% 0.31/0.46 => ? [C3: set_Pr795498619_state] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert311944171_state @ B2 @ C3 ) )
% 0.31/0.46 & ~ ( member1389040324_state @ B2 @ C3 )
% 0.31/0.46 & ( B
% 0.31/0.46 = ( insert311944171_state @ A @ C3 ) )
% 0.31/0.46 & ~ ( member1389040324_state @ A @ C3 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_eq_iff
% 0.31/0.46 thf(fact_57_insert__eq__iff,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat,B2: product_prod_nat_nat,B: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ~ ( member701585322at_nat @ A @ A2 )
% 0.31/0.46 => ( ~ ( member701585322at_nat @ B2 @ B )
% 0.31/0.46 => ( ( ( insert271595217at_nat @ A @ A2 )
% 0.31/0.46 = ( insert271595217at_nat @ B2 @ B ) )
% 0.31/0.46 = ( ( ( A = B2 )
% 0.31/0.46 => ( A2 = B ) )
% 0.31/0.46 & ( ( A != B2 )
% 0.31/0.46 => ? [C3: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert271595217at_nat @ B2 @ C3 ) )
% 0.31/0.46 & ~ ( member701585322at_nat @ B2 @ C3 )
% 0.31/0.46 & ( B
% 0.31/0.46 = ( insert271595217at_nat @ A @ C3 ) )
% 0.31/0.46 & ~ ( member701585322at_nat @ A @ C3 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_eq_iff
% 0.31/0.46 thf(fact_58_insert__eq__iff,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o,B2: produc696469763tate_o,B: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ~ ( member1838112666tate_o @ A @ A2 )
% 0.31/0.46 => ( ~ ( member1838112666tate_o @ B2 @ B )
% 0.31/0.46 => ( ( ( insert2053719859tate_o @ A @ A2 )
% 0.31/0.46 = ( insert2053719859tate_o @ B2 @ B ) )
% 0.31/0.46 = ( ( ( A = B2 )
% 0.31/0.46 => ( A2 = B ) )
% 0.31/0.46 & ( ( A != B2 )
% 0.31/0.46 => ? [C3: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert2053719859tate_o @ B2 @ C3 ) )
% 0.31/0.46 & ~ ( member1838112666tate_o @ B2 @ C3 )
% 0.31/0.46 & ( B
% 0.31/0.46 = ( insert2053719859tate_o @ A @ C3 ) )
% 0.31/0.46 & ~ ( member1838112666tate_o @ A @ C3 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_eq_iff
% 0.31/0.46 thf(fact_59_insert__absorb,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( member1389040324_state @ A @ A2 )
% 0.31/0.46 => ( ( insert311944171_state @ A @ A2 )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_absorb
% 0.31/0.46 thf(fact_60_insert__absorb,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ A @ A2 )
% 0.31/0.46 => ( ( insert271595217at_nat @ A @ A2 )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_absorb
% 0.31/0.46 thf(fact_61_insert__absorb,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ A @ A2 )
% 0.31/0.46 => ( ( insert2053719859tate_o @ A @ A2 )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_absorb
% 0.31/0.46 thf(fact_62_insert__ident,axiom,
% 0.31/0.46 ! [X2: produc1115495963_state,A2: set_Pr795498619_state,B: set_Pr795498619_state] :
% 0.31/0.46 ( ~ ( member1389040324_state @ X2 @ A2 )
% 0.31/0.46 => ( ~ ( member1389040324_state @ X2 @ B )
% 0.31/0.46 => ( ( ( insert311944171_state @ X2 @ A2 )
% 0.31/0.46 = ( insert311944171_state @ X2 @ B ) )
% 0.31/0.46 = ( A2 = B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_ident
% 0.31/0.46 thf(fact_63_insert__ident,axiom,
% 0.31/0.46 ! [X2: product_prod_nat_nat,A2: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ~ ( member701585322at_nat @ X2 @ A2 )
% 0.31/0.46 => ( ~ ( member701585322at_nat @ X2 @ B )
% 0.31/0.46 => ( ( ( insert271595217at_nat @ X2 @ A2 )
% 0.31/0.46 = ( insert271595217at_nat @ X2 @ B ) )
% 0.31/0.46 = ( A2 = B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_ident
% 0.31/0.46 thf(fact_64_insert__ident,axiom,
% 0.31/0.46 ! [X2: produc696469763tate_o,A2: set_Pr1590995257tate_o,B: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ~ ( member1838112666tate_o @ X2 @ A2 )
% 0.31/0.46 => ( ~ ( member1838112666tate_o @ X2 @ B )
% 0.31/0.46 => ( ( ( insert2053719859tate_o @ X2 @ A2 )
% 0.31/0.46 = ( insert2053719859tate_o @ X2 @ B ) )
% 0.31/0.46 = ( A2 = B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_ident
% 0.31/0.46 thf(fact_65_Set_Oset__insert,axiom,
% 0.31/0.46 ! [X2: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( member1389040324_state @ X2 @ A2 )
% 0.31/0.46 => ~ ! [B3: set_Pr795498619_state] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert311944171_state @ X2 @ B3 ) )
% 0.31/0.46 => ( member1389040324_state @ X2 @ B3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Set.set_insert
% 0.31/0.46 thf(fact_66_Set_Oset__insert,axiom,
% 0.31/0.46 ! [X2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ X2 @ A2 )
% 0.31/0.46 => ~ ! [B3: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert271595217at_nat @ X2 @ B3 ) )
% 0.31/0.46 => ( member701585322at_nat @ X2 @ B3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Set.set_insert
% 0.31/0.46 thf(fact_67_Set_Oset__insert,axiom,
% 0.31/0.46 ! [X2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ X2 @ A2 )
% 0.31/0.46 => ~ ! [B3: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert2053719859tate_o @ X2 @ B3 ) )
% 0.31/0.46 => ( member1838112666tate_o @ X2 @ B3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Set.set_insert
% 0.31/0.46 thf(fact_68_insertI2,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,B: set_Pr795498619_state,B2: produc1115495963_state] :
% 0.31/0.46 ( ( member1389040324_state @ A @ B )
% 0.31/0.46 => ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertI2
% 0.31/0.46 thf(fact_69_insertI2,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,B2: product_prod_nat_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ A @ B )
% 0.31/0.46 => ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertI2
% 0.31/0.46 thf(fact_70_insertI2,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,B: set_Pr1590995257tate_o,B2: produc696469763tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ A @ B )
% 0.31/0.46 => ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ B ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertI2
% 0.31/0.46 thf(fact_71_insertI1,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,B: set_Pr795498619_state] : ( member1389040324_state @ A @ ( insert311944171_state @ A @ B ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertI1
% 0.31/0.46 thf(fact_72_insertI1,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ B ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertI1
% 0.31/0.46 thf(fact_73_insertI1,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,B: set_Pr1590995257tate_o] : ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ A @ B ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertI1
% 0.31/0.46 thf(fact_74_insertE,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,B2: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ A2 ) )
% 0.31/0.46 => ( ( A != B2 )
% 0.31/0.46 => ( member1389040324_state @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertE
% 0.31/0.46 thf(fact_75_insertE,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ A2 ) )
% 0.31/0.46 => ( ( A != B2 )
% 0.31/0.46 => ( member701585322at_nat @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertE
% 0.31/0.46 thf(fact_76_insertE,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,B2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ A2 ) )
% 0.31/0.46 => ( ( A != B2 )
% 0.31/0.46 => ( member1838112666tate_o @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertE
% 0.31/0.46 thf(fact_77_empty__def,axiom,
% 0.31/0.46 ( bot_bo170732493tate_o
% 0.31/0.46 = ( collec1499596504tate_o
% 0.31/0.46 @ ^ [X: produc696469763tate_o] : $false ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_def
% 0.31/0.46 thf(fact_78_empty__def,axiom,
% 0.31/0.46 ( bot_bo2130386637at_nat
% 0.31/0.46 = ( collec7649004at_nat
% 0.31/0.46 @ ^ [X: product_prod_nat_nat] : $false ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_def
% 0.31/0.46 thf(fact_79_empty__def,axiom,
% 0.31/0.46 ( bot_bo1625160935_state
% 0.31/0.46 = ( collec496201222_state
% 0.31/0.46 @ ^ [X: produc1115495963_state] : $false ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_def
% 0.31/0.46 thf(fact_80_insert__Collect,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,P: produc1115495963_state > $o] :
% 0.31/0.46 ( ( insert311944171_state @ A @ ( collec496201222_state @ P ) )
% 0.31/0.46 = ( collec496201222_state
% 0.31/0.46 @ ^ [U: produc1115495963_state] :
% 0.31/0.46 ( ( U != A )
% 0.31/0.46 => ( P @ U ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_Collect
% 0.31/0.46 thf(fact_81_insert__Collect,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.31/0.46 ( ( insert271595217at_nat @ A @ ( collec7649004at_nat @ P ) )
% 0.31/0.46 = ( collec7649004at_nat
% 0.31/0.46 @ ^ [U: product_prod_nat_nat] :
% 0.31/0.46 ( ( U != A )
% 0.31/0.46 => ( P @ U ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_Collect
% 0.31/0.46 thf(fact_82_insert__Collect,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,P: produc696469763tate_o > $o] :
% 0.31/0.46 ( ( insert2053719859tate_o @ A @ ( collec1499596504tate_o @ P ) )
% 0.31/0.46 = ( collec1499596504tate_o
% 0.31/0.46 @ ^ [U: produc696469763tate_o] :
% 0.31/0.46 ( ( U != A )
% 0.31/0.46 => ( P @ U ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_Collect
% 0.31/0.46 thf(fact_83_insert__compr,axiom,
% 0.31/0.46 ( insert311944171_state
% 0.31/0.46 = ( ^ [A3: produc1115495963_state,B4: set_Pr795498619_state] :
% 0.31/0.46 ( collec496201222_state
% 0.31/0.46 @ ^ [X: produc1115495963_state] :
% 0.31/0.46 ( ( X = A3 )
% 0.31/0.46 | ( member1389040324_state @ X @ B4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_compr
% 0.31/0.46 thf(fact_84_insert__compr,axiom,
% 0.31/0.46 ( insert271595217at_nat
% 0.31/0.46 = ( ^ [A3: product_prod_nat_nat,B4: set_Pr1986765409at_nat] :
% 0.31/0.46 ( collec7649004at_nat
% 0.31/0.46 @ ^ [X: product_prod_nat_nat] :
% 0.31/0.46 ( ( X = A3 )
% 0.31/0.46 | ( member701585322at_nat @ X @ B4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_compr
% 0.31/0.46 thf(fact_85_insert__compr,axiom,
% 0.31/0.46 ( insert2053719859tate_o
% 0.31/0.46 = ( ^ [A3: produc696469763tate_o,B4: set_Pr1590995257tate_o] :
% 0.31/0.46 ( collec1499596504tate_o
% 0.31/0.46 @ ^ [X: produc696469763tate_o] :
% 0.31/0.46 ( ( X = A3 )
% 0.31/0.46 | ( member1838112666tate_o @ X @ B4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_compr
% 0.31/0.46 thf(fact_86_singleton__inject,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,B2: produc696469763tate_o] :
% 0.31/0.46 ( ( ( insert2053719859tate_o @ A @ bot_bo170732493tate_o )
% 0.31/0.46 = ( insert2053719859tate_o @ B2 @ bot_bo170732493tate_o ) )
% 0.31/0.46 => ( A = B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_inject
% 0.31/0.46 thf(fact_87_singleton__inject,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 0.31/0.46 ( ( ( insert271595217at_nat @ A @ bot_bo2130386637at_nat )
% 0.31/0.46 = ( insert271595217at_nat @ B2 @ bot_bo2130386637at_nat ) )
% 0.31/0.46 => ( A = B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_inject
% 0.31/0.46 thf(fact_88_singleton__inject,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,B2: produc1115495963_state] :
% 0.31/0.46 ( ( ( insert311944171_state @ A @ bot_bo1625160935_state )
% 0.31/0.46 = ( insert311944171_state @ B2 @ bot_bo1625160935_state ) )
% 0.31/0.46 => ( A = B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_inject
% 0.31/0.46 thf(fact_89_insert__not__empty,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( insert2053719859tate_o @ A @ A2 )
% 0.31/0.46 != bot_bo170732493tate_o ) ).
% 0.31/0.46
% 0.31/0.46 % insert_not_empty
% 0.31/0.46 thf(fact_90_insert__not__empty,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( insert271595217at_nat @ A @ A2 )
% 0.31/0.46 != bot_bo2130386637at_nat ) ).
% 0.31/0.46
% 0.31/0.46 % insert_not_empty
% 0.31/0.46 thf(fact_91_insert__not__empty,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( insert311944171_state @ A @ A2 )
% 0.31/0.46 != bot_bo1625160935_state ) ).
% 0.31/0.46
% 0.31/0.46 % insert_not_empty
% 0.31/0.46 thf(fact_92_doubleton__eq__iff,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,B2: produc696469763tate_o,C2: produc696469763tate_o,D: produc696469763tate_o] :
% 0.31/0.46 ( ( ( insert2053719859tate_o @ A @ ( insert2053719859tate_o @ B2 @ bot_bo170732493tate_o ) )
% 0.31/0.46 = ( insert2053719859tate_o @ C2 @ ( insert2053719859tate_o @ D @ bot_bo170732493tate_o ) ) )
% 0.31/0.46 = ( ( ( A = C2 )
% 0.31/0.46 & ( B2 = D ) )
% 0.31/0.46 | ( ( A = D )
% 0.31/0.46 & ( B2 = C2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % doubleton_eq_iff
% 0.31/0.46 thf(fact_93_doubleton__eq__iff,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,C2: product_prod_nat_nat,D: product_prod_nat_nat] :
% 0.31/0.46 ( ( ( insert271595217at_nat @ A @ ( insert271595217at_nat @ B2 @ bot_bo2130386637at_nat ) )
% 0.31/0.46 = ( insert271595217at_nat @ C2 @ ( insert271595217at_nat @ D @ bot_bo2130386637at_nat ) ) )
% 0.31/0.46 = ( ( ( A = C2 )
% 0.31/0.46 & ( B2 = D ) )
% 0.31/0.46 | ( ( A = D )
% 0.31/0.46 & ( B2 = C2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % doubleton_eq_iff
% 0.31/0.46 thf(fact_94_doubleton__eq__iff,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,B2: produc1115495963_state,C2: produc1115495963_state,D: produc1115495963_state] :
% 0.31/0.46 ( ( ( insert311944171_state @ A @ ( insert311944171_state @ B2 @ bot_bo1625160935_state ) )
% 0.31/0.46 = ( insert311944171_state @ C2 @ ( insert311944171_state @ D @ bot_bo1625160935_state ) ) )
% 0.31/0.46 = ( ( ( A = C2 )
% 0.31/0.46 & ( B2 = D ) )
% 0.31/0.46 | ( ( A = D )
% 0.31/0.46 & ( B2 = C2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % doubleton_eq_iff
% 0.31/0.46 thf(fact_95_singleton__iff,axiom,
% 0.31/0.46 ! [B2: produc696469763tate_o,A: produc696469763tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ B2 @ ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) )
% 0.31/0.46 = ( B2 = A ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_iff
% 0.31/0.46 thf(fact_96_singleton__iff,axiom,
% 0.31/0.46 ! [B2: product_prod_nat_nat,A: product_prod_nat_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ B2 @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) )
% 0.31/0.46 = ( B2 = A ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_iff
% 0.31/0.46 thf(fact_97_singleton__iff,axiom,
% 0.31/0.46 ! [B2: produc1115495963_state,A: produc1115495963_state] :
% 0.31/0.46 ( ( member1389040324_state @ B2 @ ( insert311944171_state @ A @ bot_bo1625160935_state ) )
% 0.31/0.46 = ( B2 = A ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_iff
% 0.31/0.46 thf(fact_98_singletonD,axiom,
% 0.31/0.46 ! [B2: produc696469763tate_o,A: produc696469763tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ B2 @ ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) )
% 0.31/0.46 => ( B2 = A ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonD
% 0.31/0.46 thf(fact_99_singletonD,axiom,
% 0.31/0.46 ! [B2: product_prod_nat_nat,A: product_prod_nat_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ B2 @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) )
% 0.31/0.46 => ( B2 = A ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonD
% 0.31/0.46 thf(fact_100_singletonD,axiom,
% 0.31/0.46 ! [B2: produc1115495963_state,A: produc1115495963_state] :
% 0.31/0.46 ( ( member1389040324_state @ B2 @ ( insert311944171_state @ A @ bot_bo1625160935_state ) )
% 0.31/0.46 => ( B2 = A ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonD
% 0.31/0.46 thf(fact_101_hoare_OAsm,axiom,
% 0.31/0.46 ! [P: a > state > $o,Q: a > state > $o] : ( hoare_a @ ( insert2053719859tate_o @ ( produc33908149tate_o @ P @ ( produc1948644831tate_o @ call @ Q ) ) @ bot_bo170732493tate_o ) @ P @ call @ Q ) ).
% 0.31/0.46
% 0.31/0.46 % hoare.Asm
% 0.31/0.46 thf(fact_102_Collect__conv__if2,axiom,
% 0.31/0.46 ! [P: produc696469763tate_o > $o,A: produc696469763tate_o] :
% 0.31/0.46 ( ( ( P @ A )
% 0.31/0.46 => ( ( collec1499596504tate_o
% 0.31/0.46 @ ^ [X: produc696469763tate_o] :
% 0.31/0.46 ( ( A = X )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) )
% 0.31/0.46 & ( ~ ( P @ A )
% 0.31/0.46 => ( ( collec1499596504tate_o
% 0.31/0.46 @ ^ [X: produc696469763tate_o] :
% 0.31/0.46 ( ( A = X )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = bot_bo170732493tate_o ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_conv_if2
% 0.31/0.46 thf(fact_103_Collect__conv__if2,axiom,
% 0.31/0.46 ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 0.31/0.46 ( ( ( P @ A )
% 0.31/0.46 => ( ( collec7649004at_nat
% 0.31/0.46 @ ^ [X: product_prod_nat_nat] :
% 0.31/0.46 ( ( A = X )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 0.31/0.46 & ( ~ ( P @ A )
% 0.31/0.46 => ( ( collec7649004at_nat
% 0.31/0.46 @ ^ [X: product_prod_nat_nat] :
% 0.31/0.46 ( ( A = X )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = bot_bo2130386637at_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_conv_if2
% 0.31/0.46 thf(fact_104_Collect__conv__if2,axiom,
% 0.31/0.46 ! [P: produc1115495963_state > $o,A: produc1115495963_state] :
% 0.31/0.46 ( ( ( P @ A )
% 0.31/0.46 => ( ( collec496201222_state
% 0.31/0.46 @ ^ [X: produc1115495963_state] :
% 0.31/0.46 ( ( A = X )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) )
% 0.31/0.46 & ( ~ ( P @ A )
% 0.31/0.46 => ( ( collec496201222_state
% 0.31/0.46 @ ^ [X: produc1115495963_state] :
% 0.31/0.46 ( ( A = X )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = bot_bo1625160935_state ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_conv_if2
% 0.31/0.46 thf(fact_105_Collect__conv__if,axiom,
% 0.31/0.46 ! [P: produc696469763tate_o > $o,A: produc696469763tate_o] :
% 0.31/0.46 ( ( ( P @ A )
% 0.31/0.46 => ( ( collec1499596504tate_o
% 0.31/0.46 @ ^ [X: produc696469763tate_o] :
% 0.31/0.46 ( ( X = A )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) )
% 0.31/0.46 & ( ~ ( P @ A )
% 0.31/0.46 => ( ( collec1499596504tate_o
% 0.31/0.46 @ ^ [X: produc696469763tate_o] :
% 0.31/0.46 ( ( X = A )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = bot_bo170732493tate_o ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_conv_if
% 0.31/0.46 thf(fact_106_Collect__conv__if,axiom,
% 0.31/0.46 ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 0.31/0.46 ( ( ( P @ A )
% 0.31/0.46 => ( ( collec7649004at_nat
% 0.31/0.46 @ ^ [X: product_prod_nat_nat] :
% 0.31/0.46 ( ( X = A )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 0.31/0.46 & ( ~ ( P @ A )
% 0.31/0.46 => ( ( collec7649004at_nat
% 0.31/0.46 @ ^ [X: product_prod_nat_nat] :
% 0.31/0.46 ( ( X = A )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = bot_bo2130386637at_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_conv_if
% 0.31/0.46 thf(fact_107_Collect__conv__if,axiom,
% 0.31/0.46 ! [P: produc1115495963_state > $o,A: produc1115495963_state] :
% 0.31/0.46 ( ( ( P @ A )
% 0.31/0.46 => ( ( collec496201222_state
% 0.31/0.46 @ ^ [X: produc1115495963_state] :
% 0.31/0.46 ( ( X = A )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) )
% 0.31/0.46 & ( ~ ( P @ A )
% 0.31/0.46 => ( ( collec496201222_state
% 0.31/0.46 @ ^ [X: produc1115495963_state] :
% 0.31/0.46 ( ( X = A )
% 0.31/0.46 & ( P @ X ) ) )
% 0.31/0.46 = bot_bo1625160935_state ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_conv_if
% 0.31/0.46 thf(fact_108_wf__empty,axiom,
% 0.31/0.46 wf_nat @ bot_bo2130386637at_nat ).
% 0.31/0.46
% 0.31/0.46 % wf_empty
% 0.31/0.46 thf(fact_109_wf__empty,axiom,
% 0.31/0.46 wf_state @ bot_bo1625160935_state ).
% 0.31/0.46
% 0.31/0.46 % wf_empty
% 0.31/0.46 thf(fact_110_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: produc1115495963_state,P: produc1115495963_state > $o] :
% 0.31/0.46 ( ( member1389040324_state @ A @ ( collec496201222_state @ P ) )
% 0.31/0.46 = ( P @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_111_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.31/0.46 ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P ) )
% 0.31/0.46 = ( P @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_112_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: produc696469763tate_o,P: produc696469763tate_o > $o] :
% 0.31/0.46 ( ( member1838112666tate_o @ A @ ( collec1499596504tate_o @ P ) )
% 0.31/0.46 = ( P @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_113_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( collec496201222_state
% 0.31/0.46 @ ^ [X: produc1115495963_state] : ( member1389040324_state @ X @ A2 ) )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_114_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( collec7649004at_nat
% 0.31/0.46 @ ^ [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ A2 ) )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_115_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( collec1499596504tate_o
% 0.31/0.46 @ ^ [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ A2 ) )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_116_Collect__cong,axiom,
% 0.31/0.46 ! [P: produc1115495963_state > $o,Q: produc1115495963_state > $o] :
% 0.31/0.46 ( ! [X3: produc1115495963_state] :
% 0.31/0.46 ( ( P @ X3 )
% 0.31/0.46 = ( Q @ X3 ) )
% 0.31/0.46 => ( ( collec496201222_state @ P )
% 0.31/0.46 = ( collec496201222_state @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_cong
% 0.31/0.46 thf(fact_117_Collect__cong,axiom,
% 0.31/0.46 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 0.31/0.46 ( ! [X3: product_prod_nat_nat] :
% 0.31/0.46 ( ( P @ X3 )
% 0.31/0.46 = ( Q @ X3 ) )
% 0.31/0.46 => ( ( collec7649004at_nat @ P )
% 0.31/0.46 = ( collec7649004at_nat @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_cong
% 0.31/0.46 thf(fact_118_Collect__cong,axiom,
% 0.31/0.46 ! [P: produc696469763tate_o > $o,Q: produc696469763tate_o > $o] :
% 0.31/0.46 ( ! [X3: produc696469763tate_o] :
% 0.31/0.46 ( ( P @ X3 )
% 0.31/0.46 = ( Q @ X3 ) )
% 0.31/0.46 => ( ( collec1499596504tate_o @ P )
% 0.31/0.46 = ( collec1499596504tate_o @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_cong
% 0.31/0.46 thf(fact_119_wfE__min_H,axiom,
% 0.31/0.46 ! [R2: set_Pr795498619_state,Q: set_state] :
% 0.31/0.46 ( ( wf_state @ R2 )
% 0.31/0.46 => ( ( Q != bot_bot_set_state )
% 0.31/0.46 => ~ ! [Z: state] :
% 0.31/0.46 ( ( member_state @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: state] :
% 0.31/0.46 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member_state @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min'
% 0.31/0.46 thf(fact_120_wfE__min_H,axiom,
% 0.31/0.46 ! [R2: set_Pr1986765409at_nat,Q: set_nat] :
% 0.31/0.46 ( ( wf_nat @ R2 )
% 0.31/0.46 => ( ( Q != bot_bot_set_nat )
% 0.31/0.46 => ~ ! [Z: nat] :
% 0.31/0.46 ( ( member_nat @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: nat] :
% 0.31/0.46 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member_nat @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min'
% 0.31/0.46 thf(fact_121_wfE__min_H,axiom,
% 0.31/0.46 ! [R2: set_Pr1702239303tate_o,Q: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( wf_Pro309705690tate_o @ R2 )
% 0.31/0.46 => ( ( Q != bot_bo170732493tate_o )
% 0.31/0.46 => ~ ! [Z: produc696469763tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: produc696469763tate_o] :
% 0.31/0.46 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member1838112666tate_o @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min'
% 0.31/0.46 thf(fact_122_wfE__min_H,axiom,
% 0.31/0.46 ! [R2: set_Pr1490359111at_nat,Q: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( wf_Pro745352042at_nat @ R2 )
% 0.31/0.46 => ( ( Q != bot_bo2130386637at_nat )
% 0.31/0.46 => ~ ! [Z: product_prod_nat_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: product_prod_nat_nat] :
% 0.31/0.46 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member701585322at_nat @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min'
% 0.31/0.46 thf(fact_123_wfE__min_H,axiom,
% 0.31/0.46 ! [R2: set_Pr778812871_state,Q: set_Pr795498619_state] :
% 0.31/0.46 ( ( wf_Pro1783588484_state @ R2 )
% 0.31/0.46 => ( ( Q != bot_bo1625160935_state )
% 0.31/0.46 => ~ ! [Z: produc1115495963_state] :
% 0.31/0.46 ( ( member1389040324_state @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: produc1115495963_state] :
% 0.31/0.46 ( ( member768948240_state @ ( produc1964772951_state @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member1389040324_state @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min'
% 0.31/0.46 thf(fact_124_the__elem__eq,axiom,
% 0.31/0.46 ! [X2: produc696469763tate_o] :
% 0.31/0.46 ( ( the_el1569055182tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) )
% 0.31/0.46 = X2 ) ).
% 0.31/0.46
% 0.31/0.46 % the_elem_eq
% 0.31/0.46 thf(fact_125_the__elem__eq,axiom,
% 0.31/0.46 ! [X2: product_prod_nat_nat] :
% 0.31/0.46 ( ( the_el1949240438at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) )
% 0.31/0.46 = X2 ) ).
% 0.31/0.46
% 0.31/0.46 % the_elem_eq
% 0.31/0.46 thf(fact_126_the__elem__eq,axiom,
% 0.31/0.46 ! [X2: produc1115495963_state] :
% 0.31/0.46 ( ( the_el1967402896_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) )
% 0.31/0.46 = X2 ) ).
% 0.31/0.46
% 0.31/0.46 % the_elem_eq
% 0.31/0.46 thf(fact_127_old_Oprod_Oinject,axiom,
% 0.31/0.46 ! [A: a > state > $o,B2: produc204914599tate_o,A4: a > state > $o,B5: produc204914599tate_o] :
% 0.31/0.46 ( ( ( produc33908149tate_o @ A @ B2 )
% 0.31/0.46 = ( produc33908149tate_o @ A4 @ B5 ) )
% 0.31/0.46 = ( ( A = A4 )
% 0.31/0.46 & ( B2 = B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inject
% 0.31/0.46 thf(fact_128_old_Oprod_Oinject,axiom,
% 0.31/0.46 ! [A: state,B2: state,A4: state,B5: state] :
% 0.31/0.46 ( ( ( produc64584659_state @ A @ B2 )
% 0.31/0.46 = ( produc64584659_state @ A4 @ B5 ) )
% 0.31/0.46 = ( ( A = A4 )
% 0.31/0.46 & ( B2 = B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inject
% 0.31/0.46 thf(fact_129_old_Oprod_Oinject,axiom,
% 0.31/0.46 ! [A: com,B2: a > state > $o,A4: com,B5: a > state > $o] :
% 0.31/0.46 ( ( ( produc1948644831tate_o @ A @ B2 )
% 0.31/0.46 = ( produc1948644831tate_o @ A4 @ B5 ) )
% 0.31/0.46 = ( ( A = A4 )
% 0.31/0.46 & ( B2 = B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inject
% 0.31/0.46 thf(fact_130_old_Oprod_Oinject,axiom,
% 0.31/0.46 ! [A: nat,B2: nat,A4: nat,B5: nat] :
% 0.31/0.46 ( ( ( product_Pair_nat_nat @ A @ B2 )
% 0.31/0.46 = ( product_Pair_nat_nat @ A4 @ B5 ) )
% 0.31/0.46 = ( ( A = A4 )
% 0.31/0.46 & ( B2 = B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inject
% 0.31/0.46 thf(fact_131_prod_Oinject,axiom,
% 0.31/0.46 ! [X1: a > state > $o,X22: produc204914599tate_o,Y1: a > state > $o,Y22: produc204914599tate_o] :
% 0.31/0.46 ( ( ( produc33908149tate_o @ X1 @ X22 )
% 0.31/0.46 = ( produc33908149tate_o @ Y1 @ Y22 ) )
% 0.31/0.46 = ( ( X1 = Y1 )
% 0.31/0.46 & ( X22 = Y22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod.inject
% 0.31/0.46 thf(fact_132_prod_Oinject,axiom,
% 0.31/0.46 ! [X1: state,X22: state,Y1: state,Y22: state] :
% 0.31/0.46 ( ( ( produc64584659_state @ X1 @ X22 )
% 0.31/0.46 = ( produc64584659_state @ Y1 @ Y22 ) )
% 0.31/0.46 = ( ( X1 = Y1 )
% 0.31/0.46 & ( X22 = Y22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod.inject
% 0.31/0.46 thf(fact_133_prod_Oinject,axiom,
% 0.31/0.46 ! [X1: com,X22: a > state > $o,Y1: com,Y22: a > state > $o] :
% 0.31/0.46 ( ( ( produc1948644831tate_o @ X1 @ X22 )
% 0.31/0.46 = ( produc1948644831tate_o @ Y1 @ Y22 ) )
% 0.31/0.46 = ( ( X1 = Y1 )
% 0.31/0.46 & ( X22 = Y22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod.inject
% 0.31/0.46 thf(fact_134_prod_Oinject,axiom,
% 0.31/0.46 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 0.31/0.46 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 0.31/0.46 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 0.31/0.46 = ( ( X1 = Y1 )
% 0.31/0.46 & ( X22 = Y22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod.inject
% 0.31/0.46 thf(fact_135_is__singletonI,axiom,
% 0.31/0.46 ! [X2: produc696469763tate_o] : ( is_sin1547905295tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonI
% 0.31/0.46 thf(fact_136_is__singletonI,axiom,
% 0.31/0.46 ! [X2: product_prod_nat_nat] : ( is_sin1352690165at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonI
% 0.31/0.46 thf(fact_137_is__singletonI,axiom,
% 0.31/0.46 ! [X2: produc1115495963_state] : ( is_sin1132515087_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonI
% 0.31/0.46 thf(fact_138_bot__set__def,axiom,
% 0.31/0.46 ( bot_bo170732493tate_o
% 0.31/0.46 = ( collec1499596504tate_o @ bot_bo250281208te_o_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_set_def
% 0.31/0.46 thf(fact_139_bot__set__def,axiom,
% 0.31/0.46 ( bot_bo2130386637at_nat
% 0.31/0.46 = ( collec7649004at_nat @ bot_bo513358416_nat_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_set_def
% 0.31/0.46 thf(fact_140_bot__set__def,axiom,
% 0.31/0.46 ( bot_bo1625160935_state
% 0.31/0.46 = ( collec496201222_state @ bot_bo446391478tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_set_def
% 0.31/0.46 thf(fact_141_is__singleton__the__elem,axiom,
% 0.31/0.46 ( is_sin1547905295tate_o
% 0.31/0.46 = ( ^ [A5: set_Pr1590995257tate_o] :
% 0.31/0.46 ( A5
% 0.31/0.46 = ( insert2053719859tate_o @ ( the_el1569055182tate_o @ A5 ) @ bot_bo170732493tate_o ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singleton_the_elem
% 0.31/0.46 thf(fact_142_is__singleton__the__elem,axiom,
% 0.31/0.46 ( is_sin1352690165at_nat
% 0.31/0.46 = ( ^ [A5: set_Pr1986765409at_nat] :
% 0.31/0.46 ( A5
% 0.31/0.46 = ( insert271595217at_nat @ ( the_el1949240438at_nat @ A5 ) @ bot_bo2130386637at_nat ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singleton_the_elem
% 0.31/0.46 thf(fact_143_is__singleton__the__elem,axiom,
% 0.31/0.46 ( is_sin1132515087_state
% 0.31/0.46 = ( ^ [A5: set_Pr795498619_state] :
% 0.31/0.46 ( A5
% 0.31/0.46 = ( insert311944171_state @ ( the_el1967402896_state @ A5 ) @ bot_bo1625160935_state ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singleton_the_elem
% 0.31/0.46 thf(fact_144_is__singletonI_H,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( A2 != bot_bo170732493tate_o )
% 0.31/0.46 => ( ! [X3: produc696469763tate_o,Y2: produc696469763tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ X3 @ A2 )
% 0.31/0.46 => ( ( member1838112666tate_o @ Y2 @ A2 )
% 0.31/0.46 => ( X3 = Y2 ) ) )
% 0.31/0.46 => ( is_sin1547905295tate_o @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonI'
% 0.31/0.46 thf(fact_145_is__singletonI_H,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( A2 != bot_bo2130386637at_nat )
% 0.31/0.46 => ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ X3 @ A2 )
% 0.31/0.46 => ( ( member701585322at_nat @ Y2 @ A2 )
% 0.31/0.46 => ( X3 = Y2 ) ) )
% 0.31/0.46 => ( is_sin1352690165at_nat @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonI'
% 0.31/0.46 thf(fact_146_is__singletonI_H,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( A2 != bot_bo1625160935_state )
% 0.31/0.46 => ( ! [X3: produc1115495963_state,Y2: produc1115495963_state] :
% 0.31/0.46 ( ( member1389040324_state @ X3 @ A2 )
% 0.31/0.46 => ( ( member1389040324_state @ Y2 @ A2 )
% 0.31/0.46 => ( X3 = Y2 ) ) )
% 0.31/0.46 => ( is_sin1132515087_state @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonI'
% 0.31/0.46 thf(fact_147_surj__pair,axiom,
% 0.31/0.46 ! [P3: produc696469763tate_o] :
% 0.31/0.46 ? [X3: a > state > $o,Y2: produc204914599tate_o] :
% 0.31/0.46 ( P3
% 0.31/0.46 = ( produc33908149tate_o @ X3 @ Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % surj_pair
% 0.31/0.46 thf(fact_148_surj__pair,axiom,
% 0.31/0.46 ! [P3: produc1115495963_state] :
% 0.31/0.46 ? [X3: state,Y2: state] :
% 0.31/0.46 ( P3
% 0.31/0.46 = ( produc64584659_state @ X3 @ Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % surj_pair
% 0.31/0.46 thf(fact_149_surj__pair,axiom,
% 0.31/0.46 ! [P3: produc204914599tate_o] :
% 0.31/0.46 ? [X3: com,Y2: a > state > $o] :
% 0.31/0.46 ( P3
% 0.31/0.46 = ( produc1948644831tate_o @ X3 @ Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % surj_pair
% 0.31/0.46 thf(fact_150_surj__pair,axiom,
% 0.31/0.46 ! [P3: product_prod_nat_nat] :
% 0.31/0.46 ? [X3: nat,Y2: nat] :
% 0.31/0.46 ( P3
% 0.31/0.46 = ( product_Pair_nat_nat @ X3 @ Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % surj_pair
% 0.31/0.46 thf(fact_151_prod__cases,axiom,
% 0.31/0.46 ! [P: produc696469763tate_o > $o,P3: produc696469763tate_o] :
% 0.31/0.46 ( ! [A6: a > state > $o,B6: produc204914599tate_o] : ( P @ ( produc33908149tate_o @ A6 @ B6 ) )
% 0.31/0.46 => ( P @ P3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases
% 0.31/0.46 thf(fact_152_prod__cases,axiom,
% 0.31/0.46 ! [P: produc1115495963_state > $o,P3: produc1115495963_state] :
% 0.31/0.46 ( ! [A6: state,B6: state] : ( P @ ( produc64584659_state @ A6 @ B6 ) )
% 0.31/0.46 => ( P @ P3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases
% 0.31/0.46 thf(fact_153_prod__cases,axiom,
% 0.31/0.46 ! [P: produc204914599tate_o > $o,P3: produc204914599tate_o] :
% 0.31/0.46 ( ! [A6: com,B6: a > state > $o] : ( P @ ( produc1948644831tate_o @ A6 @ B6 ) )
% 0.31/0.46 => ( P @ P3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases
% 0.31/0.46 thf(fact_154_prod__cases,axiom,
% 0.31/0.46 ! [P: product_prod_nat_nat > $o,P3: product_prod_nat_nat] :
% 0.31/0.46 ( ! [A6: nat,B6: nat] : ( P @ ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.31/0.46 => ( P @ P3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases
% 0.31/0.46 thf(fact_155_Pair__inject,axiom,
% 0.31/0.46 ! [A: a > state > $o,B2: produc204914599tate_o,A4: a > state > $o,B5: produc204914599tate_o] :
% 0.31/0.46 ( ( ( produc33908149tate_o @ A @ B2 )
% 0.31/0.46 = ( produc33908149tate_o @ A4 @ B5 ) )
% 0.31/0.46 => ~ ( ( A = A4 )
% 0.31/0.46 => ( B2 != B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Pair_inject
% 0.31/0.46 thf(fact_156_Pair__inject,axiom,
% 0.31/0.46 ! [A: state,B2: state,A4: state,B5: state] :
% 0.31/0.46 ( ( ( produc64584659_state @ A @ B2 )
% 0.31/0.46 = ( produc64584659_state @ A4 @ B5 ) )
% 0.31/0.46 => ~ ( ( A = A4 )
% 0.31/0.46 => ( B2 != B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Pair_inject
% 0.31/0.46 thf(fact_157_Pair__inject,axiom,
% 0.31/0.46 ! [A: com,B2: a > state > $o,A4: com,B5: a > state > $o] :
% 0.31/0.46 ( ( ( produc1948644831tate_o @ A @ B2 )
% 0.31/0.46 = ( produc1948644831tate_o @ A4 @ B5 ) )
% 0.31/0.46 => ~ ( ( A = A4 )
% 0.31/0.46 => ( B2 != B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Pair_inject
% 0.31/0.46 thf(fact_158_Pair__inject,axiom,
% 0.31/0.46 ! [A: nat,B2: nat,A4: nat,B5: nat] :
% 0.31/0.46 ( ( ( product_Pair_nat_nat @ A @ B2 )
% 0.31/0.46 = ( product_Pair_nat_nat @ A4 @ B5 ) )
% 0.31/0.46 => ~ ( ( A = A4 )
% 0.31/0.46 => ( B2 != B5 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Pair_inject
% 0.31/0.46 thf(fact_159_old_Oprod_Oexhaust,axiom,
% 0.31/0.46 ! [Y3: produc696469763tate_o] :
% 0.31/0.46 ~ ! [A6: a > state > $o,B6: produc204914599tate_o] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( produc33908149tate_o @ A6 @ B6 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.exhaust
% 0.31/0.46 thf(fact_160_old_Oprod_Oexhaust,axiom,
% 0.31/0.46 ! [Y3: produc1115495963_state] :
% 0.31/0.46 ~ ! [A6: state,B6: state] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( produc64584659_state @ A6 @ B6 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.exhaust
% 0.31/0.46 thf(fact_161_old_Oprod_Oexhaust,axiom,
% 0.31/0.46 ! [Y3: produc204914599tate_o] :
% 0.31/0.46 ~ ! [A6: com,B6: a > state > $o] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( produc1948644831tate_o @ A6 @ B6 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.exhaust
% 0.31/0.46 thf(fact_162_old_Oprod_Oexhaust,axiom,
% 0.31/0.46 ! [Y3: product_prod_nat_nat] :
% 0.31/0.46 ~ ! [A6: nat,B6: nat] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( product_Pair_nat_nat @ A6 @ B6 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.exhaust
% 0.31/0.46 thf(fact_163_old_Oprod_Oinducts,axiom,
% 0.31/0.46 ! [P: produc696469763tate_o > $o,Prod: produc696469763tate_o] :
% 0.31/0.46 ( ! [A6: a > state > $o,B6: produc204914599tate_o] : ( P @ ( produc33908149tate_o @ A6 @ B6 ) )
% 0.31/0.46 => ( P @ Prod ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inducts
% 0.31/0.46 thf(fact_164_old_Oprod_Oinducts,axiom,
% 0.31/0.46 ! [P: produc1115495963_state > $o,Prod: produc1115495963_state] :
% 0.31/0.46 ( ! [A6: state,B6: state] : ( P @ ( produc64584659_state @ A6 @ B6 ) )
% 0.31/0.46 => ( P @ Prod ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inducts
% 0.31/0.46 thf(fact_165_old_Oprod_Oinducts,axiom,
% 0.31/0.46 ! [P: produc204914599tate_o > $o,Prod: produc204914599tate_o] :
% 0.31/0.46 ( ! [A6: com,B6: a > state > $o] : ( P @ ( produc1948644831tate_o @ A6 @ B6 ) )
% 0.31/0.46 => ( P @ Prod ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inducts
% 0.31/0.46 thf(fact_166_old_Oprod_Oinducts,axiom,
% 0.31/0.46 ! [P: product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.31/0.46 ( ! [A6: nat,B6: nat] : ( P @ ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.31/0.46 => ( P @ Prod ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.inducts
% 0.31/0.46 thf(fact_167_is__singletonE,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( is_sin1547905295tate_o @ A2 )
% 0.31/0.46 => ~ ! [X3: produc696469763tate_o] :
% 0.31/0.46 ( A2
% 0.31/0.46 != ( insert2053719859tate_o @ X3 @ bot_bo170732493tate_o ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonE
% 0.31/0.46 thf(fact_168_is__singletonE,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( is_sin1352690165at_nat @ A2 )
% 0.31/0.46 => ~ ! [X3: product_prod_nat_nat] :
% 0.31/0.46 ( A2
% 0.31/0.46 != ( insert271595217at_nat @ X3 @ bot_bo2130386637at_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonE
% 0.31/0.46 thf(fact_169_is__singletonE,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state] :
% 0.31/0.46 ( ( is_sin1132515087_state @ A2 )
% 0.31/0.46 => ~ ! [X3: produc1115495963_state] :
% 0.31/0.46 ( A2
% 0.31/0.46 != ( insert311944171_state @ X3 @ bot_bo1625160935_state ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonE
% 0.31/0.46 thf(fact_170_is__singleton__def,axiom,
% 0.31/0.46 ( is_sin1547905295tate_o
% 0.31/0.46 = ( ^ [A5: set_Pr1590995257tate_o] :
% 0.31/0.46 ? [X: produc696469763tate_o] :
% 0.31/0.46 ( A5
% 0.31/0.46 = ( insert2053719859tate_o @ X @ bot_bo170732493tate_o ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singleton_def
% 0.31/0.46 thf(fact_171_is__singleton__def,axiom,
% 0.31/0.46 ( is_sin1352690165at_nat
% 0.31/0.46 = ( ^ [A5: set_Pr1986765409at_nat] :
% 0.31/0.46 ? [X: product_prod_nat_nat] :
% 0.31/0.46 ( A5
% 0.31/0.46 = ( insert271595217at_nat @ X @ bot_bo2130386637at_nat ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singleton_def
% 0.31/0.46 thf(fact_172_is__singleton__def,axiom,
% 0.31/0.46 ( is_sin1132515087_state
% 0.31/0.46 = ( ^ [A5: set_Pr795498619_state] :
% 0.31/0.46 ? [X: produc1115495963_state] :
% 0.31/0.46 ( A5
% 0.31/0.46 = ( insert311944171_state @ X @ bot_bo1625160935_state ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singleton_def
% 0.31/0.46 thf(fact_173_wf__def,axiom,
% 0.31/0.46 ( wf_state
% 0.31/0.46 = ( ^ [R3: set_Pr795498619_state] :
% 0.31/0.46 ! [P4: state > $o] :
% 0.31/0.46 ( ! [X: state] :
% 0.31/0.46 ( ! [Y5: state] :
% 0.31/0.46 ( ( member1389040324_state @ ( produc64584659_state @ Y5 @ X ) @ R3 )
% 0.31/0.46 => ( P4 @ Y5 ) )
% 0.31/0.46 => ( P4 @ X ) )
% 0.31/0.46 => ! [X4: state] : ( P4 @ X4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_def
% 0.31/0.46 thf(fact_174_wf__def,axiom,
% 0.31/0.46 ( wf_nat
% 0.31/0.46 = ( ^ [R3: set_Pr1986765409at_nat] :
% 0.31/0.46 ! [P4: nat > $o] :
% 0.31/0.46 ( ! [X: nat] :
% 0.31/0.46 ( ! [Y5: nat] :
% 0.31/0.46 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y5 @ X ) @ R3 )
% 0.31/0.46 => ( P4 @ Y5 ) )
% 0.31/0.46 => ( P4 @ X ) )
% 0.31/0.46 => ! [X4: nat] : ( P4 @ X4 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_def
% 0.31/0.46 thf(fact_175_wfE__min,axiom,
% 0.31/0.46 ! [R2: set_Pr778812871_state,X2: produc1115495963_state,Q: set_Pr795498619_state] :
% 0.31/0.46 ( ( wf_Pro1783588484_state @ R2 )
% 0.31/0.46 => ( ( member1389040324_state @ X2 @ Q )
% 0.31/0.46 => ~ ! [Z: produc1115495963_state] :
% 0.31/0.46 ( ( member1389040324_state @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: produc1115495963_state] :
% 0.31/0.46 ( ( member768948240_state @ ( produc1964772951_state @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member1389040324_state @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min
% 0.31/0.46 thf(fact_176_wfE__min,axiom,
% 0.31/0.46 ! [R2: set_Pr1490359111at_nat,X2: product_prod_nat_nat,Q: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( wf_Pro745352042at_nat @ R2 )
% 0.31/0.46 => ( ( member701585322at_nat @ X2 @ Q )
% 0.31/0.46 => ~ ! [Z: product_prod_nat_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: product_prod_nat_nat] :
% 0.31/0.46 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member701585322at_nat @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min
% 0.31/0.46 thf(fact_177_wfE__min,axiom,
% 0.31/0.46 ! [R2: set_Pr1702239303tate_o,X2: produc696469763tate_o,Q: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( wf_Pro309705690tate_o @ R2 )
% 0.31/0.46 => ( ( member1838112666tate_o @ X2 @ Q )
% 0.31/0.46 => ~ ! [Z: produc696469763tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: produc696469763tate_o] :
% 0.31/0.46 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member1838112666tate_o @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min
% 0.31/0.46 thf(fact_178_wfE__min,axiom,
% 0.31/0.46 ! [R2: set_Pr795498619_state,X2: state,Q: set_state] :
% 0.31/0.46 ( ( wf_state @ R2 )
% 0.31/0.46 => ( ( member_state @ X2 @ Q )
% 0.31/0.46 => ~ ! [Z: state] :
% 0.31/0.46 ( ( member_state @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: state] :
% 0.31/0.46 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member_state @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min
% 0.31/0.46 thf(fact_179_wfE__min,axiom,
% 0.31/0.46 ! [R2: set_Pr1986765409at_nat,X2: nat,Q: set_nat] :
% 0.31/0.46 ( ( wf_nat @ R2 )
% 0.31/0.46 => ( ( member_nat @ X2 @ Q )
% 0.31/0.46 => ~ ! [Z: nat] :
% 0.31/0.46 ( ( member_nat @ Z @ Q )
% 0.31/0.46 => ~ ! [Y4: nat] :
% 0.31/0.46 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ Z ) @ R2 )
% 0.31/0.46 => ~ ( member_nat @ Y4 @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfE_min
% 0.31/0.46 thf(fact_180_wfI__min,axiom,
% 0.31/0.46 ! [R2: set_Pr778812871_state] :
% 0.31/0.46 ( ! [X3: produc1115495963_state,Q3: set_Pr795498619_state] :
% 0.31/0.46 ( ( member1389040324_state @ X3 @ Q3 )
% 0.31/0.46 => ? [Xa: produc1115495963_state] :
% 0.31/0.46 ( ( member1389040324_state @ Xa @ Q3 )
% 0.31/0.46 & ! [Y2: produc1115495963_state] :
% 0.31/0.46 ( ( member768948240_state @ ( produc1964772951_state @ Y2 @ Xa ) @ R2 )
% 0.31/0.46 => ~ ( member1389040324_state @ Y2 @ Q3 ) ) ) )
% 0.31/0.46 => ( wf_Pro1783588484_state @ R2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfI_min
% 0.31/0.46 thf(fact_181_wfI__min,axiom,
% 0.31/0.46 ! [R2: set_Pr1490359111at_nat] :
% 0.31/0.46 ( ! [X3: product_prod_nat_nat,Q3: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ X3 @ Q3 )
% 0.31/0.46 => ? [Xa: product_prod_nat_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ Xa @ Q3 )
% 0.31/0.46 & ! [Y2: product_prod_nat_nat] :
% 0.31/0.46 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y2 @ Xa ) @ R2 )
% 0.31/0.46 => ~ ( member701585322at_nat @ Y2 @ Q3 ) ) ) )
% 0.31/0.46 => ( wf_Pro745352042at_nat @ R2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfI_min
% 0.31/0.46 thf(fact_182_wfI__min,axiom,
% 0.31/0.46 ! [R2: set_Pr1702239303tate_o] :
% 0.31/0.46 ( ! [X3: produc696469763tate_o,Q3: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ X3 @ Q3 )
% 0.31/0.46 => ? [Xa: produc696469763tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ Xa @ Q3 )
% 0.31/0.46 & ! [Y2: produc696469763tate_o] :
% 0.31/0.46 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y2 @ Xa ) @ R2 )
% 0.31/0.46 => ~ ( member1838112666tate_o @ Y2 @ Q3 ) ) ) )
% 0.31/0.46 => ( wf_Pro309705690tate_o @ R2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfI_min
% 0.31/0.46 thf(fact_183_wfI__min,axiom,
% 0.31/0.46 ! [R2: set_Pr795498619_state] :
% 0.31/0.46 ( ! [X3: state,Q3: set_state] :
% 0.31/0.46 ( ( member_state @ X3 @ Q3 )
% 0.31/0.46 => ? [Xa: state] :
% 0.31/0.46 ( ( member_state @ Xa @ Q3 )
% 0.31/0.46 & ! [Y2: state] :
% 0.31/0.46 ( ( member1389040324_state @ ( produc64584659_state @ Y2 @ Xa ) @ R2 )
% 0.31/0.46 => ~ ( member_state @ Y2 @ Q3 ) ) ) )
% 0.31/0.46 => ( wf_state @ R2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfI_min
% 0.31/0.46 thf(fact_184_wfI__min,axiom,
% 0.31/0.46 ! [R2: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ! [X3: nat,Q3: set_nat] :
% 0.31/0.46 ( ( member_nat @ X3 @ Q3 )
% 0.31/0.46 => ? [Xa: nat] :
% 0.31/0.46 ( ( member_nat @ Xa @ Q3 )
% 0.31/0.46 & ! [Y2: nat] :
% 0.31/0.46 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ Xa ) @ R2 )
% 0.31/0.46 => ~ ( member_nat @ Y2 @ Q3 ) ) ) )
% 0.31/0.46 => ( wf_nat @ R2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfI_min
% 0.31/0.46 thf(fact_185_wfUNIVI,axiom,
% 0.31/0.46 ! [R: set_Pr795498619_state] :
% 0.31/0.46 ( ! [P5: state > $o,X3: state] :
% 0.31/0.46 ( ! [Xa: state] :
% 0.31/0.46 ( ! [Y2: state] :
% 0.31/0.46 ( ( member1389040324_state @ ( produc64584659_state @ Y2 @ Xa ) @ R )
% 0.31/0.46 => ( P5 @ Y2 ) )
% 0.31/0.46 => ( P5 @ Xa ) )
% 0.31/0.46 => ( P5 @ X3 ) )
% 0.31/0.46 => ( wf_state @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfUNIVI
% 0.31/0.46 thf(fact_186_wfUNIVI,axiom,
% 0.31/0.46 ! [R: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ! [P5: nat > $o,X3: nat] :
% 0.31/0.46 ( ! [Xa: nat] :
% 0.31/0.46 ( ! [Y2: nat] :
% 0.31/0.46 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ Xa ) @ R )
% 0.31/0.46 => ( P5 @ Y2 ) )
% 0.31/0.46 => ( P5 @ Xa ) )
% 0.31/0.46 => ( P5 @ X3 ) )
% 0.31/0.46 => ( wf_nat @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % wfUNIVI
% 0.31/0.46 thf(fact_187_wf__asym,axiom,
% 0.31/0.46 ! [R: set_Pr795498619_state,A: state,X2: state] :
% 0.31/0.46 ( ( wf_state @ R )
% 0.31/0.46 => ( ( member1389040324_state @ ( produc64584659_state @ A @ X2 ) @ R )
% 0.31/0.46 => ~ ( member1389040324_state @ ( produc64584659_state @ X2 @ A ) @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_asym
% 0.31/0.46 thf(fact_188_wf__asym,axiom,
% 0.31/0.46 ! [R: set_Pr1986765409at_nat,A: nat,X2: nat] :
% 0.31/0.46 ( ( wf_nat @ R )
% 0.31/0.46 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ X2 ) @ R )
% 0.31/0.46 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ A ) @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_asym
% 0.31/0.46 thf(fact_189_wf__induct,axiom,
% 0.31/0.46 ! [R: set_Pr795498619_state,P: state > $o,A: state] :
% 0.31/0.46 ( ( wf_state @ R )
% 0.31/0.46 => ( ! [X3: state] :
% 0.31/0.46 ( ! [Y4: state] :
% 0.31/0.46 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ X3 ) @ R )
% 0.31/0.46 => ( P @ Y4 ) )
% 0.31/0.46 => ( P @ X3 ) )
% 0.31/0.46 => ( P @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_induct
% 0.31/0.46 thf(fact_190_wf__induct,axiom,
% 0.31/0.46 ! [R: set_Pr1986765409at_nat,P: nat > $o,A: nat] :
% 0.31/0.46 ( ( wf_nat @ R )
% 0.31/0.46 => ( ! [X3: nat] :
% 0.31/0.46 ( ! [Y4: nat] :
% 0.31/0.46 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ X3 ) @ R )
% 0.31/0.46 => ( P @ Y4 ) )
% 0.31/0.46 => ( P @ X3 ) )
% 0.31/0.46 => ( P @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_induct
% 0.31/0.46 thf(fact_191_wf__irrefl,axiom,
% 0.31/0.46 ! [R: set_Pr795498619_state,A: state] :
% 0.31/0.46 ( ( wf_state @ R )
% 0.31/0.46 => ~ ( member1389040324_state @ ( produc64584659_state @ A @ A ) @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_irrefl
% 0.31/0.46 thf(fact_192_wf__irrefl,axiom,
% 0.31/0.46 ! [R: set_Pr1986765409at_nat,A: nat] :
% 0.31/0.46 ( ( wf_nat @ R )
% 0.31/0.46 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_irrefl
% 0.31/0.46 thf(fact_193_wf__not__sym,axiom,
% 0.31/0.46 ! [R: set_Pr795498619_state,A: state,X2: state] :
% 0.31/0.46 ( ( wf_state @ R )
% 0.31/0.46 => ( ( member1389040324_state @ ( produc64584659_state @ A @ X2 ) @ R )
% 0.31/0.46 => ~ ( member1389040324_state @ ( produc64584659_state @ X2 @ A ) @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_not_sym
% 0.31/0.46 thf(fact_194_wf__not__sym,axiom,
% 0.31/0.46 ! [R: set_Pr1986765409at_nat,A: nat,X2: nat] :
% 0.31/0.46 ( ( wf_nat @ R )
% 0.31/0.46 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ X2 ) @ R )
% 0.31/0.46 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ A ) @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_not_sym
% 0.31/0.46 thf(fact_195_wf__not__refl,axiom,
% 0.31/0.46 ! [R: set_Pr795498619_state,A: state] :
% 0.31/0.46 ( ( wf_state @ R )
% 0.31/0.46 => ~ ( member1389040324_state @ ( produc64584659_state @ A @ A ) @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_not_refl
% 0.31/0.46 thf(fact_196_wf__not__refl,axiom,
% 0.31/0.46 ! [R: set_Pr1986765409at_nat,A: nat] :
% 0.31/0.46 ( ( wf_nat @ R )
% 0.31/0.46 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_not_refl
% 0.31/0.46 thf(fact_197_wf__eq__minimal,axiom,
% 0.31/0.46 ( wf_Pro1783588484_state
% 0.31/0.46 = ( ^ [R3: set_Pr778812871_state] :
% 0.31/0.46 ! [Q4: set_Pr795498619_state] :
% 0.31/0.46 ( ? [X: produc1115495963_state] : ( member1389040324_state @ X @ Q4 )
% 0.31/0.46 => ? [X: produc1115495963_state] :
% 0.31/0.46 ( ( member1389040324_state @ X @ Q4 )
% 0.31/0.46 & ! [Y5: produc1115495963_state] :
% 0.31/0.46 ( ( member768948240_state @ ( produc1964772951_state @ Y5 @ X ) @ R3 )
% 0.31/0.46 => ~ ( member1389040324_state @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_eq_minimal
% 0.31/0.46 thf(fact_198_wf__eq__minimal,axiom,
% 0.31/0.46 ( wf_Pro745352042at_nat
% 0.31/0.46 = ( ^ [R3: set_Pr1490359111at_nat] :
% 0.31/0.46 ! [Q4: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ? [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ Q4 )
% 0.31/0.46 => ? [X: product_prod_nat_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ X @ Q4 )
% 0.31/0.46 & ! [Y5: product_prod_nat_nat] :
% 0.31/0.46 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y5 @ X ) @ R3 )
% 0.31/0.46 => ~ ( member701585322at_nat @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_eq_minimal
% 0.31/0.46 thf(fact_199_wf__eq__minimal,axiom,
% 0.31/0.46 ( wf_Pro309705690tate_o
% 0.31/0.46 = ( ^ [R3: set_Pr1702239303tate_o] :
% 0.31/0.46 ! [Q4: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ? [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ Q4 )
% 0.31/0.46 => ? [X: produc696469763tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ X @ Q4 )
% 0.31/0.46 & ! [Y5: produc696469763tate_o] :
% 0.31/0.46 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y5 @ X ) @ R3 )
% 0.31/0.46 => ~ ( member1838112666tate_o @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_eq_minimal
% 0.31/0.46 thf(fact_200_wf__eq__minimal,axiom,
% 0.31/0.46 ( wf_state
% 0.31/0.46 = ( ^ [R3: set_Pr795498619_state] :
% 0.31/0.46 ! [Q4: set_state] :
% 0.31/0.46 ( ? [X: state] : ( member_state @ X @ Q4 )
% 0.31/0.46 => ? [X: state] :
% 0.31/0.46 ( ( member_state @ X @ Q4 )
% 0.31/0.46 & ! [Y5: state] :
% 0.31/0.46 ( ( member1389040324_state @ ( produc64584659_state @ Y5 @ X ) @ R3 )
% 0.31/0.46 => ~ ( member_state @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_eq_minimal
% 0.31/0.46 thf(fact_201_wf__eq__minimal,axiom,
% 0.31/0.46 ( wf_nat
% 0.31/0.46 = ( ^ [R3: set_Pr1986765409at_nat] :
% 0.31/0.46 ! [Q4: set_nat] :
% 0.31/0.46 ( ? [X: nat] : ( member_nat @ X @ Q4 )
% 0.31/0.46 => ? [X: nat] :
% 0.31/0.46 ( ( member_nat @ X @ Q4 )
% 0.31/0.46 & ! [Y5: nat] :
% 0.31/0.46 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y5 @ X ) @ R3 )
% 0.31/0.46 => ~ ( member_nat @ Y5 @ Q4 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_eq_minimal
% 0.31/0.46 thf(fact_202_wf__induct__rule,axiom,
% 0.31/0.46 ! [R: set_Pr795498619_state,P: state > $o,A: state] :
% 0.31/0.46 ( ( wf_state @ R )
% 0.31/0.46 => ( ! [X3: state] :
% 0.31/0.46 ( ! [Y4: state] :
% 0.31/0.46 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ X3 ) @ R )
% 0.31/0.46 => ( P @ Y4 ) )
% 0.31/0.46 => ( P @ X3 ) )
% 0.31/0.46 => ( P @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_induct_rule
% 0.31/0.46 thf(fact_203_wf__induct__rule,axiom,
% 0.31/0.46 ! [R: set_Pr1986765409at_nat,P: nat > $o,A: nat] :
% 0.31/0.46 ( ( wf_nat @ R )
% 0.31/0.46 => ( ! [X3: nat] :
% 0.31/0.46 ( ! [Y4: nat] :
% 0.31/0.46 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ X3 ) @ R )
% 0.31/0.46 => ( P @ Y4 ) )
% 0.31/0.46 => ( P @ X3 ) )
% 0.31/0.46 => ( P @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_induct_rule
% 0.31/0.46 thf(fact_204_prod__cases3,axiom,
% 0.31/0.46 ! [Y3: produc696469763tate_o] :
% 0.31/0.46 ~ ! [A6: a > state > $o,B6: com,C4: a > state > $o] :
% 0.31/0.46 ( Y3
% 0.31/0.46 != ( produc33908149tate_o @ A6 @ ( produc1948644831tate_o @ B6 @ C4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_cases3
% 0.31/0.46 thf(fact_205_prod__induct3,axiom,
% 0.31/0.46 ! [P: produc696469763tate_o > $o,X2: produc696469763tate_o] :
% 0.31/0.46 ( ! [A6: a > state > $o,B6: com,C4: a > state > $o] : ( P @ ( produc33908149tate_o @ A6 @ ( produc1948644831tate_o @ B6 @ C4 ) ) )
% 0.31/0.46 => ( P @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod_induct3
% 0.31/0.46 thf(fact_206_bot__empty__eq2,axiom,
% 0.31/0.46 ( bot_bo935656620te_o_o
% 0.31/0.46 = ( ^ [X: com,Y5: a > state > $o] : ( member221067728tate_o @ ( produc1948644831tate_o @ X @ Y5 ) @ bot_bo1692783091tate_o ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_empty_eq2
% 0.31/0.46 thf(fact_207_bot__empty__eq2,axiom,
% 0.31/0.46 ( bot_bo2130564770te_o_o
% 0.31/0.46 = ( ^ [X: a > state > $o,Y5: produc204914599tate_o] : ( member1838112666tate_o @ ( produc33908149tate_o @ X @ Y5 ) @ bot_bo170732493tate_o ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_empty_eq2
% 0.31/0.46 thf(fact_208_bot__empty__eq2,axiom,
% 0.31/0.46 ( bot_bot_nat_nat_o
% 0.31/0.46 = ( ^ [X: nat,Y5: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ bot_bo2130386637at_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_empty_eq2
% 0.31/0.46 thf(fact_209_bot__empty__eq2,axiom,
% 0.31/0.46 ( bot_bo51534648tate_o
% 0.31/0.46 = ( ^ [X: state,Y5: state] : ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ bot_bo1625160935_state ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_empty_eq2
% 0.31/0.46 thf(fact_210_wf__measure,axiom,
% 0.31/0.46 ! [F: state > nat] : ( wf_state @ ( measure_state @ F ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_measure
% 0.31/0.46 thf(fact_211_wf__measure,axiom,
% 0.31/0.46 ! [F: nat > nat] : ( wf_nat @ ( measure_nat @ F ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_measure
% 0.31/0.46 thf(fact_212_thoare_OWhile,axiom,
% 0.31/0.46 ! [R: set_Pr795498619_state,C: set_Pr1590995257tate_o,P: a > state > $o,B2: state > $o,C2: com] :
% 0.31/0.46 ( ( wf_state @ R )
% 0.31/0.46 => ( ! [S3: state] :
% 0.31/0.46 ( pHoare382919414oare_a @ C
% 0.31/0.46 @ ^ [Z4: a,S4: state] :
% 0.31/0.46 ( ( P @ Z4 @ S4 )
% 0.31/0.46 & ( B2 @ S4 )
% 0.31/0.46 & ( S3 = S4 ) )
% 0.31/0.46 @ C2
% 0.31/0.46 @ ^ [Z4: a,S4: state] :
% 0.31/0.46 ( ( P @ Z4 @ S4 )
% 0.31/0.46 & ( member1389040324_state @ ( produc64584659_state @ S4 @ S3 ) @ R ) ) )
% 0.31/0.46 => ( pHoare382919414oare_a @ C @ P @ ( while @ B2 @ C2 )
% 0.31/0.46 @ ^ [Z4: a,S4: state] :
% 0.31/0.46 ( ( P @ Z4 @ S4 )
% 0.31/0.46 & ~ ( B2 @ S4 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % thoare.While
% 0.31/0.46 thf(fact_213_Set_Ois__empty__def,axiom,
% 0.31/0.46 ( is_emp807847857tate_o
% 0.31/0.46 = ( ^ [A5: set_Pr1590995257tate_o] : ( A5 = bot_bo170732493tate_o ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Set.is_empty_def
% 0.31/0.46 thf(fact_214_Set_Ois__empty__def,axiom,
% 0.31/0.46 ( is_emp825011411at_nat
% 0.31/0.46 = ( ^ [A5: set_Pr1986765409at_nat] : ( A5 = bot_bo2130386637at_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Set.is_empty_def
% 0.31/0.46 thf(fact_215_Set_Ois__empty__def,axiom,
% 0.31/0.46 ( is_emp1062983149_state
% 0.31/0.46 = ( ^ [A5: set_Pr795498619_state] : ( A5 = bot_bo1625160935_state ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Set.is_empty_def
% 0.31/0.46 thf(fact_216_com_Oinject_I4_J,axiom,
% 0.31/0.46 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 0.31/0.46 ( ( ( while @ X41 @ X42 )
% 0.31/0.46 = ( while @ Y41 @ Y42 ) )
% 0.31/0.46 = ( ( X41 = Y41 )
% 0.31/0.46 & ( X42 = Y42 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % com.inject(4)
% 0.31/0.46 thf(fact_217_com_Odistinct_I25_J,axiom,
% 0.31/0.46 ! [X41: state > $o,X42: com] :
% 0.31/0.46 ( ( while @ X41 @ X42 )
% 0.31/0.46 != call ) ).
% 0.31/0.46
% 0.31/0.46 % com.distinct(25)
% 0.31/0.46 thf(fact_218_exec_OWhileFalse,axiom,
% 0.31/0.46 ! [B2: state > $o,S2: state,C2: com] :
% 0.31/0.46 ( ~ ( B2 @ S2 )
% 0.31/0.46 => ( exec @ S2 @ ( while @ B2 @ C2 ) @ S2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % exec.WhileFalse
% 0.31/0.46 thf(fact_219_exec_OWhileTrue,axiom,
% 0.31/0.46 ! [B2: state > $o,S2: state,C2: com,T2: state,U2: state] :
% 0.31/0.46 ( ( B2 @ S2 )
% 0.31/0.46 => ( ( exec @ S2 @ C2 @ T2 )
% 0.31/0.46 => ( ( exec @ T2 @ ( while @ B2 @ C2 ) @ U2 )
% 0.31/0.46 => ( exec @ S2 @ ( while @ B2 @ C2 ) @ U2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % exec.WhileTrue
% 0.31/0.46 thf(fact_220_termi_OWhileFalse,axiom,
% 0.31/0.46 ! [B2: state > $o,S2: state,C2: com] :
% 0.31/0.46 ( ~ ( B2 @ S2 )
% 0.31/0.46 => ( termi @ ( while @ B2 @ C2 ) @ S2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % termi.WhileFalse
% 0.31/0.46 thf(fact_221_termi_OWhileTrue,axiom,
% 0.31/0.46 ! [B2: state > $o,S2: state,C2: com] :
% 0.31/0.46 ( ( B2 @ S2 )
% 0.31/0.46 => ( ( termi @ C2 @ S2 )
% 0.31/0.46 => ( ! [T: state] :
% 0.31/0.46 ( ( exec @ S2 @ C2 @ T )
% 0.31/0.46 => ( termi @ ( while @ B2 @ C2 ) @ T ) )
% 0.31/0.46 => ( termi @ ( while @ B2 @ C2 ) @ S2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % termi.WhileTrue
% 0.31/0.46 thf(fact_222_bot__empty__eq,axiom,
% 0.31/0.46 ( bot_bo250281208te_o_o
% 0.31/0.46 = ( ^ [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ bot_bo170732493tate_o ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_empty_eq
% 0.31/0.46 thf(fact_223_bot__empty__eq,axiom,
% 0.31/0.46 ( bot_bo513358416_nat_o
% 0.31/0.46 = ( ^ [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ bot_bo2130386637at_nat ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_empty_eq
% 0.31/0.46 thf(fact_224_bot__empty__eq,axiom,
% 0.31/0.46 ( bot_bo446391478tate_o
% 0.31/0.46 = ( ^ [X: produc1115495963_state] : ( member1389040324_state @ X @ bot_bo1625160935_state ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_empty_eq
% 0.31/0.46 thf(fact_225_pred__equals__eq2,axiom,
% 0.31/0.46 ! [R2: set_Pr1590995257tate_o,S5: set_Pr1590995257tate_o] :
% 0.31/0.46 ( ( ( ^ [X: a > state > $o,Y5: produc204914599tate_o] : ( member1838112666tate_o @ ( produc33908149tate_o @ X @ Y5 ) @ R2 ) )
% 0.31/0.46 = ( ^ [X: a > state > $o,Y5: produc204914599tate_o] : ( member1838112666tate_o @ ( produc33908149tate_o @ X @ Y5 ) @ S5 ) ) )
% 0.31/0.46 = ( R2 = S5 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pred_equals_eq2
% 0.31/0.46 thf(fact_226_pred__equals__eq2,axiom,
% 0.31/0.46 ! [R2: set_Pr795498619_state,S5: set_Pr795498619_state] :
% 0.31/0.46 ( ( ( ^ [X: state,Y5: state] : ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ R2 ) )
% 0.31/0.46 = ( ^ [X: state,Y5: state] : ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ S5 ) ) )
% 0.31/0.46 = ( R2 = S5 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pred_equals_eq2
% 0.31/0.46 thf(fact_227_pred__equals__eq2,axiom,
% 0.31/0.46 ! [R2: set_Pr1740974983tate_o,S5: set_Pr1740974983tate_o] :
% 0.31/0.46 ( ( ( ^ [X: com,Y5: a > state > $o] : ( member221067728tate_o @ ( produc1948644831tate_o @ X @ Y5 ) @ R2 ) )
% 0.31/0.46 = ( ^ [X: com,Y5: a > state > $o] : ( member221067728tate_o @ ( produc1948644831tate_o @ X @ Y5 ) @ S5 ) ) )
% 0.31/0.46 = ( R2 = S5 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pred_equals_eq2
% 0.31/0.46 thf(fact_228_pred__equals__eq2,axiom,
% 0.31/0.46 ! [R2: set_Pr1986765409at_nat,S5: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ( ( ^ [X: nat,Y5: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ R2 ) )
% 0.31/0.46 = ( ^ [X: nat,Y5: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ S5 ) ) )
% 0.31/0.46 = ( R2 = S5 ) ) ).
% 0.31/0.46
% 0.31/0.46 % pred_equals_eq2
% 0.31/0.46 thf(fact_229_Collect__empty__eq__bot,axiom,
% 0.31/0.46 ! [P: produc696469763tate_o > $o] :
% 0.31/0.46 ( ( ( collec1499596504tate_o @ P )
% 0.31/0.46 = bot_bo170732493tate_o )
% 0.31/0.46 = ( P = bot_bo250281208te_o_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_empty_eq_bot
% 0.31/0.46 thf(fact_230_Collect__empty__eq__bot,axiom,
% 0.31/0.46 ! [P: product_prod_nat_nat > $o] :
% 0.31/0.46 ( ( ( collec7649004at_nat @ P )
% 0.31/0.46 = bot_bo2130386637at_nat )
% 0.31/0.46 = ( P = bot_bo513358416_nat_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_empty_eq_bot
% 0.31/0.46 thf(fact_231_Collect__empty__eq__bot,axiom,
% 0.31/0.46 ! [P: produc1115495963_state > $o] :
% 0.31/0.46 ( ( ( collec496201222_state @ P )
% 0.31/0.46 = bot_bo1625160935_state )
% 0.31/0.46 = ( P = bot_bo446391478tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_empty_eq_bot
% 0.31/0.46 thf(fact_232_total__on__singleton,axiom,
% 0.31/0.46 ! [X2: nat] : ( total_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_singleton
% 0.31/0.46 thf(fact_233_total__on__singleton,axiom,
% 0.31/0.46 ! [X2: state] : ( total_on_state @ ( insert_state @ X2 @ bot_bot_set_state ) @ ( insert311944171_state @ ( produc64584659_state @ X2 @ X2 ) @ bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_singleton
% 0.31/0.46 thf(fact_234_total__on__singleton,axiom,
% 0.31/0.46 ! [X2: produc696469763tate_o] : ( total_795385983tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) @ ( insert1597128631tate_o @ ( produc1684562079tate_o @ X2 @ X2 ) @ bot_bo1714653363tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_singleton
% 0.31/0.46 thf(fact_235_total__on__singleton,axiom,
% 0.31/0.46 ! [X2: product_prod_nat_nat] : ( total_1775715973at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) @ ( insert584009271at_nat @ ( produc1168807639at_nat @ X2 @ X2 ) @ bot_bo34127283at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_singleton
% 0.31/0.46 thf(fact_236_total__on__singleton,axiom,
% 0.31/0.46 ! [X2: produc1115495963_state] : ( total_1316653983_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) @ ( insert1616594103_state @ ( produc1964772951_state @ X2 @ X2 ) @ bot_bo1331673139_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_singleton
% 0.31/0.46 thf(fact_237_refl__on__singleton,axiom,
% 0.31/0.46 ! [X2: nat] : ( refl_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_singleton
% 0.31/0.46 thf(fact_238_refl__on__singleton,axiom,
% 0.31/0.46 ! [X2: state] : ( refl_on_state @ ( insert_state @ X2 @ bot_bot_set_state ) @ ( insert311944171_state @ ( produc64584659_state @ X2 @ X2 ) @ bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_singleton
% 0.31/0.46 thf(fact_239_refl__on__singleton,axiom,
% 0.31/0.46 ! [X2: produc696469763tate_o] : ( refl_o489021252tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) @ ( insert1597128631tate_o @ ( produc1684562079tate_o @ X2 @ X2 ) @ bot_bo1714653363tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_singleton
% 0.31/0.46 thf(fact_240_refl__on__singleton,axiom,
% 0.31/0.46 ! [X2: product_prod_nat_nat] : ( refl_o1619599232at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) @ ( insert584009271at_nat @ ( produc1168807639at_nat @ X2 @ X2 ) @ bot_bo34127283at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_singleton
% 0.31/0.46 thf(fact_241_refl__on__singleton,axiom,
% 0.31/0.46 ! [X2: produc1115495963_state] : ( refl_o1438232218_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) @ ( insert1616594103_state @ ( produc1964772951_state @ X2 @ X2 ) @ bot_bo1331673139_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_singleton
% 0.31/0.46 thf(fact_242_wf__termi,axiom,
% 0.31/0.46 ! [B2: state > $o,C2: com] :
% 0.31/0.46 ( wf_state
% 0.31/0.46 @ ( collec496201222_state
% 0.31/0.46 @ ( produc789892016tate_o
% 0.31/0.46 @ ^ [T3: state,S4: state] :
% 0.31/0.46 ( ( termi @ ( while @ B2 @ C2 ) @ S4 )
% 0.31/0.46 & ( B2 @ S4 )
% 0.31/0.46 & ( exec @ S4 @ C2 @ T3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % wf_termi
% 0.31/0.46 thf(fact_243_linear__order__on__singleton,axiom,
% 0.31/0.46 ! [X2: nat] : ( order_130026331on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2130386637at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % linear_order_on_singleton
% 0.31/0.46 thf(fact_244_linear__order__on__singleton,axiom,
% 0.31/0.46 ! [X2: state] : ( order_286167592_state @ ( insert_state @ X2 @ bot_bot_set_state ) @ ( insert311944171_state @ ( produc64584659_state @ X2 @ X2 ) @ bot_bo1625160935_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % linear_order_on_singleton
% 0.31/0.46 thf(fact_245_linear__order__on__singleton,axiom,
% 0.31/0.46 ! [X2: produc696469763tate_o] : ( order_50454158tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) @ ( insert1597128631tate_o @ ( produc1684562079tate_o @ X2 @ X2 ) @ bot_bo1714653363tate_o ) ) ).
% 0.31/0.46
% 0.31/0.46 % linear_order_on_singleton
% 0.31/0.46 thf(fact_246_linear__order__on__singleton,axiom,
% 0.31/0.46 ! [X2: product_prod_nat_nat] : ( order_721919926at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) @ ( insert584009271at_nat @ ( produc1168807639at_nat @ X2 @ X2 ) @ bot_bo34127283at_nat ) ) ).
% 0.31/0.46
% 0.31/0.46 % linear_order_on_singleton
% 0.31/0.46 thf(fact_247_linear__order__on__singleton,axiom,
% 0.31/0.46 ! [X2: produc1115495963_state] : ( order_178668240_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) @ ( insert1616594103_state @ ( produc1964772951_state @ X2 @ X2 ) @ bot_bo1331673139_state ) ) ).
% 0.31/0.46
% 0.31/0.46 % linear_order_on_singleton
% 0.31/0.46 thf(fact_248_split__part,axiom,
% 0.31/0.46 ! [P: $o,Q: state > state > $o] :
% 0.31/0.46 ( ( produc789892016tate_o
% 0.31/0.46 @ ^ [A3: state,B7: state] :
% 0.31/0.46 ( P
% 0.31/0.46 & ( Q @ A3 @ B7 ) ) )
% 0.31/0.46 = ( ^ [Ab: produc1115495963_state] :
% 0.31/0.46 ( P
% 0.31/0.46 & ( produc789892016tate_o @ Q @ Ab ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_part
% 0.31/0.46 thf(fact_249_split__part,axiom,
% 0.31/0.46 ! [P: $o,Q: nat > nat > $o] :
% 0.31/0.46 ( ( produc949581770_nat_o
% 0.31/0.46 @ ^ [A3: nat,B7: nat] :
% 0.31/0.46 ( P
% 0.31/0.46 & ( Q @ A3 @ B7 ) ) )
% 0.31/0.46 = ( ^ [Ab: product_prod_nat_nat] :
% 0.31/0.46 ( P
% 0.31/0.46 & ( produc949581770_nat_o @ Q @ Ab ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_part
% 0.31/0.46 thf(fact_250_case__prod__conv,axiom,
% 0.31/0.46 ! [F: state > state > $o,A: state,B2: state] :
% 0.31/0.46 ( ( produc789892016tate_o @ F @ ( produc64584659_state @ A @ B2 ) )
% 0.31/0.46 = ( F @ A @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prod_conv
% 0.31/0.46 thf(fact_251_case__prod__conv,axiom,
% 0.31/0.46 ! [F: nat > nat > $o,A: nat,B2: nat] :
% 0.31/0.46 ( ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ A @ B2 ) )
% 0.31/0.46 = ( F @ A @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prod_conv
% 0.31/0.46 thf(fact_252_case__prodI,axiom,
% 0.31/0.46 ! [F: ( a > state > $o ) > produc204914599tate_o > $o,A: a > state > $o,B2: produc204914599tate_o] :
% 0.31/0.46 ( ( F @ A @ B2 )
% 0.31/0.46 => ( produc1271576886te_o_o @ F @ ( produc33908149tate_o @ A @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodI
% 0.31/0.46 thf(fact_253_case__prodI,axiom,
% 0.31/0.46 ! [F: com > ( a > state > $o ) > $o,A: com,B2: a > state > $o] :
% 0.31/0.46 ( ( F @ A @ B2 )
% 0.31/0.46 => ( produc281270436te_o_o @ F @ ( produc1948644831tate_o @ A @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodI
% 0.31/0.46 thf(fact_254_case__prodI,axiom,
% 0.31/0.46 ! [F: state > state > $o,A: state,B2: state] :
% 0.31/0.46 ( ( F @ A @ B2 )
% 0.31/0.46 => ( produc789892016tate_o @ F @ ( produc64584659_state @ A @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodI
% 0.31/0.46 thf(fact_255_case__prodI,axiom,
% 0.31/0.46 ! [F: nat > nat > $o,A: nat,B2: nat] :
% 0.31/0.46 ( ( F @ A @ B2 )
% 0.31/0.46 => ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ A @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodI
% 0.31/0.46 thf(fact_256_case__prodI2,axiom,
% 0.31/0.46 ! [P3: produc696469763tate_o,C2: ( a > state > $o ) > produc204914599tate_o > $o] :
% 0.31/0.46 ( ! [A6: a > state > $o,B6: produc204914599tate_o] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( produc33908149tate_o @ A6 @ B6 ) )
% 0.31/0.46 => ( C2 @ A6 @ B6 ) )
% 0.31/0.46 => ( produc1271576886te_o_o @ C2 @ P3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodI2
% 0.31/0.46 thf(fact_257_case__prodI2,axiom,
% 0.31/0.46 ! [P3: produc204914599tate_o,C2: com > ( a > state > $o ) > $o] :
% 0.31/0.46 ( ! [A6: com,B6: a > state > $o] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( produc1948644831tate_o @ A6 @ B6 ) )
% 0.31/0.46 => ( C2 @ A6 @ B6 ) )
% 0.31/0.46 => ( produc281270436te_o_o @ C2 @ P3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodI2
% 0.31/0.46 thf(fact_258_case__prodI2,axiom,
% 0.31/0.46 ! [P3: produc1115495963_state,C2: state > state > $o] :
% 0.31/0.46 ( ! [A6: state,B6: state] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( produc64584659_state @ A6 @ B6 ) )
% 0.31/0.46 => ( C2 @ A6 @ B6 ) )
% 0.31/0.46 => ( produc789892016tate_o @ C2 @ P3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodI2
% 0.31/0.46 thf(fact_259_case__prodI2,axiom,
% 0.31/0.46 ! [P3: product_prod_nat_nat,C2: nat > nat > $o] :
% 0.31/0.46 ( ! [A6: nat,B6: nat] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.31/0.46 => ( C2 @ A6 @ B6 ) )
% 0.31/0.46 => ( produc949581770_nat_o @ C2 @ P3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodI2
% 0.31/0.46 thf(fact_260_refl__on__domain,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,A: produc1115495963_state,B2: produc1115495963_state] :
% 0.31/0.46 ( ( refl_o1438232218_state @ A2 @ R )
% 0.31/0.46 => ( ( member768948240_state @ ( produc1964772951_state @ A @ B2 ) @ R )
% 0.31/0.46 => ( ( member1389040324_state @ A @ A2 )
% 0.31/0.46 & ( member1389040324_state @ B2 @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_domain
% 0.31/0.46 thf(fact_261_refl__on__domain,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,A: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 0.31/0.46 ( ( refl_o1619599232at_nat @ A2 @ R )
% 0.31/0.46 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ B2 ) @ R )
% 0.31/0.46 => ( ( member701585322at_nat @ A @ A2 )
% 0.31/0.46 & ( member701585322at_nat @ B2 @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_domain
% 0.31/0.46 thf(fact_262_refl__on__domain,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,A: produc696469763tate_o,B2: produc696469763tate_o] :
% 0.31/0.46 ( ( refl_o489021252tate_o @ A2 @ R )
% 0.31/0.46 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ A @ B2 ) @ R )
% 0.31/0.46 => ( ( member1838112666tate_o @ A @ A2 )
% 0.31/0.46 & ( member1838112666tate_o @ B2 @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_domain
% 0.31/0.46 thf(fact_263_refl__on__domain,axiom,
% 0.31/0.46 ! [A2: set_state,R: set_Pr795498619_state,A: state,B2: state] :
% 0.31/0.46 ( ( refl_on_state @ A2 @ R )
% 0.31/0.46 => ( ( member1389040324_state @ ( produc64584659_state @ A @ B2 ) @ R )
% 0.31/0.46 => ( ( member_state @ A @ A2 )
% 0.31/0.46 & ( member_state @ B2 @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_domain
% 0.31/0.46 thf(fact_264_refl__on__domain,axiom,
% 0.31/0.46 ! [A2: set_nat,R: set_Pr1986765409at_nat,A: nat,B2: nat] :
% 0.31/0.46 ( ( refl_on_nat @ A2 @ R )
% 0.31/0.46 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B2 ) @ R )
% 0.31/0.46 => ( ( member_nat @ A @ A2 )
% 0.31/0.46 & ( member_nat @ B2 @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_on_domain
% 0.31/0.46 thf(fact_265_prod_Ocase__distrib,axiom,
% 0.31/0.46 ! [H: $o > $o,F: state > state > $o,Prod: produc1115495963_state] :
% 0.31/0.46 ( ( H @ ( produc789892016tate_o @ F @ Prod ) )
% 0.31/0.46 = ( produc789892016tate_o
% 0.31/0.46 @ ^ [X12: state,X23: state] : ( H @ ( F @ X12 @ X23 ) )
% 0.31/0.46 @ Prod ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod.case_distrib
% 0.31/0.46 thf(fact_266_prod_Ocase__distrib,axiom,
% 0.31/0.46 ! [H: $o > $o,F: nat > nat > $o,Prod: product_prod_nat_nat] :
% 0.31/0.46 ( ( H @ ( produc949581770_nat_o @ F @ Prod ) )
% 0.31/0.46 = ( produc949581770_nat_o
% 0.31/0.46 @ ^ [X12: nat,X23: nat] : ( H @ ( F @ X12 @ X23 ) )
% 0.31/0.46 @ Prod ) ) ).
% 0.31/0.46
% 0.31/0.46 % prod.case_distrib
% 0.31/0.46 thf(fact_267_prod_Odisc__eq__case,axiom,
% 0.31/0.46 ! [Prod: produc1115495963_state] :
% 0.31/0.46 ( produc789892016tate_o
% 0.31/0.46 @ ^ [Uu: state,Uv: state] : $true
% 0.31/0.46 @ Prod ) ).
% 0.31/0.46
% 0.31/0.46 % prod.disc_eq_case
% 0.31/0.46 thf(fact_268_prod_Odisc__eq__case,axiom,
% 0.31/0.46 ! [Prod: product_prod_nat_nat] :
% 0.31/0.46 ( produc949581770_nat_o
% 0.31/0.46 @ ^ [Uu: nat,Uv: nat] : $true
% 0.31/0.46 @ Prod ) ).
% 0.31/0.46
% 0.31/0.46 % prod.disc_eq_case
% 0.31/0.46 thf(fact_269_old_Oprod_Ocase,axiom,
% 0.31/0.46 ! [F: state > state > $o,X1: state,X22: state] :
% 0.31/0.46 ( ( produc789892016tate_o @ F @ ( produc64584659_state @ X1 @ X22 ) )
% 0.31/0.46 = ( F @ X1 @ X22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.case
% 0.31/0.46 thf(fact_270_old_Oprod_Ocase,axiom,
% 0.31/0.46 ! [F: nat > nat > $o,X1: nat,X22: nat] :
% 0.31/0.46 ( ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.31/0.46 = ( F @ X1 @ X22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % old.prod.case
% 0.31/0.46 thf(fact_271_refl__onD2,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,X2: produc1115495963_state,Y3: produc1115495963_state] :
% 0.31/0.46 ( ( refl_o1438232218_state @ A2 @ R )
% 0.31/0.46 => ( ( member768948240_state @ ( produc1964772951_state @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member1389040324_state @ Y3 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD2
% 0.31/0.46 thf(fact_272_refl__onD2,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.31/0.46 ( ( refl_o1619599232at_nat @ A2 @ R )
% 0.31/0.46 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member701585322at_nat @ Y3 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD2
% 0.31/0.46 thf(fact_273_refl__onD2,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,X2: produc696469763tate_o,Y3: produc696469763tate_o] :
% 0.31/0.46 ( ( refl_o489021252tate_o @ A2 @ R )
% 0.31/0.46 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member1838112666tate_o @ Y3 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD2
% 0.31/0.46 thf(fact_274_refl__onD2,axiom,
% 0.31/0.46 ! [A2: set_state,R: set_Pr795498619_state,X2: state,Y3: state] :
% 0.31/0.46 ( ( refl_on_state @ A2 @ R )
% 0.31/0.46 => ( ( member1389040324_state @ ( produc64584659_state @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member_state @ Y3 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD2
% 0.31/0.46 thf(fact_275_refl__onD2,axiom,
% 0.31/0.46 ! [A2: set_nat,R: set_Pr1986765409at_nat,X2: nat,Y3: nat] :
% 0.31/0.46 ( ( refl_on_nat @ A2 @ R )
% 0.31/0.46 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member_nat @ Y3 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD2
% 0.31/0.46 thf(fact_276_refl__onD1,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,X2: produc1115495963_state,Y3: produc1115495963_state] :
% 0.31/0.46 ( ( refl_o1438232218_state @ A2 @ R )
% 0.31/0.46 => ( ( member768948240_state @ ( produc1964772951_state @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member1389040324_state @ X2 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD1
% 0.31/0.46 thf(fact_277_refl__onD1,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.31/0.46 ( ( refl_o1619599232at_nat @ A2 @ R )
% 0.31/0.46 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member701585322at_nat @ X2 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD1
% 0.31/0.46 thf(fact_278_refl__onD1,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,X2: produc696469763tate_o,Y3: produc696469763tate_o] :
% 0.31/0.46 ( ( refl_o489021252tate_o @ A2 @ R )
% 0.31/0.46 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member1838112666tate_o @ X2 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD1
% 0.31/0.46 thf(fact_279_refl__onD1,axiom,
% 0.31/0.46 ! [A2: set_state,R: set_Pr795498619_state,X2: state,Y3: state] :
% 0.31/0.46 ( ( refl_on_state @ A2 @ R )
% 0.31/0.46 => ( ( member1389040324_state @ ( produc64584659_state @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member_state @ X2 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD1
% 0.31/0.46 thf(fact_280_refl__onD1,axiom,
% 0.31/0.46 ! [A2: set_nat,R: set_Pr1986765409at_nat,X2: nat,Y3: nat] :
% 0.31/0.46 ( ( refl_on_nat @ A2 @ R )
% 0.31/0.46 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 0.31/0.46 => ( member_nat @ X2 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD1
% 0.31/0.46 thf(fact_281_refl__onD,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,A: produc1115495963_state] :
% 0.31/0.46 ( ( refl_o1438232218_state @ A2 @ R )
% 0.31/0.46 => ( ( member1389040324_state @ A @ A2 )
% 0.31/0.46 => ( member768948240_state @ ( produc1964772951_state @ A @ A ) @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD
% 0.31/0.46 thf(fact_282_refl__onD,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,A: product_prod_nat_nat] :
% 0.31/0.46 ( ( refl_o1619599232at_nat @ A2 @ R )
% 0.31/0.46 => ( ( member701585322at_nat @ A @ A2 )
% 0.31/0.46 => ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ A ) @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD
% 0.31/0.46 thf(fact_283_refl__onD,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,A: produc696469763tate_o] :
% 0.31/0.46 ( ( refl_o489021252tate_o @ A2 @ R )
% 0.31/0.46 => ( ( member1838112666tate_o @ A @ A2 )
% 0.31/0.46 => ( member1629320336tate_o @ ( produc1684562079tate_o @ A @ A ) @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD
% 0.31/0.46 thf(fact_284_refl__onD,axiom,
% 0.31/0.46 ! [A2: set_state,R: set_Pr795498619_state,A: state] :
% 0.31/0.46 ( ( refl_on_state @ A2 @ R )
% 0.31/0.46 => ( ( member_state @ A @ A2 )
% 0.31/0.46 => ( member1389040324_state @ ( produc64584659_state @ A @ A ) @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD
% 0.31/0.46 thf(fact_285_refl__onD,axiom,
% 0.31/0.46 ! [A2: set_nat,R: set_Pr1986765409at_nat,A: nat] :
% 0.31/0.46 ( ( refl_on_nat @ A2 @ R )
% 0.31/0.46 => ( ( member_nat @ A @ A2 )
% 0.31/0.46 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % refl_onD
% 0.31/0.46 thf(fact_286_case__prodD,axiom,
% 0.31/0.46 ! [F: ( a > state > $o ) > produc204914599tate_o > $o,A: a > state > $o,B2: produc204914599tate_o] :
% 0.31/0.46 ( ( produc1271576886te_o_o @ F @ ( produc33908149tate_o @ A @ B2 ) )
% 0.31/0.46 => ( F @ A @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodD
% 0.31/0.46 thf(fact_287_case__prodD,axiom,
% 0.31/0.46 ! [F: com > ( a > state > $o ) > $o,A: com,B2: a > state > $o] :
% 0.31/0.46 ( ( produc281270436te_o_o @ F @ ( produc1948644831tate_o @ A @ B2 ) )
% 0.31/0.46 => ( F @ A @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodD
% 0.31/0.46 thf(fact_288_case__prodD,axiom,
% 0.31/0.46 ! [F: state > state > $o,A: state,B2: state] :
% 0.31/0.46 ( ( produc789892016tate_o @ F @ ( produc64584659_state @ A @ B2 ) )
% 0.31/0.46 => ( F @ A @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodD
% 0.31/0.46 thf(fact_289_case__prodD,axiom,
% 0.31/0.46 ! [F: nat > nat > $o,A: nat,B2: nat] :
% 0.31/0.46 ( ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ A @ B2 ) )
% 0.31/0.46 => ( F @ A @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodD
% 0.31/0.46 thf(fact_290_case__prodE,axiom,
% 0.31/0.46 ! [C2: ( a > state > $o ) > produc204914599tate_o > $o,P3: produc696469763tate_o] :
% 0.31/0.46 ( ( produc1271576886te_o_o @ C2 @ P3 )
% 0.31/0.46 => ~ ! [X3: a > state > $o,Y2: produc204914599tate_o] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( produc33908149tate_o @ X3 @ Y2 ) )
% 0.31/0.46 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodE
% 0.31/0.46 thf(fact_291_case__prodE,axiom,
% 0.31/0.46 ! [C2: com > ( a > state > $o ) > $o,P3: produc204914599tate_o] :
% 0.31/0.46 ( ( produc281270436te_o_o @ C2 @ P3 )
% 0.31/0.46 => ~ ! [X3: com,Y2: a > state > $o] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( produc1948644831tate_o @ X3 @ Y2 ) )
% 0.31/0.46 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodE
% 0.31/0.46 thf(fact_292_case__prodE,axiom,
% 0.31/0.46 ! [C2: state > state > $o,P3: produc1115495963_state] :
% 0.31/0.46 ( ( produc789892016tate_o @ C2 @ P3 )
% 0.31/0.46 => ~ ! [X3: state,Y2: state] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( produc64584659_state @ X3 @ Y2 ) )
% 0.31/0.46 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodE
% 0.31/0.46 thf(fact_293_case__prodE,axiom,
% 0.31/0.46 ! [C2: nat > nat > $o,P3: product_prod_nat_nat] :
% 0.31/0.46 ( ( produc949581770_nat_o @ C2 @ P3 )
% 0.31/0.46 => ~ ! [X3: nat,Y2: nat] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( product_Pair_nat_nat @ X3 @ Y2 ) )
% 0.31/0.46 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodE
% 0.31/0.46 thf(fact_294_total__on__def,axiom,
% 0.31/0.46 ( total_on_state
% 0.31/0.46 = ( ^ [A5: set_state,R3: set_Pr795498619_state] :
% 0.31/0.46 ! [X: state] :
% 0.31/0.46 ( ( member_state @ X @ A5 )
% 0.31/0.46 => ! [Y5: state] :
% 0.31/0.46 ( ( member_state @ Y5 @ A5 )
% 0.31/0.46 => ( ( X != Y5 )
% 0.31/0.46 => ( ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ R3 )
% 0.31/0.46 | ( member1389040324_state @ ( produc64584659_state @ Y5 @ X ) @ R3 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_def
% 0.31/0.46 thf(fact_295_total__on__def,axiom,
% 0.31/0.46 ( total_on_nat
% 0.31/0.46 = ( ^ [A5: set_nat,R3: set_Pr1986765409at_nat] :
% 0.31/0.46 ! [X: nat] :
% 0.31/0.46 ( ( member_nat @ X @ A5 )
% 0.31/0.46 => ! [Y5: nat] :
% 0.31/0.46 ( ( member_nat @ Y5 @ A5 )
% 0.31/0.46 => ( ( X != Y5 )
% 0.31/0.46 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ R3 )
% 0.31/0.46 | ( member701585322at_nat @ ( product_Pair_nat_nat @ Y5 @ X ) @ R3 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_def
% 0.31/0.46 thf(fact_296_total__onI,axiom,
% 0.31/0.46 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state] :
% 0.31/0.46 ( ! [X3: produc1115495963_state,Y2: produc1115495963_state] :
% 0.31/0.46 ( ( member1389040324_state @ X3 @ A2 )
% 0.31/0.46 => ( ( member1389040324_state @ Y2 @ A2 )
% 0.31/0.46 => ( ( X3 != Y2 )
% 0.31/0.46 => ( ( member768948240_state @ ( produc1964772951_state @ X3 @ Y2 ) @ R )
% 0.31/0.46 | ( member768948240_state @ ( produc1964772951_state @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.31/0.46 => ( total_1316653983_state @ A2 @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_onI
% 0.31/0.46 thf(fact_297_total__onI,axiom,
% 0.31/0.46 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat] :
% 0.31/0.46 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.31/0.46 ( ( member701585322at_nat @ X3 @ A2 )
% 0.31/0.46 => ( ( member701585322at_nat @ Y2 @ A2 )
% 0.31/0.46 => ( ( X3 != Y2 )
% 0.31/0.46 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ X3 @ Y2 ) @ R )
% 0.31/0.46 | ( member2027625872at_nat @ ( produc1168807639at_nat @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.31/0.46 => ( total_1775715973at_nat @ A2 @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_onI
% 0.31/0.46 thf(fact_298_total__onI,axiom,
% 0.31/0.46 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o] :
% 0.31/0.46 ( ! [X3: produc696469763tate_o,Y2: produc696469763tate_o] :
% 0.31/0.46 ( ( member1838112666tate_o @ X3 @ A2 )
% 0.31/0.46 => ( ( member1838112666tate_o @ Y2 @ A2 )
% 0.31/0.46 => ( ( X3 != Y2 )
% 0.31/0.46 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ X3 @ Y2 ) @ R )
% 0.31/0.46 | ( member1629320336tate_o @ ( produc1684562079tate_o @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.31/0.46 => ( total_795385983tate_o @ A2 @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_onI
% 0.31/0.46 thf(fact_299_total__onI,axiom,
% 0.31/0.46 ! [A2: set_state,R: set_Pr795498619_state] :
% 0.31/0.46 ( ! [X3: state,Y2: state] :
% 0.31/0.46 ( ( member_state @ X3 @ A2 )
% 0.31/0.46 => ( ( member_state @ Y2 @ A2 )
% 0.31/0.46 => ( ( X3 != Y2 )
% 0.31/0.46 => ( ( member1389040324_state @ ( produc64584659_state @ X3 @ Y2 ) @ R )
% 0.31/0.46 | ( member1389040324_state @ ( produc64584659_state @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.31/0.46 => ( total_on_state @ A2 @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_onI
% 0.31/0.46 thf(fact_300_total__onI,axiom,
% 0.31/0.46 ! [A2: set_nat,R: set_Pr1986765409at_nat] :
% 0.31/0.46 ( ! [X3: nat,Y2: nat] :
% 0.31/0.46 ( ( member_nat @ X3 @ A2 )
% 0.31/0.46 => ( ( member_nat @ Y2 @ A2 )
% 0.31/0.46 => ( ( X3 != Y2 )
% 0.31/0.46 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R )
% 0.31/0.46 | ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ X3 ) @ R ) ) ) ) )
% 0.31/0.46 => ( total_on_nat @ A2 @ R ) ) ).
% 0.31/0.46
% 0.31/0.46 % total_onI
% 0.31/0.46 thf(fact_301_total__on__empty,axiom,
% 0.31/0.46 ! [R: set_Pr1986765409at_nat] : ( total_on_nat @ bot_bot_set_nat @ R ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_empty
% 0.31/0.46 thf(fact_302_total__on__empty,axiom,
% 0.31/0.46 ! [R: set_Pr1702239303tate_o] : ( total_795385983tate_o @ bot_bo170732493tate_o @ R ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_empty
% 0.31/0.46 thf(fact_303_total__on__empty,axiom,
% 0.31/0.46 ! [R: set_Pr1490359111at_nat] : ( total_1775715973at_nat @ bot_bo2130386637at_nat @ R ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_empty
% 0.31/0.46 thf(fact_304_total__on__empty,axiom,
% 0.31/0.46 ! [R: set_Pr778812871_state] : ( total_1316653983_state @ bot_bo1625160935_state @ R ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_empty
% 0.31/0.46 thf(fact_305_case__prodE2,axiom,
% 0.31/0.46 ! [Q: $o > $o,P: state > state > $o,Z5: produc1115495963_state] :
% 0.31/0.46 ( ( Q @ ( produc789892016tate_o @ P @ Z5 ) )
% 0.31/0.46 => ~ ! [X3: state,Y2: state] :
% 0.31/0.46 ( ( Z5
% 0.31/0.46 = ( produc64584659_state @ X3 @ Y2 ) )
% 0.31/0.46 => ~ ( Q @ ( P @ X3 @ Y2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodE2
% 0.31/0.46 thf(fact_306_case__prodE2,axiom,
% 0.31/0.46 ! [Q: $o > $o,P: nat > nat > $o,Z5: product_prod_nat_nat] :
% 0.31/0.46 ( ( Q @ ( produc949581770_nat_o @ P @ Z5 ) )
% 0.31/0.46 => ~ ! [X3: nat,Y2: nat] :
% 0.31/0.46 ( ( Z5
% 0.31/0.46 = ( product_Pair_nat_nat @ X3 @ Y2 ) )
% 0.31/0.46 => ~ ( Q @ ( P @ X3 @ Y2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % case_prodE2
% 0.31/0.46 thf(fact_307_case__prod__eta,axiom,
% 0.31/0.46 ! [F: produc1115495963_state > $o] :
% 0.31/0.46 ( ( produc789892016tate_o
% 0.31/0.46 @ ^ [X: state,Y5: state] : ( F @ ( produc64584659_state @ X @ Y5 ) ) )
% 0.31/0.46 = F ) ).
% 0.31/0.46
% 0.31/0.46 % case_prod_eta
% 0.31/0.46 thf(fact_308_case__prod__eta,axiom,
% 0.31/0.46 ! [F: product_prod_nat_nat > $o] :
% 0.31/0.46 ( ( produc949581770_nat_o
% 0.31/0.46 @ ^ [X: nat,Y5: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y5 ) ) )
% 0.31/0.46 = F ) ).
% 0.31/0.46
% 0.31/0.46 % case_prod_eta
% 0.31/0.46 thf(fact_309_cond__case__prod__eta,axiom,
% 0.31/0.46 ! [F: state > state > $o,G: produc1115495963_state > $o] :
% 0.31/0.46 ( ! [X3: state,Y2: state] :
% 0.31/0.46 ( ( F @ X3 @ Y2 )
% 0.31/0.46 = ( G @ ( produc64584659_state @ X3 @ Y2 ) ) )
% 0.31/0.46 => ( ( produc789892016tate_o @ F )
% 0.31/0.46 = G ) ) ).
% 0.31/0.46
% 0.31/0.46 % cond_case_prod_eta
% 0.31/0.46 thf(fact_310_cond__case__prod__eta,axiom,
% 0.31/0.46 ! [F: nat > nat > $o,G: product_prod_nat_nat > $o] :
% 0.31/0.46 ( ! [X3: nat,Y2: nat] :
% 0.31/0.46 ( ( F @ X3 @ Y2 )
% 0.31/0.46 = ( G @ ( product_Pair_nat_nat @ X3 @ Y2 ) ) )
% 0.31/0.46 => ( ( produc949581770_nat_o @ F )
% 0.31/0.46 = G ) ) ).
% 0.31/0.46
% 0.31/0.46 % cond_case_prod_eta
% 0.31/0.46 thf(fact_311_lnear__order__on__empty,axiom,
% 0.31/0.46 order_130026331on_nat @ bot_bot_set_nat @ bot_bo2130386637at_nat ).
% 0.31/0.46
% 0.31/0.46 % lnear_order_on_empty
% 0.31/0.46 thf(fact_312_lnear__order__on__empty,axiom,
% 0.31/0.46 order_286167592_state @ bot_bot_set_state @ bot_bo1625160935_state ).
% 0.31/0.46
% 0.31/0.46 % lnear_order_on_empty
% 0.31/0.46 thf(fact_313_lnear__order__on__empty,axiom,
% 0.31/0.46 order_50454158tate_o @ bot_bo170732493tate_o @ bot_bo1714653363tate_o ).
% 0.31/0.46
% 0.31/0.46 % lnear_order_on_empty
% 0.31/0.46 thf(fact_314_lnear__order__on__empty,axiom,
% 0.31/0.46 order_721919926at_nat @ bot_bo2130386637at_nat @ bot_bo34127283at_nat ).
% 0.31/0.46
% 0.31/0.46 % lnear_order_on_empty
% 0.31/0.46 thf(fact_315_lnear__order__on__empty,axiom,
% 0.31/0.46 order_178668240_state @ bot_bo1625160935_state @ bot_bo1331673139_state ).
% 0.31/0.46
% 0.31/0.46 % lnear_order_on_empty
% 0.31/0.46 thf(fact_316_refl__on__empty,axiom,
% 0.31/0.46 refl_on_nat @ bot_bot_set_nat @ bot_bo2130386637at_nat ).
% 0.31/0.46
% 0.31/0.46 % refl_on_empty
% 0.31/0.46 thf(fact_317_refl__on__empty,axiom,
% 0.31/0.46 refl_on_state @ bot_bot_set_state @ bot_bo1625160935_state ).
% 0.31/0.46
% 0.31/0.46 % refl_on_empty
% 0.31/0.46 thf(fact_318_refl__on__empty,axiom,
% 0.31/0.46 refl_o489021252tate_o @ bot_bo170732493tate_o @ bot_bo1714653363tate_o ).
% 0.31/0.46
% 0.31/0.46 % refl_on_empty
% 0.31/0.46 thf(fact_319_refl__on__empty,axiom,
% 0.31/0.46 refl_o1619599232at_nat @ bot_bo2130386637at_nat @ bot_bo34127283at_nat ).
% 0.31/0.46
% 0.31/0.46 % refl_on_empty
% 0.31/0.46 thf(fact_320_refl__on__empty,axiom,
% 0.31/0.46 refl_o1438232218_state @ bot_bo1625160935_state @ bot_bo1331673139_state ).
% 0.31/0.46
% 0.31/0.46 % refl_on_empty
% 0.31/0.46 thf(fact_321_split__cong,axiom,
% 0.31/0.46 ! [Q5: produc1115495963_state,F: state > state > $o,G: state > state > $o,P3: produc1115495963_state] :
% 0.31/0.46 ( ! [X3: state,Y2: state] :
% 0.31/0.46 ( ( ( produc64584659_state @ X3 @ Y2 )
% 0.31/0.46 = Q5 )
% 0.31/0.46 => ( ( F @ X3 @ Y2 )
% 0.31/0.46 = ( G @ X3 @ Y2 ) ) )
% 0.31/0.46 => ( ( P3 = Q5 )
% 0.31/0.46 => ( ( produc789892016tate_o @ F @ P3 )
% 0.31/0.46 = ( produc789892016tate_o @ G @ Q5 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_cong
% 0.31/0.46 thf(fact_322_split__cong,axiom,
% 0.31/0.46 ! [Q5: product_prod_nat_nat,F: nat > nat > $o,G: nat > nat > $o,P3: product_prod_nat_nat] :
% 0.31/0.46 ( ! [X3: nat,Y2: nat] :
% 0.31/0.46 ( ( ( product_Pair_nat_nat @ X3 @ Y2 )
% 0.31/0.46 = Q5 )
% 0.31/0.46 => ( ( F @ X3 @ Y2 )
% 0.31/0.46 = ( G @ X3 @ Y2 ) ) )
% 0.31/0.46 => ( ( P3 = Q5 )
% 0.31/0.46 => ( ( produc949581770_nat_o @ F @ P3 )
% 0.31/0.46 = ( produc949581770_nat_o @ G @ Q5 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % split_cong
% 0.31/0.46 thf(fact_323_aboveS__def,axiom,
% 0.31/0.46 ( order_2027321734_state
% 0.31/0.46 = ( ^ [R3: set_Pr778812871_state,A3: produc1115495963_state] :
% 0.31/0.46 ( collec496201222_state
% 0.31/0.46 @ ^ [B7: produc1115495963_state] :
% 0.31/0.46 ( ( B7 != A3 )
% 0.31/0.46 & ( member768948240_state @ ( produc1964772951_state @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % aboveS_def
% 0.31/0.46 thf(fact_324_aboveS__def,axiom,
% 0.31/0.46 ( order_665764460at_nat
% 0.31/0.46 = ( ^ [R3: set_Pr1490359111at_nat,A3: product_prod_nat_nat] :
% 0.31/0.46 ( collec7649004at_nat
% 0.31/0.46 @ ^ [B7: product_prod_nat_nat] :
% 0.31/0.46 ( ( B7 != A3 )
% 0.31/0.46 & ( member2027625872at_nat @ ( produc1168807639at_nat @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % aboveS_def
% 0.31/0.46 thf(fact_325_aboveS__def,axiom,
% 0.31/0.46 ( order_1121016664tate_o
% 0.31/0.46 = ( ^ [R3: set_Pr1702239303tate_o,A3: produc696469763tate_o] :
% 0.31/0.46 ( collec1499596504tate_o
% 0.31/0.46 @ ^ [B7: produc696469763tate_o] :
% 0.31/0.46 ( ( B7 != A3 )
% 0.31/0.46 & ( member1629320336tate_o @ ( produc1684562079tate_o @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % aboveS_def
% 0.31/0.46 thf(fact_326_aboveS__def,axiom,
% 0.31/0.46 ( order_aboveS_state
% 0.31/0.46 = ( ^ [R3: set_Pr795498619_state,A3: state] :
% 0.31/0.46 ( collect_state
% 0.31/0.46 @ ^ [B7: state] :
% 0.31/0.46 ( ( B7 != A3 )
% 0.31/0.46 & ( member1389040324_state @ ( produc64584659_state @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % aboveS_def
% 0.31/0.46 thf(fact_327_aboveS__def,axiom,
% 0.31/0.46 ( order_aboveS_nat
% 0.31/0.46 = ( ^ [R3: set_Pr1986765409at_nat,A3: nat] :
% 0.31/0.46 ( collect_nat
% 0.31/0.46 @ ^ [B7: nat] :
% 0.31/0.46 ( ( B7 != A3 )
% 0.31/0.46 & ( member701585322at_nat @ ( product_Pair_nat_nat @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % aboveS_def
% 0.31/0.46 thf(fact_328_internal__case__prod__def,axiom,
% 0.31/0.46 produc938968666tate_o = produc789892016tate_o ).
% 0.31/0.46
% 0.31/0.46 % internal_case_prod_def
% 0.31/0.46 thf(fact_329_internal__case__prod__def,axiom,
% 0.31/0.46 produc385877620_nat_o = produc949581770_nat_o ).
% 0.31/0.46
% 0.31/0.46 % internal_case_prod_def
% 0.31/0.46 thf(fact_330_mem__case__prodI2,axiom,
% 0.31/0.46 ! [P3: product_prod_nat_nat,Z5: produc1115495963_state,C2: nat > nat > set_Pr795498619_state] :
% 0.31/0.46 ( ! [A6: nat,B6: nat] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.31/0.46 => ( member1389040324_state @ Z5 @ ( C2 @ A6 @ B6 ) ) )
% 0.31/0.46 => ( member1389040324_state @ Z5 @ ( produc1654445_state @ C2 @ P3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_case_prodI2
% 0.31/0.46 thf(fact_331_mem__case__prodI2,axiom,
% 0.31/0.46 ! [P3: product_prod_nat_nat,Z5: product_prod_nat_nat,C2: nat > nat > set_Pr1986765409at_nat] :
% 0.31/0.46 ( ! [A6: nat,B6: nat] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.31/0.46 => ( member701585322at_nat @ Z5 @ ( C2 @ A6 @ B6 ) ) )
% 0.31/0.46 => ( member701585322at_nat @ Z5 @ ( produc1915186323at_nat @ C2 @ P3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_case_prodI2
% 0.31/0.46 thf(fact_332_mem__case__prodI2,axiom,
% 0.31/0.46 ! [P3: product_prod_nat_nat,Z5: produc696469763tate_o,C2: nat > nat > set_Pr1590995257tate_o] :
% 0.31/0.46 ( ! [A6: nat,B6: nat] :
% 0.31/0.46 ( ( P3
% 0.31/0.46 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 0.31/0.46 => ( member1838112666tate_o @ Z5 @ ( C2 @ A6 @ B6 ) ) )
% 0.31/0.46 => ( member1838112666tate_o @ Z5 @ ( produc1610543495tate_o @ C2 @ P3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_case_prodI2
% 0.31/0.46 thf(fact_333_termi__while,axiom,
% 0.31/0.46 ! [B2: state > $o,C2: com,F: nat > state,K: nat] :
% 0.31/0.46 ( ( termi @ ( while @ B2 @ C2 ) @ ( F @ K ) )
% 0.31/0.46 => ( ! [I: nat] : ( exec @ ( F @ I ) @ C2 @ ( F @ ( suc @ I ) ) )
% 0.31/0.46 => ? [I: nat] :
% 0.31/0.46 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % termi_while
% 0.31/0.46 thf(fact_334_termi__while__lemma,axiom,
% 0.31/0.46 ! [W: com,Fk: state,F: nat > state,K: nat,B2: state > $o,C2: com] :
% 0.31/0.46 ( ( termi @ W @ Fk )
% 0.31/0.46 => ( ( ( Fk
% 0.31/0.46 = ( F @ K ) )
% 0.31/0.46 & ( W
% 0.31/0.46 = ( while @ B2 @ C2 ) )
% 0.31/0.46 & ! [I: nat] : ( exec @ ( F @ I ) @ C2 @ ( F @ ( suc @ I ) ) ) )
% 0.31/0.46 => ? [I: nat] :
% 0.31/0.46 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % termi_while_lemma
% 0.31/0.46 thf(fact_335_execn_Ointros_I7_J,axiom,
% 0.31/0.46 ! [S2: state,N: nat,T2: state] :
% 0.31/0.46 ( ( execn @ S2 @ body @ N @ T2 )
% 0.31/0.46 => ( execn @ S2 @ call @ ( suc @ N ) @ T2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % execn.intros(7)
% 0.31/0.46 thf(fact_336_pred__nat__def,axiom,
% 0.31/0.46 ( pred_nat
% 0.31/0.46 = ( collec7649004at_nat
% 0.31/0.46 @ ( produc949581770_nat_o
% 0.31/0.46 @ ^ [M: nat,N2: nat] :
% 0.31/0.46 ( N2
% 0.31/0.46 = ( suc @ M ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % pred_nat_def
% 0.31/0.46 thf(fact_337_while__rule,axiom,
% 0.31/0.46 ! [S2: state,B2: state > $o,C2: com,N: nat,T2: state,P: state > $o] :
% 0.31/0.46 ( ( execn @ S2 @ ( while @ B2 @ C2 ) @ N @ T2 )
% 0.31/0.46 => ( ( P @ S2 )
% 0.31/0.46 => ( ! [S: state,S3: state] :
% 0.31/0.46 ( ( P @ S )
% 0.31/0.46 => ( ( B2 @ S )
% 0.31/0.46 => ( ( execn @ S @ C2 @ N @ S3 )
% 0.31/0.46 => ( P @ S3 ) ) ) )
% 0.31/0.46 => ( ( P @ T2 )
% 0.31/0.46 & ~ ( B2 @ T2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % while_rule
% 0.31/0.46 thf(fact_338_while__lemma,axiom,
% 0.31/0.46 ! [S2: state,W: com,N: nat,T2: state,B2: state > $o,C2: com,P: state > $o] :
% 0.31/0.46 ( ( execn @ S2 @ W @ N @ T2 )
% 0.31/0.46 => ( ( ( W
% 0.31/0.46 = ( while @ B2 @ C2 ) )
% 0.31/0.46 & ( P @ S2 )
% 0.31/0.46 & ! [S: state,S3: state] :
% 0.31/0.46 ( ( ( P @ S )
% 0.31/0.46 & ( B2 @ S )
% 0.31/0.46 & ( execn @ S @ C2 @ N @ S3 ) )
% 0.31/0.46 => ( P @ S3 ) ) )
% 0.31/0.46 => ( ( P @ T2 )
% 0.31/0.46 & ~ ( B2 @ T2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % while_lemma
% 0.31/0.46 thf(fact_339_execn_OWhileTrue,axiom,
% 0.31/0.46 ! [B2: state > $o,S2: state,C2: com,N: nat,T2: state,U2: state] :
% 0.31/0.46 ( ( B2 @ S2 )
% 0.31/0.46 => ( ( execn @ S2 @ C2 @ N @ T2 )
% 0.31/0.46 => ( ( execn @ T2 @ ( while @ B2 @ C2 ) @ N @ U2 )
% 0.31/0.46 => ( execn @ S2 @ ( while @ B2 @ C2 ) @ N @ U2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % execn.WhileTrue
% 0.31/0.46 thf(fact_340_execn_OWhileFalse,axiom,
% 0.31/0.46 ! [B2: state > $o,S2: state,C2: com,N: nat] :
% 0.31/0.46 ( ~ ( B2 @ S2 )
% 0.31/0.46 => ( execn @ S2 @ ( while @ B2 @ C2 ) @ N @ S2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % execn.WhileFalse
% 0.31/0.46 thf(fact_341_exec__iff__execn,axiom,
% 0.31/0.46 ( exec
% 0.31/0.46 = ( ^ [S4: state,C5: com,T3: state] :
% 0.31/0.46 ? [N2: nat] : ( execn @ S4 @ C5 @ N2 @ T3 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % exec_iff_execn
% 0.31/0.46 thf(fact_342_wf__pred__nat,axiom,
% 0.31/0.46 wf_nat @ pred_nat ).
% 0.31/0.46
% 0.31/0.46 % wf_pred_nat
% 0.31/0.46 thf(fact_343_termi_OSemi,axiom,
% 0.31/0.46 ! [C1: com,S0: state,C22: com] :
% 0.31/0.46 ( ( termi @ C1 @ S0 )
% 0.31/0.46 => ( ! [S1: state] :
% 0.31/0.46 ( ( exec @ S0 @ C1 @ S1 )
% 0.31/0.46 => ( termi @ C22 @ S1 ) )
% 0.31/0.46 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % termi.Semi
% 0.31/0.46 thf(fact_344_com_Oinject_I2_J,axiom,
% 0.31/0.46 ! [X21: com,X222: com,Y21: com,Y222: com] :
% 0.31/0.46 ( ( ( semi @ X21 @ X222 )
% 0.31/0.46 = ( semi @ Y21 @ Y222 ) )
% 0.31/0.46 = ( ( X21 = Y21 )
% 0.31/0.46 & ( X222 = Y222 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % com.inject(2)
% 0.31/0.46 thf(fact_345_execn_Ointros_I2_J,axiom,
% 0.31/0.46 ! [S0: state,C1: com,N: nat,S12: state,C22: com,S22: state] :
% 0.31/0.46 ( ( execn @ S0 @ C1 @ N @ S12 )
% 0.31/0.46 => ( ( execn @ S12 @ C22 @ N @ S22 )
% 0.31/0.46 => ( execn @ S0 @ ( semi @ C1 @ C22 ) @ N @ S22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % execn.intros(2)
% 0.31/0.46 thf(fact_346_com_Odistinct_I13_J,axiom,
% 0.31/0.46 ! [X21: com,X222: com,X41: state > $o,X42: com] :
% 0.31/0.46 ( ( semi @ X21 @ X222 )
% 0.31/0.46 != ( while @ X41 @ X42 ) ) ).
% 0.31/0.46
% 0.31/0.46 % com.distinct(13)
% 0.31/0.46 thf(fact_347_com_Odistinct_I15_J,axiom,
% 0.31/0.46 ! [X21: com,X222: com] :
% 0.31/0.46 ( ( semi @ X21 @ X222 )
% 0.31/0.46 != call ) ).
% 0.31/0.46
% 0.31/0.46 % com.distinct(15)
% 0.31/0.46 thf(fact_348_exec_OSemi,axiom,
% 0.31/0.46 ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 0.31/0.46 ( ( exec @ S0 @ C1 @ S12 )
% 0.31/0.46 => ( ( exec @ S12 @ C22 @ S22 )
% 0.31/0.46 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % exec.Semi
% 0.31/0.46 thf(fact_349_wf__less__than,axiom,
% 0.31/0.46 wf_nat @ less_than ).
% 0.31/0.46
% 0.31/0.46 % wf_less_than
% 0.31/0.46 thf(fact_350_total__on__less__than,axiom,
% 0.31/0.46 ! [A2: set_nat] : ( total_on_nat @ A2 @ less_than ) ).
% 0.31/0.46
% 0.31/0.46 % total_on_less_than
% 0.31/0.46 thf(fact_351_irrefl__less__than,axiom,
% 0.31/0.46 irrefl_nat @ less_than ).
% 0.31/0.46
% 0.31/0.46 % irrefl_less_than
% 0.31/0.46 thf(fact_352_trans__less__than,axiom,
% 0.31/0.46 trans_nat @ less_than ).
% 0.31/0.46
% 0.31/0.46 % trans_less_than
% 0.31/0.46 thf(fact_353_less__than__iff,axiom,
% 0.31/0.46 ! [X2: nat,Y3: nat] :
% 0.31/0.46 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ less_than )
% 0.31/0.46 = ( ord_less_nat @ X2 @ Y3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % less_than_iff
% 0.31/0.46
% 0.31/0.46 % Conjectures (3)
% 0.31/0.46 thf(conj_0,hypothesis,
% 0.31/0.46 ! [S6: state] :
% 0.31/0.46 ( ( pHoare382919414oare_a
% 0.31/0.46 @ ( insert2053719859tate_o
% 0.31/0.46 @ ( produc33908149tate_o
% 0.31/0.46 @ ^ [Z4: a,S4: state] :
% 0.31/0.46 ( ( pa @ Z4 @ S4 )
% 0.31/0.46 & ( member1389040324_state @ ( produc64584659_state @ S4 @ S6 ) @ r ) )
% 0.31/0.46 @ ( produc1948644831tate_o @ call @ qa ) )
% 0.31/0.46 @ bot_bo170732493tate_o )
% 0.31/0.46 @ ^ [Z4: a,S4: state] :
% 0.31/0.46 ( ( pa @ Z4 @ S4 )
% 0.31/0.46 & ( S4 = S6 ) )
% 0.31/0.46 @ body
% 0.31/0.46 @ qa )
% 0.31/0.46 & ( ( ! [S: state,T: state] :
% 0.31/0.46 ( ( exec @ S @ body @ T )
% 0.31/0.46 => ! [Z: a] :
% 0.31/0.46 ( ( ( pa @ Z @ S )
% 0.31/0.46 & ( member1389040324_state @ ( produc64584659_state @ S @ S6 ) @ r ) )
% 0.31/0.46 => ( qa @ Z @ T ) ) )
% 0.31/0.46 & ! [Z: a,S: state] :
% 0.31/0.46 ( ( ( pa @ Z @ S )
% 0.31/0.46 & ( member1389040324_state @ ( produc64584659_state @ S @ S6 ) @ r ) )
% 0.31/0.46 => ( termi @ body @ S ) ) )
% 0.31/0.46 => ( ! [S7: state,T4: state] :
% 0.31/0.46 ( ( exec @ S7 @ body @ T4 )
% 0.31/0.46 => ! [Z2: a] :
% 0.31/0.46 ( ( ( pa @ Z2 @ S7 )
% 0.31/0.46 & ( S7 = S6 ) )
% 0.31/0.46 => ( qa @ Z2 @ T4 ) ) )
% 0.31/0.46 & ! [Z2: a,S7: state] :
% 0.31/0.46 ( ( ( pa @ Z2 @ S7 )
% 0.31/0.46 & ( S7 = S6 ) )
% 0.31/0.46 => ( termi @ body @ S7 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(conj_1,hypothesis,
% 0.31/0.46 ! [Y4: state] :
% 0.31/0.46 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ x ) @ r )
% 0.31/0.46 => ( ! [S7: state,T4: state] :
% 0.31/0.46 ( ( exec @ S7 @ body @ T4 )
% 0.31/0.46 => ! [Z2: a] :
% 0.31/0.46 ( ( ( pa @ Z2 @ S7 )
% 0.31/0.46 & ( S7 = Y4 ) )
% 0.31/0.46 => ( qa @ Z2 @ T4 ) ) )
% 0.31/0.46 & ! [Z2: a,S7: state] :
% 0.31/0.46 ( ( ( pa @ Z2 @ S7 )
% 0.31/0.46 & ( S7 = Y4 ) )
% 0.31/0.46 => ( termi @ body @ S7 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(conj_2,conjecture,
% 0.31/0.46 ( ! [S: state,T: state] :
% 0.31/0.46 ( ~ ( exec @ S @ body @ T )
% 0.31/0.46 | ! [Z: a] :
% 0.31/0.46 ( ~ ( pa @ Z @ S )
% 0.31/0.46 | ( S != x )
% 0.31/0.46 | ( qa @ Z @ T ) ) )
% 0.31/0.46 & ! [Z: a,S: state] :
% 0.31/0.46 ( ~ ( pa @ Z @ S )
% 0.31/0.46 | ( S != x )
% 0.31/0.46 | ( termi @ body @ S ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 2.76/1.46 ---- Embedded in THF ---
% 2.76/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.76/1.46 %%% Generated on Tue Feb 24 08:26:12 EST 2026
% 2.76/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.76/1.46 %%% Logic specification used:
% 2.76/1.46 %%% thf(spec, logic, $$dhol).
% 2.76/1.46
% 2.76/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.H5mA5wl1hp/DTF2DTF16650.p
% See solution above
% 2.76/1.46 ------------------------
% 2.76/1.49 ---- Cleaned THF ---
% 2.76/1.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J_J,type,
% 2.76/1.49 set_Pr1702239303tate_o: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J,type,
% 2.76/1.49 produc1307154919tate_o: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J,type,
% 2.76/1.49 set_Pr1590995257tate_o: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J_J,type,
% 2.76/1.49 set_Pr778812871_state: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 2.76/1.49 produc696469763tate_o: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.76/1.49 set_Pr1490359111at_nat: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J,type,
% 2.76/1.49 produc1390548711_state: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.76/1.49 produc842455143at_nat: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 2.76/1.49 set_Pr1740974983tate_o: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J,type,
% 2.76/1.49 produc204914599tate_o: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J,type,
% 2.76/1.49 set_Pr795498619_state: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.76/1.49 set_Pr1986765409at_nat: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 2.76/1.49 produc1115495963_state: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.76/1.49 product_prod_nat_nat: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Set__Oset_It__PLang__Ostate_J,type,
% 2.76/1.49 set_state: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.76/1.49 set_nat: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__PLang__Ostate,type,
% 2.76/1.49 state: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__PLang__Ocom,type,
% 2.76/1.49 com: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_t__Nat__Onat,type,
% 2.76/1.49 nat: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(ty_n_tf__a,type,
% 2.76/1.49 a: $tType ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Nat_OSuc,type,
% 2.76/1.49 suc: nat > nat ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_OaboveS_001t__Nat__Onat,type,
% 2.76/1.49 order_aboveS_nat: set_Pr1986765409at_nat > nat > set_nat ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_OaboveS_001t__PLang__Ostate,type,
% 2.76/1.49 order_aboveS_state: set_Pr795498619_state > state > set_state ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_OaboveS_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 2.76/1.49 order_1121016664tate_o: set_Pr1702239303tate_o > produc696469763tate_o > set_Pr1590995257tate_o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_OaboveS_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.76/1.49 order_665764460at_nat: set_Pr1490359111at_nat > product_prod_nat_nat > set_Pr1986765409at_nat ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_OaboveS_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 2.76/1.49 order_2027321734_state: set_Pr778812871_state > produc1115495963_state > set_Pr795498619_state ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_Olinear__order__on_001t__Nat__Onat,type,
% 2.76/1.49 order_130026331on_nat: set_nat > set_Pr1986765409at_nat > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_Olinear__order__on_001t__PLang__Ostate,type,
% 2.76/1.49 order_286167592_state: set_state > set_Pr795498619_state > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_Olinear__order__on_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 2.76/1.49 order_50454158tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_Olinear__order__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.76/1.49 order_721919926at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Order__Relation_Olinear__order__on_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
% 2.76/1.49 order_178668240_state: set_Pr795498619_state > set_Pr778812871_state > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_M_062_It__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_M_Eo_J_J,type,
% 2.76/1.49 bot_bo2130564770te_o_o: ( a > state > $o ) > produc204914599tate_o > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 2.76/1.49 bot_bot_nat_nat_o: nat > nat > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__PLang__Ocom_M_062_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_M_Eo_J_J,type,
% 2.76/1.49 bot_bo935656620te_o_o: com > ( a > state > $o ) > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__PLang__Ostate_M_062_It__PLang__Ostate_M_Eo_J_J,type,
% 2.76/1.49 bot_bo51534648tate_o: state > state > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_M_Eo_J,type,
% 2.76/1.49 bot_bo250281208te_o_o: produc696469763tate_o > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 2.76/1.49 bot_bo513358416_nat_o: product_prod_nat_nat > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_M_Eo_J,type,
% 2.76/1.49 bot_bo446391478tate_o: produc1115495963_state > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.76/1.49 bot_bot_set_nat: set_nat ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__PLang__Ostate_J,type,
% 2.76/1.49 bot_bot_set_state: set_state ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J,type,
% 2.76/1.49 bot_bo170732493tate_o: set_Pr1590995257tate_o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.76/1.49 bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 2.76/1.49 bot_bo1692783091tate_o: set_Pr1740974983tate_o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J,type,
% 2.76/1.49 bot_bo1625160935_state: set_Pr795498619_state ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J_J,type,
% 2.76/1.49 bot_bo1714653363tate_o: set_Pr1702239303tate_o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.76/1.49 bot_bo34127283at_nat: set_Pr1490359111at_nat ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_Mt__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_J_J,type,
% 2.76/1.49 bot_bo1331673139_state: set_Pr778812871_state ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 2.76/1.49 ord_less_nat: nat > nat > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_PHoareTotal__Mirabelle__ynemugpbor_Othoare_001tf__a,type,
% 2.76/1.49 pHoare382919414oare_a: set_Pr1590995257tate_o > ( a > state > $o ) > com > ( a > state > $o ) > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_PHoare_Ohoare_001tf__a,type,
% 2.76/1.49 hoare_a: set_Pr1590995257tate_o > ( a > state > $o ) > com > ( a > state > $o ) > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_PLang_Obody,type,
% 2.76/1.49 body: com ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_PLang_Ocom_OCALL,type,
% 2.76/1.49 call: com ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_PLang_Ocom_OSemi,type,
% 2.76/1.49 semi: com > com > com ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_PLang_Ocom_OWhile,type,
% 2.76/1.49 while: ( state > $o ) > com > com ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_PLang_Oexec,type,
% 2.76/1.49 exec: state > com > state > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_PLang_Oexecn,type,
% 2.76/1.49 execn: state > com > nat > state > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_PTermi_Otermi,type,
% 2.76/1.49 termi: com > state > $o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_OPair_001_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_001t__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J,type,
% 2.76/1.49 produc33908149tate_o: ( a > state > $o ) > produc204914599tate_o > produc696469763tate_o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.76/1.49 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_OPair_001t__PLang__Ocom_001_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J,type,
% 2.76/1.49 produc1948644831tate_o: com > ( a > state > $o ) > produc204914599tate_o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_OPair_001t__PLang__Ostate_001t__PLang__Ostate,type,
% 2.76/1.49 produc64584659_state: state > state > produc1115495963_state ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_001t__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J,type,
% 2.76/1.49 produc1684562079tate_o: produc696469763tate_o > produc696469763tate_o > produc1307154919tate_o ).
% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J_001t__Product____Type__Oprod_It__PLang__Ostate_Mt__PLang__Ostate_J,type,
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% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_Ointernal__case__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
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% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_Ointernal__case__prod_001t__PLang__Ostate_001t__PLang__Ostate_001_Eo,type,
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% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_001t__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_001_Eo,type,
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% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
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% 2.76/1.49
% 2.76/1.49 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_Mt__Product____Type__Oprod_It__PLang__Ocom_M_062_Itf__a_M_062_It__PLang__Ostate_M_Eo_J_J_J_J_J,type,
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% 2.76/1.49 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_7_singleton__conv2,axiom,
% 2.76/1.49 ! [A: produc1115495963_state] :
% 2.76/1.49 ( ( collec496201222_state
% 2.76/1.49 @ ( ^ [Y: produc1115495963_state,Z3: produc1115495963_state] : ( Y = Z3 )
% 2.76/1.49 @ A ) )
% 2.76/1.49 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_8_singleton__conv2,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat] :
% 2.76/1.49 ( ( collec7649004at_nat
% 2.76/1.49 @ ( ^ [Y: product_prod_nat_nat,Z3: product_prod_nat_nat] : ( Y = Z3 )
% 2.76/1.49 @ A ) )
% 2.76/1.49 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_9_singleton__conv2,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o] :
% 2.76/1.49 ( ( collec1499596504tate_o
% 2.76/1.49 @ ( ^ [Y: produc696469763tate_o,Z3: produc696469763tate_o] : ( Y = Z3 )
% 2.76/1.49 @ A ) )
% 2.76/1.49 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_10_singletonI,axiom,
% 2.76/1.49 ! [A: produc1115495963_state] : ( member1389040324_state @ A @ ( insert311944171_state @ A @ bot_bo1625160935_state ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_11_singletonI,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_12_singletonI,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o] : ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_13_termi_Ointros_I7_J,axiom,
% 2.76/1.49 ! [S2: state] :
% 2.76/1.49 ( ( termi @ body @ S2 )
% 2.76/1.49 => ( termi @ call @ S2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_14_exec_Ointros_I7_J,axiom,
% 2.76/1.49 ! [S2: state,T2: state] :
% 2.76/1.49 ( ( exec @ S2 @ body @ T2 )
% 2.76/1.49 => ( exec @ S2 @ call @ T2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_15_thoare_OCall,axiom,
% 2.76/1.49 ! [R: set_Pr795498619_state,P: a > state > $o,Q: a > state > $o] :
% 2.76/1.49 ( ( wf_state @ R )
% 2.76/1.49 => ( ! [S3: state] :
% 2.76/1.49 ( pHoare382919414oare_a
% 2.76/1.49 @ ( insert2053719859tate_o
% 2.76/1.49 @ ( produc33908149tate_o
% 2.76/1.49 @ ^ [Z4: a,S4: state] :
% 2.76/1.49 ( ( P @ Z4 @ S4 )
% 2.76/1.49 & ( member1389040324_state @ ( produc64584659_state @ S4 @ S3 ) @ R ) )
% 2.76/1.49 @ ( produc1948644831tate_o @ call @ Q ) )
% 2.76/1.49 @ bot_bo170732493tate_o )
% 2.76/1.49 @ ^ [Z4: a,S4: state] :
% 2.76/1.49 ( ( P @ Z4 @ S4 )
% 2.76/1.49 & ( S4 = S3 ) )
% 2.76/1.49 @ body
% 2.76/1.49 @ Q )
% 2.76/1.49 => ( pHoare382919414oare_a @ bot_bo170732493tate_o @ P @ call @ Q ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_16_insertCI,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,B: set_Pr795498619_state,B2: produc1115495963_state] :
% 2.76/1.49 ( ( ~ ( member1389040324_state @ A @ B )
% 2.76/1.49 => ( A = B2 ) )
% 2.76/1.49 => ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ B ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_17_insertCI,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,B2: product_prod_nat_nat] :
% 2.76/1.49 ( ( ~ ( member701585322at_nat @ A @ B )
% 2.76/1.49 => ( A = B2 ) )
% 2.76/1.49 => ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ B ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_18_insertCI,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,B: set_Pr1590995257tate_o,B2: produc696469763tate_o] :
% 2.76/1.49 ( ( ~ ( member1838112666tate_o @ A @ B )
% 2.76/1.49 => ( A = B2 ) )
% 2.76/1.49 => ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ B ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_19_insert__iff,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,B2: produc1115495963_state,A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ A2 ) )
% 2.76/1.49 = ( ( A = B2 )
% 2.76/1.49 | ( member1389040324_state @ A @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_20_insert__iff,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ A2 ) )
% 2.76/1.49 = ( ( A = B2 )
% 2.76/1.49 | ( member701585322at_nat @ A @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_21_insert__iff,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,B2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ A2 ) )
% 2.76/1.49 = ( ( A = B2 )
% 2.76/1.49 | ( member1838112666tate_o @ A @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_22_insert__absorb2,axiom,
% 2.76/1.49 ! [X2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( insert2053719859tate_o @ X2 @ ( insert2053719859tate_o @ X2 @ A2 ) )
% 2.76/1.49 = ( insert2053719859tate_o @ X2 @ A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_23_insert__absorb2,axiom,
% 2.76/1.49 ! [X2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( insert271595217at_nat @ X2 @ ( insert271595217at_nat @ X2 @ A2 ) )
% 2.76/1.49 = ( insert271595217at_nat @ X2 @ A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_24_insert__absorb2,axiom,
% 2.76/1.49 ! [X2: produc1115495963_state,A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( insert311944171_state @ X2 @ ( insert311944171_state @ X2 @ A2 ) )
% 2.76/1.49 = ( insert311944171_state @ X2 @ A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_25_hoare_OCall,axiom,
% 2.76/1.49 ! [P: a > state > $o,Q: a > state > $o] :
% 2.76/1.49 ( ( hoare_a @ ( insert2053719859tate_o @ ( produc33908149tate_o @ P @ ( produc1948644831tate_o @ call @ Q ) ) @ bot_bo170732493tate_o ) @ P @ body @ Q )
% 2.76/1.49 => ( hoare_a @ bot_bo170732493tate_o @ P @ call @ Q ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_26_empty__iff,axiom,
% 2.76/1.49 ! [C2: produc696469763tate_o] :
% 2.76/1.49 ~ ( member1838112666tate_o @ C2 @ bot_bo170732493tate_o ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_27_empty__iff,axiom,
% 2.76/1.49 ! [C2: product_prod_nat_nat] :
% 2.76/1.49 ~ ( member701585322at_nat @ C2 @ bot_bo2130386637at_nat ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_28_empty__iff,axiom,
% 2.76/1.49 ! [C2: produc1115495963_state] :
% 2.76/1.49 ~ ( member1389040324_state @ C2 @ bot_bo1625160935_state ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_29_all__not__in__conv,axiom,
% 2.76/1.49 ! [A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( ! [X: produc696469763tate_o] :
% 2.76/1.49 ~ ( member1838112666tate_o @ X @ A2 ) )
% 2.76/1.49 = ( A2 = bot_bo170732493tate_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_30_all__not__in__conv,axiom,
% 2.76/1.49 ! [A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( ! [X: product_prod_nat_nat] :
% 2.76/1.49 ~ ( member701585322at_nat @ X @ A2 ) )
% 2.76/1.49 = ( A2 = bot_bo2130386637at_nat ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_31_all__not__in__conv,axiom,
% 2.76/1.49 ! [A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( ! [X: produc1115495963_state] :
% 2.76/1.49 ~ ( member1389040324_state @ X @ A2 ) )
% 2.76/1.49 = ( A2 = bot_bo1625160935_state ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_32_empty__Collect__eq,axiom,
% 2.76/1.49 ! [P: produc696469763tate_o > $o] :
% 2.76/1.49 ( ( bot_bo170732493tate_o
% 2.76/1.49 = ( collec1499596504tate_o @ P ) )
% 2.76/1.49 = ( ! [X: produc696469763tate_o] :
% 2.76/1.49 ~ ( P @ X ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_33_empty__Collect__eq,axiom,
% 2.76/1.49 ! [P: product_prod_nat_nat > $o] :
% 2.76/1.49 ( ( bot_bo2130386637at_nat
% 2.76/1.49 = ( collec7649004at_nat @ P ) )
% 2.76/1.49 = ( ! [X: product_prod_nat_nat] :
% 2.76/1.49 ~ ( P @ X ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_34_empty__Collect__eq,axiom,
% 2.76/1.49 ! [P: produc1115495963_state > $o] :
% 2.76/1.49 ( ( bot_bo1625160935_state
% 2.76/1.49 = ( collec496201222_state @ P ) )
% 2.76/1.49 = ( ! [X: produc1115495963_state] :
% 2.76/1.49 ~ ( P @ X ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_35_Collect__empty__eq,axiom,
% 2.76/1.49 ! [P: produc696469763tate_o > $o] :
% 2.76/1.49 ( ( ( collec1499596504tate_o @ P )
% 2.76/1.49 = bot_bo170732493tate_o )
% 2.76/1.49 = ( ! [X: produc696469763tate_o] :
% 2.76/1.49 ~ ( P @ X ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_36_Collect__empty__eq,axiom,
% 2.76/1.49 ! [P: product_prod_nat_nat > $o] :
% 2.76/1.49 ( ( ( collec7649004at_nat @ P )
% 2.76/1.49 = bot_bo2130386637at_nat )
% 2.76/1.49 = ( ! [X: product_prod_nat_nat] :
% 2.76/1.49 ~ ( P @ X ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_37_Collect__empty__eq,axiom,
% 2.76/1.49 ! [P: produc1115495963_state > $o] :
% 2.76/1.49 ( ( ( collec496201222_state @ P )
% 2.76/1.49 = bot_bo1625160935_state )
% 2.76/1.49 = ( ! [X: produc1115495963_state] :
% 2.76/1.49 ~ ( P @ X ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_38_ex__in__conv,axiom,
% 2.76/1.49 ! [A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( ? [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ A2 ) )
% 2.76/1.49 = ( A2 != bot_bo170732493tate_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_39_ex__in__conv,axiom,
% 2.76/1.49 ! [A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( ? [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ A2 ) )
% 2.76/1.49 = ( A2 != bot_bo2130386637at_nat ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_40_ex__in__conv,axiom,
% 2.76/1.49 ! [A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( ? [X: produc1115495963_state] : ( member1389040324_state @ X @ A2 ) )
% 2.76/1.49 = ( A2 != bot_bo1625160935_state ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_41_equals0I,axiom,
% 2.76/1.49 ! [A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ! [Y2: produc696469763tate_o] :
% 2.76/1.49 ~ ( member1838112666tate_o @ Y2 @ A2 )
% 2.76/1.49 => ( A2 = bot_bo170732493tate_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_42_equals0I,axiom,
% 2.76/1.49 ! [A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ! [Y2: product_prod_nat_nat] :
% 2.76/1.49 ~ ( member701585322at_nat @ Y2 @ A2 )
% 2.76/1.49 => ( A2 = bot_bo2130386637at_nat ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_43_equals0I,axiom,
% 2.76/1.49 ! [A2: set_Pr795498619_state] :
% 2.76/1.49 ( ! [Y2: produc1115495963_state] :
% 2.76/1.49 ~ ( member1389040324_state @ Y2 @ A2 )
% 2.76/1.49 => ( A2 = bot_bo1625160935_state ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_44_equals0D,axiom,
% 2.76/1.49 ! [A2: set_Pr1590995257tate_o,A: produc696469763tate_o] :
% 2.76/1.49 ( ( A2 = bot_bo170732493tate_o )
% 2.76/1.49 => ~ ( member1838112666tate_o @ A @ A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_45_equals0D,axiom,
% 2.76/1.49 ! [A2: set_Pr1986765409at_nat,A: product_prod_nat_nat] :
% 2.76/1.49 ( ( A2 = bot_bo2130386637at_nat )
% 2.76/1.49 => ~ ( member701585322at_nat @ A @ A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_46_equals0D,axiom,
% 2.76/1.49 ! [A2: set_Pr795498619_state,A: produc1115495963_state] :
% 2.76/1.49 ( ( A2 = bot_bo1625160935_state )
% 2.76/1.49 => ~ ( member1389040324_state @ A @ A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_47_emptyE,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o] :
% 2.76/1.49 ~ ( member1838112666tate_o @ A @ bot_bo170732493tate_o ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_48_emptyE,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat] :
% 2.76/1.49 ~ ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_49_emptyE,axiom,
% 2.76/1.49 ! [A: produc1115495963_state] :
% 2.76/1.49 ~ ( member1389040324_state @ A @ bot_bo1625160935_state ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_50_mk__disjoint__insert,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( member1389040324_state @ A @ A2 )
% 2.76/1.49 => ? [B3: set_Pr795498619_state] :
% 2.76/1.49 ( ( A2
% 2.76/1.49 = ( insert311944171_state @ A @ B3 ) )
% 2.76/1.49 & ~ ( member1389040324_state @ A @ B3 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_51_mk__disjoint__insert,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ A @ A2 )
% 2.76/1.49 => ? [B3: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( A2
% 2.76/1.49 = ( insert271595217at_nat @ A @ B3 ) )
% 2.76/1.49 & ~ ( member701585322at_nat @ A @ B3 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_52_mk__disjoint__insert,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ A @ A2 )
% 2.76/1.49 => ? [B3: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( A2
% 2.76/1.49 = ( insert2053719859tate_o @ A @ B3 ) )
% 2.76/1.49 & ~ ( member1838112666tate_o @ A @ B3 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_53_insert__commute,axiom,
% 2.76/1.49 ! [X2: produc696469763tate_o,Y3: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( insert2053719859tate_o @ X2 @ ( insert2053719859tate_o @ Y3 @ A2 ) )
% 2.76/1.49 = ( insert2053719859tate_o @ Y3 @ ( insert2053719859tate_o @ X2 @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_54_insert__commute,axiom,
% 2.76/1.49 ! [X2: product_prod_nat_nat,Y3: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( insert271595217at_nat @ X2 @ ( insert271595217at_nat @ Y3 @ A2 ) )
% 2.76/1.49 = ( insert271595217at_nat @ Y3 @ ( insert271595217at_nat @ X2 @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_55_insert__commute,axiom,
% 2.76/1.49 ! [X2: produc1115495963_state,Y3: produc1115495963_state,A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( insert311944171_state @ X2 @ ( insert311944171_state @ Y3 @ A2 ) )
% 2.76/1.49 = ( insert311944171_state @ Y3 @ ( insert311944171_state @ X2 @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_56_insert__eq__iff,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,A2: set_Pr795498619_state,B2: produc1115495963_state,B: set_Pr795498619_state] :
% 2.76/1.49 ( ~ ( member1389040324_state @ A @ A2 )
% 2.76/1.49 => ( ~ ( member1389040324_state @ B2 @ B )
% 2.76/1.49 => ( ( ( insert311944171_state @ A @ A2 )
% 2.76/1.49 = ( insert311944171_state @ B2 @ B ) )
% 2.76/1.49 = ( ( ( A = B2 )
% 2.76/1.49 => ( A2 = B ) )
% 2.76/1.49 & ( ( A != B2 )
% 2.76/1.49 => ? [C3: set_Pr795498619_state] :
% 2.76/1.49 ( ( A2
% 2.76/1.49 = ( insert311944171_state @ B2 @ C3 ) )
% 2.76/1.49 & ~ ( member1389040324_state @ B2 @ C3 )
% 2.76/1.49 & ( B
% 2.76/1.49 = ( insert311944171_state @ A @ C3 ) )
% 2.76/1.49 & ~ ( member1389040324_state @ A @ C3 ) ) ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_57_insert__eq__iff,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat,B2: product_prod_nat_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ~ ( member701585322at_nat @ A @ A2 )
% 2.76/1.49 => ( ~ ( member701585322at_nat @ B2 @ B )
% 2.76/1.49 => ( ( ( insert271595217at_nat @ A @ A2 )
% 2.76/1.49 = ( insert271595217at_nat @ B2 @ B ) )
% 2.76/1.49 = ( ( ( A = B2 )
% 2.76/1.49 => ( A2 = B ) )
% 2.76/1.49 & ( ( A != B2 )
% 2.76/1.49 => ? [C3: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( A2
% 2.76/1.49 = ( insert271595217at_nat @ B2 @ C3 ) )
% 2.76/1.49 & ~ ( member701585322at_nat @ B2 @ C3 )
% 2.76/1.49 & ( B
% 2.76/1.49 = ( insert271595217at_nat @ A @ C3 ) )
% 2.76/1.49 & ~ ( member701585322at_nat @ A @ C3 ) ) ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_58_insert__eq__iff,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o,B2: produc696469763tate_o,B: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ~ ( member1838112666tate_o @ A @ A2 )
% 2.76/1.49 => ( ~ ( member1838112666tate_o @ B2 @ B )
% 2.76/1.49 => ( ( ( insert2053719859tate_o @ A @ A2 )
% 2.76/1.49 = ( insert2053719859tate_o @ B2 @ B ) )
% 2.76/1.49 = ( ( ( A = B2 )
% 2.76/1.49 => ( A2 = B ) )
% 2.76/1.49 & ( ( A != B2 )
% 2.76/1.49 => ? [C3: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( A2
% 2.76/1.49 = ( insert2053719859tate_o @ B2 @ C3 ) )
% 2.76/1.49 & ~ ( member1838112666tate_o @ B2 @ C3 )
% 2.76/1.49 & ( B
% 2.76/1.49 = ( insert2053719859tate_o @ A @ C3 ) )
% 2.76/1.49 & ~ ( member1838112666tate_o @ A @ C3 ) ) ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_59_insert__absorb,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( member1389040324_state @ A @ A2 )
% 2.76/1.49 => ( ( insert311944171_state @ A @ A2 )
% 2.76/1.49 = A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_60_insert__absorb,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ A @ A2 )
% 2.76/1.49 => ( ( insert271595217at_nat @ A @ A2 )
% 2.76/1.49 = A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_61_insert__absorb,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ A @ A2 )
% 2.76/1.49 => ( ( insert2053719859tate_o @ A @ A2 )
% 2.76/1.49 = A2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_62_insert__ident,axiom,
% 2.76/1.49 ! [X2: produc1115495963_state,A2: set_Pr795498619_state,B: set_Pr795498619_state] :
% 2.76/1.49 ( ~ ( member1389040324_state @ X2 @ A2 )
% 2.76/1.49 => ( ~ ( member1389040324_state @ X2 @ B )
% 2.76/1.49 => ( ( ( insert311944171_state @ X2 @ A2 )
% 2.76/1.49 = ( insert311944171_state @ X2 @ B ) )
% 2.76/1.49 = ( A2 = B ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_63_insert__ident,axiom,
% 2.76/1.49 ! [X2: product_prod_nat_nat,A2: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ~ ( member701585322at_nat @ X2 @ A2 )
% 2.76/1.49 => ( ~ ( member701585322at_nat @ X2 @ B )
% 2.76/1.49 => ( ( ( insert271595217at_nat @ X2 @ A2 )
% 2.76/1.49 = ( insert271595217at_nat @ X2 @ B ) )
% 2.76/1.49 = ( A2 = B ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_64_insert__ident,axiom,
% 2.76/1.49 ! [X2: produc696469763tate_o,A2: set_Pr1590995257tate_o,B: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ~ ( member1838112666tate_o @ X2 @ A2 )
% 2.76/1.49 => ( ~ ( member1838112666tate_o @ X2 @ B )
% 2.76/1.49 => ( ( ( insert2053719859tate_o @ X2 @ A2 )
% 2.76/1.49 = ( insert2053719859tate_o @ X2 @ B ) )
% 2.76/1.49 = ( A2 = B ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_65_Set_Oset__insert,axiom,
% 2.76/1.49 ! [X2: produc1115495963_state,A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( member1389040324_state @ X2 @ A2 )
% 2.76/1.49 => ~ ! [B3: set_Pr795498619_state] :
% 2.76/1.49 ( ( A2
% 2.76/1.49 = ( insert311944171_state @ X2 @ B3 ) )
% 2.76/1.49 => ( member1389040324_state @ X2 @ B3 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_66_Set_Oset__insert,axiom,
% 2.76/1.49 ! [X2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ X2 @ A2 )
% 2.76/1.49 => ~ ! [B3: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( A2
% 2.76/1.49 = ( insert271595217at_nat @ X2 @ B3 ) )
% 2.76/1.49 => ( member701585322at_nat @ X2 @ B3 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_67_Set_Oset__insert,axiom,
% 2.76/1.49 ! [X2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ X2 @ A2 )
% 2.76/1.49 => ~ ! [B3: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( A2
% 2.76/1.49 = ( insert2053719859tate_o @ X2 @ B3 ) )
% 2.76/1.49 => ( member1838112666tate_o @ X2 @ B3 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_68_insertI2,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,B: set_Pr795498619_state,B2: produc1115495963_state] :
% 2.76/1.49 ( ( member1389040324_state @ A @ B )
% 2.76/1.49 => ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ B ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_69_insertI2,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,B2: product_prod_nat_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ A @ B )
% 2.76/1.49 => ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ B ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_70_insertI2,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,B: set_Pr1590995257tate_o,B2: produc696469763tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ A @ B )
% 2.76/1.49 => ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ B ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_71_insertI1,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,B: set_Pr795498619_state] : ( member1389040324_state @ A @ ( insert311944171_state @ A @ B ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_72_insertI1,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ B ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_73_insertI1,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,B: set_Pr1590995257tate_o] : ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ A @ B ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_74_insertE,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,B2: produc1115495963_state,A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( member1389040324_state @ A @ ( insert311944171_state @ B2 @ A2 ) )
% 2.76/1.49 => ( ( A != B2 )
% 2.76/1.49 => ( member1389040324_state @ A @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_75_insertE,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B2 @ A2 ) )
% 2.76/1.49 => ( ( A != B2 )
% 2.76/1.49 => ( member701585322at_nat @ A @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_76_insertE,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,B2: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ A @ ( insert2053719859tate_o @ B2 @ A2 ) )
% 2.76/1.49 => ( ( A != B2 )
% 2.76/1.49 => ( member1838112666tate_o @ A @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_77_empty__def,axiom,
% 2.76/1.49 ( bot_bo170732493tate_o
% 2.76/1.49 = ( collec1499596504tate_o
% 2.76/1.49 @ ^ [X: produc696469763tate_o] : $false ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_78_empty__def,axiom,
% 2.76/1.49 ( bot_bo2130386637at_nat
% 2.76/1.49 = ( collec7649004at_nat
% 2.76/1.49 @ ^ [X: product_prod_nat_nat] : $false ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_79_empty__def,axiom,
% 2.76/1.49 ( bot_bo1625160935_state
% 2.76/1.49 = ( collec496201222_state
% 2.76/1.49 @ ^ [X: produc1115495963_state] : $false ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_80_insert__Collect,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,P: produc1115495963_state > $o] :
% 2.76/1.49 ( ( insert311944171_state @ A @ ( collec496201222_state @ P ) )
% 2.76/1.49 = ( collec496201222_state
% 2.76/1.49 @ ^ [U: produc1115495963_state] :
% 2.76/1.49 ( ( U != A )
% 2.76/1.49 => ( P @ U ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_81_insert__Collect,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 2.76/1.49 ( ( insert271595217at_nat @ A @ ( collec7649004at_nat @ P ) )
% 2.76/1.49 = ( collec7649004at_nat
% 2.76/1.49 @ ^ [U: product_prod_nat_nat] :
% 2.76/1.49 ( ( U != A )
% 2.76/1.49 => ( P @ U ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_82_insert__Collect,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,P: produc696469763tate_o > $o] :
% 2.76/1.49 ( ( insert2053719859tate_o @ A @ ( collec1499596504tate_o @ P ) )
% 2.76/1.49 = ( collec1499596504tate_o
% 2.76/1.49 @ ^ [U: produc696469763tate_o] :
% 2.76/1.49 ( ( U != A )
% 2.76/1.49 => ( P @ U ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_83_insert__compr,axiom,
% 2.76/1.49 ( insert311944171_state
% 2.76/1.49 = ( ^ [A3: produc1115495963_state,B4: set_Pr795498619_state] :
% 2.76/1.49 ( collec496201222_state
% 2.76/1.49 @ ^ [X: produc1115495963_state] :
% 2.76/1.49 ( ( X = A3 )
% 2.76/1.49 | ( member1389040324_state @ X @ B4 ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_84_insert__compr,axiom,
% 2.76/1.49 ( insert271595217at_nat
% 2.76/1.49 = ( ^ [A3: product_prod_nat_nat,B4: set_Pr1986765409at_nat] :
% 2.76/1.49 ( collec7649004at_nat
% 2.76/1.49 @ ^ [X: product_prod_nat_nat] :
% 2.76/1.49 ( ( X = A3 )
% 2.76/1.49 | ( member701585322at_nat @ X @ B4 ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_85_insert__compr,axiom,
% 2.76/1.49 ( insert2053719859tate_o
% 2.76/1.49 = ( ^ [A3: produc696469763tate_o,B4: set_Pr1590995257tate_o] :
% 2.76/1.49 ( collec1499596504tate_o
% 2.76/1.49 @ ^ [X: produc696469763tate_o] :
% 2.76/1.49 ( ( X = A3 )
% 2.76/1.49 | ( member1838112666tate_o @ X @ B4 ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_86_singleton__inject,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,B2: produc696469763tate_o] :
% 2.76/1.49 ( ( ( insert2053719859tate_o @ A @ bot_bo170732493tate_o )
% 2.76/1.49 = ( insert2053719859tate_o @ B2 @ bot_bo170732493tate_o ) )
% 2.76/1.49 => ( A = B2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_87_singleton__inject,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 2.76/1.49 ( ( ( insert271595217at_nat @ A @ bot_bo2130386637at_nat )
% 2.76/1.49 = ( insert271595217at_nat @ B2 @ bot_bo2130386637at_nat ) )
% 2.76/1.49 => ( A = B2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_88_singleton__inject,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,B2: produc1115495963_state] :
% 2.76/1.49 ( ( ( insert311944171_state @ A @ bot_bo1625160935_state )
% 2.76/1.49 = ( insert311944171_state @ B2 @ bot_bo1625160935_state ) )
% 2.76/1.49 => ( A = B2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_89_insert__not__empty,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( insert2053719859tate_o @ A @ A2 )
% 2.76/1.49 != bot_bo170732493tate_o ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_90_insert__not__empty,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( insert271595217at_nat @ A @ A2 )
% 2.76/1.49 != bot_bo2130386637at_nat ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_91_insert__not__empty,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( insert311944171_state @ A @ A2 )
% 2.76/1.49 != bot_bo1625160935_state ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_92_doubleton__eq__iff,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,B2: produc696469763tate_o,C2: produc696469763tate_o,D: produc696469763tate_o] :
% 2.76/1.49 ( ( ( insert2053719859tate_o @ A @ ( insert2053719859tate_o @ B2 @ bot_bo170732493tate_o ) )
% 2.76/1.49 = ( insert2053719859tate_o @ C2 @ ( insert2053719859tate_o @ D @ bot_bo170732493tate_o ) ) )
% 2.76/1.49 = ( ( ( A = C2 )
% 2.76/1.49 & ( B2 = D ) )
% 2.76/1.49 | ( ( A = D )
% 2.76/1.49 & ( B2 = C2 ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_93_doubleton__eq__iff,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,C2: product_prod_nat_nat,D: product_prod_nat_nat] :
% 2.76/1.49 ( ( ( insert271595217at_nat @ A @ ( insert271595217at_nat @ B2 @ bot_bo2130386637at_nat ) )
% 2.76/1.49 = ( insert271595217at_nat @ C2 @ ( insert271595217at_nat @ D @ bot_bo2130386637at_nat ) ) )
% 2.76/1.49 = ( ( ( A = C2 )
% 2.76/1.49 & ( B2 = D ) )
% 2.76/1.49 | ( ( A = D )
% 2.76/1.49 & ( B2 = C2 ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_94_doubleton__eq__iff,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,B2: produc1115495963_state,C2: produc1115495963_state,D: produc1115495963_state] :
% 2.76/1.49 ( ( ( insert311944171_state @ A @ ( insert311944171_state @ B2 @ bot_bo1625160935_state ) )
% 2.76/1.49 = ( insert311944171_state @ C2 @ ( insert311944171_state @ D @ bot_bo1625160935_state ) ) )
% 2.76/1.49 = ( ( ( A = C2 )
% 2.76/1.49 & ( B2 = D ) )
% 2.76/1.49 | ( ( A = D )
% 2.76/1.49 & ( B2 = C2 ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_95_singleton__iff,axiom,
% 2.76/1.49 ! [B2: produc696469763tate_o,A: produc696469763tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ B2 @ ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) )
% 2.76/1.49 = ( B2 = A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_96_singleton__iff,axiom,
% 2.76/1.49 ! [B2: product_prod_nat_nat,A: product_prod_nat_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ B2 @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) )
% 2.76/1.49 = ( B2 = A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_97_singleton__iff,axiom,
% 2.76/1.49 ! [B2: produc1115495963_state,A: produc1115495963_state] :
% 2.76/1.49 ( ( member1389040324_state @ B2 @ ( insert311944171_state @ A @ bot_bo1625160935_state ) )
% 2.76/1.49 = ( B2 = A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_98_singletonD,axiom,
% 2.76/1.49 ! [B2: produc696469763tate_o,A: produc696469763tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ B2 @ ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) )
% 2.76/1.49 => ( B2 = A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_99_singletonD,axiom,
% 2.76/1.49 ! [B2: product_prod_nat_nat,A: product_prod_nat_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ B2 @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) )
% 2.76/1.49 => ( B2 = A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_100_singletonD,axiom,
% 2.76/1.49 ! [B2: produc1115495963_state,A: produc1115495963_state] :
% 2.76/1.49 ( ( member1389040324_state @ B2 @ ( insert311944171_state @ A @ bot_bo1625160935_state ) )
% 2.76/1.49 => ( B2 = A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_101_hoare_OAsm,axiom,
% 2.76/1.49 ! [P: a > state > $o,Q: a > state > $o] : ( hoare_a @ ( insert2053719859tate_o @ ( produc33908149tate_o @ P @ ( produc1948644831tate_o @ call @ Q ) ) @ bot_bo170732493tate_o ) @ P @ call @ Q ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_102_Collect__conv__if2,axiom,
% 2.76/1.49 ! [P: produc696469763tate_o > $o,A: produc696469763tate_o] :
% 2.76/1.49 ( ( ( P @ A )
% 2.76/1.49 => ( ( collec1499596504tate_o
% 2.76/1.49 @ ^ [X: produc696469763tate_o] :
% 2.76/1.49 ( ( A = X )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) )
% 2.76/1.49 & ( ~ ( P @ A )
% 2.76/1.49 => ( ( collec1499596504tate_o
% 2.76/1.49 @ ^ [X: produc696469763tate_o] :
% 2.76/1.49 ( ( A = X )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = bot_bo170732493tate_o ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_103_Collect__conv__if2,axiom,
% 2.76/1.49 ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 2.76/1.49 ( ( ( P @ A )
% 2.76/1.49 => ( ( collec7649004at_nat
% 2.76/1.49 @ ^ [X: product_prod_nat_nat] :
% 2.76/1.49 ( ( A = X )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 2.76/1.49 & ( ~ ( P @ A )
% 2.76/1.49 => ( ( collec7649004at_nat
% 2.76/1.49 @ ^ [X: product_prod_nat_nat] :
% 2.76/1.49 ( ( A = X )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = bot_bo2130386637at_nat ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_104_Collect__conv__if2,axiom,
% 2.76/1.49 ! [P: produc1115495963_state > $o,A: produc1115495963_state] :
% 2.76/1.49 ( ( ( P @ A )
% 2.76/1.49 => ( ( collec496201222_state
% 2.76/1.49 @ ^ [X: produc1115495963_state] :
% 2.76/1.49 ( ( A = X )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) )
% 2.76/1.49 & ( ~ ( P @ A )
% 2.76/1.49 => ( ( collec496201222_state
% 2.76/1.49 @ ^ [X: produc1115495963_state] :
% 2.76/1.49 ( ( A = X )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = bot_bo1625160935_state ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_105_Collect__conv__if,axiom,
% 2.76/1.49 ! [P: produc696469763tate_o > $o,A: produc696469763tate_o] :
% 2.76/1.49 ( ( ( P @ A )
% 2.76/1.49 => ( ( collec1499596504tate_o
% 2.76/1.49 @ ^ [X: produc696469763tate_o] :
% 2.76/1.49 ( ( X = A )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = ( insert2053719859tate_o @ A @ bot_bo170732493tate_o ) ) )
% 2.76/1.49 & ( ~ ( P @ A )
% 2.76/1.49 => ( ( collec1499596504tate_o
% 2.76/1.49 @ ^ [X: produc696469763tate_o] :
% 2.76/1.49 ( ( X = A )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = bot_bo170732493tate_o ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_106_Collect__conv__if,axiom,
% 2.76/1.49 ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 2.76/1.49 ( ( ( P @ A )
% 2.76/1.49 => ( ( collec7649004at_nat
% 2.76/1.49 @ ^ [X: product_prod_nat_nat] :
% 2.76/1.49 ( ( X = A )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 2.76/1.49 & ( ~ ( P @ A )
% 2.76/1.49 => ( ( collec7649004at_nat
% 2.76/1.49 @ ^ [X: product_prod_nat_nat] :
% 2.76/1.49 ( ( X = A )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = bot_bo2130386637at_nat ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_107_Collect__conv__if,axiom,
% 2.76/1.49 ! [P: produc1115495963_state > $o,A: produc1115495963_state] :
% 2.76/1.49 ( ( ( P @ A )
% 2.76/1.49 => ( ( collec496201222_state
% 2.76/1.49 @ ^ [X: produc1115495963_state] :
% 2.76/1.49 ( ( X = A )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = ( insert311944171_state @ A @ bot_bo1625160935_state ) ) )
% 2.76/1.49 & ( ~ ( P @ A )
% 2.76/1.49 => ( ( collec496201222_state
% 2.76/1.49 @ ^ [X: produc1115495963_state] :
% 2.76/1.49 ( ( X = A )
% 2.76/1.49 & ( P @ X ) ) )
% 2.76/1.49 = bot_bo1625160935_state ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_108_wf__empty,axiom,
% 2.76/1.49 wf_nat @ bot_bo2130386637at_nat ).
% 2.76/1.49
% 2.76/1.49 thf(fact_109_wf__empty,axiom,
% 2.76/1.49 wf_state @ bot_bo1625160935_state ).
% 2.76/1.49
% 2.76/1.49 thf(fact_110_mem__Collect__eq,axiom,
% 2.76/1.49 ! [A: produc1115495963_state,P: produc1115495963_state > $o] :
% 2.76/1.49 ( ( member1389040324_state @ A @ ( collec496201222_state @ P ) )
% 2.76/1.49 = ( P @ A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_111_mem__Collect__eq,axiom,
% 2.76/1.49 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 2.76/1.49 ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P ) )
% 2.76/1.49 = ( P @ A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_112_mem__Collect__eq,axiom,
% 2.76/1.49 ! [A: produc696469763tate_o,P: produc696469763tate_o > $o] :
% 2.76/1.49 ( ( member1838112666tate_o @ A @ ( collec1499596504tate_o @ P ) )
% 2.76/1.49 = ( P @ A ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_113_Collect__mem__eq,axiom,
% 2.76/1.49 ! [A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( collec496201222_state
% 2.76/1.49 @ ^ [X: produc1115495963_state] : ( member1389040324_state @ X @ A2 ) )
% 2.76/1.49 = A2 ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_114_Collect__mem__eq,axiom,
% 2.76/1.49 ! [A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( collec7649004at_nat
% 2.76/1.49 @ ^ [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ A2 ) )
% 2.76/1.49 = A2 ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_115_Collect__mem__eq,axiom,
% 2.76/1.49 ! [A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( collec1499596504tate_o
% 2.76/1.49 @ ^ [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ A2 ) )
% 2.76/1.49 = A2 ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_116_Collect__cong,axiom,
% 2.76/1.49 ! [P: produc1115495963_state > $o,Q: produc1115495963_state > $o] :
% 2.76/1.49 ( ! [X3: produc1115495963_state] :
% 2.76/1.49 ( ( P @ X3 )
% 2.76/1.49 = ( Q @ X3 ) )
% 2.76/1.49 => ( ( collec496201222_state @ P )
% 2.76/1.49 = ( collec496201222_state @ Q ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_117_Collect__cong,axiom,
% 2.76/1.49 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 2.76/1.49 ( ! [X3: product_prod_nat_nat] :
% 2.76/1.49 ( ( P @ X3 )
% 2.76/1.49 = ( Q @ X3 ) )
% 2.76/1.49 => ( ( collec7649004at_nat @ P )
% 2.76/1.49 = ( collec7649004at_nat @ Q ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_118_Collect__cong,axiom,
% 2.76/1.49 ! [P: produc696469763tate_o > $o,Q: produc696469763tate_o > $o] :
% 2.76/1.49 ( ! [X3: produc696469763tate_o] :
% 2.76/1.49 ( ( P @ X3 )
% 2.76/1.49 = ( Q @ X3 ) )
% 2.76/1.49 => ( ( collec1499596504tate_o @ P )
% 2.76/1.49 = ( collec1499596504tate_o @ Q ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_119_wfE__min_H,axiom,
% 2.76/1.49 ! [R2: set_Pr795498619_state,Q: set_state] :
% 2.76/1.49 ( ( wf_state @ R2 )
% 2.76/1.49 => ( ( Q != bot_bot_set_state )
% 2.76/1.49 => ~ ! [Z: state] :
% 2.76/1.49 ( ( member_state @ Z @ Q )
% 2.76/1.49 => ~ ! [Y4: state] :
% 2.76/1.49 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ Z ) @ R2 )
% 2.76/1.49 => ~ ( member_state @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_120_wfE__min_H,axiom,
% 2.76/1.49 ! [R2: set_Pr1986765409at_nat,Q: set_nat] :
% 2.76/1.49 ( ( wf_nat @ R2 )
% 2.76/1.49 => ( ( Q != bot_bot_set_nat )
% 2.76/1.49 => ~ ! [Z: nat] :
% 2.76/1.49 ( ( member_nat @ Z @ Q )
% 2.76/1.49 => ~ ! [Y4: nat] :
% 2.76/1.49 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ Z ) @ R2 )
% 2.76/1.49 => ~ ( member_nat @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_121_wfE__min_H,axiom,
% 2.76/1.49 ! [R2: set_Pr1702239303tate_o,Q: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( wf_Pro309705690tate_o @ R2 )
% 2.76/1.49 => ( ( Q != bot_bo170732493tate_o )
% 2.76/1.49 => ~ ! [Z: produc696469763tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ Z @ Q )
% 2.76/1.49 => ~ ! [Y4: produc696469763tate_o] :
% 2.76/1.49 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y4 @ Z ) @ R2 )
% 2.76/1.49 => ~ ( member1838112666tate_o @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_122_wfE__min_H,axiom,
% 2.76/1.49 ! [R2: set_Pr1490359111at_nat,Q: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( wf_Pro745352042at_nat @ R2 )
% 2.76/1.49 => ( ( Q != bot_bo2130386637at_nat )
% 2.76/1.49 => ~ ! [Z: product_prod_nat_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ Z @ Q )
% 2.76/1.49 => ~ ! [Y4: product_prod_nat_nat] :
% 2.76/1.49 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y4 @ Z ) @ R2 )
% 2.76/1.49 => ~ ( member701585322at_nat @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_123_wfE__min_H,axiom,
% 2.76/1.49 ! [R2: set_Pr778812871_state,Q: set_Pr795498619_state] :
% 2.76/1.49 ( ( wf_Pro1783588484_state @ R2 )
% 2.76/1.49 => ( ( Q != bot_bo1625160935_state )
% 2.76/1.49 => ~ ! [Z: produc1115495963_state] :
% 2.76/1.49 ( ( member1389040324_state @ Z @ Q )
% 2.76/1.49 => ~ ! [Y4: produc1115495963_state] :
% 2.76/1.49 ( ( member768948240_state @ ( produc1964772951_state @ Y4 @ Z ) @ R2 )
% 2.76/1.49 => ~ ( member1389040324_state @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_124_the__elem__eq,axiom,
% 2.76/1.49 ! [X2: produc696469763tate_o] :
% 2.76/1.49 ( ( the_el1569055182tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) )
% 2.76/1.49 = X2 ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_125_the__elem__eq,axiom,
% 2.76/1.49 ! [X2: product_prod_nat_nat] :
% 2.76/1.49 ( ( the_el1949240438at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) )
% 2.76/1.49 = X2 ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_126_the__elem__eq,axiom,
% 2.76/1.49 ! [X2: produc1115495963_state] :
% 2.76/1.49 ( ( the_el1967402896_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) )
% 2.76/1.49 = X2 ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_127_old_Oprod_Oinject,axiom,
% 2.76/1.49 ! [A: a > state > $o,B2: produc204914599tate_o,A4: a > state > $o,B5: produc204914599tate_o] :
% 2.76/1.49 ( ( ( produc33908149tate_o @ A @ B2 )
% 2.76/1.49 = ( produc33908149tate_o @ A4 @ B5 ) )
% 2.76/1.49 = ( ( A = A4 )
% 2.76/1.49 & ( B2 = B5 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_128_old_Oprod_Oinject,axiom,
% 2.76/1.49 ! [A: state,B2: state,A4: state,B5: state] :
% 2.76/1.49 ( ( ( produc64584659_state @ A @ B2 )
% 2.76/1.49 = ( produc64584659_state @ A4 @ B5 ) )
% 2.76/1.49 = ( ( A = A4 )
% 2.76/1.49 & ( B2 = B5 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_129_old_Oprod_Oinject,axiom,
% 2.76/1.49 ! [A: com,B2: a > state > $o,A4: com,B5: a > state > $o] :
% 2.76/1.49 ( ( ( produc1948644831tate_o @ A @ B2 )
% 2.76/1.49 = ( produc1948644831tate_o @ A4 @ B5 ) )
% 2.76/1.49 = ( ( A = A4 )
% 2.76/1.49 & ( B2 = B5 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_130_old_Oprod_Oinject,axiom,
% 2.76/1.49 ! [A: nat,B2: nat,A4: nat,B5: nat] :
% 2.76/1.49 ( ( ( product_Pair_nat_nat @ A @ B2 )
% 2.76/1.49 = ( product_Pair_nat_nat @ A4 @ B5 ) )
% 2.76/1.49 = ( ( A = A4 )
% 2.76/1.49 & ( B2 = B5 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_131_prod_Oinject,axiom,
% 2.76/1.49 ! [X1: a > state > $o,X22: produc204914599tate_o,Y1: a > state > $o,Y22: produc204914599tate_o] :
% 2.76/1.49 ( ( ( produc33908149tate_o @ X1 @ X22 )
% 2.76/1.49 = ( produc33908149tate_o @ Y1 @ Y22 ) )
% 2.76/1.49 = ( ( X1 = Y1 )
% 2.76/1.49 & ( X22 = Y22 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_132_prod_Oinject,axiom,
% 2.76/1.49 ! [X1: state,X22: state,Y1: state,Y22: state] :
% 2.76/1.49 ( ( ( produc64584659_state @ X1 @ X22 )
% 2.76/1.49 = ( produc64584659_state @ Y1 @ Y22 ) )
% 2.76/1.49 = ( ( X1 = Y1 )
% 2.76/1.49 & ( X22 = Y22 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_133_prod_Oinject,axiom,
% 2.76/1.49 ! [X1: com,X22: a > state > $o,Y1: com,Y22: a > state > $o] :
% 2.76/1.49 ( ( ( produc1948644831tate_o @ X1 @ X22 )
% 2.76/1.49 = ( produc1948644831tate_o @ Y1 @ Y22 ) )
% 2.76/1.49 = ( ( X1 = Y1 )
% 2.76/1.49 & ( X22 = Y22 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_134_prod_Oinject,axiom,
% 2.76/1.49 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 2.76/1.49 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 2.76/1.49 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 2.76/1.49 = ( ( X1 = Y1 )
% 2.76/1.49 & ( X22 = Y22 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_135_is__singletonI,axiom,
% 2.76/1.49 ! [X2: produc696469763tate_o] : ( is_sin1547905295tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_136_is__singletonI,axiom,
% 2.76/1.49 ! [X2: product_prod_nat_nat] : ( is_sin1352690165at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_137_is__singletonI,axiom,
% 2.76/1.49 ! [X2: produc1115495963_state] : ( is_sin1132515087_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_138_bot__set__def,axiom,
% 2.76/1.49 ( bot_bo170732493tate_o
% 2.76/1.49 = ( collec1499596504tate_o @ bot_bo250281208te_o_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_139_bot__set__def,axiom,
% 2.76/1.49 ( bot_bo2130386637at_nat
% 2.76/1.49 = ( collec7649004at_nat @ bot_bo513358416_nat_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_140_bot__set__def,axiom,
% 2.76/1.49 ( bot_bo1625160935_state
% 2.76/1.49 = ( collec496201222_state @ bot_bo446391478tate_o ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_141_is__singleton__the__elem,axiom,
% 2.76/1.49 ( is_sin1547905295tate_o
% 2.76/1.49 = ( ^ [A5: set_Pr1590995257tate_o] :
% 2.76/1.49 ( A5
% 2.76/1.49 = ( insert2053719859tate_o @ ( the_el1569055182tate_o @ A5 ) @ bot_bo170732493tate_o ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_142_is__singleton__the__elem,axiom,
% 2.76/1.49 ( is_sin1352690165at_nat
% 2.76/1.49 = ( ^ [A5: set_Pr1986765409at_nat] :
% 2.76/1.49 ( A5
% 2.76/1.49 = ( insert271595217at_nat @ ( the_el1949240438at_nat @ A5 ) @ bot_bo2130386637at_nat ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_143_is__singleton__the__elem,axiom,
% 2.76/1.49 ( is_sin1132515087_state
% 2.76/1.49 = ( ^ [A5: set_Pr795498619_state] :
% 2.76/1.49 ( A5
% 2.76/1.49 = ( insert311944171_state @ ( the_el1967402896_state @ A5 ) @ bot_bo1625160935_state ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_144_is__singletonI_H,axiom,
% 2.76/1.49 ! [A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( A2 != bot_bo170732493tate_o )
% 2.76/1.49 => ( ! [X3: produc696469763tate_o,Y2: produc696469763tate_o] :
% 2.76/1.49 ( ( member1838112666tate_o @ X3 @ A2 )
% 2.76/1.49 => ( ( member1838112666tate_o @ Y2 @ A2 )
% 2.76/1.49 => ( X3 = Y2 ) ) )
% 2.76/1.49 => ( is_sin1547905295tate_o @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_145_is__singletonI_H,axiom,
% 2.76/1.49 ! [A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( A2 != bot_bo2130386637at_nat )
% 2.76/1.49 => ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 2.76/1.49 ( ( member701585322at_nat @ X3 @ A2 )
% 2.76/1.49 => ( ( member701585322at_nat @ Y2 @ A2 )
% 2.76/1.49 => ( X3 = Y2 ) ) )
% 2.76/1.49 => ( is_sin1352690165at_nat @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_146_is__singletonI_H,axiom,
% 2.76/1.49 ! [A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( A2 != bot_bo1625160935_state )
% 2.76/1.49 => ( ! [X3: produc1115495963_state,Y2: produc1115495963_state] :
% 2.76/1.49 ( ( member1389040324_state @ X3 @ A2 )
% 2.76/1.49 => ( ( member1389040324_state @ Y2 @ A2 )
% 2.76/1.49 => ( X3 = Y2 ) ) )
% 2.76/1.49 => ( is_sin1132515087_state @ A2 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_147_surj__pair,axiom,
% 2.76/1.49 ! [P3: produc696469763tate_o] :
% 2.76/1.49 ? [X3: a > state > $o,Y2: produc204914599tate_o] :
% 2.76/1.49 ( P3
% 2.76/1.49 = ( produc33908149tate_o @ X3 @ Y2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_148_surj__pair,axiom,
% 2.76/1.49 ! [P3: produc1115495963_state] :
% 2.76/1.49 ? [X3: state,Y2: state] :
% 2.76/1.49 ( P3
% 2.76/1.49 = ( produc64584659_state @ X3 @ Y2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_149_surj__pair,axiom,
% 2.76/1.49 ! [P3: produc204914599tate_o] :
% 2.76/1.49 ? [X3: com,Y2: a > state > $o] :
% 2.76/1.49 ( P3
% 2.76/1.49 = ( produc1948644831tate_o @ X3 @ Y2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_150_surj__pair,axiom,
% 2.76/1.49 ! [P3: product_prod_nat_nat] :
% 2.76/1.49 ? [X3: nat,Y2: nat] :
% 2.76/1.49 ( P3
% 2.76/1.49 = ( product_Pair_nat_nat @ X3 @ Y2 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_151_prod__cases,axiom,
% 2.76/1.49 ! [P: produc696469763tate_o > $o,P3: produc696469763tate_o] :
% 2.76/1.49 ( ! [A6: a > state > $o,B6: produc204914599tate_o] : ( P @ ( produc33908149tate_o @ A6 @ B6 ) )
% 2.76/1.49 => ( P @ P3 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_152_prod__cases,axiom,
% 2.76/1.49 ! [P: produc1115495963_state > $o,P3: produc1115495963_state] :
% 2.76/1.49 ( ! [A6: state,B6: state] : ( P @ ( produc64584659_state @ A6 @ B6 ) )
% 2.76/1.49 => ( P @ P3 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_153_prod__cases,axiom,
% 2.76/1.49 ! [P: produc204914599tate_o > $o,P3: produc204914599tate_o] :
% 2.76/1.49 ( ! [A6: com,B6: a > state > $o] : ( P @ ( produc1948644831tate_o @ A6 @ B6 ) )
% 2.76/1.49 => ( P @ P3 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_154_prod__cases,axiom,
% 2.76/1.49 ! [P: product_prod_nat_nat > $o,P3: product_prod_nat_nat] :
% 2.76/1.49 ( ! [A6: nat,B6: nat] : ( P @ ( product_Pair_nat_nat @ A6 @ B6 ) )
% 2.76/1.49 => ( P @ P3 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_155_Pair__inject,axiom,
% 2.76/1.49 ! [A: a > state > $o,B2: produc204914599tate_o,A4: a > state > $o,B5: produc204914599tate_o] :
% 2.76/1.49 ( ( ( produc33908149tate_o @ A @ B2 )
% 2.76/1.49 = ( produc33908149tate_o @ A4 @ B5 ) )
% 2.76/1.49 => ~ ( ( A = A4 )
% 2.76/1.49 => ( B2 != B5 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_156_Pair__inject,axiom,
% 2.76/1.49 ! [A: state,B2: state,A4: state,B5: state] :
% 2.76/1.49 ( ( ( produc64584659_state @ A @ B2 )
% 2.76/1.49 = ( produc64584659_state @ A4 @ B5 ) )
% 2.76/1.49 => ~ ( ( A = A4 )
% 2.76/1.49 => ( B2 != B5 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_157_Pair__inject,axiom,
% 2.76/1.49 ! [A: com,B2: a > state > $o,A4: com,B5: a > state > $o] :
% 2.76/1.49 ( ( ( produc1948644831tate_o @ A @ B2 )
% 2.76/1.49 = ( produc1948644831tate_o @ A4 @ B5 ) )
% 2.76/1.49 => ~ ( ( A = A4 )
% 2.76/1.49 => ( B2 != B5 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_158_Pair__inject,axiom,
% 2.76/1.49 ! [A: nat,B2: nat,A4: nat,B5: nat] :
% 2.76/1.49 ( ( ( product_Pair_nat_nat @ A @ B2 )
% 2.76/1.49 = ( product_Pair_nat_nat @ A4 @ B5 ) )
% 2.76/1.49 => ~ ( ( A = A4 )
% 2.76/1.49 => ( B2 != B5 ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_159_old_Oprod_Oexhaust,axiom,
% 2.76/1.49 ! [Y3: produc696469763tate_o] :
% 2.76/1.49 ~ ! [A6: a > state > $o,B6: produc204914599tate_o] :
% 2.76/1.49 ( Y3
% 2.76/1.49 != ( produc33908149tate_o @ A6 @ B6 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_160_old_Oprod_Oexhaust,axiom,
% 2.76/1.49 ! [Y3: produc1115495963_state] :
% 2.76/1.49 ~ ! [A6: state,B6: state] :
% 2.76/1.49 ( Y3
% 2.76/1.49 != ( produc64584659_state @ A6 @ B6 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_161_old_Oprod_Oexhaust,axiom,
% 2.76/1.49 ! [Y3: produc204914599tate_o] :
% 2.76/1.49 ~ ! [A6: com,B6: a > state > $o] :
% 2.76/1.49 ( Y3
% 2.76/1.49 != ( produc1948644831tate_o @ A6 @ B6 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_162_old_Oprod_Oexhaust,axiom,
% 2.76/1.49 ! [Y3: product_prod_nat_nat] :
% 2.76/1.49 ~ ! [A6: nat,B6: nat] :
% 2.76/1.49 ( Y3
% 2.76/1.49 != ( product_Pair_nat_nat @ A6 @ B6 ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_163_old_Oprod_Oinducts,axiom,
% 2.76/1.49 ! [P: produc696469763tate_o > $o,Prod: produc696469763tate_o] :
% 2.76/1.49 ( ! [A6: a > state > $o,B6: produc204914599tate_o] : ( P @ ( produc33908149tate_o @ A6 @ B6 ) )
% 2.76/1.49 => ( P @ Prod ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_164_old_Oprod_Oinducts,axiom,
% 2.76/1.49 ! [P: produc1115495963_state > $o,Prod: produc1115495963_state] :
% 2.76/1.49 ( ! [A6: state,B6: state] : ( P @ ( produc64584659_state @ A6 @ B6 ) )
% 2.76/1.49 => ( P @ Prod ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_165_old_Oprod_Oinducts,axiom,
% 2.76/1.49 ! [P: produc204914599tate_o > $o,Prod: produc204914599tate_o] :
% 2.76/1.49 ( ! [A6: com,B6: a > state > $o] : ( P @ ( produc1948644831tate_o @ A6 @ B6 ) )
% 2.76/1.49 => ( P @ Prod ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_166_old_Oprod_Oinducts,axiom,
% 2.76/1.49 ! [P: product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 2.76/1.49 ( ! [A6: nat,B6: nat] : ( P @ ( product_Pair_nat_nat @ A6 @ B6 ) )
% 2.76/1.49 => ( P @ Prod ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_167_is__singletonE,axiom,
% 2.76/1.49 ! [A2: set_Pr1590995257tate_o] :
% 2.76/1.49 ( ( is_sin1547905295tate_o @ A2 )
% 2.76/1.49 => ~ ! [X3: produc696469763tate_o] :
% 2.76/1.49 ( A2
% 2.76/1.49 != ( insert2053719859tate_o @ X3 @ bot_bo170732493tate_o ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_168_is__singletonE,axiom,
% 2.76/1.49 ! [A2: set_Pr1986765409at_nat] :
% 2.76/1.49 ( ( is_sin1352690165at_nat @ A2 )
% 2.76/1.49 => ~ ! [X3: product_prod_nat_nat] :
% 2.76/1.49 ( A2
% 2.76/1.49 != ( insert271595217at_nat @ X3 @ bot_bo2130386637at_nat ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_169_is__singletonE,axiom,
% 2.76/1.49 ! [A2: set_Pr795498619_state] :
% 2.76/1.49 ( ( is_sin1132515087_state @ A2 )
% 2.76/1.49 => ~ ! [X3: produc1115495963_state] :
% 2.76/1.49 ( A2
% 2.76/1.49 != ( insert311944171_state @ X3 @ bot_bo1625160935_state ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_170_is__singleton__def,axiom,
% 2.76/1.49 ( is_sin1547905295tate_o
% 2.76/1.49 = ( ^ [A5: set_Pr1590995257tate_o] :
% 2.76/1.49 ? [X: produc696469763tate_o] :
% 2.76/1.49 ( A5
% 2.76/1.49 = ( insert2053719859tate_o @ X @ bot_bo170732493tate_o ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_171_is__singleton__def,axiom,
% 2.76/1.49 ( is_sin1352690165at_nat
% 2.76/1.49 = ( ^ [A5: set_Pr1986765409at_nat] :
% 2.76/1.49 ? [X: product_prod_nat_nat] :
% 2.76/1.49 ( A5
% 2.76/1.49 = ( insert271595217at_nat @ X @ bot_bo2130386637at_nat ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_172_is__singleton__def,axiom,
% 2.76/1.49 ( is_sin1132515087_state
% 2.76/1.49 = ( ^ [A5: set_Pr795498619_state] :
% 2.76/1.49 ? [X: produc1115495963_state] :
% 2.76/1.49 ( A5
% 2.76/1.49 = ( insert311944171_state @ X @ bot_bo1625160935_state ) ) ) ) ).
% 2.76/1.49
% 2.76/1.49 thf(fact_173_wf__def,axiom,
% 2.76/1.49 ( wf_state
% 2.76/1.49 = ( ^ [R3: set_Pr795498619_state] :
% 2.76/1.49 ! [P4: state > $o] :
% 2.76/1.49 ( ! [X: state] :
% 2.76/1.49 ( ! [Y5: state] :
% 2.76/1.49 ( ( member1389040324_state @ ( produc64584659_state @ Y5 @ X ) @ R3 )
% 2.76/1.49 => ( P4 @ Y5 ) )
% 2.76/1.49 => ( P4 @ X ) )
% 2.76/1.49 => ! [X4: state] : ( P4 @ X4 ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_174_wf__def,axiom,
% 2.76/1.50 ( wf_nat
% 2.76/1.50 = ( ^ [R3: set_Pr1986765409at_nat] :
% 2.76/1.50 ! [P4: nat > $o] :
% 2.76/1.50 ( ! [X: nat] :
% 2.76/1.50 ( ! [Y5: nat] :
% 2.76/1.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y5 @ X ) @ R3 )
% 2.76/1.50 => ( P4 @ Y5 ) )
% 2.76/1.50 => ( P4 @ X ) )
% 2.76/1.50 => ! [X4: nat] : ( P4 @ X4 ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_175_wfE__min,axiom,
% 2.76/1.50 ! [R2: set_Pr778812871_state,X2: produc1115495963_state,Q: set_Pr795498619_state] :
% 2.76/1.50 ( ( wf_Pro1783588484_state @ R2 )
% 2.76/1.50 => ( ( member1389040324_state @ X2 @ Q )
% 2.76/1.50 => ~ ! [Z: produc1115495963_state] :
% 2.76/1.50 ( ( member1389040324_state @ Z @ Q )
% 2.76/1.50 => ~ ! [Y4: produc1115495963_state] :
% 2.76/1.50 ( ( member768948240_state @ ( produc1964772951_state @ Y4 @ Z ) @ R2 )
% 2.76/1.50 => ~ ( member1389040324_state @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_176_wfE__min,axiom,
% 2.76/1.50 ! [R2: set_Pr1490359111at_nat,X2: product_prod_nat_nat,Q: set_Pr1986765409at_nat] :
% 2.76/1.50 ( ( wf_Pro745352042at_nat @ R2 )
% 2.76/1.50 => ( ( member701585322at_nat @ X2 @ Q )
% 2.76/1.50 => ~ ! [Z: product_prod_nat_nat] :
% 2.76/1.50 ( ( member701585322at_nat @ Z @ Q )
% 2.76/1.50 => ~ ! [Y4: product_prod_nat_nat] :
% 2.76/1.50 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y4 @ Z ) @ R2 )
% 2.76/1.50 => ~ ( member701585322at_nat @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_177_wfE__min,axiom,
% 2.76/1.50 ! [R2: set_Pr1702239303tate_o,X2: produc696469763tate_o,Q: set_Pr1590995257tate_o] :
% 2.76/1.50 ( ( wf_Pro309705690tate_o @ R2 )
% 2.76/1.50 => ( ( member1838112666tate_o @ X2 @ Q )
% 2.76/1.50 => ~ ! [Z: produc696469763tate_o] :
% 2.76/1.50 ( ( member1838112666tate_o @ Z @ Q )
% 2.76/1.50 => ~ ! [Y4: produc696469763tate_o] :
% 2.76/1.50 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y4 @ Z ) @ R2 )
% 2.76/1.50 => ~ ( member1838112666tate_o @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_178_wfE__min,axiom,
% 2.76/1.50 ! [R2: set_Pr795498619_state,X2: state,Q: set_state] :
% 2.76/1.50 ( ( wf_state @ R2 )
% 2.76/1.50 => ( ( member_state @ X2 @ Q )
% 2.76/1.50 => ~ ! [Z: state] :
% 2.76/1.50 ( ( member_state @ Z @ Q )
% 2.76/1.50 => ~ ! [Y4: state] :
% 2.76/1.50 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ Z ) @ R2 )
% 2.76/1.50 => ~ ( member_state @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_179_wfE__min,axiom,
% 2.76/1.50 ! [R2: set_Pr1986765409at_nat,X2: nat,Q: set_nat] :
% 2.76/1.50 ( ( wf_nat @ R2 )
% 2.76/1.50 => ( ( member_nat @ X2 @ Q )
% 2.76/1.50 => ~ ! [Z: nat] :
% 2.76/1.50 ( ( member_nat @ Z @ Q )
% 2.76/1.50 => ~ ! [Y4: nat] :
% 2.76/1.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ Z ) @ R2 )
% 2.76/1.50 => ~ ( member_nat @ Y4 @ Q ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_180_wfI__min,axiom,
% 2.76/1.50 ! [R2: set_Pr778812871_state] :
% 2.76/1.50 ( ! [X3: produc1115495963_state,Q3: set_Pr795498619_state] :
% 2.76/1.50 ( ( member1389040324_state @ X3 @ Q3 )
% 2.76/1.50 => ? [Xa: produc1115495963_state] :
% 2.76/1.50 ( ( member1389040324_state @ Xa @ Q3 )
% 2.76/1.50 & ! [Y2: produc1115495963_state] :
% 2.76/1.50 ( ( member768948240_state @ ( produc1964772951_state @ Y2 @ Xa ) @ R2 )
% 2.76/1.50 => ~ ( member1389040324_state @ Y2 @ Q3 ) ) ) )
% 2.76/1.50 => ( wf_Pro1783588484_state @ R2 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_181_wfI__min,axiom,
% 2.76/1.50 ! [R2: set_Pr1490359111at_nat] :
% 2.76/1.50 ( ! [X3: product_prod_nat_nat,Q3: set_Pr1986765409at_nat] :
% 2.76/1.50 ( ( member701585322at_nat @ X3 @ Q3 )
% 2.76/1.50 => ? [Xa: product_prod_nat_nat] :
% 2.76/1.50 ( ( member701585322at_nat @ Xa @ Q3 )
% 2.76/1.50 & ! [Y2: product_prod_nat_nat] :
% 2.76/1.50 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y2 @ Xa ) @ R2 )
% 2.76/1.50 => ~ ( member701585322at_nat @ Y2 @ Q3 ) ) ) )
% 2.76/1.50 => ( wf_Pro745352042at_nat @ R2 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_182_wfI__min,axiom,
% 2.76/1.50 ! [R2: set_Pr1702239303tate_o] :
% 2.76/1.50 ( ! [X3: produc696469763tate_o,Q3: set_Pr1590995257tate_o] :
% 2.76/1.50 ( ( member1838112666tate_o @ X3 @ Q3 )
% 2.76/1.50 => ? [Xa: produc696469763tate_o] :
% 2.76/1.50 ( ( member1838112666tate_o @ Xa @ Q3 )
% 2.76/1.50 & ! [Y2: produc696469763tate_o] :
% 2.76/1.50 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y2 @ Xa ) @ R2 )
% 2.76/1.50 => ~ ( member1838112666tate_o @ Y2 @ Q3 ) ) ) )
% 2.76/1.50 => ( wf_Pro309705690tate_o @ R2 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_183_wfI__min,axiom,
% 2.76/1.50 ! [R2: set_Pr795498619_state] :
% 2.76/1.50 ( ! [X3: state,Q3: set_state] :
% 2.76/1.50 ( ( member_state @ X3 @ Q3 )
% 2.76/1.50 => ? [Xa: state] :
% 2.76/1.50 ( ( member_state @ Xa @ Q3 )
% 2.76/1.50 & ! [Y2: state] :
% 2.76/1.50 ( ( member1389040324_state @ ( produc64584659_state @ Y2 @ Xa ) @ R2 )
% 2.76/1.50 => ~ ( member_state @ Y2 @ Q3 ) ) ) )
% 2.76/1.50 => ( wf_state @ R2 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_184_wfI__min,axiom,
% 2.76/1.50 ! [R2: set_Pr1986765409at_nat] :
% 2.76/1.50 ( ! [X3: nat,Q3: set_nat] :
% 2.76/1.50 ( ( member_nat @ X3 @ Q3 )
% 2.76/1.50 => ? [Xa: nat] :
% 2.76/1.50 ( ( member_nat @ Xa @ Q3 )
% 2.76/1.50 & ! [Y2: nat] :
% 2.76/1.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ Xa ) @ R2 )
% 2.76/1.50 => ~ ( member_nat @ Y2 @ Q3 ) ) ) )
% 2.76/1.50 => ( wf_nat @ R2 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_185_wfUNIVI,axiom,
% 2.76/1.50 ! [R: set_Pr795498619_state] :
% 2.76/1.50 ( ! [P5: state > $o,X3: state] :
% 2.76/1.50 ( ! [Xa: state] :
% 2.76/1.50 ( ! [Y2: state] :
% 2.76/1.50 ( ( member1389040324_state @ ( produc64584659_state @ Y2 @ Xa ) @ R )
% 2.76/1.50 => ( P5 @ Y2 ) )
% 2.76/1.50 => ( P5 @ Xa ) )
% 2.76/1.50 => ( P5 @ X3 ) )
% 2.76/1.50 => ( wf_state @ R ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_186_wfUNIVI,axiom,
% 2.76/1.50 ! [R: set_Pr1986765409at_nat] :
% 2.76/1.50 ( ! [P5: nat > $o,X3: nat] :
% 2.76/1.50 ( ! [Xa: nat] :
% 2.76/1.50 ( ! [Y2: nat] :
% 2.76/1.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ Xa ) @ R )
% 2.76/1.50 => ( P5 @ Y2 ) )
% 2.76/1.50 => ( P5 @ Xa ) )
% 2.76/1.50 => ( P5 @ X3 ) )
% 2.76/1.50 => ( wf_nat @ R ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_187_wf__asym,axiom,
% 2.76/1.50 ! [R: set_Pr795498619_state,A: state,X2: state] :
% 2.76/1.50 ( ( wf_state @ R )
% 2.76/1.50 => ( ( member1389040324_state @ ( produc64584659_state @ A @ X2 ) @ R )
% 2.76/1.50 => ~ ( member1389040324_state @ ( produc64584659_state @ X2 @ A ) @ R ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_188_wf__asym,axiom,
% 2.76/1.50 ! [R: set_Pr1986765409at_nat,A: nat,X2: nat] :
% 2.76/1.50 ( ( wf_nat @ R )
% 2.76/1.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ X2 ) @ R )
% 2.76/1.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ A ) @ R ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_189_wf__induct,axiom,
% 2.76/1.50 ! [R: set_Pr795498619_state,P: state > $o,A: state] :
% 2.76/1.50 ( ( wf_state @ R )
% 2.76/1.50 => ( ! [X3: state] :
% 2.76/1.50 ( ! [Y4: state] :
% 2.76/1.50 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ X3 ) @ R )
% 2.76/1.50 => ( P @ Y4 ) )
% 2.76/1.50 => ( P @ X3 ) )
% 2.76/1.50 => ( P @ A ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_190_wf__induct,axiom,
% 2.76/1.50 ! [R: set_Pr1986765409at_nat,P: nat > $o,A: nat] :
% 2.76/1.50 ( ( wf_nat @ R )
% 2.76/1.50 => ( ! [X3: nat] :
% 2.76/1.50 ( ! [Y4: nat] :
% 2.76/1.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ X3 ) @ R )
% 2.76/1.50 => ( P @ Y4 ) )
% 2.76/1.50 => ( P @ X3 ) )
% 2.76/1.50 => ( P @ A ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_191_wf__irrefl,axiom,
% 2.76/1.50 ! [R: set_Pr795498619_state,A: state] :
% 2.76/1.50 ( ( wf_state @ R )
% 2.76/1.50 => ~ ( member1389040324_state @ ( produc64584659_state @ A @ A ) @ R ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_192_wf__irrefl,axiom,
% 2.76/1.50 ! [R: set_Pr1986765409at_nat,A: nat] :
% 2.76/1.50 ( ( wf_nat @ R )
% 2.76/1.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_193_wf__not__sym,axiom,
% 2.76/1.50 ! [R: set_Pr795498619_state,A: state,X2: state] :
% 2.76/1.50 ( ( wf_state @ R )
% 2.76/1.50 => ( ( member1389040324_state @ ( produc64584659_state @ A @ X2 ) @ R )
% 2.76/1.50 => ~ ( member1389040324_state @ ( produc64584659_state @ X2 @ A ) @ R ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_194_wf__not__sym,axiom,
% 2.76/1.50 ! [R: set_Pr1986765409at_nat,A: nat,X2: nat] :
% 2.76/1.50 ( ( wf_nat @ R )
% 2.76/1.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ X2 ) @ R )
% 2.76/1.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ A ) @ R ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_195_wf__not__refl,axiom,
% 2.76/1.50 ! [R: set_Pr795498619_state,A: state] :
% 2.76/1.50 ( ( wf_state @ R )
% 2.76/1.50 => ~ ( member1389040324_state @ ( produc64584659_state @ A @ A ) @ R ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_196_wf__not__refl,axiom,
% 2.76/1.50 ! [R: set_Pr1986765409at_nat,A: nat] :
% 2.76/1.50 ( ( wf_nat @ R )
% 2.76/1.50 => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_197_wf__eq__minimal,axiom,
% 2.76/1.50 ( wf_Pro1783588484_state
% 2.76/1.50 = ( ^ [R3: set_Pr778812871_state] :
% 2.76/1.50 ! [Q4: set_Pr795498619_state] :
% 2.76/1.50 ( ? [X: produc1115495963_state] : ( member1389040324_state @ X @ Q4 )
% 2.76/1.50 => ? [X: produc1115495963_state] :
% 2.76/1.50 ( ( member1389040324_state @ X @ Q4 )
% 2.76/1.50 & ! [Y5: produc1115495963_state] :
% 2.76/1.50 ( ( member768948240_state @ ( produc1964772951_state @ Y5 @ X ) @ R3 )
% 2.76/1.50 => ~ ( member1389040324_state @ Y5 @ Q4 ) ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_198_wf__eq__minimal,axiom,
% 2.76/1.50 ( wf_Pro745352042at_nat
% 2.76/1.50 = ( ^ [R3: set_Pr1490359111at_nat] :
% 2.76/1.50 ! [Q4: set_Pr1986765409at_nat] :
% 2.76/1.50 ( ? [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ Q4 )
% 2.76/1.50 => ? [X: product_prod_nat_nat] :
% 2.76/1.50 ( ( member701585322at_nat @ X @ Q4 )
% 2.76/1.50 & ! [Y5: product_prod_nat_nat] :
% 2.76/1.50 ( ( member2027625872at_nat @ ( produc1168807639at_nat @ Y5 @ X ) @ R3 )
% 2.76/1.50 => ~ ( member701585322at_nat @ Y5 @ Q4 ) ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_199_wf__eq__minimal,axiom,
% 2.76/1.50 ( wf_Pro309705690tate_o
% 2.76/1.50 = ( ^ [R3: set_Pr1702239303tate_o] :
% 2.76/1.50 ! [Q4: set_Pr1590995257tate_o] :
% 2.76/1.50 ( ? [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ Q4 )
% 2.76/1.50 => ? [X: produc696469763tate_o] :
% 2.76/1.50 ( ( member1838112666tate_o @ X @ Q4 )
% 2.76/1.50 & ! [Y5: produc696469763tate_o] :
% 2.76/1.50 ( ( member1629320336tate_o @ ( produc1684562079tate_o @ Y5 @ X ) @ R3 )
% 2.76/1.50 => ~ ( member1838112666tate_o @ Y5 @ Q4 ) ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_200_wf__eq__minimal,axiom,
% 2.76/1.50 ( wf_state
% 2.76/1.50 = ( ^ [R3: set_Pr795498619_state] :
% 2.76/1.50 ! [Q4: set_state] :
% 2.76/1.50 ( ? [X: state] : ( member_state @ X @ Q4 )
% 2.76/1.50 => ? [X: state] :
% 2.76/1.50 ( ( member_state @ X @ Q4 )
% 2.76/1.50 & ! [Y5: state] :
% 2.76/1.50 ( ( member1389040324_state @ ( produc64584659_state @ Y5 @ X ) @ R3 )
% 2.76/1.50 => ~ ( member_state @ Y5 @ Q4 ) ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_201_wf__eq__minimal,axiom,
% 2.76/1.50 ( wf_nat
% 2.76/1.50 = ( ^ [R3: set_Pr1986765409at_nat] :
% 2.76/1.50 ! [Q4: set_nat] :
% 2.76/1.50 ( ? [X: nat] : ( member_nat @ X @ Q4 )
% 2.76/1.50 => ? [X: nat] :
% 2.76/1.50 ( ( member_nat @ X @ Q4 )
% 2.76/1.50 & ! [Y5: nat] :
% 2.76/1.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y5 @ X ) @ R3 )
% 2.76/1.50 => ~ ( member_nat @ Y5 @ Q4 ) ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_202_wf__induct__rule,axiom,
% 2.76/1.50 ! [R: set_Pr795498619_state,P: state > $o,A: state] :
% 2.76/1.50 ( ( wf_state @ R )
% 2.76/1.50 => ( ! [X3: state] :
% 2.76/1.50 ( ! [Y4: state] :
% 2.76/1.50 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ X3 ) @ R )
% 2.76/1.50 => ( P @ Y4 ) )
% 2.76/1.50 => ( P @ X3 ) )
% 2.76/1.50 => ( P @ A ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_203_wf__induct__rule,axiom,
% 2.76/1.50 ! [R: set_Pr1986765409at_nat,P: nat > $o,A: nat] :
% 2.76/1.50 ( ( wf_nat @ R )
% 2.76/1.50 => ( ! [X3: nat] :
% 2.76/1.50 ( ! [Y4: nat] :
% 2.76/1.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y4 @ X3 ) @ R )
% 2.76/1.50 => ( P @ Y4 ) )
% 2.76/1.50 => ( P @ X3 ) )
% 2.76/1.50 => ( P @ A ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_204_prod__cases3,axiom,
% 2.76/1.50 ! [Y3: produc696469763tate_o] :
% 2.76/1.50 ~ ! [A6: a > state > $o,B6: com,C4: a > state > $o] :
% 2.76/1.50 ( Y3
% 2.76/1.50 != ( produc33908149tate_o @ A6 @ ( produc1948644831tate_o @ B6 @ C4 ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_205_prod__induct3,axiom,
% 2.76/1.50 ! [P: produc696469763tate_o > $o,X2: produc696469763tate_o] :
% 2.76/1.50 ( ! [A6: a > state > $o,B6: com,C4: a > state > $o] : ( P @ ( produc33908149tate_o @ A6 @ ( produc1948644831tate_o @ B6 @ C4 ) ) )
% 2.76/1.50 => ( P @ X2 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_206_bot__empty__eq2,axiom,
% 2.76/1.50 ( bot_bo935656620te_o_o
% 2.76/1.50 = ( ^ [X: com,Y5: a > state > $o] : ( member221067728tate_o @ ( produc1948644831tate_o @ X @ Y5 ) @ bot_bo1692783091tate_o ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_207_bot__empty__eq2,axiom,
% 2.76/1.50 ( bot_bo2130564770te_o_o
% 2.76/1.50 = ( ^ [X: a > state > $o,Y5: produc204914599tate_o] : ( member1838112666tate_o @ ( produc33908149tate_o @ X @ Y5 ) @ bot_bo170732493tate_o ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_208_bot__empty__eq2,axiom,
% 2.76/1.50 ( bot_bot_nat_nat_o
% 2.76/1.50 = ( ^ [X: nat,Y5: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ bot_bo2130386637at_nat ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_209_bot__empty__eq2,axiom,
% 2.76/1.50 ( bot_bo51534648tate_o
% 2.76/1.50 = ( ^ [X: state,Y5: state] : ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ bot_bo1625160935_state ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_210_wf__measure,axiom,
% 2.76/1.50 ! [F: state > nat] : ( wf_state @ ( measure_state @ F ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_211_wf__measure,axiom,
% 2.76/1.50 ! [F: nat > nat] : ( wf_nat @ ( measure_nat @ F ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_212_thoare_OWhile,axiom,
% 2.76/1.50 ! [R: set_Pr795498619_state,C: set_Pr1590995257tate_o,P: a > state > $o,B2: state > $o,C2: com] :
% 2.76/1.50 ( ( wf_state @ R )
% 2.76/1.50 => ( ! [S3: state] :
% 2.76/1.50 ( pHoare382919414oare_a @ C
% 2.76/1.50 @ ^ [Z4: a,S4: state] :
% 2.76/1.50 ( ( P @ Z4 @ S4 )
% 2.76/1.50 & ( B2 @ S4 )
% 2.76/1.50 & ( S3 = S4 ) )
% 2.76/1.50 @ C2
% 2.76/1.50 @ ^ [Z4: a,S4: state] :
% 2.76/1.50 ( ( P @ Z4 @ S4 )
% 2.76/1.50 & ( member1389040324_state @ ( produc64584659_state @ S4 @ S3 ) @ R ) ) )
% 2.76/1.50 => ( pHoare382919414oare_a @ C @ P @ ( while @ B2 @ C2 )
% 2.76/1.50 @ ^ [Z4: a,S4: state] :
% 2.76/1.50 ( ( P @ Z4 @ S4 )
% 2.76/1.50 & ~ ( B2 @ S4 ) ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_213_Set_Ois__empty__def,axiom,
% 2.76/1.50 ( is_emp807847857tate_o
% 2.76/1.50 = ( ^ [A5: set_Pr1590995257tate_o] : ( A5 = bot_bo170732493tate_o ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_214_Set_Ois__empty__def,axiom,
% 2.76/1.50 ( is_emp825011411at_nat
% 2.76/1.50 = ( ^ [A5: set_Pr1986765409at_nat] : ( A5 = bot_bo2130386637at_nat ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_215_Set_Ois__empty__def,axiom,
% 2.76/1.50 ( is_emp1062983149_state
% 2.76/1.50 = ( ^ [A5: set_Pr795498619_state] : ( A5 = bot_bo1625160935_state ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_216_com_Oinject_I4_J,axiom,
% 2.76/1.50 ! [X41: state > $o,X42: com,Y41: state > $o,Y42: com] :
% 2.76/1.50 ( ( ( while @ X41 @ X42 )
% 2.76/1.50 = ( while @ Y41 @ Y42 ) )
% 2.76/1.50 = ( ( X41 = Y41 )
% 2.76/1.50 & ( X42 = Y42 ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_217_com_Odistinct_I25_J,axiom,
% 2.76/1.50 ! [X41: state > $o,X42: com] :
% 2.76/1.50 ( ( while @ X41 @ X42 )
% 2.76/1.50 != call ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_218_exec_OWhileFalse,axiom,
% 2.76/1.50 ! [B2: state > $o,S2: state,C2: com] :
% 2.76/1.50 ( ~ ( B2 @ S2 )
% 2.76/1.50 => ( exec @ S2 @ ( while @ B2 @ C2 ) @ S2 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_219_exec_OWhileTrue,axiom,
% 2.76/1.50 ! [B2: state > $o,S2: state,C2: com,T2: state,U2: state] :
% 2.76/1.50 ( ( B2 @ S2 )
% 2.76/1.50 => ( ( exec @ S2 @ C2 @ T2 )
% 2.76/1.50 => ( ( exec @ T2 @ ( while @ B2 @ C2 ) @ U2 )
% 2.76/1.50 => ( exec @ S2 @ ( while @ B2 @ C2 ) @ U2 ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_220_termi_OWhileFalse,axiom,
% 2.76/1.50 ! [B2: state > $o,S2: state,C2: com] :
% 2.76/1.50 ( ~ ( B2 @ S2 )
% 2.76/1.50 => ( termi @ ( while @ B2 @ C2 ) @ S2 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_221_termi_OWhileTrue,axiom,
% 2.76/1.50 ! [B2: state > $o,S2: state,C2: com] :
% 2.76/1.50 ( ( B2 @ S2 )
% 2.76/1.50 => ( ( termi @ C2 @ S2 )
% 2.76/1.50 => ( ! [T: state] :
% 2.76/1.50 ( ( exec @ S2 @ C2 @ T )
% 2.76/1.50 => ( termi @ ( while @ B2 @ C2 ) @ T ) )
% 2.76/1.50 => ( termi @ ( while @ B2 @ C2 ) @ S2 ) ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_222_bot__empty__eq,axiom,
% 2.76/1.50 ( bot_bo250281208te_o_o
% 2.76/1.50 = ( ^ [X: produc696469763tate_o] : ( member1838112666tate_o @ X @ bot_bo170732493tate_o ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_223_bot__empty__eq,axiom,
% 2.76/1.50 ( bot_bo513358416_nat_o
% 2.76/1.50 = ( ^ [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ bot_bo2130386637at_nat ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_224_bot__empty__eq,axiom,
% 2.76/1.50 ( bot_bo446391478tate_o
% 2.76/1.50 = ( ^ [X: produc1115495963_state] : ( member1389040324_state @ X @ bot_bo1625160935_state ) ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_225_pred__equals__eq2,axiom,
% 2.76/1.50 ! [R2: set_Pr1590995257tate_o,S5: set_Pr1590995257tate_o] :
% 2.76/1.50 ( ( ( ^ [X: a > state > $o,Y5: produc204914599tate_o] : ( member1838112666tate_o @ ( produc33908149tate_o @ X @ Y5 ) @ R2 ) )
% 2.76/1.50 = ( ^ [X: a > state > $o,Y5: produc204914599tate_o] : ( member1838112666tate_o @ ( produc33908149tate_o @ X @ Y5 ) @ S5 ) ) )
% 2.76/1.50 = ( R2 = S5 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_226_pred__equals__eq2,axiom,
% 2.76/1.50 ! [R2: set_Pr795498619_state,S5: set_Pr795498619_state] :
% 2.76/1.50 ( ( ( ^ [X: state,Y5: state] : ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ R2 ) )
% 2.76/1.50 = ( ^ [X: state,Y5: state] : ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ S5 ) ) )
% 2.76/1.50 = ( R2 = S5 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_227_pred__equals__eq2,axiom,
% 2.76/1.50 ! [R2: set_Pr1740974983tate_o,S5: set_Pr1740974983tate_o] :
% 2.76/1.50 ( ( ( ^ [X: com,Y5: a > state > $o] : ( member221067728tate_o @ ( produc1948644831tate_o @ X @ Y5 ) @ R2 ) )
% 2.76/1.50 = ( ^ [X: com,Y5: a > state > $o] : ( member221067728tate_o @ ( produc1948644831tate_o @ X @ Y5 ) @ S5 ) ) )
% 2.76/1.50 = ( R2 = S5 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_228_pred__equals__eq2,axiom,
% 2.76/1.50 ! [R2: set_Pr1986765409at_nat,S5: set_Pr1986765409at_nat] :
% 2.76/1.50 ( ( ( ^ [X: nat,Y5: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ R2 ) )
% 2.76/1.50 = ( ^ [X: nat,Y5: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ S5 ) ) )
% 2.76/1.50 = ( R2 = S5 ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_229_Collect__empty__eq__bot,axiom,
% 2.76/1.50 ! [P: produc696469763tate_o > $o] :
% 2.76/1.50 ( ( ( collec1499596504tate_o @ P )
% 2.76/1.50 = bot_bo170732493tate_o )
% 2.76/1.50 = ( P = bot_bo250281208te_o_o ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_230_Collect__empty__eq__bot,axiom,
% 2.76/1.50 ! [P: product_prod_nat_nat > $o] :
% 2.76/1.50 ( ( ( collec7649004at_nat @ P )
% 2.76/1.50 = bot_bo2130386637at_nat )
% 2.76/1.50 = ( P = bot_bo513358416_nat_o ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_231_Collect__empty__eq__bot,axiom,
% 2.76/1.50 ! [P: produc1115495963_state > $o] :
% 2.76/1.50 ( ( ( collec496201222_state @ P )
% 2.76/1.50 = bot_bo1625160935_state )
% 2.76/1.50 = ( P = bot_bo446391478tate_o ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_232_total__on__singleton,axiom,
% 2.76/1.50 ! [X2: nat] : ( total_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2130386637at_nat ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_233_total__on__singleton,axiom,
% 2.76/1.50 ! [X2: state] : ( total_on_state @ ( insert_state @ X2 @ bot_bot_set_state ) @ ( insert311944171_state @ ( produc64584659_state @ X2 @ X2 ) @ bot_bo1625160935_state ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_234_total__on__singleton,axiom,
% 2.76/1.50 ! [X2: produc696469763tate_o] : ( total_795385983tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) @ ( insert1597128631tate_o @ ( produc1684562079tate_o @ X2 @ X2 ) @ bot_bo1714653363tate_o ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_235_total__on__singleton,axiom,
% 2.76/1.50 ! [X2: product_prod_nat_nat] : ( total_1775715973at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) @ ( insert584009271at_nat @ ( produc1168807639at_nat @ X2 @ X2 ) @ bot_bo34127283at_nat ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_236_total__on__singleton,axiom,
% 2.76/1.50 ! [X2: produc1115495963_state] : ( total_1316653983_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) @ ( insert1616594103_state @ ( produc1964772951_state @ X2 @ X2 ) @ bot_bo1331673139_state ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_237_refl__on__singleton,axiom,
% 2.76/1.50 ! [X2: nat] : ( refl_on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2130386637at_nat ) ) ).
% 2.76/1.50
% 2.76/1.50 thf(fact_238_refl__on__singleton,axiom,
% 2.76/1.50 ! [X2: state] : ( refl_on_state @ ( insert_state @ X2 @ bot_bot_set_state ) @ ( insert311944171_state @ ( produc64584659_state @ X2 @ X2 ) @ bot_bo1625160935_state ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_239_refl__on__singleton,axiom,
% 2.92/1.50 ! [X2: produc696469763tate_o] : ( refl_o489021252tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) @ ( insert1597128631tate_o @ ( produc1684562079tate_o @ X2 @ X2 ) @ bot_bo1714653363tate_o ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_240_refl__on__singleton,axiom,
% 2.92/1.50 ! [X2: product_prod_nat_nat] : ( refl_o1619599232at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) @ ( insert584009271at_nat @ ( produc1168807639at_nat @ X2 @ X2 ) @ bot_bo34127283at_nat ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_241_refl__on__singleton,axiom,
% 2.92/1.50 ! [X2: produc1115495963_state] : ( refl_o1438232218_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) @ ( insert1616594103_state @ ( produc1964772951_state @ X2 @ X2 ) @ bot_bo1331673139_state ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_242_wf__termi,axiom,
% 2.92/1.50 ! [B2: state > $o,C2: com] :
% 2.92/1.50 ( wf_state
% 2.92/1.50 @ ( collec496201222_state
% 2.92/1.50 @ ( produc789892016tate_o
% 2.92/1.50 @ ^ [T3: state,S4: state] :
% 2.92/1.50 ( ( termi @ ( while @ B2 @ C2 ) @ S4 )
% 2.92/1.50 & ( B2 @ S4 )
% 2.92/1.50 & ( exec @ S4 @ C2 @ T3 ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_243_linear__order__on__singleton,axiom,
% 2.92/1.50 ! [X2: nat] : ( order_130026331on_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ bot_bo2130386637at_nat ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_244_linear__order__on__singleton,axiom,
% 2.92/1.50 ! [X2: state] : ( order_286167592_state @ ( insert_state @ X2 @ bot_bot_set_state ) @ ( insert311944171_state @ ( produc64584659_state @ X2 @ X2 ) @ bot_bo1625160935_state ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_245_linear__order__on__singleton,axiom,
% 2.92/1.50 ! [X2: produc696469763tate_o] : ( order_50454158tate_o @ ( insert2053719859tate_o @ X2 @ bot_bo170732493tate_o ) @ ( insert1597128631tate_o @ ( produc1684562079tate_o @ X2 @ X2 ) @ bot_bo1714653363tate_o ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_246_linear__order__on__singleton,axiom,
% 2.92/1.50 ! [X2: product_prod_nat_nat] : ( order_721919926at_nat @ ( insert271595217at_nat @ X2 @ bot_bo2130386637at_nat ) @ ( insert584009271at_nat @ ( produc1168807639at_nat @ X2 @ X2 ) @ bot_bo34127283at_nat ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_247_linear__order__on__singleton,axiom,
% 2.92/1.50 ! [X2: produc1115495963_state] : ( order_178668240_state @ ( insert311944171_state @ X2 @ bot_bo1625160935_state ) @ ( insert1616594103_state @ ( produc1964772951_state @ X2 @ X2 ) @ bot_bo1331673139_state ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_248_split__part,axiom,
% 2.92/1.50 ! [P: $o,Q: state > state > $o] :
% 2.92/1.50 ( ( produc789892016tate_o
% 2.92/1.50 @ ^ [A3: state,B7: state] :
% 2.92/1.50 ( P
% 2.92/1.50 & ( Q @ A3 @ B7 ) ) )
% 2.92/1.50 = ( ^ [Ab: produc1115495963_state] :
% 2.92/1.50 ( P
% 2.92/1.50 & ( produc789892016tate_o @ Q @ Ab ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_249_split__part,axiom,
% 2.92/1.50 ! [P: $o,Q: nat > nat > $o] :
% 2.92/1.50 ( ( produc949581770_nat_o
% 2.92/1.50 @ ^ [A3: nat,B7: nat] :
% 2.92/1.50 ( P
% 2.92/1.50 & ( Q @ A3 @ B7 ) ) )
% 2.92/1.50 = ( ^ [Ab: product_prod_nat_nat] :
% 2.92/1.50 ( P
% 2.92/1.50 & ( produc949581770_nat_o @ Q @ Ab ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_250_case__prod__conv,axiom,
% 2.92/1.50 ! [F: state > state > $o,A: state,B2: state] :
% 2.92/1.50 ( ( produc789892016tate_o @ F @ ( produc64584659_state @ A @ B2 ) )
% 2.92/1.50 = ( F @ A @ B2 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_251_case__prod__conv,axiom,
% 2.92/1.50 ! [F: nat > nat > $o,A: nat,B2: nat] :
% 2.92/1.50 ( ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ A @ B2 ) )
% 2.92/1.50 = ( F @ A @ B2 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_252_case__prodI,axiom,
% 2.92/1.50 ! [F: ( a > state > $o ) > produc204914599tate_o > $o,A: a > state > $o,B2: produc204914599tate_o] :
% 2.92/1.50 ( ( F @ A @ B2 )
% 2.92/1.50 => ( produc1271576886te_o_o @ F @ ( produc33908149tate_o @ A @ B2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_253_case__prodI,axiom,
% 2.92/1.50 ! [F: com > ( a > state > $o ) > $o,A: com,B2: a > state > $o] :
% 2.92/1.50 ( ( F @ A @ B2 )
% 2.92/1.50 => ( produc281270436te_o_o @ F @ ( produc1948644831tate_o @ A @ B2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_254_case__prodI,axiom,
% 2.92/1.50 ! [F: state > state > $o,A: state,B2: state] :
% 2.92/1.50 ( ( F @ A @ B2 )
% 2.92/1.50 => ( produc789892016tate_o @ F @ ( produc64584659_state @ A @ B2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_255_case__prodI,axiom,
% 2.92/1.50 ! [F: nat > nat > $o,A: nat,B2: nat] :
% 2.92/1.50 ( ( F @ A @ B2 )
% 2.92/1.50 => ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ A @ B2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_256_case__prodI2,axiom,
% 2.92/1.50 ! [P3: produc696469763tate_o,C2: ( a > state > $o ) > produc204914599tate_o > $o] :
% 2.92/1.50 ( ! [A6: a > state > $o,B6: produc204914599tate_o] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( produc33908149tate_o @ A6 @ B6 ) )
% 2.92/1.50 => ( C2 @ A6 @ B6 ) )
% 2.92/1.50 => ( produc1271576886te_o_o @ C2 @ P3 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_257_case__prodI2,axiom,
% 2.92/1.50 ! [P3: produc204914599tate_o,C2: com > ( a > state > $o ) > $o] :
% 2.92/1.50 ( ! [A6: com,B6: a > state > $o] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( produc1948644831tate_o @ A6 @ B6 ) )
% 2.92/1.50 => ( C2 @ A6 @ B6 ) )
% 2.92/1.50 => ( produc281270436te_o_o @ C2 @ P3 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_258_case__prodI2,axiom,
% 2.92/1.50 ! [P3: produc1115495963_state,C2: state > state > $o] :
% 2.92/1.50 ( ! [A6: state,B6: state] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( produc64584659_state @ A6 @ B6 ) )
% 2.92/1.50 => ( C2 @ A6 @ B6 ) )
% 2.92/1.50 => ( produc789892016tate_o @ C2 @ P3 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_259_case__prodI2,axiom,
% 2.92/1.50 ! [P3: product_prod_nat_nat,C2: nat > nat > $o] :
% 2.92/1.50 ( ! [A6: nat,B6: nat] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 2.92/1.50 => ( C2 @ A6 @ B6 ) )
% 2.92/1.50 => ( produc949581770_nat_o @ C2 @ P3 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_260_refl__on__domain,axiom,
% 2.92/1.50 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,A: produc1115495963_state,B2: produc1115495963_state] :
% 2.92/1.50 ( ( refl_o1438232218_state @ A2 @ R )
% 2.92/1.50 => ( ( member768948240_state @ ( produc1964772951_state @ A @ B2 ) @ R )
% 2.92/1.50 => ( ( member1389040324_state @ A @ A2 )
% 2.92/1.50 & ( member1389040324_state @ B2 @ A2 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_261_refl__on__domain,axiom,
% 2.92/1.50 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,A: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 2.92/1.50 ( ( refl_o1619599232at_nat @ A2 @ R )
% 2.92/1.50 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ B2 ) @ R )
% 2.92/1.50 => ( ( member701585322at_nat @ A @ A2 )
% 2.92/1.50 & ( member701585322at_nat @ B2 @ A2 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_262_refl__on__domain,axiom,
% 2.92/1.50 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,A: produc696469763tate_o,B2: produc696469763tate_o] :
% 2.92/1.50 ( ( refl_o489021252tate_o @ A2 @ R )
% 2.92/1.50 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ A @ B2 ) @ R )
% 2.92/1.50 => ( ( member1838112666tate_o @ A @ A2 )
% 2.92/1.50 & ( member1838112666tate_o @ B2 @ A2 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_263_refl__on__domain,axiom,
% 2.92/1.50 ! [A2: set_state,R: set_Pr795498619_state,A: state,B2: state] :
% 2.92/1.50 ( ( refl_on_state @ A2 @ R )
% 2.92/1.50 => ( ( member1389040324_state @ ( produc64584659_state @ A @ B2 ) @ R )
% 2.92/1.50 => ( ( member_state @ A @ A2 )
% 2.92/1.50 & ( member_state @ B2 @ A2 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_264_refl__on__domain,axiom,
% 2.92/1.50 ! [A2: set_nat,R: set_Pr1986765409at_nat,A: nat,B2: nat] :
% 2.92/1.50 ( ( refl_on_nat @ A2 @ R )
% 2.92/1.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B2 ) @ R )
% 2.92/1.50 => ( ( member_nat @ A @ A2 )
% 2.92/1.50 & ( member_nat @ B2 @ A2 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_265_prod_Ocase__distrib,axiom,
% 2.92/1.50 ! [H: $o > $o,F: state > state > $o,Prod: produc1115495963_state] :
% 2.92/1.50 ( ( H @ ( produc789892016tate_o @ F @ Prod ) )
% 2.92/1.50 = ( produc789892016tate_o
% 2.92/1.50 @ ^ [X12: state,X23: state] : ( H @ ( F @ X12 @ X23 ) )
% 2.92/1.50 @ Prod ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_266_prod_Ocase__distrib,axiom,
% 2.92/1.50 ! [H: $o > $o,F: nat > nat > $o,Prod: product_prod_nat_nat] :
% 2.92/1.50 ( ( H @ ( produc949581770_nat_o @ F @ Prod ) )
% 2.92/1.50 = ( produc949581770_nat_o
% 2.92/1.50 @ ^ [X12: nat,X23: nat] : ( H @ ( F @ X12 @ X23 ) )
% 2.92/1.50 @ Prod ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_267_prod_Odisc__eq__case,axiom,
% 2.92/1.50 ! [Prod: produc1115495963_state] :
% 2.92/1.50 ( produc789892016tate_o
% 2.92/1.50 @ ^ [Uu: state,Uv: state] : $true
% 2.92/1.50 @ Prod ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_268_prod_Odisc__eq__case,axiom,
% 2.92/1.50 ! [Prod: product_prod_nat_nat] :
% 2.92/1.50 ( produc949581770_nat_o
% 2.92/1.50 @ ^ [Uu: nat,Uv: nat] : $true
% 2.92/1.50 @ Prod ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_269_old_Oprod_Ocase,axiom,
% 2.92/1.50 ! [F: state > state > $o,X1: state,X22: state] :
% 2.92/1.50 ( ( produc789892016tate_o @ F @ ( produc64584659_state @ X1 @ X22 ) )
% 2.92/1.50 = ( F @ X1 @ X22 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_270_old_Oprod_Ocase,axiom,
% 2.92/1.50 ! [F: nat > nat > $o,X1: nat,X22: nat] :
% 2.92/1.50 ( ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 2.92/1.50 = ( F @ X1 @ X22 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_271_refl__onD2,axiom,
% 2.92/1.50 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,X2: produc1115495963_state,Y3: produc1115495963_state] :
% 2.92/1.50 ( ( refl_o1438232218_state @ A2 @ R )
% 2.92/1.50 => ( ( member768948240_state @ ( produc1964772951_state @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member1389040324_state @ Y3 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_272_refl__onD2,axiom,
% 2.92/1.50 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 2.92/1.50 ( ( refl_o1619599232at_nat @ A2 @ R )
% 2.92/1.50 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member701585322at_nat @ Y3 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_273_refl__onD2,axiom,
% 2.92/1.50 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,X2: produc696469763tate_o,Y3: produc696469763tate_o] :
% 2.92/1.50 ( ( refl_o489021252tate_o @ A2 @ R )
% 2.92/1.50 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member1838112666tate_o @ Y3 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_274_refl__onD2,axiom,
% 2.92/1.50 ! [A2: set_state,R: set_Pr795498619_state,X2: state,Y3: state] :
% 2.92/1.50 ( ( refl_on_state @ A2 @ R )
% 2.92/1.50 => ( ( member1389040324_state @ ( produc64584659_state @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member_state @ Y3 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_275_refl__onD2,axiom,
% 2.92/1.50 ! [A2: set_nat,R: set_Pr1986765409at_nat,X2: nat,Y3: nat] :
% 2.92/1.50 ( ( refl_on_nat @ A2 @ R )
% 2.92/1.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member_nat @ Y3 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_276_refl__onD1,axiom,
% 2.92/1.50 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,X2: produc1115495963_state,Y3: produc1115495963_state] :
% 2.92/1.50 ( ( refl_o1438232218_state @ A2 @ R )
% 2.92/1.50 => ( ( member768948240_state @ ( produc1964772951_state @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member1389040324_state @ X2 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_277_refl__onD1,axiom,
% 2.92/1.50 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,X2: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 2.92/1.50 ( ( refl_o1619599232at_nat @ A2 @ R )
% 2.92/1.50 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member701585322at_nat @ X2 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_278_refl__onD1,axiom,
% 2.92/1.50 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,X2: produc696469763tate_o,Y3: produc696469763tate_o] :
% 2.92/1.50 ( ( refl_o489021252tate_o @ A2 @ R )
% 2.92/1.50 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member1838112666tate_o @ X2 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_279_refl__onD1,axiom,
% 2.92/1.50 ! [A2: set_state,R: set_Pr795498619_state,X2: state,Y3: state] :
% 2.92/1.50 ( ( refl_on_state @ A2 @ R )
% 2.92/1.50 => ( ( member1389040324_state @ ( produc64584659_state @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member_state @ X2 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_280_refl__onD1,axiom,
% 2.92/1.50 ! [A2: set_nat,R: set_Pr1986765409at_nat,X2: nat,Y3: nat] :
% 2.92/1.50 ( ( refl_on_nat @ A2 @ R )
% 2.92/1.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 2.92/1.50 => ( member_nat @ X2 @ A2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_281_refl__onD,axiom,
% 2.92/1.50 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state,A: produc1115495963_state] :
% 2.92/1.50 ( ( refl_o1438232218_state @ A2 @ R )
% 2.92/1.50 => ( ( member1389040324_state @ A @ A2 )
% 2.92/1.50 => ( member768948240_state @ ( produc1964772951_state @ A @ A ) @ R ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_282_refl__onD,axiom,
% 2.92/1.50 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat,A: product_prod_nat_nat] :
% 2.92/1.50 ( ( refl_o1619599232at_nat @ A2 @ R )
% 2.92/1.50 => ( ( member701585322at_nat @ A @ A2 )
% 2.92/1.50 => ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ A ) @ R ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_283_refl__onD,axiom,
% 2.92/1.50 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o,A: produc696469763tate_o] :
% 2.92/1.50 ( ( refl_o489021252tate_o @ A2 @ R )
% 2.92/1.50 => ( ( member1838112666tate_o @ A @ A2 )
% 2.92/1.50 => ( member1629320336tate_o @ ( produc1684562079tate_o @ A @ A ) @ R ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_284_refl__onD,axiom,
% 2.92/1.50 ! [A2: set_state,R: set_Pr795498619_state,A: state] :
% 2.92/1.50 ( ( refl_on_state @ A2 @ R )
% 2.92/1.50 => ( ( member_state @ A @ A2 )
% 2.92/1.50 => ( member1389040324_state @ ( produc64584659_state @ A @ A ) @ R ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_285_refl__onD,axiom,
% 2.92/1.50 ! [A2: set_nat,R: set_Pr1986765409at_nat,A: nat] :
% 2.92/1.50 ( ( refl_on_nat @ A2 @ R )
% 2.92/1.50 => ( ( member_nat @ A @ A2 )
% 2.92/1.50 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_286_case__prodD,axiom,
% 2.92/1.50 ! [F: ( a > state > $o ) > produc204914599tate_o > $o,A: a > state > $o,B2: produc204914599tate_o] :
% 2.92/1.50 ( ( produc1271576886te_o_o @ F @ ( produc33908149tate_o @ A @ B2 ) )
% 2.92/1.50 => ( F @ A @ B2 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_287_case__prodD,axiom,
% 2.92/1.50 ! [F: com > ( a > state > $o ) > $o,A: com,B2: a > state > $o] :
% 2.92/1.50 ( ( produc281270436te_o_o @ F @ ( produc1948644831tate_o @ A @ B2 ) )
% 2.92/1.50 => ( F @ A @ B2 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_288_case__prodD,axiom,
% 2.92/1.50 ! [F: state > state > $o,A: state,B2: state] :
% 2.92/1.50 ( ( produc789892016tate_o @ F @ ( produc64584659_state @ A @ B2 ) )
% 2.92/1.50 => ( F @ A @ B2 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_289_case__prodD,axiom,
% 2.92/1.50 ! [F: nat > nat > $o,A: nat,B2: nat] :
% 2.92/1.50 ( ( produc949581770_nat_o @ F @ ( product_Pair_nat_nat @ A @ B2 ) )
% 2.92/1.50 => ( F @ A @ B2 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_290_case__prodE,axiom,
% 2.92/1.50 ! [C2: ( a > state > $o ) > produc204914599tate_o > $o,P3: produc696469763tate_o] :
% 2.92/1.50 ( ( produc1271576886te_o_o @ C2 @ P3 )
% 2.92/1.50 => ~ ! [X3: a > state > $o,Y2: produc204914599tate_o] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( produc33908149tate_o @ X3 @ Y2 ) )
% 2.92/1.50 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_291_case__prodE,axiom,
% 2.92/1.50 ! [C2: com > ( a > state > $o ) > $o,P3: produc204914599tate_o] :
% 2.92/1.50 ( ( produc281270436te_o_o @ C2 @ P3 )
% 2.92/1.50 => ~ ! [X3: com,Y2: a > state > $o] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( produc1948644831tate_o @ X3 @ Y2 ) )
% 2.92/1.50 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_292_case__prodE,axiom,
% 2.92/1.50 ! [C2: state > state > $o,P3: produc1115495963_state] :
% 2.92/1.50 ( ( produc789892016tate_o @ C2 @ P3 )
% 2.92/1.50 => ~ ! [X3: state,Y2: state] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( produc64584659_state @ X3 @ Y2 ) )
% 2.92/1.50 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_293_case__prodE,axiom,
% 2.92/1.50 ! [C2: nat > nat > $o,P3: product_prod_nat_nat] :
% 2.92/1.50 ( ( produc949581770_nat_o @ C2 @ P3 )
% 2.92/1.50 => ~ ! [X3: nat,Y2: nat] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( product_Pair_nat_nat @ X3 @ Y2 ) )
% 2.92/1.50 => ~ ( C2 @ X3 @ Y2 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_294_total__on__def,axiom,
% 2.92/1.50 ( total_on_state
% 2.92/1.50 = ( ^ [A5: set_state,R3: set_Pr795498619_state] :
% 2.92/1.50 ! [X: state] :
% 2.92/1.50 ( ( member_state @ X @ A5 )
% 2.92/1.50 => ! [Y5: state] :
% 2.92/1.50 ( ( member_state @ Y5 @ A5 )
% 2.92/1.50 => ( ( X != Y5 )
% 2.92/1.50 => ( ( member1389040324_state @ ( produc64584659_state @ X @ Y5 ) @ R3 )
% 2.92/1.50 | ( member1389040324_state @ ( produc64584659_state @ Y5 @ X ) @ R3 ) ) ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_295_total__on__def,axiom,
% 2.92/1.50 ( total_on_nat
% 2.92/1.50 = ( ^ [A5: set_nat,R3: set_Pr1986765409at_nat] :
% 2.92/1.50 ! [X: nat] :
% 2.92/1.50 ( ( member_nat @ X @ A5 )
% 2.92/1.50 => ! [Y5: nat] :
% 2.92/1.50 ( ( member_nat @ Y5 @ A5 )
% 2.92/1.50 => ( ( X != Y5 )
% 2.92/1.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y5 ) @ R3 )
% 2.92/1.50 | ( member701585322at_nat @ ( product_Pair_nat_nat @ Y5 @ X ) @ R3 ) ) ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_296_total__onI,axiom,
% 2.92/1.50 ! [A2: set_Pr795498619_state,R: set_Pr778812871_state] :
% 2.92/1.50 ( ! [X3: produc1115495963_state,Y2: produc1115495963_state] :
% 2.92/1.50 ( ( member1389040324_state @ X3 @ A2 )
% 2.92/1.50 => ( ( member1389040324_state @ Y2 @ A2 )
% 2.92/1.50 => ( ( X3 != Y2 )
% 2.92/1.50 => ( ( member768948240_state @ ( produc1964772951_state @ X3 @ Y2 ) @ R )
% 2.92/1.50 | ( member768948240_state @ ( produc1964772951_state @ Y2 @ X3 ) @ R ) ) ) ) )
% 2.92/1.50 => ( total_1316653983_state @ A2 @ R ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_297_total__onI,axiom,
% 2.92/1.50 ! [A2: set_Pr1986765409at_nat,R: set_Pr1490359111at_nat] :
% 2.92/1.50 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 2.92/1.50 ( ( member701585322at_nat @ X3 @ A2 )
% 2.92/1.50 => ( ( member701585322at_nat @ Y2 @ A2 )
% 2.92/1.50 => ( ( X3 != Y2 )
% 2.92/1.50 => ( ( member2027625872at_nat @ ( produc1168807639at_nat @ X3 @ Y2 ) @ R )
% 2.92/1.50 | ( member2027625872at_nat @ ( produc1168807639at_nat @ Y2 @ X3 ) @ R ) ) ) ) )
% 2.92/1.50 => ( total_1775715973at_nat @ A2 @ R ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_298_total__onI,axiom,
% 2.92/1.50 ! [A2: set_Pr1590995257tate_o,R: set_Pr1702239303tate_o] :
% 2.92/1.50 ( ! [X3: produc696469763tate_o,Y2: produc696469763tate_o] :
% 2.92/1.50 ( ( member1838112666tate_o @ X3 @ A2 )
% 2.92/1.50 => ( ( member1838112666tate_o @ Y2 @ A2 )
% 2.92/1.50 => ( ( X3 != Y2 )
% 2.92/1.50 => ( ( member1629320336tate_o @ ( produc1684562079tate_o @ X3 @ Y2 ) @ R )
% 2.92/1.50 | ( member1629320336tate_o @ ( produc1684562079tate_o @ Y2 @ X3 ) @ R ) ) ) ) )
% 2.92/1.50 => ( total_795385983tate_o @ A2 @ R ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_299_total__onI,axiom,
% 2.92/1.50 ! [A2: set_state,R: set_Pr795498619_state] :
% 2.92/1.50 ( ! [X3: state,Y2: state] :
% 2.92/1.50 ( ( member_state @ X3 @ A2 )
% 2.92/1.50 => ( ( member_state @ Y2 @ A2 )
% 2.92/1.50 => ( ( X3 != Y2 )
% 2.92/1.50 => ( ( member1389040324_state @ ( produc64584659_state @ X3 @ Y2 ) @ R )
% 2.92/1.50 | ( member1389040324_state @ ( produc64584659_state @ Y2 @ X3 ) @ R ) ) ) ) )
% 2.92/1.50 => ( total_on_state @ A2 @ R ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_300_total__onI,axiom,
% 2.92/1.50 ! [A2: set_nat,R: set_Pr1986765409at_nat] :
% 2.92/1.50 ( ! [X3: nat,Y2: nat] :
% 2.92/1.50 ( ( member_nat @ X3 @ A2 )
% 2.92/1.50 => ( ( member_nat @ Y2 @ A2 )
% 2.92/1.50 => ( ( X3 != Y2 )
% 2.92/1.50 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R )
% 2.92/1.50 | ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ X3 ) @ R ) ) ) ) )
% 2.92/1.50 => ( total_on_nat @ A2 @ R ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_301_total__on__empty,axiom,
% 2.92/1.50 ! [R: set_Pr1986765409at_nat] : ( total_on_nat @ bot_bot_set_nat @ R ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_302_total__on__empty,axiom,
% 2.92/1.50 ! [R: set_Pr1702239303tate_o] : ( total_795385983tate_o @ bot_bo170732493tate_o @ R ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_303_total__on__empty,axiom,
% 2.92/1.50 ! [R: set_Pr1490359111at_nat] : ( total_1775715973at_nat @ bot_bo2130386637at_nat @ R ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_304_total__on__empty,axiom,
% 2.92/1.50 ! [R: set_Pr778812871_state] : ( total_1316653983_state @ bot_bo1625160935_state @ R ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_305_case__prodE2,axiom,
% 2.92/1.50 ! [Q: $o > $o,P: state > state > $o,Z5: produc1115495963_state] :
% 2.92/1.50 ( ( Q @ ( produc789892016tate_o @ P @ Z5 ) )
% 2.92/1.50 => ~ ! [X3: state,Y2: state] :
% 2.92/1.50 ( ( Z5
% 2.92/1.50 = ( produc64584659_state @ X3 @ Y2 ) )
% 2.92/1.50 => ~ ( Q @ ( P @ X3 @ Y2 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_306_case__prodE2,axiom,
% 2.92/1.50 ! [Q: $o > $o,P: nat > nat > $o,Z5: product_prod_nat_nat] :
% 2.92/1.50 ( ( Q @ ( produc949581770_nat_o @ P @ Z5 ) )
% 2.92/1.50 => ~ ! [X3: nat,Y2: nat] :
% 2.92/1.50 ( ( Z5
% 2.92/1.50 = ( product_Pair_nat_nat @ X3 @ Y2 ) )
% 2.92/1.50 => ~ ( Q @ ( P @ X3 @ Y2 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_307_case__prod__eta,axiom,
% 2.92/1.50 ! [F: produc1115495963_state > $o] :
% 2.92/1.50 ( ( produc789892016tate_o
% 2.92/1.50 @ ^ [X: state,Y5: state] : ( F @ ( produc64584659_state @ X @ Y5 ) ) )
% 2.92/1.50 = F ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_308_case__prod__eta,axiom,
% 2.92/1.50 ! [F: product_prod_nat_nat > $o] :
% 2.92/1.50 ( ( produc949581770_nat_o
% 2.92/1.50 @ ^ [X: nat,Y5: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y5 ) ) )
% 2.92/1.50 = F ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_309_cond__case__prod__eta,axiom,
% 2.92/1.50 ! [F: state > state > $o,G: produc1115495963_state > $o] :
% 2.92/1.50 ( ! [X3: state,Y2: state] :
% 2.92/1.50 ( ( F @ X3 @ Y2 )
% 2.92/1.50 = ( G @ ( produc64584659_state @ X3 @ Y2 ) ) )
% 2.92/1.50 => ( ( produc789892016tate_o @ F )
% 2.92/1.50 = G ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_310_cond__case__prod__eta,axiom,
% 2.92/1.50 ! [F: nat > nat > $o,G: product_prod_nat_nat > $o] :
% 2.92/1.50 ( ! [X3: nat,Y2: nat] :
% 2.92/1.50 ( ( F @ X3 @ Y2 )
% 2.92/1.50 = ( G @ ( product_Pair_nat_nat @ X3 @ Y2 ) ) )
% 2.92/1.50 => ( ( produc949581770_nat_o @ F )
% 2.92/1.50 = G ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_311_lnear__order__on__empty,axiom,
% 2.92/1.50 order_130026331on_nat @ bot_bot_set_nat @ bot_bo2130386637at_nat ).
% 2.92/1.50
% 2.92/1.50 thf(fact_312_lnear__order__on__empty,axiom,
% 2.92/1.50 order_286167592_state @ bot_bot_set_state @ bot_bo1625160935_state ).
% 2.92/1.50
% 2.92/1.50 thf(fact_313_lnear__order__on__empty,axiom,
% 2.92/1.50 order_50454158tate_o @ bot_bo170732493tate_o @ bot_bo1714653363tate_o ).
% 2.92/1.50
% 2.92/1.50 thf(fact_314_lnear__order__on__empty,axiom,
% 2.92/1.50 order_721919926at_nat @ bot_bo2130386637at_nat @ bot_bo34127283at_nat ).
% 2.92/1.50
% 2.92/1.50 thf(fact_315_lnear__order__on__empty,axiom,
% 2.92/1.50 order_178668240_state @ bot_bo1625160935_state @ bot_bo1331673139_state ).
% 2.92/1.50
% 2.92/1.50 thf(fact_316_refl__on__empty,axiom,
% 2.92/1.50 refl_on_nat @ bot_bot_set_nat @ bot_bo2130386637at_nat ).
% 2.92/1.50
% 2.92/1.50 thf(fact_317_refl__on__empty,axiom,
% 2.92/1.50 refl_on_state @ bot_bot_set_state @ bot_bo1625160935_state ).
% 2.92/1.50
% 2.92/1.50 thf(fact_318_refl__on__empty,axiom,
% 2.92/1.50 refl_o489021252tate_o @ bot_bo170732493tate_o @ bot_bo1714653363tate_o ).
% 2.92/1.50
% 2.92/1.50 thf(fact_319_refl__on__empty,axiom,
% 2.92/1.50 refl_o1619599232at_nat @ bot_bo2130386637at_nat @ bot_bo34127283at_nat ).
% 2.92/1.50
% 2.92/1.50 thf(fact_320_refl__on__empty,axiom,
% 2.92/1.50 refl_o1438232218_state @ bot_bo1625160935_state @ bot_bo1331673139_state ).
% 2.92/1.50
% 2.92/1.50 thf(fact_321_split__cong,axiom,
% 2.92/1.50 ! [Q5: produc1115495963_state,F: state > state > $o,G: state > state > $o,P3: produc1115495963_state] :
% 2.92/1.50 ( ! [X3: state,Y2: state] :
% 2.92/1.50 ( ( ( produc64584659_state @ X3 @ Y2 )
% 2.92/1.50 = Q5 )
% 2.92/1.50 => ( ( F @ X3 @ Y2 )
% 2.92/1.50 = ( G @ X3 @ Y2 ) ) )
% 2.92/1.50 => ( ( P3 = Q5 )
% 2.92/1.50 => ( ( produc789892016tate_o @ F @ P3 )
% 2.92/1.50 = ( produc789892016tate_o @ G @ Q5 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_322_split__cong,axiom,
% 2.92/1.50 ! [Q5: product_prod_nat_nat,F: nat > nat > $o,G: nat > nat > $o,P3: product_prod_nat_nat] :
% 2.92/1.50 ( ! [X3: nat,Y2: nat] :
% 2.92/1.50 ( ( ( product_Pair_nat_nat @ X3 @ Y2 )
% 2.92/1.50 = Q5 )
% 2.92/1.50 => ( ( F @ X3 @ Y2 )
% 2.92/1.50 = ( G @ X3 @ Y2 ) ) )
% 2.92/1.50 => ( ( P3 = Q5 )
% 2.92/1.50 => ( ( produc949581770_nat_o @ F @ P3 )
% 2.92/1.50 = ( produc949581770_nat_o @ G @ Q5 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_323_aboveS__def,axiom,
% 2.92/1.50 ( order_2027321734_state
% 2.92/1.50 = ( ^ [R3: set_Pr778812871_state,A3: produc1115495963_state] :
% 2.92/1.50 ( collec496201222_state
% 2.92/1.50 @ ^ [B7: produc1115495963_state] :
% 2.92/1.50 ( ( B7 != A3 )
% 2.92/1.50 & ( member768948240_state @ ( produc1964772951_state @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_324_aboveS__def,axiom,
% 2.92/1.50 ( order_665764460at_nat
% 2.92/1.50 = ( ^ [R3: set_Pr1490359111at_nat,A3: product_prod_nat_nat] :
% 2.92/1.50 ( collec7649004at_nat
% 2.92/1.50 @ ^ [B7: product_prod_nat_nat] :
% 2.92/1.50 ( ( B7 != A3 )
% 2.92/1.50 & ( member2027625872at_nat @ ( produc1168807639at_nat @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_325_aboveS__def,axiom,
% 2.92/1.50 ( order_1121016664tate_o
% 2.92/1.50 = ( ^ [R3: set_Pr1702239303tate_o,A3: produc696469763tate_o] :
% 2.92/1.50 ( collec1499596504tate_o
% 2.92/1.50 @ ^ [B7: produc696469763tate_o] :
% 2.92/1.50 ( ( B7 != A3 )
% 2.92/1.50 & ( member1629320336tate_o @ ( produc1684562079tate_o @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_326_aboveS__def,axiom,
% 2.92/1.50 ( order_aboveS_state
% 2.92/1.50 = ( ^ [R3: set_Pr795498619_state,A3: state] :
% 2.92/1.50 ( collect_state
% 2.92/1.50 @ ^ [B7: state] :
% 2.92/1.50 ( ( B7 != A3 )
% 2.92/1.50 & ( member1389040324_state @ ( produc64584659_state @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_327_aboveS__def,axiom,
% 2.92/1.50 ( order_aboveS_nat
% 2.92/1.50 = ( ^ [R3: set_Pr1986765409at_nat,A3: nat] :
% 2.92/1.50 ( collect_nat
% 2.92/1.50 @ ^ [B7: nat] :
% 2.92/1.50 ( ( B7 != A3 )
% 2.92/1.50 & ( member701585322at_nat @ ( product_Pair_nat_nat @ A3 @ B7 ) @ R3 ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_328_internal__case__prod__def,axiom,
% 2.92/1.50 produc938968666tate_o = produc789892016tate_o ).
% 2.92/1.50
% 2.92/1.50 thf(fact_329_internal__case__prod__def,axiom,
% 2.92/1.50 produc385877620_nat_o = produc949581770_nat_o ).
% 2.92/1.50
% 2.92/1.50 thf(fact_330_mem__case__prodI2,axiom,
% 2.92/1.50 ! [P3: product_prod_nat_nat,Z5: produc1115495963_state,C2: nat > nat > set_Pr795498619_state] :
% 2.92/1.50 ( ! [A6: nat,B6: nat] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 2.92/1.50 => ( member1389040324_state @ Z5 @ ( C2 @ A6 @ B6 ) ) )
% 2.92/1.50 => ( member1389040324_state @ Z5 @ ( produc1654445_state @ C2 @ P3 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_331_mem__case__prodI2,axiom,
% 2.92/1.50 ! [P3: product_prod_nat_nat,Z5: product_prod_nat_nat,C2: nat > nat > set_Pr1986765409at_nat] :
% 2.92/1.50 ( ! [A6: nat,B6: nat] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 2.92/1.50 => ( member701585322at_nat @ Z5 @ ( C2 @ A6 @ B6 ) ) )
% 2.92/1.50 => ( member701585322at_nat @ Z5 @ ( produc1915186323at_nat @ C2 @ P3 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_332_mem__case__prodI2,axiom,
% 2.92/1.50 ! [P3: product_prod_nat_nat,Z5: produc696469763tate_o,C2: nat > nat > set_Pr1590995257tate_o] :
% 2.92/1.50 ( ! [A6: nat,B6: nat] :
% 2.92/1.50 ( ( P3
% 2.92/1.50 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 2.92/1.50 => ( member1838112666tate_o @ Z5 @ ( C2 @ A6 @ B6 ) ) )
% 2.92/1.50 => ( member1838112666tate_o @ Z5 @ ( produc1610543495tate_o @ C2 @ P3 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_333_termi__while,axiom,
% 2.92/1.50 ! [B2: state > $o,C2: com,F: nat > state,K: nat] :
% 2.92/1.50 ( ( termi @ ( while @ B2 @ C2 ) @ ( F @ K ) )
% 2.92/1.50 => ( ! [I: nat] : ( exec @ ( F @ I ) @ C2 @ ( F @ ( suc @ I ) ) )
% 2.92/1.50 => ? [I: nat] :
% 2.92/1.50 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_334_termi__while__lemma,axiom,
% 2.92/1.50 ! [W: com,Fk: state,F: nat > state,K: nat,B2: state > $o,C2: com] :
% 2.92/1.50 ( ( termi @ W @ Fk )
% 2.92/1.50 => ( ( ( Fk
% 2.92/1.50 = ( F @ K ) )
% 2.92/1.50 & ( W
% 2.92/1.50 = ( while @ B2 @ C2 ) )
% 2.92/1.50 & ! [I: nat] : ( exec @ ( F @ I ) @ C2 @ ( F @ ( suc @ I ) ) ) )
% 2.92/1.50 => ? [I: nat] :
% 2.92/1.50 ~ ( B2 @ ( F @ I ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_335_execn_Ointros_I7_J,axiom,
% 2.92/1.50 ! [S2: state,N: nat,T2: state] :
% 2.92/1.50 ( ( execn @ S2 @ body @ N @ T2 )
% 2.92/1.50 => ( execn @ S2 @ call @ ( suc @ N ) @ T2 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_336_pred__nat__def,axiom,
% 2.92/1.50 ( pred_nat
% 2.92/1.50 = ( collec7649004at_nat
% 2.92/1.50 @ ( produc949581770_nat_o
% 2.92/1.50 @ ^ [M: nat,N2: nat] :
% 2.92/1.50 ( N2
% 2.92/1.50 = ( suc @ M ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_337_while__rule,axiom,
% 2.92/1.50 ! [S2: state,B2: state > $o,C2: com,N: nat,T2: state,P: state > $o] :
% 2.92/1.50 ( ( execn @ S2 @ ( while @ B2 @ C2 ) @ N @ T2 )
% 2.92/1.50 => ( ( P @ S2 )
% 2.92/1.50 => ( ! [S: state,S3: state] :
% 2.92/1.50 ( ( P @ S )
% 2.92/1.50 => ( ( B2 @ S )
% 2.92/1.50 => ( ( execn @ S @ C2 @ N @ S3 )
% 2.92/1.50 => ( P @ S3 ) ) ) )
% 2.92/1.50 => ( ( P @ T2 )
% 2.92/1.50 & ~ ( B2 @ T2 ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_338_while__lemma,axiom,
% 2.92/1.50 ! [S2: state,W: com,N: nat,T2: state,B2: state > $o,C2: com,P: state > $o] :
% 2.92/1.50 ( ( execn @ S2 @ W @ N @ T2 )
% 2.92/1.50 => ( ( ( W
% 2.92/1.50 = ( while @ B2 @ C2 ) )
% 2.92/1.50 & ( P @ S2 )
% 2.92/1.50 & ! [S: state,S3: state] :
% 2.92/1.50 ( ( ( P @ S )
% 2.92/1.50 & ( B2 @ S )
% 2.92/1.50 & ( execn @ S @ C2 @ N @ S3 ) )
% 2.92/1.50 => ( P @ S3 ) ) )
% 2.92/1.50 => ( ( P @ T2 )
% 2.92/1.50 & ~ ( B2 @ T2 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_339_execn_OWhileTrue,axiom,
% 2.92/1.50 ! [B2: state > $o,S2: state,C2: com,N: nat,T2: state,U2: state] :
% 2.92/1.50 ( ( B2 @ S2 )
% 2.92/1.50 => ( ( execn @ S2 @ C2 @ N @ T2 )
% 2.92/1.50 => ( ( execn @ T2 @ ( while @ B2 @ C2 ) @ N @ U2 )
% 2.92/1.50 => ( execn @ S2 @ ( while @ B2 @ C2 ) @ N @ U2 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_340_execn_OWhileFalse,axiom,
% 2.92/1.50 ! [B2: state > $o,S2: state,C2: com,N: nat] :
% 2.92/1.50 ( ~ ( B2 @ S2 )
% 2.92/1.50 => ( execn @ S2 @ ( while @ B2 @ C2 ) @ N @ S2 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_341_exec__iff__execn,axiom,
% 2.92/1.50 ( exec
% 2.92/1.50 = ( ^ [S4: state,C5: com,T3: state] :
% 2.92/1.50 ? [N2: nat] : ( execn @ S4 @ C5 @ N2 @ T3 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_342_wf__pred__nat,axiom,
% 2.92/1.50 wf_nat @ pred_nat ).
% 2.92/1.50
% 2.92/1.50 thf(fact_343_termi_OSemi,axiom,
% 2.92/1.50 ! [C1: com,S0: state,C22: com] :
% 2.92/1.50 ( ( termi @ C1 @ S0 )
% 2.92/1.50 => ( ! [S1: state] :
% 2.92/1.50 ( ( exec @ S0 @ C1 @ S1 )
% 2.92/1.50 => ( termi @ C22 @ S1 ) )
% 2.92/1.50 => ( termi @ ( semi @ C1 @ C22 ) @ S0 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_344_com_Oinject_I2_J,axiom,
% 2.92/1.50 ! [X21: com,X222: com,Y21: com,Y222: com] :
% 2.92/1.50 ( ( ( semi @ X21 @ X222 )
% 2.92/1.50 = ( semi @ Y21 @ Y222 ) )
% 2.92/1.50 = ( ( X21 = Y21 )
% 2.92/1.50 & ( X222 = Y222 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_345_execn_Ointros_I2_J,axiom,
% 2.92/1.50 ! [S0: state,C1: com,N: nat,S12: state,C22: com,S22: state] :
% 2.92/1.50 ( ( execn @ S0 @ C1 @ N @ S12 )
% 2.92/1.50 => ( ( execn @ S12 @ C22 @ N @ S22 )
% 2.92/1.50 => ( execn @ S0 @ ( semi @ C1 @ C22 ) @ N @ S22 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_346_com_Odistinct_I13_J,axiom,
% 2.92/1.50 ! [X21: com,X222: com,X41: state > $o,X42: com] :
% 2.92/1.50 ( ( semi @ X21 @ X222 )
% 2.92/1.50 != ( while @ X41 @ X42 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_347_com_Odistinct_I15_J,axiom,
% 2.92/1.50 ! [X21: com,X222: com] :
% 2.92/1.50 ( ( semi @ X21 @ X222 )
% 2.92/1.50 != call ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_348_exec_OSemi,axiom,
% 2.92/1.50 ! [S0: state,C1: com,S12: state,C22: com,S22: state] :
% 2.92/1.50 ( ( exec @ S0 @ C1 @ S12 )
% 2.92/1.50 => ( ( exec @ S12 @ C22 @ S22 )
% 2.92/1.50 => ( exec @ S0 @ ( semi @ C1 @ C22 ) @ S22 ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_349_wf__less__than,axiom,
% 2.92/1.50 wf_nat @ less_than ).
% 2.92/1.50
% 2.92/1.50 thf(fact_350_total__on__less__than,axiom,
% 2.92/1.50 ! [A2: set_nat] : ( total_on_nat @ A2 @ less_than ) ).
% 2.92/1.50
% 2.92/1.50 thf(fact_351_irrefl__less__than,axiom,
% 2.92/1.50 irrefl_nat @ less_than ).
% 2.92/1.50
% 2.92/1.50 thf(fact_352_trans__less__than,axiom,
% 2.92/1.50 trans_nat @ less_than ).
% 2.92/1.50
% 2.92/1.50 thf(fact_353_less__than__iff,axiom,
% 2.92/1.50 ! [X2: nat,Y3: nat] :
% 2.92/1.50 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ less_than )
% 2.92/1.50 = ( ord_less_nat @ X2 @ Y3 ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(conj_0,hypothesis,
% 2.92/1.50 ! [S6: state] :
% 2.92/1.50 ( ( pHoare382919414oare_a
% 2.92/1.50 @ ( insert2053719859tate_o
% 2.92/1.50 @ ( produc33908149tate_o
% 2.92/1.50 @ ^ [Z4: a,S4: state] :
% 2.92/1.50 ( ( pa @ Z4 @ S4 )
% 2.92/1.50 & ( member1389040324_state @ ( produc64584659_state @ S4 @ S6 ) @ r ) )
% 2.92/1.50 @ ( produc1948644831tate_o @ call @ qa ) )
% 2.92/1.50 @ bot_bo170732493tate_o )
% 2.92/1.50 @ ^ [Z4: a,S4: state] :
% 2.92/1.50 ( ( pa @ Z4 @ S4 )
% 2.92/1.50 & ( S4 = S6 ) )
% 2.92/1.50 @ body
% 2.92/1.50 @ qa )
% 2.92/1.50 & ( ( ! [S: state,T: state] :
% 2.92/1.50 ( ( exec @ S @ body @ T )
% 2.92/1.50 => ! [Z: a] :
% 2.92/1.50 ( ( ( pa @ Z @ S )
% 2.92/1.50 & ( member1389040324_state @ ( produc64584659_state @ S @ S6 ) @ r ) )
% 2.92/1.50 => ( qa @ Z @ T ) ) )
% 2.92/1.50 & ! [Z: a,S: state] :
% 2.92/1.50 ( ( ( pa @ Z @ S )
% 2.92/1.50 & ( member1389040324_state @ ( produc64584659_state @ S @ S6 ) @ r ) )
% 2.92/1.50 => ( termi @ body @ S ) ) )
% 2.92/1.50 => ( ! [S7: state,T4: state] :
% 2.92/1.50 ( ( exec @ S7 @ body @ T4 )
% 2.92/1.50 => ! [Z2: a] :
% 2.92/1.50 ( ( ( pa @ Z2 @ S7 )
% 2.92/1.50 & ( S7 = S6 ) )
% 2.92/1.50 => ( qa @ Z2 @ T4 ) ) )
% 2.92/1.50 & ! [Z2: a,S7: state] :
% 2.92/1.50 ( ( ( pa @ Z2 @ S7 )
% 2.92/1.50 & ( S7 = S6 ) )
% 2.92/1.50 => ( termi @ body @ S7 ) ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(conj_1,hypothesis,
% 2.92/1.50 ! [Y4: state] :
% 2.92/1.50 ( ( member1389040324_state @ ( produc64584659_state @ Y4 @ x ) @ r )
% 2.92/1.50 => ( ! [S7: state,T4: state] :
% 2.92/1.50 ( ( exec @ S7 @ body @ T4 )
% 2.92/1.50 => ! [Z2: a] :
% 2.92/1.50 ( ( ( pa @ Z2 @ S7 )
% 2.92/1.50 & ( S7 = Y4 ) )
% 2.92/1.50 => ( qa @ Z2 @ T4 ) ) )
% 2.92/1.50 & ! [Z2: a,S7: state] :
% 2.92/1.50 ( ( ( pa @ Z2 @ S7 )
% 2.92/1.50 & ( S7 = Y4 ) )
% 2.92/1.50 => ( termi @ body @ S7 ) ) ) ) ).
% 2.92/1.50
% 2.92/1.50 thf(conj_2,conjecture,
% 2.92/1.50 ( ! [S: state,T: state] :
% 2.92/1.50 ( ~ ( exec @ S @ body @ T )
% 2.92/1.50 | ! [Z: a] :
% 2.92/1.50 ( ~ ( pa @ Z @ S )
% 2.92/1.50 | ( S != x )
% 2.92/1.50 | ( qa @ Z @ T ) ) )
% 2.92/1.50 & ! [Z: a,S: state] :
% 2.92/1.50 ( ~ ( pa @ Z @ S )
% 2.92/1.50 | ( S != x )
% 2.92/1.50 | ( termi @ body @ S ) ) ) ).
% 2.92/1.50 ------------------------
% 2.92/1.53 % (16861)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_16650 for (2999ds/27Mi)
% 2.92/1.53 % (16860)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_16650 for (2999ds/4Mi)
% 2.92/1.53 % (16862)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/2Mi)
% 2.92/1.53 % (16860)Instruction limit reached!
% 2.92/1.53 % (16860)------------------------------
% 2.92/1.53 % (16860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.53 % (16860)Termination reason: Unknown
% 2.92/1.53 % (16860)Termination phase: shuffling
% 2.92/1.53
% 2.92/1.53 % (16860)Memory used [KB]: 1663
% 2.92/1.53 % (16860)Time elapsed: 0.003 s
% 2.92/1.53 % (16860)Instructions burned: 5 (million)
% 2.92/1.53 % (16860)------------------------------
% 2.92/1.53 % (16860)------------------------------
% 2.92/1.53 % (16862)Instruction limit reached!
% 2.92/1.53 % (16862)------------------------------
% 2.92/1.53 % (16862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.53 % (16862)Termination reason: Unknown
% 2.92/1.53 % (16862)Termination phase: shuffling
% 2.92/1.53
% 2.92/1.53 % (16862)Memory used [KB]: 1535
% 2.92/1.53 % (16862)Time elapsed: 0.002 s
% 2.92/1.53 % (16862)Instructions burned: 2 (million)
% 2.92/1.53 % (16862)------------------------------
% 2.92/1.53 % (16862)------------------------------
% 2.92/1.54 % (16859)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/183Mi)
% 2.92/1.54 % (16863)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_16650 for (2999ds/2Mi)
% 2.92/1.54 % (16864)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_16650 for (2999ds/275Mi)
% 2.92/1.54 % (16865)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/18Mi)
% 2.92/1.54 % (16861)Instruction limit reached!
% 2.92/1.54 % (16861)------------------------------
% 2.92/1.54 % (16861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.54 % (16861)Termination reason: Unknown
% 2.92/1.54 % (16861)Termination phase: shuffling
% 2.92/1.54
% 2.92/1.54 % (16861)Memory used [KB]: 2046
% 2.92/1.54 % (16861)Time elapsed: 0.011 s
% 2.92/1.54 % (16861)Instructions burned: 29 (million)
% 2.92/1.54 % (16861)------------------------------
% 2.92/1.54 % (16861)------------------------------
% 2.92/1.54 % (16863)Instruction limit reached!
% 2.92/1.54 % (16863)------------------------------
% 2.92/1.54 % (16863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.54 % (16863)Termination reason: Unknown
% 2.92/1.54 % (16863)Termination phase: shuffling
% 2.92/1.54
% 2.92/1.54 % (16863)Memory used [KB]: 1535
% 2.92/1.54 % (16863)Time elapsed: 0.004 s
% 2.92/1.54 % (16863)Instructions burned: 3 (million)
% 2.92/1.54 % (16863)------------------------------
% 2.92/1.54 % (16863)------------------------------
% 2.92/1.54 % (16866)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/3Mi)
% 2.92/1.54 % (16867)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_16650 for (2999ds/37Mi)
% 2.92/1.54 % (16866)Instruction limit reached!
% 2.92/1.54 % (16866)------------------------------
% 2.92/1.54 % (16866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.54 % (16866)Termination reason: Unknown
% 2.92/1.54 % (16866)Termination phase: shuffling
% 2.92/1.54
% 2.92/1.54 % (16866)Memory used [KB]: 1535
% 2.92/1.54 % (16866)Time elapsed: 0.003 s
% 2.92/1.54 % (16866)Instructions burned: 5 (million)
% 2.92/1.54 % (16866)------------------------------
% 2.92/1.54 % (16866)------------------------------
% 2.92/1.55 % (16868)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_16650 for (2999ds/15Mi)
% 2.92/1.55 % (16865)Instruction limit reached!
% 2.92/1.55 % (16865)------------------------------
% 2.92/1.55 % (16865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.55 % (16865)Termination reason: Unknown
% 2.92/1.55 % (16865)Termination phase: shuffling
% 2.92/1.55
% 2.92/1.55 % (16865)Memory used [KB]: 1918
% 2.92/1.55 % (16865)Time elapsed: 0.014 s
% 2.92/1.55 % (16865)Instructions burned: 19 (million)
% 2.92/1.55 % (16865)------------------------------
% 2.92/1.55 % (16865)------------------------------
% 2.92/1.55 % (16870)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_16650 for (2999ds/1041Mi)
% 2.92/1.55 % (16867)Instruction limit reached!
% 2.92/1.55 % (16867)------------------------------
% 2.92/1.55 % (16867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.55 % (16867)Termination reason: Unknown
% 2.92/1.55 % (16867)Termination phase: shuffling
% 2.92/1.55
% 2.92/1.55 % (16867)Memory used [KB]: 2302
% 2.92/1.55 % (16867)Time elapsed: 0.012 s
% 2.92/1.55 % (16867)Instructions burned: 38 (million)
% 2.92/1.55 % (16867)------------------------------
% 2.92/1.55 % (16867)------------------------------
% 2.92/1.55 % (16868)Instruction limit reached!
% 2.92/1.55 % (16868)------------------------------
% 2.92/1.55 % (16868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.55 % (16868)Termination reason: Unknown
% 2.92/1.55 % (16868)Termination phase: shuffling
% 2.92/1.55
% 2.92/1.55 % (16868)Memory used [KB]: 1791
% 2.92/1.55 % (16868)Time elapsed: 0.006 s
% 2.92/1.55 % (16868)Instructions burned: 15 (million)
% 2.92/1.55 % (16868)------------------------------
% 2.92/1.55 % (16868)------------------------------
% 2.92/1.56 % (16869)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_16650 for (2999ds/3Mi)
% 2.92/1.56 % (16869)Instruction limit reached!
% 2.92/1.56 % (16869)------------------------------
% 2.92/1.56 % (16869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.56 % (16869)Termination reason: Unknown
% 2.92/1.56 % (16869)Termination phase: shuffling
% 2.92/1.56
% 2.92/1.56 % (16869)Memory used [KB]: 1535
% 2.92/1.56 % (16869)Time elapsed: 0.004 s
% 2.92/1.56 % (16869)Instructions burned: 3 (million)
% 2.92/1.56 % (16869)------------------------------
% 2.92/1.56 % (16869)------------------------------
% 2.92/1.56 % (16872)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/16Mi)
% 2.92/1.56 % (16873)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_16650 for (2999ds/3Mi)
% 2.92/1.56 % (16873)Instruction limit reached!
% 2.92/1.56 % (16873)------------------------------
% 2.92/1.56 % (16873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.56 % (16873)Termination reason: Unknown
% 2.92/1.56 % (16873)Termination phase: shuffling
% 2.92/1.56
% 2.92/1.56 % (16873)Memory used [KB]: 1535
% 2.92/1.56 % (16873)Time elapsed: 0.002 s
% 2.92/1.56 % (16873)Instructions burned: 3 (million)
% 2.92/1.56 % (16873)------------------------------
% 2.92/1.56 % (16873)------------------------------
% 2.92/1.57 % (16871)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/7Mi)
% 2.92/1.57 % (16872)Instruction limit reached!
% 2.92/1.57 % (16872)------------------------------
% 2.92/1.57 % (16872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.57 % (16872)Termination reason: Unknown
% 2.92/1.57 % (16872)Termination phase: shuffling
% 2.92/1.57
% 2.92/1.57 % (16872)Memory used [KB]: 1918
% 2.92/1.57 % (16872)Time elapsed: 0.008 s
% 2.92/1.57 % (16872)Instructions burned: 18 (million)
% 2.92/1.57 % (16872)------------------------------
% 2.92/1.57 % (16872)------------------------------
% 2.92/1.57 % (16871)Instruction limit reached!
% 2.92/1.57 % (16871)------------------------------
% 2.92/1.57 % (16871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.57 % (16871)Termination reason: Unknown
% 2.92/1.57 % (16871)Termination phase: shuffling
% 2.92/1.57
% 2.92/1.57 % (16871)Memory used [KB]: 1663
% 2.92/1.57 % (16871)Time elapsed: 0.007 s
% 2.92/1.57 % (16871)Instructions burned: 8 (million)
% 2.92/1.57 % (16871)------------------------------
% 2.92/1.57 % (16871)------------------------------
% 2.92/1.57 % (16875)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/7Mi)
% 2.92/1.58 % (16875)Instruction limit reached!
% 2.92/1.58 % (16875)------------------------------
% 2.92/1.58 % (16875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.58 % (16875)Termination reason: Unknown
% 2.92/1.58 % (16875)Termination phase: shuffling
% 2.92/1.58
% 2.92/1.58 % (16875)Memory used [KB]: 1791
% 2.92/1.58 % (16875)Time elapsed: 0.004 s
% 2.92/1.58 % (16875)Instructions burned: 9 (million)
% 2.92/1.58 % (16875)------------------------------
% 2.92/1.58 % (16875)------------------------------
% 2.92/1.58 % (16874)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_16650 for (2999ds/3Mi)
% 2.92/1.58 % (16874)Instruction limit reached!
% 2.92/1.58 % (16874)------------------------------
% 2.92/1.58 % (16874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.58 % (16874)Termination reason: Unknown
% 2.92/1.58 % (16874)Termination phase: shuffling
% 2.92/1.58
% 2.92/1.58 % (16874)Memory used [KB]: 1535
% 2.92/1.58 % (16874)Time elapsed: 0.004 s
% 2.92/1.58 % (16874)Instructions burned: 3 (million)
% 2.92/1.58 % (16874)------------------------------
% 2.92/1.58 % (16874)------------------------------
% 2.92/1.58 % (16876)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/3Mi)
% 2.92/1.58 % (16876)Instruction limit reached!
% 2.92/1.58 % (16876)------------------------------
% 2.92/1.58 % (16876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.58 % (16876)Termination reason: Unknown
% 2.92/1.58 % (16876)Termination phase: shuffling
% 2.92/1.58
% 2.92/1.58 % (16876)Memory used [KB]: 1535
% 2.92/1.58 % (16876)Time elapsed: 0.003 s
% 2.92/1.58 % (16876)Instructions burned: 4 (million)
% 2.92/1.58 % (16876)------------------------------
% 2.92/1.58 % (16876)------------------------------
% 2.92/1.59 % (16878)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/18Mi)
% 2.92/1.59 % (16877)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/4Mi)
% 2.92/1.59 % (16880)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/6Mi)
% 2.92/1.59 % (16878)Instruction limit reached!
% 2.92/1.59 % (16878)------------------------------
% 2.92/1.59 % (16878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.59 % (16878)Termination reason: Unknown
% 2.92/1.59 % (16878)Termination phase: shuffling
% 2.92/1.59
% 2.92/1.59 % (16878)Memory used [KB]: 1918
% 2.92/1.59 % (16878)Time elapsed: 0.007 s
% 2.92/1.59 % (16878)Instructions burned: 18 (million)
% 2.92/1.59 % (16878)------------------------------
% 2.92/1.59 % (16878)------------------------------
% 2.92/1.59 % (16877)Instruction limit reached!
% 2.92/1.59 % (16877)------------------------------
% 2.92/1.59 % (16877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.59 % (16877)Termination reason: Unknown
% 2.92/1.59 % (16877)Termination phase: shuffling
% 2.92/1.59
% 2.92/1.59 % (16877)Memory used [KB]: 1535
% 2.92/1.59 % (16877)Time elapsed: 0.005 s
% 2.92/1.59 % (16877)Instructions burned: 5 (million)
% 2.92/1.59 % (16877)------------------------------
% 2.92/1.59 % (16877)------------------------------
% 2.92/1.59 % (16880)Instruction limit reached!
% 2.92/1.59 % (16880)------------------------------
% 2.92/1.59 % (16880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.59 % (16880)Termination reason: Unknown
% 2.92/1.59 % (16880)Termination phase: shuffling
% 2.92/1.59
% 2.92/1.59 % (16880)Memory used [KB]: 1663
% 2.92/1.59 % (16880)Time elapsed: 0.004 s
% 2.92/1.59 % (16880)Instructions burned: 6 (million)
% 2.92/1.59 % (16880)------------------------------
% 2.92/1.59 % (16880)------------------------------
% 2.92/1.60 % (16879)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/710Mi)
% 2.92/1.60 % (16881)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_16650 for (2999ds/902Mi)
% 2.92/1.60 % (16882)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_16650 for (2999ds/21Mi)
% 2.92/1.61 % (16864)Refutation not found, incomplete strategy
% 2.92/1.61 % (16864)------------------------------
% 2.92/1.61 % (16864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (16864)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.61
% 2.92/1.61
% 2.92/1.61 % (16864)Memory used [KB]: 7419
% 2.92/1.61 % (16864)Time elapsed: 0.072 s
% 2.92/1.61 % (16864)Instructions burned: 138 (million)
% 2.92/1.61 % (16864)------------------------------
% 2.92/1.61 % (16864)------------------------------
% 2.92/1.61 % (16882)Instruction limit reached!
% 2.92/1.61 % (16882)------------------------------
% 2.92/1.61 % (16882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (16882)Termination reason: Unknown
% 2.92/1.61 % (16882)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (16882)Memory used [KB]: 1918
% 2.92/1.61 % (16882)Time elapsed: 0.009 s
% 2.92/1.61 % (16882)Instructions burned: 21 (million)
% 2.92/1.61 % (16882)------------------------------
% 2.92/1.61 % (16882)------------------------------
% 2.92/1.61 % (16883)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16650 for (2999ds/5Mi)
% 2.92/1.61 % (16883)Instruction limit reached!
% 2.92/1.61 % (16883)------------------------------
% 2.92/1.61 % (16883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (16883)Termination reason: Unknown
% 2.92/1.61 % (16883)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (16883)Memory used [KB]: 1663
% 2.92/1.61 % (16883)Time elapsed: 0.005 s
% 2.92/1.61 % (16883)Instructions burned: 5 (million)
% 2.92/1.61 % (16883)------------------------------
% 2.92/1.61 % (16883)------------------------------
% 2.92/1.62 % (16884)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_16650 for (2998ds/6Mi)
% 2.92/1.62 % (16885)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16650 for (2998ds/377Mi)
% 2.92/1.62 % (16884)Instruction limit reached!
% 2.92/1.62 % (16884)------------------------------
% 2.92/1.62 % (16884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (16884)Termination reason: Unknown
% 2.92/1.62 % (16884)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (16884)Memory used [KB]: 1663
% 2.92/1.62 % (16884)Time elapsed: 0.004 s
% 2.92/1.62 % (16884)Instructions burned: 7 (million)
% 2.92/1.62 % (16884)------------------------------
% 2.92/1.62 % (16884)------------------------------
% 2.92/1.63 % (16886)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_16650 for (2998ds/779Mi)
% 2.92/1.63 % (16887)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_16650 for (2998ds/19Mi)
% 2.92/1.63 % (16859)Instruction limit reached!
% 2.92/1.63 % (16859)------------------------------
% 2.92/1.63 % (16859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (16859)Termination reason: Unknown
% 2.92/1.63 % (16859)Termination phase: Saturation
% 2.92/1.63
% 2.92/1.63 % (16859)Memory used [KB]: 7547
% 2.92/1.63 % (16859)Time elapsed: 0.097 s
% 2.92/1.63 % (16859)Instructions burned: 183 (million)
% 2.92/1.63 % (16859)------------------------------
% 2.92/1.63 % (16859)------------------------------
% 2.92/1.64 % (16887)Instruction limit reached!
% 2.92/1.64 % (16887)------------------------------
% 2.92/1.64 % (16887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (16887)Termination reason: Unknown
% 2.92/1.64 % (16887)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (16887)Memory used [KB]: 2046
% 2.92/1.64 % (16887)Time elapsed: 0.008 s
% 2.92/1.64 % (16887)Instructions burned: 20 (million)
% 2.92/1.64 % (16887)------------------------------
% 2.92/1.64 % (16887)------------------------------
% 2.92/1.65 % (16889)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16650 for (2998ds/17Mi)
% 2.92/1.65 % (16888)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16650 for (2998ds/879Mi)
% 2.92/1.65 % (16889)Instruction limit reached!
% 2.92/1.65 % (16889)------------------------------
% 2.92/1.65 % (16889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (16889)Termination reason: Unknown
% 2.92/1.65 % (16889)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (16889)Memory used [KB]: 1918
% 2.92/1.65 % (16889)Time elapsed: 0.008 s
% 2.92/1.65 % (16889)Instructions burned: 18 (million)
% 2.92/1.65 % (16889)------------------------------
% 2.92/1.65 % (16889)------------------------------
% 2.92/1.66 % (16890)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16650 for (2998ds/3Mi)
% 2.92/1.67 % (16890)Instruction limit reached!
% 2.92/1.67 % (16890)------------------------------
% 2.92/1.67 % (16890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (16890)Termination reason: Unknown
% 2.92/1.67 % (16890)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (16890)Memory used [KB]: 1535
% 2.92/1.67 % (16890)Time elapsed: 0.003 s
% 2.92/1.67 % (16890)Instructions burned: 3 (million)
% 2.92/1.67 % (16890)------------------------------
% 2.92/1.67 % (16890)------------------------------
% 2.92/1.68 % (16891)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16650 for (2998ds/30Mi)
% 2.92/1.69 % (16891)Instruction limit reached!
% 2.92/1.69 % (16891)------------------------------
% 2.92/1.69 % (16891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.69 % (16891)Termination reason: Unknown
% 2.92/1.69 % (16891)Termination phase: shuffling
% 2.92/1.69
% 2.92/1.69 % (16891)Memory used [KB]: 2046
% 2.92/1.69 % (16891)Time elapsed: 0.012 s
% 2.92/1.69 % (16891)Instructions burned: 30 (million)
% 2.92/1.69 % (16891)------------------------------
% 2.92/1.69 % (16891)------------------------------
% 2.92/1.70 % (16892)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16650 for (2998ds/127Mi)
% 2.92/1.73 % (16885)Instruction limit reached!
% 2.92/1.73 % (16885)------------------------------
% 2.92/1.73 % (16885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.73 % (16885)Termination reason: Unknown
% 2.92/1.73 % (16885)Termination phase: Saturation
% 2.92/1.73
% 2.92/1.73 % (16885)Memory used [KB]: 9083
% 2.92/1.73 % (16885)Time elapsed: 0.115 s
% 2.92/1.73 % (16885)Instructions burned: 379 (million)
% 2.92/1.73 % (16885)------------------------------
% 2.92/1.73 % (16885)------------------------------
% 2.92/1.73 % (16892)Instruction limit reached!
% 2.92/1.73 % (16892)------------------------------
% 2.92/1.73 % (16892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.73 % (16892)Termination reason: Unknown
% 2.92/1.73 % (16892)Termination phase: Property scanning
% 2.92/1.73
% 2.92/1.73 % (16892)Memory used [KB]: 2814
% 2.92/1.73 % (16892)Time elapsed: 0.040 s
% 2.92/1.73 % (16892)Instructions burned: 127 (million)
% 2.92/1.73 % (16892)------------------------------
% 2.92/1.73 % (16892)------------------------------
% 2.92/1.74 % (16893)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16650 for (2997ds/100Mi)
% 2.92/1.74 % (16894)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_16650 for (2997ds/3Mi)
% 2.92/1.75 % (16894)Instruction limit reached!
% 2.92/1.75 % (16894)------------------------------
% 2.92/1.75 % (16894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.75 % (16894)Termination reason: Unknown
% 2.92/1.75 % (16894)Termination phase: shuffling
% 2.92/1.75
% 2.92/1.75 % (16894)Memory used [KB]: 1535
% 2.92/1.75 % (16894)Time elapsed: 0.002 s
% 2.92/1.75 % (16894)Instructions burned: 3 (million)
% 2.92/1.75 % (16894)------------------------------
% 2.92/1.75 % (16894)------------------------------
% 2.92/1.76 % (16895)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_16650 for (2997ds/20Mi)
% 2.92/1.76 % (16895)Instruction limit reached!
% 2.92/1.76 % (16895)------------------------------
% 2.92/1.76 % (16895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.76 % (16895)Termination reason: Unknown
% 2.92/1.76 % (16895)Termination phase: shuffling
% 2.92/1.76
% 2.92/1.76 % (16895)Memory used [KB]: 1918
% 2.92/1.76 % (16895)Time elapsed: 0.009 s
% 2.92/1.76 % (16895)Instructions burned: 21 (million)
% 2.92/1.76 % (16895)------------------------------
% 2.92/1.76 % (16895)------------------------------
% 2.92/1.77 % (16893)Instruction limit reached!
% 2.92/1.77 % (16893)------------------------------
% 2.92/1.77 % (16893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.77 % (16893)Termination reason: Unknown
% 2.92/1.77 % (16893)Termination phase: Property scanning
% 2.92/1.77
% 2.92/1.77 % (16893)Memory used [KB]: 2814
% 2.92/1.77 % (16893)Time elapsed: 0.028 s
% 2.92/1.77 % (16893)Instructions burned: 101 (million)
% 2.92/1.77 % (16893)------------------------------
% 2.92/1.77 % (16893)------------------------------
% 2.92/1.77 % (16896)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_16650 for (2997ds/86Mi)
% 2.92/1.78 % (16897)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_16650 for (2997ds/107Mi)
% 2.92/1.80 % (16896)Instruction limit reached!
% 2.92/1.80 % (16896)------------------------------
% 2.92/1.80 % (16896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.80 % (16896)Termination reason: Unknown
% 2.92/1.80 % (16896)Termination phase: Function definition elimination
% 2.92/1.80
% 2.92/1.80 % (16896)Memory used [KB]: 2686
% 2.92/1.80 % (16896)Time elapsed: 0.029 s
% 2.92/1.80 % (16896)Instructions burned: 88 (million)
% 2.92/1.80 % (16896)------------------------------
% 2.92/1.80 % (16896)------------------------------
% 2.92/1.81 % (16898)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_16650 for (2997ds/39Mi)
% 2.92/1.81 % (16897)Instruction limit reached!
% 2.92/1.81 % (16897)------------------------------
% 2.92/1.81 % (16897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.81 % (16897)Termination reason: Unknown
% 2.92/1.81 % (16897)Termination phase: Property scanning
% 2.92/1.81
% 2.92/1.81 % (16897)Memory used [KB]: 2686
% 2.92/1.81 % (16897)Time elapsed: 0.033 s
% 2.92/1.81 % (16897)Instructions burned: 110 (million)
% 2.92/1.81 % (16897)------------------------------
% 2.92/1.81 % (16897)------------------------------
% 2.92/1.82 % (16899)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_16650 for (2997ds/448Mi)
% 2.92/1.82 % (16898)Instruction limit reached!
% 2.92/1.82 % (16898)------------------------------
% 2.92/1.82 % (16898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.82 % (16898)Termination reason: Unknown
% 2.92/1.82 % (16898)Termination phase: shuffling
% 2.92/1.82
% 2.92/1.82 % (16898)Memory used [KB]: 2430
% 2.92/1.82 % (16898)Time elapsed: 0.013 s
% 2.92/1.82 % (16898)Instructions burned: 41 (million)
% 2.92/1.82 % (16898)------------------------------
% 2.92/1.82 % (16898)------------------------------
% 2.92/1.83 % (16879)Instruction limit reached!
% 2.92/1.83 % (16879)------------------------------
% 2.92/1.83 % (16879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.83 % (16879)Termination reason: Unknown
% 2.92/1.83 % (16879)Termination phase: Saturation
% 2.92/1.83
% 2.92/1.83 % (16879)Memory used [KB]: 8059
% 2.92/1.83 % (16879)Time elapsed: 0.232 s
% 2.92/1.83 % (16879)Instructions burned: 710 (million)
% 2.92/1.83 % (16879)------------------------------
% 2.92/1.83 % (16879)------------------------------
% 2.92/1.83 % (16900)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_16650 for (2996ds/46Mi)
% 2.92/1.84 % (16901)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_16650 for (2996ds/98Mi)
% 2.92/1.85 % (16900)Instruction limit reached!
% 2.92/1.85 % (16900)------------------------------
% 2.92/1.85 % (16900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.85 % (16900)Termination reason: Unknown
% 2.92/1.85 % (16900)Termination phase: SInE selection
% 2.92/1.85
% 2.92/1.85 % (16900)Memory used [KB]: 2046
% 2.92/1.85 % (16900)Time elapsed: 0.017 s
% 2.92/1.85 % (16900)Instructions burned: 48 (million)
% 2.92/1.85 % (16900)------------------------------
% 2.92/1.85 % (16900)------------------------------
% 2.92/1.86 % (16902)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_16650 for (2996ds/507Mi)
% 2.92/1.86 % (16901)Instruction limit reached!
% 2.92/1.86 % (16901)------------------------------
% 2.92/1.86 % (16901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.86 % (16901)Termination reason: Unknown
% 2.92/1.86 % (16901)Termination phase: Property scanning
% 2.92/1.86
% 2.92/1.86 % (16901)Memory used [KB]: 2814
% 2.92/1.86 % (16901)Time elapsed: 0.028 s
% 2.92/1.86 % (16901)Instructions burned: 98 (million)
% 2.92/1.86 % (16901)------------------------------
% 2.92/1.86 % (16901)------------------------------
% 2.92/1.86 % (16881)Instruction limit reached!
% 2.92/1.86 % (16881)------------------------------
% 2.92/1.86 % (16881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.86 % (16881)Termination reason: Unknown
% 2.92/1.86 % (16881)Termination phase: Saturation
% 2.92/1.86
% 2.92/1.86 % (16881)Memory used [KB]: 8571
% 2.92/1.86 % (16881)Time elapsed: 0.263 s
% 2.92/1.86 % (16881)Instructions burned: 904 (million)
% 2.92/1.86 % (16881)------------------------------
% 2.92/1.86 % (16881)------------------------------
% 2.92/1.87 % (16870)Instruction limit reached!
% 2.92/1.87 % (16870)------------------------------
% 2.92/1.87 % (16870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.87 % (16870)Termination reason: Unknown
% 2.92/1.87 % (16870)Termination phase: Saturation
% 2.92/1.87
% 2.92/1.87 % (16870)Memory used [KB]: 10490
% 2.92/1.87 % (16870)Time elapsed: 0.321 s
% 2.92/1.87 % (16870)Instructions burned: 1041 (million)
% 2.92/1.87 % (16870)------------------------------
% 2.92/1.87 % (16870)------------------------------
% 2.92/1.87 % (16903)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_16650 for (2996ds/149Mi)
% 2.92/1.87 % (16904)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_16650 for (2996ds/39Mi)
% 2.92/1.88 % (16905)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_16650 for (2996ds/6Mi)
% 2.92/1.88 % (16905)Instruction limit reached!
% 2.92/1.88 % (16905)------------------------------
% 2.92/1.88 % (16905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.88 % (16905)Termination reason: Unknown
% 2.92/1.88 % (16905)Termination phase: shuffling
% 2.92/1.88
% 2.92/1.88 % (16905)Memory used [KB]: 1663
% 2.92/1.88 % (16905)Time elapsed: 0.004 s
% 2.92/1.88 % (16905)Instructions burned: 8 (million)
% 2.92/1.88 % (16905)------------------------------
% 2.92/1.88 % (16905)------------------------------
% 2.92/1.89 % (16904)Instruction limit reached!
% 2.92/1.89 % (16904)------------------------------
% 2.92/1.89 % (16904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.89 % (16904)Termination reason: Unknown
% 2.92/1.89 % (16904)Termination phase: Property scanning
% 2.92/1.89
% 2.92/1.89 % (16904)Memory used [KB]: 2046
% 2.92/1.89 % (16904)Time elapsed: 0.014 s
% 2.92/1.89 % (16904)Instructions burned: 41 (million)
% 2.92/1.89 % (16904)------------------------------
% 2.92/1.89 % (16904)------------------------------
% 2.92/1.89 % (16886)Instruction limit reached!
% 2.92/1.89 % (16886)------------------------------
% 2.92/1.89 % (16886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.89 % (16886)Termination reason: Unknown
% 2.92/1.89 % (16886)Termination phase: Saturation
% 2.92/1.89
% 2.92/1.89 % (16886)Memory used [KB]: 9850
% 2.92/1.89 % (16886)Time elapsed: 0.262 s
% 2.92/1.89 % (16886)Instructions burned: 780 (million)
% 2.92/1.89 % (16886)------------------------------
% 2.92/1.89 % (16886)------------------------------
% 2.92/1.89 % (16906)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_16650 for (2996ds/1087Mi)
% 2.92/1.89 % (16907)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_16650 for (2996ds/47Mi)
% 2.92/1.90 % (16908)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_16650 for (2996ds/44Mi)
% 2.92/1.91 % (16907)Instruction limit reached!
% 2.92/1.91 % (16907)------------------------------
% 2.92/1.91 % (16907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.91 % (16907)Termination reason: Unknown
% 2.92/1.91 % (16907)Termination phase: Preprocessing 1
% 2.92/1.91
% 2.92/1.91 % (16907)Memory used [KB]: 2174
% 2.92/1.91 % (16907)Time elapsed: 0.016 s
% 2.92/1.91 % (16907)Instructions burned: 49 (million)
% 2.92/1.91 % (16907)------------------------------
% 2.92/1.91 % (16907)------------------------------
% 2.92/1.91 % (16903)Instruction limit reached!
% 2.92/1.91 % (16903)------------------------------
% 2.92/1.91 % (16903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.91 % (16903)Termination reason: Unknown
% 2.92/1.91 % (16903)Termination phase: Saturation
% 2.92/1.91
% 2.92/1.91 % (16903)Memory used [KB]: 7419
% 2.92/1.91 % (16903)Time elapsed: 0.043 s
% 2.92/1.91 % (16903)Instructions burned: 149 (million)
% 2.92/1.91 % (16903)------------------------------
% 2.92/1.91 % (16903)------------------------------
% 2.92/1.92 % (16908)Instruction limit reached!
% 2.92/1.92 % (16908)------------------------------
% 2.92/1.92 % (16908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.92 % (16908)Termination reason: Unknown
% 2.92/1.92 % (16908)Termination phase: shuffling
% 2.92/1.92
% 2.92/1.92 % (16908)Memory used [KB]: 2430
% 2.92/1.92 % (16908)Time elapsed: 0.015 s
% 2.92/1.92 % (16908)Instructions burned: 46 (million)
% 2.92/1.92 % (16908)------------------------------
% 2.92/1.92 % (16908)------------------------------
% 2.92/1.92 % (16909)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/432Mi)
% 2.92/1.92 % (16910)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/62Mi)
% 2.92/1.93 % (16911)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/31Mi)
% 2.92/1.94 % (16911)Instruction limit reached!
% 2.92/1.94 % (16911)------------------------------
% 2.92/1.94 % (16911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.94 % (16911)Termination reason: Unknown
% 2.92/1.94 % (16911)Termination phase: Property scanning
% 2.92/1.94
% 2.92/1.94 % (16911)Memory used [KB]: 2046
% 2.92/1.94 % (16911)Time elapsed: 0.013 s
% 2.92/1.94 % (16911)Instructions burned: 34 (million)
% 2.92/1.94 % (16911)------------------------------
% 2.92/1.94 % (16911)------------------------------
% 2.92/1.94 % (16910)Instruction limit reached!
% 2.92/1.94 % (16910)------------------------------
% 2.92/1.94 % (16910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.94 % (16910)Termination reason: Unknown
% 2.92/1.94 % (16910)Termination phase: Property scanning
% 2.92/1.94
% 2.92/1.94 % (16910)Memory used [KB]: 2814
% 2.92/1.94 % (16910)Time elapsed: 0.018 s
% 2.92/1.94 % (16910)Instructions burned: 63 (million)
% 2.92/1.94 % (16910)------------------------------
% 2.92/1.94 % (16910)------------------------------
% 2.92/1.95 % (16899)Instruction limit reached!
% 2.92/1.95 % (16899)------------------------------
% 2.92/1.95 % (16899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.95 % (16899)Termination reason: Unknown
% 2.92/1.95 % (16899)Termination phase: Saturation
% 2.92/1.95
% 2.92/1.95 % (16899)Memory used [KB]: 9466
% 2.92/1.95 % (16899)Time elapsed: 0.127 s
% 2.92/1.95 % (16899)Instructions burned: 448 (million)
% 2.92/1.95 % (16899)------------------------------
% 2.92/1.95 % (16899)------------------------------
% 2.92/1.95 % (16912)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/96Mi)
% 2.92/1.95 % (16888)Refutation not found, non-redundant clauses discarded% (16888)------------------------------
% 2.92/1.95 % (16888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.95 % (16888)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.92/1.95
% 2.92/1.95 % (16888)Memory used [KB]: 8955
% 2.92/1.95 % (16888)Time elapsed: 0.300 s
% 2.92/1.95 % (16888)Instructions burned: 863 (million)
% 2.92/1.95 % (16888)------------------------------
% 2.92/1.95 % (16888)------------------------------
% 2.92/1.95 % (16913)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/453Mi)
% 2.92/1.96 % (16914)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/71Mi)
% 2.92/1.96 % (16915)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/83Mi)
% 2.92/1.98 % (16912)Instruction limit reached!
% 2.92/1.98 % (16912)------------------------------
% 2.92/1.98 % (16912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.98 % (16912)Termination reason: Unknown
% 2.92/1.98 % (16912)Termination phase: Property scanning
% 2.92/1.98
% 2.92/1.98 % (16912)Memory used [KB]: 2814
% 2.92/1.98 % (16912)Time elapsed: 0.032 s
% 2.92/1.98 % (16912)Instructions burned: 98 (million)
% 2.92/1.98 % (16912)------------------------------
% 2.92/1.98 % (16912)------------------------------
% 2.92/1.98 % (16914)Instruction limit reached!
% 2.92/1.98 % (16914)------------------------------
% 2.92/1.98 % (16914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.98 % (16914)Termination reason: Unknown
% 2.92/1.98 % (16914)Termination phase: Property scanning
% 2.92/1.98
% 2.92/1.98 % (16914)Memory used [KB]: 2686
% 2.92/1.98 % (16914)Time elapsed: 0.023 s
% 2.92/1.98 % (16914)Instructions burned: 73 (million)
% 2.92/1.98 % (16914)------------------------------
% 2.92/1.98 % (16914)------------------------------
% 2.92/1.99 % (16915)Instruction limit reached!
% 2.92/1.99 % (16915)------------------------------
% 2.92/1.99 % (16915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.99 % (16915)Termination reason: Unknown
% 2.92/1.99 % (16915)Termination phase: Saturation
% 2.92/1.99
% 2.92/1.99 % (16915)Memory used [KB]: 6908
% 2.92/1.99 % (16915)Time elapsed: 0.028 s
% 2.92/1.99 % (16915)Instructions burned: 83 (million)
% 2.92/1.99 % (16915)------------------------------
% 2.92/1.99 % (16915)------------------------------
% 2.92/1.99 % (16916)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/11Mi)
% 2.92/1.99 % (16917)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/41Mi)
% 2.92/1.99 % (16916)Instruction limit reached!
% 2.92/1.99 % (16916)------------------------------
% 2.92/1.99 % (16916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.99 % (16916)Termination reason: Unknown
% 2.92/1.99 % (16916)Termination phase: shuffling
% 2.92/1.99
% 2.92/1.99 % (16916)Memory used [KB]: 1791
% 2.92/1.99 % (16916)Time elapsed: 0.005 s
% 2.92/1.99 % (16916)Instructions burned: 11 (million)
% 2.92/1.99 % (16916)------------------------------
% 2.92/1.99 % (16916)------------------------------
% 2.92/2.00 % (16918)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/6Mi)
% 2.92/2.00 % (16918)Instruction limit reached!
% 2.92/2.00 % (16918)------------------------------
% 2.92/2.00 % (16918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/2.00 % (16918)Termination reason: Unknown
% 2.92/2.00 % (16918)Termination phase: shuffling
% 2.92/2.00
% 2.92/2.00 % (16918)Memory used [KB]: 1663
% 2.92/2.00 % (16918)Time elapsed: 0.004 s
% 2.92/2.00 % (16918)Instructions burned: 6 (million)
% 2.92/2.00 % (16918)------------------------------
% 2.92/2.00 % (16918)------------------------------
% 2.92/2.00 % (16917)Instruction limit reached!
% 2.92/2.00 % (16917)------------------------------
% 2.92/2.00 % (16917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/2.00 % (16917)Termination reason: Unknown
% 2.92/2.00 % (16917)Termination phase: shuffling
% 2.92/2.00
% 2.92/2.00 % (16917)Memory used [KB]: 2430
% 2.92/2.00 % (16917)Time elapsed: 0.012 s
% 2.92/2.00 % (16917)Instructions burned: 41 (million)
% 2.92/2.00 % (16917)------------------------------
% 2.92/2.00 % (16917)------------------------------
% 2.92/2.00 % (16902)First to succeed.
% 2.92/2.01 % (16919)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_16650 for (2995ds/150Mi)
% 2.92/2.01 % (16902)Refutation found. Thanks to Tanya!
% 2.92/2.01 % SZS status Theorem for DTF2THF_16650
% 2.92/2.01 % SZS output start Proof for DTF2THF_16650
% 2.92/2.01 thf(type_def_5, type, nat: $tType).
% 2.92/2.01 thf(type_def_7, type, set_Pr1986765409at_nat: $tType).
% 2.92/2.01 thf(type_def_8, type, set_nat: $tType).
% 2.92/2.01 thf(type_def_9, type, set_Pr795498619_state: $tType).
% 2.92/2.01 thf(type_def_10, type, state: $tType).
% 2.92/2.01 thf(type_def_11, type, set_state: $tType).
% 2.92/2.01 thf(type_def_12, type, set_Pr1702239303tate_o: $tType).
% 2.92/2.01 thf(type_def_13, type, produc696469763tate_o: $tType).
% 2.92/2.01 thf(type_def_14, type, set_Pr1590995257tate_o: $tType).
% 2.92/2.01 thf(type_def_15, type, set_Pr1490359111at_nat: $tType).
% 2.92/2.01 thf(type_def_16, type, product_prod_nat_nat: $tType).
% 2.92/2.01 thf(type_def_17, type, set_Pr778812871_state: $tType).
% 2.92/2.01 thf(type_def_18, type, produc1115495963_state: $tType).
% 2.92/2.01 thf(type_def_19, type, a: $tType).
% 2.92/2.01 thf(type_def_20, type, produc204914599tate_o: $tType).
% 2.92/2.01 thf(type_def_21, type, com: $tType).
% 2.92/2.01 thf(type_def_22, type, set_Pr1740974983tate_o: $tType).
% 2.92/2.01 thf(type_def_23, type, produc1307154919tate_o: $tType).
% 2.92/2.01 thf(type_def_24, type, produc842455143at_nat: $tType).
% 2.92/2.01 thf(type_def_25, type, produc1390548711_state: $tType).
% 2.92/2.01 thf(func_def_0, type, set_Pr1702239303tate_o: $tType).
% 2.92/2.01 thf(func_def_1, type, produc1307154919tate_o: $tType).
% 2.92/2.01 thf(func_def_2, type, set_Pr1590995257tate_o: $tType).
% 2.92/2.01 thf(func_def_3, type, set_Pr778812871_state: $tType).
% 2.92/2.01 thf(func_def_4, type, produc696469763tate_o: $tType).
% 2.92/2.01 thf(func_def_5, type, set_Pr1490359111at_nat: $tType).
% 2.92/2.01 thf(func_def_6, type, produc1390548711_state: $tType).
% 2.92/2.01 thf(func_def_7, type, produc842455143at_nat: $tType).
% 2.92/2.01 thf(func_def_8, type, set_Pr1740974983tate_o: $tType).
% 2.92/2.01 thf(func_def_9, type, produc204914599tate_o: $tType).
% 2.92/2.01 thf(func_def_10, type, set_Pr795498619_state: $tType).
% 2.92/2.01 thf(func_def_11, type, set_Pr1986765409at_nat: $tType).
% 2.92/2.01 thf(func_def_12, type, produc1115495963_state: $tType).
% 2.92/2.01 thf(func_def_13, type, product_prod_nat_nat: $tType).
% 2.92/2.01 thf(func_def_14, type, set_state: $tType).
% 2.92/2.01 thf(func_def_15, type, set_nat: $tType).
% 2.92/2.01 thf(func_def_16, type, state: $tType).
% 2.92/2.01 thf(func_def_17, type, com: $tType).
% 2.92/2.01 thf(func_def_18, type, nat: $tType).
% 2.92/2.01 thf(func_def_19, type, a: $tType).
% 2.92/2.01 thf(func_def_20, type, suc: nat > nat).
% 2.92/2.01 thf(func_def_21, type, order_aboveS_nat: set_Pr1986765409at_nat > nat > set_nat).
% 2.92/2.01 thf(func_def_22, type, order_aboveS_state: set_Pr795498619_state > state > set_state).
% 2.92/2.01 thf(func_def_23, type, order_1121016664tate_o: set_Pr1702239303tate_o > produc696469763tate_o > set_Pr1590995257tate_o).
% 2.92/2.01 thf(func_def_24, type, order_665764460at_nat: set_Pr1490359111at_nat > product_prod_nat_nat > set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_25, type, order_2027321734_state: set_Pr778812871_state > produc1115495963_state > set_Pr795498619_state).
% 2.92/2.01 thf(func_def_26, type, order_130026331on_nat: set_nat > set_Pr1986765409at_nat > $o).
% 2.92/2.01 thf(func_def_27, type, order_286167592_state: set_state > set_Pr795498619_state > $o).
% 2.92/2.01 thf(func_def_28, type, order_50454158tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o).
% 2.92/2.01 thf(func_def_29, type, order_721919926at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o).
% 2.92/2.01 thf(func_def_30, type, order_178668240_state: set_Pr795498619_state > set_Pr778812871_state > $o).
% 2.92/2.01 thf(func_def_31, type, bot_bo2130564770te_o_o: (a > state > $o) > produc204914599tate_o > $o).
% 2.92/2.01 thf(func_def_32, type, bot_bot_nat_nat_o: nat > nat > $o).
% 2.92/2.01 thf(func_def_33, type, bot_bo935656620te_o_o: com > (a > state > $o) > $o).
% 2.92/2.01 thf(func_def_34, type, bot_bo51534648tate_o: state > state > $o).
% 2.92/2.01 thf(func_def_35, type, bot_bo250281208te_o_o: produc696469763tate_o > $o).
% 2.92/2.01 thf(func_def_36, type, bot_bo513358416_nat_o: product_prod_nat_nat > $o).
% 2.92/2.01 thf(func_def_37, type, bot_bo446391478tate_o: produc1115495963_state > $o).
% 2.92/2.01 thf(func_def_38, type, bot_bot_set_nat: set_nat).
% 2.92/2.01 thf(func_def_39, type, bot_bot_set_state: set_state).
% 2.92/2.01 thf(func_def_40, type, bot_bo170732493tate_o: set_Pr1590995257tate_o).
% 2.92/2.01 thf(func_def_41, type, bot_bo2130386637at_nat: set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_42, type, bot_bo1692783091tate_o: set_Pr1740974983tate_o).
% 2.92/2.01 thf(func_def_43, type, bot_bo1625160935_state: set_Pr795498619_state).
% 2.92/2.01 thf(func_def_44, type, bot_bo1714653363tate_o: set_Pr1702239303tate_o).
% 2.92/2.01 thf(func_def_45, type, bot_bo34127283at_nat: set_Pr1490359111at_nat).
% 2.92/2.01 thf(func_def_46, type, bot_bo1331673139_state: set_Pr778812871_state).
% 2.92/2.01 thf(func_def_47, type, ord_less_nat: nat > nat > $o).
% 2.92/2.01 thf(func_def_48, type, pHoare382919414oare_a: set_Pr1590995257tate_o > (a > state > $o) > com > (a > state > $o) > $o).
% 2.92/2.01 thf(func_def_49, type, hoare_a: set_Pr1590995257tate_o > (a > state > $o) > com > (a > state > $o) > $o).
% 2.92/2.01 thf(func_def_50, type, body: com).
% 2.92/2.01 thf(func_def_51, type, call: com).
% 2.92/2.01 thf(func_def_52, type, semi: com > com > com).
% 2.92/2.01 thf(func_def_53, type, while: (state > $o) > com > com).
% 2.92/2.01 thf(func_def_54, type, exec: state > com > state > $o).
% 2.92/2.01 thf(func_def_55, type, execn: state > com > nat > state > $o).
% 2.92/2.01 thf(func_def_56, type, termi: com > state > $o).
% 2.92/2.01 thf(func_def_57, type, produc33908149tate_o: (a > state > $o) > produc204914599tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_58, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_59, type, produc1948644831tate_o: com > (a > state > $o) > produc204914599tate_o).
% 2.92/2.01 thf(func_def_60, type, produc64584659_state: state > state > produc1115495963_state).
% 2.92/2.01 thf(func_def_61, type, produc1684562079tate_o: produc696469763tate_o > produc696469763tate_o > produc1307154919tate_o).
% 2.92/2.01 thf(func_def_62, type, produc1168807639at_nat: product_prod_nat_nat > product_prod_nat_nat > produc842455143at_nat).
% 2.92/2.01 thf(func_def_63, type, produc1964772951_state: produc1115495963_state > produc1115495963_state > produc1390548711_state).
% 2.92/2.01 thf(func_def_64, type, produc385877620_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 2.92/2.01 thf(func_def_65, type, produc938968666tate_o: (state > state > $o) > produc1115495963_state > $o).
% 2.92/2.01 thf(func_def_66, type, produc1271576886te_o_o: ((a > state > $o) > produc204914599tate_o > $o) > produc696469763tate_o > $o).
% 2.92/2.01 thf(func_def_67, type, produc949581770_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 2.92/2.01 thf(func_def_68, type, produc1610543495tate_o: (nat > nat > set_Pr1590995257tate_o) > product_prod_nat_nat > set_Pr1590995257tate_o).
% 2.92/2.01 thf(func_def_69, type, produc1915186323at_nat: (nat > nat > set_Pr1986765409at_nat) > product_prod_nat_nat > set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_70, type, produc1654445_state: (nat > nat > set_Pr795498619_state) > product_prod_nat_nat > set_Pr795498619_state).
% 2.92/2.01 thf(func_def_71, type, produc281270436te_o_o: (com > (a > state > $o) > $o) > produc204914599tate_o > $o).
% 2.92/2.01 thf(func_def_72, type, produc789892016tate_o: (state > state > $o) > produc1115495963_state > $o).
% 2.92/2.01 thf(func_def_73, type, irrefl_nat: set_Pr1986765409at_nat > $o).
% 2.92/2.01 thf(func_def_74, type, refl_on_nat: set_nat > set_Pr1986765409at_nat > $o).
% 2.92/2.01 thf(func_def_75, type, refl_on_state: set_state > set_Pr795498619_state > $o).
% 2.92/2.01 thf(func_def_76, type, refl_o489021252tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o).
% 2.92/2.01 thf(func_def_77, type, refl_o1619599232at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o).
% 2.92/2.01 thf(func_def_78, type, refl_o1438232218_state: set_Pr795498619_state > set_Pr778812871_state > $o).
% 2.92/2.01 thf(func_def_79, type, total_on_nat: set_nat > set_Pr1986765409at_nat > $o).
% 2.92/2.01 thf(func_def_80, type, total_on_state: set_state > set_Pr795498619_state > $o).
% 2.92/2.01 thf(func_def_81, type, total_795385983tate_o: set_Pr1590995257tate_o > set_Pr1702239303tate_o > $o).
% 2.92/2.01 thf(func_def_82, type, total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o).
% 2.92/2.01 thf(func_def_83, type, total_1316653983_state: set_Pr795498619_state > set_Pr778812871_state > $o).
% 2.92/2.01 thf(func_def_84, type, trans_nat: set_Pr1986765409at_nat > $o).
% 2.92/2.01 thf(func_def_85, type, collect_nat: (nat > $o) > set_nat).
% 2.92/2.01 thf(func_def_86, type, collect_state: (state > $o) > set_state).
% 2.92/2.01 thf(func_def_87, type, collec1499596504tate_o: (produc696469763tate_o > $o) > set_Pr1590995257tate_o).
% 2.92/2.01 thf(func_def_88, type, collec7649004at_nat: (product_prod_nat_nat > $o) > set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_89, type, collec496201222_state: (produc1115495963_state > $o) > set_Pr795498619_state).
% 2.92/2.01 thf(func_def_90, type, insert_nat: nat > set_nat > set_nat).
% 2.92/2.01 thf(func_def_91, type, insert_state: state > set_state > set_state).
% 2.92/2.01 thf(func_def_92, type, insert2053719859tate_o: produc696469763tate_o > set_Pr1590995257tate_o > set_Pr1590995257tate_o).
% 2.92/2.01 thf(func_def_93, type, insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_94, type, insert311944171_state: produc1115495963_state > set_Pr795498619_state > set_Pr795498619_state).
% 2.92/2.01 thf(func_def_95, type, insert1597128631tate_o: produc1307154919tate_o > set_Pr1702239303tate_o > set_Pr1702239303tate_o).
% 2.92/2.01 thf(func_def_96, type, insert584009271at_nat: produc842455143at_nat > set_Pr1490359111at_nat > set_Pr1490359111at_nat).
% 2.92/2.01 thf(func_def_97, type, insert1616594103_state: produc1390548711_state > set_Pr778812871_state > set_Pr778812871_state).
% 2.92/2.01 thf(func_def_98, type, is_emp807847857tate_o: set_Pr1590995257tate_o > $o).
% 2.92/2.01 thf(func_def_99, type, is_emp825011411at_nat: set_Pr1986765409at_nat > $o).
% 2.92/2.01 thf(func_def_100, type, is_emp1062983149_state: set_Pr795498619_state > $o).
% 2.92/2.01 thf(func_def_101, type, is_sin1547905295tate_o: set_Pr1590995257tate_o > $o).
% 2.92/2.01 thf(func_def_102, type, is_sin1352690165at_nat: set_Pr1986765409at_nat > $o).
% 2.92/2.01 thf(func_def_103, type, is_sin1132515087_state: set_Pr795498619_state > $o).
% 2.92/2.01 thf(func_def_104, type, the_el1569055182tate_o: set_Pr1590995257tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_105, type, the_el1949240438at_nat: set_Pr1986765409at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_106, type, the_el1967402896_state: set_Pr795498619_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_107, type, less_than: set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_108, type, measure_nat: (nat > nat) > set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_109, type, measure_state: (state > nat) > set_Pr795498619_state).
% 2.92/2.01 thf(func_def_110, type, pred_nat: set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_111, type, wf_nat: set_Pr1986765409at_nat > $o).
% 2.92/2.01 thf(func_def_112, type, wf_state: set_Pr795498619_state > $o).
% 2.92/2.01 thf(func_def_113, type, wf_Pro309705690tate_o: set_Pr1702239303tate_o > $o).
% 2.92/2.01 thf(func_def_114, type, wf_Pro745352042at_nat: set_Pr1490359111at_nat > $o).
% 2.92/2.01 thf(func_def_115, type, wf_Pro1783588484_state: set_Pr778812871_state > $o).
% 2.92/2.01 thf(func_def_116, type, member_nat: nat > set_nat > $o).
% 2.92/2.01 thf(func_def_117, type, member_state: state > set_state > $o).
% 2.92/2.01 thf(func_def_118, type, member1838112666tate_o: produc696469763tate_o > set_Pr1590995257tate_o > $o).
% 2.92/2.01 thf(func_def_119, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 2.92/2.01 thf(func_def_120, type, member221067728tate_o: produc204914599tate_o > set_Pr1740974983tate_o > $o).
% 2.92/2.01 thf(func_def_121, type, member1389040324_state: produc1115495963_state > set_Pr795498619_state > $o).
% 2.92/2.01 thf(func_def_122, type, member1629320336tate_o: produc1307154919tate_o > set_Pr1702239303tate_o > $o).
% 2.92/2.01 thf(func_def_123, type, member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o).
% 2.92/2.01 thf(func_def_124, type, member768948240_state: produc1390548711_state > set_Pr778812871_state > $o).
% 2.92/2.01 thf(func_def_125, type, pa: a > state > $o).
% 2.92/2.01 thf(func_def_126, type, qa: a > state > $o).
% 2.92/2.01 thf(func_def_127, type, r: set_Pr795498619_state).
% 2.92/2.01 thf(func_def_128, type, x: state).
% 2.92/2.01 thf(func_def_144, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.92/2.01 thf(func_def_145, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.92/2.01 thf(func_def_147, type, sP3: state > $o).
% 2.92/2.01 thf(func_def_148, type, sK4: set_Pr1590995257tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_149, type, sK5: set_Pr1986765409at_nat > set_nat > nat).
% 2.92/2.01 thf(func_def_150, type, sK6: set_Pr1986765409at_nat > set_nat > nat).
% 2.92/2.01 thf(func_def_151, type, sK7: set_Pr1986765409at_nat > (nat > $o) > nat).
% 2.92/2.01 thf(func_def_152, type, sK8: produc1115495963_state > set_Pr795498619_state > set_Pr795498619_state).
% 2.92/2.01 thf(func_def_153, type, sK9: produc696469763tate_o > set_Pr1590995257tate_o > set_Pr1590995257tate_o).
% 2.92/2.01 thf(func_def_154, type, sK10: (state > state > $o) > (state > state > $o) > produc1115495963_state > state).
% 2.92/2.01 thf(func_def_155, type, sK11: (state > state > $o) > (state > state > $o) > produc1115495963_state > state).
% 2.92/2.01 thf(func_def_156, type, sK12: state > com > com > state).
% 2.92/2.01 thf(func_def_157, type, sK13: set_Pr1590995257tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_158, type, sK14: set_Pr1590995257tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_159, type, sK15: (nat > nat > $o) > product_prod_nat_nat > nat).
% 2.92/2.01 thf(func_def_160, type, sK16: (nat > nat > $o) > product_prod_nat_nat > nat).
% 2.92/2.01 thf(func_def_161, type, sK17: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_162, type, sK18: state > (state > $o) > com > state).
% 2.92/2.01 thf(func_def_163, type, sK19: produc1115495963_state > (state > state > $o) > state).
% 2.92/2.01 thf(func_def_164, type, sK20: produc1115495963_state > (state > state > $o) > state).
% 2.92/2.01 thf(func_def_165, type, sK21: (produc696469763tate_o > $o) > a > state > $o).
% 2.92/2.01 thf(func_def_166, type, sK22: (produc696469763tate_o > $o) > produc204914599tate_o).
% 2.92/2.01 thf(func_def_167, type, sK23: ((a > state > $o) > produc204914599tate_o > $o) > produc696469763tate_o > produc204914599tate_o).
% 2.92/2.01 thf(func_def_168, type, sK24: ((a > state > $o) > produc204914599tate_o > $o) > produc696469763tate_o > a > state > $o).
% 2.92/2.01 thf(func_def_169, type, sK25: set_Pr795498619_state > state > $o).
% 2.92/2.01 thf(func_def_170, type, sK26: set_Pr795498619_state > state).
% 2.92/2.01 thf(func_def_171, type, sK27: state > set_Pr795498619_state > state).
% 2.92/2.01 thf(func_def_172, type, sK28: (a > state > $o) > (a > state > $o) > state).
% 2.92/2.01 thf(func_def_173, type, sK29: (a > state > $o) > (a > state > $o) > a).
% 2.92/2.01 thf(func_def_174, type, sK30: set_Pr1986765409at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_175, type, sK31: (produc696469763tate_o > $o) > (produc696469763tate_o > $o) > produc696469763tate_o).
% 2.92/2.01 thf(func_def_176, type, sK32: set_Pr795498619_state > set_Pr778812871_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_177, type, sK33: produc1115495963_state > state).
% 2.92/2.01 thf(func_def_178, type, sK34: produc1115495963_state > state).
% 2.92/2.01 thf(func_def_179, type, sK35: produc696469763tate_o > produc204914599tate_o).
% 2.92/2.01 thf(func_def_180, type, sK36: produc696469763tate_o > a > state > $o).
% 2.92/2.01 thf(func_def_181, type, sK37: set_Pr1986765409at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_182, type, sK38: set_Pr1986765409at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_183, type, sK39: set_Pr1590995257tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_184, type, sK40: produc204914599tate_o > a > state > $o).
% 2.92/2.01 thf(func_def_185, type, sK41: produc204914599tate_o > com).
% 2.92/2.01 thf(func_def_186, type, sK42: com > nat > (state > $o) > (state > $o) > state).
% 2.92/2.01 thf(func_def_187, type, sK43: com > nat > (state > $o) > (state > $o) > state).
% 2.92/2.01 thf(func_def_188, type, sK44: set_Pr795498619_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_189, type, sK45: set_Pr795498619_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_190, type, sK46: (produc1115495963_state > $o) > (produc1115495963_state > $o) > produc1115495963_state).
% 2.92/2.01 thf(func_def_191, type, sK47: produc204914599tate_o > a > state > $o).
% 2.92/2.01 thf(func_def_192, type, sK48: produc204914599tate_o > com).
% 2.92/2.01 thf(func_def_193, type, sK49: (state > $o) > set_Pr795498619_state > state).
% 2.92/2.01 thf(func_def_194, type, sK50: set_Pr1986765409at_nat > nat).
% 2.92/2.01 thf(func_def_195, type, sK51: set_Pr1986765409at_nat > set_nat).
% 2.92/2.01 thf(func_def_196, type, sK52: nat > set_Pr1986765409at_nat > nat).
% 2.92/2.01 thf(func_def_197, type, sK53: (produc1115495963_state > $o) > (state > state > $o) > state).
% 2.92/2.01 thf(func_def_198, type, sK54: (produc1115495963_state > $o) > (state > state > $o) > state).
% 2.92/2.01 thf(func_def_199, type, sK55: produc204914599tate_o > (com > (a > state > $o) > $o) > com).
% 2.92/2.01 thf(func_def_200, type, sK56: produc204914599tate_o > (com > (a > state > $o) > $o) > a > state > $o).
% 2.92/2.01 thf(func_def_201, type, sK57: (nat > nat > $o) > product_prod_nat_nat > nat).
% 2.92/2.01 thf(func_def_202, type, sK58: (nat > nat > $o) > product_prod_nat_nat > nat).
% 2.92/2.01 thf(func_def_203, type, sK59: product_prod_nat_nat > nat).
% 2.92/2.01 thf(func_def_204, type, sK60: product_prod_nat_nat > nat).
% 2.92/2.01 thf(func_def_205, type, sK61: set_Pr795498619_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_206, type, sK62: (produc696469763tate_o > $o) > a > state > $o).
% 2.92/2.01 thf(func_def_207, type, sK63: (produc696469763tate_o > $o) > produc204914599tate_o).
% 2.92/2.01 thf(func_def_208, type, sK64: (produc1115495963_state > $o) > state).
% 2.92/2.01 thf(func_def_209, type, sK65: (produc1115495963_state > $o) > state).
% 2.92/2.01 thf(func_def_210, type, sK66: (state > state > $o) > produc1115495963_state > state).
% 2.92/2.01 thf(func_def_211, type, sK67: (state > state > $o) > produc1115495963_state > state).
% 2.92/2.01 thf(func_def_212, type, sK68: (produc204914599tate_o > $o) > a > state > $o).
% 2.92/2.01 thf(func_def_213, type, sK69: (produc204914599tate_o > $o) > com).
% 2.92/2.01 thf(func_def_214, type, sK70: produc696469763tate_o > a > state > $o).
% 2.92/2.01 thf(func_def_215, type, sK71: produc696469763tate_o > a > state > $o).
% 2.92/2.01 thf(func_def_216, type, sK72: produc696469763tate_o > com).
% 2.92/2.01 thf(func_def_217, type, sK73: set_Pr795498619_state > set_state).
% 2.92/2.01 thf(func_def_218, type, sK74: set_Pr795498619_state > state).
% 2.92/2.01 thf(func_def_219, type, sK75: state > set_Pr795498619_state > state).
% 2.92/2.01 thf(func_def_220, type, sK76: set_Pr778812871_state > set_Pr795498619_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_221, type, sK77: set_Pr1702239303tate_o > set_Pr1590995257tate_o).
% 2.92/2.01 thf(func_def_222, type, sK78: set_Pr1702239303tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_223, type, sK79: produc696469763tate_o > set_Pr1702239303tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_224, type, sK80: product_prod_nat_nat > product_prod_nat_nat > (nat > nat > set_Pr1986765409at_nat) > nat).
% 2.92/2.01 thf(func_def_225, type, sK81: product_prod_nat_nat > product_prod_nat_nat > (nat > nat > set_Pr1986765409at_nat) > nat).
% 2.92/2.01 thf(func_def_226, type, sK82: (nat > $o) > set_Pr1986765409at_nat > nat).
% 2.92/2.01 thf(func_def_227, type, sK83: (a > state > $o) > (a > state > $o) > set_Pr795498619_state > state).
% 2.92/2.01 thf(func_def_228, type, sK84: (produc204914599tate_o > $o) > com).
% 2.92/2.01 thf(func_def_229, type, sK85: (produc204914599tate_o > $o) > a > state > $o).
% 2.92/2.01 thf(func_def_230, type, sK86: (product_prod_nat_nat > $o) > nat).
% 2.92/2.01 thf(func_def_231, type, sK87: (product_prod_nat_nat > $o) > nat).
% 2.92/2.01 thf(func_def_232, type, sK88: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_233, type, sK89: (a > state > $o) > (a > state > $o) > state).
% 2.92/2.01 thf(func_def_234, type, sK90: (a > state > $o) > (a > state > $o) > a).
% 2.92/2.01 thf(func_def_235, type, sK91: (a > state > $o) > (a > state > $o) > (a > state > $o) > (a > state > $o) > state).
% 2.92/2.01 thf(func_def_236, type, sK92: (a > state > $o) > (a > state > $o) > (a > state > $o) > (a > state > $o) > state).
% 2.92/2.01 thf(func_def_237, type, sK93: (a > state > $o) > (a > state > $o) > (a > state > $o) > (a > state > $o) > a).
% 2.92/2.01 thf(func_def_238, type, sK94: (produc1115495963_state > $o) > state).
% 2.92/2.01 thf(func_def_239, type, sK95: (produc1115495963_state > $o) > state).
% 2.92/2.01 thf(func_def_240, type, sK96: (com > (a > state > $o) > $o) > produc204914599tate_o > com).
% 2.92/2.01 thf(func_def_241, type, sK97: (com > (a > state > $o) > $o) > produc204914599tate_o > a > state > $o).
% 2.92/2.01 thf(func_def_242, type, sK98: ((a > state > $o) > produc204914599tate_o > $o) > produc696469763tate_o > produc204914599tate_o).
% 2.92/2.01 thf(func_def_243, type, sK99: ((a > state > $o) > produc204914599tate_o > $o) > produc696469763tate_o > a > state > $o).
% 2.92/2.01 thf(func_def_244, type, sK100: set_Pr795498619_state > set_Pr778812871_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_245, type, sK101: set_Pr795498619_state > set_Pr778812871_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_246, type, sK102: set_Pr1986765409at_nat > set_Pr1490359111at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_247, type, sK103: set_state > set_Pr795498619_state > state).
% 2.92/2.01 thf(func_def_248, type, sK104: set_Pr1702239303tate_o > set_Pr1590995257tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_249, type, sK105: set_Pr1702239303tate_o > set_Pr1590995257tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_250, type, sK106: set_Pr1702239303tate_o > set_Pr1590995257tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_251, type, sK107: set_Pr1986765409at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_252, type, sK108: product_prod_nat_nat > produc696469763tate_o > (nat > nat > set_Pr1590995257tate_o) > nat).
% 2.92/2.01 thf(func_def_253, type, sK109: product_prod_nat_nat > produc696469763tate_o > (nat > nat > set_Pr1590995257tate_o) > nat).
% 2.92/2.01 thf(func_def_254, type, sK110: set_Pr1702239303tate_o > set_Pr1590995257tate_o > produc696469763tate_o).
% 2.92/2.01 thf(func_def_255, type, sK111: set_Pr1490359111at_nat > set_Pr1986765409at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_256, type, sK112: (produc696469763tate_o > $o) > com).
% 2.92/2.01 thf(func_def_257, type, sK113: (produc696469763tate_o > $o) > a > state > $o).
% 2.92/2.01 thf(func_def_258, type, sK114: (produc696469763tate_o > $o) > a > state > $o).
% 2.92/2.01 thf(func_def_259, type, sK115: produc696469763tate_o > a > state > $o).
% 2.92/2.01 thf(func_def_260, type, sK116: produc696469763tate_o > produc204914599tate_o).
% 2.92/2.01 thf(func_def_261, type, sK117: set_Pr778812871_state > set_Pr795498619_state).
% 2.92/2.01 thf(func_def_262, type, sK118: set_Pr778812871_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_263, type, sK119: produc1115495963_state > set_Pr778812871_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_264, type, sK120: set_Pr1986765409at_nat > nat).
% 2.92/2.01 thf(func_def_265, type, sK121: set_Pr1986765409at_nat > nat > $o).
% 2.92/2.01 thf(func_def_266, type, sK122: nat > set_Pr1986765409at_nat > nat).
% 2.92/2.01 thf(func_def_267, type, sK123: set_Pr795498619_state > produc1115495963_state > set_Pr795498619_state).
% 2.92/2.01 thf(func_def_268, type, sK124: set_Pr795498619_state > produc1115495963_state).
% 2.92/2.01 thf(func_def_269, type, sK125: (state > state > $o) > produc1115495963_state > ($o > $o) > state).
% 2.92/2.01 thf(func_def_270, type, sK126: (state > state > $o) > produc1115495963_state > ($o > $o) > state).
% 2.92/2.01 thf(func_def_271, type, sK127: (state > $o) > (nat > state) > nat).
% 2.92/2.01 thf(func_def_272, type, sK128: com > (nat > state) > nat).
% 2.92/2.01 thf(func_def_273, type, sK129: product_prod_nat_nat > (nat > nat > $o) > (nat > nat > $o) > nat).
% 2.92/2.01 thf(func_def_274, type, sK130: product_prod_nat_nat > (nat > nat > $o) > (nat > nat > $o) > nat).
% 2.92/2.01 thf(func_def_275, type, sK131: set_Pr1490359111at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_276, type, sK132: set_Pr1490359111at_nat > set_Pr1986765409at_nat).
% 2.92/2.01 thf(func_def_277, type, sK133: product_prod_nat_nat > set_Pr1490359111at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_278, type, sK134: product_prod_nat_nat > ($o > $o) > (nat > nat > $o) > nat).
% 2.92/2.01 thf(func_def_279, type, sK135: product_prod_nat_nat > ($o > $o) > (nat > nat > $o) > nat).
% 2.92/2.01 thf(func_def_280, type, sK136: (nat > state) > (state > $o) > nat).
% 2.92/2.01 thf(func_def_281, type, sK137: com > (nat > state) > nat).
% 2.92/2.01 thf(func_def_282, type, sK138: (a > state > $o) > (state > $o) > set_Pr795498619_state > com > set_Pr1590995257tate_o > state).
% 2.92/2.01 thf(func_def_283, type, sK139: state).
% 2.92/2.01 thf(func_def_284, type, sK140: state).
% 2.92/2.01 thf(func_def_285, type, sK141: a).
% 2.92/2.01 thf(func_def_286, type, sK142: state).
% 2.92/2.01 thf(func_def_287, type, sK143: a).
% 2.92/2.01 thf(func_def_288, type, sK144: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_289, type, sK145: set_nat > set_Pr1986765409at_nat > nat).
% 2.92/2.01 thf(func_def_290, type, sK146: product_prod_nat_nat > nat).
% 2.92/2.01 thf(func_def_291, type, sK147: product_prod_nat_nat > nat).
% 2.92/2.01 thf(func_def_292, type, sK148: produc1115495963_state > state).
% 2.92/2.01 thf(func_def_293, type, sK149: produc1115495963_state > state).
% 2.92/2.01 thf(func_def_294, type, sK150: (state > $o) > set_Pr795498619_state > state).
% 2.92/2.01 thf(func_def_295, type, sK151: (state > $o) > nat > com > (state > $o) > state).
% 2.92/2.01 thf(func_def_296, type, sK152: (state > $o) > nat > com > (state > $o) > state).
% 2.92/2.01 thf(func_def_297, type, sK153: set_Pr1490359111at_nat > set_Pr1986765409at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_298, type, sK154: set_Pr1490359111at_nat > set_Pr1986765409at_nat > product_prod_nat_nat).
% 2.92/2.01 thf(func_def_299, type, sK155: (product_prod_nat_nat > $o) > (nat > nat > $o) > nat).
% 2.92/2.01 thf(func_def_300, type, sK156: (product_prod_nat_nat > $o) > (nat > nat > $o) > nat).
% 2.92/2.01 thf(func_def_301, type, sK157: set_state > set_Pr795498619_state > state).
% 2.92/2.01 thf(func_def_302, type, sK158: set_nat > set_Pr1986765409at_nat > nat).
% 2.92/2.01 thf(func_def_303, type, sK159: (product_prod_nat_nat > $o) > nat).
% 2.92/2.01 thf(func_def_304, type, sK160: (product_prod_nat_nat > $o) > nat).
% 2.92/2.01 thf(func_def_305, type, sK161: state > state).
% 2.92/2.01 thf(func_def_306, type, sK162: state > state).
% 2.92/2.01 thf(func_def_307, type, sK163: state > a).
% 2.92/2.01 thf(func_def_308, type, sK164: state > a).
% 2.92/2.01 thf(func_def_309, type, sK165: state > state).
% 2.92/2.01 thf(func_def_310, type, sK166: (nat > nat > set_Pr795498619_state) > product_prod_nat_nat > produc1115495963_state > nat).
% 2.92/2.01 thf(func_def_311, type, sK167: (nat > nat > set_Pr795498619_state) > product_prod_nat_nat > produc1115495963_state > nat).
% 2.92/2.01 thf(func_def_312, type, sK168: set_Pr795498619_state > set_state > state).
% 2.92/2.01 thf(func_def_313, type, sK169: set_Pr795498619_state > set_state > state).
% 2.92/2.01 thf(func_def_314, type, sK170: (a > state > $o) > (a > state > $o) > a).
% 2.92/2.01 thf(func_def_315, type, sK171: (a > state > $o) > (a > state > $o) > state).
% 2.92/2.01 thf(func_def_316, type, sK172: set_Pr1590995257tate_o > produc696469763tate_o > set_Pr1590995257tate_o).
% 2.92/2.01 thf(func_def_318, type, ph174: !>[X0: $tType]:(X0)).
% 2.92/2.01 thf(f3155,plain,(
% 2.92/2.01 $false),
% 2.92/2.01 inference(avatar_sat_refutation,[status(thm)],[f2646,f2651,f2656,f2746,f2774,f2782,f2784,f2785,f2854,f2862,f2867,f2908,f3065,f3075,f3149,f3154])).
% 2.92/2.01 thf(f3154,plain,(
% 2.92/2.01 spl173_8 | spl173_5 | spl173_10 | ~spl173_28),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f3153,f3073,f2684,f2664,f2677])).
% 2.92/2.01 thf(f2677,definition,(
% 2.92/2.01 spl173_8 <=> ! [X0 : a] : ((pa @ X0 @ x) != $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_8])],[avatar_definition])).
% 2.92/2.01 thf(f2664,definition,(
% 2.92/2.01 spl173_5 <=> ((sP3 @ x) = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_5])],[avatar_definition])).
% 2.92/2.01 thf(f2684,definition,(
% 2.92/2.01 spl173_10 <=> ((termi @ body @ x) = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_10])],[avatar_definition])).
% 2.92/2.01 thf(f3073,definition,(
% 2.92/2.01 spl173_28 <=> ! [X0 : a] : ((pa @ X0 @ (sK165 @ x)) != $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_28])],[avatar_definition])).
% 2.92/2.01 thf(f3153,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((pa @ X0 @ x) != $true)) ) | (spl173_5 | spl173_10 | ~spl173_28)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f3152,f2685])).
% 2.92/2.01 thf(f2685,plain,(
% 2.92/2.01 ((termi @ body @ x) != $true) | spl173_10),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2684])).
% 2.92/2.01 thf(f3152,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((pa @ X0 @ x) != $true) | ((termi @ body @ x) = $true)) ) | (spl173_5 | ~spl173_28)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f3151,f2666])).
% 2.92/2.01 thf(f2666,plain,(
% 2.92/2.01 ((sP3 @ x) != $true) | spl173_5),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2664])).
% 2.92/2.01 thf(f3151,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((sP3 @ x) = $true) | ((pa @ X0 @ x) != $true) | ((termi @ body @ x) = $true)) ) | ~spl173_28),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f3150])).
% 2.92/2.01 thf(f3150,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((sP3 @ x) = $true) | ((termi @ body @ x) = $true) | ($true != $true) | ((pa @ X0 @ x) != $true)) ) | ~spl173_28),
% 2.92/2.01 inference(superposition,[status(thm)],[f3074,f2431])).
% 2.92/2.01 thf(f2431,plain,(
% 2.92/2.01 ( ! [X6 : state,X7 : a] : (((pa @ (sK164 @ X6) @ (sK165 @ X6)) = $true) | ((pa @ X7 @ X6) != $true) | ((termi @ body @ X6) = $true) | ((sP3 @ X6) = $true)) )),
% 2.92/2.01 inference(equality_resolution,[status(thm)],[f2078])).
% 2.92/2.01 thf(f2078,plain,(
% 2.92/2.01 ( ! [X0 : state,X6 : state,X7 : a] : (((pa @ (sK164 @ X0) @ (sK165 @ X0)) = $true) | ((sP3 @ X0) = $true) | ((termi @ body @ X6) = $true) | (X0 != X6) | ((pa @ X7 @ X6) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1602])).
% 2.92/2.01 thf(f1602,plain,(
% 2.92/2.01 ! [X0 : state] : (((((termi @ body @ (sK165 @ X0)) != $true) & ((member1389040324_state @ (produc64584659_state @ (sK165 @ X0) @ X0) @ r) = $true) & ((pa @ (sK164 @ X0) @ (sK165 @ X0)) = $true)) | ((sP3 @ X0) = $true) | (! [X3 : state,X4 : state] : (! [X5 : a] : (((pa @ X5 @ X4) != $true) | (X0 != X4) | ((qa @ X5 @ X3) = $true)) | ((exec @ X4 @ body @ X3) != $true)) & ! [X6 : state,X7 : a] : (((termi @ body @ X6) = $true) | (X0 != X6) | ((pa @ X7 @ X6) != $true)))) & ((pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^[Y0 : a]: ((^[Y1 : state]: ((member1389040324_state @ (produc64584659_state @ Y1 @ X0) @ r) & (pa @ Y0 @ Y1))))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^[Y0 : a]: ((^[Y1 : state]: ((pa @ Y0 @ Y1) & (X0 = Y1))))) @ body @ qa) = $true))),
% 2.92/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK164,sK165])],[f1600,f1601])).
% 2.92/2.01 thf(f1601,plain,(
% 2.92/2.01 ! [X0 : state] : (? [X1 : a,X2 : state] : (((termi @ body @ X2) != $true) & ((member1389040324_state @ (produc64584659_state @ X2 @ X0) @ r) = $true) & ((pa @ X1 @ X2) = $true)) => (((termi @ body @ (sK165 @ X0)) != $true) & ((member1389040324_state @ (produc64584659_state @ (sK165 @ X0) @ X0) @ r) = $true) & ((pa @ (sK164 @ X0) @ (sK165 @ X0)) = $true)))),
% 2.92/2.01 introduced(definition,[],[choice_axiom])).
% 2.92/2.01 thf(f1600,plain,(
% 2.92/2.01 ! [X0 : state] : ((? [X1 : a,X2 : state] : (((termi @ body @ X2) != $true) & ((member1389040324_state @ (produc64584659_state @ X2 @ X0) @ r) = $true) & ((pa @ X1 @ X2) = $true)) | ((sP3 @ X0) = $true) | (! [X3 : state,X4 : state] : (! [X5 : a] : (((pa @ X5 @ X4) != $true) | (X0 != X4) | ((qa @ X5 @ X3) = $true)) | ((exec @ X4 @ body @ X3) != $true)) & ! [X6 : state,X7 : a] : (((termi @ body @ X6) = $true) | (X0 != X6) | ((pa @ X7 @ X6) != $true)))) & ((pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^[Y0 : a]: ((^[Y1 : state]: ((member1389040324_state @ (produc64584659_state @ Y1 @ X0) @ r) & (pa @ Y0 @ Y1))))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^[Y0 : a]: ((^[Y1 : state]: ((pa @ Y0 @ Y1) & (X0 = Y1))))) @ body @ qa) = $true))),
% 2.92/2.01 inference(rectify,[status(thm)],[f1401])).
% 2.92/2.01 thf(f1401,plain,(
% 2.92/2.01 ! [X0 : state] : ((? [X4 : a,X5 : state] : (((termi @ body @ X5) != $true) & ((member1389040324_state @ (produc64584659_state @ X5 @ X0) @ r) = $true) & ((pa @ X4 @ X5) = $true)) | ((sP3 @ X0) = $true) | (! [X8 : state,X9 : state] : (! [X10 : a] : (((pa @ X10 @ X9) != $true) | (X0 != X9) | ((qa @ X10 @ X8) = $true)) | ((exec @ X9 @ body @ X8) != $true)) & ! [X6 : state,X7 : a] : (((termi @ body @ X6) = $true) | (X0 != X6) | ((pa @ X7 @ X6) != $true)))) & ((pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^[Y0 : a]: ((^[Y1 : state]: ((member1389040324_state @ (produc64584659_state @ Y1 @ X0) @ r) & (pa @ Y0 @ Y1))))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^[Y0 : a]: ((^[Y1 : state]: ((pa @ Y0 @ Y1) & (X0 = Y1))))) @ body @ qa) = $true))),
% 2.92/2.01 inference(definition_folding,[status(thm)],[f1393,f1400])).
% 2.92/2.01 thf(f1400,plain,(
% 2.92/2.01 ! [X0 : state] : (? [X1 : state,X2 : state] : (? [X3 : a] : (((member1389040324_state @ (produc64584659_state @ X1 @ X0) @ r) = $true) & ((qa @ X3 @ X2) != $true) & ((pa @ X3 @ X1) = $true)) & ((exec @ X1 @ body @ X2) = $true)) | ~((sP3 @ X0) = $true))),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 2.92/2.01 thf(f1393,plain,(
% 2.92/2.01 ! [X0 : state] : ((? [X4 : a,X5 : state] : (((termi @ body @ X5) != $true) & ((member1389040324_state @ (produc64584659_state @ X5 @ X0) @ r) = $true) & ((pa @ X4 @ X5) = $true)) | ? [X1 : state,X2 : state] : (? [X3 : a] : (((member1389040324_state @ (produc64584659_state @ X1 @ X0) @ r) = $true) & ((qa @ X3 @ X2) != $true) & ((pa @ X3 @ X1) = $true)) & ((exec @ X1 @ body @ X2) = $true)) | (! [X8 : state,X9 : state] : (! [X10 : a] : (((pa @ X10 @ X9) != $true) | (X0 != X9) | ((qa @ X10 @ X8) = $true)) | ((exec @ X9 @ body @ X8) != $true)) & ! [X6 : state,X7 : a] : (((termi @ body @ X6) = $true) | (X0 != X6) | ((pa @ X7 @ X6) != $true)))) & ((pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^[Y0 : a]: ((^[Y1 : state]: ((member1389040324_state @ (produc64584659_state @ Y1 @ X0) @ r) & (pa @ Y0 @ Y1))))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^[Y0 : a]: ((^[Y1 : state]: ((pa @ Y0 @ Y1) & (X0 = Y1))))) @ body @ qa) = $true))),
% 2.92/2.01 inference(flattening,[status(thm)],[f1392])).
% 2.92/2.01 thf(f1392,plain,(
% 2.92/2.01 ! [X0 : state] : (((pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^[Y0 : a]: ((^[Y1 : state]: ((member1389040324_state @ (produc64584659_state @ Y1 @ X0) @ r) & (pa @ Y0 @ Y1))))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^[Y0 : a]: ((^[Y1 : state]: ((pa @ Y0 @ Y1) & (X0 = Y1))))) @ body @ qa) = $true) & ((! [X8 : state,X9 : state] : (! [X10 : a] : (((qa @ X10 @ X8) = $true) | (((pa @ X10 @ X9) != $true) | (X0 != X9))) | ((exec @ X9 @ body @ X8) != $true)) & ! [X6 : state,X7 : a] : (((termi @ body @ X6) = $true) | (((pa @ X7 @ X6) != $true) | (X0 != X6)))) | (? [X4 : a,X5 : state] : (((termi @ body @ X5) != $true) & (((member1389040324_state @ (produc64584659_state @ X5 @ X0) @ r) = $true) & ((pa @ X4 @ X5) = $true))) | ? [X1 : state,X2 : state] : (? [X3 : a] : (((qa @ X3 @ X2) != $true) & (((pa @ X3 @ X1) = $true) & ((member1389040324_state @ (produc64584659_state @ X1 @ X0) @ r) = $true))) & ((exec @ X1 @ body @ X2) = $true)))))),
% 2.92/2.01 inference(ennf_transformation,[status(thm)],[f1111])).
% 2.92/2.01 thf(f1111,plain,(
% 2.92/2.01 ! [X0 : state] : (((pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^[Y0 : a]: ((^[Y1 : state]: ((member1389040324_state @ (produc64584659_state @ Y1 @ X0) @ r) & (pa @ Y0 @ Y1))))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^[Y0 : a]: ((^[Y1 : state]: ((pa @ Y0 @ Y1) & (X0 = Y1))))) @ body @ qa) = $true) & ((! [X4 : a,X5 : state] : ((((member1389040324_state @ (produc64584659_state @ X5 @ X0) @ r) = $true) & ((pa @ X4 @ X5) = $true)) => ((termi @ body @ X5) = $true)) & ! [X1 : state,X2 : state] : (((exec @ X1 @ body @ X2) = $true) => ! [X3 : a] : ((((pa @ X3 @ X1) = $true) & ((member1389040324_state @ (produc64584659_state @ X1 @ X0) @ r) = $true)) => ((qa @ X3 @ X2) = $true)))) => (! [X8 : state,X9 : state] : (((exec @ X9 @ body @ X8) = $true) => ! [X10 : a] : ((((pa @ X10 @ X9) = $true) & (X0 = X9)) => ((qa @ X10 @ X8) = $true))) & ! [X6 : state,X7 : a] : ((((pa @ X7 @ X6) = $true) & (X0 = X6)) => ((termi @ body @ X6) = $true)))))),
% 2.92/2.01 inference(rectify,[status(thm)],[f634])).
% 2.92/2.01 thf(f634,plain,(
% 2.92/2.01 ! [X0 : state] : (((pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^[Y0 : a]: ((^[Y1 : state]: ((member1389040324_state @ (produc64584659_state @ Y1 @ X0) @ r) & (pa @ Y0 @ Y1))))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^[Y0 : a]: ((^[Y1 : state]: ((pa @ Y0 @ Y1) & (X0 = Y1))))) @ body @ qa) = $true) & ((! [X5 : state,X6 : state] : (($true = (exec @ X5 @ body @ X6)) => ! [X7 : a] : ((((pa @ X7 @ X5) = $true) & ((member1389040324_state @ (produc64584659_state @ X5 @ X0) @ r) = $true)) => ((qa @ X7 @ X6) = $true))) & ! [X8 : a,X9 : state] : ((((member1389040324_state @ (produc64584659_state @ X9 @ X0) @ r) = $true) & ((pa @ X8 @ X9) = $true)) => ((termi @ body @ X9) = $true))) => (! [X10 : state,X11 : a] : ((((pa @ X11 @ X10) = $true) & (X0 = X10)) => ($true = (termi @ body @ X10))) & ! [X12 : state,X13 : state] : (($true = (exec @ X13 @ body @ X12)) => ! [X14 : a] : (((X0 = X13) & ((pa @ X14 @ X13) = $true)) => ($true = (qa @ X14 @ X12)))))))),
% 2.92/2.01 inference(fool_elimination,[status(thm)],[f633])).
% 2.92/2.01 thf(f633,plain,(
% 2.92/2.01 ! [X0 : state] : ((pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^[X1 : a, X2 : state] : ((pa @ X1 @ X2) & (member1389040324_state @ (produc64584659_state @ X2 @ X0) @ r))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^[X3 : a, X4 : state] : ((X0 = X4) & (pa @ X3 @ X4))) @ body @ qa) & ((! [X5 : state,X6 : state] : ((exec @ X5 @ body @ X6) => ! [X7 : a] : (((pa @ X7 @ X5) & (member1389040324_state @ (produc64584659_state @ X5 @ X0) @ r)) => (qa @ X7 @ X6))) & ! [X8 : a,X9 : state] : (((member1389040324_state @ (produc64584659_state @ X9 @ X0) @ r) & (pa @ X8 @ X9)) => (termi @ body @ X9))) => (! [X10 : state,X11 : a] : (((pa @ X11 @ X10) & (X0 = X10)) => (termi @ body @ X10)) & ! [X12 : state,X13 : state] : ((exec @ X13 @ body @ X12) => ! [X14 : a] : (((X0 = X13) & (pa @ X14 @ X13)) => (qa @ X14 @ X12))))))),
% 2.92/2.01 inference(rectify,[status(thm)],[f355])).
% 2.92/2.01 thf(f355,axiom,(
% 2.92/2.01 ! [X91 : state] : ((pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^[X18 : a, X19 : state] : ((pa @ X18 @ X19) & (member1389040324_state @ (produc64584659_state @ X19 @ X91) @ r))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^[X18 : a, X19 : state] : ((X19 = X91) & (pa @ X18 @ X19))) @ body @ qa) & ((! [X6 : state,X8 : state] : ((exec @ X6 @ body @ X8) => ! [X5 : a] : (((pa @ X5 @ X6) & (member1389040324_state @ (produc64584659_state @ X6 @ X91) @ r)) => (qa @ X5 @ X8))) & ! [X5 : a,X6 : state] : (((member1389040324_state @ (produc64584659_state @ X6 @ X91) @ r) & (pa @ X5 @ X6)) => (termi @ body @ X6))) => (! [X92 : state,X9 : a] : (((pa @ X9 @ X92) & (X91 = X92)) => (termi @ body @ X92)) & ! [X93 : state,X92 : state] : ((exec @ X92 @ body @ X93) => ! [X9 : a] : (((X91 = X92) & (pa @ X9 @ X92)) => (qa @ X9 @ X93))))))),
% 2.92/2.01 file('/export/starexec/sandbox2/tmp/tmp.H5mA5wl1hp/DTF2THF_16650.p',conj_0)).
% 2.92/2.01 thf(f3074,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((pa @ X0 @ (sK165 @ x)) != $true)) ) | ~spl173_28),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f3073])).
% 2.92/2.01 thf(f3149,plain,(
% 2.92/2.01 spl173_8 | spl173_5 | spl173_10 | ~spl173_16),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f3148,f2771,f2684,f2664,f2677])).
% 2.92/2.01 thf(f2771,definition,(
% 2.92/2.01 spl173_16 <=> ((termi @ body @ (sK165 @ x)) = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_16])],[avatar_definition])).
% 2.92/2.01 thf(f3148,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((pa @ X0 @ x) != $true)) ) | (spl173_5 | spl173_10 | ~spl173_16)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f3147,f2666])).
% 2.92/2.01 thf(f3147,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((sP3 @ x) = $true) | ((pa @ X0 @ x) != $true)) ) | (spl173_10 | ~spl173_16)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f3146,f2685])).
% 2.92/2.01 thf(f3146,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((termi @ body @ x) = $true) | ((pa @ X0 @ x) != $true) | ((sP3 @ x) = $true)) ) | ~spl173_16),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f3145])).
% 2.92/2.01 thf(f3145,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((termi @ body @ x) = $true) | ($true != $true) | ((pa @ X0 @ x) != $true) | ((sP3 @ x) = $true)) ) | ~spl173_16),
% 2.92/2.01 inference(superposition,[status(thm)],[f2427,f2772])).
% 2.92/2.01 thf(f2772,plain,(
% 2.92/2.01 ((termi @ body @ (sK165 @ x)) = $true) | ~spl173_16),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2771])).
% 2.92/2.01 thf(f2427,plain,(
% 2.92/2.01 ( ! [X6 : state,X7 : a] : (((termi @ body @ (sK165 @ X6)) != $true) | ((pa @ X7 @ X6) != $true) | ((termi @ body @ X6) = $true) | ((sP3 @ X6) = $true)) )),
% 2.92/2.01 inference(equality_resolution,[status(thm)],[f2082])).
% 2.92/2.01 thf(f2082,plain,(
% 2.92/2.01 ( ! [X0 : state,X6 : state,X7 : a] : (((termi @ body @ (sK165 @ X0)) != $true) | ((sP3 @ X0) = $true) | ((termi @ body @ X6) = $true) | (X0 != X6) | ((pa @ X7 @ X6) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1602])).
% 2.92/2.01 thf(f3075,plain,(
% 2.92/2.01 spl173_10 | spl173_16 | spl173_28 | spl173_8 | spl173_5),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f3071,f2664,f2677,f3073,f2771,f2684])).
% 2.92/2.01 thf(f3071,plain,(
% 2.92/2.01 ( ! [X0 : a,X1 : a] : (((pa @ X0 @ (sK165 @ x)) != $true) | ((pa @ X1 @ x) != $true) | ((termi @ body @ (sK165 @ x)) = $true) | ((termi @ body @ x) = $true)) ) | spl173_5),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2696,f2666])).
% 2.92/2.01 thf(f2696,plain,(
% 2.92/2.01 ( ! [X0 : a,X1 : a] : (((termi @ body @ (sK165 @ x)) = $true) | ((pa @ X0 @ (sK165 @ x)) != $true) | ((termi @ body @ x) = $true) | ((sP3 @ x) = $true) | ((pa @ X1 @ x) != $true)) )),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2688])).
% 2.92/2.01 thf(f2688,plain,(
% 2.92/2.01 ( ! [X0 : a,X1 : a] : (((termi @ body @ (sK165 @ x)) = $true) | ((pa @ X1 @ x) != $true) | ($true != $true) | ((pa @ X0 @ (sK165 @ x)) != $true) | ((termi @ body @ x) = $true) | ((sP3 @ x) = $true)) )),
% 2.92/2.01 inference(superposition,[status(thm)],[f2419,f2429])).
% 2.92/2.01 thf(f2429,plain,(
% 2.92/2.01 ( ! [X6 : state,X7 : a] : (((member1389040324_state @ (produc64584659_state @ (sK165 @ X6) @ X6) @ r) = $true) | ((termi @ body @ X6) = $true) | ((sP3 @ X6) = $true) | ((pa @ X7 @ X6) != $true)) )),
% 2.92/2.01 inference(equality_resolution,[status(thm)],[f2080])).
% 2.92/2.01 thf(f2080,plain,(
% 2.92/2.01 ( ! [X0 : state,X6 : state,X7 : a] : (((member1389040324_state @ (produc64584659_state @ (sK165 @ X0) @ X0) @ r) = $true) | ((sP3 @ X0) = $true) | ((termi @ body @ X6) = $true) | (X0 != X6) | ((pa @ X7 @ X6) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1602])).
% 2.92/2.01 thf(f2419,plain,(
% 2.92/2.01 ( ! [X4 : a,X5 : state] : (($true != (member1389040324_state @ (produc64584659_state @ X5 @ x) @ r)) | ((termi @ body @ X5) = $true) | ((pa @ X4 @ X5) != $true)) )),
% 2.92/2.01 inference(equality_resolution,[status(thm)],[f1769])).
% 2.92/2.01 thf(f1769,plain,(
% 2.92/2.01 ( ! [X0 : state,X4 : a,X5 : state] : (((pa @ X4 @ X5) != $true) | (X0 != X5) | ((termi @ body @ X5) = $true) | ((member1389040324_state @ (produc64584659_state @ X0 @ x) @ r) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1381])).
% 2.92/2.01 thf(f1381,plain,(
% 2.92/2.01 ! [X0 : state] : ((! [X1 : state,X2 : state] : (((exec @ X1 @ body @ X2) != $true) | ! [X3 : a] : (((pa @ X3 @ X1) != $true) | ((qa @ X3 @ X2) = $true) | (X0 != X1))) & ! [X4 : a,X5 : state] : (((pa @ X4 @ X5) != $true) | (X0 != X5) | ((termi @ body @ X5) = $true))) | ((member1389040324_state @ (produc64584659_state @ X0 @ x) @ r) != $true))),
% 2.92/2.01 inference(flattening,[status(thm)],[f1380])).
% 2.92/2.01 thf(f1380,plain,(
% 2.92/2.01 ! [X0 : state] : ((! [X4 : a,X5 : state] : (((termi @ body @ X5) = $true) | (((pa @ X4 @ X5) != $true) | (X0 != X5))) & ! [X1 : state,X2 : state] : (! [X3 : a] : (((qa @ X3 @ X2) = $true) | (((pa @ X3 @ X1) != $true) | (X0 != X1))) | ((exec @ X1 @ body @ X2) != $true))) | ((member1389040324_state @ (produc64584659_state @ X0 @ x) @ r) != $true))),
% 2.92/2.01 inference(ennf_transformation,[status(thm)],[f890])).
% 2.92/2.01 thf(f890,plain,(
% 2.92/2.01 ! [X0 : state] : (((member1389040324_state @ (produc64584659_state @ X0 @ x) @ r) = $true) => (! [X4 : a,X5 : state] : ((((pa @ X4 @ X5) = $true) & (X0 = X5)) => ((termi @ body @ X5) = $true)) & ! [X1 : state,X2 : state] : (((exec @ X1 @ body @ X2) = $true) => ! [X3 : a] : ((((pa @ X3 @ X1) = $true) & (X0 = X1)) => ((qa @ X3 @ X2) = $true)))))),
% 2.92/2.01 inference(fool_elimination,[status(thm)],[f889])).
% 2.92/2.01 thf(f889,plain,(
% 2.92/2.01 ! [X0 : state] : ((member1389040324_state @ (produc64584659_state @ X0 @ x) @ r) => (! [X1 : state,X2 : state] : ((exec @ X1 @ body @ X2) => ! [X3 : a] : (((pa @ X3 @ X1) & (X0 = X1)) => (qa @ X3 @ X2))) & ! [X4 : a,X5 : state] : (((pa @ X4 @ X5) & (X0 = X5)) => (termi @ body @ X5))))),
% 2.92/2.01 inference(rectify,[status(thm)],[f356])).
% 2.92/2.01 thf(f356,axiom,(
% 2.92/2.01 ! [X34 : state] : ((member1389040324_state @ (produc64584659_state @ X34 @ x) @ r) => (! [X92 : state,X93 : state] : ((exec @ X92 @ body @ X93) => ! [X9 : a] : (((pa @ X9 @ X92) & (X34 = X92)) => (qa @ X9 @ X93))) & ! [X9 : a,X92 : state] : (((pa @ X9 @ X92) & (X34 = X92)) => (termi @ body @ X92))))),
% 2.92/2.01 file('/export/starexec/sandbox2/tmp/tmp.H5mA5wl1hp/DTF2THF_16650.p',conj_1)).
% 2.92/2.01 thf(f3065,plain,(
% 2.92/2.01 ~spl173_1 | ~spl173_15 | spl173_16 | ~spl173_22),
% 2.92/2.01 inference(avatar_contradiction_clause,[status(thm)],[f3064])).
% 2.92/2.01 thf(f3064,plain,(
% 2.92/2.01 $false | (~spl173_1 | ~spl173_15 | spl173_16 | ~spl173_22)),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f3062])).
% 2.92/2.01 thf(f3062,plain,(
% 2.92/2.01 ($true != $true) | (~spl173_1 | ~spl173_15 | spl173_16 | ~spl173_22)),
% 2.92/2.01 inference(superposition,[status(thm)],[f3060,f2911])).
% 2.92/2.01 thf(f2911,plain,(
% 2.92/2.01 ((pa @ (sK164 @ x) @ (sK165 @ x)) = $true) | (~spl173_1 | ~spl173_15)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2910,f2641])).
% 2.92/2.01 thf(f2641,plain,(
% 2.92/2.01 (sP2 = $true) | ~spl173_1),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2639])).
% 2.92/2.01 thf(f2639,definition,(
% 2.92/2.01 spl173_1 <=> (sP2 = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_1])],[avatar_definition])).
% 2.92/2.01 thf(f2910,plain,(
% 2.92/2.01 ((pa @ (sK164 @ x) @ (sK165 @ x)) = $true) | (sP2 != $true) | ~spl173_15),
% 2.92/2.01 inference(superposition,[status(thm)],[f2765,f2004])).
% 2.92/2.01 thf(f2004,plain,(
% 2.92/2.01 (x = sK140) | (sP2 != $true)),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1570])).
% 2.92/2.01 thf(f1570,plain,(
% 2.92/2.01 (((exec @ sK140 @ body @ sK139) = $true) & (((qa @ sK141 @ sK139) != $true) & ((pa @ sK141 @ sK140) = $true) & (x = sK140))) | (sP2 != $true)),
% 2.92/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK139,sK140,sK141])],[f1567,f1569,f1568])).
% 2.92/2.01 thf(f1568,plain,(
% 2.92/2.01 ? [X0 : state,X1 : state] : (((exec @ X1 @ body @ X0) = $true) & ? [X2 : a] : (((qa @ X2 @ X0) != $true) & ((pa @ X2 @ X1) = $true) & (x = X1))) => (((exec @ sK140 @ body @ sK139) = $true) & ? [X2 : a] : (((qa @ X2 @ sK139) != $true) & ((pa @ X2 @ sK140) = $true) & (x = sK140)))),
% 2.92/2.01 introduced(definition,[],[choice_axiom])).
% 2.92/2.01 thf(f1569,plain,(
% 2.92/2.01 ? [X2 : a] : (((qa @ X2 @ sK139) != $true) & ((pa @ X2 @ sK140) = $true) & (x = sK140)) => (((qa @ sK141 @ sK139) != $true) & ((pa @ sK141 @ sK140) = $true) & (x = sK140))),
% 2.92/2.01 introduced(definition,[],[choice_axiom])).
% 2.92/2.01 thf(f1567,plain,(
% 2.92/2.01 ? [X0 : state,X1 : state] : (((exec @ X1 @ body @ X0) = $true) & ? [X2 : a] : (((qa @ X2 @ X0) != $true) & ((pa @ X2 @ X1) = $true) & (x = X1))) | (sP2 != $true)),
% 2.92/2.01 inference(nnf_transformation,[status(thm)],[f1398])).
% 2.92/2.01 thf(f1398,plain,(
% 2.92/2.01 ? [X0 : state,X1 : state] : (((exec @ X1 @ body @ X0) = $true) & ? [X2 : a] : (((qa @ X2 @ X0) != $true) & ((pa @ X2 @ X1) = $true) & (x = X1))) | ~(sP2 = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 2.92/2.01 thf(f2765,plain,(
% 2.92/2.01 ((pa @ (sK164 @ sK140) @ (sK165 @ sK140)) = $true) | ~spl173_15),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2763])).
% 2.92/2.01 thf(f2763,definition,(
% 2.92/2.01 spl173_15 <=> ((pa @ (sK164 @ sK140) @ (sK165 @ sK140)) = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_15])],[avatar_definition])).
% 2.92/2.01 thf(f3060,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((pa @ X0 @ (sK165 @ x)) != $true)) ) | (~spl173_1 | spl173_16 | ~spl173_22)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f3055,f2773])).
% 2.92/2.01 thf(f2773,plain,(
% 2.92/2.01 ((termi @ body @ (sK165 @ x)) != $true) | spl173_16),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2771])).
% 2.92/2.01 thf(f3055,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((pa @ X0 @ (sK165 @ x)) != $true) | ((termi @ body @ (sK165 @ x)) = $true)) ) | (~spl173_1 | ~spl173_22)),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f3050])).
% 2.92/2.01 thf(f3050,plain,(
% 2.92/2.01 ( ! [X0 : a] : (($true != $true) | ((pa @ X0 @ (sK165 @ x)) != $true) | ((termi @ body @ (sK165 @ x)) = $true)) ) | (~spl173_1 | ~spl173_22)),
% 2.92/2.01 inference(superposition,[status(thm)],[f2419,f2921])).
% 2.92/2.01 thf(f2921,plain,(
% 2.92/2.01 ((member1389040324_state @ (produc64584659_state @ (sK165 @ x) @ x) @ r) = $true) | (~spl173_1 | ~spl173_22)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2912,f2641])).
% 2.92/2.01 thf(f2912,plain,(
% 2.92/2.01 (sP2 != $true) | ((member1389040324_state @ (produc64584659_state @ (sK165 @ x) @ x) @ r) = $true) | ~spl173_22),
% 2.92/2.01 inference(superposition,[status(thm)],[f2861,f2004])).
% 2.92/2.01 thf(f2861,plain,(
% 2.92/2.01 ((member1389040324_state @ (produc64584659_state @ (sK165 @ sK140) @ sK140) @ r) = $true) | ~spl173_22),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2859])).
% 2.92/2.01 thf(f2859,definition,(
% 2.92/2.01 spl173_22 <=> ((member1389040324_state @ (produc64584659_state @ (sK165 @ sK140) @ sK140) @ r) = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_22])],[avatar_definition])).
% 2.92/2.01 thf(f2908,plain,(
% 2.92/2.01 ~spl173_5),
% 2.92/2.01 inference(avatar_contradiction_clause,[status(thm)],[f2907])).
% 2.92/2.01 thf(f2907,plain,(
% 2.92/2.01 $false | ~spl173_5),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2906,f2665])).
% 2.92/2.01 thf(f2665,plain,(
% 2.92/2.01 ((sP3 @ x) = $true) | ~spl173_5),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2664])).
% 2.92/2.01 thf(f2906,plain,(
% 2.92/2.01 ((sP3 @ x) != $true) | ~spl173_5),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2905])).
% 2.92/2.01 thf(f2905,plain,(
% 2.92/2.01 ((sP3 @ x) != $true) | ($true != $true) | ~spl173_5),
% 2.92/2.01 inference(superposition,[status(thm)],[f2904,f2074])).
% 2.92/2.01 thf(f2074,plain,(
% 2.92/2.01 ( ! [X0 : state] : (((pa @ (sK163 @ X0) @ (sK161 @ X0)) = $true) | ((sP3 @ X0) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1599])).
% 2.92/2.01 thf(f1599,plain,(
% 2.92/2.01 ! [X0 : state] : (((((member1389040324_state @ (produc64584659_state @ (sK161 @ X0) @ X0) @ r) = $true) & ((qa @ (sK163 @ X0) @ (sK162 @ X0)) != $true) & ((pa @ (sK163 @ X0) @ (sK161 @ X0)) = $true)) & ((exec @ (sK161 @ X0) @ body @ (sK162 @ X0)) = $true)) | ((sP3 @ X0) != $true))),
% 2.92/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK161,sK162,sK163])],[f1596,f1598,f1597])).
% 2.92/2.01 thf(f1597,plain,(
% 2.92/2.01 ! [X0 : state] : (? [X1 : state,X2 : state] : (? [X3 : a] : (((member1389040324_state @ (produc64584659_state @ X1 @ X0) @ r) = $true) & ((qa @ X3 @ X2) != $true) & ((pa @ X3 @ X1) = $true)) & ((exec @ X1 @ body @ X2) = $true)) => (? [X3 : a] : (((member1389040324_state @ (produc64584659_state @ (sK161 @ X0) @ X0) @ r) = $true) & ((qa @ X3 @ (sK162 @ X0)) != $true) & ((pa @ X3 @ (sK161 @ X0)) = $true)) & ((exec @ (sK161 @ X0) @ body @ (sK162 @ X0)) = $true)))),
% 2.92/2.01 introduced(definition,[],[choice_axiom])).
% 2.92/2.01 thf(f1598,plain,(
% 2.92/2.01 ! [X0 : state] : (? [X3 : a] : (((member1389040324_state @ (produc64584659_state @ (sK161 @ X0) @ X0) @ r) = $true) & ((qa @ X3 @ (sK162 @ X0)) != $true) & ((pa @ X3 @ (sK161 @ X0)) = $true)) => (((member1389040324_state @ (produc64584659_state @ (sK161 @ X0) @ X0) @ r) = $true) & ((qa @ (sK163 @ X0) @ (sK162 @ X0)) != $true) & ((pa @ (sK163 @ X0) @ (sK161 @ X0)) = $true)))),
% 2.92/2.01 introduced(definition,[],[choice_axiom])).
% 2.92/2.01 thf(f1596,plain,(
% 2.92/2.01 ! [X0 : state] : (? [X1 : state,X2 : state] : (? [X3 : a] : (((member1389040324_state @ (produc64584659_state @ X1 @ X0) @ r) = $true) & ((qa @ X3 @ X2) != $true) & ((pa @ X3 @ X1) = $true)) & ((exec @ X1 @ body @ X2) = $true)) | ((sP3 @ X0) != $true))),
% 2.92/2.01 inference(nnf_transformation,[status(thm)],[f1400])).
% 2.92/2.01 thf(f2904,plain,(
% 2.92/2.01 ((pa @ (sK163 @ x) @ (sK161 @ x)) != $true) | ~spl173_5),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2903,f2665])).
% 2.92/2.01 thf(f2903,plain,(
% 2.92/2.01 ((pa @ (sK163 @ x) @ (sK161 @ x)) != $true) | ((sP3 @ x) != $true) | ~spl173_5),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2902])).
% 2.92/2.01 thf(f2902,plain,(
% 2.92/2.01 ((pa @ (sK163 @ x) @ (sK161 @ x)) != $true) | ($true != $true) | ((sP3 @ x) != $true) | ~spl173_5),
% 2.92/2.01 inference(superposition,[status(thm)],[f2075,f2901])).
% 2.92/2.01 thf(f2901,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((qa @ X0 @ (sK162 @ x)) = $true) | ((pa @ X0 @ (sK161 @ x)) != $true)) ) | ~spl173_5),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2900,f2665])).
% 2.92/2.01 thf(f2900,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((pa @ X0 @ (sK161 @ x)) != $true) | ((qa @ X0 @ (sK162 @ x)) = $true) | ((sP3 @ x) != $true)) )),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2899])).
% 2.92/2.01 thf(f2899,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((pa @ X0 @ (sK161 @ x)) != $true) | ($true != $true) | ((sP3 @ x) != $true) | ((qa @ X0 @ (sK162 @ x)) = $true)) )),
% 2.92/2.01 inference(duplicate_literal_removal,[status(thm)],[f2898])).
% 2.92/2.01 thf(f2898,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((qa @ X0 @ (sK162 @ x)) = $true) | ((pa @ X0 @ (sK161 @ x)) != $true) | ($true != $true) | ((sP3 @ x) != $true) | ((sP3 @ x) != $true)) )),
% 2.92/2.01 inference(superposition,[status(thm)],[f2708,f2076])).
% 2.92/2.01 thf(f2076,plain,(
% 2.92/2.01 ( ! [X0 : state] : (((member1389040324_state @ (produc64584659_state @ (sK161 @ X0) @ X0) @ r) = $true) | ((sP3 @ X0) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1599])).
% 2.92/2.01 thf(f2708,plain,(
% 2.92/2.01 ( ! [X0 : state,X1 : a] : (((member1389040324_state @ (produc64584659_state @ (sK161 @ X0) @ x) @ r) != $true) | ((sP3 @ X0) != $true) | ((qa @ X1 @ (sK162 @ X0)) = $true) | ((pa @ X1 @ (sK161 @ X0)) != $true)) )),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2700])).
% 2.92/2.01 thf(f2700,plain,(
% 2.92/2.01 ( ! [X0 : state,X1 : a] : (((sP3 @ X0) != $true) | ((member1389040324_state @ (produc64584659_state @ (sK161 @ X0) @ x) @ r) != $true) | ((pa @ X1 @ (sK161 @ X0)) != $true) | ($true != $true) | ((qa @ X1 @ (sK162 @ X0)) = $true)) )),
% 2.92/2.01 inference(superposition,[status(thm)],[f2633,f2555])).
% 2.92/2.01 thf(f2555,plain,(
% 2.92/2.01 ( ! [X0 : state] : (((?? @ nat @ (^[Y0 : nat]: (execn @ (sK161 @ X0) @ body @ Y0 @ (sK162 @ X0)))) = $true) | ((sP3 @ X0) != $true)) )),
% 2.92/2.01 inference(beta_eta_normalization,[status(thm)],[f2390])).
% 2.92/2.01 thf(f2390,plain,(
% 2.92/2.01 ( ! [X0 : state] : ((((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ (sK161 @ X0) @ body @ (sK162 @ X0)) = $true) | ((sP3 @ X0) != $true)) )),
% 2.92/2.01 inference(definition_unfolding,[status(thm)],[f2073,f1657])).
% 2.92/2.01 thf(f1657,plain,(
% 2.92/2.01 (exec = (^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))))),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f622])).
% 2.92/2.01 thf(f622,plain,(
% 2.92/2.01 (exec = (^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))))),
% 2.92/2.01 inference(fool_elimination,[status(thm)],[f621])).
% 2.92/2.01 thf(f621,plain,(
% 2.92/2.01 (exec = (^[X0 : state, X1 : com, X2 : state] : (? [X3 : nat] : (execn @ X0 @ X1 @ X3 @ X2))))),
% 2.92/2.01 inference(rectify,[status(thm)],[f342])).
% 2.92/2.01 thf(f342,axiom,(
% 2.92/2.01 (exec = (^[X19 : state, X80 : com, X62 : state] : (? [X79 : nat] : (execn @ X19 @ X80 @ X79 @ X62))))),
% 2.92/2.01 file('/export/starexec/sandbox2/tmp/tmp.H5mA5wl1hp/DTF2THF_16650.p',fact_341_exec__iff__execn)).
% 2.92/2.01 thf(f2073,plain,(
% 2.92/2.01 ( ! [X0 : state] : (((exec @ (sK161 @ X0) @ body @ (sK162 @ X0)) = $true) | ((sP3 @ X0) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1599])).
% 2.92/2.01 thf(f2633,plain,(
% 2.92/2.01 ( ! [X2 : state,X3 : a,X1 : state] : (((?? @ nat @ (^[Y0 : nat]: (execn @ X1 @ body @ Y0 @ X2))) != $true) | ((qa @ X3 @ X2) = $true) | ((pa @ X3 @ X1) != $true) | ((member1389040324_state @ (produc64584659_state @ X1 @ x) @ r) != $true)) )),
% 2.92/2.01 inference(beta_eta_normalization,[status(thm)],[f2418])).
% 2.92/2.01 thf(f2418,plain,(
% 2.92/2.01 ( ! [X2 : state,X3 : a,X1 : state] : (((pa @ X3 @ X1) != $true) | ((member1389040324_state @ (produc64584659_state @ X1 @ x) @ r) != $true) | (((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ X1 @ body @ X2) != $true) | ((qa @ X3 @ X2) = $true)) )),
% 2.92/2.01 inference(equality_resolution,[status(thm)],[f2212])).
% 2.92/2.01 thf(f2212,plain,(
% 2.92/2.01 ( ! [X2 : state,X3 : a,X0 : state,X1 : state] : ((((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ X1 @ body @ X2) != $true) | ((pa @ X3 @ X1) != $true) | ((qa @ X3 @ X2) = $true) | (X0 != X1) | ((member1389040324_state @ (produc64584659_state @ X0 @ x) @ r) != $true)) )),
% 2.92/2.01 inference(definition_unfolding,[status(thm)],[f1770,f1657])).
% 2.92/2.01 thf(f1770,plain,(
% 2.92/2.01 ( ! [X2 : state,X3 : a,X0 : state,X1 : state] : (((exec @ X1 @ body @ X2) != $true) | ((pa @ X3 @ X1) != $true) | ((qa @ X3 @ X2) = $true) | (X0 != X1) | ((member1389040324_state @ (produc64584659_state @ X0 @ x) @ r) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1381])).
% 2.92/2.01 thf(f2075,plain,(
% 2.92/2.01 ( ! [X0 : state] : (((qa @ (sK163 @ X0) @ (sK162 @ X0)) != $true) | ((sP3 @ X0) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1599])).
% 2.92/2.01 thf(f2867,plain,(
% 2.92/2.01 spl173_5 | ~spl173_1 | ~spl173_13),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f2864,f2739,f2639,f2664])).
% 2.92/2.01 thf(f2739,definition,(
% 2.92/2.01 spl173_13 <=> ((sP3 @ sK140) = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_13])],[avatar_definition])).
% 2.92/2.01 thf(f2864,plain,(
% 2.92/2.01 ((sP3 @ x) = $true) | (~spl173_1 | ~spl173_13)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2863,f2641])).
% 2.92/2.01 thf(f2863,plain,(
% 2.92/2.01 (sP2 != $true) | ((sP3 @ x) = $true) | ~spl173_13),
% 2.92/2.01 inference(superposition,[status(thm)],[f2741,f2004])).
% 2.92/2.01 thf(f2741,plain,(
% 2.92/2.01 ((sP3 @ sK140) = $true) | ~spl173_13),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2739])).
% 2.92/2.01 thf(f2862,plain,(
% 2.92/2.01 spl173_12 | spl173_13 | spl173_22 | ~spl173_1),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f2857,f2639,f2859,f2739,f2719])).
% 2.92/2.01 thf(f2719,definition,(
% 2.92/2.01 spl173_12 <=> ! [X0 : a] : (((qa @ X0 @ sK139) = $true) | ((pa @ X0 @ sK140) != $true))),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_12])],[avatar_definition])).
% 2.92/2.01 thf(f2857,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((member1389040324_state @ (produc64584659_state @ (sK165 @ sK140) @ sK140) @ r) = $true) | ((pa @ X0 @ sK140) != $true) | ((sP3 @ sK140) = $true) | ((qa @ X0 @ sK139) = $true)) ) | ~spl173_1),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2791,f2641])).
% 2.92/2.01 thf(f2791,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((qa @ X0 @ sK139) = $true) | ((sP3 @ sK140) = $true) | ((pa @ X0 @ sK140) != $true) | (sP2 != $true) | ((member1389040324_state @ (produc64584659_state @ (sK165 @ sK140) @ sK140) @ r) = $true)) )),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2789])).
% 2.92/2.01 thf(f2789,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((sP3 @ sK140) = $true) | (sP2 != $true) | ($true != $true) | ((qa @ X0 @ sK139) = $true) | ((pa @ X0 @ sK140) != $true) | ((member1389040324_state @ (produc64584659_state @ (sK165 @ sK140) @ sK140) @ r) = $true)) )),
% 2.92/2.01 inference(superposition,[status(thm)],[f2637,f2564])).
% 2.92/2.01 thf(f2564,plain,(
% 2.92/2.01 ((?? @ nat @ (^[Y0 : nat]: (execn @ sK140 @ body @ Y0 @ sK139))) = $true) | (sP2 != $true)),
% 2.92/2.01 inference(beta_eta_normalization,[status(thm)],[f2356])).
% 2.92/2.01 thf(f2356,plain,(
% 2.92/2.01 (sP2 != $true) | (((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ sK140 @ body @ sK139) = $true)),
% 2.92/2.01 inference(definition_unfolding,[status(thm)],[f2007,f1657])).
% 2.92/2.01 thf(f2007,plain,(
% 2.92/2.01 ((exec @ sK140 @ body @ sK139) = $true) | (sP2 != $true)),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1570])).
% 2.92/2.01 thf(f2637,plain,(
% 2.92/2.01 ( ! [X3 : state,X4 : state,X5 : a] : (((?? @ nat @ (^[Y0 : nat]: (execn @ X4 @ body @ Y0 @ X3))) != $true) | ((sP3 @ X4) = $true) | ((qa @ X5 @ X3) = $true) | ((pa @ X5 @ X4) != $true) | ((member1389040324_state @ (produc64584659_state @ (sK165 @ X4) @ X4) @ r) = $true)) )),
% 2.92/2.01 inference(beta_eta_normalization,[status(thm)],[f2428])).
% 2.92/2.01 thf(f2428,plain,(
% 2.92/2.01 ( ! [X3 : state,X4 : state,X5 : a] : (((member1389040324_state @ (produc64584659_state @ (sK165 @ X4) @ X4) @ r) = $true) | ((qa @ X5 @ X3) = $true) | (((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ X4 @ body @ X3) != $true) | ((sP3 @ X4) = $true) | ((pa @ X5 @ X4) != $true)) )),
% 2.92/2.01 inference(equality_resolution,[status(thm)],[f2392])).
% 2.92/2.01 thf(f2392,plain,(
% 2.92/2.01 ( ! [X3 : state,X0 : state,X4 : state,X5 : a] : (((member1389040324_state @ (produc64584659_state @ (sK165 @ X0) @ X0) @ r) = $true) | ((sP3 @ X0) = $true) | ((pa @ X5 @ X4) != $true) | (X0 != X4) | ((qa @ X5 @ X3) = $true) | (((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ X4 @ body @ X3) != $true)) )),
% 2.92/2.01 inference(definition_unfolding,[status(thm)],[f2081,f1657])).
% 2.92/2.01 thf(f2081,plain,(
% 2.92/2.01 ( ! [X3 : state,X0 : state,X4 : state,X5 : a] : (((member1389040324_state @ (produc64584659_state @ (sK165 @ X0) @ X0) @ r) = $true) | ((sP3 @ X0) = $true) | ((pa @ X5 @ X4) != $true) | (X0 != X4) | ((qa @ X5 @ X3) = $true) | ((exec @ X4 @ body @ X3) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1602])).
% 2.92/2.01 thf(f2854,plain,(
% 2.92/2.01 ~spl173_1 | ~spl173_12),
% 2.92/2.01 inference(avatar_contradiction_clause,[status(thm)],[f2853])).
% 2.92/2.01 thf(f2853,plain,(
% 2.92/2.01 $false | (~spl173_1 | ~spl173_12)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2852,f2641])).
% 2.92/2.01 thf(f2852,plain,(
% 2.92/2.01 (sP2 != $true) | (~spl173_1 | ~spl173_12)),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2851])).
% 2.92/2.01 thf(f2851,plain,(
% 2.92/2.01 ($true != $true) | (sP2 != $true) | (~spl173_1 | ~spl173_12)),
% 2.92/2.01 inference(superposition,[status(thm)],[f2846,f2005])).
% 2.92/2.01 thf(f2005,plain,(
% 2.92/2.01 ((pa @ sK141 @ sK140) = $true) | (sP2 != $true)),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1570])).
% 2.92/2.01 thf(f2846,plain,(
% 2.92/2.01 ((pa @ sK141 @ sK140) != $true) | (~spl173_1 | ~spl173_12)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2845,f2641])).
% 2.92/2.01 thf(f2845,plain,(
% 2.92/2.01 ((pa @ sK141 @ sK140) != $true) | (sP2 != $true) | ~spl173_12),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2844])).
% 2.92/2.01 thf(f2844,plain,(
% 2.92/2.01 ((pa @ sK141 @ sK140) != $true) | (sP2 != $true) | ($true != $true) | ~spl173_12),
% 2.92/2.01 inference(superposition,[status(thm)],[f2006,f2720])).
% 2.92/2.01 thf(f2720,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((qa @ X0 @ sK139) = $true) | ((pa @ X0 @ sK140) != $true)) ) | ~spl173_12),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2719])).
% 2.92/2.01 thf(f2006,plain,(
% 2.92/2.01 ((qa @ sK141 @ sK139) != $true) | (sP2 != $true)),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1570])).
% 2.92/2.01 thf(f2785,plain,(
% 2.92/2.01 ~spl173_1 | spl173_13 | spl173_12 | spl173_15),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f2760,f2763,f2719,f2739,f2639])).
% 2.92/2.01 thf(f2760,plain,(
% 2.92/2.01 ( ! [X0 : a] : ((sP2 != $true) | ((pa @ X0 @ sK140) != $true) | ((qa @ X0 @ sK139) = $true) | ((pa @ (sK164 @ sK140) @ (sK165 @ sK140)) = $true) | ((sP3 @ sK140) = $true)) )),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2753])).
% 2.92/2.01 thf(f2753,plain,(
% 2.92/2.01 ( ! [X0 : a] : ((sP2 != $true) | ((qa @ X0 @ sK139) = $true) | ((sP3 @ sK140) = $true) | ((pa @ (sK164 @ sK140) @ (sK165 @ sK140)) = $true) | ((pa @ X0 @ sK140) != $true) | ($true != $true)) )),
% 2.92/2.01 inference(superposition,[status(thm)],[f2634,f2564])).
% 2.92/2.01 thf(f2634,plain,(
% 2.92/2.01 ( ! [X3 : state,X4 : state,X5 : a] : (((?? @ nat @ (^[Y0 : nat]: (execn @ X4 @ body @ Y0 @ X3))) != $true) | ((sP3 @ X4) = $true) | ((pa @ X5 @ X4) != $true) | ((pa @ (sK164 @ X4) @ (sK165 @ X4)) = $true) | ((qa @ X5 @ X3) = $true)) )),
% 2.92/2.01 inference(beta_eta_normalization,[status(thm)],[f2430])).
% 2.92/2.01 thf(f2430,plain,(
% 2.92/2.01 ( ! [X3 : state,X4 : state,X5 : a] : (((pa @ X5 @ X4) != $true) | ((qa @ X5 @ X3) = $true) | ((pa @ (sK164 @ X4) @ (sK165 @ X4)) = $true) | ((sP3 @ X4) = $true) | (((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ X4 @ body @ X3) != $true)) )),
% 2.92/2.01 inference(equality_resolution,[status(thm)],[f2393])).
% 2.92/2.01 thf(f2393,plain,(
% 2.92/2.01 ( ! [X3 : state,X0 : state,X4 : state,X5 : a] : (((pa @ (sK164 @ X0) @ (sK165 @ X0)) = $true) | ((sP3 @ X0) = $true) | ((pa @ X5 @ X4) != $true) | (X0 != X4) | ((qa @ X5 @ X3) = $true) | (((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ X4 @ body @ X3) != $true)) )),
% 2.92/2.01 inference(definition_unfolding,[status(thm)],[f2079,f1657])).
% 2.92/2.01 thf(f2079,plain,(
% 2.92/2.01 ( ! [X3 : state,X0 : state,X4 : state,X5 : a] : (((pa @ (sK164 @ X0) @ (sK165 @ X0)) = $true) | ((sP3 @ X0) = $true) | ((pa @ X5 @ X4) != $true) | (X0 != X4) | ((qa @ X5 @ X3) = $true) | ((exec @ X4 @ body @ X3) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1602])).
% 2.92/2.01 thf(f2784,plain,(
% 2.92/2.01 ~spl173_2 | ~spl173_3 | ~spl173_8),
% 2.92/2.01 inference(avatar_contradiction_clause,[status(thm)],[f2783])).
% 2.92/2.01 thf(f2783,plain,(
% 2.92/2.01 $false | (~spl173_2 | ~spl173_3 | ~spl173_8)),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2781,f2678])).
% 2.92/2.01 thf(f2678,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((pa @ X0 @ x) != $true)) ) | ~spl173_8),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2677])).
% 2.92/2.01 thf(f2781,plain,(
% 2.92/2.01 ((pa @ sK143 @ x) = $true) | (~spl173_2 | ~spl173_3)),
% 2.92/2.01 inference(superposition,[status(thm)],[f2650,f2645])).
% 2.92/2.01 thf(f2645,plain,(
% 2.92/2.01 (x = sK142) | ~spl173_2),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2643])).
% 2.92/2.01 thf(f2643,definition,(
% 2.92/2.01 spl173_2 <=> (x = sK142)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_2])],[avatar_definition])).
% 2.92/2.01 thf(f2650,plain,(
% 2.92/2.01 ((pa @ sK143 @ sK142) = $true) | ~spl173_3),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2648])).
% 2.92/2.01 thf(f2648,definition,(
% 2.92/2.01 spl173_3 <=> ((pa @ sK143 @ sK142) = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_3])],[avatar_definition])).
% 2.92/2.01 thf(f2782,plain,(
% 2.92/2.01 ~spl173_10 | ~spl173_2 | spl173_4),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f2780,f2653,f2643,f2684])).
% 2.92/2.01 thf(f2653,definition,(
% 2.92/2.01 spl173_4 <=> ((termi @ body @ sK142) = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_4])],[avatar_definition])).
% 2.92/2.01 thf(f2780,plain,(
% 2.92/2.01 ((termi @ body @ x) != $true) | (~spl173_2 | spl173_4)),
% 2.92/2.01 inference(superposition,[status(thm)],[f2655,f2645])).
% 2.92/2.01 thf(f2655,plain,(
% 2.92/2.01 ((termi @ body @ sK142) != $true) | spl173_4),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2653])).
% 2.92/2.01 thf(f2774,plain,(
% 2.92/2.01 ~spl173_16 | ~spl173_1 | spl173_14),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f2748,f2743,f2639,f2771])).
% 2.92/2.01 thf(f2743,definition,(
% 2.92/2.01 spl173_14 <=> ((termi @ body @ (sK165 @ sK140)) = $true)),
% 2.92/2.01 introduced(definition,[new_symbols(naming,[spl173_14])],[avatar_definition])).
% 2.92/2.01 thf(f2748,plain,(
% 2.92/2.01 (sP2 != $true) | ((termi @ body @ (sK165 @ x)) != $true) | spl173_14),
% 2.92/2.01 inference(superposition,[status(thm)],[f2745,f2004])).
% 2.92/2.01 thf(f2745,plain,(
% 2.92/2.01 ((termi @ body @ (sK165 @ sK140)) != $true) | spl173_14),
% 2.92/2.01 inference(avatar_component_clause,[status(thm)],[f2743])).
% 2.92/2.01 thf(f2746,plain,(
% 2.92/2.01 spl173_13 | spl173_12 | ~spl173_14 | ~spl173_1),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f2737,f2639,f2743,f2719,f2739])).
% 2.92/2.01 thf(f2737,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((sP3 @ sK140) = $true) | ((qa @ X0 @ sK139) = $true) | ((pa @ X0 @ sK140) != $true) | ((termi @ body @ (sK165 @ sK140)) != $true)) ) | ~spl173_1),
% 2.92/2.01 inference(subsumption_resolution,[status(thm)],[f2730,f2641])).
% 2.92/2.01 thf(f2730,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((sP3 @ sK140) = $true) | ((termi @ body @ (sK165 @ sK140)) != $true) | ((qa @ X0 @ sK139) = $true) | ((pa @ X0 @ sK140) != $true) | (sP2 != $true)) )),
% 2.92/2.01 inference(trivial_inequality_removal,[status(thm)],[f2727])).
% 2.92/2.01 thf(f2727,plain,(
% 2.92/2.01 ( ! [X0 : a] : (((sP3 @ sK140) = $true) | ((termi @ body @ (sK165 @ sK140)) != $true) | (sP2 != $true) | ((qa @ X0 @ sK139) = $true) | ($true != $true) | ((pa @ X0 @ sK140) != $true)) )),
% 2.92/2.01 inference(superposition,[status(thm)],[f2635,f2564])).
% 2.92/2.01 thf(f2635,plain,(
% 2.92/2.01 ( ! [X3 : state,X4 : state,X5 : a] : (((?? @ nat @ (^[Y0 : nat]: (execn @ X4 @ body @ Y0 @ X3))) != $true) | ($true != (termi @ body @ (sK165 @ X4))) | ((qa @ X5 @ X3) = $true) | ((pa @ X5 @ X4) != $true) | ((sP3 @ X4) = $true)) )),
% 2.92/2.01 inference(beta_eta_normalization,[status(thm)],[f2426])).
% 2.92/2.01 thf(f2426,plain,(
% 2.92/2.01 ( ! [X3 : state,X4 : state,X5 : a] : (((qa @ X5 @ X3) = $true) | ($true != (termi @ body @ (sK165 @ X4))) | ((sP3 @ X4) = $true) | (((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ X4 @ body @ X3) != $true) | ((pa @ X5 @ X4) != $true)) )),
% 2.92/2.01 inference(equality_resolution,[status(thm)],[f2391])).
% 2.92/2.01 thf(f2391,plain,(
% 2.92/2.01 ( ! [X3 : state,X0 : state,X4 : state,X5 : a] : (((termi @ body @ (sK165 @ X0)) != $true) | ((sP3 @ X0) = $true) | ((pa @ X5 @ X4) != $true) | (X0 != X4) | ((qa @ X5 @ X3) = $true) | (((^[Y0 : state]: ((^[Y1 : com]: ((^[Y2 : state]: (?? @ nat @ (^[Y3 : nat]: (execn @ Y0 @ Y1 @ Y3 @ Y2)))))))) @ X4 @ body @ X3) != $true)) )),
% 2.92/2.01 inference(definition_unfolding,[status(thm)],[f2083,f1657])).
% 2.92/2.01 thf(f2083,plain,(
% 2.92/2.01 ( ! [X3 : state,X0 : state,X4 : state,X5 : a] : (((termi @ body @ (sK165 @ X0)) != $true) | ((sP3 @ X0) = $true) | ((pa @ X5 @ X4) != $true) | (X0 != X4) | ((qa @ X5 @ X3) = $true) | ((exec @ X4 @ body @ X3) != $true)) )),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1602])).
% 2.92/2.01 thf(f2656,plain,(
% 2.92/2.01 spl173_1 | ~spl173_4),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f2009,f2653,f2639])).
% 2.92/2.01 thf(f2009,plain,(
% 2.92/2.01 ((termi @ body @ sK142) != $true) | (sP2 = $true)),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1573])).
% 2.92/2.01 thf(f1573,plain,(
% 2.92/2.01 (((pa @ sK143 @ sK142) = $true) & ((termi @ body @ sK142) != $true) & (x = sK142)) | (sP2 = $true)),
% 2.92/2.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK142,sK143])],[f1571,f1572])).
% 2.92/2.01 thf(f1572,plain,(
% 2.92/2.01 ? [X0 : state,X1 : a] : (((pa @ X1 @ X0) = $true) & ((termi @ body @ X0) != $true) & (x = X0)) => (((pa @ sK143 @ sK142) = $true) & ((termi @ body @ sK142) != $true) & (x = sK142))),
% 2.92/2.01 introduced(definition,[],[choice_axiom])).
% 2.92/2.01 thf(f1571,plain,(
% 2.92/2.01 ? [X0 : state,X1 : a] : (((pa @ X1 @ X0) = $true) & ((termi @ body @ X0) != $true) & (x = X0)) | (sP2 = $true)),
% 2.92/2.01 inference(rectify,[status(thm)],[f1399])).
% 2.92/2.01 thf(f1399,plain,(
% 2.92/2.01 ? [X3 : state,X4 : a] : (((pa @ X4 @ X3) = $true) & ((termi @ body @ X3) != $true) & (x = X3)) | (sP2 = $true)),
% 2.92/2.01 inference(definition_folding,[status(thm)],[f1240,f1398])).
% 2.92/2.01 thf(f1240,plain,(
% 2.92/2.01 ? [X3 : state,X4 : a] : (((pa @ X4 @ X3) = $true) & ((termi @ body @ X3) != $true) & (x = X3)) | ? [X0 : state,X1 : state] : (((exec @ X1 @ body @ X0) = $true) & ? [X2 : a] : (((qa @ X2 @ X0) != $true) & ((pa @ X2 @ X1) = $true) & (x = X1)))),
% 2.92/2.01 inference(ennf_transformation,[status(thm)],[f1109])).
% 2.92/2.01 thf(f1109,plain,(
% 2.92/2.01 ~(! [X0 : state,X1 : state] : (! [X2 : a] : (((qa @ X2 @ X0) = $true) | ((pa @ X2 @ X1) != $true) | (x != X1)) | ((exec @ X1 @ body @ X0) != $true)) & ! [X3 : state,X4 : a] : ((x != X3) | ((termi @ body @ X3) = $true) | ((pa @ X4 @ X3) != $true)))),
% 2.92/2.01 inference(flattening,[status(thm)],[f609])).
% 2.92/2.01 thf(f609,plain,(
% 2.92/2.01 ~(! [X0 : state,X1 : state] : (~((exec @ X1 @ body @ X0) = $true) | ! [X2 : a] : ((x != X1) | ((qa @ X2 @ X0) = $true) | ~((pa @ X2 @ X1) = $true))) & ! [X3 : state,X4 : a] : (~((pa @ X4 @ X3) = $true) | (x != X3) | ((termi @ body @ X3) = $true)))),
% 2.92/2.01 inference(fool_elimination,[status(thm)],[f608])).
% 2.92/2.01 thf(f608,plain,(
% 2.92/2.01 ~(! [X0 : state,X1 : state] : (~(exec @ X1 @ body @ X0) | ! [X2 : a] : ((x != X1) | (qa @ X2 @ X0) | ~(pa @ X2 @ X1))) & ! [X3 : state,X4 : a] : (~(pa @ X4 @ X3) | (x != X3) | (termi @ body @ X3)))),
% 2.92/2.01 inference(rectify,[status(thm)],[f358])).
% 2.92/2.01 thf(f358,negated_conjecture,(
% 2.92/2.01 ~(! [X8 : state,X6 : state] : (~(exec @ X6 @ body @ X8) | ! [X5 : a] : ((x != X6) | (qa @ X5 @ X8) | ~(pa @ X5 @ X6))) & ! [X6 : state,X5 : a] : (~(pa @ X5 @ X6) | (x != X6) | (termi @ body @ X6)))),
% 2.92/2.01 inference(negated_conjecture,[status(cth)],[f357])).
% 2.92/2.01 thf(f357,conjecture,(
% 2.92/2.01 ! [X8 : state,X6 : state] : (~(exec @ X6 @ body @ X8) | ! [X5 : a] : ((x != X6) | (qa @ X5 @ X8) | ~(pa @ X5 @ X6))) & ! [X6 : state,X5 : a] : (~(pa @ X5 @ X6) | (x != X6) | (termi @ body @ X6))),
% 2.92/2.01 file('/export/starexec/sandbox2/tmp/tmp.H5mA5wl1hp/DTF2THF_16650.p',conj_2)).
% 2.92/2.01 thf(f2651,plain,(
% 2.92/2.01 spl173_1 | spl173_3),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f2010,f2648,f2639])).
% 2.92/2.01 thf(f2010,plain,(
% 2.92/2.01 (sP2 = $true) | ((pa @ sK143 @ sK142) = $true)),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1573])).
% 2.92/2.01 thf(f2646,plain,(
% 2.92/2.01 spl173_1 | spl173_2),
% 2.92/2.01 inference(avatar_split_clause,[status(thm)],[f2008,f2643,f2639])).
% 2.92/2.01 thf(f2008,plain,(
% 2.92/2.01 (sP2 = $true) | (x = sK142)),
% 2.92/2.01 inference(cnf_transformation,[status(thm)],[f1573])).
% 2.92/2.01 % SZS output end Proof for DTF2THF_16650
% 2.92/2.01 % (16902)------------------------------
% 2.92/2.01 % (16902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/2.01 % (16902)Termination reason: Refutation
% 2.92/2.01
% 2.92/2.01 % (16902)Memory used [KB]: 8827
% 2.92/2.01 % (16902)Time elapsed: 0.169 s
% 2.92/2.01 % (16902)Instructions burned: 464 (million)
% 2.92/2.01 % (16902)------------------------------
% 2.92/2.01 % (16902)------------------------------
% 2.92/2.01 % (16858)Success in time 0.502 s
%------------------------------------------------------------------------------