%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWW474^1 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n029.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 09:48:11 AM UTC 2026
% Result : Theorem 3.50s 1.94s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 318 ( 81 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 330 ( 47 ~; 36 |; 0 &; 226 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 96 ( 93 usr; 6 con; 0-4 aty)
% Number of variables : 58 ( 8 ^; 50 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
com: $tType ).
thf(type_def_7,type,
pname: $tType ).
thf(type_def_8,type,
option_com: $tType ).
thf(type_def_9,type,
hoare_1262092251_state: $tType ).
thf(func_def_0,type,
com: $tType ).
thf(func_def_1,type,
pname: $tType ).
thf(func_def_2,type,
hoare_1262092251_state: $tType ).
thf(func_def_3,type,
option_com: $tType ).
thf(func_def_4,type,
wt: com > $o ).
thf(func_def_6,type,
body: pname > option_com ).
thf(func_def_7,type,
body_1: pname > com ).
thf(func_def_8,type,
finite1648353812_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > $o ).
thf(func_def_9,type,
finite734360985_o_o_o: ( ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ) > $o ).
thf(func_def_10,type,
finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_11,type,
finite1303896758te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
thf(func_def_12,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(func_def_13,type,
finite1423311111tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(func_def_14,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(func_def_15,type,
finite1178804552_state: ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_16,type,
hoare_Mirabelle_MGT: com > hoare_1262092251_state ).
thf(func_def_17,type,
hoare_930741239_state: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_19,type,
dom_pname_o_com: ( ( pname > $o ) > option_com ) > ( pname > $o ) > $o ).
thf(func_def_20,type,
dom_Ho1489634536_o_com: ( ( hoare_1262092251_state > $o ) > option_com ) > ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_21,type,
dom_pname_com: ( pname > option_com ) > pname > $o ).
thf(func_def_22,type,
some_com: com > option_com ).
thf(func_def_23,type,
the_com: option_com > com ).
thf(func_def_24,type,
bot_bot_pname_o_o_o: ( ( pname > $o ) > $o ) > $o ).
thf(func_def_25,type,
bot_bo388435036_o_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(func_def_26,type,
bot_bot_pname_o_o: ( pname > $o ) > $o ).
thf(func_def_27,type,
bot_bo1962689075te_o_o: ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_28,type,
bot_bot_pname_o: pname > $o ).
thf(func_def_29,type,
bot_bo113204042tate_o: hoare_1262092251_state > $o ).
thf(func_def_30,type,
ord_le1828183645_o_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_31,type,
ord_le1891858320_o_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
thf(func_def_32,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_33,type,
ord_le2012720639te_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(func_def_34,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_35,type,
ord_le870406270tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_36,type,
collect_pname_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_37,type,
collec101077467_o_o_o: ( ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
thf(func_def_38,type,
collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_39,type,
collec341954548te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(func_def_40,type,
collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_41,type,
collec313158217tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_42,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(func_def_43,type,
collec1121927558_state: ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
thf(func_def_44,type,
image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_45,type,
image_1036078444_state: ( ( ( pname > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( pname > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
thf(func_def_46,type,
image_893364936_pname: ( ( ( hoare_1262092251_state > $o ) > $o ) > pname ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_47,type,
image_165349207_state: ( ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
thf(func_def_48,type,
image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_49,type,
image_1476171975_state: ( ( pname > $o ) > hoare_1262092251_state ) > ( ( pname > $o ) > $o ) > hoare_1262092251_state > $o ).
thf(func_def_50,type,
image_1820530197_pname: ( ( hoare_1262092251_state > $o ) > pname ) > ( ( hoare_1262092251_state > $o ) > $o ) > pname > $o ).
thf(func_def_51,type,
image_234589002_state: ( ( hoare_1262092251_state > $o ) > hoare_1262092251_state ) > ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state > $o ).
thf(func_def_52,type,
image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_53,type,
image_827868872te_o_o: ( pname > ( hoare_1262092251_state > $o ) > $o ) > ( pname > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(func_def_54,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_55,type,
image_518521461tate_o: ( pname > hoare_1262092251_state > $o ) > ( pname > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_56,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(func_def_57,type,
image_669833818_state: ( pname > hoare_1262092251_state ) > ( pname > $o ) > hoare_1262092251_state > $o ).
thf(func_def_58,type,
image_333245000me_o_o: ( hoare_1262092251_state > ( pname > $o ) > $o ) > ( hoare_1262092251_state > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_59,type,
image_1731108951te_o_o: ( hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(func_def_60,type,
image_1320925383name_o: ( hoare_1262092251_state > pname > $o ) > ( hoare_1262092251_state > $o ) > ( pname > $o ) > $o ).
thf(func_def_61,type,
image_1403668518tate_o: ( hoare_1262092251_state > hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_62,type,
image_202231862_pname: ( hoare_1262092251_state > pname ) > ( hoare_1262092251_state > $o ) > pname > $o ).
thf(func_def_63,type,
insert_pname_o_o: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_64,type,
insert1691644879te_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(func_def_65,type,
insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_66,type,
insert1042460334tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_67,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(func_def_68,type,
insert81609953_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
thf(func_def_69,type,
fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_70,type,
fequal1529404211tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_71,type,
fequal_pname: pname > pname > $o ).
thf(func_def_72,type,
fequal1925511196_state: hoare_1262092251_state > hoare_1262092251_state > $o ).
thf(func_def_73,type,
member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_74,type,
member907417095tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(func_def_75,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(func_def_76,type,
member5164104_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ).
thf(func_def_77,type,
fa: hoare_1262092251_state > $o ).
thf(func_def_78,type,
pn: pname ).
thf(func_def_79,type,
y: com ).
thf(func_def_90,type,
sK0: ( pname > $o ) > pname ).
thf(func_def_91,type,
sK1: ( pname > $o ) > ( pname > hoare_1262092251_state ) > ( hoare_1262092251_state > $o ) > pname > $o ).
thf(func_def_92,type,
sK2: pname > com ).
thf(func_def_93,type,
sK3: ( hoare_1262092251_state > $o ) > pname ).
thf(func_def_94,type,
sK4: ( hoare_1262092251_state > $o ) > hoare_1262092251_state ).
thf(func_def_95,type,
sK5: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_96,type,
sK6: ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
thf(func_def_97,type,
sK7: ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > hoare_1262092251_state ).
thf(func_def_98,type,
sK8: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > hoare_1262092251_state ).
thf(func_def_99,type,
sK9: hoare_1262092251_state > ( pname > hoare_1262092251_state ) > ( pname > $o ) > pname ).
thf(func_def_100,type,
sK10: ( hoare_1262092251_state > $o ) > hoare_1262092251_state ).
thf(func_def_101,type,
sK11: ( pname > $o ) > ( pname > hoare_1262092251_state ) > ( hoare_1262092251_state > $o ) > pname > $o ).
thf(func_def_102,type,
sK12: ( pname > hoare_1262092251_state ) > hoare_1262092251_state > ( pname > $o ) > pname ).
thf(func_def_103,type,
sK13: ( pname > $o ) > pname ).
thf(func_def_104,type,
sK14: ( ( pname > $o ) > $o ) > ( pname > $o ) > pname ).
thf(func_def_105,type,
sK15: ( ( pname > $o ) > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_107,type,
ph17:
!>[X0: $tType] : X0 ).
thf(f1642,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1638,f1378]) ).
thf(f1378,plain,
( $true
= ( wt @ y ) ),
inference(equality_resolution,[status(thm)],[f1372]) ).
thf(f1372,plain,
! [X0: com] :
( ( ( some_com @ y )
!= ( some_com @ X0 ) )
| ( $true
= ( wt @ X0 ) ) ),
inference(superposition,[status(thm)],[f1368,f1209]) ).
thf(f1209,plain,
( ( body @ pn )
= ( some_com @ y ) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
thf(f314,axiom,
( ( body @ pn )
= ( some_com @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',conj_5) ).
thf(f1368,plain,
! [X0: com,X1: pname] :
( ( ( some_com @ X0 )
!= ( body @ X1 ) )
| ( $true
= ( wt @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1314]) ).
thf(f1314,plain,
! [X0: com,X1: pname] :
( ( ( some_com @ X0 )
!= ( body @ X1 ) )
| ( $true != $true )
| ( $true
= ( wt @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f1170,f1254]) ).
thf(f1254,plain,
wT_bodies = $true,
inference(cnf_transformation,[status(thm)],[f482]) ).
thf(f482,plain,
wT_bodies = $true,
inference(fool_elimination,[status(thm)],[f481]) ).
thf(f481,plain,
wT_bodies,
inference(rectify,[status(thm)],[f310]) ).
thf(f310,axiom,
wT_bodies,
file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',conj_1) ).
thf(f1170,plain,
! [X0: com,X1: pname] :
( ( ( some_com @ X0 )
!= ( body @ X1 ) )
| ( $true
= ( wt @ X0 ) )
| ( wT_bodies != $true ) ),
inference(cnf_transformation,[status(thm)],[f1005]) ).
thf(f1005,plain,
! [X0: com,X1: pname] :
( ( ( some_com @ X0 )
!= ( body @ X1 ) )
| ( $true
= ( wt @ X0 ) )
| ( wT_bodies != $true ) ),
inference(flattening,[status(thm)],[f1004]) ).
thf(f1004,plain,
! [X0: com,X1: pname] :
( ( $true
= ( wt @ X0 ) )
| ( ( some_com @ X0 )
!= ( body @ X1 ) )
| ( wT_bodies != $true ) ),
inference(ennf_transformation,[status(thm)],[f792]) ).
thf(f792,plain,
! [X0: com,X1: pname] :
( ( wT_bodies = $true )
=> ( ( ( some_com @ X0 )
= ( body @ X1 ) )
=> ( $true
= ( wt @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f791]) ).
thf(f791,plain,
! [X0: com,X1: pname] :
( wT_bodies
=> ( ( ( some_com @ X0 )
= ( body @ X1 ) )
=> ( wt @ X0 ) ) ),
inference(rectify,[status(thm)],[f289]) ).
thf(f289,axiom,
! [X192: com,X18: pname] :
( wT_bodies
=> ( ( ( body @ X18 )
= ( some_com @ X192 ) )
=> ( wt @ X192 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',fact_288_WT__bodiesD) ).
thf(f1638,plain,
( $true
!= ( wt @ y ) ),
inference(trivial_inequality_removal,[status(thm)],[f1625]) ).
thf(f1625,plain,
( ( $true
!= ( wt @ y ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1560,f1365]) ).
thf(f1365,plain,
! [X0: com] :
( ( $true
= ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo113204042tate_o ) ) )
| ( $true
!= ( wt @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1364]) ).
thf(f1364,plain,
! [X0: com] :
( ( $true != $true )
| ( $true
!= ( wt @ X0 ) )
| ( $true
= ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo113204042tate_o ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f1315]) ).
thf(f1315,plain,
! [X0: com] :
( ( $true != $true )
| ( $true
= ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo113204042tate_o ) ) )
| ( $true
!= ( wt @ X0 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f1244,f1254,f1243]) ).
thf(f1243,plain,
hoare_1821564147gleton = $true,
inference(cnf_transformation,[status(thm)],[f416]) ).
thf(f416,plain,
hoare_1821564147gleton = $true,
inference(fool_elimination,[status(thm)],[f415]) ).
thf(f415,plain,
hoare_1821564147gleton,
inference(rectify,[status(thm)],[f309]) ).
thf(f309,axiom,
hoare_1821564147gleton,
file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',conj_0) ).
thf(f1244,plain,
! [X0: com] :
( ( wT_bodies != $true )
| ( $true
!= ( wt @ X0 ) )
| ( $true
= ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo113204042tate_o ) ) )
| ( hoare_1821564147gleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f942]) ).
thf(f942,plain,
! [X0: com] :
( ( wT_bodies != $true )
| ( $true
!= ( wt @ X0 ) )
| ( $true
= ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo113204042tate_o ) ) )
| ( hoare_1821564147gleton != $true ) ),
inference(flattening,[status(thm)],[f941]) ).
thf(f941,plain,
! [X0: com] :
( ( $true
= ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo113204042tate_o ) ) )
| ( $true
!= ( wt @ X0 ) )
| ( wT_bodies != $true )
| ( hoare_1821564147gleton != $true ) ),
inference(ennf_transformation,[status(thm)],[f820]) ).
thf(f820,plain,
! [X0: com] :
( ( hoare_1821564147gleton = $true )
=> ( ( wT_bodies = $true )
=> ( ( $true
= ( wt @ X0 ) )
=> ( $true
= ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo113204042tate_o ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f819]) ).
thf(f819,plain,
! [X0: com] :
( hoare_1821564147gleton
=> ( wT_bodies
=> ( ( wt @ X0 )
=> ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo113204042tate_o ) ) ) ) ),
inference(rectify,[status(thm)],[f104]) ).
thf(f104,axiom,
! [X42: com] :
( hoare_1821564147gleton
=> ( wT_bodies
=> ( ( wt @ X42 )
=> ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ X42 ) @ bot_bo113204042tate_o ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',fact_103_MGF) ).
thf(f1560,plain,
( $true
!= ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1549]) ).
thf(f1549,plain,
( ( $true != $true )
| ( $true
!= ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ) ) ),
inference(superposition,[status(thm)],[f1424,f1302]) ).
thf(f1302,plain,
! [X0: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ X0 @ bot_bo113204042tate_o )
= $true ),
inference(cnf_transformation,[status(thm)],[f418]) ).
thf(f418,plain,
! [X0: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ X0 @ bot_bo113204042tate_o )
= $true ),
inference(fool_elimination,[status(thm)],[f417]) ).
thf(f417,plain,
! [X0: hoare_1262092251_state > $o] : ( hoare_930741239_state @ X0 @ bot_bo113204042tate_o ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: hoare_1262092251_state > $o] : ( hoare_930741239_state @ X0 @ bot_bo113204042tate_o ),
file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',fact_0_empty) ).
thf(f1424,plain,
! [X0: hoare_1262092251_state > $o] :
( ( $true
!= ( hoare_930741239_state
@ ( image_669833818_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ X0 ) )
| ( $true
!= ( hoare_930741239_state @ X0 @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1418]) ).
thf(f1418,plain,
! [X0: hoare_1262092251_state > $o] :
( ( $true
!= ( hoare_930741239_state @ X0 @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ) )
| ( $true
!= ( hoare_930741239_state
@ ( image_669833818_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1275,f1279]) ).
thf(f1279,plain,
! [X2: hoare_1262092251_state > $o,X0: hoare_1262092251_state > $o,X1: hoare_1262092251_state > $o] :
( ( $true
= ( hoare_930741239_state @ X0 @ X2 ) )
| ( ( hoare_930741239_state @ X1 @ X2 )
!= $true )
| ( ( hoare_930741239_state @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f939]) ).
thf(f939,plain,
! [X0: hoare_1262092251_state > $o,X1: hoare_1262092251_state > $o,X2: hoare_1262092251_state > $o] :
( ( $true
= ( hoare_930741239_state @ X0 @ X2 ) )
| ( ( hoare_930741239_state @ X0 @ X1 )
!= $true )
| ( ( hoare_930741239_state @ X1 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f938]) ).
thf(f938,plain,
! [X0: hoare_1262092251_state > $o,X1: hoare_1262092251_state > $o,X2: hoare_1262092251_state > $o] :
( ( $true
= ( hoare_930741239_state @ X0 @ X2 ) )
| ( ( hoare_930741239_state @ X0 @ X1 )
!= $true )
| ( ( hoare_930741239_state @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f536]) ).
thf(f536,plain,
! [X0: hoare_1262092251_state > $o,X1: hoare_1262092251_state > $o,X2: hoare_1262092251_state > $o] :
( ( ( hoare_930741239_state @ X1 @ X2 )
= $true )
=> ( ( ( hoare_930741239_state @ X0 @ X1 )
= $true )
=> ( $true
= ( hoare_930741239_state @ X0 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f535]) ).
thf(f535,plain,
! [X0: hoare_1262092251_state > $o,X1: hoare_1262092251_state > $o,X2: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ X1 @ X2 )
=> ( ( hoare_930741239_state @ X0 @ X1 )
=> ( hoare_930741239_state @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X9: hoare_1262092251_state > $o,X10: hoare_1262092251_state > $o,X11: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ X10 @ X11 )
=> ( ( hoare_930741239_state @ X9 @ X10 )
=> ( hoare_930741239_state @ X9 @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',fact_4_cut) ).
thf(f1275,plain,
( ( hoare_930741239_state
@ ( image_669833818_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f894]) ).
thf(f894,plain,
( ( hoare_930741239_state
@ ( image_669833818_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) )
!= $true ),
inference(flattening,[status(thm)],[f640]) ).
thf(f640,plain,
( ( hoare_930741239_state
@ ( image_669833818_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f639]) ).
thf(f639,plain,
~ ( hoare_930741239_state
@ ( image_669833818_state
@ ^ [X0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ),
inference(rectify,[status(thm)],[f317]) ).
thf(f317,negated_conjecture,
~ ( hoare_930741239_state
@ ( image_669833818_state
@ ^ [X212: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X212 ) )
@ ( dom_pname_com @ body ) )
@ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ),
inference(negated_conjecture,[status(cth)],[f316]) ).
thf(f316,conjecture,
( hoare_930741239_state
@ ( image_669833818_state
@ ^ [X212: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X212 ) )
@ ( dom_pname_com @ body ) )
@ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ),
file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',conj_7) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW474^1 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.32 % Computer : n029.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue Feb 24 13:40:59 EST 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.47 ---- Original DTF file ---
% 0.18/0.47 thf(spec,logic,$$dhol).
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 % File : SWW474^1 : TPTP v9.2.1. Released v5.3.0.
% 0.18/0.47 % Domain : Software Verification
% 0.18/0.47 % Problem : Hoare's Logic with Procedures line 440, 100 axioms selected
% 0.18/0.47 % Version : Especial.
% 0.18/0.47 % English :
% 0.18/0.47
% 0.18/0.47 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.18/0.47 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.18/0.47 % Source : [Bla11]
% 0.18/0.47 % Names : hoare_100_thf_l440 [Bla11]
% 0.18/0.47
% 0.18/0.47 % Status : Theorem
% 0.18/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.56 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% 0.18/0.47 % Syntax : Number of formulae : 396 ( 58 unt; 80 typ; 0 def)
% 0.18/0.47 % Number of atoms : 1340 ( 265 equ; 42 cnn)
% 0.18/0.47 % Maximal formula atoms : 10 ( 4 avg)
% 0.18/0.47 % Number of connectives : 2174 ( 94 ~; 36 |; 58 &;1615 @)
% 0.18/0.47 % ( 53 <=>; 318 =>; 0 <=; 0 <~>)
% 0.18/0.47 % Maximal formula depth : 17 ( 7 avg)
% 0.18/0.47 % Number of types : 5 ( 4 usr)
% 0.18/0.47 % Number of type conns : 1124 (1124 >; 0 *; 0 +; 0 <<)
% 0.18/0.47 % Number of symbols : 82 ( 76 usr; 9 con; 0-3 aty)
% 0.18/0.47 % Number of variables : 776 ( 89 ^; 680 !; 7 ?; 776 :)
% 0.18/0.47 % SPC : TH0_THM_EQU_NAR
% 0.18/0.47
% 0.18/0.47 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.18/0.47 % 2011-08-09 19:26:26
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 %----Should-be-implicit typings (4)
% 0.18/0.47 thf(ty_ty_tc__Com__Ocom,type,
% 0.18/0.47 com: $tType ).
% 0.18/0.47
% 0.18/0.47 thf(ty_ty_tc__Com__Opname,type,
% 0.18/0.47 pname: $tType ).
% 0.18/0.47
% 0.18/0.47 thf(ty_ty_tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 0.18/0.47 hoare_1262092251_state: $tType ).
% 0.18/0.47
% 0.18/0.47 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.18/0.47 option_com: $tType ).
% 0.18/0.47
% 0.18/0.47 %----Explicit typings (76)
% 0.18/0.47 thf(sy_c_Com_OWT,type,
% 0.18/0.47 wt: com > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Com_OWT__bodies,type,
% 0.18/0.47 wT_bodies: $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Com_Obody,type,
% 0.18/0.47 body: pname > option_com ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Com_Ocom_OBODY,type,
% 0.18/0.47 body_1: pname > com ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo,type,
% 0.18/0.47 finite1648353812_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbq,type,
% 0.18/0.47 finite734360985_o_o_o: ( ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.18/0.47 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Ot,type,
% 0.18/0.47 finite1303896758te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.18/0.47 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_,type,
% 0.18/0.47 finite1423311111tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.18/0.47 finite_finite_pname: ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__C,type,
% 0.18/0.47 finite1178804552_state: ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_OMGT,type,
% 0.18/0.47 hoare_Mirabelle_MGT: com > hoare_1262092251_state ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ohoare__derivs_000tc__Com__Ostate,type,
% 0.18/0.47 hoare_930741239_state: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ostate__not__singleton,type,
% 0.18/0.47 hoare_1821564147gleton: $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Map_Odom_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Ocom,type,
% 0.18/0.47 dom_pname_o_com: ( ( pname > $o ) > option_com ) > ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Map_Odom_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__O,type,
% 0.18/0.47 dom_Ho1489634536_o_com: ( ( hoare_1262092251_state > $o ) > option_com ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,
% 0.18/0.47 dom_pname_com: ( pname > option_com ) > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Option_Ooption_OSome_000tc__Com__Ocom,type,
% 0.18/0.47 some_com: com > option_com ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 0.18/0.47 the_com: option_com > com ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo,type,
% 0.18/0.47 bot_bot_pname_o_o_o: ( ( pname > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Hoare____Mirabelle____g,type,
% 0.18/0.47 bot_bo388435036_o_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.18/0.47 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsb,type,
% 0.18/0.47 bot_bo1962689075te_o_o: ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.18/0.47 bot_bot_pname_o: pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__O,type,
% 0.18/0.47 bot_bo113204042tate_o: hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J,type,
% 0.18/0.47 ord_le1828183645_o_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Hoare____Mirabelle,type,
% 0.18/0.47 ord_le1891858320_o_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 0.18/0.47 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____gh,type,
% 0.18/0.47 ord_le2012720639te_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.18/0.47 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____ghhkfsbq,type,
% 0.18/0.47 ord_le870406270tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.18/0.47 collect_pname_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otr,type,
% 0.18/0.47 collec101077467_o_o_o: ( ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.18/0.47 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_I,type,
% 0.18/0.47 collec341954548te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.18/0.47 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Co,type,
% 0.18/0.47 collec313158217tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.18/0.47 collect_pname: ( pname > $o ) > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 0.18/0.47 collec1121927558_state: ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 0.18/0.47 image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Hoare____Mir,type,
% 0.18/0.47 image_1036078444_state: ( ( ( pname > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( pname > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc,type,
% 0.18/0.47 image_893364936_pname: ( ( ( hoare_1262092251_state > $o ) > $o ) > pname ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc_001,type,
% 0.18/0.47 image_165349207_state: ( ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 0.18/0.47 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____ghh,type,
% 0.18/0.47 image_1476171975_state: ( ( pname > $o ) > hoare_1262092251_state ) > ( ( pname > $o ) > $o ) > hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com_,type,
% 0.18/0.47 image_1820530197_pname: ( ( hoare_1262092251_state > $o ) > pname ) > ( ( hoare_1262092251_state > $o ) > $o ) > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__002,type,
% 0.18/0.47 image_234589002_state: ( ( hoare_1262092251_state > $o ) > hoare_1262092251_state ) > ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.18/0.47 image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Hoare____Mirabelle____ghhk,type,
% 0.18/0.47 image_827868872te_o_o: ( pname > ( hoare_1262092251_state > $o ) > $o ) > ( pname > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.18/0.47 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq,type,
% 0.18/0.47 image_518521461tate_o: ( pname > hoare_1262092251_state > $o ) > ( pname > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.18/0.47 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otri,type,
% 0.18/0.47 image_669833818_state: ( pname > hoare_1262092251_state ) > ( pname > $o ) > hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat,type,
% 0.18/0.47 image_333245000me_o_o: ( hoare_1262092251_state > ( pname > $o ) > $o ) > ( hoare_1262092251_state > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_003,type,
% 0.18/0.47 image_1731108951te_o_o: ( hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_004,type,
% 0.18/0.47 image_1320925383name_o: ( hoare_1262092251_state > pname > $o ) > ( hoare_1262092251_state > $o ) > ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_005,type,
% 0.18/0.47 image_1403668518tate_o: ( hoare_1262092251_state > hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_006,type,
% 0.18/0.47 image_202231862_pname: ( hoare_1262092251_state > pname ) > ( hoare_1262092251_state > $o ) > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.18/0.47 insert_pname_o_o: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It,type,
% 0.18/0.47 insert1691644879te_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.18/0.47 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com,type,
% 0.18/0.47 insert1042460334tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.18/0.47 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Osta,type,
% 0.18/0.47 insert81609953_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.18/0.47 fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 0.18/0.47 fequal1529404211tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_fequal_000tc__Com__Opname,type,
% 0.18/0.47 fequal_pname: pname > pname > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 0.18/0.47 fequal1925511196_state: hoare_1262092251_state > hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.18/0.47 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 0.18/0.47 member907417095tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_member_000tc__Com__Opname,type,
% 0.18/0.47 member_pname: pname > ( pname > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_c_member_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 0.18/0.47 member5164104_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_v_Fa,type,
% 0.18/0.47 fa: hoare_1262092251_state > $o ).
% 0.18/0.47
% 0.18/0.47 thf(sy_v_pn,type,
% 0.18/0.47 pn: pname ).
% 0.18/0.47
% 0.18/0.47 thf(sy_v_y,type,
% 0.18/0.47 y: com ).
% 0.18/0.47
% 0.18/0.47 %----Relevant facts (300)
% 0.18/0.47 thf(fact_0_empty,axiom,
% 0.18/0.47 ! [G: hoare_1262092251_state > $o] : ( hoare_930741239_state @ G @ bot_bo113204042tate_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_1_asm,axiom,
% 0.18/0.47 ! [Ts_6: hoare_1262092251_state > $o,G_8: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ Ts_6 @ G_8 )
% 0.18/0.47 => ( hoare_930741239_state @ G_8 @ Ts_6 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_2_weaken,axiom,
% 0.18/0.47 ! [Ts_5: hoare_1262092251_state > $o,G_7: hoare_1262092251_state > $o,Ts_4: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( hoare_930741239_state @ G_7 @ Ts_4 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ Ts_5 @ Ts_4 )
% 0.18/0.47 => ( hoare_930741239_state @ G_7 @ Ts_5 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_3_thin,axiom,
% 0.18/0.47 ! [G_6: hoare_1262092251_state > $o,G_5: hoare_1262092251_state > $o,Ts_3: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( hoare_930741239_state @ G_5 @ Ts_3 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ G_5 @ G_6 )
% 0.18/0.47 => ( hoare_930741239_state @ G_6 @ Ts_3 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_4_cut,axiom,
% 0.18/0.47 ! [G_4: hoare_1262092251_state > $o,G_3: hoare_1262092251_state > $o,Ts_2: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( hoare_930741239_state @ G_3 @ Ts_2 )
% 0.18/0.47 => ( ( hoare_930741239_state @ G_4 @ G_3 )
% 0.18/0.47 => ( hoare_930741239_state @ G_4 @ Ts_2 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_5_hoare__derivs_Oinsert,axiom,
% 0.18/0.47 ! [Ts_1: hoare_1262092251_state > $o,G_2: hoare_1262092251_state > $o,T_1: hoare_1262092251_state] :
% 0.18/0.47 ( ( hoare_930741239_state @ G_2 @ ( insert81609953_state @ T_1 @ bot_bo113204042tate_o ) )
% 0.18/0.47 => ( ( hoare_930741239_state @ G_2 @ Ts_1 )
% 0.18/0.47 => ( hoare_930741239_state @ G_2 @ ( insert81609953_state @ T_1 @ Ts_1 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_6_derivs__insertD,axiom,
% 0.18/0.47 ! [G_1: hoare_1262092251_state > $o,T: hoare_1262092251_state,Ts: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( hoare_930741239_state @ G_1 @ ( insert81609953_state @ T @ Ts ) )
% 0.18/0.47 => ( ( hoare_930741239_state @ G_1 @ ( insert81609953_state @ T @ bot_bo113204042tate_o ) )
% 0.18/0.47 & ( hoare_930741239_state @ G_1 @ Ts ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_7_MGT__BodyN,axiom,
% 0.18/0.47 ! [Pn_1: pname,G: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( hoare_930741239_state @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ G ) @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn_1 ) ) ) @ bot_bo113204042tate_o ) )
% 0.18/0.47 => ( hoare_930741239_state @ G @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ bot_bo113204042tate_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_8_finite__Collect__subsets,axiom,
% 0.18/0.47 ! [A_77: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ A_77 )
% 0.18/0.47 => ( finite297249702name_o
% 0.18/0.47 @ ( collect_pname_o
% 0.18/0.47 @ ^ [B_41: pname > $o] : ( ord_less_eq_pname_o @ B_41 @ A_77 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_9_finite__Collect__subsets,axiom,
% 0.18/0.47 ! [A_77: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ A_77 )
% 0.18/0.47 => ( finite1423311111tate_o
% 0.18/0.47 @ ( collec313158217tate_o
% 0.18/0.47 @ ^ [B_41: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ B_41 @ A_77 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_10_finite__Collect__subsets,axiom,
% 0.18/0.47 ! [A_77: ( ( pname > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1066544169me_o_o @ A_77 )
% 0.18/0.47 => ( finite1648353812_o_o_o
% 0.18/0.47 @ ( collect_pname_o_o_o
% 0.18/0.47 @ ^ [B_41: ( ( pname > $o ) > $o ) > $o] : ( ord_le1828183645_o_o_o @ B_41 @ A_77 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_11_finite__Collect__subsets,axiom,
% 0.18/0.47 ! [A_77: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1303896758te_o_o @ A_77 )
% 0.18/0.47 => ( finite734360985_o_o_o
% 0.18/0.47 @ ( collec101077467_o_o_o
% 0.18/0.47 @ ^ [B_41: ( ( hoare_1262092251_state > $o ) > $o ) > $o] : ( ord_le1891858320_o_o_o @ B_41 @ A_77 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_12_finite__Collect__subsets,axiom,
% 0.18/0.47 ! [A_77: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ A_77 )
% 0.18/0.47 => ( finite1303896758te_o_o
% 0.18/0.47 @ ( collec341954548te_o_o
% 0.18/0.47 @ ^ [B_41: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ B_41 @ A_77 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_13_finite__Collect__subsets,axiom,
% 0.18/0.47 ! [A_77: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ A_77 )
% 0.18/0.47 => ( finite1066544169me_o_o
% 0.18/0.47 @ ( collect_pname_o_o
% 0.18/0.47 @ ^ [B_41: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_41 @ A_77 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_14_finite__imageI,axiom,
% 0.18/0.47 ! [H: pname > hoare_1262092251_state,F_17: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ F_17 )
% 0.18/0.47 => ( finite1178804552_state @ ( image_669833818_state @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_15_finite__imageI,axiom,
% 0.18/0.47 ! [H: ( ( pname > $o ) > $o ) > pname,F_17: ( ( pname > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1066544169me_o_o @ F_17 )
% 0.18/0.47 => ( finite_finite_pname @ ( image_471733107_pname @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_16_finite__imageI,axiom,
% 0.18/0.47 ! [H: ( ( hoare_1262092251_state > $o ) > $o ) > pname,F_17: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1303896758te_o_o @ F_17 )
% 0.18/0.47 => ( finite_finite_pname @ ( image_893364936_pname @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_17_finite__imageI,axiom,
% 0.18/0.47 ! [H: ( hoare_1262092251_state > $o ) > pname,F_17: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ F_17 )
% 0.18/0.47 => ( finite_finite_pname @ ( image_1820530197_pname @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_18_finite__imageI,axiom,
% 0.18/0.47 ! [H: ( pname > $o ) > pname,F_17: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ F_17 )
% 0.18/0.47 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_19_finite__imageI,axiom,
% 0.18/0.47 ! [H: ( ( pname > $o ) > $o ) > hoare_1262092251_state,F_17: ( ( pname > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1066544169me_o_o @ F_17 )
% 0.18/0.47 => ( finite1178804552_state @ ( image_1036078444_state @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_20_finite__imageI,axiom,
% 0.18/0.47 ! [H: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,F_17: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1303896758te_o_o @ F_17 )
% 0.18/0.47 => ( finite1178804552_state @ ( image_165349207_state @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_21_finite__imageI,axiom,
% 0.18/0.47 ! [H: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,F_17: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ F_17 )
% 0.18/0.47 => ( finite1178804552_state @ ( image_234589002_state @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_22_finite__imageI,axiom,
% 0.18/0.47 ! [H: ( pname > $o ) > hoare_1262092251_state,F_17: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ F_17 )
% 0.18/0.47 => ( finite1178804552_state @ ( image_1476171975_state @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_23_finite__imageI,axiom,
% 0.18/0.47 ! [H: pname > ( pname > $o ) > $o,F_17: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ F_17 )
% 0.18/0.47 => ( finite1066544169me_o_o @ ( image_504089495me_o_o @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_24_finite__imageI,axiom,
% 0.18/0.47 ! [H: pname > ( hoare_1262092251_state > $o ) > $o,F_17: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ F_17 )
% 0.18/0.47 => ( finite1303896758te_o_o @ ( image_827868872te_o_o @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_25_finite__imageI,axiom,
% 0.18/0.47 ! [H: pname > hoare_1262092251_state > $o,F_17: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ F_17 )
% 0.18/0.47 => ( finite1423311111tate_o @ ( image_518521461tate_o @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_26_finite__imageI,axiom,
% 0.18/0.47 ! [H: pname > pname > $o,F_17: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ F_17 )
% 0.18/0.47 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_27_finite__imageI,axiom,
% 0.18/0.47 ! [H: hoare_1262092251_state > ( pname > $o ) > $o,F_17: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ F_17 )
% 0.18/0.47 => ( finite1066544169me_o_o @ ( image_333245000me_o_o @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_28_finite__imageI,axiom,
% 0.18/0.47 ! [H: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o,F_17: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ F_17 )
% 0.18/0.47 => ( finite1303896758te_o_o @ ( image_1731108951te_o_o @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_29_finite__imageI,axiom,
% 0.18/0.47 ! [H: hoare_1262092251_state > hoare_1262092251_state > $o,F_17: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ F_17 )
% 0.18/0.47 => ( finite1423311111tate_o @ ( image_1403668518tate_o @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_30_finite__imageI,axiom,
% 0.18/0.47 ! [H: hoare_1262092251_state > pname > $o,F_17: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ F_17 )
% 0.18/0.47 => ( finite297249702name_o @ ( image_1320925383name_o @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_31_finite__imageI,axiom,
% 0.18/0.47 ! [H: hoare_1262092251_state > pname,F_17: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ F_17 )
% 0.18/0.47 => ( finite_finite_pname @ ( image_202231862_pname @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_32_finite__imageI,axiom,
% 0.18/0.47 ! [H: pname > pname,F_17: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ F_17 )
% 0.18/0.47 => ( finite_finite_pname @ ( image_pname_pname @ H @ F_17 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_33_empty__subsetI,axiom,
% 0.18/0.47 ! [A_76: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ bot_bo113204042tate_o @ A_76 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_34_empty__subsetI,axiom,
% 0.18/0.47 ! [A_76: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ bot_bot_pname_o_o @ A_76 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_35_empty__subsetI,axiom,
% 0.18/0.47 ! [A_76: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ bot_bo1962689075te_o_o @ A_76 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_36_empty__subsetI,axiom,
% 0.18/0.47 ! [A_76: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_76 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_37_finite_OinsertI,axiom,
% 0.18/0.47 ! [A_75: hoare_1262092251_state,A_74: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ A_74 )
% 0.18/0.47 => ( finite1178804552_state @ ( insert81609953_state @ A_75 @ A_74 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_38_finite_OinsertI,axiom,
% 0.18/0.47 ! [A_75: pname,A_74: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ A_74 )
% 0.18/0.47 => ( finite_finite_pname @ ( insert_pname @ A_75 @ A_74 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_39_finite_OinsertI,axiom,
% 0.18/0.47 ! [A_75: ( pname > $o ) > $o,A_74: ( ( pname > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1066544169me_o_o @ A_74 )
% 0.18/0.47 => ( finite1066544169me_o_o @ ( insert_pname_o_o @ A_75 @ A_74 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_40_finite_OinsertI,axiom,
% 0.18/0.47 ! [A_75: ( hoare_1262092251_state > $o ) > $o,A_74: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1303896758te_o_o @ A_74 )
% 0.18/0.47 => ( finite1303896758te_o_o @ ( insert1691644879te_o_o @ A_75 @ A_74 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_41_finite_OinsertI,axiom,
% 0.18/0.47 ! [A_75: hoare_1262092251_state > $o,A_74: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ A_74 )
% 0.18/0.47 => ( finite1423311111tate_o @ ( insert1042460334tate_o @ A_75 @ A_74 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_42_finite_OinsertI,axiom,
% 0.18/0.47 ! [A_75: pname > $o,A_74: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ A_74 )
% 0.18/0.47 => ( finite297249702name_o @ ( insert_pname_o @ A_75 @ A_74 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_43_finite_OemptyI,axiom,
% 0.18/0.47 finite_finite_pname @ bot_bot_pname_o ).
% 0.18/0.47
% 0.18/0.47 thf(fact_44_finite_OemptyI,axiom,
% 0.18/0.47 finite1178804552_state @ bot_bo113204042tate_o ).
% 0.18/0.47
% 0.18/0.47 thf(fact_45_finite_OemptyI,axiom,
% 0.18/0.47 finite1066544169me_o_o @ bot_bot_pname_o_o_o ).
% 0.18/0.47
% 0.18/0.47 thf(fact_46_finite_OemptyI,axiom,
% 0.18/0.47 finite1303896758te_o_o @ bot_bo388435036_o_o_o ).
% 0.18/0.47
% 0.18/0.47 thf(fact_47_finite_OemptyI,axiom,
% 0.18/0.47 finite1423311111tate_o @ bot_bo1962689075te_o_o ).
% 0.18/0.47
% 0.18/0.47 thf(fact_48_finite_OemptyI,axiom,
% 0.18/0.47 finite297249702name_o @ bot_bot_pname_o_o ).
% 0.18/0.47
% 0.18/0.47 thf(fact_49_finite__Collect__conjI,axiom,
% 0.18/0.47 ! [Q_1: pname > $o,P_9: pname > $o] :
% 0.18/0.47 ( ( ( finite_finite_pname @ ( collect_pname @ P_9 ) )
% 0.18/0.47 | ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
% 0.18/0.47 => ( finite_finite_pname
% 0.18/0.47 @ ( collect_pname
% 0.18/0.47 @ ^ [X_1: pname] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_50_finite__Collect__conjI,axiom,
% 0.18/0.47 ! [Q_1: hoare_1262092251_state > $o,P_9: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ( finite1178804552_state @ ( collec1121927558_state @ P_9 ) )
% 0.18/0.47 | ( finite1178804552_state @ ( collec1121927558_state @ Q_1 ) ) )
% 0.18/0.47 => ( finite1178804552_state
% 0.18/0.47 @ ( collec1121927558_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_51_finite__Collect__conjI,axiom,
% 0.18/0.47 ! [Q_1: ( ( pname > $o ) > $o ) > $o,P_9: ( ( pname > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( ( finite1066544169me_o_o @ ( collect_pname_o_o @ P_9 ) )
% 0.18/0.47 | ( finite1066544169me_o_o @ ( collect_pname_o_o @ Q_1 ) ) )
% 0.18/0.47 => ( finite1066544169me_o_o
% 0.18/0.47 @ ( collect_pname_o_o
% 0.18/0.47 @ ^ [X_1: ( pname > $o ) > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_52_finite__Collect__conjI,axiom,
% 0.18/0.47 ! [Q_1: ( ( hoare_1262092251_state > $o ) > $o ) > $o,P_9: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( ( finite1303896758te_o_o @ ( collec341954548te_o_o @ P_9 ) )
% 0.18/0.47 | ( finite1303896758te_o_o @ ( collec341954548te_o_o @ Q_1 ) ) )
% 0.18/0.47 => ( finite1303896758te_o_o
% 0.18/0.47 @ ( collec341954548te_o_o
% 0.18/0.47 @ ^ [X_1: ( hoare_1262092251_state > $o ) > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_53_finite__Collect__conjI,axiom,
% 0.18/0.47 ! [Q_1: ( hoare_1262092251_state > $o ) > $o,P_9: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( ( finite1423311111tate_o @ ( collec313158217tate_o @ P_9 ) )
% 0.18/0.47 | ( finite1423311111tate_o @ ( collec313158217tate_o @ Q_1 ) ) )
% 0.18/0.47 => ( finite1423311111tate_o
% 0.18/0.47 @ ( collec313158217tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_54_finite__Collect__conjI,axiom,
% 0.18/0.47 ! [Q_1: ( pname > $o ) > $o,P_9: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_9 ) )
% 0.18/0.47 | ( finite297249702name_o @ ( collect_pname_o @ Q_1 ) ) )
% 0.18/0.47 => ( finite297249702name_o
% 0.18/0.47 @ ( collect_pname_o
% 0.18/0.47 @ ^ [X_1: pname > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_55_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: hoare_1262092251_state,A_73: pname > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bot_pname_o )
% 0.18/0.47 => ( ( image_669833818_state
% 0.18/0.47 @ ^ [X_1: pname] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bo113204042tate_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bot_pname_o )
% 0.18/0.47 => ( ( image_669833818_state
% 0.18/0.47 @ ^ [X_1: pname] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert81609953_state @ C_8 @ bot_bo113204042tate_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_56_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: pname,A_73: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bo113204042tate_o )
% 0.18/0.47 => ( ( image_202231862_pname
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bot_pname_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bo113204042tate_o )
% 0.18/0.47 => ( ( image_202231862_pname
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_57_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: pname > $o,A_73: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bo113204042tate_o )
% 0.18/0.47 => ( ( image_1320925383name_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bot_pname_o_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bo113204042tate_o )
% 0.18/0.47 => ( ( image_1320925383name_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert_pname_o @ C_8 @ bot_bot_pname_o_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_58_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: hoare_1262092251_state > $o,A_73: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bo113204042tate_o )
% 0.18/0.47 => ( ( image_1403668518tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bo1962689075te_o_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bo113204042tate_o )
% 0.18/0.47 => ( ( image_1403668518tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert1042460334tate_o @ C_8 @ bot_bo1962689075te_o_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_59_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: pname > $o,A_73: pname > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bot_pname_o )
% 0.18/0.47 => ( ( image_pname_pname_o
% 0.18/0.47 @ ^ [X_1: pname] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bot_pname_o_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bot_pname_o )
% 0.18/0.47 => ( ( image_pname_pname_o
% 0.18/0.47 @ ^ [X_1: pname] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert_pname_o @ C_8 @ bot_bot_pname_o_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_60_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: hoare_1262092251_state > $o,A_73: pname > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bot_pname_o )
% 0.18/0.47 => ( ( image_518521461tate_o
% 0.18/0.47 @ ^ [X_1: pname] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bo1962689075te_o_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bot_pname_o )
% 0.18/0.47 => ( ( image_518521461tate_o
% 0.18/0.47 @ ^ [X_1: pname] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert1042460334tate_o @ C_8 @ bot_bo1962689075te_o_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_61_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: pname,A_73: pname > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bot_pname_o )
% 0.18/0.47 => ( ( image_pname_pname
% 0.18/0.47 @ ^ [X_1: pname] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bot_pname_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bot_pname_o )
% 0.18/0.47 => ( ( image_pname_pname
% 0.18/0.47 @ ^ [X_1: pname] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_62_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: hoare_1262092251_state,A_73: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bot_pname_o_o )
% 0.18/0.47 => ( ( image_1476171975_state
% 0.18/0.47 @ ^ [X_1: pname > $o] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bo113204042tate_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bot_pname_o_o )
% 0.18/0.47 => ( ( image_1476171975_state
% 0.18/0.47 @ ^ [X_1: pname > $o] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert81609953_state @ C_8 @ bot_bo113204042tate_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_63_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: hoare_1262092251_state,A_73: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bo1962689075te_o_o )
% 0.18/0.47 => ( ( image_234589002_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bo113204042tate_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bo1962689075te_o_o )
% 0.18/0.47 => ( ( image_234589002_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert81609953_state @ C_8 @ bot_bo113204042tate_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_64_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: pname,A_73: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bot_pname_o_o )
% 0.18/0.47 => ( ( image_pname_o_pname
% 0.18/0.47 @ ^ [X_1: pname > $o] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bot_pname_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bot_pname_o_o )
% 0.18/0.47 => ( ( image_pname_o_pname
% 0.18/0.47 @ ^ [X_1: pname > $o] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_65_image__constant__conv,axiom,
% 0.18/0.47 ! [C_8: pname,A_73: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( ( A_73 = bot_bo1962689075te_o_o )
% 0.18/0.47 => ( ( image_1820530197_pname
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = bot_bot_pname_o ) )
% 0.18/0.47 & ( ( A_73 != bot_bo1962689075te_o_o )
% 0.18/0.47 => ( ( image_1820530197_pname
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 0.18/0.47 @ A_73 )
% 0.18/0.47 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_66_image__constant,axiom,
% 0.18/0.47 ! [C_7: hoare_1262092251_state,X_18: pname,A_72: pname > $o] :
% 0.18/0.47 ( ( member_pname @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_669833818_state
% 0.18/0.47 @ ^ [X_1: pname] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert81609953_state @ C_7 @ bot_bo113204042tate_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_67_image__constant,axiom,
% 0.18/0.47 ! [C_7: pname,X_18: hoare_1262092251_state,A_72: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( member5164104_state @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_202231862_pname
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_68_image__constant,axiom,
% 0.18/0.47 ! [C_7: pname > $o,X_18: hoare_1262092251_state,A_72: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( member5164104_state @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_1320925383name_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert_pname_o @ C_7 @ bot_bot_pname_o_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_69_image__constant,axiom,
% 0.18/0.47 ! [C_7: hoare_1262092251_state > $o,X_18: hoare_1262092251_state,A_72: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( member5164104_state @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_1403668518tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert1042460334tate_o @ C_7 @ bot_bo1962689075te_o_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_70_image__constant,axiom,
% 0.18/0.47 ! [C_7: pname > $o,X_18: pname,A_72: pname > $o] :
% 0.18/0.47 ( ( member_pname @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_pname_pname_o
% 0.18/0.47 @ ^ [X_1: pname] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert_pname_o @ C_7 @ bot_bot_pname_o_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_71_image__constant,axiom,
% 0.18/0.47 ! [C_7: hoare_1262092251_state > $o,X_18: pname,A_72: pname > $o] :
% 0.18/0.47 ( ( member_pname @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_518521461tate_o
% 0.18/0.47 @ ^ [X_1: pname] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert1042460334tate_o @ C_7 @ bot_bo1962689075te_o_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_72_image__constant,axiom,
% 0.18/0.47 ! [C_7: pname,X_18: pname,A_72: pname > $o] :
% 0.18/0.47 ( ( member_pname @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_pname_pname
% 0.18/0.47 @ ^ [X_1: pname] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_73_image__constant,axiom,
% 0.18/0.47 ! [C_7: hoare_1262092251_state,X_18: pname > $o,A_72: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( member_pname_o @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_1476171975_state
% 0.18/0.47 @ ^ [X_1: pname > $o] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert81609953_state @ C_7 @ bot_bo113204042tate_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_74_image__constant,axiom,
% 0.18/0.47 ! [C_7: hoare_1262092251_state,X_18: hoare_1262092251_state > $o,A_72: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( member907417095tate_o @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_234589002_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert81609953_state @ C_7 @ bot_bo113204042tate_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_75_image__constant,axiom,
% 0.18/0.47 ! [C_7: pname,X_18: pname > $o,A_72: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( member_pname_o @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_pname_o_pname
% 0.18/0.47 @ ^ [X_1: pname > $o] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_76_image__constant,axiom,
% 0.18/0.47 ! [C_7: pname,X_18: hoare_1262092251_state > $o,A_72: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( member907417095tate_o @ X_18 @ A_72 )
% 0.18/0.47 => ( ( image_1820530197_pname
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : C_7
% 0.18/0.47 @ A_72 )
% 0.18/0.47 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_77_insert__dom,axiom,
% 0.18/0.47 ! [F_16: pname > option_com,X_17: pname,Y_4: com] :
% 0.18/0.47 ( ( ( F_16 @ X_17 )
% 0.18/0.47 = ( some_com @ Y_4 ) )
% 0.18/0.47 => ( ( insert_pname @ X_17 @ ( dom_pname_com @ F_16 ) )
% 0.18/0.47 = ( dom_pname_com @ F_16 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_78_insert__dom,axiom,
% 0.18/0.47 ! [F_16: ( pname > $o ) > option_com,X_17: pname > $o,Y_4: com] :
% 0.18/0.47 ( ( ( F_16 @ X_17 )
% 0.18/0.47 = ( some_com @ Y_4 ) )
% 0.18/0.47 => ( ( insert_pname_o @ X_17 @ ( dom_pname_o_com @ F_16 ) )
% 0.18/0.47 = ( dom_pname_o_com @ F_16 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_79_insert__dom,axiom,
% 0.18/0.47 ! [F_16: ( hoare_1262092251_state > $o ) > option_com,X_17: hoare_1262092251_state > $o,Y_4: com] :
% 0.18/0.47 ( ( ( F_16 @ X_17 )
% 0.18/0.47 = ( some_com @ Y_4 ) )
% 0.18/0.47 => ( ( insert1042460334tate_o @ X_17 @ ( dom_Ho1489634536_o_com @ F_16 ) )
% 0.18/0.47 = ( dom_Ho1489634536_o_com @ F_16 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_80_finite__surj,axiom,
% 0.18/0.47 ! [B_40: hoare_1262092251_state > $o,F_15: pname > hoare_1262092251_state,A_71: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ A_71 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ B_40 @ ( image_669833818_state @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_81_finite__surj,axiom,
% 0.18/0.47 ! [B_40: pname > $o,F_15: ( ( pname > $o ) > $o ) > pname,A_71: ( ( pname > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1066544169me_o_o @ A_71 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_471733107_pname @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_82_finite__surj,axiom,
% 0.18/0.47 ! [B_40: pname > $o,F_15: ( ( hoare_1262092251_state > $o ) > $o ) > pname,A_71: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1303896758te_o_o @ A_71 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_893364936_pname @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_83_finite__surj,axiom,
% 0.18/0.47 ! [B_40: pname > $o,F_15: ( hoare_1262092251_state > $o ) > pname,A_71: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ A_71 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_1820530197_pname @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_84_finite__surj,axiom,
% 0.18/0.47 ! [B_40: pname > $o,F_15: ( pname > $o ) > pname,A_71: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ A_71 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_pname_o_pname @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_85_finite__surj,axiom,
% 0.18/0.47 ! [B_40: hoare_1262092251_state > $o,F_15: ( ( pname > $o ) > $o ) > hoare_1262092251_state,A_71: ( ( pname > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1066544169me_o_o @ A_71 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ B_40 @ ( image_1036078444_state @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_86_finite__surj,axiom,
% 0.18/0.47 ! [B_40: hoare_1262092251_state > $o,F_15: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,A_71: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( finite1303896758te_o_o @ A_71 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ B_40 @ ( image_165349207_state @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_87_finite__surj,axiom,
% 0.18/0.47 ! [B_40: hoare_1262092251_state > $o,F_15: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,A_71: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ A_71 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ B_40 @ ( image_234589002_state @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_88_finite__surj,axiom,
% 0.18/0.47 ! [B_40: hoare_1262092251_state > $o,F_15: ( pname > $o ) > hoare_1262092251_state,A_71: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ A_71 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ B_40 @ ( image_1476171975_state @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_89_finite__surj,axiom,
% 0.18/0.47 ! [B_40: ( ( pname > $o ) > $o ) > $o,F_15: pname > ( pname > $o ) > $o,A_71: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ A_71 )
% 0.18/0.47 => ( ( ord_le1828183645_o_o_o @ B_40 @ ( image_504089495me_o_o @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1066544169me_o_o @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_90_finite__surj,axiom,
% 0.18/0.47 ! [B_40: ( ( hoare_1262092251_state > $o ) > $o ) > $o,F_15: pname > ( hoare_1262092251_state > $o ) > $o,A_71: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ A_71 )
% 0.18/0.47 => ( ( ord_le1891858320_o_o_o @ B_40 @ ( image_827868872te_o_o @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1303896758te_o_o @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_91_finite__surj,axiom,
% 0.18/0.47 ! [B_40: pname > $o,F_15: pname > pname,A_71: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ A_71 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_pname_pname @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_92_finite__surj,axiom,
% 0.18/0.47 ! [B_40: ( hoare_1262092251_state > $o ) > $o,F_15: pname > hoare_1262092251_state > $o,A_71: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ A_71 )
% 0.18/0.47 => ( ( ord_le2012720639te_o_o @ B_40 @ ( image_518521461tate_o @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1423311111tate_o @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_93_finite__surj,axiom,
% 0.18/0.47 ! [B_40: ( pname > $o ) > $o,F_15: pname > pname > $o,A_71: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ A_71 )
% 0.18/0.47 => ( ( ord_le1205211808me_o_o @ B_40 @ ( image_pname_pname_o @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite297249702name_o @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_94_finite__surj,axiom,
% 0.18/0.47 ! [B_40: ( ( pname > $o ) > $o ) > $o,F_15: hoare_1262092251_state > ( pname > $o ) > $o,A_71: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ A_71 )
% 0.18/0.47 => ( ( ord_le1828183645_o_o_o @ B_40 @ ( image_333245000me_o_o @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1066544169me_o_o @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_95_finite__surj,axiom,
% 0.18/0.47 ! [B_40: ( ( hoare_1262092251_state > $o ) > $o ) > $o,F_15: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o,A_71: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ A_71 )
% 0.18/0.47 => ( ( ord_le1891858320_o_o_o @ B_40 @ ( image_1731108951te_o_o @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1303896758te_o_o @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_96_finite__surj,axiom,
% 0.18/0.47 ! [B_40: pname > $o,F_15: hoare_1262092251_state > pname,A_71: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ A_71 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_202231862_pname @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_97_finite__surj,axiom,
% 0.18/0.47 ! [B_40: ( hoare_1262092251_state > $o ) > $o,F_15: hoare_1262092251_state > hoare_1262092251_state > $o,A_71: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ A_71 )
% 0.18/0.47 => ( ( ord_le2012720639te_o_o @ B_40 @ ( image_1403668518tate_o @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite1423311111tate_o @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_98_finite__surj,axiom,
% 0.18/0.47 ! [B_40: ( pname > $o ) > $o,F_15: hoare_1262092251_state > pname > $o,A_71: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ A_71 )
% 0.18/0.47 => ( ( ord_le1205211808me_o_o @ B_40 @ ( image_1320925383name_o @ F_15 @ A_71 ) )
% 0.18/0.47 => ( finite297249702name_o @ B_40 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_99_subset__singletonD,axiom,
% 0.18/0.47 ! [A_70: hoare_1262092251_state > $o,X_16: hoare_1262092251_state] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ A_70 @ ( insert81609953_state @ X_16 @ bot_bo113204042tate_o ) )
% 0.18/0.47 => ( ( A_70 = bot_bo113204042tate_o )
% 0.18/0.47 | ( A_70
% 0.18/0.47 = ( insert81609953_state @ X_16 @ bot_bo113204042tate_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_100_subset__singletonD,axiom,
% 0.18/0.47 ! [A_70: ( pname > $o ) > $o,X_16: pname > $o] :
% 0.18/0.47 ( ( ord_le1205211808me_o_o @ A_70 @ ( insert_pname_o @ X_16 @ bot_bot_pname_o_o ) )
% 0.18/0.47 => ( ( A_70 = bot_bot_pname_o_o )
% 0.18/0.47 | ( A_70
% 0.18/0.47 = ( insert_pname_o @ X_16 @ bot_bot_pname_o_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_101_subset__singletonD,axiom,
% 0.18/0.47 ! [A_70: ( hoare_1262092251_state > $o ) > $o,X_16: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le2012720639te_o_o @ A_70 @ ( insert1042460334tate_o @ X_16 @ bot_bo1962689075te_o_o ) )
% 0.18/0.47 => ( ( A_70 = bot_bo1962689075te_o_o )
% 0.18/0.47 | ( A_70
% 0.18/0.47 = ( insert1042460334tate_o @ X_16 @ bot_bo1962689075te_o_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_102_subset__singletonD,axiom,
% 0.18/0.47 ! [A_70: pname > $o,X_16: pname] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_70 @ ( insert_pname @ X_16 @ bot_bot_pname_o ) )
% 0.18/0.47 => ( ( A_70 = bot_bot_pname_o )
% 0.18/0.47 | ( A_70
% 0.18/0.47 = ( insert_pname @ X_16 @ bot_bot_pname_o ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_103_MGF,axiom,
% 0.18/0.47 ! [C_1: com] :
% 0.18/0.47 ( hoare_1821564147gleton
% 0.18/0.47 => ( wT_bodies
% 0.18/0.47 => ( ( wt @ C_1 )
% 0.18/0.47 => ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ C_1 ) @ bot_bo113204042tate_o ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_104_emptyE,axiom,
% 0.18/0.47 ! [A_69: hoare_1262092251_state] :
% 0.18/0.47 ~ ( member5164104_state @ A_69 @ bot_bo113204042tate_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_105_emptyE,axiom,
% 0.18/0.47 ! [A_69: pname > $o] :
% 0.18/0.47 ~ ( member_pname_o @ A_69 @ bot_bot_pname_o_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_106_emptyE,axiom,
% 0.18/0.47 ! [A_69: hoare_1262092251_state > $o] :
% 0.18/0.47 ~ ( member907417095tate_o @ A_69 @ bot_bo1962689075te_o_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_107_emptyE,axiom,
% 0.18/0.47 ! [A_69: pname] :
% 0.18/0.47 ~ ( member_pname @ A_69 @ bot_bot_pname_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_108_insertCI,axiom,
% 0.18/0.47 ! [B_39: hoare_1262092251_state,A_68: hoare_1262092251_state,B_38: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ~ ( member5164104_state @ A_68 @ B_38 )
% 0.18/0.47 => ( A_68 = B_39 ) )
% 0.18/0.47 => ( member5164104_state @ A_68 @ ( insert81609953_state @ B_39 @ B_38 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_109_insertCI,axiom,
% 0.18/0.47 ! [B_39: pname > $o,A_68: pname > $o,B_38: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( ~ ( member_pname_o @ A_68 @ B_38 )
% 0.18/0.47 => ( A_68 = B_39 ) )
% 0.18/0.47 => ( member_pname_o @ A_68 @ ( insert_pname_o @ B_39 @ B_38 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_110_insertCI,axiom,
% 0.18/0.47 ! [B_39: hoare_1262092251_state > $o,A_68: hoare_1262092251_state > $o,B_38: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( ~ ( member907417095tate_o @ A_68 @ B_38 )
% 0.18/0.47 => ( A_68 = B_39 ) )
% 0.18/0.47 => ( member907417095tate_o @ A_68 @ ( insert1042460334tate_o @ B_39 @ B_38 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_111_insertCI,axiom,
% 0.18/0.47 ! [B_39: pname,A_68: pname,B_38: pname > $o] :
% 0.18/0.47 ( ( ~ ( member_pname @ A_68 @ B_38 )
% 0.18/0.47 => ( A_68 = B_39 ) )
% 0.18/0.47 => ( member_pname @ A_68 @ ( insert_pname @ B_39 @ B_38 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_112_insertE,axiom,
% 0.18/0.47 ! [A_67: hoare_1262092251_state,B_37: hoare_1262092251_state,A_66: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( member5164104_state @ A_67 @ ( insert81609953_state @ B_37 @ A_66 ) )
% 0.18/0.47 => ( ( A_67 != B_37 )
% 0.18/0.47 => ( member5164104_state @ A_67 @ A_66 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_113_insertE,axiom,
% 0.18/0.47 ! [A_67: pname > $o,B_37: pname > $o,A_66: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( member_pname_o @ A_67 @ ( insert_pname_o @ B_37 @ A_66 ) )
% 0.18/0.47 => ( ( A_67 != B_37 )
% 0.18/0.47 => ( member_pname_o @ A_67 @ A_66 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_114_insertE,axiom,
% 0.18/0.47 ! [A_67: hoare_1262092251_state > $o,B_37: hoare_1262092251_state > $o,A_66: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( member907417095tate_o @ A_67 @ ( insert1042460334tate_o @ B_37 @ A_66 ) )
% 0.18/0.47 => ( ( A_67 != B_37 )
% 0.18/0.47 => ( member907417095tate_o @ A_67 @ A_66 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_115_insertE,axiom,
% 0.18/0.47 ! [A_67: pname,B_37: pname,A_66: pname > $o] :
% 0.18/0.47 ( ( member_pname @ A_67 @ ( insert_pname @ B_37 @ A_66 ) )
% 0.18/0.47 => ( ( A_67 != B_37 )
% 0.18/0.47 => ( member_pname @ A_67 @ A_66 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_116_equalityI,axiom,
% 0.18/0.47 ! [A_65: hoare_1262092251_state > $o,B_36: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ A_65 @ B_36 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ B_36 @ A_65 )
% 0.18/0.47 => ( A_65 = B_36 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_117_equalityI,axiom,
% 0.18/0.47 ! [A_65: ( pname > $o ) > $o,B_36: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( ord_le1205211808me_o_o @ A_65 @ B_36 )
% 0.18/0.47 => ( ( ord_le1205211808me_o_o @ B_36 @ A_65 )
% 0.18/0.47 => ( A_65 = B_36 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_118_equalityI,axiom,
% 0.18/0.47 ! [A_65: ( hoare_1262092251_state > $o ) > $o,B_36: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( ord_le2012720639te_o_o @ A_65 @ B_36 )
% 0.18/0.47 => ( ( ord_le2012720639te_o_o @ B_36 @ A_65 )
% 0.18/0.47 => ( A_65 = B_36 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_119_equalityI,axiom,
% 0.18/0.47 ! [A_65: pname > $o,B_36: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_65 @ B_36 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ B_36 @ A_65 )
% 0.18/0.47 => ( A_65 = B_36 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_120_subsetD,axiom,
% 0.18/0.47 ! [C_6: hoare_1262092251_state,A_64: hoare_1262092251_state > $o,B_35: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ A_64 @ B_35 )
% 0.18/0.47 => ( ( member5164104_state @ C_6 @ A_64 )
% 0.18/0.47 => ( member5164104_state @ C_6 @ B_35 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_121_subsetD,axiom,
% 0.18/0.47 ! [C_6: pname > $o,A_64: ( pname > $o ) > $o,B_35: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( ord_le1205211808me_o_o @ A_64 @ B_35 )
% 0.18/0.47 => ( ( member_pname_o @ C_6 @ A_64 )
% 0.18/0.47 => ( member_pname_o @ C_6 @ B_35 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_122_subsetD,axiom,
% 0.18/0.47 ! [C_6: hoare_1262092251_state > $o,A_64: ( hoare_1262092251_state > $o ) > $o,B_35: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( ord_le2012720639te_o_o @ A_64 @ B_35 )
% 0.18/0.47 => ( ( member907417095tate_o @ C_6 @ A_64 )
% 0.18/0.47 => ( member907417095tate_o @ C_6 @ B_35 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_123_subsetD,axiom,
% 0.18/0.47 ! [C_6: pname,A_64: pname > $o,B_35: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_64 @ B_35 )
% 0.18/0.47 => ( ( member_pname @ C_6 @ A_64 )
% 0.18/0.47 => ( member_pname @ C_6 @ B_35 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_124_image__eqI,axiom,
% 0.18/0.47 ! [A_63: hoare_1262092251_state > $o,B_34: pname > $o,F_14: hoare_1262092251_state > pname > $o,X_15: hoare_1262092251_state] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member5164104_state @ X_15 @ A_63 )
% 0.18/0.47 => ( member_pname_o @ B_34 @ ( image_1320925383name_o @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_125_image__eqI,axiom,
% 0.18/0.47 ! [A_63: hoare_1262092251_state > $o,B_34: hoare_1262092251_state > $o,F_14: hoare_1262092251_state > hoare_1262092251_state > $o,X_15: hoare_1262092251_state] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member5164104_state @ X_15 @ A_63 )
% 0.18/0.47 => ( member907417095tate_o @ B_34 @ ( image_1403668518tate_o @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_126_image__eqI,axiom,
% 0.18/0.47 ! [A_63: pname > $o,B_34: pname > $o,F_14: pname > pname > $o,X_15: pname] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member_pname @ X_15 @ A_63 )
% 0.18/0.47 => ( member_pname_o @ B_34 @ ( image_pname_pname_o @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_127_image__eqI,axiom,
% 0.18/0.47 ! [A_63: pname > $o,B_34: hoare_1262092251_state > $o,F_14: pname > hoare_1262092251_state > $o,X_15: pname] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member_pname @ X_15 @ A_63 )
% 0.18/0.47 => ( member907417095tate_o @ B_34 @ ( image_518521461tate_o @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_128_image__eqI,axiom,
% 0.18/0.47 ! [A_63: ( pname > $o ) > $o,B_34: hoare_1262092251_state,F_14: ( pname > $o ) > hoare_1262092251_state,X_15: pname > $o] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member_pname_o @ X_15 @ A_63 )
% 0.18/0.47 => ( member5164104_state @ B_34 @ ( image_1476171975_state @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_129_image__eqI,axiom,
% 0.18/0.47 ! [A_63: ( hoare_1262092251_state > $o ) > $o,B_34: hoare_1262092251_state,F_14: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,X_15: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member907417095tate_o @ X_15 @ A_63 )
% 0.18/0.47 => ( member5164104_state @ B_34 @ ( image_234589002_state @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_130_image__eqI,axiom,
% 0.18/0.47 ! [A_63: hoare_1262092251_state > $o,B_34: pname,F_14: hoare_1262092251_state > pname,X_15: hoare_1262092251_state] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member5164104_state @ X_15 @ A_63 )
% 0.18/0.47 => ( member_pname @ B_34 @ ( image_202231862_pname @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_131_image__eqI,axiom,
% 0.18/0.47 ! [A_63: pname > $o,B_34: pname,F_14: pname > pname,X_15: pname] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member_pname @ X_15 @ A_63 )
% 0.18/0.47 => ( member_pname @ B_34 @ ( image_pname_pname @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_132_image__eqI,axiom,
% 0.18/0.47 ! [A_63: ( pname > $o ) > $o,B_34: pname,F_14: ( pname > $o ) > pname,X_15: pname > $o] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member_pname_o @ X_15 @ A_63 )
% 0.18/0.47 => ( member_pname @ B_34 @ ( image_pname_o_pname @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_133_image__eqI,axiom,
% 0.18/0.47 ! [A_63: ( hoare_1262092251_state > $o ) > $o,B_34: pname,F_14: ( hoare_1262092251_state > $o ) > pname,X_15: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member907417095tate_o @ X_15 @ A_63 )
% 0.18/0.47 => ( member_pname @ B_34 @ ( image_1820530197_pname @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_134_image__eqI,axiom,
% 0.18/0.47 ! [A_63: pname > $o,B_34: hoare_1262092251_state,F_14: pname > hoare_1262092251_state,X_15: pname] :
% 0.18/0.47 ( ( B_34
% 0.18/0.47 = ( F_14 @ X_15 ) )
% 0.18/0.47 => ( ( member_pname @ X_15 @ A_63 )
% 0.18/0.47 => ( member5164104_state @ B_34 @ ( image_669833818_state @ F_14 @ A_63 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_135_equals0D,axiom,
% 0.18/0.47 ! [A_62: pname > $o,A_61: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( A_61 = bot_bot_pname_o_o )
% 0.18/0.47 => ~ ( member_pname_o @ A_62 @ A_61 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_136_equals0D,axiom,
% 0.18/0.47 ! [A_62: hoare_1262092251_state > $o,A_61: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( A_61 = bot_bo1962689075te_o_o )
% 0.18/0.47 => ~ ( member907417095tate_o @ A_62 @ A_61 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_137_equals0D,axiom,
% 0.18/0.47 ! [A_62: hoare_1262092251_state,A_61: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( A_61 = bot_bo113204042tate_o )
% 0.18/0.47 => ~ ( member5164104_state @ A_62 @ A_61 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_138_equals0D,axiom,
% 0.18/0.47 ! [A_62: pname,A_61: pname > $o] :
% 0.18/0.47 ( ( A_61 = bot_bot_pname_o )
% 0.18/0.47 => ~ ( member_pname @ A_62 @ A_61 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_139_Collect__empty__eq,axiom,
% 0.18/0.47 ! [P_8: ( ( pname > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( ( collect_pname_o_o @ P_8 )
% 0.18/0.47 = bot_bot_pname_o_o_o )
% 0.18/0.47 <=> ! [X_1: ( pname > $o ) > $o] :
% 0.18/0.47 ~ ( P_8 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_140_Collect__empty__eq,axiom,
% 0.18/0.47 ! [P_8: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( ( collec341954548te_o_o @ P_8 )
% 0.18/0.47 = bot_bo388435036_o_o_o )
% 0.18/0.47 <=> ! [X_1: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ~ ( P_8 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_141_Collect__empty__eq,axiom,
% 0.18/0.47 ! [P_8: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( ( collec313158217tate_o @ P_8 )
% 0.18/0.47 = bot_bo1962689075te_o_o )
% 0.18/0.47 <=> ! [X_1: hoare_1262092251_state > $o] :
% 0.18/0.47 ~ ( P_8 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_142_Collect__empty__eq,axiom,
% 0.18/0.47 ! [P_8: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( ( collect_pname_o @ P_8 )
% 0.18/0.47 = bot_bot_pname_o_o )
% 0.18/0.47 <=> ! [X_1: pname > $o] :
% 0.18/0.47 ~ ( P_8 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_143_Collect__empty__eq,axiom,
% 0.18/0.47 ! [P_8: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ( collec1121927558_state @ P_8 )
% 0.18/0.47 = bot_bo113204042tate_o )
% 0.18/0.47 <=> ! [X_1: hoare_1262092251_state] :
% 0.18/0.47 ~ ( P_8 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_144_Collect__empty__eq,axiom,
% 0.18/0.47 ! [P_8: pname > $o] :
% 0.18/0.47 ( ( ( collect_pname @ P_8 )
% 0.18/0.47 = bot_bot_pname_o )
% 0.18/0.47 <=> ! [X_1: pname] :
% 0.18/0.47 ~ ( P_8 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_145_empty__iff,axiom,
% 0.18/0.47 ! [C_5: pname > $o] :
% 0.18/0.47 ~ ( member_pname_o @ C_5 @ bot_bot_pname_o_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_146_empty__iff,axiom,
% 0.18/0.47 ! [C_5: hoare_1262092251_state > $o] :
% 0.18/0.47 ~ ( member907417095tate_o @ C_5 @ bot_bo1962689075te_o_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_147_empty__iff,axiom,
% 0.18/0.47 ! [C_5: hoare_1262092251_state] :
% 0.18/0.47 ~ ( member5164104_state @ C_5 @ bot_bo113204042tate_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_148_empty__iff,axiom,
% 0.18/0.47 ! [C_5: pname] :
% 0.18/0.47 ~ ( member_pname @ C_5 @ bot_bot_pname_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_149_empty__Collect__eq,axiom,
% 0.18/0.47 ! [P_7: ( ( pname > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( bot_bot_pname_o_o_o
% 0.18/0.47 = ( collect_pname_o_o @ P_7 ) )
% 0.18/0.47 <=> ! [X_1: ( pname > $o ) > $o] :
% 0.18/0.47 ~ ( P_7 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_150_empty__Collect__eq,axiom,
% 0.18/0.47 ! [P_7: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.18/0.47 ( ( bot_bo388435036_o_o_o
% 0.18/0.47 = ( collec341954548te_o_o @ P_7 ) )
% 0.18/0.47 <=> ! [X_1: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ~ ( P_7 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_151_empty__Collect__eq,axiom,
% 0.18/0.47 ! [P_7: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( bot_bo1962689075te_o_o
% 0.18/0.47 = ( collec313158217tate_o @ P_7 ) )
% 0.18/0.47 <=> ! [X_1: hoare_1262092251_state > $o] :
% 0.18/0.47 ~ ( P_7 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_152_empty__Collect__eq,axiom,
% 0.18/0.47 ! [P_7: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( bot_bot_pname_o_o
% 0.18/0.47 = ( collect_pname_o @ P_7 ) )
% 0.18/0.47 <=> ! [X_1: pname > $o] :
% 0.18/0.47 ~ ( P_7 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_153_empty__Collect__eq,axiom,
% 0.18/0.47 ! [P_7: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( bot_bo113204042tate_o
% 0.18/0.47 = ( collec1121927558_state @ P_7 ) )
% 0.18/0.47 <=> ! [X_1: hoare_1262092251_state] :
% 0.18/0.47 ~ ( P_7 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_154_empty__Collect__eq,axiom,
% 0.18/0.47 ! [P_7: pname > $o] :
% 0.18/0.47 ( ( bot_bot_pname_o
% 0.18/0.47 = ( collect_pname @ P_7 ) )
% 0.18/0.47 <=> ! [X_1: pname] :
% 0.18/0.47 ~ ( P_7 @ X_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_155_ex__in__conv,axiom,
% 0.18/0.47 ! [A_60: ( pname > $o ) > $o] :
% 0.18/0.47 ( ? [X_1: pname > $o] : ( member_pname_o @ X_1 @ A_60 )
% 0.18/0.47 <=> ( A_60 != bot_bot_pname_o_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_156_ex__in__conv,axiom,
% 0.18/0.47 ! [A_60: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ? [X_1: hoare_1262092251_state > $o] : ( member907417095tate_o @ X_1 @ A_60 )
% 0.18/0.47 <=> ( A_60 != bot_bo1962689075te_o_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_157_ex__in__conv,axiom,
% 0.18/0.47 ! [A_60: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ? [X_1: hoare_1262092251_state] : ( member5164104_state @ X_1 @ A_60 )
% 0.18/0.47 <=> ( A_60 != bot_bo113204042tate_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_158_ex__in__conv,axiom,
% 0.18/0.47 ! [A_60: pname > $o] :
% 0.18/0.47 ( ? [X_1: pname] : ( member_pname @ X_1 @ A_60 )
% 0.18/0.47 <=> ( A_60 != bot_bot_pname_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_159_all__not__in__conv,axiom,
% 0.18/0.47 ! [A_59: ( pname > $o ) > $o] :
% 0.18/0.47 ( ! [X_1: pname > $o] :
% 0.18/0.47 ~ ( member_pname_o @ X_1 @ A_59 )
% 0.18/0.47 <=> ( A_59 = bot_bot_pname_o_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_160_all__not__in__conv,axiom,
% 0.18/0.47 ! [A_59: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ! [X_1: hoare_1262092251_state > $o] :
% 0.18/0.47 ~ ( member907417095tate_o @ X_1 @ A_59 )
% 0.18/0.47 <=> ( A_59 = bot_bo1962689075te_o_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_161_all__not__in__conv,axiom,
% 0.18/0.47 ! [A_59: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ! [X_1: hoare_1262092251_state] :
% 0.18/0.47 ~ ( member5164104_state @ X_1 @ A_59 )
% 0.18/0.47 <=> ( A_59 = bot_bo113204042tate_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_162_all__not__in__conv,axiom,
% 0.18/0.47 ! [A_59: pname > $o] :
% 0.18/0.47 ( ! [X_1: pname] :
% 0.18/0.47 ~ ( member_pname @ X_1 @ A_59 )
% 0.18/0.47 <=> ( A_59 = bot_bot_pname_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_163_empty__def,axiom,
% 0.18/0.47 ( bot_bo388435036_o_o_o
% 0.18/0.47 = ( collec341954548te_o_o
% 0.18/0.47 @ ^ [X_1: ( hoare_1262092251_state > $o ) > $o] : $false ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_164_empty__def,axiom,
% 0.18/0.47 ( bot_bo1962689075te_o_o
% 0.18/0.47 = ( collec313158217tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : $false ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_165_empty__def,axiom,
% 0.18/0.47 ( bot_bot_pname_o_o
% 0.18/0.47 = ( collect_pname_o
% 0.18/0.47 @ ^ [X_1: pname > $o] : $false ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_166_empty__def,axiom,
% 0.18/0.47 ( bot_bo113204042tate_o
% 0.18/0.47 = ( collec1121927558_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : $false ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_167_empty__def,axiom,
% 0.18/0.47 ( bot_bot_pname_o
% 0.18/0.47 = ( collect_pname
% 0.18/0.47 @ ^ [X_1: pname] : $false ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_168_insert__absorb,axiom,
% 0.18/0.47 ! [A_58: pname,A_57: pname > $o] :
% 0.18/0.47 ( ( member_pname @ A_58 @ A_57 )
% 0.18/0.47 => ( ( insert_pname @ A_58 @ A_57 )
% 0.18/0.47 = A_57 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_169_insert__absorb,axiom,
% 0.18/0.47 ! [A_58: hoare_1262092251_state,A_57: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( member5164104_state @ A_58 @ A_57 )
% 0.18/0.47 => ( ( insert81609953_state @ A_58 @ A_57 )
% 0.18/0.47 = A_57 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_170_insertI2,axiom,
% 0.18/0.47 ! [B_33: pname,A_56: pname,B_32: pname > $o] :
% 0.18/0.47 ( ( member_pname @ A_56 @ B_32 )
% 0.18/0.47 => ( member_pname @ A_56 @ ( insert_pname @ B_33 @ B_32 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_171_insertI2,axiom,
% 0.18/0.47 ! [B_33: hoare_1262092251_state,A_56: hoare_1262092251_state,B_32: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( member5164104_state @ A_56 @ B_32 )
% 0.18/0.47 => ( member5164104_state @ A_56 @ ( insert81609953_state @ B_33 @ B_32 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_172_insert__ident,axiom,
% 0.18/0.47 ! [B_31: pname > $o,X_14: pname,A_55: pname > $o] :
% 0.18/0.47 ( ~ ( member_pname @ X_14 @ A_55 )
% 0.18/0.47 => ( ~ ( member_pname @ X_14 @ B_31 )
% 0.18/0.47 => ( ( ( insert_pname @ X_14 @ A_55 )
% 0.18/0.47 = ( insert_pname @ X_14 @ B_31 ) )
% 0.18/0.47 <=> ( A_55 = B_31 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_173_insert__ident,axiom,
% 0.18/0.47 ! [B_31: hoare_1262092251_state > $o,X_14: hoare_1262092251_state,A_55: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ~ ( member5164104_state @ X_14 @ A_55 )
% 0.18/0.47 => ( ~ ( member5164104_state @ X_14 @ B_31 )
% 0.18/0.47 => ( ( ( insert81609953_state @ X_14 @ A_55 )
% 0.18/0.47 = ( insert81609953_state @ X_14 @ B_31 ) )
% 0.18/0.47 <=> ( A_55 = B_31 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_174_insert__code,axiom,
% 0.18/0.47 ! [Y_3: pname,A_54: pname > $o,X_13: pname] :
% 0.18/0.47 ( ( insert_pname @ Y_3 @ A_54 @ X_13 )
% 0.18/0.47 <=> ( ( Y_3 = X_13 )
% 0.18/0.47 | ( A_54 @ X_13 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_175_insert__code,axiom,
% 0.18/0.47 ! [Y_3: hoare_1262092251_state,A_54: hoare_1262092251_state > $o,X_13: hoare_1262092251_state] :
% 0.18/0.47 ( ( insert81609953_state @ Y_3 @ A_54 @ X_13 )
% 0.18/0.47 <=> ( ( Y_3 = X_13 )
% 0.18/0.47 | ( A_54 @ X_13 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_176_insert__iff,axiom,
% 0.18/0.47 ! [A_53: pname,B_30: pname,A_52: pname > $o] :
% 0.18/0.47 ( ( member_pname @ A_53 @ ( insert_pname @ B_30 @ A_52 ) )
% 0.18/0.47 <=> ( ( A_53 = B_30 )
% 0.18/0.47 | ( member_pname @ A_53 @ A_52 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_177_insert__iff,axiom,
% 0.18/0.47 ! [A_53: hoare_1262092251_state,B_30: hoare_1262092251_state,A_52: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( member5164104_state @ A_53 @ ( insert81609953_state @ B_30 @ A_52 ) )
% 0.18/0.47 <=> ( ( A_53 = B_30 )
% 0.18/0.47 | ( member5164104_state @ A_53 @ A_52 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_178_insert__commute,axiom,
% 0.18/0.47 ! [X_12: pname,Y_2: pname,A_51: pname > $o] :
% 0.18/0.47 ( ( insert_pname @ X_12 @ ( insert_pname @ Y_2 @ A_51 ) )
% 0.18/0.47 = ( insert_pname @ Y_2 @ ( insert_pname @ X_12 @ A_51 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_179_insert__commute,axiom,
% 0.18/0.47 ! [X_12: hoare_1262092251_state,Y_2: hoare_1262092251_state,A_51: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( insert81609953_state @ X_12 @ ( insert81609953_state @ Y_2 @ A_51 ) )
% 0.18/0.47 = ( insert81609953_state @ Y_2 @ ( insert81609953_state @ X_12 @ A_51 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_180_insert__absorb2,axiom,
% 0.18/0.47 ! [X_11: pname,A_50: pname > $o] :
% 0.18/0.47 ( ( insert_pname @ X_11 @ ( insert_pname @ X_11 @ A_50 ) )
% 0.18/0.47 = ( insert_pname @ X_11 @ A_50 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_181_insert__absorb2,axiom,
% 0.18/0.47 ! [X_11: hoare_1262092251_state,A_50: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( insert81609953_state @ X_11 @ ( insert81609953_state @ X_11 @ A_50 ) )
% 0.18/0.47 = ( insert81609953_state @ X_11 @ A_50 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_182_insert__Collect,axiom,
% 0.18/0.47 ! [A_49: pname,P_6: pname > $o] :
% 0.18/0.47 ( ( insert_pname @ A_49 @ ( collect_pname @ P_6 ) )
% 0.18/0.47 = ( collect_pname
% 0.18/0.47 @ ^ [U: pname] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_183_insert__Collect,axiom,
% 0.18/0.47 ! [A_49: hoare_1262092251_state,P_6: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( insert81609953_state @ A_49 @ ( collec1121927558_state @ P_6 ) )
% 0.18/0.47 = ( collec1121927558_state
% 0.18/0.47 @ ^ [U: hoare_1262092251_state] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_184_insert__Collect,axiom,
% 0.18/0.47 ! [A_49: pname > $o,P_6: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( insert_pname_o @ A_49 @ ( collect_pname_o @ P_6 ) )
% 0.18/0.47 = ( collect_pname_o
% 0.18/0.47 @ ^ [U: pname > $o] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_185_insert__Collect,axiom,
% 0.18/0.47 ! [A_49: hoare_1262092251_state > $o,P_6: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( insert1042460334tate_o @ A_49 @ ( collec313158217tate_o @ P_6 ) )
% 0.18/0.47 = ( collec313158217tate_o
% 0.18/0.47 @ ^ [U: hoare_1262092251_state > $o] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_186_insert__compr,axiom,
% 0.18/0.47 ! [A_48: pname,B_29: pname > $o] :
% 0.18/0.47 ( ( insert_pname @ A_48 @ B_29 )
% 0.18/0.47 = ( collect_pname
% 0.18/0.47 @ ^ [X_1: pname] : ( (|) @ ( X_1 = A_48 ) @ ( member_pname @ X_1 @ B_29 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_187_insert__compr,axiom,
% 0.18/0.47 ! [A_48: hoare_1262092251_state,B_29: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( insert81609953_state @ A_48 @ B_29 )
% 0.18/0.47 = ( collec1121927558_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : ( (|) @ ( X_1 = A_48 ) @ ( member5164104_state @ X_1 @ B_29 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_188_insert__compr,axiom,
% 0.18/0.47 ! [A_48: pname > $o,B_29: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( insert_pname_o @ A_48 @ B_29 )
% 0.18/0.47 = ( collect_pname_o
% 0.18/0.47 @ ^ [X_1: pname > $o] : ( (|) @ ( X_1 = A_48 ) @ ( member_pname_o @ X_1 @ B_29 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_189_insert__compr,axiom,
% 0.18/0.47 ! [A_48: hoare_1262092251_state > $o,B_29: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( insert1042460334tate_o @ A_48 @ B_29 )
% 0.18/0.47 = ( collec313158217tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : ( (|) @ ( X_1 = A_48 ) @ ( member907417095tate_o @ X_1 @ B_29 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_190_insertI1,axiom,
% 0.18/0.47 ! [A_47: pname,B_28: pname > $o] : ( member_pname @ A_47 @ ( insert_pname @ A_47 @ B_28 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_191_insertI1,axiom,
% 0.18/0.47 ! [A_47: hoare_1262092251_state,B_28: hoare_1262092251_state > $o] : ( member5164104_state @ A_47 @ ( insert81609953_state @ A_47 @ B_28 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_192_equalityE,axiom,
% 0.18/0.47 ! [A_46: pname > $o,B_27: pname > $o] :
% 0.18/0.47 ( ( A_46 = B_27 )
% 0.18/0.47 => ~ ( ( ord_less_eq_pname_o @ A_46 @ B_27 )
% 0.18/0.47 => ~ ( ord_less_eq_pname_o @ B_27 @ A_46 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_193_equalityE,axiom,
% 0.18/0.47 ! [A_46: hoare_1262092251_state > $o,B_27: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( A_46 = B_27 )
% 0.18/0.47 => ~ ( ( ord_le870406270tate_o @ A_46 @ B_27 )
% 0.18/0.47 => ~ ( ord_le870406270tate_o @ B_27 @ A_46 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_194_subset__trans,axiom,
% 0.18/0.47 ! [C_4: pname > $o,A_45: pname > $o,B_26: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_45 @ B_26 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ B_26 @ C_4 )
% 0.18/0.47 => ( ord_less_eq_pname_o @ A_45 @ C_4 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_195_subset__trans,axiom,
% 0.18/0.47 ! [C_4: hoare_1262092251_state > $o,A_45: hoare_1262092251_state > $o,B_26: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ A_45 @ B_26 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ B_26 @ C_4 )
% 0.18/0.47 => ( ord_le870406270tate_o @ A_45 @ C_4 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_196_set__mp,axiom,
% 0.18/0.47 ! [X_10: pname,A_44: pname > $o,B_25: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_44 @ B_25 )
% 0.18/0.47 => ( ( member_pname @ X_10 @ A_44 )
% 0.18/0.47 => ( member_pname @ X_10 @ B_25 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_197_set__mp,axiom,
% 0.18/0.47 ! [X_10: hoare_1262092251_state,A_44: hoare_1262092251_state > $o,B_25: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ A_44 @ B_25 )
% 0.18/0.47 => ( ( member5164104_state @ X_10 @ A_44 )
% 0.18/0.47 => ( member5164104_state @ X_10 @ B_25 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_198_set__rev__mp,axiom,
% 0.18/0.47 ! [B_24: pname > $o,X_9: pname,A_43: pname > $o] :
% 0.18/0.47 ( ( member_pname @ X_9 @ A_43 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ A_43 @ B_24 )
% 0.18/0.47 => ( member_pname @ X_9 @ B_24 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_199_set__rev__mp,axiom,
% 0.18/0.47 ! [B_24: hoare_1262092251_state > $o,X_9: hoare_1262092251_state,A_43: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( member5164104_state @ X_9 @ A_43 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ A_43 @ B_24 )
% 0.18/0.47 => ( member5164104_state @ X_9 @ B_24 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_200_in__mono,axiom,
% 0.18/0.47 ! [X_8: pname,A_42: pname > $o,B_23: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_42 @ B_23 )
% 0.18/0.47 => ( ( member_pname @ X_8 @ A_42 )
% 0.18/0.47 => ( member_pname @ X_8 @ B_23 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_201_in__mono,axiom,
% 0.18/0.47 ! [X_8: hoare_1262092251_state,A_42: hoare_1262092251_state > $o,B_23: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ A_42 @ B_23 )
% 0.18/0.47 => ( ( member5164104_state @ X_8 @ A_42 )
% 0.18/0.47 => ( member5164104_state @ X_8 @ B_23 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_202_equalityD2,axiom,
% 0.18/0.47 ! [A_41: pname > $o,B_22: pname > $o] :
% 0.18/0.47 ( ( A_41 = B_22 )
% 0.18/0.47 => ( ord_less_eq_pname_o @ B_22 @ A_41 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_203_equalityD2,axiom,
% 0.18/0.47 ! [A_41: hoare_1262092251_state > $o,B_22: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( A_41 = B_22 )
% 0.18/0.47 => ( ord_le870406270tate_o @ B_22 @ A_41 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_204_equalityD1,axiom,
% 0.18/0.47 ! [A_40: pname > $o,B_21: pname > $o] :
% 0.18/0.47 ( ( A_40 = B_21 )
% 0.18/0.47 => ( ord_less_eq_pname_o @ A_40 @ B_21 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_205_equalityD1,axiom,
% 0.18/0.47 ! [A_40: hoare_1262092251_state > $o,B_21: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( A_40 = B_21 )
% 0.18/0.47 => ( ord_le870406270tate_o @ A_40 @ B_21 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_206_set__eq__subset,axiom,
% 0.18/0.47 ! [A_39: pname > $o,B_20: pname > $o] :
% 0.18/0.47 ( ( A_39 = B_20 )
% 0.18/0.47 <=> ( ( ord_less_eq_pname_o @ A_39 @ B_20 )
% 0.18/0.47 & ( ord_less_eq_pname_o @ B_20 @ A_39 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_207_set__eq__subset,axiom,
% 0.18/0.47 ! [A_39: hoare_1262092251_state > $o,B_20: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( A_39 = B_20 )
% 0.18/0.47 <=> ( ( ord_le870406270tate_o @ A_39 @ B_20 )
% 0.18/0.47 & ( ord_le870406270tate_o @ B_20 @ A_39 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_208_subset__refl,axiom,
% 0.18/0.47 ! [A_38: pname > $o] : ( ord_less_eq_pname_o @ A_38 @ A_38 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_209_subset__refl,axiom,
% 0.18/0.47 ! [A_38: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ A_38 @ A_38 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_210_rev__image__eqI,axiom,
% 0.18/0.47 ! [B_19: hoare_1262092251_state,F_13: pname > hoare_1262092251_state,X_7: pname,A_37: pname > $o] :
% 0.18/0.47 ( ( member_pname @ X_7 @ A_37 )
% 0.18/0.47 => ( ( B_19
% 0.18/0.47 = ( F_13 @ X_7 ) )
% 0.18/0.47 => ( member5164104_state @ B_19 @ ( image_669833818_state @ F_13 @ A_37 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_211_imageI,axiom,
% 0.18/0.47 ! [F_12: pname > hoare_1262092251_state,X_6: pname,A_36: pname > $o] :
% 0.18/0.47 ( ( member_pname @ X_6 @ A_36 )
% 0.18/0.47 => ( member5164104_state @ ( F_12 @ X_6 ) @ ( image_669833818_state @ F_12 @ A_36 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_212_image__iff,axiom,
% 0.18/0.47 ! [Z: hoare_1262092251_state,F_11: pname > hoare_1262092251_state,A_35: pname > $o] :
% 0.18/0.47 ( ( member5164104_state @ Z @ ( image_669833818_state @ F_11 @ A_35 ) )
% 0.18/0.47 <=> ? [X_1: pname] :
% 0.18/0.47 ( ( member_pname @ X_1 @ A_35 )
% 0.18/0.47 & ( Z
% 0.18/0.47 = ( F_11 @ X_1 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_213_finite__Collect__disjI,axiom,
% 0.18/0.47 ! [P_5: pname > $o,Q: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname
% 0.18/0.47 @ ( collect_pname
% 0.18/0.47 @ ^ [X_1: pname] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.18/0.47 <=> ( ( finite_finite_pname @ ( collect_pname @ P_5 ) )
% 0.18/0.47 & ( finite_finite_pname @ ( collect_pname @ Q ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_214_finite__Collect__disjI,axiom,
% 0.18/0.47 ! [P_5: hoare_1262092251_state > $o,Q: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state
% 0.18/0.47 @ ( collec1121927558_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.18/0.47 <=> ( ( finite1178804552_state @ ( collec1121927558_state @ P_5 ) )
% 0.18/0.47 & ( finite1178804552_state @ ( collec1121927558_state @ Q ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_215_finite__Collect__disjI,axiom,
% 0.18/0.47 ! [P_5: ( pname > $o ) > $o,Q: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o
% 0.18/0.47 @ ( collect_pname_o
% 0.18/0.47 @ ^ [X_1: pname > $o] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.18/0.47 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_5 ) )
% 0.18/0.47 & ( finite297249702name_o @ ( collect_pname_o @ Q ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_216_finite__Collect__disjI,axiom,
% 0.18/0.47 ! [P_5: ( hoare_1262092251_state > $o ) > $o,Q: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o
% 0.18/0.47 @ ( collec313158217tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.18/0.47 <=> ( ( finite1423311111tate_o @ ( collec313158217tate_o @ P_5 ) )
% 0.18/0.47 & ( finite1423311111tate_o @ ( collec313158217tate_o @ Q ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_217_insert__compr__raw,axiom,
% 0.18/0.47 ! [X_1: pname,Xa: pname > $o] :
% 0.18/0.47 ( ( insert_pname @ X_1 @ Xa )
% 0.18/0.47 = ( collect_pname
% 0.18/0.47 @ ^ [Y_1: pname] : ( (|) @ ( Y_1 = X_1 ) @ ( member_pname @ Y_1 @ Xa ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_218_insert__compr__raw,axiom,
% 0.18/0.47 ! [X_1: hoare_1262092251_state,Xa: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( insert81609953_state @ X_1 @ Xa )
% 0.18/0.47 = ( collec1121927558_state
% 0.18/0.47 @ ^ [Y_1: hoare_1262092251_state] : ( (|) @ ( Y_1 = X_1 ) @ ( member5164104_state @ Y_1 @ Xa ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_219_insert__compr__raw,axiom,
% 0.18/0.47 ! [X_1: pname > $o,Xa: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( insert_pname_o @ X_1 @ Xa )
% 0.18/0.47 = ( collect_pname_o
% 0.18/0.47 @ ^ [Y_1: pname > $o] : ( (|) @ ( Y_1 = X_1 ) @ ( member_pname_o @ Y_1 @ Xa ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_220_insert__compr__raw,axiom,
% 0.18/0.47 ! [X_1: hoare_1262092251_state > $o,Xa: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( insert1042460334tate_o @ X_1 @ Xa )
% 0.18/0.47 = ( collec313158217tate_o
% 0.18/0.47 @ ^ [Y_1: hoare_1262092251_state > $o] : ( (|) @ ( Y_1 = X_1 ) @ ( member907417095tate_o @ Y_1 @ Xa ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_221_singleton__inject,axiom,
% 0.18/0.47 ! [A_34: pname,B_18: pname] :
% 0.18/0.47 ( ( ( insert_pname @ A_34 @ bot_bot_pname_o )
% 0.18/0.47 = ( insert_pname @ B_18 @ bot_bot_pname_o ) )
% 0.18/0.47 => ( A_34 = B_18 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_222_singleton__inject,axiom,
% 0.18/0.47 ! [A_34: hoare_1262092251_state,B_18: hoare_1262092251_state] :
% 0.18/0.47 ( ( ( insert81609953_state @ A_34 @ bot_bo113204042tate_o )
% 0.18/0.47 = ( insert81609953_state @ B_18 @ bot_bo113204042tate_o ) )
% 0.18/0.47 => ( A_34 = B_18 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_223_singletonE,axiom,
% 0.18/0.47 ! [B_17: pname,A_33: pname] :
% 0.18/0.47 ( ( member_pname @ B_17 @ ( insert_pname @ A_33 @ bot_bot_pname_o ) )
% 0.18/0.47 => ( B_17 = A_33 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_224_singletonE,axiom,
% 0.18/0.47 ! [B_17: hoare_1262092251_state,A_33: hoare_1262092251_state] :
% 0.18/0.47 ( ( member5164104_state @ B_17 @ ( insert81609953_state @ A_33 @ bot_bo113204042tate_o ) )
% 0.18/0.47 => ( B_17 = A_33 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_225_doubleton__eq__iff,axiom,
% 0.18/0.47 ! [A_32: pname,B_16: pname,C_3: pname,D_1: pname] :
% 0.18/0.47 ( ( ( insert_pname @ A_32 @ ( insert_pname @ B_16 @ bot_bot_pname_o ) )
% 0.18/0.47 = ( insert_pname @ C_3 @ ( insert_pname @ D_1 @ bot_bot_pname_o ) ) )
% 0.18/0.47 <=> ( ( ( A_32 = C_3 )
% 0.18/0.47 & ( B_16 = D_1 ) )
% 0.18/0.47 | ( ( A_32 = D_1 )
% 0.18/0.47 & ( B_16 = C_3 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_226_doubleton__eq__iff,axiom,
% 0.18/0.47 ! [A_32: hoare_1262092251_state,B_16: hoare_1262092251_state,C_3: hoare_1262092251_state,D_1: hoare_1262092251_state] :
% 0.18/0.47 ( ( ( insert81609953_state @ A_32 @ ( insert81609953_state @ B_16 @ bot_bo113204042tate_o ) )
% 0.18/0.47 = ( insert81609953_state @ C_3 @ ( insert81609953_state @ D_1 @ bot_bo113204042tate_o ) ) )
% 0.18/0.47 <=> ( ( ( A_32 = C_3 )
% 0.18/0.47 & ( B_16 = D_1 ) )
% 0.18/0.47 | ( ( A_32 = D_1 )
% 0.18/0.47 & ( B_16 = C_3 ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_227_singleton__iff,axiom,
% 0.18/0.47 ! [B_15: pname,A_31: pname] :
% 0.18/0.47 ( ( member_pname @ B_15 @ ( insert_pname @ A_31 @ bot_bot_pname_o ) )
% 0.18/0.47 <=> ( B_15 = A_31 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_228_singleton__iff,axiom,
% 0.18/0.47 ! [B_15: hoare_1262092251_state,A_31: hoare_1262092251_state] :
% 0.18/0.47 ( ( member5164104_state @ B_15 @ ( insert81609953_state @ A_31 @ bot_bo113204042tate_o ) )
% 0.18/0.47 <=> ( B_15 = A_31 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_229_insert__not__empty,axiom,
% 0.18/0.47 ! [A_30: pname,A_29: pname > $o] :
% 0.18/0.47 ( ( insert_pname @ A_30 @ A_29 )
% 0.18/0.47 != bot_bot_pname_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_230_insert__not__empty,axiom,
% 0.18/0.47 ! [A_30: hoare_1262092251_state,A_29: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( insert81609953_state @ A_30 @ A_29 )
% 0.18/0.47 != bot_bo113204042tate_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_231_empty__not__insert,axiom,
% 0.18/0.47 ! [A_28: pname,A_27: pname > $o] :
% 0.18/0.47 ( bot_bot_pname_o
% 0.18/0.47 != ( insert_pname @ A_28 @ A_27 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_232_empty__not__insert,axiom,
% 0.18/0.47 ! [A_28: hoare_1262092251_state,A_27: hoare_1262092251_state > $o] :
% 0.18/0.47 ( bot_bo113204042tate_o
% 0.18/0.47 != ( insert81609953_state @ A_28 @ A_27 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_233_finite__insert,axiom,
% 0.18/0.47 ! [A_26: pname,A_25: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ ( insert_pname @ A_26 @ A_25 ) )
% 0.18/0.47 <=> ( finite_finite_pname @ A_25 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_234_finite__insert,axiom,
% 0.18/0.47 ! [A_26: hoare_1262092251_state,A_25: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ ( insert81609953_state @ A_26 @ A_25 ) )
% 0.18/0.47 <=> ( finite1178804552_state @ A_25 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_235_finite__insert,axiom,
% 0.18/0.47 ! [A_26: pname > $o,A_25: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ ( insert_pname_o @ A_26 @ A_25 ) )
% 0.18/0.47 <=> ( finite297249702name_o @ A_25 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_236_finite__insert,axiom,
% 0.18/0.47 ! [A_26: hoare_1262092251_state > $o,A_25: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ ( insert1042460334tate_o @ A_26 @ A_25 ) )
% 0.18/0.47 <=> ( finite1423311111tate_o @ A_25 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_237_subset__empty,axiom,
% 0.18/0.47 ! [A_24: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_24 @ bot_bot_pname_o )
% 0.18/0.47 <=> ( A_24 = bot_bot_pname_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_238_subset__empty,axiom,
% 0.18/0.47 ! [A_24: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ A_24 @ bot_bo113204042tate_o )
% 0.18/0.47 <=> ( A_24 = bot_bo113204042tate_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_239_image__is__empty,axiom,
% 0.18/0.47 ! [F_10: pname > hoare_1262092251_state,A_23: pname > $o] :
% 0.18/0.47 ( ( ( image_669833818_state @ F_10 @ A_23 )
% 0.18/0.47 = bot_bo113204042tate_o )
% 0.18/0.47 <=> ( A_23 = bot_bot_pname_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_240_image__empty,axiom,
% 0.18/0.47 ! [F_9: pname > hoare_1262092251_state] :
% 0.18/0.47 ( ( image_669833818_state @ F_9 @ bot_bot_pname_o )
% 0.18/0.47 = bot_bo113204042tate_o ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_241_empty__is__image,axiom,
% 0.18/0.47 ! [F_8: pname > hoare_1262092251_state,A_22: pname > $o] :
% 0.18/0.47 ( ( bot_bo113204042tate_o
% 0.18/0.47 = ( image_669833818_state @ F_8 @ A_22 ) )
% 0.18/0.47 <=> ( A_22 = bot_bot_pname_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_242_finite__subset,axiom,
% 0.18/0.47 ! [A_21: ( pname > $o ) > $o,B_14: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( ord_le1205211808me_o_o @ A_21 @ B_14 )
% 0.18/0.47 => ( ( finite297249702name_o @ B_14 )
% 0.18/0.47 => ( finite297249702name_o @ A_21 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_243_finite__subset,axiom,
% 0.18/0.47 ! [A_21: ( hoare_1262092251_state > $o ) > $o,B_14: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( ord_le2012720639te_o_o @ A_21 @ B_14 )
% 0.18/0.47 => ( ( finite1423311111tate_o @ B_14 )
% 0.18/0.47 => ( finite1423311111tate_o @ A_21 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_244_finite__subset,axiom,
% 0.18/0.47 ! [A_21: pname > $o,B_14: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_21 @ B_14 )
% 0.18/0.47 => ( ( finite_finite_pname @ B_14 )
% 0.18/0.47 => ( finite_finite_pname @ A_21 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_245_finite__subset,axiom,
% 0.18/0.47 ! [A_21: hoare_1262092251_state > $o,B_14: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ A_21 @ B_14 )
% 0.18/0.47 => ( ( finite1178804552_state @ B_14 )
% 0.18/0.47 => ( finite1178804552_state @ A_21 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_246_rev__finite__subset,axiom,
% 0.18/0.47 ! [A_20: ( pname > $o ) > $o,B_13: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ B_13 )
% 0.18/0.47 => ( ( ord_le1205211808me_o_o @ A_20 @ B_13 )
% 0.18/0.47 => ( finite297249702name_o @ A_20 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_247_rev__finite__subset,axiom,
% 0.18/0.47 ! [A_20: ( hoare_1262092251_state > $o ) > $o,B_13: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ B_13 )
% 0.18/0.47 => ( ( ord_le2012720639te_o_o @ A_20 @ B_13 )
% 0.18/0.47 => ( finite1423311111tate_o @ A_20 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_248_rev__finite__subset,axiom,
% 0.18/0.47 ! [A_20: pname > $o,B_13: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ B_13 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ A_20 @ B_13 )
% 0.18/0.47 => ( finite_finite_pname @ A_20 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_249_rev__finite__subset,axiom,
% 0.18/0.47 ! [A_20: hoare_1262092251_state > $o,B_13: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ B_13 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ A_20 @ B_13 )
% 0.18/0.47 => ( finite1178804552_state @ A_20 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_250_insert__mono,axiom,
% 0.18/0.47 ! [A_19: pname,C_2: pname > $o,D: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ C_2 @ D )
% 0.18/0.47 => ( ord_less_eq_pname_o @ ( insert_pname @ A_19 @ C_2 ) @ ( insert_pname @ A_19 @ D ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_251_insert__mono,axiom,
% 0.18/0.47 ! [A_19: hoare_1262092251_state,C_2: hoare_1262092251_state > $o,D: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ C_2 @ D )
% 0.18/0.47 => ( ord_le870406270tate_o @ ( insert81609953_state @ A_19 @ C_2 ) @ ( insert81609953_state @ A_19 @ D ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_252_mem__def,axiom,
% 0.18/0.47 ! [X_5: pname,A_18: pname > $o] :
% 0.18/0.47 ( ( member_pname @ X_5 @ A_18 )
% 0.18/0.47 <=> ( A_18 @ X_5 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_253_mem__def,axiom,
% 0.18/0.47 ! [X_5: hoare_1262092251_state,A_18: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( member5164104_state @ X_5 @ A_18 )
% 0.18/0.47 <=> ( A_18 @ X_5 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_254_Collect__def,axiom,
% 0.18/0.47 ! [P_4: pname > $o] :
% 0.18/0.47 ( ( collect_pname @ P_4 )
% 0.18/0.47 = P_4 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_255_Collect__def,axiom,
% 0.18/0.47 ! [P_4: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( collec1121927558_state @ P_4 )
% 0.18/0.47 = P_4 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_256_Collect__def,axiom,
% 0.18/0.47 ! [P_4: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( collect_pname_o @ P_4 )
% 0.18/0.47 = P_4 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_257_Collect__def,axiom,
% 0.18/0.47 ! [P_4: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( collec313158217tate_o @ P_4 )
% 0.18/0.47 = P_4 ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_258_subset__insertI2,axiom,
% 0.18/0.47 ! [B_12: pname,A_17: pname > $o,B_11: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_17 @ B_11 )
% 0.18/0.47 => ( ord_less_eq_pname_o @ A_17 @ ( insert_pname @ B_12 @ B_11 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_259_subset__insertI2,axiom,
% 0.18/0.47 ! [B_12: hoare_1262092251_state,A_17: hoare_1262092251_state > $o,B_11: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ A_17 @ B_11 )
% 0.18/0.47 => ( ord_le870406270tate_o @ A_17 @ ( insert81609953_state @ B_12 @ B_11 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_260_subset__insert,axiom,
% 0.18/0.47 ! [B_10: pname > $o,X_4: pname,A_16: pname > $o] :
% 0.18/0.47 ( ~ ( member_pname @ X_4 @ A_16 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ A_16 @ ( insert_pname @ X_4 @ B_10 ) )
% 0.18/0.47 <=> ( ord_less_eq_pname_o @ A_16 @ B_10 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_261_subset__insert,axiom,
% 0.18/0.47 ! [B_10: hoare_1262092251_state > $o,X_4: hoare_1262092251_state,A_16: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ~ ( member5164104_state @ X_4 @ A_16 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ A_16 @ ( insert81609953_state @ X_4 @ B_10 ) )
% 0.18/0.47 <=> ( ord_le870406270tate_o @ A_16 @ B_10 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_262_insert__subset,axiom,
% 0.18/0.47 ! [X_3: pname,A_15: pname > $o,B_9: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_3 @ A_15 ) @ B_9 )
% 0.18/0.47 <=> ( ( member_pname @ X_3 @ B_9 )
% 0.18/0.47 & ( ord_less_eq_pname_o @ A_15 @ B_9 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_263_insert__subset,axiom,
% 0.18/0.47 ! [X_3: hoare_1262092251_state,A_15: hoare_1262092251_state > $o,B_9: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ ( insert81609953_state @ X_3 @ A_15 ) @ B_9 )
% 0.18/0.47 <=> ( ( member5164104_state @ X_3 @ B_9 )
% 0.18/0.47 & ( ord_le870406270tate_o @ A_15 @ B_9 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_264_subset__insertI,axiom,
% 0.18/0.47 ! [B_8: pname > $o,A_14: pname] : ( ord_less_eq_pname_o @ B_8 @ ( insert_pname @ A_14 @ B_8 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_265_subset__insertI,axiom,
% 0.18/0.47 ! [B_8: hoare_1262092251_state > $o,A_14: hoare_1262092251_state] : ( ord_le870406270tate_o @ B_8 @ ( insert81609953_state @ A_14 @ B_8 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_266_insert__image,axiom,
% 0.18/0.47 ! [F_7: pname > hoare_1262092251_state,X_2: pname,A_13: pname > $o] :
% 0.18/0.47 ( ( member_pname @ X_2 @ A_13 )
% 0.18/0.47 => ( ( insert81609953_state @ ( F_7 @ X_2 ) @ ( image_669833818_state @ F_7 @ A_13 ) )
% 0.18/0.47 = ( image_669833818_state @ F_7 @ A_13 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_267_image__insert,axiom,
% 0.18/0.47 ! [F_6: pname > hoare_1262092251_state,A_12: pname,B_7: pname > $o] :
% 0.18/0.47 ( ( image_669833818_state @ F_6 @ ( insert_pname @ A_12 @ B_7 ) )
% 0.18/0.47 = ( insert81609953_state @ ( F_6 @ A_12 ) @ ( image_669833818_state @ F_6 @ B_7 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_268_image__mono,axiom,
% 0.18/0.47 ! [F_5: pname > hoare_1262092251_state,A_11: pname > $o,B_6: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ A_11 @ B_6 )
% 0.18/0.47 => ( ord_le870406270tate_o @ ( image_669833818_state @ F_5 @ A_11 ) @ ( image_669833818_state @ F_5 @ B_6 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_269_subset__image__iff,axiom,
% 0.18/0.47 ! [B_5: hoare_1262092251_state > $o,F_4: pname > hoare_1262092251_state,A_10: pname > $o] :
% 0.18/0.47 ( ( ord_le870406270tate_o @ B_5 @ ( image_669833818_state @ F_4 @ A_10 ) )
% 0.18/0.47 <=> ? [AA: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ AA @ A_10 )
% 0.18/0.47 & ( B_5
% 0.18/0.47 = ( image_669833818_state @ F_4 @ AA ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_270_domI,axiom,
% 0.18/0.47 ! [M: pname > option_com,A_9: pname,B_4: com] :
% 0.18/0.47 ( ( ( M @ A_9 )
% 0.18/0.47 = ( some_com @ B_4 ) )
% 0.18/0.47 => ( member_pname @ A_9 @ ( dom_pname_com @ M ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_271_Collect__conv__if,axiom,
% 0.18/0.47 ! [P_3: pname > $o,A_8: pname] :
% 0.18/0.47 ( ( ( P_3 @ A_8 )
% 0.18/0.47 => ( ( collect_pname
% 0.18/0.47 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.18/0.47 = ( insert_pname @ A_8 @ bot_bot_pname_o ) ) )
% 0.18/0.47 & ( ~ ( P_3 @ A_8 )
% 0.18/0.47 => ( ( collect_pname
% 0.18/0.47 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.18/0.47 = bot_bot_pname_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_272_Collect__conv__if,axiom,
% 0.18/0.47 ! [P_3: hoare_1262092251_state > $o,A_8: hoare_1262092251_state] :
% 0.18/0.47 ( ( ( P_3 @ A_8 )
% 0.18/0.47 => ( ( collec1121927558_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.18/0.47 = ( insert81609953_state @ A_8 @ bot_bo113204042tate_o ) ) )
% 0.18/0.47 & ( ~ ( P_3 @ A_8 )
% 0.18/0.47 => ( ( collec1121927558_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.18/0.47 = bot_bo113204042tate_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_273_Collect__conv__if,axiom,
% 0.18/0.47 ! [P_3: ( pname > $o ) > $o,A_8: pname > $o] :
% 0.18/0.47 ( ( ( P_3 @ A_8 )
% 0.18/0.47 => ( ( collect_pname_o
% 0.18/0.47 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.18/0.47 = ( insert_pname_o @ A_8 @ bot_bot_pname_o_o ) ) )
% 0.18/0.47 & ( ~ ( P_3 @ A_8 )
% 0.18/0.47 => ( ( collect_pname_o
% 0.18/0.47 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.18/0.47 = bot_bot_pname_o_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_274_Collect__conv__if,axiom,
% 0.18/0.47 ! [P_3: ( hoare_1262092251_state > $o ) > $o,A_8: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ( P_3 @ A_8 )
% 0.18/0.47 => ( ( collec313158217tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.18/0.47 = ( insert1042460334tate_o @ A_8 @ bot_bo1962689075te_o_o ) ) )
% 0.18/0.47 & ( ~ ( P_3 @ A_8 )
% 0.18/0.47 => ( ( collec313158217tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.18/0.47 = bot_bo1962689075te_o_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_275_Collect__conv__if2,axiom,
% 0.18/0.47 ! [P_2: pname > $o,A_7: pname] :
% 0.18/0.47 ( ( ( P_2 @ A_7 )
% 0.18/0.47 => ( ( collect_pname
% 0.18/0.47 @ ^ [X_1: pname] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.18/0.47 = ( insert_pname @ A_7 @ bot_bot_pname_o ) ) )
% 0.18/0.47 & ( ~ ( P_2 @ A_7 )
% 0.18/0.47 => ( ( collect_pname
% 0.18/0.47 @ ^ [X_1: pname] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.18/0.47 = bot_bot_pname_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_276_Collect__conv__if2,axiom,
% 0.18/0.47 ! [P_2: hoare_1262092251_state > $o,A_7: hoare_1262092251_state] :
% 0.18/0.47 ( ( ( P_2 @ A_7 )
% 0.18/0.47 => ( ( collec1121927558_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.18/0.47 = ( insert81609953_state @ A_7 @ bot_bo113204042tate_o ) ) )
% 0.18/0.47 & ( ~ ( P_2 @ A_7 )
% 0.18/0.47 => ( ( collec1121927558_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.18/0.47 = bot_bo113204042tate_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_277_Collect__conv__if2,axiom,
% 0.18/0.47 ! [P_2: ( pname > $o ) > $o,A_7: pname > $o] :
% 0.18/0.47 ( ( ( P_2 @ A_7 )
% 0.18/0.47 => ( ( collect_pname_o
% 0.18/0.47 @ ^ [X_1: pname > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.18/0.47 = ( insert_pname_o @ A_7 @ bot_bot_pname_o_o ) ) )
% 0.18/0.47 & ( ~ ( P_2 @ A_7 )
% 0.18/0.47 => ( ( collect_pname_o
% 0.18/0.47 @ ^ [X_1: pname > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.18/0.47 = bot_bot_pname_o_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_278_Collect__conv__if2,axiom,
% 0.18/0.47 ! [P_2: ( hoare_1262092251_state > $o ) > $o,A_7: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( ( P_2 @ A_7 )
% 0.18/0.47 => ( ( collec313158217tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.18/0.47 = ( insert1042460334tate_o @ A_7 @ bot_bo1962689075te_o_o ) ) )
% 0.18/0.47 & ( ~ ( P_2 @ A_7 )
% 0.18/0.47 => ( ( collec313158217tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.18/0.47 = bot_bo1962689075te_o_o ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_279_singleton__conv,axiom,
% 0.18/0.47 ! [A_6: pname] :
% 0.18/0.47 ( ( collect_pname
% 0.18/0.47 @ ^ [X_1: pname] : ( X_1 = A_6 ) )
% 0.18/0.47 = ( insert_pname @ A_6 @ bot_bot_pname_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_280_singleton__conv,axiom,
% 0.18/0.47 ! [A_6: hoare_1262092251_state] :
% 0.18/0.47 ( ( collec1121927558_state
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state] : ( X_1 = A_6 ) )
% 0.18/0.47 = ( insert81609953_state @ A_6 @ bot_bo113204042tate_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_281_singleton__conv,axiom,
% 0.18/0.47 ! [A_6: pname > $o] :
% 0.18/0.47 ( ( collect_pname_o
% 0.18/0.47 @ ^ [X_1: pname > $o] : ( X_1 = A_6 ) )
% 0.18/0.47 = ( insert_pname_o @ A_6 @ bot_bot_pname_o_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_282_singleton__conv,axiom,
% 0.18/0.47 ! [A_6: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( collec313158217tate_o
% 0.18/0.47 @ ^ [X_1: hoare_1262092251_state > $o] : ( X_1 = A_6 ) )
% 0.18/0.47 = ( insert1042460334tate_o @ A_6 @ bot_bo1962689075te_o_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_283_singleton__conv2,axiom,
% 0.18/0.47 ! [A_5: pname] :
% 0.18/0.47 ( ( collect_pname @ ( fequal_pname @ A_5 ) )
% 0.18/0.47 = ( insert_pname @ A_5 @ bot_bot_pname_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_284_singleton__conv2,axiom,
% 0.18/0.47 ! [A_5: hoare_1262092251_state] :
% 0.18/0.47 ( ( collec1121927558_state @ ( fequal1925511196_state @ A_5 ) )
% 0.18/0.47 = ( insert81609953_state @ A_5 @ bot_bo113204042tate_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_285_singleton__conv2,axiom,
% 0.18/0.47 ! [A_5: pname > $o] :
% 0.18/0.47 ( ( collect_pname_o @ ( fequal_pname_o @ A_5 ) )
% 0.18/0.47 = ( insert_pname_o @ A_5 @ bot_bot_pname_o_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_286_singleton__conv2,axiom,
% 0.18/0.47 ! [A_5: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( collec313158217tate_o @ ( fequal1529404211tate_o @ A_5 ) )
% 0.18/0.47 = ( insert1042460334tate_o @ A_5 @ bot_bo1962689075te_o_o ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_287_MGF__lemma1,axiom,
% 0.18/0.47 ! [C_1: com,G: hoare_1262092251_state > $o] :
% 0.18/0.47 ( hoare_1821564147gleton
% 0.18/0.47 => ( ! [X_1: pname] :
% 0.18/0.47 ( ( member_pname @ X_1 @ ( dom_pname_com @ body ) )
% 0.18/0.47 => ( hoare_930741239_state @ G @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ X_1 ) ) @ bot_bo113204042tate_o ) ) )
% 0.18/0.47 => ( ( wt @ C_1 )
% 0.18/0.47 => ( hoare_930741239_state @ G @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ C_1 ) @ bot_bo113204042tate_o ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_288_WT__bodiesD,axiom,
% 0.18/0.47 ! [Pn_1: pname,B_3: com] :
% 0.18/0.47 ( wT_bodies
% 0.18/0.47 => ( ( ( body @ Pn_1 )
% 0.18/0.47 = ( some_com @ B_3 ) )
% 0.18/0.47 => ( wt @ B_3 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_289_imageE,axiom,
% 0.18/0.47 ! [B_2: hoare_1262092251_state,F_3: pname > hoare_1262092251_state,A_4: pname > $o] :
% 0.18/0.47 ( ( member5164104_state @ B_2 @ ( image_669833818_state @ F_3 @ A_4 ) )
% 0.18/0.47 => ~ ! [X_1: pname] :
% 0.18/0.47 ( ( B_2
% 0.18/0.47 = ( F_3 @ X_1 ) )
% 0.18/0.47 => ~ ( member_pname @ X_1 @ A_4 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_290_finite__subset__induct,axiom,
% 0.18/0.47 ! [P_1: ( pname > $o ) > $o,A_2: pname > $o,F_1: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ F_1 )
% 0.18/0.47 => ( ( ord_less_eq_pname_o @ F_1 @ A_2 )
% 0.18/0.47 => ( ( P_1 @ bot_bot_pname_o )
% 0.18/0.47 => ( ! [A_3: pname,F_2: pname > $o] :
% 0.18/0.47 ( ( finite_finite_pname @ F_2 )
% 0.18/0.47 => ( ( member_pname @ A_3 @ A_2 )
% 0.18/0.47 => ( ~ ( member_pname @ A_3 @ F_2 )
% 0.18/0.47 => ( ( P_1 @ F_2 )
% 0.18/0.47 => ( P_1 @ ( insert_pname @ A_3 @ F_2 ) ) ) ) ) )
% 0.18/0.47 => ( P_1 @ F_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_291_finite__subset__induct,axiom,
% 0.18/0.47 ! [P_1: ( hoare_1262092251_state > $o ) > $o,A_2: hoare_1262092251_state > $o,F_1: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ F_1 )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ F_1 @ A_2 )
% 0.18/0.47 => ( ( P_1 @ bot_bo113204042tate_o )
% 0.18/0.47 => ( ! [A_3: hoare_1262092251_state,F_2: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ F_2 )
% 0.18/0.47 => ( ( member5164104_state @ A_3 @ A_2 )
% 0.18/0.47 => ( ~ ( member5164104_state @ A_3 @ F_2 )
% 0.18/0.47 => ( ( P_1 @ F_2 )
% 0.18/0.47 => ( P_1 @ ( insert81609953_state @ A_3 @ F_2 ) ) ) ) ) )
% 0.18/0.47 => ( P_1 @ F_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_292_finite__subset__induct,axiom,
% 0.18/0.47 ! [P_1: ( ( pname > $o ) > $o ) > $o,A_2: ( pname > $o ) > $o,F_1: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ F_1 )
% 0.18/0.47 => ( ( ord_le1205211808me_o_o @ F_1 @ A_2 )
% 0.18/0.47 => ( ( P_1 @ bot_bot_pname_o_o )
% 0.18/0.47 => ( ! [A_3: pname > $o,F_2: ( pname > $o ) > $o] :
% 0.18/0.47 ( ( finite297249702name_o @ F_2 )
% 0.18/0.47 => ( ( member_pname_o @ A_3 @ A_2 )
% 0.18/0.47 => ( ~ ( member_pname_o @ A_3 @ F_2 )
% 0.18/0.47 => ( ( P_1 @ F_2 )
% 0.18/0.47 => ( P_1 @ ( insert_pname_o @ A_3 @ F_2 ) ) ) ) ) )
% 0.18/0.47 => ( P_1 @ F_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_293_finite__subset__induct,axiom,
% 0.18/0.47 ! [P_1: ( ( hoare_1262092251_state > $o ) > $o ) > $o,A_2: ( hoare_1262092251_state > $o ) > $o,F_1: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ F_1 )
% 0.18/0.47 => ( ( ord_le2012720639te_o_o @ F_1 @ A_2 )
% 0.18/0.47 => ( ( P_1 @ bot_bo1962689075te_o_o )
% 0.18/0.47 => ( ! [A_3: hoare_1262092251_state > $o,F_2: ( hoare_1262092251_state > $o ) > $o] :
% 0.18/0.47 ( ( finite1423311111tate_o @ F_2 )
% 0.18/0.47 => ( ( member907417095tate_o @ A_3 @ A_2 )
% 0.18/0.47 => ( ~ ( member907417095tate_o @ A_3 @ F_2 )
% 0.18/0.47 => ( ( P_1 @ F_2 )
% 0.18/0.47 => ( P_1 @ ( insert1042460334tate_o @ A_3 @ F_2 ) ) ) ) ) )
% 0.18/0.47 => ( P_1 @ F_1 ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_294_WTs__elim__cases_I7_J,axiom,
% 0.18/0.47 ! [P: pname] :
% 0.18/0.47 ( ( wt @ ( body_1 @ P ) )
% 0.18/0.47 => ~ ! [Y_1: com] :
% 0.18/0.47 ( ( body @ P )
% 0.18/0.47 != ( some_com @ Y_1 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_295_subsetI,axiom,
% 0.18/0.47 ! [B_1: pname > $o,A_1: pname > $o] :
% 0.18/0.47 ( ! [X_1: pname] :
% 0.18/0.47 ( ( member_pname @ X_1 @ A_1 )
% 0.18/0.47 => ( member_pname @ X_1 @ B_1 ) )
% 0.18/0.47 => ( ord_less_eq_pname_o @ A_1 @ B_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_296_subsetI,axiom,
% 0.18/0.47 ! [B_1: hoare_1262092251_state > $o,A_1: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ! [X_1: hoare_1262092251_state] :
% 0.18/0.47 ( ( member5164104_state @ X_1 @ A_1 )
% 0.18/0.47 => ( member5164104_state @ X_1 @ B_1 ) )
% 0.18/0.47 => ( ord_le870406270tate_o @ A_1 @ B_1 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_297_finite__subset__image,axiom,
% 0.18/0.47 ! [F: pname > hoare_1262092251_state,A: pname > $o,B: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( finite1178804552_state @ B )
% 0.18/0.47 => ( ( ord_le870406270tate_o @ B @ ( image_669833818_state @ F @ A ) )
% 0.18/0.47 => ? [C: pname > $o] :
% 0.18/0.47 ( ( ord_less_eq_pname_o @ C @ A )
% 0.18/0.47 & ( finite_finite_pname @ C )
% 0.18/0.47 & ( B
% 0.18/0.47 = ( image_669833818_state @ F @ C ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_298_finite__dom__body,axiom,
% 0.18/0.47 finite_finite_pname @ ( dom_pname_com @ body ) ).
% 0.18/0.47
% 0.18/0.47 thf(fact_299_com_Osimps_I6_J,axiom,
% 0.18/0.47 ! [Pname_1: pname,Pname: pname] :
% 0.18/0.47 ( ( ( body_1 @ Pname_1 )
% 0.18/0.47 = ( body_1 @ Pname ) )
% 0.18/0.47 <=> ( Pname_1 = Pname ) ) ).
% 0.18/0.47
% 0.18/0.47 %----Helper facts (8)
% 0.18/0.47 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 0.18/0.47 ! [X: pname,Y: pname] :
% 0.18/0.47 ( ~ ( fequal_pname @ X @ Y )
% 0.18/0.47 | ( X = Y ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 0.18/0.47 ! [X: pname,Y: pname] :
% 0.18/0.47 ( ( X != Y )
% 0.18/0.47 | ( fequal_pname @ X @ Y ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.18/0.47 ! [X: pname > $o,Y: pname > $o] :
% 0.18/0.47 ( ~ ( fequal_pname_o @ X @ Y )
% 0.18/0.47 | ( X = Y ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.18/0.47 ! [X: pname > $o,Y: pname > $o] :
% 0.18/0.47 ( ( X != Y )
% 0.18/0.47 | ( fequal_pname_o @ X @ Y ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com,axiom,
% 0.18/0.47 ! [X: hoare_1262092251_state,Y: hoare_1262092251_state] :
% 0.18/0.47 ( ~ ( fequal1925511196_state @ X @ Y )
% 0.18/0.47 | ( X = Y ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com,axiom,
% 0.18/0.47 ! [X: hoare_1262092251_state,Y: hoare_1262092251_state] :
% 0.18/0.47 ( ( X != Y )
% 0.18/0.47 | ( fequal1925511196_state @ X @ Y ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It,axiom,
% 0.18/0.47 ! [X: hoare_1262092251_state > $o,Y: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ~ ( fequal1529404211tate_o @ X @ Y )
% 0.18/0.47 | ( X = Y ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It,axiom,
% 0.18/0.47 ! [X: hoare_1262092251_state > $o,Y: hoare_1262092251_state > $o] :
% 0.18/0.47 ( ( X != Y )
% 0.18/0.47 | ( fequal1529404211tate_o @ X @ Y ) ) ).
% 0.18/0.47
% 0.18/0.47 %----Conjectures (8)
% 0.18/0.47 thf(conj_0,hypothesis,
% 0.18/0.47 hoare_1821564147gleton ).
% 0.18/0.47
% 0.18/0.47 thf(conj_1,hypothesis,
% 0.18/0.47 wT_bodies ).
% 0.18/0.47
% 0.18/0.47 thf(conj_2,hypothesis,
% 0.18/0.47 finite1178804552_state @ fa ).
% 0.18/0.47
% 0.18/0.47 thf(conj_3,hypothesis,
% 0.18/0.47 ~ ( member5164104_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) ).
% 0.18/0.47
% 0.18/0.47 thf(conj_4,hypothesis,
% 0.18/0.47 ( ord_le870406270tate_o @ fa
% 0.18/0.47 @ ( image_669833818_state
% 0.18/0.47 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 0.18/0.47 @ ( dom_pname_com @ body ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(conj_5,hypothesis,
% 0.18/0.47 ( ( body @ pn )
% 0.18/0.47 = ( some_com @ y ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(conj_6,hypothesis,
% 0.18/0.47 ( hoare_930741239_state
% 0.18/0.47 @ ( image_669833818_state
% 0.18/0.47 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.18/0.47 @ ( dom_pname_com @ body ) )
% 0.18/0.47 @ fa ) ).
% 0.18/0.47
% 0.18/0.47 thf(conj_7,conjecture,
% 0.18/0.47 ( hoare_930741239_state
% 0.18/0.47 @ ( image_669833818_state
% 0.18/0.47 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.18/0.47 @ ( dom_pname_com @ body ) )
% 0.18/0.47 @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ) ).
% 0.18/0.47
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 ------------------------
% 3.27/1.75 ---- Embedded in THF ---
% 3.27/1.75 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.27/1.75 %%% Generated on Tue Feb 24 13:41:00 EST 2026
% 3.27/1.75 %%% using '$$dhol' embedding, version 1.3.0.
% 3.27/1.75 %%% Logic specification used:
% 3.27/1.75 %%% thf(spec, logic, $$dhol).
% 3.27/1.75
% 3.27/1.75 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2DTF3501.p
% See solution above
% 3.27/1.76 ------------------------
% 3.45/1.80 ---- Cleaned THF ---
% 3.45/1.80 thf(ty_ty_tc__Com__Ocom,type,
% 3.45/1.80 com: $tType ).
% 3.45/1.80
% 3.45/1.80 thf(ty_ty_tc__Com__Opname,type,
% 3.45/1.80 pname: $tType ).
% 3.45/1.80
% 3.45/1.80 thf(ty_ty_tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 3.45/1.80 hoare_1262092251_state: $tType ).
% 3.45/1.80
% 3.45/1.80 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 3.45/1.80 option_com: $tType ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Com_OWT,type,
% 3.45/1.80 wt: com > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Com_OWT__bodies,type,
% 3.45/1.80 wT_bodies: $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Com_Obody,type,
% 3.45/1.80 body: pname > option_com ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Com_Ocom_OBODY,type,
% 3.45/1.80 body_1: pname > com ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo,type,
% 3.45/1.80 finite1648353812_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbq,type,
% 3.45/1.80 finite734360985_o_o_o: ( ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.45/1.80 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Ot,type,
% 3.45/1.80 finite1303896758te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.45/1.80 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_,type,
% 3.45/1.80 finite1423311111tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 3.45/1.80 finite_finite_pname: ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__C,type,
% 3.45/1.80 finite1178804552_state: ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_OMGT,type,
% 3.45/1.80 hoare_Mirabelle_MGT: com > hoare_1262092251_state ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ohoare__derivs_000tc__Com__Ostate,type,
% 3.45/1.80 hoare_930741239_state: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ostate__not__singleton,type,
% 3.45/1.80 hoare_1821564147gleton: $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Map_Odom_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Ocom,type,
% 3.45/1.80 dom_pname_o_com: ( ( pname > $o ) > option_com ) > ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Map_Odom_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__O,type,
% 3.45/1.80 dom_Ho1489634536_o_com: ( ( hoare_1262092251_state > $o ) > option_com ) > ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,
% 3.45/1.80 dom_pname_com: ( pname > option_com ) > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Option_Ooption_OSome_000tc__Com__Ocom,type,
% 3.45/1.80 some_com: com > option_com ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 3.45/1.80 the_com: option_com > com ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo,type,
% 3.45/1.80 bot_bot_pname_o_o_o: ( ( pname > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Hoare____Mirabelle____g,type,
% 3.45/1.80 bot_bo388435036_o_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.45/1.80 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsb,type,
% 3.45/1.80 bot_bo1962689075te_o_o: ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.45/1.80 bot_bot_pname_o: pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__O,type,
% 3.45/1.80 bot_bo113204042tate_o: hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J,type,
% 3.45/1.80 ord_le1828183645_o_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Hoare____Mirabelle,type,
% 3.45/1.80 ord_le1891858320_o_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 3.45/1.80 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____gh,type,
% 3.45/1.80 ord_le2012720639te_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.45/1.80 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____ghhkfsbq,type,
% 3.45/1.80 ord_le870406270tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 3.45/1.80 collect_pname_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otr,type,
% 3.45/1.80 collec101077467_o_o_o: ( ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.45/1.80 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_I,type,
% 3.45/1.80 collec341954548te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.45/1.80 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Co,type,
% 3.45/1.80 collec313158217tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 3.45/1.80 collect_pname: ( pname > $o ) > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 3.45/1.80 collec1121927558_state: ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 3.45/1.80 image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Hoare____Mir,type,
% 3.45/1.80 image_1036078444_state: ( ( ( pname > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( pname > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc,type,
% 3.45/1.80 image_893364936_pname: ( ( ( hoare_1262092251_state > $o ) > $o ) > pname ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc_001,type,
% 3.45/1.80 image_165349207_state: ( ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 3.45/1.80 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____ghh,type,
% 3.45/1.80 image_1476171975_state: ( ( pname > $o ) > hoare_1262092251_state ) > ( ( pname > $o ) > $o ) > hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com_,type,
% 3.45/1.80 image_1820530197_pname: ( ( hoare_1262092251_state > $o ) > pname ) > ( ( hoare_1262092251_state > $o ) > $o ) > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__002,type,
% 3.45/1.80 image_234589002_state: ( ( hoare_1262092251_state > $o ) > hoare_1262092251_state ) > ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.45/1.80 image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Hoare____Mirabelle____ghhk,type,
% 3.45/1.80 image_827868872te_o_o: ( pname > ( hoare_1262092251_state > $o ) > $o ) > ( pname > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.45/1.80 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq,type,
% 3.45/1.80 image_518521461tate_o: ( pname > hoare_1262092251_state > $o ) > ( pname > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 3.45/1.80 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otri,type,
% 3.45/1.80 image_669833818_state: ( pname > hoare_1262092251_state ) > ( pname > $o ) > hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat,type,
% 3.45/1.80 image_333245000me_o_o: ( hoare_1262092251_state > ( pname > $o ) > $o ) > ( hoare_1262092251_state > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_003,type,
% 3.45/1.80 image_1731108951te_o_o: ( hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_004,type,
% 3.45/1.80 image_1320925383name_o: ( hoare_1262092251_state > pname > $o ) > ( hoare_1262092251_state > $o ) > ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_005,type,
% 3.45/1.80 image_1403668518tate_o: ( hoare_1262092251_state > hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_006,type,
% 3.45/1.80 image_202231862_pname: ( hoare_1262092251_state > pname ) > ( hoare_1262092251_state > $o ) > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.45/1.80 insert_pname_o_o: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It,type,
% 3.45/1.80 insert1691644879te_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.45/1.80 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com,type,
% 3.45/1.80 insert1042460334tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 3.45/1.80 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Osta,type,
% 3.45/1.80 insert81609953_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.45/1.80 fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 3.45/1.80 fequal1529404211tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_fequal_000tc__Com__Opname,type,
% 3.45/1.80 fequal_pname: pname > pname > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 3.45/1.80 fequal1925511196_state: hoare_1262092251_state > hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.45/1.80 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 3.45/1.80 member907417095tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_member_000tc__Com__Opname,type,
% 3.45/1.80 member_pname: pname > ( pname > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_c_member_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 3.45/1.80 member5164104_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_v_Fa,type,
% 3.45/1.80 fa: hoare_1262092251_state > $o ).
% 3.45/1.80
% 3.45/1.80 thf(sy_v_pn,type,
% 3.45/1.80 pn: pname ).
% 3.45/1.80
% 3.45/1.80 thf(sy_v_y,type,
% 3.45/1.80 y: com ).
% 3.45/1.80
% 3.45/1.80 thf(fact_0_empty,axiom,
% 3.45/1.80 ! [G: hoare_1262092251_state > $o] : ( hoare_930741239_state @ G @ bot_bo113204042tate_o ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_1_asm,axiom,
% 3.45/1.80 ! [Ts_6: hoare_1262092251_state > $o,G_8: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( ord_le870406270tate_o @ Ts_6 @ G_8 )
% 3.45/1.80 => ( hoare_930741239_state @ G_8 @ Ts_6 ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_2_weaken,axiom,
% 3.45/1.80 ! [Ts_5: hoare_1262092251_state > $o,G_7: hoare_1262092251_state > $o,Ts_4: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( hoare_930741239_state @ G_7 @ Ts_4 )
% 3.45/1.80 => ( ( ord_le870406270tate_o @ Ts_5 @ Ts_4 )
% 3.45/1.80 => ( hoare_930741239_state @ G_7 @ Ts_5 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_3_thin,axiom,
% 3.45/1.80 ! [G_6: hoare_1262092251_state > $o,G_5: hoare_1262092251_state > $o,Ts_3: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( hoare_930741239_state @ G_5 @ Ts_3 )
% 3.45/1.80 => ( ( ord_le870406270tate_o @ G_5 @ G_6 )
% 3.45/1.80 => ( hoare_930741239_state @ G_6 @ Ts_3 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_4_cut,axiom,
% 3.45/1.80 ! [G_4: hoare_1262092251_state > $o,G_3: hoare_1262092251_state > $o,Ts_2: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( hoare_930741239_state @ G_3 @ Ts_2 )
% 3.45/1.80 => ( ( hoare_930741239_state @ G_4 @ G_3 )
% 3.45/1.80 => ( hoare_930741239_state @ G_4 @ Ts_2 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_5_hoare__derivs_Oinsert,axiom,
% 3.45/1.80 ! [Ts_1: hoare_1262092251_state > $o,G_2: hoare_1262092251_state > $o,T_1: hoare_1262092251_state] :
% 3.45/1.80 ( ( hoare_930741239_state @ G_2 @ ( insert81609953_state @ T_1 @ bot_bo113204042tate_o ) )
% 3.45/1.80 => ( ( hoare_930741239_state @ G_2 @ Ts_1 )
% 3.45/1.80 => ( hoare_930741239_state @ G_2 @ ( insert81609953_state @ T_1 @ Ts_1 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_6_derivs__insertD,axiom,
% 3.45/1.80 ! [G_1: hoare_1262092251_state > $o,T: hoare_1262092251_state,Ts: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( hoare_930741239_state @ G_1 @ ( insert81609953_state @ T @ Ts ) )
% 3.45/1.80 => ( ( hoare_930741239_state @ G_1 @ ( insert81609953_state @ T @ bot_bo113204042tate_o ) )
% 3.45/1.80 & ( hoare_930741239_state @ G_1 @ Ts ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_7_MGT__BodyN,axiom,
% 3.45/1.80 ! [Pn_1: pname,G: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( hoare_930741239_state @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ G ) @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn_1 ) ) ) @ bot_bo113204042tate_o ) )
% 3.45/1.80 => ( hoare_930741239_state @ G @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ bot_bo113204042tate_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_8_finite__Collect__subsets,axiom,
% 3.45/1.80 ! [A_77: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ A_77 )
% 3.45/1.80 => ( finite297249702name_o
% 3.45/1.80 @ ( collect_pname_o
% 3.45/1.80 @ ^ [B_41: pname > $o] : ( ord_less_eq_pname_o @ B_41 @ A_77 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_9_finite__Collect__subsets,axiom,
% 3.45/1.80 ! [A_77: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ A_77 )
% 3.45/1.80 => ( finite1423311111tate_o
% 3.45/1.80 @ ( collec313158217tate_o
% 3.45/1.80 @ ^ [B_41: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ B_41 @ A_77 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_10_finite__Collect__subsets,axiom,
% 3.45/1.80 ! [A_77: ( ( pname > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1066544169me_o_o @ A_77 )
% 3.45/1.80 => ( finite1648353812_o_o_o
% 3.45/1.80 @ ( collect_pname_o_o_o
% 3.45/1.80 @ ^ [B_41: ( ( pname > $o ) > $o ) > $o] : ( ord_le1828183645_o_o_o @ B_41 @ A_77 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_11_finite__Collect__subsets,axiom,
% 3.45/1.80 ! [A_77: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1303896758te_o_o @ A_77 )
% 3.45/1.80 => ( finite734360985_o_o_o
% 3.45/1.80 @ ( collec101077467_o_o_o
% 3.45/1.80 @ ^ [B_41: ( ( hoare_1262092251_state > $o ) > $o ) > $o] : ( ord_le1891858320_o_o_o @ B_41 @ A_77 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_12_finite__Collect__subsets,axiom,
% 3.45/1.80 ! [A_77: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( finite1423311111tate_o @ A_77 )
% 3.45/1.80 => ( finite1303896758te_o_o
% 3.45/1.80 @ ( collec341954548te_o_o
% 3.45/1.80 @ ^ [B_41: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ B_41 @ A_77 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_13_finite__Collect__subsets,axiom,
% 3.45/1.80 ! [A_77: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( finite297249702name_o @ A_77 )
% 3.45/1.80 => ( finite1066544169me_o_o
% 3.45/1.80 @ ( collect_pname_o_o
% 3.45/1.80 @ ^ [B_41: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_41 @ A_77 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_14_finite__imageI,axiom,
% 3.45/1.80 ! [H: pname > hoare_1262092251_state,F_17: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ F_17 )
% 3.45/1.80 => ( finite1178804552_state @ ( image_669833818_state @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_15_finite__imageI,axiom,
% 3.45/1.80 ! [H: ( ( pname > $o ) > $o ) > pname,F_17: ( ( pname > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1066544169me_o_o @ F_17 )
% 3.45/1.80 => ( finite_finite_pname @ ( image_471733107_pname @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_16_finite__imageI,axiom,
% 3.45/1.80 ! [H: ( ( hoare_1262092251_state > $o ) > $o ) > pname,F_17: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1303896758te_o_o @ F_17 )
% 3.45/1.80 => ( finite_finite_pname @ ( image_893364936_pname @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_17_finite__imageI,axiom,
% 3.45/1.80 ! [H: ( hoare_1262092251_state > $o ) > pname,F_17: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( finite1423311111tate_o @ F_17 )
% 3.45/1.80 => ( finite_finite_pname @ ( image_1820530197_pname @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_18_finite__imageI,axiom,
% 3.45/1.80 ! [H: ( pname > $o ) > pname,F_17: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( finite297249702name_o @ F_17 )
% 3.45/1.80 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_19_finite__imageI,axiom,
% 3.45/1.80 ! [H: ( ( pname > $o ) > $o ) > hoare_1262092251_state,F_17: ( ( pname > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1066544169me_o_o @ F_17 )
% 3.45/1.80 => ( finite1178804552_state @ ( image_1036078444_state @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_20_finite__imageI,axiom,
% 3.45/1.80 ! [H: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,F_17: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1303896758te_o_o @ F_17 )
% 3.45/1.80 => ( finite1178804552_state @ ( image_165349207_state @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_21_finite__imageI,axiom,
% 3.45/1.80 ! [H: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,F_17: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( finite1423311111tate_o @ F_17 )
% 3.45/1.80 => ( finite1178804552_state @ ( image_234589002_state @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_22_finite__imageI,axiom,
% 3.45/1.80 ! [H: ( pname > $o ) > hoare_1262092251_state,F_17: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( finite297249702name_o @ F_17 )
% 3.45/1.80 => ( finite1178804552_state @ ( image_1476171975_state @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_23_finite__imageI,axiom,
% 3.45/1.80 ! [H: pname > ( pname > $o ) > $o,F_17: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ F_17 )
% 3.45/1.80 => ( finite1066544169me_o_o @ ( image_504089495me_o_o @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_24_finite__imageI,axiom,
% 3.45/1.80 ! [H: pname > ( hoare_1262092251_state > $o ) > $o,F_17: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ F_17 )
% 3.45/1.80 => ( finite1303896758te_o_o @ ( image_827868872te_o_o @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_25_finite__imageI,axiom,
% 3.45/1.80 ! [H: pname > hoare_1262092251_state > $o,F_17: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ F_17 )
% 3.45/1.80 => ( finite1423311111tate_o @ ( image_518521461tate_o @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_26_finite__imageI,axiom,
% 3.45/1.80 ! [H: pname > pname > $o,F_17: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ F_17 )
% 3.45/1.80 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_27_finite__imageI,axiom,
% 3.45/1.80 ! [H: hoare_1262092251_state > ( pname > $o ) > $o,F_17: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ F_17 )
% 3.45/1.80 => ( finite1066544169me_o_o @ ( image_333245000me_o_o @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_28_finite__imageI,axiom,
% 3.45/1.80 ! [H: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o,F_17: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ F_17 )
% 3.45/1.80 => ( finite1303896758te_o_o @ ( image_1731108951te_o_o @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_29_finite__imageI,axiom,
% 3.45/1.80 ! [H: hoare_1262092251_state > hoare_1262092251_state > $o,F_17: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ F_17 )
% 3.45/1.80 => ( finite1423311111tate_o @ ( image_1403668518tate_o @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_30_finite__imageI,axiom,
% 3.45/1.80 ! [H: hoare_1262092251_state > pname > $o,F_17: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ F_17 )
% 3.45/1.80 => ( finite297249702name_o @ ( image_1320925383name_o @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_31_finite__imageI,axiom,
% 3.45/1.80 ! [H: hoare_1262092251_state > pname,F_17: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ F_17 )
% 3.45/1.80 => ( finite_finite_pname @ ( image_202231862_pname @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_32_finite__imageI,axiom,
% 3.45/1.80 ! [H: pname > pname,F_17: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ F_17 )
% 3.45/1.80 => ( finite_finite_pname @ ( image_pname_pname @ H @ F_17 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_33_empty__subsetI,axiom,
% 3.45/1.80 ! [A_76: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ bot_bo113204042tate_o @ A_76 ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_34_empty__subsetI,axiom,
% 3.45/1.80 ! [A_76: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ bot_bot_pname_o_o @ A_76 ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_35_empty__subsetI,axiom,
% 3.45/1.80 ! [A_76: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ bot_bo1962689075te_o_o @ A_76 ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_36_empty__subsetI,axiom,
% 3.45/1.80 ! [A_76: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_76 ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_37_finite_OinsertI,axiom,
% 3.45/1.80 ! [A_75: hoare_1262092251_state,A_74: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ A_74 )
% 3.45/1.80 => ( finite1178804552_state @ ( insert81609953_state @ A_75 @ A_74 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_38_finite_OinsertI,axiom,
% 3.45/1.80 ! [A_75: pname,A_74: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ A_74 )
% 3.45/1.80 => ( finite_finite_pname @ ( insert_pname @ A_75 @ A_74 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_39_finite_OinsertI,axiom,
% 3.45/1.80 ! [A_75: ( pname > $o ) > $o,A_74: ( ( pname > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1066544169me_o_o @ A_74 )
% 3.45/1.80 => ( finite1066544169me_o_o @ ( insert_pname_o_o @ A_75 @ A_74 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_40_finite_OinsertI,axiom,
% 3.45/1.80 ! [A_75: ( hoare_1262092251_state > $o ) > $o,A_74: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1303896758te_o_o @ A_74 )
% 3.45/1.80 => ( finite1303896758te_o_o @ ( insert1691644879te_o_o @ A_75 @ A_74 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_41_finite_OinsertI,axiom,
% 3.45/1.80 ! [A_75: hoare_1262092251_state > $o,A_74: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( finite1423311111tate_o @ A_74 )
% 3.45/1.80 => ( finite1423311111tate_o @ ( insert1042460334tate_o @ A_75 @ A_74 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_42_finite_OinsertI,axiom,
% 3.45/1.80 ! [A_75: pname > $o,A_74: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( finite297249702name_o @ A_74 )
% 3.45/1.80 => ( finite297249702name_o @ ( insert_pname_o @ A_75 @ A_74 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_43_finite_OemptyI,axiom,
% 3.45/1.80 finite_finite_pname @ bot_bot_pname_o ).
% 3.45/1.80
% 3.45/1.80 thf(fact_44_finite_OemptyI,axiom,
% 3.45/1.80 finite1178804552_state @ bot_bo113204042tate_o ).
% 3.45/1.80
% 3.45/1.80 thf(fact_45_finite_OemptyI,axiom,
% 3.45/1.80 finite1066544169me_o_o @ bot_bot_pname_o_o_o ).
% 3.45/1.80
% 3.45/1.80 thf(fact_46_finite_OemptyI,axiom,
% 3.45/1.80 finite1303896758te_o_o @ bot_bo388435036_o_o_o ).
% 3.45/1.80
% 3.45/1.80 thf(fact_47_finite_OemptyI,axiom,
% 3.45/1.80 finite1423311111tate_o @ bot_bo1962689075te_o_o ).
% 3.45/1.80
% 3.45/1.80 thf(fact_48_finite_OemptyI,axiom,
% 3.45/1.80 finite297249702name_o @ bot_bot_pname_o_o ).
% 3.45/1.80
% 3.45/1.80 thf(fact_49_finite__Collect__conjI,axiom,
% 3.45/1.80 ! [Q_1: pname > $o,P_9: pname > $o] :
% 3.45/1.80 ( ( ( finite_finite_pname @ ( collect_pname @ P_9 ) )
% 3.45/1.80 | ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
% 3.45/1.80 => ( finite_finite_pname
% 3.45/1.80 @ ( collect_pname
% 3.45/1.80 @ ^ [X_1: pname] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_50_finite__Collect__conjI,axiom,
% 3.45/1.80 ! [Q_1: hoare_1262092251_state > $o,P_9: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( ( finite1178804552_state @ ( collec1121927558_state @ P_9 ) )
% 3.45/1.80 | ( finite1178804552_state @ ( collec1121927558_state @ Q_1 ) ) )
% 3.45/1.80 => ( finite1178804552_state
% 3.45/1.80 @ ( collec1121927558_state
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_51_finite__Collect__conjI,axiom,
% 3.45/1.80 ! [Q_1: ( ( pname > $o ) > $o ) > $o,P_9: ( ( pname > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( ( finite1066544169me_o_o @ ( collect_pname_o_o @ P_9 ) )
% 3.45/1.80 | ( finite1066544169me_o_o @ ( collect_pname_o_o @ Q_1 ) ) )
% 3.45/1.80 => ( finite1066544169me_o_o
% 3.45/1.80 @ ( collect_pname_o_o
% 3.45/1.80 @ ^ [X_1: ( pname > $o ) > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_52_finite__Collect__conjI,axiom,
% 3.45/1.80 ! [Q_1: ( ( hoare_1262092251_state > $o ) > $o ) > $o,P_9: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( ( finite1303896758te_o_o @ ( collec341954548te_o_o @ P_9 ) )
% 3.45/1.80 | ( finite1303896758te_o_o @ ( collec341954548te_o_o @ Q_1 ) ) )
% 3.45/1.80 => ( finite1303896758te_o_o
% 3.45/1.80 @ ( collec341954548te_o_o
% 3.45/1.80 @ ^ [X_1: ( hoare_1262092251_state > $o ) > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_53_finite__Collect__conjI,axiom,
% 3.45/1.80 ! [Q_1: ( hoare_1262092251_state > $o ) > $o,P_9: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( ( finite1423311111tate_o @ ( collec313158217tate_o @ P_9 ) )
% 3.45/1.80 | ( finite1423311111tate_o @ ( collec313158217tate_o @ Q_1 ) ) )
% 3.45/1.80 => ( finite1423311111tate_o
% 3.45/1.80 @ ( collec313158217tate_o
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_54_finite__Collect__conjI,axiom,
% 3.45/1.80 ! [Q_1: ( pname > $o ) > $o,P_9: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_9 ) )
% 3.45/1.80 | ( finite297249702name_o @ ( collect_pname_o @ Q_1 ) ) )
% 3.45/1.80 => ( finite297249702name_o
% 3.45/1.80 @ ( collect_pname_o
% 3.45/1.80 @ ^ [X_1: pname > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_55_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: hoare_1262092251_state,A_73: pname > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bot_pname_o )
% 3.45/1.80 => ( ( image_669833818_state
% 3.45/1.80 @ ^ [X_1: pname] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bo113204042tate_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bot_pname_o )
% 3.45/1.80 => ( ( image_669833818_state
% 3.45/1.80 @ ^ [X_1: pname] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert81609953_state @ C_8 @ bot_bo113204042tate_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_56_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: pname,A_73: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bo113204042tate_o )
% 3.45/1.80 => ( ( image_202231862_pname
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bot_pname_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bo113204042tate_o )
% 3.45/1.80 => ( ( image_202231862_pname
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_57_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: pname > $o,A_73: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bo113204042tate_o )
% 3.45/1.80 => ( ( image_1320925383name_o
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bot_pname_o_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bo113204042tate_o )
% 3.45/1.80 => ( ( image_1320925383name_o
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert_pname_o @ C_8 @ bot_bot_pname_o_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_58_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: hoare_1262092251_state > $o,A_73: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bo113204042tate_o )
% 3.45/1.80 => ( ( image_1403668518tate_o
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bo1962689075te_o_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bo113204042tate_o )
% 3.45/1.80 => ( ( image_1403668518tate_o
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert1042460334tate_o @ C_8 @ bot_bo1962689075te_o_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_59_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: pname > $o,A_73: pname > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bot_pname_o )
% 3.45/1.80 => ( ( image_pname_pname_o
% 3.45/1.80 @ ^ [X_1: pname] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bot_pname_o_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bot_pname_o )
% 3.45/1.80 => ( ( image_pname_pname_o
% 3.45/1.80 @ ^ [X_1: pname] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert_pname_o @ C_8 @ bot_bot_pname_o_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_60_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: hoare_1262092251_state > $o,A_73: pname > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bot_pname_o )
% 3.45/1.80 => ( ( image_518521461tate_o
% 3.45/1.80 @ ^ [X_1: pname] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bo1962689075te_o_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bot_pname_o )
% 3.45/1.80 => ( ( image_518521461tate_o
% 3.45/1.80 @ ^ [X_1: pname] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert1042460334tate_o @ C_8 @ bot_bo1962689075te_o_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_61_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: pname,A_73: pname > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bot_pname_o )
% 3.45/1.80 => ( ( image_pname_pname
% 3.45/1.80 @ ^ [X_1: pname] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bot_pname_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bot_pname_o )
% 3.45/1.80 => ( ( image_pname_pname
% 3.45/1.80 @ ^ [X_1: pname] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_62_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: hoare_1262092251_state,A_73: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bot_pname_o_o )
% 3.45/1.80 => ( ( image_1476171975_state
% 3.45/1.80 @ ^ [X_1: pname > $o] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bo113204042tate_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bot_pname_o_o )
% 3.45/1.80 => ( ( image_1476171975_state
% 3.45/1.80 @ ^ [X_1: pname > $o] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert81609953_state @ C_8 @ bot_bo113204042tate_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_63_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: hoare_1262092251_state,A_73: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bo1962689075te_o_o )
% 3.45/1.80 => ( ( image_234589002_state
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bo113204042tate_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bo1962689075te_o_o )
% 3.45/1.80 => ( ( image_234589002_state
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert81609953_state @ C_8 @ bot_bo113204042tate_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_64_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: pname,A_73: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bot_pname_o_o )
% 3.45/1.80 => ( ( image_pname_o_pname
% 3.45/1.80 @ ^ [X_1: pname > $o] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bot_pname_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bot_pname_o_o )
% 3.45/1.80 => ( ( image_pname_o_pname
% 3.45/1.80 @ ^ [X_1: pname > $o] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_65_image__constant__conv,axiom,
% 3.45/1.80 ! [C_8: pname,A_73: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( ( A_73 = bot_bo1962689075te_o_o )
% 3.45/1.80 => ( ( image_1820530197_pname
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = bot_bot_pname_o ) )
% 3.45/1.80 & ( ( A_73 != bot_bo1962689075te_o_o )
% 3.45/1.80 => ( ( image_1820530197_pname
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 3.45/1.80 @ A_73 )
% 3.45/1.80 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_66_image__constant,axiom,
% 3.45/1.80 ! [C_7: hoare_1262092251_state,X_18: pname,A_72: pname > $o] :
% 3.45/1.80 ( ( member_pname @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_669833818_state
% 3.45/1.80 @ ^ [X_1: pname] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert81609953_state @ C_7 @ bot_bo113204042tate_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_67_image__constant,axiom,
% 3.45/1.80 ! [C_7: pname,X_18: hoare_1262092251_state,A_72: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( member5164104_state @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_202231862_pname
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_68_image__constant,axiom,
% 3.45/1.80 ! [C_7: pname > $o,X_18: hoare_1262092251_state,A_72: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( member5164104_state @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_1320925383name_o
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert_pname_o @ C_7 @ bot_bot_pname_o_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_69_image__constant,axiom,
% 3.45/1.80 ! [C_7: hoare_1262092251_state > $o,X_18: hoare_1262092251_state,A_72: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( member5164104_state @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_1403668518tate_o
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert1042460334tate_o @ C_7 @ bot_bo1962689075te_o_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_70_image__constant,axiom,
% 3.45/1.80 ! [C_7: pname > $o,X_18: pname,A_72: pname > $o] :
% 3.45/1.80 ( ( member_pname @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_pname_pname_o
% 3.45/1.80 @ ^ [X_1: pname] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert_pname_o @ C_7 @ bot_bot_pname_o_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_71_image__constant,axiom,
% 3.45/1.80 ! [C_7: hoare_1262092251_state > $o,X_18: pname,A_72: pname > $o] :
% 3.45/1.80 ( ( member_pname @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_518521461tate_o
% 3.45/1.80 @ ^ [X_1: pname] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert1042460334tate_o @ C_7 @ bot_bo1962689075te_o_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_72_image__constant,axiom,
% 3.45/1.80 ! [C_7: pname,X_18: pname,A_72: pname > $o] :
% 3.45/1.80 ( ( member_pname @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_pname_pname
% 3.45/1.80 @ ^ [X_1: pname] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_73_image__constant,axiom,
% 3.45/1.80 ! [C_7: hoare_1262092251_state,X_18: pname > $o,A_72: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( member_pname_o @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_1476171975_state
% 3.45/1.80 @ ^ [X_1: pname > $o] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert81609953_state @ C_7 @ bot_bo113204042tate_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_74_image__constant,axiom,
% 3.45/1.80 ! [C_7: hoare_1262092251_state,X_18: hoare_1262092251_state > $o,A_72: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( member907417095tate_o @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_234589002_state
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state > $o] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert81609953_state @ C_7 @ bot_bo113204042tate_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_75_image__constant,axiom,
% 3.45/1.80 ! [C_7: pname,X_18: pname > $o,A_72: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( member_pname_o @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_pname_o_pname
% 3.45/1.80 @ ^ [X_1: pname > $o] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_76_image__constant,axiom,
% 3.45/1.80 ! [C_7: pname,X_18: hoare_1262092251_state > $o,A_72: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( member907417095tate_o @ X_18 @ A_72 )
% 3.45/1.80 => ( ( image_1820530197_pname
% 3.45/1.80 @ ^ [X_1: hoare_1262092251_state > $o] : C_7
% 3.45/1.80 @ A_72 )
% 3.45/1.80 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_77_insert__dom,axiom,
% 3.45/1.80 ! [F_16: pname > option_com,X_17: pname,Y_4: com] :
% 3.45/1.80 ( ( ( F_16 @ X_17 )
% 3.45/1.80 = ( some_com @ Y_4 ) )
% 3.45/1.80 => ( ( insert_pname @ X_17 @ ( dom_pname_com @ F_16 ) )
% 3.45/1.80 = ( dom_pname_com @ F_16 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_78_insert__dom,axiom,
% 3.45/1.80 ! [F_16: ( pname > $o ) > option_com,X_17: pname > $o,Y_4: com] :
% 3.45/1.80 ( ( ( F_16 @ X_17 )
% 3.45/1.80 = ( some_com @ Y_4 ) )
% 3.45/1.80 => ( ( insert_pname_o @ X_17 @ ( dom_pname_o_com @ F_16 ) )
% 3.45/1.80 = ( dom_pname_o_com @ F_16 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_79_insert__dom,axiom,
% 3.45/1.80 ! [F_16: ( hoare_1262092251_state > $o ) > option_com,X_17: hoare_1262092251_state > $o,Y_4: com] :
% 3.45/1.80 ( ( ( F_16 @ X_17 )
% 3.45/1.80 = ( some_com @ Y_4 ) )
% 3.45/1.80 => ( ( insert1042460334tate_o @ X_17 @ ( dom_Ho1489634536_o_com @ F_16 ) )
% 3.45/1.80 = ( dom_Ho1489634536_o_com @ F_16 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_80_finite__surj,axiom,
% 3.45/1.80 ! [B_40: hoare_1262092251_state > $o,F_15: pname > hoare_1262092251_state,A_71: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ A_71 )
% 3.45/1.80 => ( ( ord_le870406270tate_o @ B_40 @ ( image_669833818_state @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1178804552_state @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_81_finite__surj,axiom,
% 3.45/1.80 ! [B_40: pname > $o,F_15: ( ( pname > $o ) > $o ) > pname,A_71: ( ( pname > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1066544169me_o_o @ A_71 )
% 3.45/1.80 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_471733107_pname @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite_finite_pname @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_82_finite__surj,axiom,
% 3.45/1.80 ! [B_40: pname > $o,F_15: ( ( hoare_1262092251_state > $o ) > $o ) > pname,A_71: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1303896758te_o_o @ A_71 )
% 3.45/1.80 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_893364936_pname @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite_finite_pname @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_83_finite__surj,axiom,
% 3.45/1.80 ! [B_40: pname > $o,F_15: ( hoare_1262092251_state > $o ) > pname,A_71: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( finite1423311111tate_o @ A_71 )
% 3.45/1.80 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_1820530197_pname @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite_finite_pname @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_84_finite__surj,axiom,
% 3.45/1.80 ! [B_40: pname > $o,F_15: ( pname > $o ) > pname,A_71: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( finite297249702name_o @ A_71 )
% 3.45/1.80 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_pname_o_pname @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite_finite_pname @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_85_finite__surj,axiom,
% 3.45/1.80 ! [B_40: hoare_1262092251_state > $o,F_15: ( ( pname > $o ) > $o ) > hoare_1262092251_state,A_71: ( ( pname > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1066544169me_o_o @ A_71 )
% 3.45/1.80 => ( ( ord_le870406270tate_o @ B_40 @ ( image_1036078444_state @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1178804552_state @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_86_finite__surj,axiom,
% 3.45/1.80 ! [B_40: hoare_1262092251_state > $o,F_15: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,A_71: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 3.45/1.80 ( ( finite1303896758te_o_o @ A_71 )
% 3.45/1.80 => ( ( ord_le870406270tate_o @ B_40 @ ( image_165349207_state @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1178804552_state @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_87_finite__surj,axiom,
% 3.45/1.80 ! [B_40: hoare_1262092251_state > $o,F_15: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,A_71: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( finite1423311111tate_o @ A_71 )
% 3.45/1.80 => ( ( ord_le870406270tate_o @ B_40 @ ( image_234589002_state @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1178804552_state @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_88_finite__surj,axiom,
% 3.45/1.80 ! [B_40: hoare_1262092251_state > $o,F_15: ( pname > $o ) > hoare_1262092251_state,A_71: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( finite297249702name_o @ A_71 )
% 3.45/1.80 => ( ( ord_le870406270tate_o @ B_40 @ ( image_1476171975_state @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1178804552_state @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_89_finite__surj,axiom,
% 3.45/1.80 ! [B_40: ( ( pname > $o ) > $o ) > $o,F_15: pname > ( pname > $o ) > $o,A_71: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ A_71 )
% 3.45/1.80 => ( ( ord_le1828183645_o_o_o @ B_40 @ ( image_504089495me_o_o @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1066544169me_o_o @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_90_finite__surj,axiom,
% 3.45/1.80 ! [B_40: ( ( hoare_1262092251_state > $o ) > $o ) > $o,F_15: pname > ( hoare_1262092251_state > $o ) > $o,A_71: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ A_71 )
% 3.45/1.80 => ( ( ord_le1891858320_o_o_o @ B_40 @ ( image_827868872te_o_o @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1303896758te_o_o @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_91_finite__surj,axiom,
% 3.45/1.80 ! [B_40: pname > $o,F_15: pname > pname,A_71: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ A_71 )
% 3.45/1.80 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_pname_pname @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite_finite_pname @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_92_finite__surj,axiom,
% 3.45/1.80 ! [B_40: ( hoare_1262092251_state > $o ) > $o,F_15: pname > hoare_1262092251_state > $o,A_71: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ A_71 )
% 3.45/1.80 => ( ( ord_le2012720639te_o_o @ B_40 @ ( image_518521461tate_o @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1423311111tate_o @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_93_finite__surj,axiom,
% 3.45/1.80 ! [B_40: ( pname > $o ) > $o,F_15: pname > pname > $o,A_71: pname > $o] :
% 3.45/1.80 ( ( finite_finite_pname @ A_71 )
% 3.45/1.80 => ( ( ord_le1205211808me_o_o @ B_40 @ ( image_pname_pname_o @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite297249702name_o @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_94_finite__surj,axiom,
% 3.45/1.80 ! [B_40: ( ( pname > $o ) > $o ) > $o,F_15: hoare_1262092251_state > ( pname > $o ) > $o,A_71: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ A_71 )
% 3.45/1.80 => ( ( ord_le1828183645_o_o_o @ B_40 @ ( image_333245000me_o_o @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1066544169me_o_o @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_95_finite__surj,axiom,
% 3.45/1.80 ! [B_40: ( ( hoare_1262092251_state > $o ) > $o ) > $o,F_15: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o,A_71: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ A_71 )
% 3.45/1.80 => ( ( ord_le1891858320_o_o_o @ B_40 @ ( image_1731108951te_o_o @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1303896758te_o_o @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_96_finite__surj,axiom,
% 3.45/1.80 ! [B_40: pname > $o,F_15: hoare_1262092251_state > pname,A_71: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ A_71 )
% 3.45/1.80 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_202231862_pname @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite_finite_pname @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_97_finite__surj,axiom,
% 3.45/1.80 ! [B_40: ( hoare_1262092251_state > $o ) > $o,F_15: hoare_1262092251_state > hoare_1262092251_state > $o,A_71: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ A_71 )
% 3.45/1.80 => ( ( ord_le2012720639te_o_o @ B_40 @ ( image_1403668518tate_o @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite1423311111tate_o @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_98_finite__surj,axiom,
% 3.45/1.80 ! [B_40: ( pname > $o ) > $o,F_15: hoare_1262092251_state > pname > $o,A_71: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( finite1178804552_state @ A_71 )
% 3.45/1.80 => ( ( ord_le1205211808me_o_o @ B_40 @ ( image_1320925383name_o @ F_15 @ A_71 ) )
% 3.45/1.80 => ( finite297249702name_o @ B_40 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_99_subset__singletonD,axiom,
% 3.45/1.80 ! [A_70: hoare_1262092251_state > $o,X_16: hoare_1262092251_state] :
% 3.45/1.80 ( ( ord_le870406270tate_o @ A_70 @ ( insert81609953_state @ X_16 @ bot_bo113204042tate_o ) )
% 3.45/1.80 => ( ( A_70 = bot_bo113204042tate_o )
% 3.45/1.80 | ( A_70
% 3.45/1.80 = ( insert81609953_state @ X_16 @ bot_bo113204042tate_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_100_subset__singletonD,axiom,
% 3.45/1.80 ! [A_70: ( pname > $o ) > $o,X_16: pname > $o] :
% 3.45/1.80 ( ( ord_le1205211808me_o_o @ A_70 @ ( insert_pname_o @ X_16 @ bot_bot_pname_o_o ) )
% 3.45/1.80 => ( ( A_70 = bot_bot_pname_o_o )
% 3.45/1.80 | ( A_70
% 3.45/1.80 = ( insert_pname_o @ X_16 @ bot_bot_pname_o_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_101_subset__singletonD,axiom,
% 3.45/1.80 ! [A_70: ( hoare_1262092251_state > $o ) > $o,X_16: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( ord_le2012720639te_o_o @ A_70 @ ( insert1042460334tate_o @ X_16 @ bot_bo1962689075te_o_o ) )
% 3.45/1.80 => ( ( A_70 = bot_bo1962689075te_o_o )
% 3.45/1.80 | ( A_70
% 3.45/1.80 = ( insert1042460334tate_o @ X_16 @ bot_bo1962689075te_o_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_102_subset__singletonD,axiom,
% 3.45/1.80 ! [A_70: pname > $o,X_16: pname] :
% 3.45/1.80 ( ( ord_less_eq_pname_o @ A_70 @ ( insert_pname @ X_16 @ bot_bot_pname_o ) )
% 3.45/1.80 => ( ( A_70 = bot_bot_pname_o )
% 3.45/1.80 | ( A_70
% 3.45/1.80 = ( insert_pname @ X_16 @ bot_bot_pname_o ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_103_MGF,axiom,
% 3.45/1.80 ! [C_1: com] :
% 3.45/1.80 ( hoare_1821564147gleton
% 3.45/1.80 => ( wT_bodies
% 3.45/1.80 => ( ( wt @ C_1 )
% 3.45/1.80 => ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ C_1 ) @ bot_bo113204042tate_o ) ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_104_emptyE,axiom,
% 3.45/1.80 ! [A_69: hoare_1262092251_state] :
% 3.45/1.80 ~ ( member5164104_state @ A_69 @ bot_bo113204042tate_o ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_105_emptyE,axiom,
% 3.45/1.80 ! [A_69: pname > $o] :
% 3.45/1.80 ~ ( member_pname_o @ A_69 @ bot_bot_pname_o_o ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_106_emptyE,axiom,
% 3.45/1.80 ! [A_69: hoare_1262092251_state > $o] :
% 3.45/1.80 ~ ( member907417095tate_o @ A_69 @ bot_bo1962689075te_o_o ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_107_emptyE,axiom,
% 3.45/1.80 ! [A_69: pname] :
% 3.45/1.80 ~ ( member_pname @ A_69 @ bot_bot_pname_o ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_108_insertCI,axiom,
% 3.45/1.80 ! [B_39: hoare_1262092251_state,A_68: hoare_1262092251_state,B_38: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( ~ ( member5164104_state @ A_68 @ B_38 )
% 3.45/1.80 => ( A_68 = B_39 ) )
% 3.45/1.80 => ( member5164104_state @ A_68 @ ( insert81609953_state @ B_39 @ B_38 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_109_insertCI,axiom,
% 3.45/1.80 ! [B_39: pname > $o,A_68: pname > $o,B_38: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( ~ ( member_pname_o @ A_68 @ B_38 )
% 3.45/1.80 => ( A_68 = B_39 ) )
% 3.45/1.80 => ( member_pname_o @ A_68 @ ( insert_pname_o @ B_39 @ B_38 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_110_insertCI,axiom,
% 3.45/1.80 ! [B_39: hoare_1262092251_state > $o,A_68: hoare_1262092251_state > $o,B_38: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( ~ ( member907417095tate_o @ A_68 @ B_38 )
% 3.45/1.80 => ( A_68 = B_39 ) )
% 3.45/1.80 => ( member907417095tate_o @ A_68 @ ( insert1042460334tate_o @ B_39 @ B_38 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_111_insertCI,axiom,
% 3.45/1.80 ! [B_39: pname,A_68: pname,B_38: pname > $o] :
% 3.45/1.80 ( ( ~ ( member_pname @ A_68 @ B_38 )
% 3.45/1.80 => ( A_68 = B_39 ) )
% 3.45/1.80 => ( member_pname @ A_68 @ ( insert_pname @ B_39 @ B_38 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_112_insertE,axiom,
% 3.45/1.80 ! [A_67: hoare_1262092251_state,B_37: hoare_1262092251_state,A_66: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( member5164104_state @ A_67 @ ( insert81609953_state @ B_37 @ A_66 ) )
% 3.45/1.80 => ( ( A_67 != B_37 )
% 3.45/1.80 => ( member5164104_state @ A_67 @ A_66 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_113_insertE,axiom,
% 3.45/1.80 ! [A_67: pname > $o,B_37: pname > $o,A_66: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( member_pname_o @ A_67 @ ( insert_pname_o @ B_37 @ A_66 ) )
% 3.45/1.80 => ( ( A_67 != B_37 )
% 3.45/1.80 => ( member_pname_o @ A_67 @ A_66 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_114_insertE,axiom,
% 3.45/1.80 ! [A_67: hoare_1262092251_state > $o,B_37: hoare_1262092251_state > $o,A_66: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( member907417095tate_o @ A_67 @ ( insert1042460334tate_o @ B_37 @ A_66 ) )
% 3.45/1.80 => ( ( A_67 != B_37 )
% 3.45/1.80 => ( member907417095tate_o @ A_67 @ A_66 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_115_insertE,axiom,
% 3.45/1.80 ! [A_67: pname,B_37: pname,A_66: pname > $o] :
% 3.45/1.80 ( ( member_pname @ A_67 @ ( insert_pname @ B_37 @ A_66 ) )
% 3.45/1.80 => ( ( A_67 != B_37 )
% 3.45/1.80 => ( member_pname @ A_67 @ A_66 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_116_equalityI,axiom,
% 3.45/1.80 ! [A_65: hoare_1262092251_state > $o,B_36: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( ord_le870406270tate_o @ A_65 @ B_36 )
% 3.45/1.80 => ( ( ord_le870406270tate_o @ B_36 @ A_65 )
% 3.45/1.80 => ( A_65 = B_36 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_117_equalityI,axiom,
% 3.45/1.80 ! [A_65: ( pname > $o ) > $o,B_36: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( ord_le1205211808me_o_o @ A_65 @ B_36 )
% 3.45/1.80 => ( ( ord_le1205211808me_o_o @ B_36 @ A_65 )
% 3.45/1.80 => ( A_65 = B_36 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_118_equalityI,axiom,
% 3.45/1.80 ! [A_65: ( hoare_1262092251_state > $o ) > $o,B_36: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( ord_le2012720639te_o_o @ A_65 @ B_36 )
% 3.45/1.80 => ( ( ord_le2012720639te_o_o @ B_36 @ A_65 )
% 3.45/1.80 => ( A_65 = B_36 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_119_equalityI,axiom,
% 3.45/1.80 ! [A_65: pname > $o,B_36: pname > $o] :
% 3.45/1.80 ( ( ord_less_eq_pname_o @ A_65 @ B_36 )
% 3.45/1.80 => ( ( ord_less_eq_pname_o @ B_36 @ A_65 )
% 3.45/1.80 => ( A_65 = B_36 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_120_subsetD,axiom,
% 3.45/1.80 ! [C_6: hoare_1262092251_state,A_64: hoare_1262092251_state > $o,B_35: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( ord_le870406270tate_o @ A_64 @ B_35 )
% 3.45/1.80 => ( ( member5164104_state @ C_6 @ A_64 )
% 3.45/1.80 => ( member5164104_state @ C_6 @ B_35 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_121_subsetD,axiom,
% 3.45/1.80 ! [C_6: pname > $o,A_64: ( pname > $o ) > $o,B_35: ( pname > $o ) > $o] :
% 3.45/1.80 ( ( ord_le1205211808me_o_o @ A_64 @ B_35 )
% 3.45/1.80 => ( ( member_pname_o @ C_6 @ A_64 )
% 3.45/1.80 => ( member_pname_o @ C_6 @ B_35 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_122_subsetD,axiom,
% 3.45/1.80 ! [C_6: hoare_1262092251_state > $o,A_64: ( hoare_1262092251_state > $o ) > $o,B_35: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.80 ( ( ord_le2012720639te_o_o @ A_64 @ B_35 )
% 3.45/1.80 => ( ( member907417095tate_o @ C_6 @ A_64 )
% 3.45/1.80 => ( member907417095tate_o @ C_6 @ B_35 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_123_subsetD,axiom,
% 3.45/1.80 ! [C_6: pname,A_64: pname > $o,B_35: pname > $o] :
% 3.45/1.80 ( ( ord_less_eq_pname_o @ A_64 @ B_35 )
% 3.45/1.80 => ( ( member_pname @ C_6 @ A_64 )
% 3.45/1.80 => ( member_pname @ C_6 @ B_35 ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_124_image__eqI,axiom,
% 3.45/1.80 ! [A_63: hoare_1262092251_state > $o,B_34: pname > $o,F_14: hoare_1262092251_state > pname > $o,X_15: hoare_1262092251_state] :
% 3.45/1.80 ( ( B_34
% 3.45/1.80 = ( F_14 @ X_15 ) )
% 3.45/1.80 => ( ( member5164104_state @ X_15 @ A_63 )
% 3.45/1.80 => ( member_pname_o @ B_34 @ ( image_1320925383name_o @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_125_image__eqI,axiom,
% 3.45/1.80 ! [A_63: hoare_1262092251_state > $o,B_34: hoare_1262092251_state > $o,F_14: hoare_1262092251_state > hoare_1262092251_state > $o,X_15: hoare_1262092251_state] :
% 3.45/1.80 ( ( B_34
% 3.45/1.80 = ( F_14 @ X_15 ) )
% 3.45/1.80 => ( ( member5164104_state @ X_15 @ A_63 )
% 3.45/1.80 => ( member907417095tate_o @ B_34 @ ( image_1403668518tate_o @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_126_image__eqI,axiom,
% 3.45/1.80 ! [A_63: pname > $o,B_34: pname > $o,F_14: pname > pname > $o,X_15: pname] :
% 3.45/1.80 ( ( B_34
% 3.45/1.80 = ( F_14 @ X_15 ) )
% 3.45/1.80 => ( ( member_pname @ X_15 @ A_63 )
% 3.45/1.80 => ( member_pname_o @ B_34 @ ( image_pname_pname_o @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_127_image__eqI,axiom,
% 3.45/1.80 ! [A_63: pname > $o,B_34: hoare_1262092251_state > $o,F_14: pname > hoare_1262092251_state > $o,X_15: pname] :
% 3.45/1.80 ( ( B_34
% 3.45/1.80 = ( F_14 @ X_15 ) )
% 3.45/1.80 => ( ( member_pname @ X_15 @ A_63 )
% 3.45/1.80 => ( member907417095tate_o @ B_34 @ ( image_518521461tate_o @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_128_image__eqI,axiom,
% 3.45/1.80 ! [A_63: ( pname > $o ) > $o,B_34: hoare_1262092251_state,F_14: ( pname > $o ) > hoare_1262092251_state,X_15: pname > $o] :
% 3.45/1.80 ( ( B_34
% 3.45/1.80 = ( F_14 @ X_15 ) )
% 3.45/1.80 => ( ( member_pname_o @ X_15 @ A_63 )
% 3.45/1.80 => ( member5164104_state @ B_34 @ ( image_1476171975_state @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_129_image__eqI,axiom,
% 3.45/1.80 ! [A_63: ( hoare_1262092251_state > $o ) > $o,B_34: hoare_1262092251_state,F_14: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,X_15: hoare_1262092251_state > $o] :
% 3.45/1.80 ( ( B_34
% 3.45/1.80 = ( F_14 @ X_15 ) )
% 3.45/1.80 => ( ( member907417095tate_o @ X_15 @ A_63 )
% 3.45/1.80 => ( member5164104_state @ B_34 @ ( image_234589002_state @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_130_image__eqI,axiom,
% 3.45/1.80 ! [A_63: hoare_1262092251_state > $o,B_34: pname,F_14: hoare_1262092251_state > pname,X_15: hoare_1262092251_state] :
% 3.45/1.80 ( ( B_34
% 3.45/1.80 = ( F_14 @ X_15 ) )
% 3.45/1.80 => ( ( member5164104_state @ X_15 @ A_63 )
% 3.45/1.80 => ( member_pname @ B_34 @ ( image_202231862_pname @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.80
% 3.45/1.80 thf(fact_131_image__eqI,axiom,
% 3.45/1.80 ! [A_63: pname > $o,B_34: pname,F_14: pname > pname,X_15: pname] :
% 3.45/1.80 ( ( B_34
% 3.45/1.80 = ( F_14 @ X_15 ) )
% 3.45/1.80 => ( ( member_pname @ X_15 @ A_63 )
% 3.45/1.80 => ( member_pname @ B_34 @ ( image_pname_pname @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_132_image__eqI,axiom,
% 3.45/1.81 ! [A_63: ( pname > $o ) > $o,B_34: pname,F_14: ( pname > $o ) > pname,X_15: pname > $o] :
% 3.45/1.81 ( ( B_34
% 3.45/1.81 = ( F_14 @ X_15 ) )
% 3.45/1.81 => ( ( member_pname_o @ X_15 @ A_63 )
% 3.45/1.81 => ( member_pname @ B_34 @ ( image_pname_o_pname @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_133_image__eqI,axiom,
% 3.45/1.81 ! [A_63: ( hoare_1262092251_state > $o ) > $o,B_34: pname,F_14: ( hoare_1262092251_state > $o ) > pname,X_15: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( B_34
% 3.45/1.81 = ( F_14 @ X_15 ) )
% 3.45/1.81 => ( ( member907417095tate_o @ X_15 @ A_63 )
% 3.45/1.81 => ( member_pname @ B_34 @ ( image_1820530197_pname @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_134_image__eqI,axiom,
% 3.45/1.81 ! [A_63: pname > $o,B_34: hoare_1262092251_state,F_14: pname > hoare_1262092251_state,X_15: pname] :
% 3.45/1.81 ( ( B_34
% 3.45/1.81 = ( F_14 @ X_15 ) )
% 3.45/1.81 => ( ( member_pname @ X_15 @ A_63 )
% 3.45/1.81 => ( member5164104_state @ B_34 @ ( image_669833818_state @ F_14 @ A_63 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_135_equals0D,axiom,
% 3.45/1.81 ! [A_62: pname > $o,A_61: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( A_61 = bot_bot_pname_o_o )
% 3.45/1.81 => ~ ( member_pname_o @ A_62 @ A_61 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_136_equals0D,axiom,
% 3.45/1.81 ! [A_62: hoare_1262092251_state > $o,A_61: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( A_61 = bot_bo1962689075te_o_o )
% 3.45/1.81 => ~ ( member907417095tate_o @ A_62 @ A_61 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_137_equals0D,axiom,
% 3.45/1.81 ! [A_62: hoare_1262092251_state,A_61: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( A_61 = bot_bo113204042tate_o )
% 3.45/1.81 => ~ ( member5164104_state @ A_62 @ A_61 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_138_equals0D,axiom,
% 3.45/1.81 ! [A_62: pname,A_61: pname > $o] :
% 3.45/1.81 ( ( A_61 = bot_bot_pname_o )
% 3.45/1.81 => ~ ( member_pname @ A_62 @ A_61 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_139_Collect__empty__eq,axiom,
% 3.45/1.81 ! [P_8: ( ( pname > $o ) > $o ) > $o] :
% 3.45/1.81 ( ( ( collect_pname_o_o @ P_8 )
% 3.45/1.81 = bot_bot_pname_o_o_o )
% 3.45/1.81 <=> ! [X_1: ( pname > $o ) > $o] :
% 3.45/1.81 ~ ( P_8 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_140_Collect__empty__eq,axiom,
% 3.45/1.81 ! [P_8: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 3.45/1.81 ( ( ( collec341954548te_o_o @ P_8 )
% 3.45/1.81 = bot_bo388435036_o_o_o )
% 3.45/1.81 <=> ! [X_1: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ~ ( P_8 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_141_Collect__empty__eq,axiom,
% 3.45/1.81 ! [P_8: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( ( collec313158217tate_o @ P_8 )
% 3.45/1.81 = bot_bo1962689075te_o_o )
% 3.45/1.81 <=> ! [X_1: hoare_1262092251_state > $o] :
% 3.45/1.81 ~ ( P_8 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_142_Collect__empty__eq,axiom,
% 3.45/1.81 ! [P_8: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( ( collect_pname_o @ P_8 )
% 3.45/1.81 = bot_bot_pname_o_o )
% 3.45/1.81 <=> ! [X_1: pname > $o] :
% 3.45/1.81 ~ ( P_8 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_143_Collect__empty__eq,axiom,
% 3.45/1.81 ! [P_8: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ( collec1121927558_state @ P_8 )
% 3.45/1.81 = bot_bo113204042tate_o )
% 3.45/1.81 <=> ! [X_1: hoare_1262092251_state] :
% 3.45/1.81 ~ ( P_8 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_144_Collect__empty__eq,axiom,
% 3.45/1.81 ! [P_8: pname > $o] :
% 3.45/1.81 ( ( ( collect_pname @ P_8 )
% 3.45/1.81 = bot_bot_pname_o )
% 3.45/1.81 <=> ! [X_1: pname] :
% 3.45/1.81 ~ ( P_8 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_145_empty__iff,axiom,
% 3.45/1.81 ! [C_5: pname > $o] :
% 3.45/1.81 ~ ( member_pname_o @ C_5 @ bot_bot_pname_o_o ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_146_empty__iff,axiom,
% 3.45/1.81 ! [C_5: hoare_1262092251_state > $o] :
% 3.45/1.81 ~ ( member907417095tate_o @ C_5 @ bot_bo1962689075te_o_o ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_147_empty__iff,axiom,
% 3.45/1.81 ! [C_5: hoare_1262092251_state] :
% 3.45/1.81 ~ ( member5164104_state @ C_5 @ bot_bo113204042tate_o ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_148_empty__iff,axiom,
% 3.45/1.81 ! [C_5: pname] :
% 3.45/1.81 ~ ( member_pname @ C_5 @ bot_bot_pname_o ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_149_empty__Collect__eq,axiom,
% 3.45/1.81 ! [P_7: ( ( pname > $o ) > $o ) > $o] :
% 3.45/1.81 ( ( bot_bot_pname_o_o_o
% 3.45/1.81 = ( collect_pname_o_o @ P_7 ) )
% 3.45/1.81 <=> ! [X_1: ( pname > $o ) > $o] :
% 3.45/1.81 ~ ( P_7 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_150_empty__Collect__eq,axiom,
% 3.45/1.81 ! [P_7: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 3.45/1.81 ( ( bot_bo388435036_o_o_o
% 3.45/1.81 = ( collec341954548te_o_o @ P_7 ) )
% 3.45/1.81 <=> ! [X_1: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ~ ( P_7 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_151_empty__Collect__eq,axiom,
% 3.45/1.81 ! [P_7: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( bot_bo1962689075te_o_o
% 3.45/1.81 = ( collec313158217tate_o @ P_7 ) )
% 3.45/1.81 <=> ! [X_1: hoare_1262092251_state > $o] :
% 3.45/1.81 ~ ( P_7 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_152_empty__Collect__eq,axiom,
% 3.45/1.81 ! [P_7: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( bot_bot_pname_o_o
% 3.45/1.81 = ( collect_pname_o @ P_7 ) )
% 3.45/1.81 <=> ! [X_1: pname > $o] :
% 3.45/1.81 ~ ( P_7 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_153_empty__Collect__eq,axiom,
% 3.45/1.81 ! [P_7: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( bot_bo113204042tate_o
% 3.45/1.81 = ( collec1121927558_state @ P_7 ) )
% 3.45/1.81 <=> ! [X_1: hoare_1262092251_state] :
% 3.45/1.81 ~ ( P_7 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_154_empty__Collect__eq,axiom,
% 3.45/1.81 ! [P_7: pname > $o] :
% 3.45/1.81 ( ( bot_bot_pname_o
% 3.45/1.81 = ( collect_pname @ P_7 ) )
% 3.45/1.81 <=> ! [X_1: pname] :
% 3.45/1.81 ~ ( P_7 @ X_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_155_ex__in__conv,axiom,
% 3.45/1.81 ! [A_60: ( pname > $o ) > $o] :
% 3.45/1.81 ( ? [X_1: pname > $o] : ( member_pname_o @ X_1 @ A_60 )
% 3.45/1.81 <=> ( A_60 != bot_bot_pname_o_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_156_ex__in__conv,axiom,
% 3.45/1.81 ! [A_60: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ? [X_1: hoare_1262092251_state > $o] : ( member907417095tate_o @ X_1 @ A_60 )
% 3.45/1.81 <=> ( A_60 != bot_bo1962689075te_o_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_157_ex__in__conv,axiom,
% 3.45/1.81 ! [A_60: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ? [X_1: hoare_1262092251_state] : ( member5164104_state @ X_1 @ A_60 )
% 3.45/1.81 <=> ( A_60 != bot_bo113204042tate_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_158_ex__in__conv,axiom,
% 3.45/1.81 ! [A_60: pname > $o] :
% 3.45/1.81 ( ? [X_1: pname] : ( member_pname @ X_1 @ A_60 )
% 3.45/1.81 <=> ( A_60 != bot_bot_pname_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_159_all__not__in__conv,axiom,
% 3.45/1.81 ! [A_59: ( pname > $o ) > $o] :
% 3.45/1.81 ( ! [X_1: pname > $o] :
% 3.45/1.81 ~ ( member_pname_o @ X_1 @ A_59 )
% 3.45/1.81 <=> ( A_59 = bot_bot_pname_o_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_160_all__not__in__conv,axiom,
% 3.45/1.81 ! [A_59: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ! [X_1: hoare_1262092251_state > $o] :
% 3.45/1.81 ~ ( member907417095tate_o @ X_1 @ A_59 )
% 3.45/1.81 <=> ( A_59 = bot_bo1962689075te_o_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_161_all__not__in__conv,axiom,
% 3.45/1.81 ! [A_59: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ! [X_1: hoare_1262092251_state] :
% 3.45/1.81 ~ ( member5164104_state @ X_1 @ A_59 )
% 3.45/1.81 <=> ( A_59 = bot_bo113204042tate_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_162_all__not__in__conv,axiom,
% 3.45/1.81 ! [A_59: pname > $o] :
% 3.45/1.81 ( ! [X_1: pname] :
% 3.45/1.81 ~ ( member_pname @ X_1 @ A_59 )
% 3.45/1.81 <=> ( A_59 = bot_bot_pname_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_163_empty__def,axiom,
% 3.45/1.81 ( bot_bo388435036_o_o_o
% 3.45/1.81 = ( collec341954548te_o_o
% 3.45/1.81 @ ^ [X_1: ( hoare_1262092251_state > $o ) > $o] : $false ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_164_empty__def,axiom,
% 3.45/1.81 ( bot_bo1962689075te_o_o
% 3.45/1.81 = ( collec313158217tate_o
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state > $o] : $false ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_165_empty__def,axiom,
% 3.45/1.81 ( bot_bot_pname_o_o
% 3.45/1.81 = ( collect_pname_o
% 3.45/1.81 @ ^ [X_1: pname > $o] : $false ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_166_empty__def,axiom,
% 3.45/1.81 ( bot_bo113204042tate_o
% 3.45/1.81 = ( collec1121927558_state
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state] : $false ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_167_empty__def,axiom,
% 3.45/1.81 ( bot_bot_pname_o
% 3.45/1.81 = ( collect_pname
% 3.45/1.81 @ ^ [X_1: pname] : $false ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_168_insert__absorb,axiom,
% 3.45/1.81 ! [A_58: pname,A_57: pname > $o] :
% 3.45/1.81 ( ( member_pname @ A_58 @ A_57 )
% 3.45/1.81 => ( ( insert_pname @ A_58 @ A_57 )
% 3.45/1.81 = A_57 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_169_insert__absorb,axiom,
% 3.45/1.81 ! [A_58: hoare_1262092251_state,A_57: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( member5164104_state @ A_58 @ A_57 )
% 3.45/1.81 => ( ( insert81609953_state @ A_58 @ A_57 )
% 3.45/1.81 = A_57 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_170_insertI2,axiom,
% 3.45/1.81 ! [B_33: pname,A_56: pname,B_32: pname > $o] :
% 3.45/1.81 ( ( member_pname @ A_56 @ B_32 )
% 3.45/1.81 => ( member_pname @ A_56 @ ( insert_pname @ B_33 @ B_32 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_171_insertI2,axiom,
% 3.45/1.81 ! [B_33: hoare_1262092251_state,A_56: hoare_1262092251_state,B_32: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( member5164104_state @ A_56 @ B_32 )
% 3.45/1.81 => ( member5164104_state @ A_56 @ ( insert81609953_state @ B_33 @ B_32 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_172_insert__ident,axiom,
% 3.45/1.81 ! [B_31: pname > $o,X_14: pname,A_55: pname > $o] :
% 3.45/1.81 ( ~ ( member_pname @ X_14 @ A_55 )
% 3.45/1.81 => ( ~ ( member_pname @ X_14 @ B_31 )
% 3.45/1.81 => ( ( ( insert_pname @ X_14 @ A_55 )
% 3.45/1.81 = ( insert_pname @ X_14 @ B_31 ) )
% 3.45/1.81 <=> ( A_55 = B_31 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_173_insert__ident,axiom,
% 3.45/1.81 ! [B_31: hoare_1262092251_state > $o,X_14: hoare_1262092251_state,A_55: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ~ ( member5164104_state @ X_14 @ A_55 )
% 3.45/1.81 => ( ~ ( member5164104_state @ X_14 @ B_31 )
% 3.45/1.81 => ( ( ( insert81609953_state @ X_14 @ A_55 )
% 3.45/1.81 = ( insert81609953_state @ X_14 @ B_31 ) )
% 3.45/1.81 <=> ( A_55 = B_31 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_174_insert__code,axiom,
% 3.45/1.81 ! [Y_3: pname,A_54: pname > $o,X_13: pname] :
% 3.45/1.81 ( ( insert_pname @ Y_3 @ A_54 @ X_13 )
% 3.45/1.81 <=> ( ( Y_3 = X_13 )
% 3.45/1.81 | ( A_54 @ X_13 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_175_insert__code,axiom,
% 3.45/1.81 ! [Y_3: hoare_1262092251_state,A_54: hoare_1262092251_state > $o,X_13: hoare_1262092251_state] :
% 3.45/1.81 ( ( insert81609953_state @ Y_3 @ A_54 @ X_13 )
% 3.45/1.81 <=> ( ( Y_3 = X_13 )
% 3.45/1.81 | ( A_54 @ X_13 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_176_insert__iff,axiom,
% 3.45/1.81 ! [A_53: pname,B_30: pname,A_52: pname > $o] :
% 3.45/1.81 ( ( member_pname @ A_53 @ ( insert_pname @ B_30 @ A_52 ) )
% 3.45/1.81 <=> ( ( A_53 = B_30 )
% 3.45/1.81 | ( member_pname @ A_53 @ A_52 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_177_insert__iff,axiom,
% 3.45/1.81 ! [A_53: hoare_1262092251_state,B_30: hoare_1262092251_state,A_52: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( member5164104_state @ A_53 @ ( insert81609953_state @ B_30 @ A_52 ) )
% 3.45/1.81 <=> ( ( A_53 = B_30 )
% 3.45/1.81 | ( member5164104_state @ A_53 @ A_52 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_178_insert__commute,axiom,
% 3.45/1.81 ! [X_12: pname,Y_2: pname,A_51: pname > $o] :
% 3.45/1.81 ( ( insert_pname @ X_12 @ ( insert_pname @ Y_2 @ A_51 ) )
% 3.45/1.81 = ( insert_pname @ Y_2 @ ( insert_pname @ X_12 @ A_51 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_179_insert__commute,axiom,
% 3.45/1.81 ! [X_12: hoare_1262092251_state,Y_2: hoare_1262092251_state,A_51: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( insert81609953_state @ X_12 @ ( insert81609953_state @ Y_2 @ A_51 ) )
% 3.45/1.81 = ( insert81609953_state @ Y_2 @ ( insert81609953_state @ X_12 @ A_51 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_180_insert__absorb2,axiom,
% 3.45/1.81 ! [X_11: pname,A_50: pname > $o] :
% 3.45/1.81 ( ( insert_pname @ X_11 @ ( insert_pname @ X_11 @ A_50 ) )
% 3.45/1.81 = ( insert_pname @ X_11 @ A_50 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_181_insert__absorb2,axiom,
% 3.45/1.81 ! [X_11: hoare_1262092251_state,A_50: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( insert81609953_state @ X_11 @ ( insert81609953_state @ X_11 @ A_50 ) )
% 3.45/1.81 = ( insert81609953_state @ X_11 @ A_50 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_182_insert__Collect,axiom,
% 3.45/1.81 ! [A_49: pname,P_6: pname > $o] :
% 3.45/1.81 ( ( insert_pname @ A_49 @ ( collect_pname @ P_6 ) )
% 3.45/1.81 = ( collect_pname
% 3.45/1.81 @ ^ [U: pname] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_183_insert__Collect,axiom,
% 3.45/1.81 ! [A_49: hoare_1262092251_state,P_6: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( insert81609953_state @ A_49 @ ( collec1121927558_state @ P_6 ) )
% 3.45/1.81 = ( collec1121927558_state
% 3.45/1.81 @ ^ [U: hoare_1262092251_state] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_184_insert__Collect,axiom,
% 3.45/1.81 ! [A_49: pname > $o,P_6: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( insert_pname_o @ A_49 @ ( collect_pname_o @ P_6 ) )
% 3.45/1.81 = ( collect_pname_o
% 3.45/1.81 @ ^ [U: pname > $o] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_185_insert__Collect,axiom,
% 3.45/1.81 ! [A_49: hoare_1262092251_state > $o,P_6: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( insert1042460334tate_o @ A_49 @ ( collec313158217tate_o @ P_6 ) )
% 3.45/1.81 = ( collec313158217tate_o
% 3.45/1.81 @ ^ [U: hoare_1262092251_state > $o] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_186_insert__compr,axiom,
% 3.45/1.81 ! [A_48: pname,B_29: pname > $o] :
% 3.45/1.81 ( ( insert_pname @ A_48 @ B_29 )
% 3.45/1.81 = ( collect_pname
% 3.45/1.81 @ ^ [X_1: pname] : ( (|) @ ( X_1 = A_48 ) @ ( member_pname @ X_1 @ B_29 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_187_insert__compr,axiom,
% 3.45/1.81 ! [A_48: hoare_1262092251_state,B_29: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( insert81609953_state @ A_48 @ B_29 )
% 3.45/1.81 = ( collec1121927558_state
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state] : ( (|) @ ( X_1 = A_48 ) @ ( member5164104_state @ X_1 @ B_29 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_188_insert__compr,axiom,
% 3.45/1.81 ! [A_48: pname > $o,B_29: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( insert_pname_o @ A_48 @ B_29 )
% 3.45/1.81 = ( collect_pname_o
% 3.45/1.81 @ ^ [X_1: pname > $o] : ( (|) @ ( X_1 = A_48 ) @ ( member_pname_o @ X_1 @ B_29 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_189_insert__compr,axiom,
% 3.45/1.81 ! [A_48: hoare_1262092251_state > $o,B_29: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( insert1042460334tate_o @ A_48 @ B_29 )
% 3.45/1.81 = ( collec313158217tate_o
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state > $o] : ( (|) @ ( X_1 = A_48 ) @ ( member907417095tate_o @ X_1 @ B_29 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_190_insertI1,axiom,
% 3.45/1.81 ! [A_47: pname,B_28: pname > $o] : ( member_pname @ A_47 @ ( insert_pname @ A_47 @ B_28 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_191_insertI1,axiom,
% 3.45/1.81 ! [A_47: hoare_1262092251_state,B_28: hoare_1262092251_state > $o] : ( member5164104_state @ A_47 @ ( insert81609953_state @ A_47 @ B_28 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_192_equalityE,axiom,
% 3.45/1.81 ! [A_46: pname > $o,B_27: pname > $o] :
% 3.45/1.81 ( ( A_46 = B_27 )
% 3.45/1.81 => ~ ( ( ord_less_eq_pname_o @ A_46 @ B_27 )
% 3.45/1.81 => ~ ( ord_less_eq_pname_o @ B_27 @ A_46 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_193_equalityE,axiom,
% 3.45/1.81 ! [A_46: hoare_1262092251_state > $o,B_27: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( A_46 = B_27 )
% 3.45/1.81 => ~ ( ( ord_le870406270tate_o @ A_46 @ B_27 )
% 3.45/1.81 => ~ ( ord_le870406270tate_o @ B_27 @ A_46 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_194_subset__trans,axiom,
% 3.45/1.81 ! [C_4: pname > $o,A_45: pname > $o,B_26: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ A_45 @ B_26 )
% 3.45/1.81 => ( ( ord_less_eq_pname_o @ B_26 @ C_4 )
% 3.45/1.81 => ( ord_less_eq_pname_o @ A_45 @ C_4 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_195_subset__trans,axiom,
% 3.45/1.81 ! [C_4: hoare_1262092251_state > $o,A_45: hoare_1262092251_state > $o,B_26: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ord_le870406270tate_o @ A_45 @ B_26 )
% 3.45/1.81 => ( ( ord_le870406270tate_o @ B_26 @ C_4 )
% 3.45/1.81 => ( ord_le870406270tate_o @ A_45 @ C_4 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_196_set__mp,axiom,
% 3.45/1.81 ! [X_10: pname,A_44: pname > $o,B_25: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ A_44 @ B_25 )
% 3.45/1.81 => ( ( member_pname @ X_10 @ A_44 )
% 3.45/1.81 => ( member_pname @ X_10 @ B_25 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_197_set__mp,axiom,
% 3.45/1.81 ! [X_10: hoare_1262092251_state,A_44: hoare_1262092251_state > $o,B_25: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ord_le870406270tate_o @ A_44 @ B_25 )
% 3.45/1.81 => ( ( member5164104_state @ X_10 @ A_44 )
% 3.45/1.81 => ( member5164104_state @ X_10 @ B_25 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_198_set__rev__mp,axiom,
% 3.45/1.81 ! [B_24: pname > $o,X_9: pname,A_43: pname > $o] :
% 3.45/1.81 ( ( member_pname @ X_9 @ A_43 )
% 3.45/1.81 => ( ( ord_less_eq_pname_o @ A_43 @ B_24 )
% 3.45/1.81 => ( member_pname @ X_9 @ B_24 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_199_set__rev__mp,axiom,
% 3.45/1.81 ! [B_24: hoare_1262092251_state > $o,X_9: hoare_1262092251_state,A_43: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( member5164104_state @ X_9 @ A_43 )
% 3.45/1.81 => ( ( ord_le870406270tate_o @ A_43 @ B_24 )
% 3.45/1.81 => ( member5164104_state @ X_9 @ B_24 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_200_in__mono,axiom,
% 3.45/1.81 ! [X_8: pname,A_42: pname > $o,B_23: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ A_42 @ B_23 )
% 3.45/1.81 => ( ( member_pname @ X_8 @ A_42 )
% 3.45/1.81 => ( member_pname @ X_8 @ B_23 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_201_in__mono,axiom,
% 3.45/1.81 ! [X_8: hoare_1262092251_state,A_42: hoare_1262092251_state > $o,B_23: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ord_le870406270tate_o @ A_42 @ B_23 )
% 3.45/1.81 => ( ( member5164104_state @ X_8 @ A_42 )
% 3.45/1.81 => ( member5164104_state @ X_8 @ B_23 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_202_equalityD2,axiom,
% 3.45/1.81 ! [A_41: pname > $o,B_22: pname > $o] :
% 3.45/1.81 ( ( A_41 = B_22 )
% 3.45/1.81 => ( ord_less_eq_pname_o @ B_22 @ A_41 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_203_equalityD2,axiom,
% 3.45/1.81 ! [A_41: hoare_1262092251_state > $o,B_22: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( A_41 = B_22 )
% 3.45/1.81 => ( ord_le870406270tate_o @ B_22 @ A_41 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_204_equalityD1,axiom,
% 3.45/1.81 ! [A_40: pname > $o,B_21: pname > $o] :
% 3.45/1.81 ( ( A_40 = B_21 )
% 3.45/1.81 => ( ord_less_eq_pname_o @ A_40 @ B_21 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_205_equalityD1,axiom,
% 3.45/1.81 ! [A_40: hoare_1262092251_state > $o,B_21: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( A_40 = B_21 )
% 3.45/1.81 => ( ord_le870406270tate_o @ A_40 @ B_21 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_206_set__eq__subset,axiom,
% 3.45/1.81 ! [A_39: pname > $o,B_20: pname > $o] :
% 3.45/1.81 ( ( A_39 = B_20 )
% 3.45/1.81 <=> ( ( ord_less_eq_pname_o @ A_39 @ B_20 )
% 3.45/1.81 & ( ord_less_eq_pname_o @ B_20 @ A_39 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_207_set__eq__subset,axiom,
% 3.45/1.81 ! [A_39: hoare_1262092251_state > $o,B_20: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( A_39 = B_20 )
% 3.45/1.81 <=> ( ( ord_le870406270tate_o @ A_39 @ B_20 )
% 3.45/1.81 & ( ord_le870406270tate_o @ B_20 @ A_39 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_208_subset__refl,axiom,
% 3.45/1.81 ! [A_38: pname > $o] : ( ord_less_eq_pname_o @ A_38 @ A_38 ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_209_subset__refl,axiom,
% 3.45/1.81 ! [A_38: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ A_38 @ A_38 ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_210_rev__image__eqI,axiom,
% 3.45/1.81 ! [B_19: hoare_1262092251_state,F_13: pname > hoare_1262092251_state,X_7: pname,A_37: pname > $o] :
% 3.45/1.81 ( ( member_pname @ X_7 @ A_37 )
% 3.45/1.81 => ( ( B_19
% 3.45/1.81 = ( F_13 @ X_7 ) )
% 3.45/1.81 => ( member5164104_state @ B_19 @ ( image_669833818_state @ F_13 @ A_37 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_211_imageI,axiom,
% 3.45/1.81 ! [F_12: pname > hoare_1262092251_state,X_6: pname,A_36: pname > $o] :
% 3.45/1.81 ( ( member_pname @ X_6 @ A_36 )
% 3.45/1.81 => ( member5164104_state @ ( F_12 @ X_6 ) @ ( image_669833818_state @ F_12 @ A_36 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_212_image__iff,axiom,
% 3.45/1.81 ! [Z: hoare_1262092251_state,F_11: pname > hoare_1262092251_state,A_35: pname > $o] :
% 3.45/1.81 ( ( member5164104_state @ Z @ ( image_669833818_state @ F_11 @ A_35 ) )
% 3.45/1.81 <=> ? [X_1: pname] :
% 3.45/1.81 ( ( member_pname @ X_1 @ A_35 )
% 3.45/1.81 & ( Z
% 3.45/1.81 = ( F_11 @ X_1 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_213_finite__Collect__disjI,axiom,
% 3.45/1.81 ! [P_5: pname > $o,Q: pname > $o] :
% 3.45/1.81 ( ( finite_finite_pname
% 3.45/1.81 @ ( collect_pname
% 3.45/1.81 @ ^ [X_1: pname] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 3.45/1.81 <=> ( ( finite_finite_pname @ ( collect_pname @ P_5 ) )
% 3.45/1.81 & ( finite_finite_pname @ ( collect_pname @ Q ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_214_finite__Collect__disjI,axiom,
% 3.45/1.81 ! [P_5: hoare_1262092251_state > $o,Q: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( finite1178804552_state
% 3.45/1.81 @ ( collec1121927558_state
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 3.45/1.81 <=> ( ( finite1178804552_state @ ( collec1121927558_state @ P_5 ) )
% 3.45/1.81 & ( finite1178804552_state @ ( collec1121927558_state @ Q ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_215_finite__Collect__disjI,axiom,
% 3.45/1.81 ! [P_5: ( pname > $o ) > $o,Q: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( finite297249702name_o
% 3.45/1.81 @ ( collect_pname_o
% 3.45/1.81 @ ^ [X_1: pname > $o] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 3.45/1.81 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_5 ) )
% 3.45/1.81 & ( finite297249702name_o @ ( collect_pname_o @ Q ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_216_finite__Collect__disjI,axiom,
% 3.45/1.81 ! [P_5: ( hoare_1262092251_state > $o ) > $o,Q: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( finite1423311111tate_o
% 3.45/1.81 @ ( collec313158217tate_o
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state > $o] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 3.45/1.81 <=> ( ( finite1423311111tate_o @ ( collec313158217tate_o @ P_5 ) )
% 3.45/1.81 & ( finite1423311111tate_o @ ( collec313158217tate_o @ Q ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_217_insert__compr__raw,axiom,
% 3.45/1.81 ! [X_1: pname,Xa: pname > $o] :
% 3.45/1.81 ( ( insert_pname @ X_1 @ Xa )
% 3.45/1.81 = ( collect_pname
% 3.45/1.81 @ ^ [Y_1: pname] : ( (|) @ ( Y_1 = X_1 ) @ ( member_pname @ Y_1 @ Xa ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_218_insert__compr__raw,axiom,
% 3.45/1.81 ! [X_1: hoare_1262092251_state,Xa: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( insert81609953_state @ X_1 @ Xa )
% 3.45/1.81 = ( collec1121927558_state
% 3.45/1.81 @ ^ [Y_1: hoare_1262092251_state] : ( (|) @ ( Y_1 = X_1 ) @ ( member5164104_state @ Y_1 @ Xa ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_219_insert__compr__raw,axiom,
% 3.45/1.81 ! [X_1: pname > $o,Xa: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( insert_pname_o @ X_1 @ Xa )
% 3.45/1.81 = ( collect_pname_o
% 3.45/1.81 @ ^ [Y_1: pname > $o] : ( (|) @ ( Y_1 = X_1 ) @ ( member_pname_o @ Y_1 @ Xa ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_220_insert__compr__raw,axiom,
% 3.45/1.81 ! [X_1: hoare_1262092251_state > $o,Xa: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( insert1042460334tate_o @ X_1 @ Xa )
% 3.45/1.81 = ( collec313158217tate_o
% 3.45/1.81 @ ^ [Y_1: hoare_1262092251_state > $o] : ( (|) @ ( Y_1 = X_1 ) @ ( member907417095tate_o @ Y_1 @ Xa ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_221_singleton__inject,axiom,
% 3.45/1.81 ! [A_34: pname,B_18: pname] :
% 3.45/1.81 ( ( ( insert_pname @ A_34 @ bot_bot_pname_o )
% 3.45/1.81 = ( insert_pname @ B_18 @ bot_bot_pname_o ) )
% 3.45/1.81 => ( A_34 = B_18 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_222_singleton__inject,axiom,
% 3.45/1.81 ! [A_34: hoare_1262092251_state,B_18: hoare_1262092251_state] :
% 3.45/1.81 ( ( ( insert81609953_state @ A_34 @ bot_bo113204042tate_o )
% 3.45/1.81 = ( insert81609953_state @ B_18 @ bot_bo113204042tate_o ) )
% 3.45/1.81 => ( A_34 = B_18 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_223_singletonE,axiom,
% 3.45/1.81 ! [B_17: pname,A_33: pname] :
% 3.45/1.81 ( ( member_pname @ B_17 @ ( insert_pname @ A_33 @ bot_bot_pname_o ) )
% 3.45/1.81 => ( B_17 = A_33 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_224_singletonE,axiom,
% 3.45/1.81 ! [B_17: hoare_1262092251_state,A_33: hoare_1262092251_state] :
% 3.45/1.81 ( ( member5164104_state @ B_17 @ ( insert81609953_state @ A_33 @ bot_bo113204042tate_o ) )
% 3.45/1.81 => ( B_17 = A_33 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_225_doubleton__eq__iff,axiom,
% 3.45/1.81 ! [A_32: pname,B_16: pname,C_3: pname,D_1: pname] :
% 3.45/1.81 ( ( ( insert_pname @ A_32 @ ( insert_pname @ B_16 @ bot_bot_pname_o ) )
% 3.45/1.81 = ( insert_pname @ C_3 @ ( insert_pname @ D_1 @ bot_bot_pname_o ) ) )
% 3.45/1.81 <=> ( ( ( A_32 = C_3 )
% 3.45/1.81 & ( B_16 = D_1 ) )
% 3.45/1.81 | ( ( A_32 = D_1 )
% 3.45/1.81 & ( B_16 = C_3 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_226_doubleton__eq__iff,axiom,
% 3.45/1.81 ! [A_32: hoare_1262092251_state,B_16: hoare_1262092251_state,C_3: hoare_1262092251_state,D_1: hoare_1262092251_state] :
% 3.45/1.81 ( ( ( insert81609953_state @ A_32 @ ( insert81609953_state @ B_16 @ bot_bo113204042tate_o ) )
% 3.45/1.81 = ( insert81609953_state @ C_3 @ ( insert81609953_state @ D_1 @ bot_bo113204042tate_o ) ) )
% 3.45/1.81 <=> ( ( ( A_32 = C_3 )
% 3.45/1.81 & ( B_16 = D_1 ) )
% 3.45/1.81 | ( ( A_32 = D_1 )
% 3.45/1.81 & ( B_16 = C_3 ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_227_singleton__iff,axiom,
% 3.45/1.81 ! [B_15: pname,A_31: pname] :
% 3.45/1.81 ( ( member_pname @ B_15 @ ( insert_pname @ A_31 @ bot_bot_pname_o ) )
% 3.45/1.81 <=> ( B_15 = A_31 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_228_singleton__iff,axiom,
% 3.45/1.81 ! [B_15: hoare_1262092251_state,A_31: hoare_1262092251_state] :
% 3.45/1.81 ( ( member5164104_state @ B_15 @ ( insert81609953_state @ A_31 @ bot_bo113204042tate_o ) )
% 3.45/1.81 <=> ( B_15 = A_31 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_229_insert__not__empty,axiom,
% 3.45/1.81 ! [A_30: pname,A_29: pname > $o] :
% 3.45/1.81 ( ( insert_pname @ A_30 @ A_29 )
% 3.45/1.81 != bot_bot_pname_o ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_230_insert__not__empty,axiom,
% 3.45/1.81 ! [A_30: hoare_1262092251_state,A_29: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( insert81609953_state @ A_30 @ A_29 )
% 3.45/1.81 != bot_bo113204042tate_o ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_231_empty__not__insert,axiom,
% 3.45/1.81 ! [A_28: pname,A_27: pname > $o] :
% 3.45/1.81 ( bot_bot_pname_o
% 3.45/1.81 != ( insert_pname @ A_28 @ A_27 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_232_empty__not__insert,axiom,
% 3.45/1.81 ! [A_28: hoare_1262092251_state,A_27: hoare_1262092251_state > $o] :
% 3.45/1.81 ( bot_bo113204042tate_o
% 3.45/1.81 != ( insert81609953_state @ A_28 @ A_27 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_233_finite__insert,axiom,
% 3.45/1.81 ! [A_26: pname,A_25: pname > $o] :
% 3.45/1.81 ( ( finite_finite_pname @ ( insert_pname @ A_26 @ A_25 ) )
% 3.45/1.81 <=> ( finite_finite_pname @ A_25 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_234_finite__insert,axiom,
% 3.45/1.81 ! [A_26: hoare_1262092251_state,A_25: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( finite1178804552_state @ ( insert81609953_state @ A_26 @ A_25 ) )
% 3.45/1.81 <=> ( finite1178804552_state @ A_25 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_235_finite__insert,axiom,
% 3.45/1.81 ! [A_26: pname > $o,A_25: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( finite297249702name_o @ ( insert_pname_o @ A_26 @ A_25 ) )
% 3.45/1.81 <=> ( finite297249702name_o @ A_25 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_236_finite__insert,axiom,
% 3.45/1.81 ! [A_26: hoare_1262092251_state > $o,A_25: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( finite1423311111tate_o @ ( insert1042460334tate_o @ A_26 @ A_25 ) )
% 3.45/1.81 <=> ( finite1423311111tate_o @ A_25 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_237_subset__empty,axiom,
% 3.45/1.81 ! [A_24: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ A_24 @ bot_bot_pname_o )
% 3.45/1.81 <=> ( A_24 = bot_bot_pname_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_238_subset__empty,axiom,
% 3.45/1.81 ! [A_24: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ord_le870406270tate_o @ A_24 @ bot_bo113204042tate_o )
% 3.45/1.81 <=> ( A_24 = bot_bo113204042tate_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_239_image__is__empty,axiom,
% 3.45/1.81 ! [F_10: pname > hoare_1262092251_state,A_23: pname > $o] :
% 3.45/1.81 ( ( ( image_669833818_state @ F_10 @ A_23 )
% 3.45/1.81 = bot_bo113204042tate_o )
% 3.45/1.81 <=> ( A_23 = bot_bot_pname_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_240_image__empty,axiom,
% 3.45/1.81 ! [F_9: pname > hoare_1262092251_state] :
% 3.45/1.81 ( ( image_669833818_state @ F_9 @ bot_bot_pname_o )
% 3.45/1.81 = bot_bo113204042tate_o ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_241_empty__is__image,axiom,
% 3.45/1.81 ! [F_8: pname > hoare_1262092251_state,A_22: pname > $o] :
% 3.45/1.81 ( ( bot_bo113204042tate_o
% 3.45/1.81 = ( image_669833818_state @ F_8 @ A_22 ) )
% 3.45/1.81 <=> ( A_22 = bot_bot_pname_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_242_finite__subset,axiom,
% 3.45/1.81 ! [A_21: ( pname > $o ) > $o,B_14: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( ord_le1205211808me_o_o @ A_21 @ B_14 )
% 3.45/1.81 => ( ( finite297249702name_o @ B_14 )
% 3.45/1.81 => ( finite297249702name_o @ A_21 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_243_finite__subset,axiom,
% 3.45/1.81 ! [A_21: ( hoare_1262092251_state > $o ) > $o,B_14: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( ord_le2012720639te_o_o @ A_21 @ B_14 )
% 3.45/1.81 => ( ( finite1423311111tate_o @ B_14 )
% 3.45/1.81 => ( finite1423311111tate_o @ A_21 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_244_finite__subset,axiom,
% 3.45/1.81 ! [A_21: pname > $o,B_14: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ A_21 @ B_14 )
% 3.45/1.81 => ( ( finite_finite_pname @ B_14 )
% 3.45/1.81 => ( finite_finite_pname @ A_21 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_245_finite__subset,axiom,
% 3.45/1.81 ! [A_21: hoare_1262092251_state > $o,B_14: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ord_le870406270tate_o @ A_21 @ B_14 )
% 3.45/1.81 => ( ( finite1178804552_state @ B_14 )
% 3.45/1.81 => ( finite1178804552_state @ A_21 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_246_rev__finite__subset,axiom,
% 3.45/1.81 ! [A_20: ( pname > $o ) > $o,B_13: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( finite297249702name_o @ B_13 )
% 3.45/1.81 => ( ( ord_le1205211808me_o_o @ A_20 @ B_13 )
% 3.45/1.81 => ( finite297249702name_o @ A_20 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_247_rev__finite__subset,axiom,
% 3.45/1.81 ! [A_20: ( hoare_1262092251_state > $o ) > $o,B_13: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( finite1423311111tate_o @ B_13 )
% 3.45/1.81 => ( ( ord_le2012720639te_o_o @ A_20 @ B_13 )
% 3.45/1.81 => ( finite1423311111tate_o @ A_20 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_248_rev__finite__subset,axiom,
% 3.45/1.81 ! [A_20: pname > $o,B_13: pname > $o] :
% 3.45/1.81 ( ( finite_finite_pname @ B_13 )
% 3.45/1.81 => ( ( ord_less_eq_pname_o @ A_20 @ B_13 )
% 3.45/1.81 => ( finite_finite_pname @ A_20 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_249_rev__finite__subset,axiom,
% 3.45/1.81 ! [A_20: hoare_1262092251_state > $o,B_13: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( finite1178804552_state @ B_13 )
% 3.45/1.81 => ( ( ord_le870406270tate_o @ A_20 @ B_13 )
% 3.45/1.81 => ( finite1178804552_state @ A_20 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_250_insert__mono,axiom,
% 3.45/1.81 ! [A_19: pname,C_2: pname > $o,D: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ C_2 @ D )
% 3.45/1.81 => ( ord_less_eq_pname_o @ ( insert_pname @ A_19 @ C_2 ) @ ( insert_pname @ A_19 @ D ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_251_insert__mono,axiom,
% 3.45/1.81 ! [A_19: hoare_1262092251_state,C_2: hoare_1262092251_state > $o,D: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ord_le870406270tate_o @ C_2 @ D )
% 3.45/1.81 => ( ord_le870406270tate_o @ ( insert81609953_state @ A_19 @ C_2 ) @ ( insert81609953_state @ A_19 @ D ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_252_mem__def,axiom,
% 3.45/1.81 ! [X_5: pname,A_18: pname > $o] :
% 3.45/1.81 ( ( member_pname @ X_5 @ A_18 )
% 3.45/1.81 <=> ( A_18 @ X_5 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_253_mem__def,axiom,
% 3.45/1.81 ! [X_5: hoare_1262092251_state,A_18: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( member5164104_state @ X_5 @ A_18 )
% 3.45/1.81 <=> ( A_18 @ X_5 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_254_Collect__def,axiom,
% 3.45/1.81 ! [P_4: pname > $o] :
% 3.45/1.81 ( ( collect_pname @ P_4 )
% 3.45/1.81 = P_4 ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_255_Collect__def,axiom,
% 3.45/1.81 ! [P_4: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( collec1121927558_state @ P_4 )
% 3.45/1.81 = P_4 ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_256_Collect__def,axiom,
% 3.45/1.81 ! [P_4: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( collect_pname_o @ P_4 )
% 3.45/1.81 = P_4 ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_257_Collect__def,axiom,
% 3.45/1.81 ! [P_4: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( collec313158217tate_o @ P_4 )
% 3.45/1.81 = P_4 ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_258_subset__insertI2,axiom,
% 3.45/1.81 ! [B_12: pname,A_17: pname > $o,B_11: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ A_17 @ B_11 )
% 3.45/1.81 => ( ord_less_eq_pname_o @ A_17 @ ( insert_pname @ B_12 @ B_11 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_259_subset__insertI2,axiom,
% 3.45/1.81 ! [B_12: hoare_1262092251_state,A_17: hoare_1262092251_state > $o,B_11: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ord_le870406270tate_o @ A_17 @ B_11 )
% 3.45/1.81 => ( ord_le870406270tate_o @ A_17 @ ( insert81609953_state @ B_12 @ B_11 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_260_subset__insert,axiom,
% 3.45/1.81 ! [B_10: pname > $o,X_4: pname,A_16: pname > $o] :
% 3.45/1.81 ( ~ ( member_pname @ X_4 @ A_16 )
% 3.45/1.81 => ( ( ord_less_eq_pname_o @ A_16 @ ( insert_pname @ X_4 @ B_10 ) )
% 3.45/1.81 <=> ( ord_less_eq_pname_o @ A_16 @ B_10 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_261_subset__insert,axiom,
% 3.45/1.81 ! [B_10: hoare_1262092251_state > $o,X_4: hoare_1262092251_state,A_16: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ~ ( member5164104_state @ X_4 @ A_16 )
% 3.45/1.81 => ( ( ord_le870406270tate_o @ A_16 @ ( insert81609953_state @ X_4 @ B_10 ) )
% 3.45/1.81 <=> ( ord_le870406270tate_o @ A_16 @ B_10 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_262_insert__subset,axiom,
% 3.45/1.81 ! [X_3: pname,A_15: pname > $o,B_9: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_3 @ A_15 ) @ B_9 )
% 3.45/1.81 <=> ( ( member_pname @ X_3 @ B_9 )
% 3.45/1.81 & ( ord_less_eq_pname_o @ A_15 @ B_9 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_263_insert__subset,axiom,
% 3.45/1.81 ! [X_3: hoare_1262092251_state,A_15: hoare_1262092251_state > $o,B_9: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ord_le870406270tate_o @ ( insert81609953_state @ X_3 @ A_15 ) @ B_9 )
% 3.45/1.81 <=> ( ( member5164104_state @ X_3 @ B_9 )
% 3.45/1.81 & ( ord_le870406270tate_o @ A_15 @ B_9 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_264_subset__insertI,axiom,
% 3.45/1.81 ! [B_8: pname > $o,A_14: pname] : ( ord_less_eq_pname_o @ B_8 @ ( insert_pname @ A_14 @ B_8 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_265_subset__insertI,axiom,
% 3.45/1.81 ! [B_8: hoare_1262092251_state > $o,A_14: hoare_1262092251_state] : ( ord_le870406270tate_o @ B_8 @ ( insert81609953_state @ A_14 @ B_8 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_266_insert__image,axiom,
% 3.45/1.81 ! [F_7: pname > hoare_1262092251_state,X_2: pname,A_13: pname > $o] :
% 3.45/1.81 ( ( member_pname @ X_2 @ A_13 )
% 3.45/1.81 => ( ( insert81609953_state @ ( F_7 @ X_2 ) @ ( image_669833818_state @ F_7 @ A_13 ) )
% 3.45/1.81 = ( image_669833818_state @ F_7 @ A_13 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_267_image__insert,axiom,
% 3.45/1.81 ! [F_6: pname > hoare_1262092251_state,A_12: pname,B_7: pname > $o] :
% 3.45/1.81 ( ( image_669833818_state @ F_6 @ ( insert_pname @ A_12 @ B_7 ) )
% 3.45/1.81 = ( insert81609953_state @ ( F_6 @ A_12 ) @ ( image_669833818_state @ F_6 @ B_7 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_268_image__mono,axiom,
% 3.45/1.81 ! [F_5: pname > hoare_1262092251_state,A_11: pname > $o,B_6: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ A_11 @ B_6 )
% 3.45/1.81 => ( ord_le870406270tate_o @ ( image_669833818_state @ F_5 @ A_11 ) @ ( image_669833818_state @ F_5 @ B_6 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_269_subset__image__iff,axiom,
% 3.45/1.81 ! [B_5: hoare_1262092251_state > $o,F_4: pname > hoare_1262092251_state,A_10: pname > $o] :
% 3.45/1.81 ( ( ord_le870406270tate_o @ B_5 @ ( image_669833818_state @ F_4 @ A_10 ) )
% 3.45/1.81 <=> ? [AA: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ AA @ A_10 )
% 3.45/1.81 & ( B_5
% 3.45/1.81 = ( image_669833818_state @ F_4 @ AA ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_270_domI,axiom,
% 3.45/1.81 ! [M: pname > option_com,A_9: pname,B_4: com] :
% 3.45/1.81 ( ( ( M @ A_9 )
% 3.45/1.81 = ( some_com @ B_4 ) )
% 3.45/1.81 => ( member_pname @ A_9 @ ( dom_pname_com @ M ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_271_Collect__conv__if,axiom,
% 3.45/1.81 ! [P_3: pname > $o,A_8: pname] :
% 3.45/1.81 ( ( ( P_3 @ A_8 )
% 3.45/1.81 => ( ( collect_pname
% 3.45/1.81 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 3.45/1.81 = ( insert_pname @ A_8 @ bot_bot_pname_o ) ) )
% 3.45/1.81 & ( ~ ( P_3 @ A_8 )
% 3.45/1.81 => ( ( collect_pname
% 3.45/1.81 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 3.45/1.81 = bot_bot_pname_o ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_272_Collect__conv__if,axiom,
% 3.45/1.81 ! [P_3: hoare_1262092251_state > $o,A_8: hoare_1262092251_state] :
% 3.45/1.81 ( ( ( P_3 @ A_8 )
% 3.45/1.81 => ( ( collec1121927558_state
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 3.45/1.81 = ( insert81609953_state @ A_8 @ bot_bo113204042tate_o ) ) )
% 3.45/1.81 & ( ~ ( P_3 @ A_8 )
% 3.45/1.81 => ( ( collec1121927558_state
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 3.45/1.81 = bot_bo113204042tate_o ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_273_Collect__conv__if,axiom,
% 3.45/1.81 ! [P_3: ( pname > $o ) > $o,A_8: pname > $o] :
% 3.45/1.81 ( ( ( P_3 @ A_8 )
% 3.45/1.81 => ( ( collect_pname_o
% 3.45/1.81 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 3.45/1.81 = ( insert_pname_o @ A_8 @ bot_bot_pname_o_o ) ) )
% 3.45/1.81 & ( ~ ( P_3 @ A_8 )
% 3.45/1.81 => ( ( collect_pname_o
% 3.45/1.81 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 3.45/1.81 = bot_bot_pname_o_o ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_274_Collect__conv__if,axiom,
% 3.45/1.81 ! [P_3: ( hoare_1262092251_state > $o ) > $o,A_8: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ( P_3 @ A_8 )
% 3.45/1.81 => ( ( collec313158217tate_o
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 3.45/1.81 = ( insert1042460334tate_o @ A_8 @ bot_bo1962689075te_o_o ) ) )
% 3.45/1.81 & ( ~ ( P_3 @ A_8 )
% 3.45/1.81 => ( ( collec313158217tate_o
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 3.45/1.81 = bot_bo1962689075te_o_o ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_275_Collect__conv__if2,axiom,
% 3.45/1.81 ! [P_2: pname > $o,A_7: pname] :
% 3.45/1.81 ( ( ( P_2 @ A_7 )
% 3.45/1.81 => ( ( collect_pname
% 3.45/1.81 @ ^ [X_1: pname] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 3.45/1.81 = ( insert_pname @ A_7 @ bot_bot_pname_o ) ) )
% 3.45/1.81 & ( ~ ( P_2 @ A_7 )
% 3.45/1.81 => ( ( collect_pname
% 3.45/1.81 @ ^ [X_1: pname] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 3.45/1.81 = bot_bot_pname_o ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_276_Collect__conv__if2,axiom,
% 3.45/1.81 ! [P_2: hoare_1262092251_state > $o,A_7: hoare_1262092251_state] :
% 3.45/1.81 ( ( ( P_2 @ A_7 )
% 3.45/1.81 => ( ( collec1121927558_state
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 3.45/1.81 = ( insert81609953_state @ A_7 @ bot_bo113204042tate_o ) ) )
% 3.45/1.81 & ( ~ ( P_2 @ A_7 )
% 3.45/1.81 => ( ( collec1121927558_state
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 3.45/1.81 = bot_bo113204042tate_o ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_277_Collect__conv__if2,axiom,
% 3.45/1.81 ! [P_2: ( pname > $o ) > $o,A_7: pname > $o] :
% 3.45/1.81 ( ( ( P_2 @ A_7 )
% 3.45/1.81 => ( ( collect_pname_o
% 3.45/1.81 @ ^ [X_1: pname > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 3.45/1.81 = ( insert_pname_o @ A_7 @ bot_bot_pname_o_o ) ) )
% 3.45/1.81 & ( ~ ( P_2 @ A_7 )
% 3.45/1.81 => ( ( collect_pname_o
% 3.45/1.81 @ ^ [X_1: pname > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 3.45/1.81 = bot_bot_pname_o_o ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_278_Collect__conv__if2,axiom,
% 3.45/1.81 ! [P_2: ( hoare_1262092251_state > $o ) > $o,A_7: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( ( P_2 @ A_7 )
% 3.45/1.81 => ( ( collec313158217tate_o
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 3.45/1.81 = ( insert1042460334tate_o @ A_7 @ bot_bo1962689075te_o_o ) ) )
% 3.45/1.81 & ( ~ ( P_2 @ A_7 )
% 3.45/1.81 => ( ( collec313158217tate_o
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 3.45/1.81 = bot_bo1962689075te_o_o ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_279_singleton__conv,axiom,
% 3.45/1.81 ! [A_6: pname] :
% 3.45/1.81 ( ( collect_pname
% 3.45/1.81 @ ^ [X_1: pname] : ( X_1 = A_6 ) )
% 3.45/1.81 = ( insert_pname @ A_6 @ bot_bot_pname_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_280_singleton__conv,axiom,
% 3.45/1.81 ! [A_6: hoare_1262092251_state] :
% 3.45/1.81 ( ( collec1121927558_state
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state] : ( X_1 = A_6 ) )
% 3.45/1.81 = ( insert81609953_state @ A_6 @ bot_bo113204042tate_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_281_singleton__conv,axiom,
% 3.45/1.81 ! [A_6: pname > $o] :
% 3.45/1.81 ( ( collect_pname_o
% 3.45/1.81 @ ^ [X_1: pname > $o] : ( X_1 = A_6 ) )
% 3.45/1.81 = ( insert_pname_o @ A_6 @ bot_bot_pname_o_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_282_singleton__conv,axiom,
% 3.45/1.81 ! [A_6: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( collec313158217tate_o
% 3.45/1.81 @ ^ [X_1: hoare_1262092251_state > $o] : ( X_1 = A_6 ) )
% 3.45/1.81 = ( insert1042460334tate_o @ A_6 @ bot_bo1962689075te_o_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_283_singleton__conv2,axiom,
% 3.45/1.81 ! [A_5: pname] :
% 3.45/1.81 ( ( collect_pname @ ( fequal_pname @ A_5 ) )
% 3.45/1.81 = ( insert_pname @ A_5 @ bot_bot_pname_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_284_singleton__conv2,axiom,
% 3.45/1.81 ! [A_5: hoare_1262092251_state] :
% 3.45/1.81 ( ( collec1121927558_state @ ( fequal1925511196_state @ A_5 ) )
% 3.45/1.81 = ( insert81609953_state @ A_5 @ bot_bo113204042tate_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_285_singleton__conv2,axiom,
% 3.45/1.81 ! [A_5: pname > $o] :
% 3.45/1.81 ( ( collect_pname_o @ ( fequal_pname_o @ A_5 ) )
% 3.45/1.81 = ( insert_pname_o @ A_5 @ bot_bot_pname_o_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_286_singleton__conv2,axiom,
% 3.45/1.81 ! [A_5: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( collec313158217tate_o @ ( fequal1529404211tate_o @ A_5 ) )
% 3.45/1.81 = ( insert1042460334tate_o @ A_5 @ bot_bo1962689075te_o_o ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_287_MGF__lemma1,axiom,
% 3.45/1.81 ! [C_1: com,G: hoare_1262092251_state > $o] :
% 3.45/1.81 ( hoare_1821564147gleton
% 3.45/1.81 => ( ! [X_1: pname] :
% 3.45/1.81 ( ( member_pname @ X_1 @ ( dom_pname_com @ body ) )
% 3.45/1.81 => ( hoare_930741239_state @ G @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ X_1 ) ) @ bot_bo113204042tate_o ) ) )
% 3.45/1.81 => ( ( wt @ C_1 )
% 3.45/1.81 => ( hoare_930741239_state @ G @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ C_1 ) @ bot_bo113204042tate_o ) ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_288_WT__bodiesD,axiom,
% 3.45/1.81 ! [Pn_1: pname,B_3: com] :
% 3.45/1.81 ( wT_bodies
% 3.45/1.81 => ( ( ( body @ Pn_1 )
% 3.45/1.81 = ( some_com @ B_3 ) )
% 3.45/1.81 => ( wt @ B_3 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_289_imageE,axiom,
% 3.45/1.81 ! [B_2: hoare_1262092251_state,F_3: pname > hoare_1262092251_state,A_4: pname > $o] :
% 3.45/1.81 ( ( member5164104_state @ B_2 @ ( image_669833818_state @ F_3 @ A_4 ) )
% 3.45/1.81 => ~ ! [X_1: pname] :
% 3.45/1.81 ( ( B_2
% 3.45/1.81 = ( F_3 @ X_1 ) )
% 3.45/1.81 => ~ ( member_pname @ X_1 @ A_4 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_290_finite__subset__induct,axiom,
% 3.45/1.81 ! [P_1: ( pname > $o ) > $o,A_2: pname > $o,F_1: pname > $o] :
% 3.45/1.81 ( ( finite_finite_pname @ F_1 )
% 3.45/1.81 => ( ( ord_less_eq_pname_o @ F_1 @ A_2 )
% 3.45/1.81 => ( ( P_1 @ bot_bot_pname_o )
% 3.45/1.81 => ( ! [A_3: pname,F_2: pname > $o] :
% 3.45/1.81 ( ( finite_finite_pname @ F_2 )
% 3.45/1.81 => ( ( member_pname @ A_3 @ A_2 )
% 3.45/1.81 => ( ~ ( member_pname @ A_3 @ F_2 )
% 3.45/1.81 => ( ( P_1 @ F_2 )
% 3.45/1.81 => ( P_1 @ ( insert_pname @ A_3 @ F_2 ) ) ) ) ) )
% 3.45/1.81 => ( P_1 @ F_1 ) ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_291_finite__subset__induct,axiom,
% 3.45/1.81 ! [P_1: ( hoare_1262092251_state > $o ) > $o,A_2: hoare_1262092251_state > $o,F_1: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( finite1178804552_state @ F_1 )
% 3.45/1.81 => ( ( ord_le870406270tate_o @ F_1 @ A_2 )
% 3.45/1.81 => ( ( P_1 @ bot_bo113204042tate_o )
% 3.45/1.81 => ( ! [A_3: hoare_1262092251_state,F_2: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( finite1178804552_state @ F_2 )
% 3.45/1.81 => ( ( member5164104_state @ A_3 @ A_2 )
% 3.45/1.81 => ( ~ ( member5164104_state @ A_3 @ F_2 )
% 3.45/1.81 => ( ( P_1 @ F_2 )
% 3.45/1.81 => ( P_1 @ ( insert81609953_state @ A_3 @ F_2 ) ) ) ) ) )
% 3.45/1.81 => ( P_1 @ F_1 ) ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_292_finite__subset__induct,axiom,
% 3.45/1.81 ! [P_1: ( ( pname > $o ) > $o ) > $o,A_2: ( pname > $o ) > $o,F_1: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( finite297249702name_o @ F_1 )
% 3.45/1.81 => ( ( ord_le1205211808me_o_o @ F_1 @ A_2 )
% 3.45/1.81 => ( ( P_1 @ bot_bot_pname_o_o )
% 3.45/1.81 => ( ! [A_3: pname > $o,F_2: ( pname > $o ) > $o] :
% 3.45/1.81 ( ( finite297249702name_o @ F_2 )
% 3.45/1.81 => ( ( member_pname_o @ A_3 @ A_2 )
% 3.45/1.81 => ( ~ ( member_pname_o @ A_3 @ F_2 )
% 3.45/1.81 => ( ( P_1 @ F_2 )
% 3.45/1.81 => ( P_1 @ ( insert_pname_o @ A_3 @ F_2 ) ) ) ) ) )
% 3.45/1.81 => ( P_1 @ F_1 ) ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_293_finite__subset__induct,axiom,
% 3.45/1.81 ! [P_1: ( ( hoare_1262092251_state > $o ) > $o ) > $o,A_2: ( hoare_1262092251_state > $o ) > $o,F_1: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( finite1423311111tate_o @ F_1 )
% 3.45/1.81 => ( ( ord_le2012720639te_o_o @ F_1 @ A_2 )
% 3.45/1.81 => ( ( P_1 @ bot_bo1962689075te_o_o )
% 3.45/1.81 => ( ! [A_3: hoare_1262092251_state > $o,F_2: ( hoare_1262092251_state > $o ) > $o] :
% 3.45/1.81 ( ( finite1423311111tate_o @ F_2 )
% 3.45/1.81 => ( ( member907417095tate_o @ A_3 @ A_2 )
% 3.45/1.81 => ( ~ ( member907417095tate_o @ A_3 @ F_2 )
% 3.45/1.81 => ( ( P_1 @ F_2 )
% 3.45/1.81 => ( P_1 @ ( insert1042460334tate_o @ A_3 @ F_2 ) ) ) ) ) )
% 3.45/1.81 => ( P_1 @ F_1 ) ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_294_WTs__elim__cases_I7_J,axiom,
% 3.45/1.81 ! [P: pname] :
% 3.45/1.81 ( ( wt @ ( body_1 @ P ) )
% 3.45/1.81 => ~ ! [Y_1: com] :
% 3.45/1.81 ( ( body @ P )
% 3.45/1.81 != ( some_com @ Y_1 ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_295_subsetI,axiom,
% 3.45/1.81 ! [B_1: pname > $o,A_1: pname > $o] :
% 3.45/1.81 ( ! [X_1: pname] :
% 3.45/1.81 ( ( member_pname @ X_1 @ A_1 )
% 3.45/1.81 => ( member_pname @ X_1 @ B_1 ) )
% 3.45/1.81 => ( ord_less_eq_pname_o @ A_1 @ B_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_296_subsetI,axiom,
% 3.45/1.81 ! [B_1: hoare_1262092251_state > $o,A_1: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ! [X_1: hoare_1262092251_state] :
% 3.45/1.81 ( ( member5164104_state @ X_1 @ A_1 )
% 3.45/1.81 => ( member5164104_state @ X_1 @ B_1 ) )
% 3.45/1.81 => ( ord_le870406270tate_o @ A_1 @ B_1 ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_297_finite__subset__image,axiom,
% 3.45/1.81 ! [F: pname > hoare_1262092251_state,A: pname > $o,B: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( finite1178804552_state @ B )
% 3.45/1.81 => ( ( ord_le870406270tate_o @ B @ ( image_669833818_state @ F @ A ) )
% 3.45/1.81 => ? [C: pname > $o] :
% 3.45/1.81 ( ( ord_less_eq_pname_o @ C @ A )
% 3.45/1.81 & ( finite_finite_pname @ C )
% 3.45/1.81 & ( B
% 3.45/1.81 = ( image_669833818_state @ F @ C ) ) ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_298_finite__dom__body,axiom,
% 3.45/1.81 finite_finite_pname @ ( dom_pname_com @ body ) ).
% 3.45/1.81
% 3.45/1.81 thf(fact_299_com_Osimps_I6_J,axiom,
% 3.45/1.81 ! [Pname_1: pname,Pname: pname] :
% 3.45/1.81 ( ( ( body_1 @ Pname_1 )
% 3.45/1.81 = ( body_1 @ Pname ) )
% 3.45/1.81 <=> ( Pname_1 = Pname ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 3.45/1.81 ! [X: pname,Y: pname] :
% 3.45/1.81 ( ~ ( fequal_pname @ X @ Y )
% 3.45/1.81 | ( X = Y ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 3.45/1.81 ! [X: pname,Y: pname] :
% 3.45/1.81 ( ( X != Y )
% 3.45/1.81 | ( fequal_pname @ X @ Y ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 3.45/1.81 ! [X: pname > $o,Y: pname > $o] :
% 3.45/1.81 ( ~ ( fequal_pname_o @ X @ Y )
% 3.45/1.81 | ( X = Y ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 3.45/1.81 ! [X: pname > $o,Y: pname > $o] :
% 3.45/1.81 ( ( X != Y )
% 3.45/1.81 | ( fequal_pname_o @ X @ Y ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com,axiom,
% 3.45/1.81 ! [X: hoare_1262092251_state,Y: hoare_1262092251_state] :
% 3.45/1.81 ( ~ ( fequal1925511196_state @ X @ Y )
% 3.45/1.81 | ( X = Y ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com,axiom,
% 3.45/1.81 ! [X: hoare_1262092251_state,Y: hoare_1262092251_state] :
% 3.45/1.81 ( ( X != Y )
% 3.45/1.81 | ( fequal1925511196_state @ X @ Y ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It,axiom,
% 3.45/1.81 ! [X: hoare_1262092251_state > $o,Y: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ~ ( fequal1529404211tate_o @ X @ Y )
% 3.45/1.81 | ( X = Y ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It,axiom,
% 3.45/1.81 ! [X: hoare_1262092251_state > $o,Y: hoare_1262092251_state > $o] :
% 3.45/1.81 ( ( X != Y )
% 3.45/1.81 | ( fequal1529404211tate_o @ X @ Y ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(conj_0,hypothesis,
% 3.45/1.81 hoare_1821564147gleton ).
% 3.45/1.81
% 3.45/1.81 thf(conj_1,hypothesis,
% 3.45/1.81 wT_bodies ).
% 3.45/1.81
% 3.45/1.81 thf(conj_2,hypothesis,
% 3.45/1.81 finite1178804552_state @ fa ).
% 3.45/1.81
% 3.45/1.81 thf(conj_3,hypothesis,
% 3.45/1.81 ~ ( member5164104_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) ).
% 3.45/1.81
% 3.45/1.81 thf(conj_4,hypothesis,
% 3.45/1.81 ( ord_le870406270tate_o @ fa
% 3.45/1.81 @ ( image_669833818_state
% 3.45/1.81 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 3.45/1.81 @ ( dom_pname_com @ body ) ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(conj_5,hypothesis,
% 3.45/1.81 ( ( body @ pn )
% 3.45/1.81 = ( some_com @ y ) ) ).
% 3.45/1.81
% 3.45/1.81 thf(conj_6,hypothesis,
% 3.45/1.81 ( hoare_930741239_state
% 3.45/1.81 @ ( image_669833818_state
% 3.45/1.81 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.45/1.81 @ ( dom_pname_com @ body ) )
% 3.45/1.81 @ fa ) ).
% 3.45/1.81
% 3.45/1.81 thf(conj_7,conjecture,
% 3.45/1.81 ( hoare_930741239_state
% 3.45/1.81 @ ( image_669833818_state
% 3.45/1.81 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.45/1.81 @ ( dom_pname_com @ body ) )
% 3.45/1.81 @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ) ).
% 3.45/1.81 ------------------------
% 3.45/1.84 % (3630)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_3501 for (2999ds/2Mi)
% 3.45/1.84 % (3626)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/183Mi)
% 3.45/1.84 % (3632)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/18Mi)
% 3.45/1.84 % (3627)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_3501 for (2999ds/4Mi)
% 3.45/1.84 % (3631)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_3501 for (2999ds/275Mi)
% 3.45/1.84 % (3629)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/2Mi)
% 3.45/1.84 % (3628)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_3501 for (2999ds/27Mi)
% 3.45/1.84 % (3629)Instruction limit reached!
% 3.45/1.84 % (3629)------------------------------
% 3.45/1.84 % (3629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.84 % (3629)Termination reason: Unknown
% 3.45/1.84 % (3629)Termination phase: shuffling
% 3.45/1.84
% 3.45/1.84 % (3629)Memory used [KB]: 1407
% 3.45/1.84 % (3629)Time elapsed: 0.003 s
% 3.45/1.84 % (3629)Instructions burned: 2 (million)
% 3.45/1.84 % (3629)------------------------------
% 3.45/1.84 % (3629)------------------------------
% 3.45/1.84 % (3630)Instruction limit reached!
% 3.45/1.84 % (3630)------------------------------
% 3.45/1.84 % (3630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.84 % (3630)Termination reason: Unknown
% 3.45/1.84 % (3630)Termination phase: shuffling
% 3.45/1.84
% 3.45/1.84 % (3630)Memory used [KB]: 1407
% 3.45/1.84 % (3630)Time elapsed: 0.003 s
% 3.45/1.84 % (3630)Instructions burned: 2 (million)
% 3.45/1.84 % (3630)------------------------------
% 3.45/1.84 % (3630)------------------------------
% 3.45/1.84 % (3627)Instruction limit reached!
% 3.45/1.84 % (3627)------------------------------
% 3.45/1.84 % (3627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.84 % (3627)Termination reason: Unknown
% 3.45/1.84 % (3627)Termination phase: shuffling
% 3.45/1.84
% 3.45/1.84 % (3627)Memory used [KB]: 1535
% 3.45/1.84 % (3627)Time elapsed: 0.004 s
% 3.45/1.84 % (3627)Instructions burned: 4 (million)
% 3.45/1.84 % (3627)------------------------------
% 3.45/1.84 % (3627)------------------------------
% 3.45/1.85 % (3632)Instruction limit reached!
% 3.45/1.85 % (3632)------------------------------
% 3.45/1.85 % (3632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.85 % (3632)Termination reason: Unknown
% 3.45/1.85 % (3632)Termination phase: shuffling
% 3.45/1.85
% 3.45/1.85 % (3632)Memory used [KB]: 1918
% 3.45/1.85 % (3632)Time elapsed: 0.011 s
% 3.45/1.85 % (3632)Instructions burned: 18 (million)
% 3.45/1.85 % (3632)------------------------------
% 3.45/1.85 % (3632)------------------------------
% 3.45/1.86 % (3628)Instruction limit reached!
% 3.45/1.86 % (3628)------------------------------
% 3.45/1.86 % (3628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.86 % (3628)Termination reason: Unknown
% 3.45/1.86 % (3628)Termination phase: Property scanning
% 3.45/1.86
% 3.45/1.86 % (3628)Memory used [KB]: 2046
% 3.45/1.86 % (3628)Time elapsed: 0.016 s
% 3.45/1.86 % (3628)Instructions burned: 28 (million)
% 3.45/1.86 % (3628)------------------------------
% 3.45/1.86 % (3628)------------------------------
% 3.45/1.86 % (3633)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/3Mi)
% 3.45/1.86 % (3634)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_3501 for (2999ds/37Mi)
% 3.45/1.86 % (3635)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_3501 for (2999ds/15Mi)
% 3.45/1.86 % (3633)Instruction limit reached!
% 3.45/1.86 % (3633)------------------------------
% 3.45/1.86 % (3633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.86 % (3633)Termination reason: Unknown
% 3.45/1.86 % (3633)Termination phase: shuffling
% 3.45/1.86
% 3.45/1.86 % (3633)Memory used [KB]: 1407
% 3.45/1.86 % (3633)Time elapsed: 0.003 s
% 3.45/1.86 % (3633)Instructions burned: 3 (million)
% 3.45/1.86 % (3633)------------------------------
% 3.45/1.86 % (3633)------------------------------
% 3.45/1.87 % (3635)Instruction limit reached!
% 3.45/1.87 % (3635)------------------------------
% 3.45/1.87 % (3635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.87 % (3635)Termination reason: Unknown
% 3.45/1.87 % (3635)Termination phase: shuffling
% 3.45/1.87
% 3.45/1.87 % (3635)Memory used [KB]: 1791
% 3.45/1.87 % (3635)Time elapsed: 0.009 s
% 3.45/1.87 % (3635)Instructions burned: 15 (million)
% 3.45/1.87 % (3635)------------------------------
% 3.45/1.87 % (3635)------------------------------
% 3.45/1.87 % (3636)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_3501 for (2999ds/3Mi)
% 3.45/1.87 % (3636)Instruction limit reached!
% 3.45/1.87 % (3636)------------------------------
% 3.45/1.87 % (3636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.87 % (3636)Termination reason: Unknown
% 3.45/1.87 % (3636)Termination phase: shuffling
% 3.45/1.87
% 3.45/1.87 % (3636)Memory used [KB]: 1407
% 3.45/1.87 % (3636)Time elapsed: 0.003 s
% 3.45/1.87 % (3636)Instructions burned: 3 (million)
% 3.45/1.87 % (3636)------------------------------
% 3.45/1.87 % (3636)------------------------------
% 3.45/1.87 % (3637)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_3501 for (2999ds/1041Mi)
% 3.45/1.88 % (3638)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/7Mi)
% 3.45/1.88 % (3634)Instruction limit reached!
% 3.45/1.88 % (3634)------------------------------
% 3.45/1.88 % (3634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.88 % (3634)Termination reason: Unknown
% 3.45/1.88 % (3634)Termination phase: shuffling
% 3.45/1.88
% 3.45/1.88 % (3634)Memory used [KB]: 2430
% 3.45/1.88 % (3634)Time elapsed: 0.019 s
% 3.45/1.88 % (3634)Instructions burned: 38 (million)
% 3.45/1.88 % (3634)------------------------------
% 3.45/1.88 % (3634)------------------------------
% 3.45/1.88 % (3638)Instruction limit reached!
% 3.45/1.88 % (3638)------------------------------
% 3.45/1.88 % (3638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.88 % (3638)Termination reason: Unknown
% 3.45/1.88 % (3638)Termination phase: shuffling
% 3.45/1.88
% 3.45/1.88 % (3638)Memory used [KB]: 1535
% 3.45/1.88 % (3638)Time elapsed: 0.005 s
% 3.45/1.88 % (3638)Instructions burned: 7 (million)
% 3.45/1.88 % (3638)------------------------------
% 3.45/1.88 % (3638)------------------------------
% 3.45/1.88 % (3639)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/16Mi)
% 3.45/1.88 % (3640)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_3501 for (2999ds/3Mi)
% 3.45/1.89 % (3640)Instruction limit reached!
% 3.45/1.89 % (3640)------------------------------
% 3.45/1.89 % (3640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.89 % (3640)Termination reason: Unknown
% 3.45/1.89 % (3640)Termination phase: shuffling
% 3.45/1.89
% 3.45/1.89 % (3640)Memory used [KB]: 1535
% 3.45/1.89 % (3640)Time elapsed: 0.003 s
% 3.45/1.89 % (3640)Instructions burned: 3 (million)
% 3.45/1.89 % (3640)------------------------------
% 3.45/1.89 % (3640)------------------------------
% 3.45/1.89 % (3639)Instruction limit reached!
% 3.45/1.89 % (3639)------------------------------
% 3.45/1.89 % (3639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.89 % (3639)Termination reason: Unknown
% 3.45/1.89 % (3639)Termination phase: shuffling
% 3.45/1.89
% 3.45/1.89 % (3639)Memory used [KB]: 1791
% 3.45/1.89 % (3639)Time elapsed: 0.010 s
% 3.45/1.89 % (3639)Instructions burned: 17 (million)
% 3.45/1.89 % (3639)------------------------------
% 3.45/1.89 % (3639)------------------------------
% 3.45/1.89 % (3641)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_3501 for (2999ds/3Mi)
% 3.45/1.89 % (3641)Instruction limit reached!
% 3.45/1.89 % (3641)------------------------------
% 3.45/1.89 % (3641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.89 % (3641)Termination reason: Unknown
% 3.45/1.89 % (3641)Termination phase: shuffling
% 3.45/1.89
% 3.45/1.89 % (3641)Memory used [KB]: 1535
% 3.45/1.89 % (3641)Time elapsed: 0.003 s
% 3.45/1.89 % (3641)Instructions burned: 3 (million)
% 3.45/1.89 % (3641)------------------------------
% 3.45/1.89 % (3641)------------------------------
% 3.45/1.90 % (3642)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/7Mi)
% 3.50/1.90 % (3642)Instruction limit reached!
% 3.50/1.90 % (3642)------------------------------
% 3.50/1.90 % (3642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.50/1.90 % (3642)Termination reason: Unknown
% 3.50/1.90 % (3642)Termination phase: shuffling
% 3.50/1.90
% 3.50/1.90 % (3642)Memory used [KB]: 1535
% 3.50/1.90 % (3642)Time elapsed: 0.005 s
% 3.50/1.90 % (3642)Instructions burned: 7 (million)
% 3.50/1.90 % (3642)------------------------------
% 3.50/1.90 % (3642)------------------------------
% 3.50/1.90 % (3643)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/3Mi)
% 3.50/1.90 % (3643)Instruction limit reached!
% 3.50/1.90 % (3643)------------------------------
% 3.50/1.90 % (3643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.50/1.90 % (3643)Termination reason: Unknown
% 3.50/1.90 % (3643)Termination phase: shuffling
% 3.50/1.90
% 3.50/1.90 % (3643)Memory used [KB]: 1535
% 3.50/1.90 % (3643)Time elapsed: 0.004 s
% 3.50/1.90 % (3643)Instructions burned: 4 (million)
% 3.50/1.90 % (3643)------------------------------
% 3.50/1.90 % (3643)------------------------------
% 3.50/1.91 % (3644)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/4Mi)
% 3.50/1.91 % (3644)Instruction limit reached!
% 3.50/1.91 % (3644)------------------------------
% 3.50/1.91 % (3644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.50/1.91 % (3644)Termination reason: Unknown
% 3.50/1.91 % (3644)Termination phase: shuffling
% 3.50/1.91
% 3.50/1.91 % (3644)Memory used [KB]: 1535
% 3.50/1.91 % (3644)Time elapsed: 0.004 s
% 3.50/1.91 % (3644)Instructions burned: 5 (million)
% 3.50/1.91 % (3644)------------------------------
% 3.50/1.91 % (3644)------------------------------
% 3.50/1.91 % (3645)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/18Mi)
% 3.50/1.92 % (3646)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/710Mi)
% 3.50/1.92 % (3645)Instruction limit reached!
% 3.50/1.92 % (3645)------------------------------
% 3.50/1.92 % (3645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.50/1.92 % (3645)Termination reason: Unknown
% 3.50/1.92 % (3645)Termination phase: shuffling
% 3.50/1.92
% 3.50/1.92 % (3645)Memory used [KB]: 1918
% 3.50/1.92 % (3645)Time elapsed: 0.011 s
% 3.50/1.92 % (3645)Instructions burned: 19 (million)
% 3.50/1.92 % (3645)------------------------------
% 3.50/1.92 % (3645)------------------------------
% 3.50/1.92 % (3647)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3501 for (2999ds/6Mi)
% 3.50/1.92 % (3647)Instruction limit reached!
% 3.50/1.92 % (3647)------------------------------
% 3.50/1.92 % (3647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.50/1.92 % (3647)Termination reason: Unknown
% 3.50/1.92 % (3647)Termination phase: shuffling
% 3.50/1.92
% 3.50/1.92 % (3647)Memory used [KB]: 1535
% 3.50/1.92 % (3647)Time elapsed: 0.005 s
% 3.50/1.92 % (3647)Instructions burned: 7 (million)
% 3.50/1.92 % (3647)------------------------------
% 3.50/1.92 % (3647)------------------------------
% 3.50/1.93 % (3648)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_3501 for (2999ds/902Mi)
% 3.50/1.93 % (3626)Instruction limit reached!
% 3.50/1.93 % (3626)------------------------------
% 3.50/1.93 % (3626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.50/1.93 % (3626)Termination reason: Unknown
% 3.50/1.93 % (3626)Termination phase: Saturation
% 3.50/1.93
% 3.50/1.93 % (3626)Memory used [KB]: 7419
% 3.50/1.93 % (3626)Time elapsed: 0.091 s
% 3.50/1.93 % (3626)Instructions burned: 183 (million)
% 3.50/1.93 % (3626)------------------------------
% 3.50/1.93 % (3626)------------------------------
% 3.50/1.94 % (3649)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_3501 for (2998ds/21Mi)
% 3.50/1.94 % (3631)First to succeed.
% 3.50/1.94 % (3650)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3501 for (2998ds/5Mi)
% 3.50/1.94 % (3631)Refutation found. Thanks to Tanya!
% 3.50/1.94 % SZS status Theorem for DTF2THF_3501
% 3.50/1.94 % SZS output start Proof for DTF2THF_3501
% 3.50/1.94 thf(type_def_5, type, com: $tType).
% 3.50/1.94 thf(type_def_7, type, pname: $tType).
% 3.50/1.94 thf(type_def_8, type, option_com: $tType).
% 3.50/1.94 thf(type_def_9, type, hoare_1262092251_state: $tType).
% 3.50/1.94 thf(func_def_0, type, com: $tType).
% 3.50/1.94 thf(func_def_1, type, pname: $tType).
% 3.50/1.94 thf(func_def_2, type, hoare_1262092251_state: $tType).
% 3.50/1.94 thf(func_def_3, type, option_com: $tType).
% 3.50/1.94 thf(func_def_4, type, wt: com > $o).
% 3.50/1.94 thf(func_def_6, type, body: pname > option_com).
% 3.50/1.94 thf(func_def_7, type, body_1: pname > com).
% 3.50/1.94 thf(func_def_8, type, finite1648353812_o_o_o: ((((pname > $o) > $o) > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_9, type, finite734360985_o_o_o: ((((hoare_1262092251_state > $o) > $o) > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_10, type, finite1066544169me_o_o: (((pname > $o) > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_11, type, finite1303896758te_o_o: (((hoare_1262092251_state > $o) > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_12, type, finite297249702name_o: ((pname > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_13, type, finite1423311111tate_o: ((hoare_1262092251_state > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_14, type, finite_finite_pname: (pname > $o) > $o).
% 3.50/1.94 thf(func_def_15, type, finite1178804552_state: (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_16, type, hoare_Mirabelle_MGT: com > hoare_1262092251_state).
% 3.50/1.94 thf(func_def_17, type, hoare_930741239_state: (hoare_1262092251_state > $o) > (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_19, type, dom_pname_o_com: ((pname > $o) > option_com) > (pname > $o) > $o).
% 3.50/1.94 thf(func_def_20, type, dom_Ho1489634536_o_com: ((hoare_1262092251_state > $o) > option_com) > (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_21, type, dom_pname_com: (pname > option_com) > pname > $o).
% 3.50/1.94 thf(func_def_22, type, some_com: com > option_com).
% 3.50/1.94 thf(func_def_23, type, the_com: option_com > com).
% 3.50/1.94 thf(func_def_24, type, bot_bot_pname_o_o_o: ((pname > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_25, type, bot_bo388435036_o_o_o: ((hoare_1262092251_state > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_26, type, bot_bot_pname_o_o: (pname > $o) > $o).
% 3.50/1.94 thf(func_def_27, type, bot_bo1962689075te_o_o: (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_28, type, bot_bot_pname_o: pname > $o).
% 3.50/1.94 thf(func_def_29, type, bot_bo113204042tate_o: hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_30, type, ord_le1828183645_o_o_o: (((pname > $o) > $o) > $o) > (((pname > $o) > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_31, type, ord_le1891858320_o_o_o: (((hoare_1262092251_state > $o) > $o) > $o) > (((hoare_1262092251_state > $o) > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_32, type, ord_le1205211808me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_33, type, ord_le2012720639te_o_o: ((hoare_1262092251_state > $o) > $o) > ((hoare_1262092251_state > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_34, type, ord_less_eq_pname_o: (pname > $o) > (pname > $o) > $o).
% 3.50/1.94 thf(func_def_35, type, ord_le870406270tate_o: (hoare_1262092251_state > $o) > (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_36, type, collect_pname_o_o_o: ((((pname > $o) > $o) > $o) > $o) > (((pname > $o) > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_37, type, collec101077467_o_o_o: ((((hoare_1262092251_state > $o) > $o) > $o) > $o) > (((hoare_1262092251_state > $o) > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_38, type, collect_pname_o_o: (((pname > $o) > $o) > $o) > ((pname > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_39, type, collec341954548te_o_o: (((hoare_1262092251_state > $o) > $o) > $o) > ((hoare_1262092251_state > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_40, type, collect_pname_o: ((pname > $o) > $o) > (pname > $o) > $o).
% 3.50/1.94 thf(func_def_41, type, collec313158217tate_o: ((hoare_1262092251_state > $o) > $o) > (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_42, type, collect_pname: (pname > $o) > pname > $o).
% 3.50/1.94 thf(func_def_43, type, collec1121927558_state: (hoare_1262092251_state > $o) > hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_44, type, image_471733107_pname: (((pname > $o) > $o) > pname) > (((pname > $o) > $o) > $o) > pname > $o).
% 3.50/1.94 thf(func_def_45, type, image_1036078444_state: (((pname > $o) > $o) > hoare_1262092251_state) > (((pname > $o) > $o) > $o) > hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_46, type, image_893364936_pname: (((hoare_1262092251_state > $o) > $o) > pname) > (((hoare_1262092251_state > $o) > $o) > $o) > pname > $o).
% 3.50/1.94 thf(func_def_47, type, image_165349207_state: (((hoare_1262092251_state > $o) > $o) > hoare_1262092251_state) > (((hoare_1262092251_state > $o) > $o) > $o) > hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_48, type, image_pname_o_pname: ((pname > $o) > pname) > ((pname > $o) > $o) > pname > $o).
% 3.50/1.94 thf(func_def_49, type, image_1476171975_state: ((pname > $o) > hoare_1262092251_state) > ((pname > $o) > $o) > hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_50, type, image_1820530197_pname: ((hoare_1262092251_state > $o) > pname) > ((hoare_1262092251_state > $o) > $o) > pname > $o).
% 3.50/1.94 thf(func_def_51, type, image_234589002_state: ((hoare_1262092251_state > $o) > hoare_1262092251_state) > ((hoare_1262092251_state > $o) > $o) > hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_52, type, image_504089495me_o_o: (pname > (pname > $o) > $o) > (pname > $o) > ((pname > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_53, type, image_827868872te_o_o: (pname > (hoare_1262092251_state > $o) > $o) > (pname > $o) > ((hoare_1262092251_state > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_54, type, image_pname_pname_o: (pname > pname > $o) > (pname > $o) > (pname > $o) > $o).
% 3.50/1.94 thf(func_def_55, type, image_518521461tate_o: (pname > hoare_1262092251_state > $o) > (pname > $o) > (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_56, type, image_pname_pname: (pname > pname) > (pname > $o) > pname > $o).
% 3.50/1.94 thf(func_def_57, type, image_669833818_state: (pname > hoare_1262092251_state) > (pname > $o) > hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_58, type, image_333245000me_o_o: (hoare_1262092251_state > (pname > $o) > $o) > (hoare_1262092251_state > $o) > ((pname > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_59, type, image_1731108951te_o_o: (hoare_1262092251_state > (hoare_1262092251_state > $o) > $o) > (hoare_1262092251_state > $o) > ((hoare_1262092251_state > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_60, type, image_1320925383name_o: (hoare_1262092251_state > pname > $o) > (hoare_1262092251_state > $o) > (pname > $o) > $o).
% 3.50/1.94 thf(func_def_61, type, image_1403668518tate_o: (hoare_1262092251_state > hoare_1262092251_state > $o) > (hoare_1262092251_state > $o) > (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_62, type, image_202231862_pname: (hoare_1262092251_state > pname) > (hoare_1262092251_state > $o) > pname > $o).
% 3.50/1.94 thf(func_def_63, type, insert_pname_o_o: ((pname > $o) > $o) > (((pname > $o) > $o) > $o) > ((pname > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_64, type, insert1691644879te_o_o: ((hoare_1262092251_state > $o) > $o) > (((hoare_1262092251_state > $o) > $o) > $o) > ((hoare_1262092251_state > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_65, type, insert_pname_o: (pname > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 3.50/1.94 thf(func_def_66, type, insert1042460334tate_o: (hoare_1262092251_state > $o) > ((hoare_1262092251_state > $o) > $o) > (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_67, type, insert_pname: pname > (pname > $o) > pname > $o).
% 3.50/1.94 thf(func_def_68, type, insert81609953_state: hoare_1262092251_state > (hoare_1262092251_state > $o) > hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_69, type, fequal_pname_o: (pname > $o) > (pname > $o) > $o).
% 3.50/1.94 thf(func_def_70, type, fequal1529404211tate_o: (hoare_1262092251_state > $o) > (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_71, type, fequal_pname: pname > pname > $o).
% 3.50/1.94 thf(func_def_72, type, fequal1925511196_state: hoare_1262092251_state > hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_73, type, member_pname_o: (pname > $o) > ((pname > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_74, type, member907417095tate_o: (hoare_1262092251_state > $o) > ((hoare_1262092251_state > $o) > $o) > $o).
% 3.50/1.94 thf(func_def_75, type, member_pname: pname > (pname > $o) > $o).
% 3.50/1.94 thf(func_def_76, type, member5164104_state: hoare_1262092251_state > (hoare_1262092251_state > $o) > $o).
% 3.50/1.94 thf(func_def_77, type, fa: hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_78, type, pn: pname).
% 3.50/1.94 thf(func_def_79, type, y: com).
% 3.50/1.94 thf(func_def_90, type, sK0: (pname > $o) > pname).
% 3.50/1.94 thf(func_def_91, type, sK1: (pname > $o) > (pname > hoare_1262092251_state) > (hoare_1262092251_state > $o) > pname > $o).
% 3.50/1.94 thf(func_def_92, type, sK2: pname > com).
% 3.50/1.94 thf(func_def_93, type, sK3: (hoare_1262092251_state > $o) > pname).
% 3.50/1.94 thf(func_def_94, type, sK4: (hoare_1262092251_state > $o) > hoare_1262092251_state).
% 3.50/1.94 thf(func_def_95, type, sK5: (pname > $o) > (pname > $o) > pname).
% 3.50/1.94 thf(func_def_96, type, sK6: ((hoare_1262092251_state > $o) > $o) > (hoare_1262092251_state > $o) > hoare_1262092251_state > $o).
% 3.50/1.94 thf(func_def_97, type, sK7: ((hoare_1262092251_state > $o) > $o) > (hoare_1262092251_state > $o) > hoare_1262092251_state).
% 3.50/1.94 thf(func_def_98, type, sK8: (hoare_1262092251_state > $o) > (hoare_1262092251_state > $o) > hoare_1262092251_state).
% 3.50/1.94 thf(func_def_99, type, sK9: hoare_1262092251_state > (pname > hoare_1262092251_state) > (pname > $o) > pname).
% 3.50/1.94 thf(func_def_100, type, sK10: (hoare_1262092251_state > $o) > hoare_1262092251_state).
% 3.50/1.94 thf(func_def_101, type, sK11: (pname > $o) > (pname > hoare_1262092251_state) > (hoare_1262092251_state > $o) > pname > $o).
% 3.50/1.94 thf(func_def_102, type, sK12: (pname > hoare_1262092251_state) > hoare_1262092251_state > (pname > $o) > pname).
% 3.50/1.94 thf(func_def_103, type, sK13: (pname > $o) > pname).
% 3.50/1.94 thf(func_def_104, type, sK14: ((pname > $o) > $o) > (pname > $o) > pname).
% 3.50/1.94 thf(func_def_105, type, sK15: ((pname > $o) > $o) > (pname > $o) > pname > $o).
% 3.50/1.94 thf(func_def_107, type, ph17: !>[X0: $tType]:(X0)).
% 3.50/1.94 thf(f1642,plain,(
% 3.50/1.94 $false),
% 3.50/1.94 inference(subsumption_resolution,[status(thm)],[f1638,f1378])).
% 3.50/1.94 thf(f1378,plain,(
% 3.50/1.94 ($true = (wt @ y))),
% 3.50/1.94 inference(equality_resolution,[status(thm)],[f1372])).
% 3.50/1.94 thf(f1372,plain,(
% 3.50/1.94 ( ! [X0 : com] : (((some_com @ y) != (some_com @ X0)) | ($true = (wt @ X0))) )),
% 3.50/1.94 inference(superposition,[status(thm)],[f1368,f1209])).
% 3.50/1.94 thf(f1209,plain,(
% 3.50/1.94 ((body @ pn) = (some_com @ y))),
% 3.50/1.94 inference(cnf_transformation,[status(thm)],[f314])).
% 3.50/1.94 thf(f314,axiom,(
% 3.50/1.94 ((body @ pn) = (some_com @ y))),
% 3.50/1.94 file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',conj_5)).
% 3.50/1.94 thf(f1368,plain,(
% 3.50/1.94 ( ! [X0 : com,X1 : pname] : (((some_com @ X0) != (body @ X1)) | ($true = (wt @ X0))) )),
% 3.50/1.94 inference(trivial_inequality_removal,[status(thm)],[f1314])).
% 3.50/1.94 thf(f1314,plain,(
% 3.50/1.94 ( ! [X0 : com,X1 : pname] : (((some_com @ X0) != (body @ X1)) | ($true != $true) | ($true = (wt @ X0))) )),
% 3.50/1.94 inference(definition_unfolding,[status(thm)],[f1170,f1254])).
% 3.50/1.94 thf(f1254,plain,(
% 3.50/1.94 (wT_bodies = $true)),
% 3.50/1.94 inference(cnf_transformation,[status(thm)],[f482])).
% 3.50/1.94 thf(f482,plain,(
% 3.50/1.94 (wT_bodies = $true)),
% 3.50/1.94 inference(fool_elimination,[status(thm)],[f481])).
% 3.50/1.94 thf(f481,plain,(
% 3.50/1.94 wT_bodies),
% 3.50/1.94 inference(rectify,[status(thm)],[f310])).
% 3.50/1.94 thf(f310,axiom,(
% 3.50/1.94 wT_bodies),
% 3.50/1.94 file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',conj_1)).
% 3.50/1.94 thf(f1170,plain,(
% 3.50/1.94 ( ! [X0 : com,X1 : pname] : (((some_com @ X0) != (body @ X1)) | ($true = (wt @ X0)) | (wT_bodies != $true)) )),
% 3.50/1.94 inference(cnf_transformation,[status(thm)],[f1005])).
% 3.50/1.94 thf(f1005,plain,(
% 3.50/1.94 ! [X0 : com,X1 : pname] : (((some_com @ X0) != (body @ X1)) | ($true = (wt @ X0)) | (wT_bodies != $true))),
% 3.50/1.94 inference(flattening,[status(thm)],[f1004])).
% 3.50/1.94 thf(f1004,plain,(
% 3.50/1.94 ! [X0 : com,X1 : pname] : ((($true = (wt @ X0)) | ((some_com @ X0) != (body @ X1))) | (wT_bodies != $true))),
% 3.50/1.94 inference(ennf_transformation,[status(thm)],[f792])).
% 3.50/1.94 thf(f792,plain,(
% 3.50/1.94 ! [X0 : com,X1 : pname] : ((wT_bodies = $true) => (((some_com @ X0) = (body @ X1)) => ($true = (wt @ X0))))),
% 3.50/1.94 inference(fool_elimination,[status(thm)],[f791])).
% 3.50/1.94 thf(f791,plain,(
% 3.50/1.94 ! [X0 : com,X1 : pname] : (wT_bodies => (((some_com @ X0) = (body @ X1)) => (wt @ X0)))),
% 3.50/1.94 inference(rectify,[status(thm)],[f289])).
% 3.50/1.94 thf(f289,axiom,(
% 3.50/1.94 ! [X192 : com,X18 : pname] : (wT_bodies => (((body @ X18) = (some_com @ X192)) => (wt @ X192)))),
% 3.50/1.94 file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',fact_288_WT__bodiesD)).
% 3.50/1.94 thf(f1638,plain,(
% 3.50/1.94 ($true != (wt @ y))),
% 3.50/1.94 inference(trivial_inequality_removal,[status(thm)],[f1625])).
% 3.50/1.94 thf(f1625,plain,(
% 3.50/1.94 ($true != (wt @ y)) | ($true != $true)),
% 3.50/1.94 inference(superposition,[status(thm)],[f1560,f1365])).
% 3.50/1.94 thf(f1365,plain,(
% 3.50/1.94 ( ! [X0 : com] : (($true = (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo113204042tate_o))) | ($true != (wt @ X0))) )),
% 3.50/1.94 inference(trivial_inequality_removal,[status(thm)],[f1364])).
% 3.50/1.94 thf(f1364,plain,(
% 3.50/1.94 ( ! [X0 : com] : (($true != $true) | ($true != (wt @ X0)) | ($true = (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo113204042tate_o)))) )),
% 3.50/1.94 inference(duplicate_literal_removal,[status(thm)],[f1315])).
% 3.50/1.94 thf(f1315,plain,(
% 3.50/1.94 ( ! [X0 : com] : (($true != $true) | ($true = (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo113204042tate_o))) | ($true != (wt @ X0)) | ($true != $true)) )),
% 3.50/1.94 inference(definition_unfolding,[status(thm)],[f1244,f1254,f1243])).
% 3.50/1.94 thf(f1243,plain,(
% 3.50/1.94 (hoare_1821564147gleton = $true)),
% 3.50/1.94 inference(cnf_transformation,[status(thm)],[f416])).
% 3.50/1.94 thf(f416,plain,(
% 3.50/1.94 (hoare_1821564147gleton = $true)),
% 3.50/1.94 inference(fool_elimination,[status(thm)],[f415])).
% 3.50/1.94 thf(f415,plain,(
% 3.50/1.94 hoare_1821564147gleton),
% 3.50/1.94 inference(rectify,[status(thm)],[f309])).
% 3.50/1.94 thf(f309,axiom,(
% 3.50/1.94 hoare_1821564147gleton),
% 3.50/1.94 file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',conj_0)).
% 3.50/1.94 thf(f1244,plain,(
% 3.50/1.94 ( ! [X0 : com] : ((wT_bodies != $true) | ($true != (wt @ X0)) | ($true = (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo113204042tate_o))) | (hoare_1821564147gleton != $true)) )),
% 3.50/1.94 inference(cnf_transformation,[status(thm)],[f942])).
% 3.50/1.94 thf(f942,plain,(
% 3.50/1.94 ! [X0 : com] : ((wT_bodies != $true) | ($true != (wt @ X0)) | ($true = (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo113204042tate_o))) | (hoare_1821564147gleton != $true))),
% 3.50/1.94 inference(flattening,[status(thm)],[f941])).
% 3.50/1.94 thf(f941,plain,(
% 3.50/1.94 ! [X0 : com] : (((($true = (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo113204042tate_o))) | ($true != (wt @ X0))) | (wT_bodies != $true)) | (hoare_1821564147gleton != $true))),
% 3.50/1.94 inference(ennf_transformation,[status(thm)],[f820])).
% 3.50/1.94 thf(f820,plain,(
% 3.50/1.94 ! [X0 : com] : ((hoare_1821564147gleton = $true) => ((wT_bodies = $true) => (($true = (wt @ X0)) => ($true = (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo113204042tate_o))))))),
% 3.50/1.94 inference(fool_elimination,[status(thm)],[f819])).
% 3.50/1.94 thf(f819,plain,(
% 3.50/1.94 ! [X0 : com] : (hoare_1821564147gleton => (wT_bodies => ((wt @ X0) => (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo113204042tate_o)))))),
% 3.50/1.94 inference(rectify,[status(thm)],[f104])).
% 3.50/1.94 thf(f104,axiom,(
% 3.50/1.94 ! [X42 : com] : (hoare_1821564147gleton => (wT_bodies => ((wt @ X42) => (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ X42) @ bot_bo113204042tate_o)))))),
% 3.50/1.94 file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',fact_103_MGF)).
% 3.50/1.94 thf(f1560,plain,(
% 3.50/1.94 ($true != (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o)))),
% 3.50/1.94 inference(trivial_inequality_removal,[status(thm)],[f1549])).
% 3.50/1.94 thf(f1549,plain,(
% 3.50/1.94 ($true != $true) | ($true != (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o)))),
% 3.50/1.94 inference(superposition,[status(thm)],[f1424,f1302])).
% 3.50/1.94 thf(f1302,plain,(
% 3.50/1.94 ( ! [X0 : hoare_1262092251_state > $o] : (((hoare_930741239_state @ X0 @ bot_bo113204042tate_o) = $true)) )),
% 3.50/1.94 inference(cnf_transformation,[status(thm)],[f418])).
% 3.50/1.94 thf(f418,plain,(
% 3.50/1.94 ! [X0 : hoare_1262092251_state > $o] : ((hoare_930741239_state @ X0 @ bot_bo113204042tate_o) = $true)),
% 3.50/1.94 inference(fool_elimination,[status(thm)],[f417])).
% 3.50/1.94 thf(f417,plain,(
% 3.50/1.94 ! [X0 : hoare_1262092251_state > $o] : (hoare_930741239_state @ X0 @ bot_bo113204042tate_o)),
% 3.50/1.94 inference(rectify,[status(thm)],[f1])).
% 3.50/1.94 thf(f1,axiom,(
% 3.50/1.94 ! [X0 : hoare_1262092251_state > $o] : (hoare_930741239_state @ X0 @ bot_bo113204042tate_o)),
% 3.50/1.94 file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',fact_0_empty)).
% 3.50/1.94 thf(f1424,plain,(
% 3.50/1.94 ( ! [X0 : hoare_1262092251_state > $o] : (($true != (hoare_930741239_state @ (image_669833818_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ X0)) | ($true != (hoare_930741239_state @ X0 @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o)))) )),
% 3.50/1.94 inference(trivial_inequality_removal,[status(thm)],[f1418])).
% 3.50/1.94 thf(f1418,plain,(
% 3.50/1.94 ( ! [X0 : hoare_1262092251_state > $o] : (($true != (hoare_930741239_state @ X0 @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o))) | ($true != (hoare_930741239_state @ (image_669833818_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ X0)) | ($true != $true)) )),
% 3.50/1.94 inference(superposition,[status(thm)],[f1275,f1279])).
% 3.50/1.94 thf(f1279,plain,(
% 3.50/1.94 ( ! [X2 : hoare_1262092251_state > $o,X0 : hoare_1262092251_state > $o,X1 : hoare_1262092251_state > $o] : (($true = (hoare_930741239_state @ X0 @ X2)) | ((hoare_930741239_state @ X1 @ X2) != $true) | ((hoare_930741239_state @ X0 @ X1) != $true)) )),
% 3.50/1.94 inference(cnf_transformation,[status(thm)],[f939])).
% 3.50/1.94 thf(f939,plain,(
% 3.50/1.94 ! [X0 : hoare_1262092251_state > $o,X1 : hoare_1262092251_state > $o,X2 : hoare_1262092251_state > $o] : (($true = (hoare_930741239_state @ X0 @ X2)) | ((hoare_930741239_state @ X0 @ X1) != $true) | ((hoare_930741239_state @ X1 @ X2) != $true))),
% 3.50/1.94 inference(flattening,[status(thm)],[f938])).
% 3.50/1.94 thf(f938,plain,(
% 3.50/1.94 ! [X0 : hoare_1262092251_state > $o,X1 : hoare_1262092251_state > $o,X2 : hoare_1262092251_state > $o] : ((($true = (hoare_930741239_state @ X0 @ X2)) | ((hoare_930741239_state @ X0 @ X1) != $true)) | ((hoare_930741239_state @ X1 @ X2) != $true))),
% 3.50/1.94 inference(ennf_transformation,[status(thm)],[f536])).
% 3.50/1.94 thf(f536,plain,(
% 3.50/1.94 ! [X0 : hoare_1262092251_state > $o,X1 : hoare_1262092251_state > $o,X2 : hoare_1262092251_state > $o] : (((hoare_930741239_state @ X1 @ X2) = $true) => (((hoare_930741239_state @ X0 @ X1) = $true) => ($true = (hoare_930741239_state @ X0 @ X2))))),
% 3.50/1.94 inference(fool_elimination,[status(thm)],[f535])).
% 3.50/1.94 thf(f535,plain,(
% 3.50/1.94 ! [X0 : hoare_1262092251_state > $o,X1 : hoare_1262092251_state > $o,X2 : hoare_1262092251_state > $o] : ((hoare_930741239_state @ X1 @ X2) => ((hoare_930741239_state @ X0 @ X1) => (hoare_930741239_state @ X0 @ X2)))),
% 3.50/1.94 inference(rectify,[status(thm)],[f5])).
% 3.50/1.94 thf(f5,axiom,(
% 3.50/1.94 ! [X9 : hoare_1262092251_state > $o,X10 : hoare_1262092251_state > $o,X11 : hoare_1262092251_state > $o] : ((hoare_930741239_state @ X10 @ X11) => ((hoare_930741239_state @ X9 @ X10) => (hoare_930741239_state @ X9 @ X11)))),
% 3.50/1.94 file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',fact_4_cut)).
% 3.50/1.94 thf(f1275,plain,(
% 3.50/1.94 ((hoare_930741239_state @ (image_669833818_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o)) != $true)),
% 3.50/1.94 inference(cnf_transformation,[status(thm)],[f894])).
% 3.50/1.94 thf(f894,plain,(
% 3.50/1.94 ((hoare_930741239_state @ (image_669833818_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o)) != $true)),
% 3.50/1.94 inference(flattening,[status(thm)],[f640])).
% 3.50/1.94 thf(f640,plain,(
% 3.50/1.94 ~((hoare_930741239_state @ (image_669833818_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o)) = $true)),
% 3.50/1.94 inference(fool_elimination,[status(thm)],[f639])).
% 3.50/1.94 thf(f639,plain,(
% 3.50/1.94 ~(hoare_930741239_state @ (image_669833818_state @ (^[X0 : pname] : (hoare_Mirabelle_MGT @ (body_1 @ X0))) @ (dom_pname_com @ body)) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o))),
% 3.50/1.94 inference(rectify,[status(thm)],[f317])).
% 3.50/1.94 thf(f317,negated_conjecture,(
% 3.50/1.94 ~(hoare_930741239_state @ (image_669833818_state @ (^[X212 : pname] : (hoare_Mirabelle_MGT @ (body_1 @ X212))) @ (dom_pname_com @ body)) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o))),
% 3.50/1.94 inference(negated_conjecture,[status(cth)],[f316])).
% 3.50/1.94 thf(f316,conjecture,(
% 3.50/1.94 (hoare_930741239_state @ (image_669833818_state @ (^[X212 : pname] : (hoare_Mirabelle_MGT @ (body_1 @ X212))) @ (dom_pname_com @ body)) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o))),
% 3.50/1.94 file('/export/starexec/sandbox/tmp/tmp.lvQVJwV2HN/DTF2THF_3501.p',conj_7)).
% 3.50/1.94 % SZS output end Proof for DTF2THF_3501
% 3.50/1.94 % (3631)------------------------------
% 3.50/1.94 % (3631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.50/1.94 % (3631)Termination reason: Refutation
% 3.50/1.94
% 3.50/1.94 % (3631)Memory used [KB]: 7036
% 3.50/1.94 % (3631)Time elapsed: 0.099 s
% 3.50/1.94 % (3631)Instructions burned: 194 (million)
% 3.50/1.94 % (3631)------------------------------
% 3.50/1.94 % (3631)------------------------------
% 3.50/1.94 % (3625)Success in time 0.123 s
%------------------------------------------------------------------------------