%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP057^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 : Sat Feb 28 09:03:39 AM UTC 2026
% Result : Theorem 2.96s 1.68s
% Output : Refutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 24 unt; 0 typ; 3 def)
% Number of atoms : 272 ( 85 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 690 ( 36 ~; 23 |; 20 &; 583 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 77 usr; 23 con; 0-6 aty)
% Number of variables : 46 ( 34 ^; 6 !; 6 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
p: $tType ).
thf(type_def_6,type,
s: $tType ).
thf(type_def_7,type,
messageValue_v: $tType ).
thf(type_def_9,type,
message_p_v: $tType ).
thf(type_def_10,type,
nat: $tType ).
thf(type_def_11,type,
config256849571t_unit: $tType ).
thf(type_def_12,type,
set_p: $tType ).
thf(type_def_13,type,
list_c1059388851t_unit: $tType ).
thf(type_def_14,type,
list_message_p_v: $tType ).
thf(type_def_15,type,
set_o: $tType ).
thf(func_def_0,type,
list_c1059388851t_unit: $tType ).
thf(func_def_1,type,
config256849571t_unit: $tType ).
thf(func_def_2,type,
list_message_p_v: $tType ).
thf(func_def_3,type,
message_p_v: $tType ).
thf(func_def_4,type,
messageValue_v: $tType ).
thf(func_def_5,type,
set_p: $tType ).
thf(func_def_6,type,
set_o: $tType ).
thf(func_def_7,type,
nat: $tType ).
thf(func_def_8,type,
s: $tType ).
thf(func_def_9,type,
p: $tType ).
thf(func_def_10,type,
initReachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > config256849571t_unit > $o ).
thf(func_def_11,type,
initial_p_s_v: ( p > s ) > config256849571t_unit > $o ).
thf(func_def_12,type,
qReachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > set_p > config256849571t_unit > $o ).
thf(func_def_13,type,
reachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_14,type,
stepReachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > message_p_v > config256849571t_unit > $o ).
thf(func_def_15,type,
steps_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > message_p_v > config256849571t_unit > $o ).
thf(func_def_16,type,
msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat ).
thf(func_def_17,type,
states1228886952t_unit: config256849571t_unit > p > s ).
thf(func_def_18,type,
enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
thf(func_def_19,type,
isReceiverOf_p_v: p > message_p_v > $o ).
thf(func_def_20,type,
outMsg_p_v: $o > message_p_v ).
thf(func_def_21,type,
execution_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > list_c1059388851t_unit > list_message_p_v > $o ).
thf(func_def_22,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(func_def_23,type,
minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o ).
thf(func_def_24,type,
flpSystem_p_s_v: ( p > s > messageValue_v > message_p_v > nat ) > $o ).
thf(func_def_25,type,
agreementInit_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_26,type,
agreement_p_v_s: config256849571t_unit > $o ).
thf(func_def_27,type,
pSilDecVal_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o > p > config256849571t_unit > $o ).
thf(func_def_28,type,
termin1618267753_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > nat > config256849571t_unit > set_p > $o ).
thf(func_def_29,type,
vUniform_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o > config256849571t_unit > $o ).
thf(func_def_30,type,
validity_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_31,type,
fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
thf(func_def_32,type,
one_one_nat: nat ).
thf(func_def_33,type,
zero_zero_nat: nat ).
thf(func_def_34,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(func_def_35,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(func_def_36,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_37,type,
last_message_p_v: list_message_p_v > message_p_v ).
thf(func_def_38,type,
bot_bot_o_o: $o > $o ).
thf(func_def_39,type,
bot_bot_nat: nat ).
thf(func_def_40,type,
bot_bot_set_o: set_o ).
thf(func_def_41,type,
bot_bot_set_p: set_p ).
thf(func_def_42,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_43,type,
ord_less_set_o: set_o > set_o > $o ).
thf(func_def_44,type,
ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_45,type,
ord_less_eq_p_o: ( p > $o ) > ( p > $o ) > $o ).
thf(func_def_46,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_47,type,
ord_less_eq_set_o: set_o > set_o > $o ).
thf(func_def_48,type,
ord_less_eq_set_p: set_p > set_p > $o ).
thf(func_def_49,type,
collect_o: ( $o > $o ) > set_o ).
thf(func_def_50,type,
collect_p: ( p > $o ) > set_p ).
thf(func_def_51,type,
insert_o: $o > set_o > set_o ).
thf(func_def_52,type,
insert_p: p > set_p > set_p ).
thf(func_def_53,type,
member_o: $o > set_o > $o ).
thf(func_def_54,type,
member_p: p > set_p > $o ).
thf(func_def_55,type,
cMsg: config256849571t_unit ).
thf(func_def_56,type,
c: config256849571t_unit ).
thf(func_def_57,type,
exec: list_c1059388851t_unit ).
thf(func_def_58,type,
execMsga: list_c1059388851t_unit ).
thf(func_def_59,type,
exec2: list_c1059388851t_unit ).
thf(func_def_60,type,
msg: message_p_v ).
thf(func_def_61,type,
p2: p ).
thf(func_def_62,type,
sends: p > s > messageValue_v > message_p_v > nat ).
thf(func_def_63,type,
start: p > s ).
thf(func_def_64,type,
trace: list_message_p_v ).
thf(func_def_65,type,
traceMsga: list_message_p_v ).
thf(func_def_66,type,
trace2: list_message_p_v ).
thf(func_def_67,type,
trans: p > s > messageValue_v > s ).
thf(func_def_87,type,
sK0: list_message_p_v ).
thf(func_def_88,type,
sK1: list_c1059388851t_unit ).
thf(func_def_89,type,
sK2: ( set_o > set_o ) > set_o ).
thf(func_def_90,type,
sK3: ( set_o > set_o ) > set_o ).
thf(func_def_91,type,
sK4: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_92,type,
sK5: ( set_o > set_o ) > set_o ).
thf(func_def_93,type,
sK6: ( set_o > set_o ) > set_o ).
thf(func_def_94,type,
sK7: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_95,type,
sK8: ( $o > $o ) > $o ).
thf(func_def_96,type,
sK9: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_97,type,
sK10: ( set_o > set_o ) > set_o ).
thf(func_def_98,type,
sK11: ( set_o > set_o ) > set_o ).
thf(func_def_99,type,
sK12: config256849571t_unit ).
thf(func_def_100,type,
sK13: ( $o > $o ) > $o ).
thf(func_def_101,type,
sK14: ( set_o > set_o ) > set_o ).
thf(func_def_102,type,
sK15: ( set_o > set_o ) > set_o ).
thf(f1199,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1194,f1195,f1196,f1198]) ).
thf(f1198,plain,
spl16_2,
inference(avatar_split_clause,[status(thm)],[f1149,f1187]) ).
thf(f1187,definition,
( spl16_2
<=> ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl16_2])],[avatar_definition]) ).
thf(f1149,plain,
( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f857]) ).
thf(f857,plain,
( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f856]) ).
thf(f856,plain,
initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ),
file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_1_InitReachLastExec_H) ).
thf(f1196,plain,
spl16_3,
inference(avatar_split_clause,[status(thm)],[f1160,f1191]) ).
thf(f1191,definition,
( spl16_3
<=> ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ ( last_message_p_v @ sK0 ) @ ( last_c571238084t_unit @ sK1 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl16_3])],[avatar_definition]) ).
thf(f1160,plain,
( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ ( last_message_p_v @ sK0 ) @ ( last_c571238084t_unit @ sK1 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1120,f1111,f1110]) ).
thf(f1110,plain,
( cMsg
= ( last_c571238084t_unit @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f1076]) ).
thf(f1076,plain,
( ( ( prefix47729710ge_p_v @ trace2 @ sK0 )
= $true )
& ( msg
= ( last_message_p_v @ sK0 ) )
& ( cMsg
= ( last_c571238084t_unit @ sK1 ) )
& ( ( prefix1615116500t_unit @ exec2 @ sK1 )
= $true )
& ( ( execution_p_s_v @ trans @ sends @ start @ sK1 @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f1032,f1075]) ).
thf(f1075,plain,
( ? [X0: list_message_p_v,X1: list_c1059388851t_unit] :
( ( ( prefix47729710ge_p_v @ trace2 @ X0 )
= $true )
& ( msg
= ( last_message_p_v @ X0 ) )
& ( cMsg
= ( last_c571238084t_unit @ X1 ) )
& ( $true
= ( prefix1615116500t_unit @ exec2 @ X1 ) )
& ( $true
= ( execution_p_s_v @ trans @ sends @ start @ X1 @ X0 ) ) )
=> ( ( ( prefix47729710ge_p_v @ trace2 @ sK0 )
= $true )
& ( msg
= ( last_message_p_v @ sK0 ) )
& ( cMsg
= ( last_c571238084t_unit @ sK1 ) )
& ( ( prefix1615116500t_unit @ exec2 @ sK1 )
= $true )
& ( ( execution_p_s_v @ trans @ sends @ start @ sK1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1032,plain,
? [X0: list_message_p_v,X1: list_c1059388851t_unit] :
( ( ( prefix47729710ge_p_v @ trace2 @ X0 )
= $true )
& ( msg
= ( last_message_p_v @ X0 ) )
& ( cMsg
= ( last_c571238084t_unit @ X1 ) )
& ( $true
= ( prefix1615116500t_unit @ exec2 @ X1 ) )
& ( $true
= ( execution_p_s_v @ trans @ sends @ start @ X1 @ X0 ) ) ),
inference(flattening,[status(thm)],[f1031]) ).
thf(f1031,plain,
? [X0: list_message_p_v,X1: list_c1059388851t_unit] :
( ( msg
= ( last_message_p_v @ X0 ) )
& ( cMsg
= ( last_c571238084t_unit @ X1 ) )
& ( ( prefix47729710ge_p_v @ trace2 @ X0 )
= $true )
& ( $true
= ( prefix1615116500t_unit @ exec2 @ X1 ) )
& ( $true
= ( execution_p_s_v @ trans @ sends @ start @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f1013]) ).
thf(f1013,plain,
~ ! [X0: list_message_p_v,X1: list_c1059388851t_unit] :
( ( $true
= ( execution_p_s_v @ trans @ sends @ start @ X1 @ X0 ) )
=> ( ( $true
= ( prefix1615116500t_unit @ exec2 @ X1 ) )
=> ( ( ( prefix47729710ge_p_v @ trace2 @ X0 )
= $true )
=> ( ( cMsg
= ( last_c571238084t_unit @ X1 ) )
=> ( msg
!= ( last_message_p_v @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f1012]) ).
thf(f1012,plain,
~ ! [X0: list_message_p_v,X1: list_c1059388851t_unit] :
( ( execution_p_s_v @ trans @ sends @ start @ X1 @ X0 )
=> ( ( prefix1615116500t_unit @ exec2 @ X1 )
=> ( ( prefix47729710ge_p_v @ trace2 @ X0 )
=> ( ( cMsg
= ( last_c571238084t_unit @ X1 ) )
=> ( msg
!= ( last_message_p_v @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f272]) ).
thf(f272,axiom,
~ ! [X87: list_message_p_v,X86: list_c1059388851t_unit] :
( ( execution_p_s_v @ trans @ sends @ start @ X86 @ X87 )
=> ( ( prefix1615116500t_unit @ exec2 @ X86 )
=> ( ( prefix47729710ge_p_v @ trace2 @ X87 )
=> ( ( cMsg
= ( last_c571238084t_unit @ X86 ) )
=> ( msg
!= ( last_message_p_v @ X87 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_271__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062execMsg_AtraceMsg_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_AexecMsg_AtraceMsg_059_AprefixList_Aexec_H_AexecMsg_059_AprefixList_Atrace_H_AtraceMsg_059_Alast_AexecMsg_A_061_AcMsg_059_Alast_AtraceMsg_A_061_Amsg_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(f1111,plain,
( msg
= ( last_message_p_v @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f1076]) ).
thf(f1120,plain,
( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
= $true ),
inference(cnf_transformation,[status(thm)],[f558]) ).
thf(f558,plain,
( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
= $true ),
inference(fool_elimination,[status(thm)],[f557]) ).
thf(f557,plain,
steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg,
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg,
file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_3_CMsg) ).
thf(f1195,plain,
~ spl16_1,
inference(avatar_split_clause,[status(thm)],[f1161,f1183]) ).
thf(f1183,definition,
( spl16_1
<=> ( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ sK1 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl16_1])],[avatar_definition]) ).
thf(f1161,plain,
( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ sK1 ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f1150,f1110]) ).
thf(f1150,plain,
( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1024]) ).
thf(f1024,plain,
( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg ) ) )
!= $true ),
inference(flattening,[status(thm)],[f402]) ).
thf(f402,plain,
( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f401]) ).
thf(f401,plain,
~ ( ord_less_eq_set_o
@ ( collect_o
@ ^ [X0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [X1: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X1 @ p2 @ cMsg ) ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ( ord_less_eq_set_o
@ ( collect_o
@ ^ [X0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [X0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ cMsg ) ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
( ord_less_eq_set_o
@ ( collect_o
@ ^ [X0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [X0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ cMsg ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',conj_0) ).
thf(f1194,plain,
( spl16_1
| ~ spl16_2
| ~ spl16_3 ),
inference(avatar_split_clause,[status(thm)],[f1181,f1191,f1187,f1183]) ).
thf(f1181,plain,
( ( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ sK1 ) ) ) )
= $true )
| ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ ( last_message_p_v @ sK0 ) @ ( last_c571238084t_unit @ sK1 ) )
!= $true )
| ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1178,f1164]) ).
thf(f1164,plain,
( ( isReceiverOf_p_v @ p2 @ ( last_message_p_v @ sK0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1157,f1111]) ).
thf(f1157,plain,
( ( isReceiverOf_p_v @ p2 @ msg )
= $true ),
inference(cnf_transformation,[status(thm)],[f534]) ).
thf(f534,plain,
( ( isReceiverOf_p_v @ p2 @ msg )
= $true ),
inference(fool_elimination,[status(thm)],[f533]) ).
thf(f533,plain,
isReceiverOf_p_v @ p2 @ msg,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
isReceiverOf_p_v @ p2 @ msg,
file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_0_PisReceiverOf) ).
thf(f1178,plain,
( ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ ( last_message_p_v @ sK0 ) @ ( last_c571238084t_unit @ sK1 ) )
!= $true )
| ( ( isReceiverOf_p_v @ p2 @ ( last_message_p_v @ sK0 ) )
!= $true )
| ( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ sK1 ) ) ) )
= $true )
| ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1162]) ).
thf(f1162,plain,
( ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ ( last_message_p_v @ sK0 ) @ ( last_c571238084t_unit @ sK1 ) )
!= $true )
| ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
!= $true )
| ( ( isReceiverOf_p_v @ p2 @ ( last_message_p_v @ sK0 ) )
!= $true )
| ( p2 != p2 )
| ( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ sK1 ) ) ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f1154,f1111,f1110,f1111,f1110]) ).
thf(f1154,plain,
( ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
!= $true )
| ( ( isReceiverOf_p_v @ p2 @ msg )
!= $true )
| ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
!= $true )
| ( p2 != p2 )
| ( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1044]) ).
thf(f1044,plain,
( ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
!= $true )
| ( ( isReceiverOf_p_v @ p2 @ msg )
!= $true )
| ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
!= $true )
| ( p2 != p2 )
| ( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg ) ) )
= $true ) ),
inference(flattening,[status(thm)],[f1043]) ).
thf(f1043,plain,
( ( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg ) ) )
= $true )
| ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
!= $true )
| ( ( isReceiverOf_p_v @ p2 @ msg )
!= $true )
| ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
!= $true )
| ( p2 != p2 ) ),
inference(ennf_transformation,[status(thm)],[f747]) ).
thf(f747,plain,
( ( p2 = p2 )
=> ( ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
= $true )
=> ( ( ( isReceiverOf_p_v @ p2 @ msg )
= $true )
=> ( ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
= $true )
=> ( ( ord_less_eq_set_o
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [Y0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg ) ) )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f746]) ).
thf(f746,plain,
( ( p2 = p2 )
=> ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
=> ( ( isReceiverOf_p_v @ p2 @ msg )
=> ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
=> ( ord_less_eq_set_o
@ ( collect_o
@ ^ [X0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [X1: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X1 @ p2 @ cMsg ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( p2 = p2 )
=> ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
=> ( ( isReceiverOf_p_v @ p2 @ msg )
=> ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
=> ( ord_less_eq_set_o
@ ( collect_o
@ ^ [X0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
@ ( collect_o
@ ^ [X0: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ cMsg ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_6__092_060open_062_092_060lbrakk_062p_A_061_Ap_059_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_059_AisReceiverOf_Ap_Amsg_059_AinitReachable_A_Ilast_Aexec_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Aval_091p_Mlast_Aexec_H_093_A_092_060subseteq_062_Aval_091p_McMsg_093_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP057^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n011.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu Feb 26 01:02:32 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : ITP057^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.29/0.47 % Domain : Interactive Theorem Proving
% 0.29/0.47 % Problem : Sledgehammer FLPTheorem problem prob_165__3291512_1
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Des21]
% 0.29/0.47 % Names : FLPTheorem/prob_165__3291512_1 [Des21]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : ? v9.2.1
% 0.29/0.47 % Syntax : Number of formulae : 424 ( 147 unt; 68 typ; 0 def)
% 0.29/0.47 % Number of atoms : 1196 ( 323 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 12 ( 3 avg)
% 0.29/0.47 % Number of connectives : 3524 ( 130 ~; 25 |; 121 &;2765 @)
% 0.29/0.47 % ( 0 <=>; 483 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 24 ( 7 avg)
% 0.29/0.47 % Number of types : 11 ( 10 usr)
% 0.29/0.47 % Number of type conns : 645 ( 645 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 61 ( 58 usr; 17 con; 0-6 aty)
% 0.29/0.47 % Number of variables : 1128 ( 153 ^; 916 !; 59 ?;1128 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:22.046
% 0.29/0.47 % Bugfixes : Added ()s around negated sides of equations.
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % Could-be-implicit typings (10)
% 0.29/0.47 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.29/0.47 list_c1059388851t_unit: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.29/0.47 config256849571t_unit: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.29/0.47 list_message_p_v: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.29/0.47 message_p_v: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__AsynchronousSystem__OmessageValue_Itf__v_J,type,
% 0.29/0.47 messageValue_v: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Set__Oset_Itf__p_J,type,
% 0.29/0.47 set_p: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 0.29/0.47 set_o: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.29/0.47 nat: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_tf__s,type,
% 0.29/0.47 s: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_tf__p,type,
% 0.29/0.47 p: $tType ).
% 0.29/0.47
% 0.29/0.47 % Explicit typings (58)
% 0.29/0.47 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OinitReachable_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 initReachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oinitial_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 initial_p_s_v: ( p > s ) > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OqReachable_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 qReachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > set_p > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oreachable_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 reachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OstepReachable_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 stepReachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > message_p_v > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Osteps_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 steps_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > message_p_v > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs_001tf__p_001tf__v_001tf__s_001t__Product____Type__Ounit,type,
% 0.29/0.47 msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_Oconfiguration_Ostates_001tf__p_001tf__v_001tf__s_001t__Product____Type__Ounit,type,
% 0.29/0.47 states1228886952t_unit: config256849571t_unit > p > s ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
% 0.29/0.47 enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_OisReceiverOf_001tf__p_001tf__v,type,
% 0.29/0.47 isReceiverOf_p_v: p > message_p_v > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_AsynchronousSystem_Omessage_OOutMsg_001tf__p_001tf__v,type,
% 0.29/0.47 outMsg_p_v: $o > message_p_v ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Execution_Oexecution_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 execution_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > list_c1059388851t_unit > list_message_p_v > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
% 0.29/0.47 firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Execution_Oexecution_OminimalEnabled_001tf__p_001tf__v_001tf__s,type,
% 0.29/0.47 minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_FLPSystem_OflpSystem_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 flpSystem_p_s_v: ( p > s > messageValue_v > message_p_v > nat ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_FLPSystem_OflpSystem_OagreementInit_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 agreementInit_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > config256849571t_unit > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_FLPSystem_OflpSystem_Oagreement_001tf__p_001tf__v_001tf__s,type,
% 0.29/0.47 agreement_p_v_s: config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_FLPSystem_OflpSystem_OpSilDecVal_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 pSilDecVal_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o > p > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_FLPSystem_OflpSystem_OterminationPseudo_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 termin1618267753_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > nat > config256849571t_unit > set_p > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_FLPSystem_OflpSystem_OvUniform_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 vUniform_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_FLPSystem_OflpSystem_Ovalidity_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 validity_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > config256849571t_unit > config256849571t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_001tf__p_001tf__s_001tf__v,type,
% 0.29/0.47 fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.29/0.47 one_one_nat: nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.29/0.47 zero_zero_nat: nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.29/0.47 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.29/0.47 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_List_Olast_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.29/0.47 last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_List_Olast_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.29/0.47 last_message_p_v: list_message_p_v > message_p_v ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_Eo_M_Eo_J,type,
% 0.29/0.47 bot_bot_o_o: $o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 0.29/0.47 bot_bot_nat: nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_Eo_J,type,
% 0.29/0.47 bot_bot_set_o: set_o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__p_J,type,
% 0.29/0.47 bot_bot_set_p: set_p ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.29/0.47 ord_less_nat: nat > nat > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_I_Eo_J,type,
% 0.29/0.47 ord_less_set_o: set_o > set_o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_Eo_J,type,
% 0.29/0.47 ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__p_M_Eo_J,type,
% 0.29/0.47 ord_less_eq_p_o: ( p > $o ) > ( p > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.29/0.47 ord_less_eq_nat: nat > nat > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
% 0.29/0.47 ord_less_eq_set_o: set_o > set_o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__p_J,type,
% 0.29/0.47 ord_less_eq_set_p: set_p > set_p > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_OCollect_001_Eo,type,
% 0.29/0.47 collect_o: ( $o > $o ) > set_o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_OCollect_001tf__p,type,
% 0.29/0.47 collect_p: ( p > $o ) > set_p ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_Oinsert_001_Eo,type,
% 0.29/0.47 insert_o: $o > set_o > set_o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_Oinsert_001tf__p,type,
% 0.29/0.47 insert_p: p > set_p > set_p ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_member_001_Eo,type,
% 0.29/0.47 member_o: $o > set_o > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_member_001tf__p,type,
% 0.29/0.47 member_p: p > set_p > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_cMsg____,type,
% 0.29/0.47 cMsg: config256849571t_unit ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_c_H____,type,
% 0.29/0.47 c: config256849571t_unit ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_exec,type,
% 0.29/0.47 exec: list_c1059388851t_unit ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_execMsga____,type,
% 0.29/0.47 execMsga: list_c1059388851t_unit ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_exec_H____,type,
% 0.29/0.47 exec2: list_c1059388851t_unit ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_msg,type,
% 0.29/0.47 msg: message_p_v ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_p,type,
% 0.29/0.47 p2: p ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_sends,type,
% 0.29/0.47 sends: p > s > messageValue_v > message_p_v > nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_start,type,
% 0.29/0.47 start: p > s ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_trace,type,
% 0.29/0.47 trace: list_message_p_v ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_traceMsga____,type,
% 0.29/0.47 traceMsga: list_message_p_v ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_trace_H____,type,
% 0.29/0.47 trace2: list_message_p_v ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_trans,type,
% 0.29/0.47 trans: p > s > messageValue_v > s ).
% 0.29/0.47
% 0.29/0.47 % Relevant facts (355)
% 0.29/0.47 thf(fact_0_PisReceiverOf,axiom,
% 0.29/0.47 isReceiverOf_p_v @ p2 @ msg ).
% 0.29/0.47
% 0.29/0.47 % PisReceiverOf
% 0.29/0.47 thf(fact_1_InitReachLastExec_H,axiom,
% 0.29/0.47 initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) ).
% 0.29/0.47
% 0.29/0.47 % InitReachLastExec'
% 0.29/0.47 thf(fact_2_NewExec_I3_J,axiom,
% 0.29/0.47 ( ( last_c571238084t_unit @ exec2 )
% 0.29/0.47 = c ) ).
% 0.29/0.47
% 0.29/0.47 % NewExec(3)
% 0.29/0.47 thf(fact_3_CMsg,axiom,
% 0.29/0.47 steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg ).
% 0.29/0.47
% 0.29/0.47 % CMsg
% 0.29/0.47 thf(fact_4_flpPseudoConsensus__axioms,axiom,
% 0.29/0.47 fLPThe9398366_p_s_v @ trans @ sends @ start ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus_axioms
% 0.29/0.47 thf(fact_5_ExecMsg_I3_J,axiom,
% 0.29/0.47 ( ( last_c571238084t_unit @ execMsga )
% 0.29/0.47 = cMsg ) ).
% 0.29/0.47
% 0.29/0.47 % ExecMsg(3)
% 0.29/0.47 thf(fact_6__092_060open_062_092_060lbrakk_062p_A_061_Ap_059_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_059_AisReceiverOf_Ap_Amsg_059_AinitReachable_A_Ilast_Aexec_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Aval_091p_Mlast_Aexec_H_093_A_092_060subseteq_062_Aval_091p_McMsg_093_092_060close_062,axiom,
% 0.29/0.47 ( ( p2 = p2 )
% 0.29/0.47 => ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ p2 @ msg )
% 0.29/0.47 => ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
% 0.29/0.47 => ( ord_less_eq_set_o
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ cMsg ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>\<lbrakk>p = p; last exec' \<turnstile> msg \<mapsto> cMsg; isReceiverOf p msg; initReachable (last exec')\<rbrakk> \<Longrightarrow> val[p,last exec'] \<subseteq> val[p,cMsg]\<close>
% 0.29/0.47 thf(fact_7_DiamondOne,axiom,
% 0.29/0.47 ! [Cfg: config256849571t_unit,M: message_p_v,Cfg1: config256849571t_unit,P: p,Q: p,M2: message_p_v,Cfg2: config256849571t_unit] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg @ M @ Cfg1 )
% 0.29/0.47 => ( ( P != Q )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ M )
% 0.29/0.47 => ( ~ ( isReceiverOf_p_v @ P @ M2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ Q @ M2 )
% 0.29/0.47 => ( ~ ( isReceiverOf_p_v @ Q @ M )
% 0.29/0.47 => ( ( steps_p_s_v @ trans @ sends @ Cfg @ M2 @ Cfg2 )
% 0.29/0.47 => ? [Cfg3: config256849571t_unit] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M2 @ Cfg3 )
% 0.29/0.47 & ( steps_p_s_v @ trans @ sends @ Cfg2 @ M @ Cfg3 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % DiamondOne
% 0.29/0.47 thf(fact_8_True,axiom,
% 0.29/0.47 enabled_p_v_s @ ( last_c571238084t_unit @ exec2 ) @ msg ).
% 0.29/0.47
% 0.29/0.47 % True
% 0.29/0.47 thf(fact_9__092_060open_062_092_060exists_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_092_060close_062,axiom,
% 0.29/0.47 ? [X_1: config256849571t_unit] : ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ X_1 ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>\<exists>cMsg. last exec' \<turnstile> msg \<mapsto> cMsg\<close>
% 0.29/0.47 thf(fact_10__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.47 ~ ! [CMsg: config256849571t_unit] :
% 0.29/0.47 ~ ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ CMsg ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>\<And>thesis. (\<And>cMsg. last exec' \<turnstile> msg \<mapsto> cMsg \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.47 thf(fact_11_Agreement,axiom,
% 0.29/0.47 ! [I: config256849571t_unit,C: config256849571t_unit] : ( agreementInit_p_s_v @ trans @ sends @ start @ I @ C ) ).
% 0.29/0.47
% 0.29/0.47 % Agreement
% 0.29/0.47 thf(fact_12_ActiveProcessSilentDecisionValuesIncrease,axiom,
% 0.29/0.47 ! [P: p,Q: p,C: config256849571t_unit,Msg: message_p_v,C2: config256849571t_unit] :
% 0.29/0.47 ( ( P = Q )
% 0.29/0.47 => ( ( steps_p_s_v @ trans @ sends @ C @ Msg @ C2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ Msg )
% 0.29/0.47 => ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 0.29/0.47 => ( ord_less_eq_set_o
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C ) )
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C2 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ActiveProcessSilentDecisionValuesIncrease
% 0.29/0.47 thf(fact_13_InactiveProcessSilentDecisionValuesDecrease,axiom,
% 0.29/0.47 ! [P: p,Q: p,C: config256849571t_unit,Msg: message_p_v,C2: config256849571t_unit] :
% 0.29/0.47 ( ( P != Q )
% 0.29/0.47 => ( ( steps_p_s_v @ trans @ sends @ C @ Msg @ C2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ Msg )
% 0.29/0.47 => ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 0.29/0.47 => ( ord_less_eq_set_o
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C2 ) )
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % InactiveProcessSilentDecisionValuesDecrease
% 0.29/0.47 thf(fact_14_nonUniformC_H,axiom,
% 0.29/0.47 ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ ( last_c571238084t_unit @ exec2 ) )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ ( last_c571238084t_unit @ exec2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nonUniformC'
% 0.29/0.47 thf(fact_15_InitReachLastExecMsg,axiom,
% 0.29/0.47 initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ execMsga ) ).
% 0.29/0.47
% 0.29/0.47 % InitReachLastExecMsg
% 0.29/0.47 thf(fact_16_NewExec_I1_J,axiom,
% 0.29/0.47 execution_p_s_v @ trans @ sends @ start @ exec2 @ trace2 ).
% 0.29/0.47
% 0.29/0.47 % NewExec(1)
% 0.29/0.47 thf(fact_17_InitialIsInitReachable,axiom,
% 0.29/0.47 ! [C: config256849571t_unit] :
% 0.29/0.47 ( ( initial_p_s_v @ start @ C )
% 0.29/0.47 => ( initReachable_p_s_v @ trans @ sends @ start @ C ) ) ).
% 0.29/0.47
% 0.29/0.47 % InitialIsInitReachable
% 0.29/0.47 thf(fact_18_flpSystem__axioms,axiom,
% 0.29/0.47 flpSystem_p_s_v @ sends ).
% 0.29/0.47
% 0.29/0.47 % flpSystem_axioms
% 0.29/0.47 thf(fact_19_subsetI,axiom,
% 0.29/0.47 ! [A: set_p,B: set_p] :
% 0.29/0.47 ( ! [X: p] :
% 0.29/0.47 ( ( member_p @ X @ A )
% 0.29/0.47 => ( member_p @ X @ B ) )
% 0.29/0.47 => ( ord_less_eq_set_p @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % subsetI
% 0.29/0.47 thf(fact_20_subsetI,axiom,
% 0.29/0.47 ! [A: set_o,B: set_o] :
% 0.29/0.47 ( ! [X: $o] :
% 0.29/0.47 ( ( member_o @ X @ A )
% 0.29/0.47 => ( member_o @ X @ B ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % subsetI
% 0.29/0.47 thf(fact_21_subset__antisym,axiom,
% 0.29/0.47 ! [A: set_p,B: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_set_p @ B @ A )
% 0.29/0.47 => ( A = B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_antisym
% 0.29/0.47 thf(fact_22_subset__antisym,axiom,
% 0.29/0.47 ! [A: set_o,B: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ B @ A )
% 0.29/0.47 => ( A = B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_antisym
% 0.29/0.47 thf(fact_23_QReachableTrans,axiom,
% 0.29/0.47 ! [Cfg2: config256849571t_unit,Q2: set_p,Cfg32: config256849571t_unit,Cfg1: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ Cfg2 @ Q2 @ Cfg32 )
% 0.29/0.47 => ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % QReachableTrans
% 0.29/0.47 thf(fact_24_InitQ,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,Q2: set_p] : ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg1 ) ).
% 0.29/0.47
% 0.29/0.47 % InitQ
% 0.29/0.47 thf(fact_25_order__refl,axiom,
% 0.29/0.47 ! [X2: set_p] : ( ord_less_eq_set_p @ X2 @ X2 ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_26_order__refl,axiom,
% 0.29/0.47 ! [X2: $o > $o] : ( ord_less_eq_o_o @ X2 @ X2 ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_27_order__refl,axiom,
% 0.29/0.47 ! [X2: p > $o] : ( ord_less_eq_p_o @ X2 @ X2 ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_28_order__refl,axiom,
% 0.29/0.47 ! [X2: set_o] : ( ord_less_eq_set_o @ X2 @ X2 ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_29_order__refl,axiom,
% 0.29/0.47 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_30_OnlyOccurenceDisables,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,M2: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.47 => ( ( enabled_p_v_s @ Cfg1 @ M2 )
% 0.29/0.47 => ( ~ ( enabled_p_v_s @ Cfg2 @ M2 )
% 0.29/0.47 => ( M = M2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % OnlyOccurenceDisables
% 0.29/0.47 thf(fact_31_qReachable_Osimps,axiom,
% 0.29/0.47 ! [A1: config256849571t_unit,A2: set_p,A3: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ A1 @ A2 @ A3 )
% 0.29/0.47 = ( ( A3 = A1 )
% 0.29/0.47 | ? [Cfg22: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ A1 @ A2 @ Cfg22 )
% 0.29/0.47 & ? [Msg2: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg22 @ Msg2 @ A3 )
% 0.29/0.47 & ? [X3: p] :
% 0.29/0.47 ( ( member_p @ X3 @ A2 )
% 0.29/0.47 & ( isReceiverOf_p_v @ X3 @ Msg2 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % qReachable.simps
% 0.29/0.47 thf(fact_32_qReachable_Oinducts,axiom,
% 0.29/0.47 ! [X1: config256849571t_unit,X22: set_p,X32: config256849571t_unit,P2: config256849571t_unit > set_p > config256849571t_unit > $o] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ X1 @ X22 @ X32 )
% 0.29/0.47 => ( ! [Cfg12: config256849571t_unit,Q3: set_p] : ( P2 @ Cfg12 @ Q3 @ Cfg12 )
% 0.29/0.47 => ( ! [Cfg12: config256849571t_unit,Q3: set_p,Cfg23: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ Cfg12 @ Q3 @ Cfg23 )
% 0.29/0.47 => ( ( P2 @ Cfg12 @ Q3 @ Cfg23 )
% 0.29/0.47 => ! [Msg3: message_p_v,Cfg33: config256849571t_unit] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg23 @ Msg3 @ Cfg33 )
% 0.29/0.47 => ( ? [X: p] :
% 0.29/0.47 ( ( member_p @ X @ Q3 )
% 0.29/0.47 & ( isReceiverOf_p_v @ X @ Msg3 ) )
% 0.29/0.47 => ( P2 @ Cfg12 @ Q3 @ Cfg33 ) ) ) ) )
% 0.29/0.47 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % qReachable.inducts
% 0.29/0.47 thf(fact_33_qReachable_Ocases,axiom,
% 0.29/0.47 ! [A1: config256849571t_unit,A2: set_p,A3: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ A1 @ A2 @ A3 )
% 0.29/0.47 => ( ( A3 != A1 )
% 0.29/0.47 => ~ ! [Cfg23: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ A1 @ A2 @ Cfg23 )
% 0.29/0.47 => ! [Msg3: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg23 @ Msg3 @ A3 )
% 0.29/0.47 => ~ ? [X: p] :
% 0.29/0.47 ( ( member_p @ X @ A2 )
% 0.29/0.47 & ( isReceiverOf_p_v @ X @ Msg3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % qReachable.cases
% 0.29/0.47 thf(fact_34_StepQ,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,Msg: message_p_v,Cfg32: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( ( steps_p_s_v @ trans @ sends @ Cfg2 @ Msg @ Cfg32 )
% 0.29/0.47 => ( ? [X4: p] :
% 0.29/0.47 ( ( member_p @ X4 @ Q2 )
% 0.29/0.47 & ( isReceiverOf_p_v @ X4 @ Msg ) )
% 0.29/0.47 => ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % StepQ
% 0.29/0.47 thf(fact_35_ExecMsg_I1_J,axiom,
% 0.29/0.47 prefix1615116500t_unit @ exec2 @ execMsga ).
% 0.29/0.47
% 0.29/0.47 % ExecMsg(1)
% 0.29/0.47 thf(fact_36_isExecution,axiom,
% 0.29/0.47 execution_p_s_v @ trans @ sends @ start @ execMsga @ traceMsga ).
% 0.29/0.47
% 0.29/0.47 % isExecution
% 0.29/0.47 thf(fact_37_MsgEnabled,axiom,
% 0.29/0.47 enabled_p_v_s @ ( last_c571238084t_unit @ exec ) @ msg ).
% 0.29/0.47
% 0.29/0.47 % MsgEnabled
% 0.29/0.47 thf(fact_38_NonUniformLexec,axiom,
% 0.29/0.47 ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec ) )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ ( last_c571238084t_unit @ exec ) )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ ( last_c571238084t_unit @ exec ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % NonUniformLexec
% 0.29/0.47 thf(fact_39_flpPseudoConsensus_Oaxioms_I1_J,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s] :
% 0.29/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.29/0.47 => ( flpSystem_p_s_v @ Sends ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.axioms(1)
% 0.29/0.47 thf(fact_40_flpPseudoConsensus_OAgreement,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,I: config256849571t_unit,C: config256849571t_unit] :
% 0.29/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.29/0.47 => ( agreementInit_p_s_v @ Trans @ Sends @ Start @ I @ C ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.Agreement
% 0.29/0.47 thf(fact_41_less__eq__set__def,axiom,
% 0.29/0.47 ( ord_less_eq_set_p
% 0.29/0.47 = ( ^ [A4: set_p,B2: set_p] :
% 0.29/0.47 ( ord_less_eq_p_o
% 0.29/0.47 @ ^ [X3: p] : ( member_p @ X3 @ A4 )
% 0.29/0.47 @ ^ [X3: p] : ( member_p @ X3 @ B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_eq_set_def
% 0.29/0.47 thf(fact_42_less__eq__set__def,axiom,
% 0.29/0.47 ( ord_less_eq_set_o
% 0.29/0.47 = ( ^ [A4: set_o,B2: set_o] :
% 0.29/0.47 ( ord_less_eq_o_o
% 0.29/0.47 @ ^ [X3: $o] : ( member_o @ X3 @ A4 )
% 0.29/0.47 @ ^ [X3: $o] : ( member_o @ X3 @ B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_eq_set_def
% 0.29/0.47 thf(fact_43_dual__order_Oantisym,axiom,
% 0.29/0.47 ! [B3: set_p,A5: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_set_p @ A5 @ B3 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.antisym
% 0.29/0.47 thf(fact_44_dual__order_Oantisym,axiom,
% 0.29/0.47 ! [B3: $o > $o,A5: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_o_o @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_o_o @ A5 @ B3 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.antisym
% 0.29/0.47 thf(fact_45_dual__order_Oantisym,axiom,
% 0.29/0.47 ! [B3: p > $o,A5: p > $o] :
% 0.29/0.47 ( ( ord_less_eq_p_o @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_p_o @ A5 @ B3 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.antisym
% 0.29/0.47 thf(fact_46_dual__order_Oantisym,axiom,
% 0.29/0.47 ! [B3: set_o,A5: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.antisym
% 0.29/0.47 thf(fact_47_dual__order_Oantisym,axiom,
% 0.29/0.47 ! [B3: nat,A5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.antisym
% 0.29/0.47 thf(fact_48_dual__order_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: set_p,Z: set_p] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: set_p,B4: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ B4 @ A6 )
% 0.29/0.47 & ( ord_less_eq_set_p @ A6 @ B4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.eq_iff
% 0.29/0.47 thf(fact_49_dual__order_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: $o > $o,Z: $o > $o] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: $o > $o,B4: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_o_o @ B4 @ A6 )
% 0.29/0.47 & ( ord_less_eq_o_o @ A6 @ B4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.eq_iff
% 0.29/0.47 thf(fact_50_dual__order_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: p > $o,Z: p > $o] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: p > $o,B4: p > $o] :
% 0.29/0.47 ( ( ord_less_eq_p_o @ B4 @ A6 )
% 0.29/0.47 & ( ord_less_eq_p_o @ A6 @ B4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.eq_iff
% 0.29/0.47 thf(fact_51_dual__order_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: set_o,Z: set_o] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: set_o,B4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ B4 @ A6 )
% 0.29/0.47 & ( ord_less_eq_set_o @ A6 @ B4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.eq_iff
% 0.29/0.47 thf(fact_52_dual__order_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: nat,B4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ B4 @ A6 )
% 0.29/0.47 & ( ord_less_eq_nat @ A6 @ B4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.eq_iff
% 0.29/0.47 thf(fact_53_dual__order_Otrans,axiom,
% 0.29/0.47 ! [B3: set_p,A5: set_p,C: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_set_p @ C @ B3 )
% 0.29/0.47 => ( ord_less_eq_set_p @ C @ A5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.trans
% 0.29/0.47 thf(fact_54_dual__order_Otrans,axiom,
% 0.29/0.47 ! [B3: $o > $o,A5: $o > $o,C: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_o_o @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_o_o @ C @ B3 )
% 0.29/0.47 => ( ord_less_eq_o_o @ C @ A5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.trans
% 0.29/0.47 thf(fact_55_dual__order_Otrans,axiom,
% 0.29/0.47 ! [B3: p > $o,A5: p > $o,C: p > $o] :
% 0.29/0.47 ( ( ord_less_eq_p_o @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_p_o @ C @ B3 )
% 0.29/0.47 => ( ord_less_eq_p_o @ C @ A5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.trans
% 0.29/0.47 thf(fact_56_dual__order_Otrans,axiom,
% 0.29/0.47 ! [B3: set_o,A5: set_o,C: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ C @ B3 )
% 0.29/0.47 => ( ord_less_eq_set_o @ C @ A5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.trans
% 0.29/0.47 thf(fact_57_dual__order_Otrans,axiom,
% 0.29/0.47 ! [B3: nat,A5: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ B3 @ A5 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ C @ B3 )
% 0.29/0.47 => ( ord_less_eq_nat @ C @ A5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.trans
% 0.29/0.47 thf(fact_58_linorder__wlog,axiom,
% 0.29/0.47 ! [P2: nat > nat > $o,A5: nat,B3: nat] :
% 0.29/0.47 ( ! [A7: nat,B5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A7 @ B5 )
% 0.29/0.47 => ( P2 @ A7 @ B5 ) )
% 0.29/0.47 => ( ! [A7: nat,B5: nat] :
% 0.29/0.47 ( ( P2 @ B5 @ A7 )
% 0.29/0.47 => ( P2 @ A7 @ B5 ) )
% 0.29/0.47 => ( P2 @ A5 @ B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % linorder_wlog
% 0.29/0.47 thf(fact_59_dual__order_Orefl,axiom,
% 0.29/0.47 ! [A5: set_p] : ( ord_less_eq_set_p @ A5 @ A5 ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.refl
% 0.29/0.47 thf(fact_60_dual__order_Orefl,axiom,
% 0.29/0.47 ! [A5: $o > $o] : ( ord_less_eq_o_o @ A5 @ A5 ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.refl
% 0.29/0.47 thf(fact_61_dual__order_Orefl,axiom,
% 0.29/0.47 ! [A5: p > $o] : ( ord_less_eq_p_o @ A5 @ A5 ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.refl
% 0.29/0.47 thf(fact_62_dual__order_Orefl,axiom,
% 0.29/0.47 ! [A5: set_o] : ( ord_less_eq_set_o @ A5 @ A5 ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.refl
% 0.29/0.47 thf(fact_63_dual__order_Orefl,axiom,
% 0.29/0.47 ! [A5: nat] : ( ord_less_eq_nat @ A5 @ A5 ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.refl
% 0.29/0.47 thf(fact_64_order__trans,axiom,
% 0.29/0.47 ! [X2: set_p,Y2: set_p,Z2: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ X2 @ Y2 )
% 0.29/0.47 => ( ( ord_less_eq_set_p @ Y2 @ Z2 )
% 0.29/0.47 => ( ord_less_eq_set_p @ X2 @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_trans
% 0.29/0.47 thf(fact_65_order__trans,axiom,
% 0.29/0.47 ! [X2: $o > $o,Y2: $o > $o,Z2: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_o_o @ X2 @ Y2 )
% 0.29/0.47 => ( ( ord_less_eq_o_o @ Y2 @ Z2 )
% 0.29/0.47 => ( ord_less_eq_o_o @ X2 @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_trans
% 0.29/0.47 thf(fact_66_order__trans,axiom,
% 0.29/0.47 ! [X2: p > $o,Y2: p > $o,Z2: p > $o] :
% 0.29/0.47 ( ( ord_less_eq_p_o @ X2 @ Y2 )
% 0.29/0.47 => ( ( ord_less_eq_p_o @ Y2 @ Z2 )
% 0.29/0.47 => ( ord_less_eq_p_o @ X2 @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_trans
% 0.29/0.47 thf(fact_67_order__trans,axiom,
% 0.29/0.47 ! [X2: set_o,Y2: set_o,Z2: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X2 @ Y2 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ Y2 @ Z2 )
% 0.29/0.47 => ( ord_less_eq_set_o @ X2 @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_trans
% 0.29/0.47 thf(fact_68_order__trans,axiom,
% 0.29/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.29/0.47 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_trans
% 0.29/0.47 thf(fact_69_order__class_Oorder_Oantisym,axiom,
% 0.29/0.47 ! [A5: set_p,B3: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_set_p @ B3 @ A5 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.antisym
% 0.29/0.47 thf(fact_70_order__class_Oorder_Oantisym,axiom,
% 0.29/0.47 ! [A5: $o > $o,B3: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_o_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_o_o @ B3 @ A5 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.antisym
% 0.29/0.47 thf(fact_71_order__class_Oorder_Oantisym,axiom,
% 0.29/0.47 ! [A5: p > $o,B3: p > $o] :
% 0.29/0.47 ( ( ord_less_eq_p_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_p_o @ B3 @ A5 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.antisym
% 0.29/0.47 thf(fact_72_order__class_Oorder_Oantisym,axiom,
% 0.29/0.47 ! [A5: set_o,B3: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ B3 @ A5 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.antisym
% 0.29/0.47 thf(fact_73_order__class_Oorder_Oantisym,axiom,
% 0.29/0.47 ! [A5: nat,B3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B3 @ A5 )
% 0.29/0.47 => ( A5 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.antisym
% 0.29/0.47 thf(fact_74_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [A5: set_p,B3: set_p,C: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ A5 @ B3 )
% 0.29/0.47 => ( ( B3 = C )
% 0.29/0.47 => ( ord_less_eq_set_p @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_trans
% 0.29/0.47 thf(fact_75_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [A5: $o > $o,B3: $o > $o,C: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_o_o @ A5 @ B3 )
% 0.29/0.47 => ( ( B3 = C )
% 0.29/0.47 => ( ord_less_eq_o_o @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_trans
% 0.29/0.47 thf(fact_76_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [A5: p > $o,B3: p > $o,C: p > $o] :
% 0.29/0.47 ( ( ord_less_eq_p_o @ A5 @ B3 )
% 0.29/0.47 => ( ( B3 = C )
% 0.29/0.47 => ( ord_less_eq_p_o @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_trans
% 0.29/0.47 thf(fact_77_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [A5: set_o,B3: set_o,C: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.47 => ( ( B3 = C )
% 0.29/0.47 => ( ord_less_eq_set_o @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_trans
% 0.29/0.47 thf(fact_78_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [A5: nat,B3: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.47 => ( ( B3 = C )
% 0.29/0.47 => ( ord_less_eq_nat @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_trans
% 0.29/0.47 thf(fact_79_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [A5: set_p,B3: set_p,C: set_p] :
% 0.29/0.47 ( ( A5 = B3 )
% 0.29/0.47 => ( ( ord_less_eq_set_p @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_set_p @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_trans
% 0.29/0.47 thf(fact_80_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [A5: $o > $o,B3: $o > $o,C: $o > $o] :
% 0.29/0.47 ( ( A5 = B3 )
% 0.29/0.47 => ( ( ord_less_eq_o_o @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_o_o @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_trans
% 0.29/0.47 thf(fact_81_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [A5: p > $o,B3: p > $o,C: p > $o] :
% 0.29/0.47 ( ( A5 = B3 )
% 0.29/0.47 => ( ( ord_less_eq_p_o @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_p_o @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_trans
% 0.29/0.47 thf(fact_82_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [A5: set_o,B3: set_o,C: set_o] :
% 0.29/0.47 ( ( A5 = B3 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_set_o @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_trans
% 0.29/0.47 thf(fact_83_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [A5: nat,B3: nat,C: nat] :
% 0.29/0.47 ( ( A5 = B3 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_nat @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_trans
% 0.29/0.47 thf(fact_84_mem__Collect__eq,axiom,
% 0.29/0.47 ! [A5: p,P2: p > $o] :
% 0.29/0.47 ( ( member_p @ A5 @ ( collect_p @ P2 ) )
% 0.29/0.47 = ( P2 @ A5 ) ) ).
% 0.29/0.47
% 0.29/0.47 % mem_Collect_eq
% 0.29/0.47 thf(fact_85_mem__Collect__eq,axiom,
% 0.29/0.47 ! [A5: $o,P2: $o > $o] :
% 0.29/0.47 ( ( member_o @ A5 @ ( collect_o @ P2 ) )
% 0.29/0.47 = ( P2 @ A5 ) ) ).
% 0.29/0.47
% 0.29/0.47 % mem_Collect_eq
% 0.29/0.47 thf(fact_86_Collect__mem__eq,axiom,
% 0.29/0.47 ! [A: set_p] :
% 0.29/0.47 ( ( collect_p
% 0.29/0.47 @ ^ [X3: p] : ( member_p @ X3 @ A ) )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mem_eq
% 0.29/0.47 thf(fact_87_Collect__mem__eq,axiom,
% 0.29/0.47 ! [A: set_o] :
% 0.29/0.47 ( ( collect_o
% 0.29/0.47 @ ^ [X3: $o] : ( member_o @ X3 @ A ) )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mem_eq
% 0.29/0.47 thf(fact_88_Collect__cong,axiom,
% 0.29/0.47 ! [P2: p > $o,Q2: p > $o] :
% 0.29/0.47 ( ! [X: p] :
% 0.29/0.47 ( ( P2 @ X )
% 0.29/0.47 = ( Q2 @ X ) )
% 0.29/0.47 => ( ( collect_p @ P2 )
% 0.29/0.47 = ( collect_p @ Q2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_cong
% 0.29/0.47 thf(fact_89_Collect__cong,axiom,
% 0.29/0.47 ! [P2: $o > $o,Q2: $o > $o] :
% 0.29/0.47 ( ! [X: $o] :
% 0.29/0.47 ( ( P2 @ X )
% 0.29/0.47 = ( Q2 @ X ) )
% 0.29/0.47 => ( ( collect_o @ P2 )
% 0.29/0.47 = ( collect_o @ Q2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_cong
% 0.29/0.47 thf(fact_90_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: set_p,Z: set_p] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: set_p,B4: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ A6 @ B4 )
% 0.29/0.47 & ( ord_less_eq_set_p @ B4 @ A6 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.eq_iff
% 0.29/0.47 thf(fact_91_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: $o > $o,Z: $o > $o] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: $o > $o,B4: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_o_o @ A6 @ B4 )
% 0.29/0.47 & ( ord_less_eq_o_o @ B4 @ A6 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.eq_iff
% 0.29/0.47 thf(fact_92_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: p > $o,Z: p > $o] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: p > $o,B4: p > $o] :
% 0.29/0.47 ( ( ord_less_eq_p_o @ A6 @ B4 )
% 0.29/0.47 & ( ord_less_eq_p_o @ B4 @ A6 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.eq_iff
% 0.29/0.47 thf(fact_93_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: set_o,Z: set_o] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: set_o,B4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A6 @ B4 )
% 0.29/0.47 & ( ord_less_eq_set_o @ B4 @ A6 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.eq_iff
% 0.29/0.47 thf(fact_94_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A6: nat,B4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A6 @ B4 )
% 0.29/0.47 & ( ord_less_eq_nat @ B4 @ A6 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.eq_iff
% 0.29/0.47 thf(fact_95_antisym__conv,axiom,
% 0.29/0.47 ! [Y2: set_p,X2: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ Y2 @ X2 )
% 0.29/0.47 => ( ( ord_less_eq_set_p @ X2 @ Y2 )
% 0.29/0.47 = ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv
% 0.29/0.47 thf(fact_96_antisym__conv,axiom,
% 0.29/0.47 ! [Y2: $o > $o,X2: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_o_o @ Y2 @ X2 )
% 0.29/0.47 => ( ( ord_less_eq_o_o @ X2 @ Y2 )
% 0.29/0.47 = ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv
% 0.29/0.47 thf(fact_97_antisym__conv,axiom,
% 0.29/0.47 ! [Y2: p > $o,X2: p > $o] :
% 0.29/0.47 ( ( ord_less_eq_p_o @ Y2 @ X2 )
% 0.29/0.47 => ( ( ord_less_eq_p_o @ X2 @ Y2 )
% 0.29/0.47 = ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv
% 0.29/0.47 thf(fact_98_antisym__conv,axiom,
% 0.29/0.47 ! [Y2: set_o,X2: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ Y2 @ X2 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ X2 @ Y2 )
% 0.29/0.47 = ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv
% 0.29/0.47 thf(fact_99_antisym__conv,axiom,
% 0.29/0.47 ! [Y2: nat,X2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 = ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv
% 0.29/0.47 thf(fact_100_le__cases3,axiom,
% 0.29/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.29/0.47 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 0.29/0.47 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases3
% 0.29/0.47 thf(fact_101_order_Otrans,axiom,
% 0.29/0.47 ! [A5: set_p,B3: set_p,C: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_set_p @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_set_p @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_102_order_Otrans,axiom,
% 0.29/0.47 ! [A5: $o > $o,B3: $o > $o,C: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_o_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_o_o @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_o_o @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_103_order_Otrans,axiom,
% 0.29/0.47 ! [A5: p > $o,B3: p > $o,C: p > $o] :
% 0.29/0.47 ( ( ord_less_eq_p_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_p_o @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_p_o @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_104_order_Otrans,axiom,
% 0.29/0.47 ! [A5: set_o,B3: set_o,C: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_set_o @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_105_order_Otrans,axiom,
% 0.29/0.47 ! [A5: nat,B3: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.29/0.47 => ( ord_less_eq_nat @ A5 @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_106_le__cases,axiom,
% 0.29/0.47 ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases
% 0.29/0.47 thf(fact_107_eq__refl,axiom,
% 0.29/0.47 ! [X2: $o > $o,Y2: $o > $o] :
% 0.29/0.47 ( ( X2 = Y2 )
% 0.29/0.47 => ( ord_less_eq_o_o @ X2 @ Y2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_refl
% 0.29/0.47 thf(fact_108_eq__refl,axiom,
% 0.29/0.47 ! [X2: p > $o,Y2: p > $o] :
% 0.29/0.47 ( ( X2 = Y2 )
% 0.29/0.47 => ( ord_less_eq_p_o @ X2 @ Y2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_refl
% 0.29/0.47 thf(fact_109_eq__refl,axiom,
% 0.29/0.47 ! [X2: set_o,Y2: set_o] :
% 0.29/0.47 ( ( X2 = Y2 )
% 0.29/0.47 => ( ord_less_eq_set_o @ X2 @ Y2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_refl
% 0.29/0.47 thf(fact_110_eq__refl,axiom,
% 0.29/0.47 ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( X2 = Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_refl
% 0.29/0.47 thf(fact_111_linear,axiom,
% 0.29/0.47 ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % linear
% 0.29/0.47 thf(fact_112_antisym,axiom,
% 0.29/0.47 ! [X2: set_o,Y2: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X2 @ Y2 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ Y2 @ X2 )
% 0.29/0.47 => ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym
% 0.29/0.47 thf(fact_113_antisym,axiom,
% 0.29/0.47 ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.29/0.47 => ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym
% 0.29/0.47 thf(fact_114_eq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: set_o,Z: set_o] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [X3: set_o,Y3: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X3 @ Y3 )
% 0.29/0.47 & ( ord_less_eq_set_o @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_iff
% 0.29/0.47 thf(fact_115_eq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_iff
% 0.29/0.47 thf(fact_116_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A5: set_o,B3: set_o,F: set_o > set_o,C: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ( F @ B3 )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X: set_o,Y4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ A5 ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_117_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A5: set_o,B3: set_o,F: set_o > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ( F @ B3 )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X: set_o,Y4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ A5 ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_118_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A5: nat,B3: nat,F: nat > set_o,C: set_o] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.47 => ( ( ( F @ B3 )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X: nat,Y4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ A5 ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_119_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A5: nat,B3: nat,F: nat > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.47 => ( ( ( F @ B3 )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X: nat,Y4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ A5 ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_120_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A5: set_o,F: set_o > set_o,B3: set_o,C: set_o] :
% 0.29/0.47 ( ( A5
% 0.29/0.47 = ( F @ B3 ) )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ B3 @ C )
% 0.29/0.47 => ( ! [X: set_o,Y4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ A5 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_121_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A5: nat,F: set_o > nat,B3: set_o,C: set_o] :
% 0.29/0.47 ( ( A5
% 0.29/0.47 = ( F @ B3 ) )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ B3 @ C )
% 0.29/0.47 => ( ! [X: set_o,Y4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A5 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_122_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A5: set_o,F: nat > set_o,B3: nat,C: nat] :
% 0.29/0.47 ( ( A5
% 0.29/0.47 = ( F @ B3 ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.29/0.47 => ( ! [X: nat,Y4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ A5 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_123_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A5: nat,F: nat > nat,B3: nat,C: nat] :
% 0.29/0.47 ( ( A5
% 0.29/0.47 = ( F @ B3 ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.29/0.47 => ( ! [X: nat,Y4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A5 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_124_order__subst2,axiom,
% 0.29/0.47 ! [A5: set_o,B3: set_o,F: set_o > set_o,C: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ ( F @ B3 ) @ C )
% 0.29/0.47 => ( ! [X: set_o,Y4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ A5 ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_125_order__subst2,axiom,
% 0.29/0.47 ! [A5: set_o,B3: set_o,F: set_o > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C )
% 0.29/0.47 => ( ! [X: set_o,Y4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ A5 ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_126_order__subst2,axiom,
% 0.29/0.47 ! [A5: nat,B3: nat,F: nat > set_o,C: set_o] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ ( F @ B3 ) @ C )
% 0.29/0.47 => ( ! [X: nat,Y4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ A5 ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_127_order__subst2,axiom,
% 0.29/0.47 ! [A5: nat,B3: nat,F: nat > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C )
% 0.29/0.47 => ( ! [X: nat,Y4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ A5 ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_128_order__subst1,axiom,
% 0.29/0.47 ! [A5: set_o,F: set_o > set_o,B3: set_o,C: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ ( F @ B3 ) )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ B3 @ C )
% 0.29/0.47 => ( ! [X: set_o,Y4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ A5 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_129_order__subst1,axiom,
% 0.29/0.47 ! [A5: set_o,F: nat > set_o,B3: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ ( F @ B3 ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.29/0.47 => ( ! [X: nat,Y4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ A5 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_130_order__subst1,axiom,
% 0.29/0.47 ! [A5: nat,F: set_o > nat,B3: set_o,C: set_o] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ ( F @ B3 ) )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ B3 @ C )
% 0.29/0.47 => ( ! [X: set_o,Y4: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A5 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_131_order__subst1,axiom,
% 0.29/0.47 ! [A5: nat,F: nat > nat,B3: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ ( F @ B3 ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.29/0.47 => ( ! [X: nat,Y4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y4 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A5 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_132_Collect__mono__iff,axiom,
% 0.29/0.47 ! [P2: $o > $o,Q2: $o > $o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q2 ) )
% 0.29/0.47 = ( ! [X3: $o] :
% 0.29/0.47 ( ( P2 @ X3 )
% 0.29/0.47 => ( Q2 @ X3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mono_iff
% 0.29/0.47 thf(fact_133_set__eq__subset,axiom,
% 0.29/0.47 ( ( ^ [Y: set_o,Z: set_o] : ( Y = Z ) )
% 0.29/0.47 = ( ^ [A4: set_o,B2: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A4 @ B2 )
% 0.29/0.47 & ( ord_less_eq_set_o @ B2 @ A4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % set_eq_subset
% 0.29/0.47 thf(fact_134_subset__trans,axiom,
% 0.29/0.47 ! [A: set_o,B: set_o,C3: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ B @ C3 )
% 0.29/0.47 => ( ord_less_eq_set_o @ A @ C3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_trans
% 0.29/0.47 thf(fact_135_Collect__mono,axiom,
% 0.29/0.47 ! [P2: $o > $o,Q2: $o > $o] :
% 0.29/0.47 ( ! [X: $o] :
% 0.29/0.47 ( ( P2 @ X )
% 0.29/0.47 => ( Q2 @ X ) )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mono
% 0.29/0.47 thf(fact_136_subset__refl,axiom,
% 0.29/0.47 ! [A: set_o] : ( ord_less_eq_set_o @ A @ A ) ).
% 0.29/0.47
% 0.29/0.47 % subset_refl
% 0.29/0.47 thf(fact_137_subset__iff,axiom,
% 0.29/0.47 ( ord_less_eq_set_p
% 0.29/0.47 = ( ^ [A4: set_p,B2: set_p] :
% 0.29/0.47 ! [T: p] :
% 0.29/0.47 ( ( member_p @ T @ A4 )
% 0.29/0.47 => ( member_p @ T @ B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_iff
% 0.29/0.47 thf(fact_138_subset__iff,axiom,
% 0.29/0.47 ( ord_less_eq_set_o
% 0.29/0.47 = ( ^ [A4: set_o,B2: set_o] :
% 0.29/0.47 ! [T: $o] :
% 0.29/0.47 ( ( member_o @ T @ A4 )
% 0.29/0.47 => ( member_o @ T @ B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_iff
% 0.29/0.47 thf(fact_139_equalityD2,axiom,
% 0.29/0.47 ! [A: set_o,B: set_o] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ord_less_eq_set_o @ B @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % equalityD2
% 0.29/0.47 thf(fact_140_equalityD1,axiom,
% 0.29/0.47 ! [A: set_o,B: set_o] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ord_less_eq_set_o @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % equalityD1
% 0.29/0.47 thf(fact_141_subset__eq,axiom,
% 0.29/0.47 ( ord_less_eq_set_p
% 0.29/0.47 = ( ^ [A4: set_p,B2: set_p] :
% 0.29/0.47 ! [X3: p] :
% 0.29/0.47 ( ( member_p @ X3 @ A4 )
% 0.29/0.47 => ( member_p @ X3 @ B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_eq
% 0.29/0.47 thf(fact_142_subset__eq,axiom,
% 0.29/0.47 ( ord_less_eq_set_o
% 0.29/0.47 = ( ^ [A4: set_o,B2: set_o] :
% 0.29/0.47 ! [X3: $o] :
% 0.29/0.47 ( ( member_o @ X3 @ A4 )
% 0.29/0.47 => ( member_o @ X3 @ B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_eq
% 0.29/0.47 thf(fact_143_equalityE,axiom,
% 0.29/0.47 ! [A: set_o,B: set_o] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ~ ( ( ord_less_eq_set_o @ A @ B )
% 0.29/0.47 => ~ ( ord_less_eq_set_o @ B @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % equalityE
% 0.29/0.47 thf(fact_144_subsetD,axiom,
% 0.29/0.47 ! [A: set_p,B: set_p,C: p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ A @ B )
% 0.29/0.47 => ( ( member_p @ C @ A )
% 0.29/0.47 => ( member_p @ C @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subsetD
% 0.29/0.47 thf(fact_145_subsetD,axiom,
% 0.29/0.47 ! [A: set_o,B: set_o,C: $o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.29/0.47 => ( ( member_o @ C @ A )
% 0.29/0.47 => ( member_o @ C @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subsetD
% 0.29/0.47 thf(fact_146_in__mono,axiom,
% 0.29/0.47 ! [A: set_p,B: set_p,X2: p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ A @ B )
% 0.29/0.47 => ( ( member_p @ X2 @ A )
% 0.29/0.47 => ( member_p @ X2 @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_mono
% 0.29/0.47 thf(fact_147_in__mono,axiom,
% 0.29/0.47 ! [A: set_o,B: set_o,X2: $o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.29/0.47 => ( ( member_o @ X2 @ A )
% 0.29/0.47 => ( member_o @ X2 @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_mono
% 0.29/0.47 thf(fact_148_Collect__subset,axiom,
% 0.29/0.47 ! [A: set_p,P2: p > $o] :
% 0.29/0.47 ( ord_less_eq_set_p
% 0.29/0.47 @ ( collect_p
% 0.29/0.47 @ ^ [X3: p] :
% 0.29/0.47 ( ( member_p @ X3 @ A )
% 0.29/0.47 & ( P2 @ X3 ) ) )
% 0.29/0.47 @ A ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_subset
% 0.29/0.47 thf(fact_149_Collect__subset,axiom,
% 0.29/0.47 ! [A: set_o,P2: $o > $o] :
% 0.29/0.47 ( ord_less_eq_set_o
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [X3: $o] :
% 0.29/0.47 ( ( member_o @ X3 @ A )
% 0.29/0.47 & ( P2 @ X3 ) ) )
% 0.29/0.47 @ A ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_subset
% 0.29/0.47 thf(fact_150_flpSystem_OInactiveProcessSilentDecisionValuesDecrease,axiom,
% 0.29/0.47 ! [Sends: p > s > messageValue_v > message_p_v > nat,P: p,Q: p,Trans: p > s > messageValue_v > s,C: config256849571t_unit,Msg: message_p_v,C2: config256849571t_unit,Start: p > s] :
% 0.29/0.47 ( ( flpSystem_p_s_v @ Sends )
% 0.29/0.47 => ( ( P != Q )
% 0.29/0.47 => ( ( steps_p_s_v @ Trans @ Sends @ C @ Msg @ C2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ Msg )
% 0.29/0.47 => ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 0.29/0.47 => ( ord_less_eq_set_o
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C2 ) )
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.InactiveProcessSilentDecisionValuesDecrease
% 0.29/0.47 thf(fact_151_flpSystem_OActiveProcessSilentDecisionValuesIncrease,axiom,
% 0.29/0.47 ! [Sends: p > s > messageValue_v > message_p_v > nat,P: p,Q: p,Trans: p > s > messageValue_v > s,C: config256849571t_unit,Msg: message_p_v,C2: config256849571t_unit,Start: p > s] :
% 0.29/0.47 ( ( flpSystem_p_s_v @ Sends )
% 0.29/0.47 => ( ( P = Q )
% 0.29/0.47 => ( ( steps_p_s_v @ Trans @ Sends @ C @ Msg @ C2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ Msg )
% 0.29/0.47 => ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 0.29/0.47 => ( ord_less_eq_set_o
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C ) )
% 0.29/0.47 @ ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C2 ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.ActiveProcessSilentDecisionValuesIncrease
% 0.29/0.47 thf(fact_152_NotStepReachable,axiom,
% 0.29/0.47 ~ ( stepReachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ msg @ c ) ).
% 0.29/0.47
% 0.29/0.47 % NotStepReachable
% 0.29/0.47 thf(fact_153_cMsgLastReachable,axiom,
% 0.29/0.47 reachable_p_s_v @ trans @ sends @ cMsg @ ( last_c571238084t_unit @ execMsga ) ).
% 0.29/0.47
% 0.29/0.47 % cMsgLastReachable
% 0.29/0.47 thf(fact_154_NoReceivingNoChange,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,P: p] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.47 => ( ~ ( isReceiverOf_p_v @ P @ M )
% 0.29/0.47 => ( ( states1228886952t_unit @ Cfg1 @ P )
% 0.29/0.47 = ( states1228886952t_unit @ Cfg2 @ P ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % NoReceivingNoChange
% 0.29/0.47 thf(fact_155_initReachable__def,axiom,
% 0.29/0.47 ! [Cfg: config256849571t_unit] :
% 0.29/0.47 ( ( initReachable_p_s_v @ trans @ sends @ start @ Cfg )
% 0.29/0.47 = ( ? [Cfg0: config256849571t_unit] :
% 0.29/0.47 ( ( initial_p_s_v @ start @ Cfg0 )
% 0.29/0.47 & ( reachable_p_s_v @ trans @ sends @ Cfg0 @ Cfg ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % initReachable_def
% 0.29/0.47 thf(fact_156_ReachableStepFirst,axiom,
% 0.29/0.47 ! [Cfg: config256849571t_unit,Cfg4: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ Cfg @ Cfg4 )
% 0.29/0.47 => ( ( Cfg = Cfg4 )
% 0.29/0.47 | ? [Cfg12: config256849571t_unit,Msg3: message_p_v,P3: p] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg @ Msg3 @ Cfg12 )
% 0.29/0.47 & ( enabled_p_v_s @ Cfg @ Msg3 )
% 0.29/0.47 & ( isReceiverOf_p_v @ P3 @ Msg3 )
% 0.29/0.47 & ( reachable_p_s_v @ trans @ sends @ Cfg12 @ Cfg4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ReachableStepFirst
% 0.29/0.47 thf(fact_157_NotInQFrozenQReachability,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,P: p] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( ~ ( member_p @ P @ Q2 )
% 0.29/0.47 => ( ( states1228886952t_unit @ Cfg1 @ P )
% 0.29/0.47 = ( states1228886952t_unit @ Cfg2 @ P ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % NotInQFrozenQReachability
% 0.29/0.47 thf(fact_158_C_H_I2_J,axiom,
% 0.29/0.47 ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ c ) )
% 0.29/0.47 = ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % C'(2)
% 0.29/0.47 thf(fact_159_NoActivityNoMessageLoss,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,P: p,M2: message_p_v] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( ~ ( member_p @ P @ Q2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ M2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % NoActivityNoMessageLoss
% 0.29/0.47 thf(fact_160_ReachableTrans,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,Cfg32: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg2 )
% 0.29/0.47 => ( ( reachable_p_s_v @ trans @ sends @ Cfg2 @ Cfg32 )
% 0.29/0.47 => ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg32 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ReachableTrans
% 0.29/0.47 thf(fact_161_init,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit] : ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg1 ) ).
% 0.29/0.47
% 0.29/0.47 % init
% 0.29/0.47 thf(fact_162_empty__iff,axiom,
% 0.29/0.47 ! [C: p] :
% 0.29/0.47 ~ ( member_p @ C @ bot_bot_set_p ) ).
% 0.29/0.47
% 0.29/0.47 % empty_iff
% 0.29/0.47 thf(fact_163_empty__iff,axiom,
% 0.29/0.47 ! [C: $o] :
% 0.29/0.47 ~ ( member_o @ C @ bot_bot_set_o ) ).
% 0.29/0.47
% 0.29/0.47 % empty_iff
% 0.29/0.47 thf(fact_164_all__not__in__conv,axiom,
% 0.29/0.47 ! [A: set_p] :
% 0.29/0.47 ( ( ! [X3: p] :
% 0.29/0.47 ~ ( member_p @ X3 @ A ) )
% 0.29/0.47 = ( A = bot_bot_set_p ) ) ).
% 0.29/0.47
% 0.29/0.47 % all_not_in_conv
% 0.29/0.47 thf(fact_165_all__not__in__conv,axiom,
% 0.29/0.47 ! [A: set_o] :
% 0.29/0.47 ( ( ! [X3: $o] :
% 0.29/0.47 ~ ( member_o @ X3 @ A ) )
% 0.29/0.47 = ( A = bot_bot_set_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % all_not_in_conv
% 0.29/0.47 thf(fact_166_Collect__empty__eq,axiom,
% 0.29/0.47 ! [P2: $o > $o] :
% 0.29/0.47 ( ( ( collect_o @ P2 )
% 0.29/0.47 = bot_bot_set_o )
% 0.29/0.47 = ( ! [X3: $o] :
% 0.29/0.47 ~ ( P2 @ X3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_empty_eq
% 0.29/0.47 thf(fact_167_empty__Collect__eq,axiom,
% 0.29/0.47 ! [P2: $o > $o] :
% 0.29/0.47 ( ( bot_bot_set_o
% 0.29/0.47 = ( collect_o @ P2 ) )
% 0.29/0.47 = ( ! [X3: $o] :
% 0.29/0.47 ~ ( P2 @ X3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % empty_Collect_eq
% 0.29/0.47 thf(fact_168_insertCI,axiom,
% 0.29/0.47 ! [A5: $o,B: set_o,B3: $o] :
% 0.29/0.47 ( ( ~ ( member_o @ A5 @ B )
% 0.29/0.47 => ( A5 = B3 ) )
% 0.29/0.47 => ( member_o @ A5 @ ( insert_o @ B3 @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insertCI
% 0.29/0.47 thf(fact_169_insertCI,axiom,
% 0.29/0.47 ! [A5: p,B: set_p,B3: p] :
% 0.29/0.47 ( ( ~ ( member_p @ A5 @ B )
% 0.29/0.47 => ( A5 = B3 ) )
% 0.29/0.47 => ( member_p @ A5 @ ( insert_p @ B3 @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insertCI
% 0.29/0.47 thf(fact_170_insert__iff,axiom,
% 0.29/0.47 ! [A5: $o,B3: $o,A: set_o] :
% 0.29/0.47 ( ( member_o @ A5 @ ( insert_o @ B3 @ A ) )
% 0.29/0.47 = ( ( A5 = B3 )
% 0.29/0.47 | ( member_o @ A5 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_iff
% 0.29/0.47 thf(fact_171_insert__iff,axiom,
% 0.29/0.47 ! [A5: p,B3: p,A: set_p] :
% 0.29/0.47 ( ( member_p @ A5 @ ( insert_p @ B3 @ A ) )
% 0.29/0.47 = ( ( A5 = B3 )
% 0.29/0.47 | ( member_p @ A5 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_iff
% 0.29/0.47 thf(fact_172_insert__absorb2,axiom,
% 0.29/0.47 ! [X2: $o,A: set_o] :
% 0.29/0.47 ( ( insert_o @ X2 @ ( insert_o @ X2 @ A ) )
% 0.29/0.47 = ( insert_o @ X2 @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_absorb2
% 0.29/0.47 thf(fact_173_C_H_I1_J,axiom,
% 0.29/0.47 reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ c ).
% 0.29/0.47
% 0.29/0.47 % C'(1)
% 0.29/0.47 thf(fact_174_reachable_Ocases,axiom,
% 0.29/0.47 ! [A1: config256849571t_unit,A2: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ A1 @ A2 )
% 0.29/0.47 => ( ( A2 != A1 )
% 0.29/0.47 => ~ ! [Cfg23: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ A1 @ Cfg23 )
% 0.29/0.47 => ! [Msg3: message_p_v] :
% 0.29/0.47 ~ ( steps_p_s_v @ trans @ sends @ Cfg23 @ Msg3 @ A2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % reachable.cases
% 0.29/0.47 thf(fact_175_reachable_Oinducts,axiom,
% 0.29/0.47 ! [X1: config256849571t_unit,X22: config256849571t_unit,P2: config256849571t_unit > config256849571t_unit > $o] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ X1 @ X22 )
% 0.29/0.47 => ( ! [Cfg12: config256849571t_unit] : ( P2 @ Cfg12 @ Cfg12 )
% 0.29/0.47 => ( ! [Cfg12: config256849571t_unit,Cfg23: config256849571t_unit,Msg3: message_p_v,Cfg33: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ Cfg12 @ Cfg23 )
% 0.29/0.47 => ( ( P2 @ Cfg12 @ Cfg23 )
% 0.29/0.47 => ( ( steps_p_s_v @ trans @ sends @ Cfg23 @ Msg3 @ Cfg33 )
% 0.29/0.47 => ( P2 @ Cfg12 @ Cfg33 ) ) ) )
% 0.29/0.47 => ( P2 @ X1 @ X22 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % reachable.inducts
% 0.29/0.47 thf(fact_176_reachable_Osimps,axiom,
% 0.29/0.47 ! [A1: config256849571t_unit,A2: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ A1 @ A2 )
% 0.29/0.47 = ( ? [Cfg13: config256849571t_unit] :
% 0.29/0.47 ( ( A1 = Cfg13 )
% 0.29/0.47 & ( A2 = Cfg13 ) )
% 0.29/0.47 | ? [Cfg13: config256849571t_unit,Cfg22: config256849571t_unit,Msg2: message_p_v,Cfg34: config256849571t_unit] :
% 0.29/0.47 ( ( A1 = Cfg13 )
% 0.29/0.47 & ( A2 = Cfg34 )
% 0.29/0.47 & ( reachable_p_s_v @ trans @ sends @ Cfg13 @ Cfg22 )
% 0.29/0.47 & ( steps_p_s_v @ trans @ sends @ Cfg22 @ Msg2 @ Cfg34 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % reachable.simps
% 0.29/0.47 thf(fact_177_reachable_Ostep,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,Msg: message_p_v,Cfg32: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg2 )
% 0.29/0.47 => ( ( steps_p_s_v @ trans @ sends @ Cfg2 @ Msg @ Cfg32 )
% 0.29/0.47 => ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg32 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % reachable.step
% 0.29/0.47 thf(fact_178_QReachImplReach,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % QReachImplReach
% 0.29/0.47 thf(fact_179_isPrefixListExec,axiom,
% 0.29/0.47 prefix1615116500t_unit @ exec @ execMsga ).
% 0.29/0.47
% 0.29/0.47 % isPrefixListExec
% 0.29/0.47 thf(fact_180_OtherMessagesOnlyGrowing,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,M2: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.47 => ( ( M != M2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % OtherMessagesOnlyGrowing
% 0.29/0.47 thf(fact_181_stepReachable__def,axiom,
% 0.29/0.47 ! [C1: config256849571t_unit,Msg: message_p_v,C22: config256849571t_unit] :
% 0.29/0.47 ( ( stepReachable_p_s_v @ trans @ sends @ C1 @ Msg @ C22 )
% 0.29/0.47 = ( ? [C4: config256849571t_unit,C5: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ C1 @ C4 )
% 0.29/0.47 & ( steps_p_s_v @ trans @ sends @ C4 @ Msg @ C5 )
% 0.29/0.47 & ( reachable_p_s_v @ trans @ sends @ C5 @ C22 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % stepReachable_def
% 0.29/0.47 thf(fact_182_StepReachable,axiom,
% 0.29/0.47 ! [Cfg: config256849571t_unit,Cfg4: config256849571t_unit,Msg: message_p_v] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ Cfg @ Cfg4 )
% 0.29/0.47 => ( ( enabled_p_v_s @ Cfg @ Msg )
% 0.29/0.47 => ( ~ ( enabled_p_v_s @ Cfg4 @ Msg )
% 0.29/0.47 => ( stepReachable_p_s_v @ trans @ sends @ Cfg @ Msg @ Cfg4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % StepReachable
% 0.29/0.47 thf(fact_183_NoMessageLossStep,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,P: p,M2: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ M )
% 0.29/0.47 => ( ~ ( isReceiverOf_p_v @ P @ M2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % NoMessageLossStep
% 0.29/0.47 thf(fact_184_subset__empty,axiom,
% 0.29/0.47 ! [A: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 0.29/0.47 = ( A = bot_bot_set_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_empty
% 0.29/0.47 thf(fact_185_empty__subsetI,axiom,
% 0.29/0.47 ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 0.29/0.47
% 0.29/0.47 % empty_subsetI
% 0.29/0.47 thf(fact_186_singletonI,axiom,
% 0.29/0.47 ! [A5: p] : ( member_p @ A5 @ ( insert_p @ A5 @ bot_bot_set_p ) ) ).
% 0.29/0.47
% 0.29/0.47 % singletonI
% 0.29/0.47 thf(fact_187_singletonI,axiom,
% 0.29/0.47 ! [A5: $o] : ( member_o @ A5 @ ( insert_o @ A5 @ bot_bot_set_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % singletonI
% 0.29/0.47 thf(fact_188_insert__subset,axiom,
% 0.29/0.47 ! [X2: p,A: set_p,B: set_p] :
% 0.29/0.47 ( ( ord_less_eq_set_p @ ( insert_p @ X2 @ A ) @ B )
% 0.29/0.47 = ( ( member_p @ X2 @ B )
% 0.29/0.47 & ( ord_less_eq_set_p @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_subset
% 0.29/0.47 thf(fact_189_insert__subset,axiom,
% 0.29/0.47 ! [X2: $o,A: set_o,B: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ ( insert_o @ X2 @ A ) @ B )
% 0.29/0.47 = ( ( member_o @ X2 @ B )
% 0.29/0.47 & ( ord_less_eq_set_o @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_subset
% 0.29/0.47 thf(fact_190_ExecMsg_I2_J,axiom,
% 0.29/0.47 prefix47729710ge_p_v @ trace2 @ traceMsga ).
% 0.29/0.47
% 0.29/0.47 % ExecMsg(2)
% 0.29/0.47 thf(fact_191_lastExecExec_HReachable,axiom,
% 0.29/0.47 reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ ( last_c571238084t_unit @ exec2 ) ).
% 0.29/0.47
% 0.29/0.47 % lastExecExec'Reachable
% 0.29/0.47 thf(fact_192_singleton__conv,axiom,
% 0.29/0.47 ! [A5: $o] :
% 0.29/0.47 ( ( collect_o
% 0.29/0.47 @ ^ [X3: $o] : ( X3 = A5 ) )
% 0.29/0.47 = ( insert_o @ A5 @ bot_bot_set_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % singleton_conv
% 0.29/0.47 thf(fact_193_singleton__conv2,axiom,
% 0.29/0.47 ! [A5: $o] :
% 0.29/0.47 ( ( collect_o
% 0.29/0.47 @ ( ^ [Y: $o,Z: $o] : ( Y = Z )
% 0.29/0.47 @ A5 ) )
% 0.29/0.47 = ( insert_o @ A5 @ bot_bot_set_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % singleton_conv2
% 0.29/0.47 thf(fact_194_ExecIsExecution,axiom,
% 0.29/0.47 execution_p_s_v @ trans @ sends @ start @ exec @ trace ).
% 0.29/0.47
% 0.29/0.47 % ExecIsExecution
% 0.29/0.47 thf(fact_195_vUniform__def,axiom,
% 0.29/0.47 ! [V2: $o,C: config256849571t_unit] :
% 0.29/0.47 ( ( vUniform_p_s_v @ trans @ sends @ start @ V2 @ C )
% 0.29/0.47 = ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 0.29/0.47 & ! [P4: p] :
% 0.29/0.47 ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ P4 @ C ) )
% 0.29/0.47 = ( insert_o @ V2 @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % vUniform_def
% 0.29/0.47 thf(fact_196_singleton__insert__inj__eq_H,axiom,
% 0.29/0.47 ! [A5: $o,A: set_o,B3: $o] :
% 0.29/0.47 ( ( ( insert_o @ A5 @ A )
% 0.29/0.47 = ( insert_o @ B3 @ bot_bot_set_o ) )
% 0.29/0.47 = ( ( A5 = B3 )
% 0.29/0.47 & ( ord_less_eq_set_o @ A @ ( insert_o @ B3 @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % singleton_insert_inj_eq'
% 0.29/0.47 thf(fact_197_singleton__insert__inj__eq,axiom,
% 0.29/0.47 ! [B3: $o,A5: $o,A: set_o] :
% 0.29/0.47 ( ( ( insert_o @ B3 @ bot_bot_set_o )
% 0.29/0.47 = ( insert_o @ A5 @ A ) )
% 0.29/0.47 = ( ( A5 = B3 )
% 0.29/0.47 & ( ord_less_eq_set_o @ A @ ( insert_o @ B3 @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % singleton_insert_inj_eq
% 0.29/0.47 thf(fact_198_ExecMsg_I4_J,axiom,
% 0.29/0.47 ( ( last_message_p_v @ traceMsga )
% 0.29/0.47 = msg ) ).
% 0.29/0.47
% 0.29/0.47 % ExecMsg(4)
% 0.29/0.47 thf(fact_199_isStepReachable,axiom,
% 0.29/0.47 stepReachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ msg @ ( last_c571238084t_unit @ execMsga ) ).
% 0.29/0.47
% 0.29/0.47 % isStepReachable
% 0.29/0.47 thf(fact_200_SilentDecisionValueNotInverting,axiom,
% 0.29/0.47 ! [Q: p,C: config256849571t_unit,V2: $o,Msg: message_p_v,C2: config256849571t_unit,P: p] :
% 0.29/0.47 ( ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C ) )
% 0.29/0.47 = ( insert_o @ V2 @ bot_bot_set_o ) )
% 0.29/0.47 => ( ( steps_p_s_v @ trans @ sends @ C @ Msg @ C2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ Msg )
% 0.29/0.47 => ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 0.29/0.47 => ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C2 ) )
% 0.29/0.47 != ( insert_o @ ~ V2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % SilentDecisionValueNotInverting
% 0.29/0.47 thf(fact_201__092_060open_062_092_060And_062p_O_A_092_060exists_062c_H_O_Areachable_A_Ilast_Aexec_J_Ac_H_A_092_060and_062_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060close_062,axiom,
% 0.29/0.47 ! [P: p] :
% 0.29/0.47 ? [C6: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ C6 )
% 0.29/0.47 & ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ P @ C6 ) )
% 0.29/0.47 = ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>\<And>p. \<exists>c'. reachable (last exec) c' \<and> val[p,c'] = {True, False}\<close>
% 0.29/0.47 thf(fact_202__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_H_O_A_092_060lbrakk_062reachable_A_Ilast_Aexec_J_Ac_H_059_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.47 ~ ! [C6: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ C6 )
% 0.29/0.47 => ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ C6 ) )
% 0.29/0.47 != ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>\<And>thesis. (\<And>c'. \<lbrakk>reachable (last exec) c'; val[p,c'] = {True, False}\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.47 thf(fact_203_Agree,axiom,
% 0.29/0.47 ! [Cfg: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ Cfg )
% 0.29/0.47 => ( agreement_p_v_s @ Cfg ) ) ).
% 0.29/0.47
% 0.29/0.47 % Agree
% 0.29/0.47 thf(fact_204_emptyE,axiom,
% 0.29/0.47 ! [A5: p] :
% 0.29/0.47 ~ ( member_p @ A5 @ bot_bot_set_p ) ).
% 0.29/0.47
% 0.29/0.47 % emptyE
% 0.29/0.47 thf(fact_205_emptyE,axiom,
% 0.29/0.47 ! [A5: $o] :
% 0.29/0.47 ~ ( member_o @ A5 @ bot_bot_set_o ) ).
% 0.29/0.47
% 0.29/0.47 % emptyE
% 0.29/0.47 thf(fact_206_insertE,axiom,
% 0.29/0.47 ! [A5: $o,B3: $o,A: set_o] :
% 0.29/0.47 ( ( member_o @ A5 @ ( insert_o @ B3 @ A ) )
% 0.29/0.47 => ( ( A5 = ( ~ B3 ) )
% 0.29/0.47 => ( member_o @ A5 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insertE
% 0.29/0.47 thf(fact_207_insertE,axiom,
% 0.29/0.47 ! [A5: p,B3: p,A: set_p] :
% 0.29/0.47 ( ( member_p @ A5 @ ( insert_p @ B3 @ A ) )
% 0.29/0.47 => ( ( A5 != B3 )
% 0.29/0.47 => ( member_p @ A5 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insertE
% 0.29/0.47 thf(fact_208_equals0D,axiom,
% 0.29/0.47 ! [A: set_p,A5: p] :
% 0.29/0.47 ( ( A = bot_bot_set_p )
% 0.29/0.47 => ~ ( member_p @ A5 @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % equals0D
% 0.29/0.47 thf(fact_209_equals0D,axiom,
% 0.29/0.47 ! [A: set_o,A5: $o] :
% 0.29/0.47 ( ( A = bot_bot_set_o )
% 0.29/0.47 => ~ ( member_o @ A5 @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % equals0D
% 0.29/0.47 thf(fact_210_equals0I,axiom,
% 0.29/0.47 ! [A: set_p] :
% 0.29/0.47 ( ! [Y4: p] :
% 0.29/0.47 ~ ( member_p @ Y4 @ A )
% 0.29/0.47 => ( A = bot_bot_set_p ) ) ).
% 0.29/0.47
% 0.29/0.47 % equals0I
% 0.29/0.47 thf(fact_211_equals0I,axiom,
% 0.29/0.47 ! [A: set_o] :
% 0.29/0.47 ( ! [Y4: $o] :
% 0.29/0.47 ~ ( member_o @ Y4 @ A )
% 0.29/0.47 => ( A = bot_bot_set_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % equals0I
% 0.29/0.47 thf(fact_212_insertI1,axiom,
% 0.29/0.47 ! [A5: $o,B: set_o] : ( member_o @ A5 @ ( insert_o @ A5 @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % insertI1
% 0.29/0.47 thf(fact_213_insertI1,axiom,
% 0.29/0.47 ! [A5: p,B: set_p] : ( member_p @ A5 @ ( insert_p @ A5 @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % insertI1
% 0.29/0.47 thf(fact_214_insertI2,axiom,
% 0.29/0.47 ! [A5: $o,B: set_o,B3: $o] :
% 0.29/0.47 ( ( member_o @ A5 @ B )
% 0.29/0.47 => ( member_o @ A5 @ ( insert_o @ B3 @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insertI2
% 0.29/0.47 thf(fact_215_insertI2,axiom,
% 0.29/0.47 ! [A5: p,B: set_p,B3: p] :
% 0.29/0.47 ( ( member_p @ A5 @ B )
% 0.29/0.47 => ( member_p @ A5 @ ( insert_p @ B3 @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insertI2
% 0.29/0.47 thf(fact_216_ex__in__conv,axiom,
% 0.29/0.47 ! [A: set_p] :
% 0.29/0.47 ( ( ? [X3: p] : ( member_p @ X3 @ A ) )
% 0.29/0.47 = ( A != bot_bot_set_p ) ) ).
% 0.29/0.47
% 0.29/0.47 % ex_in_conv
% 0.29/0.47 thf(fact_217_ex__in__conv,axiom,
% 0.29/0.47 ! [A: set_o] :
% 0.29/0.47 ( ( ? [X3: $o] : ( member_o @ X3 @ A ) )
% 0.29/0.47 = ( A != bot_bot_set_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % ex_in_conv
% 0.29/0.47 thf(fact_218_Set_Oset__insert,axiom,
% 0.29/0.47 ! [X2: $o,A: set_o] :
% 0.29/0.47 ( ( member_o @ X2 @ A )
% 0.29/0.47 => ~ ! [B6: set_o] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( insert_o @ X2 @ B6 ) )
% 0.29/0.47 => ( member_o @ X2 @ B6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Set.set_insert
% 0.29/0.47 thf(fact_219_Set_Oset__insert,axiom,
% 0.29/0.47 ! [X2: p,A: set_p] :
% 0.29/0.47 ( ( member_p @ X2 @ A )
% 0.29/0.47 => ~ ! [B6: set_p] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( insert_p @ X2 @ B6 ) )
% 0.29/0.47 => ( member_p @ X2 @ B6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Set.set_insert
% 0.29/0.47 thf(fact_220_singletonD,axiom,
% 0.29/0.47 ! [B3: p,A5: p] :
% 0.29/0.47 ( ( member_p @ B3 @ ( insert_p @ A5 @ bot_bot_set_p ) )
% 0.29/0.47 => ( B3 = A5 ) ) ).
% 0.29/0.47
% 0.29/0.47 % singletonD
% 0.29/0.47 thf(fact_221_singletonD,axiom,
% 0.29/0.47 ! [B3: $o,A5: $o] :
% 0.29/0.47 ( ( member_o @ B3 @ ( insert_o @ A5 @ bot_bot_set_o ) )
% 0.29/0.47 => ( B3 = A5 ) ) ).
% 0.29/0.47
% 0.29/0.47 % singletonD
% 0.29/0.47 thf(fact_222_insert__ident,axiom,
% 0.29/0.47 ! [X2: $o,A: set_o,B: set_o] :
% 0.29/0.47 ( ~ ( member_o @ X2 @ A )
% 0.29/0.47 => ( ~ ( member_o @ X2 @ B )
% 0.29/0.47 => ( ( ( insert_o @ X2 @ A )
% 0.29/0.47 = ( insert_o @ X2 @ B ) )
% 0.29/0.47 = ( A = B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_ident
% 0.29/0.47 thf(fact_223_insert__ident,axiom,
% 0.29/0.47 ! [X2: p,A: set_p,B: set_p] :
% 0.29/0.47 ( ~ ( member_p @ X2 @ A )
% 0.29/0.47 => ( ~ ( member_p @ X2 @ B )
% 0.29/0.47 => ( ( ( insert_p @ X2 @ A )
% 0.29/0.47 = ( insert_p @ X2 @ B ) )
% 0.29/0.47 = ( A = B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_ident
% 0.29/0.47 thf(fact_224_insert__absorb,axiom,
% 0.29/0.47 ! [A5: $o,A: set_o] :
% 0.29/0.47 ( ( member_o @ A5 @ A )
% 0.29/0.47 => ( ( insert_o @ A5 @ A )
% 0.29/0.47 = A ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_absorb
% 0.29/0.47 thf(fact_225_insert__absorb,axiom,
% 0.29/0.47 ! [A5: p,A: set_p] :
% 0.29/0.47 ( ( member_p @ A5 @ A )
% 0.29/0.47 => ( ( insert_p @ A5 @ A )
% 0.29/0.47 = A ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_absorb
% 0.29/0.47 thf(fact_226_insert__eq__iff,axiom,
% 0.29/0.47 ! [A5: $o,A: set_o,B3: $o,B: set_o] :
% 0.29/0.47 ( ~ ( member_o @ A5 @ A )
% 0.29/0.47 => ( ~ ( member_o @ B3 @ B )
% 0.29/0.47 => ( ( ( insert_o @ A5 @ A )
% 0.29/0.47 = ( insert_o @ B3 @ B ) )
% 0.29/0.47 = ( ( ( A5 = B3 )
% 0.29/0.47 => ( A = B ) )
% 0.29/0.47 & ( ( A5 = ( ~ B3 ) )
% 0.29/0.47 => ? [C7: set_o] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( insert_o @ B3 @ C7 ) )
% 0.29/0.47 & ~ ( member_o @ B3 @ C7 )
% 0.29/0.47 & ( B
% 0.29/0.47 = ( insert_o @ A5 @ C7 ) )
% 0.29/0.47 & ~ ( member_o @ A5 @ C7 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_eq_iff
% 0.29/0.47 thf(fact_227_insert__eq__iff,axiom,
% 0.29/0.47 ! [A5: p,A: set_p,B3: p,B: set_p] :
% 0.29/0.47 ( ~ ( member_p @ A5 @ A )
% 0.29/0.47 => ( ~ ( member_p @ B3 @ B )
% 0.29/0.47 => ( ( ( insert_p @ A5 @ A )
% 0.29/0.47 = ( insert_p @ B3 @ B ) )
% 0.29/0.47 = ( ( ( A5 = B3 )
% 0.29/0.47 => ( A = B ) )
% 0.29/0.47 & ( ( A5 != B3 )
% 0.29/0.47 => ? [C7: set_p] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( insert_p @ B3 @ C7 ) )
% 0.29/0.47 & ~ ( member_p @ B3 @ C7 )
% 0.29/0.47 & ( B
% 0.29/0.47 = ( insert_p @ A5 @ C7 ) )
% 0.29/0.47 & ~ ( member_p @ A5 @ C7 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_eq_iff
% 0.29/0.47 thf(fact_228_singleton__iff,axiom,
% 0.29/0.47 ! [B3: p,A5: p] :
% 0.29/0.47 ( ( member_p @ B3 @ ( insert_p @ A5 @ bot_bot_set_p ) )
% 0.29/0.47 = ( B3 = A5 ) ) ).
% 0.29/0.47
% 0.29/0.47 % singleton_iff
% 0.29/0.47 thf(fact_229_singleton__iff,axiom,
% 0.29/0.47 ! [B3: $o,A5: $o] :
% 0.29/0.47 ( ( member_o @ B3 @ ( insert_o @ A5 @ bot_bot_set_o ) )
% 0.29/0.47 = ( B3 = A5 ) ) ).
% 0.29/0.47
% 0.29/0.47 % singleton_iff
% 0.29/0.47 thf(fact_230_insert__commute,axiom,
% 0.29/0.47 ! [X2: $o,Y2: $o,A: set_o] :
% 0.29/0.47 ( ( insert_o @ X2 @ ( insert_o @ Y2 @ A ) )
% 0.29/0.47 = ( insert_o @ Y2 @ ( insert_o @ X2 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_commute
% 0.29/0.47 thf(fact_231_Collect__conv__if,axiom,
% 0.29/0.47 ! [P2: $o > $o,A5: $o] :
% 0.29/0.47 ( ( ( P2 @ A5 )
% 0.29/0.47 => ( ( collect_o
% 0.29/0.47 @ ^ [X3: $o] :
% 0.29/0.47 ( ( X3 = A5 )
% 0.29/0.47 & ( P2 @ X3 ) ) )
% 0.29/0.47 = ( insert_o @ A5 @ bot_bot_set_o ) ) )
% 0.29/0.47 & ( ~ ( P2 @ A5 )
% 0.29/0.47 => ( ( collect_o
% 0.29/0.47 @ ^ [X3: $o] :
% 0.29/0.47 ( ( X3 = A5 )
% 0.29/0.47 & ( P2 @ X3 ) ) )
% 0.29/0.47 = bot_bot_set_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_conv_if
% 0.29/0.47 thf(fact_232_Collect__conv__if2,axiom,
% 0.29/0.47 ! [P2: $o > $o,A5: $o] :
% 0.29/0.47 ( ( ( P2 @ A5 )
% 0.29/0.47 => ( ( collect_o
% 0.29/0.47 @ ^ [X3: $o] :
% 0.29/0.47 ( ( A5 = X3 )
% 0.29/0.47 & ( P2 @ X3 ) ) )
% 0.29/0.47 = ( insert_o @ A5 @ bot_bot_set_o ) ) )
% 0.29/0.47 & ( ~ ( P2 @ A5 )
% 0.29/0.47 => ( ( collect_o
% 0.29/0.47 @ ^ [X3: $o] :
% 0.29/0.47 ( ( A5 = X3 )
% 0.29/0.47 & ( P2 @ X3 ) ) )
% 0.29/0.47 = bot_bot_set_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_conv_if2
% 0.29/0.47 thf(fact_233_doubleton__eq__iff,axiom,
% 0.29/0.47 ! [A5: $o,B3: $o,C: $o,D: $o] :
% 0.29/0.47 ( ( ( insert_o @ A5 @ ( insert_o @ B3 @ bot_bot_set_o ) )
% 0.29/0.47 = ( insert_o @ C @ ( insert_o @ D @ bot_bot_set_o ) ) )
% 0.29/0.47 = ( ( ( A5 = C )
% 0.29/0.47 & ( B3 = D ) )
% 0.29/0.47 | ( ( A5 = D )
% 0.29/0.47 & ( B3 = C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % doubleton_eq_iff
% 0.29/0.47 thf(fact_234_insert__not__empty,axiom,
% 0.29/0.47 ! [A5: $o,A: set_o] :
% 0.29/0.47 ( ( insert_o @ A5 @ A )
% 0.29/0.47 != bot_bot_set_o ) ).
% 0.29/0.47
% 0.29/0.47 % insert_not_empty
% 0.29/0.47 thf(fact_235_singleton__inject,axiom,
% 0.29/0.47 ! [A5: $o,B3: $o] :
% 0.29/0.47 ( ( ( insert_o @ A5 @ bot_bot_set_o )
% 0.29/0.47 = ( insert_o @ B3 @ bot_bot_set_o ) )
% 0.29/0.47 => ( A5 = B3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % singleton_inject
% 0.29/0.47 thf(fact_236_subset__singletonD,axiom,
% 0.29/0.47 ! [A: set_o,X2: $o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A @ ( insert_o @ X2 @ bot_bot_set_o ) )
% 0.29/0.47 => ( ( A = bot_bot_set_o )
% 0.29/0.47 | ( A
% 0.29/0.47 = ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_singletonD
% 0.29/0.47 thf(fact_237_mk__disjoint__insert,axiom,
% 0.29/0.47 ! [A5: $o,A: set_o] :
% 0.29/0.47 ( ( member_o @ A5 @ A )
% 0.29/0.47 => ? [B6: set_o] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( insert_o @ A5 @ B6 ) )
% 0.29/0.47 & ~ ( member_o @ A5 @ B6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mk_disjoint_insert
% 0.29/0.47 thf(fact_238_mk__disjoint__insert,axiom,
% 0.29/0.47 ! [A5: p,A: set_p] :
% 0.29/0.47 ( ( member_p @ A5 @ A )
% 0.29/0.47 => ? [B6: set_p] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( insert_p @ A5 @ B6 ) )
% 0.29/0.47 & ~ ( member_p @ A5 @ B6 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mk_disjoint_insert
% 0.29/0.47 thf(fact_239_subset__singleton__iff,axiom,
% 0.29/0.47 ! [X5: set_o,A5: $o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ X5 @ ( insert_o @ A5 @ bot_bot_set_o ) )
% 0.29/0.47 = ( ( X5 = bot_bot_set_o )
% 0.29/0.47 | ( X5
% 0.29/0.47 = ( insert_o @ A5 @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_singleton_iff
% 0.29/0.47 thf(fact_240_insert__Collect,axiom,
% 0.29/0.47 ! [A5: $o,P2: $o > $o] :
% 0.29/0.47 ( ( insert_o @ A5 @ ( collect_o @ P2 ) )
% 0.29/0.47 = ( collect_o
% 0.29/0.47 @ ^ [U: $o] :
% 0.29/0.47 ( ( U != A5 )
% 0.29/0.47 => ( P2 @ U ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_Collect
% 0.29/0.47 thf(fact_241_insert__compr,axiom,
% 0.29/0.47 ( insert_p
% 0.29/0.47 = ( ^ [A6: p,B2: set_p] :
% 0.29/0.47 ( collect_p
% 0.29/0.47 @ ^ [X3: p] :
% 0.29/0.47 ( ( X3 = A6 )
% 0.29/0.47 | ( member_p @ X3 @ B2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_compr
% 0.29/0.47 thf(fact_242_insert__compr,axiom,
% 0.29/0.47 ( insert_o
% 0.29/0.47 = ( ^ [A6: $o,B2: set_o] :
% 0.29/0.47 ( collect_o
% 0.29/0.47 @ ^ [X3: $o] :
% 0.29/0.47 ( ( X3 = A6 )
% 0.29/0.47 | ( member_o @ X3 @ B2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_compr
% 0.29/0.47 thf(fact_243_empty__def,axiom,
% 0.29/0.47 ( bot_bot_set_o
% 0.29/0.47 = ( collect_o
% 0.29/0.47 @ ^ [X3: $o] : $false ) ) ).
% 0.29/0.47
% 0.29/0.47 % empty_def
% 0.29/0.47 thf(fact_244_bot_Oextremum,axiom,
% 0.29/0.47 ! [A5: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A5 ) ).
% 0.29/0.47
% 0.29/0.47 % bot.extremum
% 0.29/0.47 thf(fact_245_bot_Oextremum,axiom,
% 0.29/0.47 ! [A5: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A5 ) ).
% 0.29/0.47
% 0.29/0.47 % bot.extremum
% 0.29/0.47 thf(fact_246_bot_Oextremum__unique,axiom,
% 0.29/0.47 ! [A5: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ bot_bot_set_o )
% 0.29/0.47 = ( A5 = bot_bot_set_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % bot.extremum_unique
% 0.29/0.47 thf(fact_247_bot_Oextremum__unique,axiom,
% 0.29/0.47 ! [A5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ bot_bot_nat )
% 0.29/0.47 = ( A5 = bot_bot_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 % bot.extremum_unique
% 0.29/0.47 thf(fact_248_bot_Oextremum__uniqueI,axiom,
% 0.29/0.47 ! [A5: set_o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A5 @ bot_bot_set_o )
% 0.29/0.47 => ( A5 = bot_bot_set_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % bot.extremum_uniqueI
% 0.29/0.47 thf(fact_249_bot_Oextremum__uniqueI,axiom,
% 0.29/0.47 ! [A5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A5 @ bot_bot_nat )
% 0.29/0.47 => ( A5 = bot_bot_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 % bot.extremum_uniqueI
% 0.29/0.47 thf(fact_250_insert__mono,axiom,
% 0.29/0.47 ! [C3: set_o,D2: set_o,A5: $o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ C3 @ D2 )
% 0.29/0.47 => ( ord_less_eq_set_o @ ( insert_o @ A5 @ C3 ) @ ( insert_o @ A5 @ D2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_mono
% 0.29/0.47 thf(fact_251_subset__insert,axiom,
% 0.29/0.47 ! [X2: p,A: set_p,B: set_p] :
% 0.29/0.47 ( ~ ( member_p @ X2 @ A )
% 0.29/0.47 => ( ( ord_less_eq_set_p @ A @ ( insert_p @ X2 @ B ) )
% 0.29/0.47 = ( ord_less_eq_set_p @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_insert
% 0.29/0.47 thf(fact_252_subset__insert,axiom,
% 0.29/0.47 ! [X2: $o,A: set_o,B: set_o] :
% 0.29/0.47 ( ~ ( member_o @ X2 @ A )
% 0.29/0.47 => ( ( ord_less_eq_set_o @ A @ ( insert_o @ X2 @ B ) )
% 0.29/0.47 = ( ord_less_eq_set_o @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_insert
% 0.29/0.47 thf(fact_253_subset__insertI,axiom,
% 0.29/0.47 ! [B: set_o,A5: $o] : ( ord_less_eq_set_o @ B @ ( insert_o @ A5 @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_insertI
% 0.29/0.47 thf(fact_254_subset__insertI2,axiom,
% 0.29/0.47 ! [A: set_o,B: set_o,B3: $o] :
% 0.29/0.47 ( ( ord_less_eq_set_o @ A @ B )
% 0.29/0.47 => ( ord_less_eq_set_o @ A @ ( insert_o @ B3 @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_insertI2
% 0.29/0.47 thf(fact_255_flpSystem_OvUniform__def,axiom,
% 0.29/0.47 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s,V2: $o,C: config256849571t_unit] :
% 0.29/0.47 ( ( flpSystem_p_s_v @ Sends )
% 0.29/0.47 => ( ( vUniform_p_s_v @ Trans @ Sends @ Start @ V2 @ C )
% 0.29/0.47 = ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 0.29/0.47 & ! [P4: p] :
% 0.29/0.47 ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ P4 @ C ) )
% 0.29/0.47 = ( insert_o @ V2 @ bot_bot_set_o ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.vUniform_def
% 0.29/0.47 thf(fact_256_flpSystem_OSilentDecisionValueNotInverting,axiom,
% 0.29/0.47 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s,Q: p,C: config256849571t_unit,V2: $o,Msg: message_p_v,C2: config256849571t_unit,P: p] :
% 0.29/0.47 ( ( flpSystem_p_s_v @ Sends )
% 0.29/0.47 => ( ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C ) )
% 0.29/0.47 = ( insert_o @ V2 @ bot_bot_set_o ) )
% 0.29/0.47 => ( ( steps_p_s_v @ Trans @ Sends @ C @ Msg @ C2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ Msg )
% 0.29/0.47 => ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 0.29/0.47 => ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C2 ) )
% 0.29/0.47 != ( insert_o @ ~ V2 @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.SilentDecisionValueNotInverting
% 0.29/0.47 thf(fact_257_flpSystem_OpSilDecVal_Ocong,axiom,
% 0.29/0.47 pSilDecVal_p_s_v = pSilDecVal_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.pSilDecVal.cong
% 0.29/0.47 thf(fact_258_flpSystem_OvUniform_Ocong,axiom,
% 0.29/0.47 vUniform_p_s_v = vUniform_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.vUniform.cong
% 0.29/0.47 thf(fact_259_flpSystem_OagreementInit_Ocong,axiom,
% 0.29/0.47 agreementInit_p_s_v = agreementInit_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.agreementInit.cong
% 0.29/0.47 thf(fact_260_expandExecutionReachable,axiom,
% 0.29/0.47 ! [CfgLast: config256849571t_unit,Cfg: config256849571t_unit,Exec: list_c1059388851t_unit,Trace: list_message_p_v] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ CfgLast @ Cfg )
% 0.29/0.47 => ( ( execution_p_s_v @ trans @ sends @ start @ Exec @ Trace )
% 0.29/0.47 => ( ( CfgLast
% 0.29/0.47 = ( last_c571238084t_unit @ Exec ) )
% 0.29/0.47 => ? [Exec2: list_c1059388851t_unit,Trace2: list_message_p_v] :
% 0.29/0.47 ( ( execution_p_s_v @ trans @ sends @ start @ Exec2 @ Trace2 )
% 0.29/0.47 & ( ( ( prefix1615116500t_unit @ Exec @ Exec2 )
% 0.29/0.47 & ( prefix47729710ge_p_v @ Trace @ Trace2 ) )
% 0.29/0.47 | ( ( Exec = Exec2 )
% 0.29/0.47 & ( Trace = Trace2 ) ) )
% 0.29/0.47 & ( ( last_c571238084t_unit @ Exec2 )
% 0.29/0.47 = Cfg ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % expandExecutionReachable
% 0.29/0.47 thf(fact_261_NewExec_I2_J,axiom,
% 0.29/0.47 ( ( ( prefix1615116500t_unit @ exec @ exec2 )
% 0.29/0.47 & ( prefix47729710ge_p_v @ trace @ trace2 ) )
% 0.29/0.47 | ( ( exec = exec2 )
% 0.29/0.47 & ( trace = trace2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % NewExec(2)
% 0.29/0.47 thf(fact_262_NoOutMessageLoss,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,V2: $o] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ ( outMsg_p_v @ V2 ) ) @ ( msgs_p1029620568t_unit @ Cfg2 @ ( outMsg_p_v @ V2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % NoOutMessageLoss
% 0.29/0.47 thf(fact_263_asynchronousSystem_OReachableStepFirst,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg: config256849571t_unit,Cfg4: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg @ Cfg4 )
% 0.29/0.47 => ( ( Cfg = Cfg4 )
% 0.29/0.47 | ? [Cfg12: config256849571t_unit,Msg3: message_p_v,P3: p] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ Cfg @ Msg3 @ Cfg12 )
% 0.29/0.47 & ( enabled_p_v_s @ Cfg @ Msg3 )
% 0.29/0.47 & ( isReceiverOf_p_v @ P3 @ Msg3 )
% 0.29/0.47 & ( reachable_p_s_v @ Trans @ Sends @ Cfg12 @ Cfg4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.ReachableStepFirst
% 0.29/0.47 thf(fact_264_asynchronousSystem_ONoActivityNoMessageLoss,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,P: p,M2: message_p_v] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( ~ ( member_p @ P @ Q2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ M2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.NoActivityNoMessageLoss
% 0.29/0.47 thf(fact_265_asynchronousSystem_ONoMessageLossStep,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,P: p,M2: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ M )
% 0.29/0.47 => ( ~ ( isReceiverOf_p_v @ P @ M2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.NoMessageLossStep
% 0.29/0.47 thf(fact_266_message_Oinject_I2_J,axiom,
% 0.29/0.47 ! [X22: $o,Y22: $o] :
% 0.29/0.47 ( ( ( outMsg_p_v @ X22 )
% 0.29/0.47 = ( outMsg_p_v @ Y22 ) )
% 0.29/0.47 = ( X22 = Y22 ) ) ).
% 0.29/0.47
% 0.29/0.47 % message.inject(2)
% 0.29/0.47 thf(fact_267_StepOutMsg,axiom,
% 0.29/0.47 ! [Cfg1: config256849571t_unit,V2: $o,Cfg2: config256849571t_unit] :
% 0.29/0.47 ~ ( steps_p_s_v @ trans @ sends @ Cfg1 @ ( outMsg_p_v @ V2 ) @ Cfg2 ) ).
% 0.29/0.47
% 0.29/0.47 % StepOutMsg
% 0.29/0.47 thf(fact_268_isPrefixListTrace,axiom,
% 0.29/0.47 prefix47729710ge_p_v @ trace @ traceMsga ).
% 0.29/0.47
% 0.29/0.47 % isPrefixListTrace
% 0.29/0.47 thf(fact_269_expandExecutionStep,axiom,
% 0.29/0.47 ! [Exec3: list_c1059388851t_unit,Msg: message_p_v,CMsg2: config256849571t_unit,Trace3: list_message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ Exec3 ) @ Msg @ CMsg2 )
% 0.29/0.47 => ( ( execution_p_s_v @ trans @ sends @ start @ Exec3 @ Trace3 )
% 0.29/0.47 => ? [Exec4: list_c1059388851t_unit,Trace4: list_message_p_v] :
% 0.29/0.47 ( ( execution_p_s_v @ trans @ sends @ start @ Exec4 @ Trace4 )
% 0.29/0.47 & ( prefix1615116500t_unit @ Exec3 @ Exec4 )
% 0.29/0.47 & ( prefix47729710ge_p_v @ Trace3 @ Trace4 )
% 0.29/0.47 & ( ( last_c571238084t_unit @ Exec4 )
% 0.29/0.47 = CMsg2 )
% 0.29/0.47 & ( ( last_message_p_v @ Trace4 )
% 0.29/0.47 = Msg ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % expandExecutionStep
% 0.29/0.47 thf(fact_270__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062exec_H_Atrace_H_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_Aexec_H_Atrace_H_059_AprefixList_Aexec_Aexec_H_A_092_060and_062_AprefixList_Atrace_Atrace_H_A_092_060or_062_Aexec_A_061_Aexec_H_A_092_060and_062_Atrace_A_061_Atrace_H_059_Alast_Aexec_H_A_061_Ac_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.47 ~ ! [Exec2: list_c1059388851t_unit,Trace2: list_message_p_v] :
% 0.29/0.47 ( ( execution_p_s_v @ trans @ sends @ start @ Exec2 @ Trace2 )
% 0.29/0.47 => ( ( ( ( prefix1615116500t_unit @ exec @ Exec2 )
% 0.29/0.47 & ( prefix47729710ge_p_v @ trace @ Trace2 ) )
% 0.29/0.47 | ( ( exec = Exec2 )
% 0.29/0.47 & ( trace = Trace2 ) ) )
% 0.29/0.47 => ( ( last_c571238084t_unit @ Exec2 )
% 0.29/0.47 != c ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>\<And>thesis. (\<And>exec' trace'. \<lbrakk>execution trans sends start exec' trace'; prefixList exec exec' \<and> prefixList trace trace' \<or> exec = exec' \<and> trace = trace'; last exec' = c'\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.47 thf(fact_271__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062execMsg_AtraceMsg_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_AexecMsg_AtraceMsg_059_AprefixList_Aexec_H_AexecMsg_059_AprefixList_Atrace_H_AtraceMsg_059_Alast_AexecMsg_A_061_AcMsg_059_Alast_AtraceMsg_A_061_Amsg_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.47 ~ ! [ExecMsg: list_c1059388851t_unit,TraceMsg: list_message_p_v] :
% 0.29/0.47 ( ( execution_p_s_v @ trans @ sends @ start @ ExecMsg @ TraceMsg )
% 0.29/0.47 => ( ( prefix1615116500t_unit @ exec2 @ ExecMsg )
% 0.29/0.47 => ( ( prefix47729710ge_p_v @ trace2 @ TraceMsg )
% 0.29/0.47 => ( ( ( last_c571238084t_unit @ ExecMsg )
% 0.29/0.47 = cMsg )
% 0.29/0.47 => ( ( last_message_p_v @ TraceMsg )
% 0.29/0.47 != msg ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>\<And>thesis. (\<And>execMsg traceMsg. \<lbrakk>execution trans sends start execMsg traceMsg; prefixList exec' execMsg; prefixList trace' traceMsg; last execMsg = cMsg; last traceMsg = msg\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.47 thf(fact_272_bot__set__def,axiom,
% 0.29/0.47 ( bot_bot_set_o
% 0.29/0.47 = ( collect_o @ bot_bot_o_o ) ) ).
% 0.29/0.47
% 0.29/0.47 % bot_set_def
% 0.29/0.47 thf(fact_273_asynchronousSystem_OStepOutMsg,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,V2: $o,Cfg2: config256849571t_unit] :
% 0.29/0.47 ~ ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ ( outMsg_p_v @ V2 ) @ Cfg2 ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.StepOutMsg
% 0.29/0.47 thf(fact_274_isReceiverOf_Osimps_I3_J,axiom,
% 0.29/0.47 ! [P1: p,V2: $o] :
% 0.29/0.47 ~ ( isReceiverOf_p_v @ P1 @ ( outMsg_p_v @ V2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % isReceiverOf.simps(3)
% 0.29/0.47 thf(fact_275_asynchronousSystem_ONoOutMessageLoss,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,V2: $o] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ ( outMsg_p_v @ V2 ) ) @ ( msgs_p1029620568t_unit @ Cfg2 @ ( outMsg_p_v @ V2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.NoOutMessageLoss
% 0.29/0.47 thf(fact_276_asynchronousSystem_Osteps_Ocong,axiom,
% 0.29/0.47 steps_p_s_v = steps_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.steps.cong
% 0.29/0.47 thf(fact_277_asynchronousSystem_OReachableTrans,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,Cfg32: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 0.29/0.47 => ( ( reachable_p_s_v @ Trans @ Sends @ Cfg2 @ Cfg32 )
% 0.29/0.47 => ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg32 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.ReachableTrans
% 0.29/0.47 thf(fact_278_asynchronousSystem_Oreachable_Ocong,axiom,
% 0.29/0.47 reachable_p_s_v = reachable_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.reachable.cong
% 0.29/0.47 thf(fact_279_asynchronousSystem_Oinit,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit] : ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg1 ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.init
% 0.29/0.47 thf(fact_280_UniqueReceiverOf,axiom,
% 0.29/0.47 ! [Q: p,Msg: message_p_v,P: p] :
% 0.29/0.47 ( ( isReceiverOf_p_v @ Q @ Msg )
% 0.29/0.47 => ( ( P != Q )
% 0.29/0.47 => ~ ( isReceiverOf_p_v @ P @ Msg ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % UniqueReceiverOf
% 0.29/0.47 thf(fact_281_asynchronousSystem_OQReachableTrans,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg2: config256849571t_unit,Q2: set_p,Cfg32: config256849571t_unit,Cfg1: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg2 @ Q2 @ Cfg32 )
% 0.29/0.47 => ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.QReachableTrans
% 0.29/0.47 thf(fact_282_asynchronousSystem_OqReachable_Ocong,axiom,
% 0.29/0.47 qReachable_p_s_v = qReachable_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.qReachable.cong
% 0.29/0.47 thf(fact_283_asynchronousSystem_OInitQ,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p] : ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg1 ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.InitQ
% 0.29/0.47 thf(fact_284_asynchronousSystem_OinitReachable_Ocong,axiom,
% 0.29/0.47 initReachable_p_s_v = initReachable_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.initReachable.cong
% 0.29/0.47 thf(fact_285_asynchronousSystem_Oinitial_Ocong,axiom,
% 0.29/0.47 initial_p_s_v = initial_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.initial.cong
% 0.29/0.47 thf(fact_286_asynchronousSystem_OstepReachable_Ocong,axiom,
% 0.29/0.47 stepReachable_p_s_v = stepReachable_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.stepReachable.cong
% 0.29/0.47 thf(fact_287_asynchronousSystem_Ostep,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,Msg: message_p_v,Cfg32: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 0.29/0.47 => ( ( steps_p_s_v @ Trans @ Sends @ Cfg2 @ Msg @ Cfg32 )
% 0.29/0.47 => ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg32 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.step
% 0.29/0.47 thf(fact_288_asynchronousSystem_Oreachable_Ocases,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,A1: config256849571t_unit,A2: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ A1 @ A2 )
% 0.29/0.47 => ( ( A2 != A1 )
% 0.29/0.47 => ~ ! [Cfg23: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ A1 @ Cfg23 )
% 0.29/0.47 => ! [Msg3: message_p_v] :
% 0.29/0.47 ~ ( steps_p_s_v @ Trans @ Sends @ Cfg23 @ Msg3 @ A2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.reachable.cases
% 0.29/0.47 thf(fact_289_asynchronousSystem_Oreachable_Osimps,axiom,
% 0.29/0.47 ( reachable_p_s_v
% 0.29/0.47 = ( ^ [Trans2: p > s > messageValue_v > s,Sends2: p > s > messageValue_v > message_p_v > nat,A12: config256849571t_unit,A22: config256849571t_unit] :
% 0.29/0.47 ( ? [Cfg13: config256849571t_unit] :
% 0.29/0.47 ( ( A12 = Cfg13 )
% 0.29/0.47 & ( A22 = Cfg13 ) )
% 0.29/0.47 | ? [Cfg13: config256849571t_unit,Cfg22: config256849571t_unit,Msg2: message_p_v,Cfg34: config256849571t_unit] :
% 0.29/0.47 ( ( A12 = Cfg13 )
% 0.29/0.47 & ( A22 = Cfg34 )
% 0.29/0.47 & ( reachable_p_s_v @ Trans2 @ Sends2 @ Cfg13 @ Cfg22 )
% 0.29/0.47 & ( steps_p_s_v @ Trans2 @ Sends2 @ Cfg22 @ Msg2 @ Cfg34 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.reachable.simps
% 0.29/0.47 thf(fact_290_asynchronousSystem_Oreachable_Oinducts,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,X1: config256849571t_unit,X22: config256849571t_unit,P2: config256849571t_unit > config256849571t_unit > $o] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ X1 @ X22 )
% 0.29/0.47 => ( ! [Cfg12: config256849571t_unit] : ( P2 @ Cfg12 @ Cfg12 )
% 0.29/0.47 => ( ! [Cfg12: config256849571t_unit,Cfg23: config256849571t_unit,Msg3: message_p_v,Cfg33: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg12 @ Cfg23 )
% 0.29/0.47 => ( ( P2 @ Cfg12 @ Cfg23 )
% 0.29/0.47 => ( ( steps_p_s_v @ Trans @ Sends @ Cfg23 @ Msg3 @ Cfg33 )
% 0.29/0.47 => ( P2 @ Cfg12 @ Cfg33 ) ) ) )
% 0.29/0.47 => ( P2 @ X1 @ X22 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.reachable.inducts
% 0.29/0.47 thf(fact_291_asynchronousSystem_ODiamondOne,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg: config256849571t_unit,M: message_p_v,Cfg1: config256849571t_unit,P: p,Q: p,M2: message_p_v,Cfg2: config256849571t_unit] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ Cfg @ M @ Cfg1 )
% 0.29/0.47 => ( ( P != Q )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ M )
% 0.29/0.47 => ( ~ ( isReceiverOf_p_v @ P @ M2 )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ Q @ M2 )
% 0.29/0.47 => ( ~ ( isReceiverOf_p_v @ Q @ M )
% 0.29/0.47 => ( ( steps_p_s_v @ Trans @ Sends @ Cfg @ M2 @ Cfg2 )
% 0.29/0.47 => ? [Cfg3: config256849571t_unit] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M2 @ Cfg3 )
% 0.29/0.47 & ( steps_p_s_v @ Trans @ Sends @ Cfg2 @ M @ Cfg3 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.DiamondOne
% 0.29/0.47 thf(fact_292_asynchronousSystem_OQReachImplReach,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.QReachImplReach
% 0.29/0.47 thf(fact_293_asynchronousSystem_OOnlyOccurenceDisables,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,M2: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.47 => ( ( enabled_p_v_s @ Cfg1 @ M2 )
% 0.29/0.47 => ( ~ ( enabled_p_v_s @ Cfg2 @ M2 )
% 0.29/0.47 => ( M = M2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.OnlyOccurenceDisables
% 0.29/0.47 thf(fact_294_asynchronousSystem_ONotInQFrozenQReachability,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,P: p] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( ~ ( member_p @ P @ Q2 )
% 0.29/0.47 => ( ( states1228886952t_unit @ Cfg1 @ P )
% 0.29/0.47 = ( states1228886952t_unit @ Cfg2 @ P ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.NotInQFrozenQReachability
% 0.29/0.47 thf(fact_295_asynchronousSystem_OInitialIsInitReachable,axiom,
% 0.29/0.47 ! [Start: p > s,C: config256849571t_unit,Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat] :
% 0.29/0.47 ( ( initial_p_s_v @ Start @ C )
% 0.29/0.47 => ( initReachable_p_s_v @ Trans @ Sends @ Start @ C ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.InitialIsInitReachable
% 0.29/0.47 thf(fact_296_asynchronousSystem_OOtherMessagesOnlyGrowing,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,M2: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.47 => ( ( M != M2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.OtherMessagesOnlyGrowing
% 0.29/0.47 thf(fact_297_asynchronousSystem_OStepQ,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,Msg: message_p_v,Cfg32: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 0.29/0.47 => ( ( steps_p_s_v @ Trans @ Sends @ Cfg2 @ Msg @ Cfg32 )
% 0.29/0.47 => ( ? [X4: p] :
% 0.29/0.47 ( ( member_p @ X4 @ Q2 )
% 0.29/0.47 & ( isReceiverOf_p_v @ X4 @ Msg ) )
% 0.29/0.47 => ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.StepQ
% 0.29/0.47 thf(fact_298_asynchronousSystem_OqReachable_Ocases,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,A1: config256849571t_unit,A2: set_p,A3: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans @ Sends @ A1 @ A2 @ A3 )
% 0.29/0.47 => ( ( A3 != A1 )
% 0.29/0.47 => ~ ! [Cfg23: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans @ Sends @ A1 @ A2 @ Cfg23 )
% 0.29/0.47 => ! [Msg3: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ Cfg23 @ Msg3 @ A3 )
% 0.29/0.47 => ~ ? [X: p] :
% 0.29/0.47 ( ( member_p @ X @ A2 )
% 0.29/0.47 & ( isReceiverOf_p_v @ X @ Msg3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.qReachable.cases
% 0.29/0.47 thf(fact_299_asynchronousSystem_OqReachable_Osimps,axiom,
% 0.29/0.47 ( qReachable_p_s_v
% 0.29/0.47 = ( ^ [Trans2: p > s > messageValue_v > s,Sends2: p > s > messageValue_v > message_p_v > nat,A12: config256849571t_unit,A22: set_p,A32: config256849571t_unit] :
% 0.29/0.47 ( ( A32 = A12 )
% 0.29/0.47 | ? [Cfg22: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans2 @ Sends2 @ A12 @ A22 @ Cfg22 )
% 0.29/0.47 & ? [Msg2: message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans2 @ Sends2 @ Cfg22 @ Msg2 @ A32 )
% 0.29/0.47 & ? [X3: p] :
% 0.29/0.47 ( ( member_p @ X3 @ A22 )
% 0.29/0.47 & ( isReceiverOf_p_v @ X3 @ Msg2 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.qReachable.simps
% 0.29/0.47 thf(fact_300_asynchronousSystem_OqReachable_Oinducts,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,X1: config256849571t_unit,X22: set_p,X32: config256849571t_unit,P2: config256849571t_unit > set_p > config256849571t_unit > $o] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans @ Sends @ X1 @ X22 @ X32 )
% 0.29/0.47 => ( ! [Cfg12: config256849571t_unit,Q3: set_p] : ( P2 @ Cfg12 @ Q3 @ Cfg12 )
% 0.29/0.47 => ( ! [Cfg12: config256849571t_unit,Q3: set_p,Cfg23: config256849571t_unit] :
% 0.29/0.47 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg12 @ Q3 @ Cfg23 )
% 0.29/0.47 => ( ( P2 @ Cfg12 @ Q3 @ Cfg23 )
% 0.29/0.47 => ! [Msg3: message_p_v,Cfg33: config256849571t_unit] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ Cfg23 @ Msg3 @ Cfg33 )
% 0.29/0.47 => ( ? [X: p] :
% 0.29/0.47 ( ( member_p @ X @ Q3 )
% 0.29/0.47 & ( isReceiverOf_p_v @ X @ Msg3 ) )
% 0.29/0.47 => ( P2 @ Cfg12 @ Q3 @ Cfg33 ) ) ) ) )
% 0.29/0.47 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.qReachable.inducts
% 0.29/0.47 thf(fact_301_asynchronousSystem_ONoReceivingNoChange,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,P: p] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.47 => ( ~ ( isReceiverOf_p_v @ P @ M )
% 0.29/0.47 => ( ( states1228886952t_unit @ Cfg1 @ P )
% 0.29/0.47 = ( states1228886952t_unit @ Cfg2 @ P ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.NoReceivingNoChange
% 0.29/0.47 thf(fact_302_asynchronousSystem_OinitReachable__def,axiom,
% 0.29/0.47 ( initReachable_p_s_v
% 0.29/0.47 = ( ^ [Trans2: p > s > messageValue_v > s,Sends2: p > s > messageValue_v > message_p_v > nat,Start2: p > s,Cfg5: config256849571t_unit] :
% 0.29/0.47 ? [Cfg0: config256849571t_unit] :
% 0.29/0.47 ( ( initial_p_s_v @ Start2 @ Cfg0 )
% 0.29/0.47 & ( reachable_p_s_v @ Trans2 @ Sends2 @ Cfg0 @ Cfg5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.initReachable_def
% 0.29/0.47 thf(fact_303_asynchronousSystem_OstepReachable__def,axiom,
% 0.29/0.47 ( stepReachable_p_s_v
% 0.29/0.47 = ( ^ [Trans2: p > s > messageValue_v > s,Sends2: p > s > messageValue_v > message_p_v > nat,C12: config256849571t_unit,Msg2: message_p_v,C23: config256849571t_unit] :
% 0.29/0.47 ? [C4: config256849571t_unit,C5: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans2 @ Sends2 @ C12 @ C4 )
% 0.29/0.47 & ( steps_p_s_v @ Trans2 @ Sends2 @ C4 @ Msg2 @ C5 )
% 0.29/0.47 & ( reachable_p_s_v @ Trans2 @ Sends2 @ C5 @ C23 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.stepReachable_def
% 0.29/0.47 thf(fact_304_asynchronousSystem_OStepReachable,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg: config256849571t_unit,Cfg4: config256849571t_unit,Msg: message_p_v] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg @ Cfg4 )
% 0.29/0.47 => ( ( enabled_p_v_s @ Cfg @ Msg )
% 0.29/0.47 => ( ~ ( enabled_p_v_s @ Cfg4 @ Msg )
% 0.29/0.47 => ( stepReachable_p_s_v @ Trans @ Sends @ Cfg @ Msg @ Cfg4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.StepReachable
% 0.29/0.47 thf(fact_305_asynchronousSystem_OexpandExecutionStep,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Exec3: list_c1059388851t_unit,Msg: message_p_v,CMsg2: config256849571t_unit,Start: p > s,Trace3: list_message_p_v] :
% 0.29/0.47 ( ( steps_p_s_v @ Trans @ Sends @ ( last_c571238084t_unit @ Exec3 ) @ Msg @ CMsg2 )
% 0.29/0.47 => ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec3 @ Trace3 )
% 0.29/0.47 => ? [Exec4: list_c1059388851t_unit,Trace4: list_message_p_v] :
% 0.29/0.47 ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec4 @ Trace4 )
% 0.29/0.47 & ( prefix1615116500t_unit @ Exec3 @ Exec4 )
% 0.29/0.47 & ( prefix47729710ge_p_v @ Trace3 @ Trace4 )
% 0.29/0.47 & ( ( last_c571238084t_unit @ Exec4 )
% 0.29/0.47 = CMsg2 )
% 0.29/0.47 & ( ( last_message_p_v @ Trace4 )
% 0.29/0.47 = Msg ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.expandExecutionStep
% 0.29/0.47 thf(fact_306_asynchronousSystem_OexpandExecutionReachable,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,CfgLast: config256849571t_unit,Cfg: config256849571t_unit,Start: p > s,Exec: list_c1059388851t_unit,Trace: list_message_p_v] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ CfgLast @ Cfg )
% 0.29/0.47 => ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec @ Trace )
% 0.29/0.47 => ( ( CfgLast
% 0.29/0.47 = ( last_c571238084t_unit @ Exec ) )
% 0.29/0.47 => ? [Exec2: list_c1059388851t_unit,Trace2: list_message_p_v] :
% 0.29/0.47 ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec2 @ Trace2 )
% 0.29/0.47 & ( ( ( prefix1615116500t_unit @ Exec @ Exec2 )
% 0.29/0.47 & ( prefix47729710ge_p_v @ Trace @ Trace2 ) )
% 0.29/0.47 | ( ( Exec = Exec2 )
% 0.29/0.47 & ( Trace = Trace2 ) ) )
% 0.29/0.47 & ( ( last_c571238084t_unit @ Exec2 )
% 0.29/0.47 = Cfg ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asynchronousSystem.expandExecutionReachable
% 0.29/0.47 thf(fact_307_NonUniformCanReachSilentBivalence,axiom,
% 0.29/0.47 ! [C: config256849571t_unit,P: p] :
% 0.29/0.47 ( ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ C )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ C ) )
% 0.29/0.47 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 0.29/0.47 => ( ! [Cfg6: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ C @ Cfg6 )
% 0.29/0.47 => ( agreement_p_v_s @ Cfg6 ) )
% 0.29/0.47 => ? [C6: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ C @ C6 )
% 0.29/0.47 & ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ P @ C6 ) )
% 0.29/0.47 = ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % NonUniformCanReachSilentBivalence
% 0.29/0.47 thf(fact_308_PseudoTermination,axiom,
% 0.29/0.47 ! [Cc2: config256849571t_unit,Q2: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc2 @ Q2 ) ).
% 0.29/0.47
% 0.29/0.47 % PseudoTermination
% 0.29/0.47 thf(fact_309_DecisionValuesExist,axiom,
% 0.29/0.47 ! [C: config256849571t_unit,P: p] :
% 0.29/0.47 ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 0.29/0.47 => ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 0.29/0.47 => ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ P @ C ) )
% 0.29/0.47 != bot_bot_set_o ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % DecisionValuesExist
% 0.29/0.47 thf(fact_310_InitialNonUniformCfg,axiom,
% 0.29/0.47 ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 0.29/0.47 => ( ! [I2: config256849571t_unit,X_1: config256849571t_unit] : ( validity_p_s_v @ trans @ sends @ start @ I2 @ X_1 )
% 0.29/0.47 => ( ! [I2: config256849571t_unit,X_1: config256849571t_unit] : ( agreementInit_p_s_v @ trans @ sends @ start @ I2 @ X_1 )
% 0.29/0.47 => ? [Cfg6: config256849571t_unit] :
% 0.29/0.47 ( ( initial_p_s_v @ start @ Cfg6 )
% 0.29/0.47 & ( initReachable_p_s_v @ trans @ sends @ start @ Cfg6 )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ Cfg6 )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ Cfg6 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % InitialNonUniformCfg
% 0.29/0.47 thf(fact_311_flpPseudoConsensus_OPseudoTermination,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cc2: config256849571t_unit,Q2: set_p] :
% 0.29/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.29/0.47 => ( termin1618267753_p_s_v @ Trans @ Sends @ Start @ one_one_nat @ Cc2 @ Q2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.PseudoTermination
% 0.29/0.47 thf(fact_312_flpSystem_OterminationPseudo_Ocong,axiom,
% 0.29/0.47 termin1618267753_p_s_v = termin1618267753_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.terminationPseudo.cong
% 0.29/0.47 thf(fact_313_flpSystem_ODecisionValuesExist,axiom,
% 0.29/0.47 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s,C: config256849571t_unit,P: p] :
% 0.29/0.47 ( ( flpSystem_p_s_v @ Sends )
% 0.29/0.47 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ Trans @ Sends @ Start @ one_one_nat @ Cc @ X_1 )
% 0.29/0.47 => ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 0.29/0.47 => ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ P @ C ) )
% 0.29/0.47 != bot_bot_set_o ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.DecisionValuesExist
% 0.29/0.47 thf(fact_314_flpSystem_ONonUniformCanReachSilentBivalence,axiom,
% 0.29/0.47 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s,C: config256849571t_unit,P: p] :
% 0.29/0.47 ( ( flpSystem_p_s_v @ Sends )
% 0.29/0.47 => ( ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ Trans @ Sends @ Start @ $false @ C )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ Trans @ Sends @ Start @ $true @ C ) )
% 0.29/0.47 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ Trans @ Sends @ Start @ one_one_nat @ Cc @ X_1 )
% 0.29/0.47 => ( ! [Cfg6: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ C @ Cfg6 )
% 0.29/0.47 => ( agreement_p_v_s @ Cfg6 ) )
% 0.29/0.47 => ? [C6: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ Trans @ Sends @ C @ C6 )
% 0.29/0.47 & ( ( collect_o
% 0.29/0.47 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ P @ C6 ) )
% 0.29/0.47 = ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.NonUniformCanReachSilentBivalence
% 0.29/0.47 thf(fact_315_flpSystem_OInitialNonUniformCfg,axiom,
% 0.29/0.47 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s] :
% 0.29/0.47 ( ( flpSystem_p_s_v @ Sends )
% 0.29/0.47 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ Trans @ Sends @ Start @ one_one_nat @ Cc @ X_1 )
% 0.29/0.47 => ( ! [I2: config256849571t_unit,X_1: config256849571t_unit] : ( validity_p_s_v @ Trans @ Sends @ Start @ I2 @ X_1 )
% 0.29/0.47 => ( ! [I2: config256849571t_unit,X_1: config256849571t_unit] : ( agreementInit_p_s_v @ Trans @ Sends @ Start @ I2 @ X_1 )
% 0.29/0.47 => ? [Cfg6: config256849571t_unit] :
% 0.29/0.47 ( ( initial_p_s_v @ Start @ Cfg6 )
% 0.29/0.47 & ( initReachable_p_s_v @ Trans @ Sends @ Start @ Cfg6 )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ Trans @ Sends @ Start @ $false @ Cfg6 )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ Trans @ Sends @ Start @ $true @ Cfg6 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.InitialNonUniformCfg
% 0.29/0.47 thf(fact_316_execution_OExistImpliesMinEnabled,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Exec: list_c1059388851t_unit,Trace: list_message_p_v,P: p,Msg: message_p_v] :
% 0.29/0.47 ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec @ Trace )
% 0.29/0.47 => ( ( isReceiverOf_p_v @ P @ Msg )
% 0.29/0.47 => ( ( enabled_p_v_s @ ( last_c571238084t_unit @ Exec ) @ Msg )
% 0.29/0.47 => ? [X_1: message_p_v] : ( minimalEnabled_p_v_s @ Exec @ Trace @ X_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % execution.ExistImpliesMinEnabled
% 0.29/0.47 thf(fact_317_flpSystem_Ovalidity_Ocong,axiom,
% 0.29/0.47 validity_p_s_v = validity_p_s_v ).
% 0.29/0.47
% 0.29/0.47 % flpSystem.validity.cong
% 0.29/0.47 thf(fact_318_execution_OFirstOccurrenceExists,axiom,
% 0.29/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Exec: list_c1059388851t_unit,Trace: list_message_p_v,Msg: message_p_v] :
% 0.29/0.47 ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec @ Trace )
% 0.29/0.47 => ( ( enabled_p_v_s @ ( last_c571238084t_unit @ Exec ) @ Msg )
% 0.29/0.47 => ( ? [P5: p] : ( isReceiverOf_p_v @ P5 @ Msg )
% 0.29/0.47 => ? [X_1: nat] : ( firstO1414030372_p_v_s @ Exec @ Trace @ Msg @ X_1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % execution.FirstOccurrenceExists
% 0.29/0.47 thf(fact_319_NonUniformImpliesNotDecided,axiom,
% 0.29/0.47 ! [C: config256849571t_unit,V2: $o] :
% 0.29/0.47 ( ! [Cfg6: config256849571t_unit] :
% 0.29/0.47 ( ( reachable_p_s_v @ trans @ sends @ C @ Cfg6 )
% 0.29/0.47 => ( agreement_p_v_s @ Cfg6 ) )
% 0.29/0.47 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 0.29/0.47 => ( ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ C )
% 0.29/0.47 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ C ) )
% 0.29/0.47 => ~ ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 0.29/0.47 & ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V2 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % NonUniformImpliesNotDecided
% 0.29/0.47 thf(fact_320_agreement__def,axiom,
% 0.29/0.47 ( agreement_p_v_s
% 0.29/0.47 = ( ^ [C8: config256849571t_unit] :
% 0.29/0.47 ! [V1: $o] :
% 0.29/0.47 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C8 @ ( outMsg_p_v @ V1 ) ) )
% 0.29/0.48 => ! [V22: $o] :
% 0.29/0.48 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C8 @ ( outMsg_p_v @ V22 ) ) )
% 0.29/0.48 = ( V22 = V1 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % agreement_def
% 0.29/0.48 thf(fact_321_ExistsMsg,axiom,
% 0.29/0.48 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit] :
% 0.29/0.48 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.48 => ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ExistsMsg
% 0.29/0.48 thf(fact_322_agreementInit__def,axiom,
% 0.29/0.48 ! [I: config256849571t_unit,C: config256849571t_unit] :
% 0.29/0.48 ( ( agreementInit_p_s_v @ trans @ sends @ start @ I @ C )
% 0.29/0.48 = ( ( ( initial_p_s_v @ start @ I )
% 0.29/0.48 & ( reachable_p_s_v @ trans @ sends @ I @ C ) )
% 0.29/0.48 => ! [V1: $o] :
% 0.29/0.48 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V1 ) ) )
% 0.29/0.48 => ! [V22: $o] :
% 0.29/0.48 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V22 ) ) )
% 0.29/0.48 = ( V22 = V1 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % agreementInit_def
% 0.29/0.48 thf(fact_323_DecidedImpliesUniform,axiom,
% 0.29/0.48 ! [C: config256849571t_unit,V2: $o] :
% 0.29/0.48 ( ! [Cfg6: config256849571t_unit] :
% 0.29/0.48 ( ( reachable_p_s_v @ trans @ sends @ C @ Cfg6 )
% 0.29/0.48 => ( agreement_p_v_s @ Cfg6 ) )
% 0.29/0.48 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 0.29/0.48 => ( ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 0.29/0.48 & ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V2 ) ) ) )
% 0.29/0.48 => ( vUniform_p_s_v @ trans @ sends @ start @ V2 @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % DecidedImpliesUniform
% 0.29/0.48 thf(fact_324_flpSystem_Oagreement__def,axiom,
% 0.29/0.48 ! [Sends: p > s > messageValue_v > message_p_v > nat,C: config256849571t_unit] :
% 0.29/0.48 ( ( flpSystem_p_s_v @ Sends )
% 0.29/0.48 => ( ( agreement_p_v_s @ C )
% 0.29/0.48 = ( ! [V1: $o] :
% 0.29/0.48 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V1 ) ) )
% 0.29/0.48 => ! [V22: $o] :
% 0.29/0.48 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V22 ) ) )
% 0.29/0.48 = ( V22 = V1 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % flpSystem.agreement_def
% 0.29/0.48 thf(fact_325_enabled__def,axiom,
% 0.29/0.48 ( enabled_p_v_s
% 0.29/0.48 = ( ^ [Cfg5: config256849571t_unit,Msg2: message_p_v] : ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ Cfg5 @ Msg2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % enabled_def
% 0.29/0.48 thf(fact_326_asynchronousSystem_OExistsMsg,axiom,
% 0.29/0.48 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit] :
% 0.29/0.48 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 0.29/0.48 => ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % asynchronousSystem.ExistsMsg
% 0.29/0.48 thf(fact_327_order_Onot__eq__order__implies__strict,axiom,
% 0.29/0.48 ! [A5: set_o,B3: set_o] :
% 0.29/0.48 ( ( A5 != B3 )
% 0.29/0.48 => ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.48 => ( ord_less_set_o @ A5 @ B3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.not_eq_order_implies_strict
% 0.29/0.48 thf(fact_328_order_Onot__eq__order__implies__strict,axiom,
% 0.29/0.48 ! [A5: nat,B3: nat] :
% 0.29/0.48 ( ( A5 != B3 )
% 0.29/0.48 => ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.48 => ( ord_less_nat @ A5 @ B3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.not_eq_order_implies_strict
% 0.29/0.48 thf(fact_329_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.48 ! [B3: set_o,A5: set_o] :
% 0.29/0.48 ( ( ord_less_set_o @ B3 @ A5 )
% 0.29/0.48 => ( ord_less_eq_set_o @ B3 @ A5 ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.strict_implies_order
% 0.29/0.48 thf(fact_330_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.48 ! [B3: nat,A5: nat] :
% 0.29/0.48 ( ( ord_less_nat @ B3 @ A5 )
% 0.29/0.48 => ( ord_less_eq_nat @ B3 @ A5 ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.strict_implies_order
% 0.29/0.48 thf(fact_331_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.48 ( ord_less_set_o
% 0.29/0.48 = ( ^ [B4: set_o,A6: set_o] :
% 0.29/0.48 ( ( ord_less_eq_set_o @ B4 @ A6 )
% 0.29/0.48 & ( A6 != B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.strict_iff_order
% 0.29/0.48 thf(fact_332_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.48 ( ord_less_nat
% 0.29/0.48 = ( ^ [B4: nat,A6: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ B4 @ A6 )
% 0.29/0.48 & ( A6 != B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.strict_iff_order
% 0.29/0.48 thf(fact_333_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.48 ( ord_less_eq_set_o
% 0.29/0.48 = ( ^ [B4: set_o,A6: set_o] :
% 0.29/0.48 ( ( ord_less_set_o @ B4 @ A6 )
% 0.29/0.48 | ( A6 = B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.order_iff_strict
% 0.29/0.48 thf(fact_334_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.48 ( ord_less_eq_nat
% 0.29/0.48 = ( ^ [B4: nat,A6: nat] :
% 0.29/0.48 ( ( ord_less_nat @ B4 @ A6 )
% 0.29/0.48 | ( A6 = B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.order_iff_strict
% 0.29/0.48 thf(fact_335_order_Ostrict__implies__order,axiom,
% 0.29/0.48 ! [A5: set_o,B3: set_o] :
% 0.29/0.48 ( ( ord_less_set_o @ A5 @ B3 )
% 0.29/0.48 => ( ord_less_eq_set_o @ A5 @ B3 ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_implies_order
% 0.29/0.48 thf(fact_336_order_Ostrict__implies__order,axiom,
% 0.29/0.48 ! [A5: nat,B3: nat] :
% 0.29/0.48 ( ( ord_less_nat @ A5 @ B3 )
% 0.29/0.48 => ( ord_less_eq_nat @ A5 @ B3 ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_implies_order
% 0.29/0.48 thf(fact_337_dual__order_Ostrict__trans2,axiom,
% 0.29/0.48 ! [B3: set_o,A5: set_o,C: set_o] :
% 0.29/0.48 ( ( ord_less_set_o @ B3 @ A5 )
% 0.29/0.48 => ( ( ord_less_eq_set_o @ C @ B3 )
% 0.29/0.48 => ( ord_less_set_o @ C @ A5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.strict_trans2
% 0.29/0.48 thf(fact_338_dual__order_Ostrict__trans2,axiom,
% 0.29/0.48 ! [B3: nat,A5: nat,C: nat] :
% 0.29/0.48 ( ( ord_less_nat @ B3 @ A5 )
% 0.29/0.48 => ( ( ord_less_eq_nat @ C @ B3 )
% 0.29/0.48 => ( ord_less_nat @ C @ A5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.strict_trans2
% 0.29/0.48 thf(fact_339_dual__order_Ostrict__trans1,axiom,
% 0.29/0.48 ! [B3: set_o,A5: set_o,C: set_o] :
% 0.29/0.48 ( ( ord_less_eq_set_o @ B3 @ A5 )
% 0.29/0.48 => ( ( ord_less_set_o @ C @ B3 )
% 0.29/0.48 => ( ord_less_set_o @ C @ A5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.strict_trans1
% 0.29/0.48 thf(fact_340_dual__order_Ostrict__trans1,axiom,
% 0.29/0.48 ! [B3: nat,A5: nat,C: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ B3 @ A5 )
% 0.29/0.48 => ( ( ord_less_nat @ C @ B3 )
% 0.29/0.48 => ( ord_less_nat @ C @ A5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.strict_trans1
% 0.29/0.48 thf(fact_341_order_Ostrict__iff__order,axiom,
% 0.29/0.48 ( ord_less_set_o
% 0.29/0.48 = ( ^ [A6: set_o,B4: set_o] :
% 0.29/0.48 ( ( ord_less_eq_set_o @ A6 @ B4 )
% 0.29/0.48 & ( A6 != B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_iff_order
% 0.29/0.48 thf(fact_342_order_Ostrict__iff__order,axiom,
% 0.29/0.48 ( ord_less_nat
% 0.29/0.48 = ( ^ [A6: nat,B4: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ A6 @ B4 )
% 0.29/0.48 & ( A6 != B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_iff_order
% 0.29/0.48 thf(fact_343_order_Oorder__iff__strict,axiom,
% 0.29/0.48 ( ord_less_eq_set_o
% 0.29/0.48 = ( ^ [A6: set_o,B4: set_o] :
% 0.29/0.48 ( ( ord_less_set_o @ A6 @ B4 )
% 0.29/0.48 | ( A6 = B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.order_iff_strict
% 0.29/0.48 thf(fact_344_order_Oorder__iff__strict,axiom,
% 0.29/0.48 ( ord_less_eq_nat
% 0.29/0.48 = ( ^ [A6: nat,B4: nat] :
% 0.29/0.48 ( ( ord_less_nat @ A6 @ B4 )
% 0.29/0.48 | ( A6 = B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.order_iff_strict
% 0.29/0.48 thf(fact_345_order_Ostrict__trans2,axiom,
% 0.29/0.48 ! [A5: set_o,B3: set_o,C: set_o] :
% 0.29/0.48 ( ( ord_less_set_o @ A5 @ B3 )
% 0.29/0.48 => ( ( ord_less_eq_set_o @ B3 @ C )
% 0.29/0.48 => ( ord_less_set_o @ A5 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_trans2
% 0.29/0.48 thf(fact_346_order_Ostrict__trans2,axiom,
% 0.29/0.48 ! [A5: nat,B3: nat,C: nat] :
% 0.29/0.48 ( ( ord_less_nat @ A5 @ B3 )
% 0.29/0.48 => ( ( ord_less_eq_nat @ B3 @ C )
% 0.29/0.48 => ( ord_less_nat @ A5 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_trans2
% 0.29/0.48 thf(fact_347_order_Ostrict__trans1,axiom,
% 0.29/0.48 ! [A5: set_o,B3: set_o,C: set_o] :
% 0.29/0.48 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 0.29/0.48 => ( ( ord_less_set_o @ B3 @ C )
% 0.29/0.48 => ( ord_less_set_o @ A5 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_trans1
% 0.29/0.48 thf(fact_348_order_Ostrict__trans1,axiom,
% 0.29/0.48 ! [A5: nat,B3: nat,C: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ A5 @ B3 )
% 0.29/0.48 => ( ( ord_less_nat @ B3 @ C )
% 0.29/0.48 => ( ord_less_nat @ A5 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_trans1
% 0.29/0.48 thf(fact_349_not__le__imp__less,axiom,
% 0.29/0.48 ! [Y2: nat,X2: nat] :
% 0.29/0.48 ( ~ ( ord_less_eq_nat @ Y2 @ X2 )
% 0.29/0.48 => ( ord_less_nat @ X2 @ Y2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % not_le_imp_less
% 0.29/0.48 thf(fact_350_less__le__not__le,axiom,
% 0.29/0.48 ( ord_less_set_o
% 0.29/0.48 = ( ^ [X3: set_o,Y3: set_o] :
% 0.29/0.48 ( ( ord_less_eq_set_o @ X3 @ Y3 )
% 0.29/0.48 & ~ ( ord_less_eq_set_o @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_le_not_le
% 0.29/0.48 thf(fact_351_less__le__not__le,axiom,
% 0.29/0.48 ( ord_less_nat
% 0.29/0.48 = ( ^ [X3: nat,Y3: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.48 & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_le_not_le
% 0.29/0.48 thf(fact_352_le__imp__less__or__eq,axiom,
% 0.29/0.48 ! [X2: set_o,Y2: set_o] :
% 0.29/0.48 ( ( ord_less_eq_set_o @ X2 @ Y2 )
% 0.29/0.48 => ( ( ord_less_set_o @ X2 @ Y2 )
% 0.29/0.48 | ( X2 = Y2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % le_imp_less_or_eq
% 0.29/0.48 thf(fact_353_le__imp__less__or__eq,axiom,
% 0.29/0.48 ! [X2: nat,Y2: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.48 => ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.48 | ( X2 = Y2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % le_imp_less_or_eq
% 0.29/0.48 thf(fact_354_le__less__linear,axiom,
% 0.29/0.48 ! [X2: nat,Y2: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.48 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % le_less_linear
% 0.29/0.48
% 0.29/0.48 % Conjectures (1)
% 0.29/0.48 thf(conj_0,conjecture,
% 0.29/0.48 ( ord_less_eq_set_o
% 0.29/0.48 @ ( collect_o
% 0.29/0.48 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
% 0.29/0.48 @ ( collect_o
% 0.29/0.48 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ cMsg ) ) ) ).
% 0.29/0.48
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 ------------------------
% 2.87/1.52 ---- Embedded in THF ---
% 2.87/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.87/1.52 %%% Generated on Thu Feb 26 01:02:33 EST 2026
% 2.87/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.87/1.52 %%% Logic specification used:
% 2.87/1.52 %%% thf(spec, logic, $$dhol).
% 2.87/1.52
% 2.87/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2DTF12819.p
% See solution above
% 2.87/1.52 ------------------------
% 2.87/1.55 ---- Cleaned THF ---
% 2.87/1.55 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 2.87/1.55 list_c1059388851t_unit: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.87/1.55 config256849571t_unit: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 2.87/1.55 list_message_p_v: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.87/1.55 message_p_v: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__AsynchronousSystem__OmessageValue_Itf__v_J,type,
% 2.87/1.55 messageValue_v: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__Set__Oset_Itf__p_J,type,
% 2.87/1.55 set_p: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 2.87/1.55 set_o: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_t__Nat__Onat,type,
% 2.87/1.55 nat: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_tf__s,type,
% 2.87/1.55 s: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(ty_n_tf__p,type,
% 2.87/1.55 p: $tType ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OinitReachable_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 initReachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oinitial_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 initial_p_s_v: ( p > s ) > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OqReachable_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 qReachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > set_p > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Oreachable_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 reachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_OasynchronousSystem_OstepReachable_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 stepReachable_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > message_p_v > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_OasynchronousSystem_Osteps_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 steps_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > config256849571t_unit > message_p_v > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs_001tf__p_001tf__v_001tf__s_001t__Product____Type__Ounit,type,
% 2.87/1.55 msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_Oconfiguration_Ostates_001tf__p_001tf__v_001tf__s_001t__Product____Type__Ounit,type,
% 2.87/1.55 states1228886952t_unit: config256849571t_unit > p > s ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
% 2.87/1.55 enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_OisReceiverOf_001tf__p_001tf__v,type,
% 2.87/1.55 isReceiverOf_p_v: p > message_p_v > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_AsynchronousSystem_Omessage_OOutMsg_001tf__p_001tf__v,type,
% 2.87/1.55 outMsg_p_v: $o > message_p_v ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Execution_Oexecution_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 execution_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > list_c1059388851t_unit > list_message_p_v > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
% 2.87/1.55 firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Execution_Oexecution_OminimalEnabled_001tf__p_001tf__v_001tf__s,type,
% 2.87/1.55 minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_FLPSystem_OflpSystem_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 flpSystem_p_s_v: ( p > s > messageValue_v > message_p_v > nat ) > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_FLPSystem_OflpSystem_OagreementInit_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 agreementInit_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > config256849571t_unit > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_FLPSystem_OflpSystem_Oagreement_001tf__p_001tf__v_001tf__s,type,
% 2.87/1.55 agreement_p_v_s: config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_FLPSystem_OflpSystem_OpSilDecVal_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 pSilDecVal_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o > p > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_FLPSystem_OflpSystem_OterminationPseudo_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 termin1618267753_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > nat > config256849571t_unit > set_p > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_FLPSystem_OflpSystem_OvUniform_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 vUniform_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_FLPSystem_OflpSystem_Ovalidity_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 validity_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > config256849571t_unit > config256849571t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_001tf__p_001tf__s_001tf__v,type,
% 2.87/1.55 fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 2.87/1.55 one_one_nat: nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 2.87/1.55 zero_zero_nat: nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.87/1.55 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.87/1.55 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_List_Olast_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.87/1.55 last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_List_Olast_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.87/1.55 last_message_p_v: list_message_p_v > message_p_v ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_Eo_M_Eo_J,type,
% 2.87/1.55 bot_bot_o_o: $o > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 2.87/1.55 bot_bot_nat: nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_Eo_J,type,
% 2.87/1.55 bot_bot_set_o: set_o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__p_J,type,
% 2.87/1.55 bot_bot_set_p: set_p ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 2.87/1.55 ord_less_nat: nat > nat > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_I_Eo_J,type,
% 2.87/1.55 ord_less_set_o: set_o > set_o > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_Eo_J,type,
% 2.87/1.55 ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__p_M_Eo_J,type,
% 2.87/1.55 ord_less_eq_p_o: ( p > $o ) > ( p > $o ) > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.87/1.55 ord_less_eq_nat: nat > nat > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
% 2.87/1.55 ord_less_eq_set_o: set_o > set_o > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__p_J,type,
% 2.87/1.55 ord_less_eq_set_p: set_p > set_p > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Set_OCollect_001_Eo,type,
% 2.87/1.55 collect_o: ( $o > $o ) > set_o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Set_OCollect_001tf__p,type,
% 2.87/1.55 collect_p: ( p > $o ) > set_p ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Set_Oinsert_001_Eo,type,
% 2.87/1.55 insert_o: $o > set_o > set_o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_Set_Oinsert_001tf__p,type,
% 2.87/1.55 insert_p: p > set_p > set_p ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_member_001_Eo,type,
% 2.87/1.55 member_o: $o > set_o > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_c_member_001tf__p,type,
% 2.87/1.55 member_p: p > set_p > $o ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_cMsg____,type,
% 2.87/1.55 cMsg: config256849571t_unit ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_c_H____,type,
% 2.87/1.55 c: config256849571t_unit ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_exec,type,
% 2.87/1.55 exec: list_c1059388851t_unit ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_execMsga____,type,
% 2.87/1.55 execMsga: list_c1059388851t_unit ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_exec_H____,type,
% 2.87/1.55 exec2: list_c1059388851t_unit ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_msg,type,
% 2.87/1.55 msg: message_p_v ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_p,type,
% 2.87/1.55 p2: p ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_sends,type,
% 2.87/1.55 sends: p > s > messageValue_v > message_p_v > nat ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_start,type,
% 2.87/1.55 start: p > s ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_trace,type,
% 2.87/1.55 trace: list_message_p_v ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_traceMsga____,type,
% 2.87/1.55 traceMsga: list_message_p_v ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_trace_H____,type,
% 2.87/1.55 trace2: list_message_p_v ).
% 2.87/1.55
% 2.87/1.55 thf(sy_v_trans,type,
% 2.87/1.55 trans: p > s > messageValue_v > s ).
% 2.87/1.55
% 2.87/1.55 thf(fact_0_PisReceiverOf,axiom,
% 2.87/1.55 isReceiverOf_p_v @ p2 @ msg ).
% 2.87/1.55
% 2.87/1.55 thf(fact_1_InitReachLastExec_H,axiom,
% 2.87/1.55 initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_2_NewExec_I3_J,axiom,
% 2.87/1.55 ( ( last_c571238084t_unit @ exec2 )
% 2.87/1.55 = c ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_3_CMsg,axiom,
% 2.87/1.55 steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg ).
% 2.87/1.55
% 2.87/1.55 thf(fact_4_flpPseudoConsensus__axioms,axiom,
% 2.87/1.55 fLPThe9398366_p_s_v @ trans @ sends @ start ).
% 2.87/1.55
% 2.87/1.55 thf(fact_5_ExecMsg_I3_J,axiom,
% 2.87/1.55 ( ( last_c571238084t_unit @ execMsga )
% 2.87/1.55 = cMsg ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_6__092_060open_062_092_060lbrakk_062p_A_061_Ap_059_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_059_AisReceiverOf_Ap_Amsg_059_AinitReachable_A_Ilast_Aexec_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Aval_091p_Mlast_Aexec_H_093_A_092_060subseteq_062_Aval_091p_McMsg_093_092_060close_062,axiom,
% 2.87/1.55 ( ( p2 = p2 )
% 2.87/1.55 => ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ cMsg )
% 2.87/1.55 => ( ( isReceiverOf_p_v @ p2 @ msg )
% 2.87/1.55 => ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
% 2.87/1.55 => ( ord_less_eq_set_o
% 2.87/1.55 @ ( collect_o
% 2.87/1.55 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
% 2.87/1.55 @ ( collect_o
% 2.87/1.55 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ cMsg ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_7_DiamondOne,axiom,
% 2.87/1.55 ! [Cfg: config256849571t_unit,M: message_p_v,Cfg1: config256849571t_unit,P: p,Q: p,M2: message_p_v,Cfg2: config256849571t_unit] :
% 2.87/1.55 ( ( steps_p_s_v @ trans @ sends @ Cfg @ M @ Cfg1 )
% 2.87/1.55 => ( ( P != Q )
% 2.87/1.55 => ( ( isReceiverOf_p_v @ P @ M )
% 2.87/1.55 => ( ~ ( isReceiverOf_p_v @ P @ M2 )
% 2.87/1.55 => ( ( isReceiverOf_p_v @ Q @ M2 )
% 2.87/1.55 => ( ~ ( isReceiverOf_p_v @ Q @ M )
% 2.87/1.55 => ( ( steps_p_s_v @ trans @ sends @ Cfg @ M2 @ Cfg2 )
% 2.87/1.55 => ? [Cfg3: config256849571t_unit] :
% 2.87/1.55 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M2 @ Cfg3 )
% 2.87/1.55 & ( steps_p_s_v @ trans @ sends @ Cfg2 @ M @ Cfg3 ) ) ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_8_True,axiom,
% 2.87/1.55 enabled_p_v_s @ ( last_c571238084t_unit @ exec2 ) @ msg ).
% 2.87/1.55
% 2.87/1.55 thf(fact_9__092_060open_062_092_060exists_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_092_060close_062,axiom,
% 2.87/1.55 ? [X_1: config256849571t_unit] : ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ X_1 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_10__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062cMsg_O_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.87/1.55 ~ ! [CMsg: config256849571t_unit] :
% 2.87/1.55 ~ ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec2 ) @ msg @ CMsg ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_11_Agreement,axiom,
% 2.87/1.55 ! [I: config256849571t_unit,C: config256849571t_unit] : ( agreementInit_p_s_v @ trans @ sends @ start @ I @ C ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_12_ActiveProcessSilentDecisionValuesIncrease,axiom,
% 2.87/1.55 ! [P: p,Q: p,C: config256849571t_unit,Msg: message_p_v,C2: config256849571t_unit] :
% 2.87/1.55 ( ( P = Q )
% 2.87/1.55 => ( ( steps_p_s_v @ trans @ sends @ C @ Msg @ C2 )
% 2.87/1.55 => ( ( isReceiverOf_p_v @ P @ Msg )
% 2.87/1.55 => ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 2.87/1.55 => ( ord_less_eq_set_o
% 2.87/1.55 @ ( collect_o
% 2.87/1.55 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C ) )
% 2.87/1.55 @ ( collect_o
% 2.87/1.55 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C2 ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_13_InactiveProcessSilentDecisionValuesDecrease,axiom,
% 2.87/1.55 ! [P: p,Q: p,C: config256849571t_unit,Msg: message_p_v,C2: config256849571t_unit] :
% 2.87/1.55 ( ( P != Q )
% 2.87/1.55 => ( ( steps_p_s_v @ trans @ sends @ C @ Msg @ C2 )
% 2.87/1.55 => ( ( isReceiverOf_p_v @ P @ Msg )
% 2.87/1.55 => ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 2.87/1.55 => ( ord_less_eq_set_o
% 2.87/1.55 @ ( collect_o
% 2.87/1.55 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C2 ) )
% 2.87/1.55 @ ( collect_o
% 2.87/1.55 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C ) ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_14_nonUniformC_H,axiom,
% 2.87/1.55 ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec2 ) )
% 2.87/1.55 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ ( last_c571238084t_unit @ exec2 ) )
% 2.87/1.55 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ ( last_c571238084t_unit @ exec2 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_15_InitReachLastExecMsg,axiom,
% 2.87/1.55 initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ execMsga ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_16_NewExec_I1_J,axiom,
% 2.87/1.55 execution_p_s_v @ trans @ sends @ start @ exec2 @ trace2 ).
% 2.87/1.55
% 2.87/1.55 thf(fact_17_InitialIsInitReachable,axiom,
% 2.87/1.55 ! [C: config256849571t_unit] :
% 2.87/1.55 ( ( initial_p_s_v @ start @ C )
% 2.87/1.55 => ( initReachable_p_s_v @ trans @ sends @ start @ C ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_18_flpSystem__axioms,axiom,
% 2.87/1.55 flpSystem_p_s_v @ sends ).
% 2.87/1.55
% 2.87/1.55 thf(fact_19_subsetI,axiom,
% 2.87/1.55 ! [A: set_p,B: set_p] :
% 2.87/1.55 ( ! [X: p] :
% 2.87/1.55 ( ( member_p @ X @ A )
% 2.87/1.55 => ( member_p @ X @ B ) )
% 2.87/1.55 => ( ord_less_eq_set_p @ A @ B ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_20_subsetI,axiom,
% 2.87/1.55 ! [A: set_o,B: set_o] :
% 2.87/1.55 ( ! [X: $o] :
% 2.87/1.55 ( ( member_o @ X @ A )
% 2.87/1.55 => ( member_o @ X @ B ) )
% 2.87/1.55 => ( ord_less_eq_set_o @ A @ B ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_21_subset__antisym,axiom,
% 2.87/1.55 ! [A: set_p,B: set_p] :
% 2.87/1.55 ( ( ord_less_eq_set_p @ A @ B )
% 2.87/1.55 => ( ( ord_less_eq_set_p @ B @ A )
% 2.87/1.55 => ( A = B ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_22_subset__antisym,axiom,
% 2.87/1.55 ! [A: set_o,B: set_o] :
% 2.87/1.55 ( ( ord_less_eq_set_o @ A @ B )
% 2.87/1.55 => ( ( ord_less_eq_set_o @ B @ A )
% 2.87/1.55 => ( A = B ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_23_QReachableTrans,axiom,
% 2.87/1.55 ! [Cfg2: config256849571t_unit,Q2: set_p,Cfg32: config256849571t_unit,Cfg1: config256849571t_unit] :
% 2.87/1.55 ( ( qReachable_p_s_v @ trans @ sends @ Cfg2 @ Q2 @ Cfg32 )
% 2.87/1.55 => ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.55 => ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_24_InitQ,axiom,
% 2.87/1.55 ! [Cfg1: config256849571t_unit,Q2: set_p] : ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg1 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_25_order__refl,axiom,
% 2.87/1.55 ! [X2: set_p] : ( ord_less_eq_set_p @ X2 @ X2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_26_order__refl,axiom,
% 2.87/1.55 ! [X2: $o > $o] : ( ord_less_eq_o_o @ X2 @ X2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_27_order__refl,axiom,
% 2.87/1.55 ! [X2: p > $o] : ( ord_less_eq_p_o @ X2 @ X2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_28_order__refl,axiom,
% 2.87/1.55 ! [X2: set_o] : ( ord_less_eq_set_o @ X2 @ X2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_29_order__refl,axiom,
% 2.87/1.55 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_30_OnlyOccurenceDisables,axiom,
% 2.87/1.55 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,M2: message_p_v] :
% 2.87/1.55 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.55 => ( ( enabled_p_v_s @ Cfg1 @ M2 )
% 2.87/1.55 => ( ~ ( enabled_p_v_s @ Cfg2 @ M2 )
% 2.87/1.55 => ( M = M2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_31_qReachable_Osimps,axiom,
% 2.87/1.55 ! [A1: config256849571t_unit,A2: set_p,A3: config256849571t_unit] :
% 2.87/1.55 ( ( qReachable_p_s_v @ trans @ sends @ A1 @ A2 @ A3 )
% 2.87/1.55 = ( ( A3 = A1 )
% 2.87/1.55 | ? [Cfg22: config256849571t_unit] :
% 2.87/1.55 ( ( qReachable_p_s_v @ trans @ sends @ A1 @ A2 @ Cfg22 )
% 2.87/1.55 & ? [Msg2: message_p_v] :
% 2.87/1.55 ( ( steps_p_s_v @ trans @ sends @ Cfg22 @ Msg2 @ A3 )
% 2.87/1.55 & ? [X3: p] :
% 2.87/1.55 ( ( member_p @ X3 @ A2 )
% 2.87/1.55 & ( isReceiverOf_p_v @ X3 @ Msg2 ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_32_qReachable_Oinducts,axiom,
% 2.87/1.55 ! [X1: config256849571t_unit,X22: set_p,X32: config256849571t_unit,P2: config256849571t_unit > set_p > config256849571t_unit > $o] :
% 2.87/1.55 ( ( qReachable_p_s_v @ trans @ sends @ X1 @ X22 @ X32 )
% 2.87/1.55 => ( ! [Cfg12: config256849571t_unit,Q3: set_p] : ( P2 @ Cfg12 @ Q3 @ Cfg12 )
% 2.87/1.55 => ( ! [Cfg12: config256849571t_unit,Q3: set_p,Cfg23: config256849571t_unit] :
% 2.87/1.55 ( ( qReachable_p_s_v @ trans @ sends @ Cfg12 @ Q3 @ Cfg23 )
% 2.87/1.55 => ( ( P2 @ Cfg12 @ Q3 @ Cfg23 )
% 2.87/1.55 => ! [Msg3: message_p_v,Cfg33: config256849571t_unit] :
% 2.87/1.55 ( ( steps_p_s_v @ trans @ sends @ Cfg23 @ Msg3 @ Cfg33 )
% 2.87/1.55 => ( ? [X: p] :
% 2.87/1.55 ( ( member_p @ X @ Q3 )
% 2.87/1.55 & ( isReceiverOf_p_v @ X @ Msg3 ) )
% 2.87/1.55 => ( P2 @ Cfg12 @ Q3 @ Cfg33 ) ) ) ) )
% 2.87/1.55 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_33_qReachable_Ocases,axiom,
% 2.87/1.55 ! [A1: config256849571t_unit,A2: set_p,A3: config256849571t_unit] :
% 2.87/1.55 ( ( qReachable_p_s_v @ trans @ sends @ A1 @ A2 @ A3 )
% 2.87/1.55 => ( ( A3 != A1 )
% 2.87/1.55 => ~ ! [Cfg23: config256849571t_unit] :
% 2.87/1.55 ( ( qReachable_p_s_v @ trans @ sends @ A1 @ A2 @ Cfg23 )
% 2.87/1.55 => ! [Msg3: message_p_v] :
% 2.87/1.55 ( ( steps_p_s_v @ trans @ sends @ Cfg23 @ Msg3 @ A3 )
% 2.87/1.55 => ~ ? [X: p] :
% 2.87/1.55 ( ( member_p @ X @ A2 )
% 2.87/1.55 & ( isReceiverOf_p_v @ X @ Msg3 ) ) ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_34_StepQ,axiom,
% 2.87/1.55 ! [Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,Msg: message_p_v,Cfg32: config256849571t_unit] :
% 2.87/1.55 ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.55 => ( ( steps_p_s_v @ trans @ sends @ Cfg2 @ Msg @ Cfg32 )
% 2.87/1.55 => ( ? [X4: p] :
% 2.87/1.55 ( ( member_p @ X4 @ Q2 )
% 2.87/1.55 & ( isReceiverOf_p_v @ X4 @ Msg ) )
% 2.87/1.55 => ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_35_ExecMsg_I1_J,axiom,
% 2.87/1.55 prefix1615116500t_unit @ exec2 @ execMsga ).
% 2.87/1.55
% 2.87/1.55 thf(fact_36_isExecution,axiom,
% 2.87/1.55 execution_p_s_v @ trans @ sends @ start @ execMsga @ traceMsga ).
% 2.87/1.55
% 2.87/1.55 thf(fact_37_MsgEnabled,axiom,
% 2.87/1.55 enabled_p_v_s @ ( last_c571238084t_unit @ exec ) @ msg ).
% 2.87/1.55
% 2.87/1.55 thf(fact_38_NonUniformLexec,axiom,
% 2.87/1.55 ( ( initReachable_p_s_v @ trans @ sends @ start @ ( last_c571238084t_unit @ exec ) )
% 2.87/1.55 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ ( last_c571238084t_unit @ exec ) )
% 2.87/1.55 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ ( last_c571238084t_unit @ exec ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_39_flpPseudoConsensus_Oaxioms_I1_J,axiom,
% 2.87/1.55 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s] :
% 2.87/1.55 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 2.87/1.55 => ( flpSystem_p_s_v @ Sends ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_40_flpPseudoConsensus_OAgreement,axiom,
% 2.87/1.55 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,I: config256849571t_unit,C: config256849571t_unit] :
% 2.87/1.55 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 2.87/1.55 => ( agreementInit_p_s_v @ Trans @ Sends @ Start @ I @ C ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_41_less__eq__set__def,axiom,
% 2.87/1.55 ( ord_less_eq_set_p
% 2.87/1.55 = ( ^ [A4: set_p,B2: set_p] :
% 2.87/1.55 ( ord_less_eq_p_o
% 2.87/1.55 @ ^ [X3: p] : ( member_p @ X3 @ A4 )
% 2.87/1.55 @ ^ [X3: p] : ( member_p @ X3 @ B2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_42_less__eq__set__def,axiom,
% 2.87/1.55 ( ord_less_eq_set_o
% 2.87/1.55 = ( ^ [A4: set_o,B2: set_o] :
% 2.87/1.55 ( ord_less_eq_o_o
% 2.87/1.55 @ ^ [X3: $o] : ( member_o @ X3 @ A4 )
% 2.87/1.55 @ ^ [X3: $o] : ( member_o @ X3 @ B2 ) ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_43_dual__order_Oantisym,axiom,
% 2.87/1.55 ! [B3: set_p,A5: set_p] :
% 2.87/1.55 ( ( ord_less_eq_set_p @ B3 @ A5 )
% 2.87/1.55 => ( ( ord_less_eq_set_p @ A5 @ B3 )
% 2.87/1.55 => ( A5 = B3 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_44_dual__order_Oantisym,axiom,
% 2.87/1.55 ! [B3: $o > $o,A5: $o > $o] :
% 2.87/1.55 ( ( ord_less_eq_o_o @ B3 @ A5 )
% 2.87/1.55 => ( ( ord_less_eq_o_o @ A5 @ B3 )
% 2.87/1.55 => ( A5 = B3 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_45_dual__order_Oantisym,axiom,
% 2.87/1.55 ! [B3: p > $o,A5: p > $o] :
% 2.87/1.55 ( ( ord_less_eq_p_o @ B3 @ A5 )
% 2.87/1.55 => ( ( ord_less_eq_p_o @ A5 @ B3 )
% 2.87/1.55 => ( A5 = B3 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_46_dual__order_Oantisym,axiom,
% 2.87/1.55 ! [B3: set_o,A5: set_o] :
% 2.87/1.55 ( ( ord_less_eq_set_o @ B3 @ A5 )
% 2.87/1.55 => ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.55 => ( A5 = B3 ) ) ) ).
% 2.87/1.55
% 2.87/1.55 thf(fact_47_dual__order_Oantisym,axiom,
% 2.87/1.56 ! [B3: nat,A5: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( A5 = B3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_48_dual__order_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: set_p,Z: set_p] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: set_p,B4: set_p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ B4 @ A6 )
% 2.87/1.56 & ( ord_less_eq_set_p @ A6 @ B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_49_dual__order_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: $o > $o,Z: $o > $o] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: $o > $o,B4: $o > $o] :
% 2.87/1.56 ( ( ord_less_eq_o_o @ B4 @ A6 )
% 2.87/1.56 & ( ord_less_eq_o_o @ A6 @ B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_50_dual__order_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: p > $o,Z: p > $o] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: p > $o,B4: p > $o] :
% 2.87/1.56 ( ( ord_less_eq_p_o @ B4 @ A6 )
% 2.87/1.56 & ( ord_less_eq_p_o @ A6 @ B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_51_dual__order_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: set_o,Z: set_o] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: set_o,B4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ B4 @ A6 )
% 2.87/1.56 & ( ord_less_eq_set_o @ A6 @ B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_52_dual__order_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: nat,B4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ B4 @ A6 )
% 2.87/1.56 & ( ord_less_eq_nat @ A6 @ B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_53_dual__order_Otrans,axiom,
% 2.87/1.56 ! [B3: set_p,A5: set_p,C: set_p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_eq_set_p @ C @ B3 )
% 2.87/1.56 => ( ord_less_eq_set_p @ C @ A5 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_54_dual__order_Otrans,axiom,
% 2.87/1.56 ! [B3: $o > $o,A5: $o > $o,C: $o > $o] :
% 2.87/1.56 ( ( ord_less_eq_o_o @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_eq_o_o @ C @ B3 )
% 2.87/1.56 => ( ord_less_eq_o_o @ C @ A5 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_55_dual__order_Otrans,axiom,
% 2.87/1.56 ! [B3: p > $o,A5: p > $o,C: p > $o] :
% 2.87/1.56 ( ( ord_less_eq_p_o @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_eq_p_o @ C @ B3 )
% 2.87/1.56 => ( ord_less_eq_p_o @ C @ A5 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_56_dual__order_Otrans,axiom,
% 2.87/1.56 ! [B3: set_o,A5: set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ C @ B3 )
% 2.87/1.56 => ( ord_less_eq_set_o @ C @ A5 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_57_dual__order_Otrans,axiom,
% 2.87/1.56 ! [B3: nat,A5: nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ C @ B3 )
% 2.87/1.56 => ( ord_less_eq_nat @ C @ A5 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_58_linorder__wlog,axiom,
% 2.87/1.56 ! [P2: nat > nat > $o,A5: nat,B3: nat] :
% 2.87/1.56 ( ! [A7: nat,B5: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A7 @ B5 )
% 2.87/1.56 => ( P2 @ A7 @ B5 ) )
% 2.87/1.56 => ( ! [A7: nat,B5: nat] :
% 2.87/1.56 ( ( P2 @ B5 @ A7 )
% 2.87/1.56 => ( P2 @ A7 @ B5 ) )
% 2.87/1.56 => ( P2 @ A5 @ B3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_59_dual__order_Orefl,axiom,
% 2.87/1.56 ! [A5: set_p] : ( ord_less_eq_set_p @ A5 @ A5 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_60_dual__order_Orefl,axiom,
% 2.87/1.56 ! [A5: $o > $o] : ( ord_less_eq_o_o @ A5 @ A5 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_61_dual__order_Orefl,axiom,
% 2.87/1.56 ! [A5: p > $o] : ( ord_less_eq_p_o @ A5 @ A5 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_62_dual__order_Orefl,axiom,
% 2.87/1.56 ! [A5: set_o] : ( ord_less_eq_set_o @ A5 @ A5 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_63_dual__order_Orefl,axiom,
% 2.87/1.56 ! [A5: nat] : ( ord_less_eq_nat @ A5 @ A5 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_64_order__trans,axiom,
% 2.87/1.56 ! [X2: set_p,Y2: set_p,Z2: set_p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ X2 @ Y2 )
% 2.87/1.56 => ( ( ord_less_eq_set_p @ Y2 @ Z2 )
% 2.87/1.56 => ( ord_less_eq_set_p @ X2 @ Z2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_65_order__trans,axiom,
% 2.87/1.56 ! [X2: $o > $o,Y2: $o > $o,Z2: $o > $o] :
% 2.87/1.56 ( ( ord_less_eq_o_o @ X2 @ Y2 )
% 2.87/1.56 => ( ( ord_less_eq_o_o @ Y2 @ Z2 )
% 2.87/1.56 => ( ord_less_eq_o_o @ X2 @ Z2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_66_order__trans,axiom,
% 2.87/1.56 ! [X2: p > $o,Y2: p > $o,Z2: p > $o] :
% 2.87/1.56 ( ( ord_less_eq_p_o @ X2 @ Y2 )
% 2.87/1.56 => ( ( ord_less_eq_p_o @ Y2 @ Z2 )
% 2.87/1.56 => ( ord_less_eq_p_o @ X2 @ Z2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_67_order__trans,axiom,
% 2.87/1.56 ! [X2: set_o,Y2: set_o,Z2: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X2 @ Y2 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ Y2 @ Z2 )
% 2.87/1.56 => ( ord_less_eq_set_o @ X2 @ Z2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_68_order__trans,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.87/1.56 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_69_order__class_Oorder_Oantisym,axiom,
% 2.87/1.56 ! [A5: set_p,B3: set_p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_p @ B3 @ A5 )
% 2.87/1.56 => ( A5 = B3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_70_order__class_Oorder_Oantisym,axiom,
% 2.87/1.56 ! [A5: $o > $o,B3: $o > $o] :
% 2.87/1.56 ( ( ord_less_eq_o_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_o_o @ B3 @ A5 )
% 2.87/1.56 => ( A5 = B3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_71_order__class_Oorder_Oantisym,axiom,
% 2.87/1.56 ! [A5: p > $o,B3: p > $o] :
% 2.87/1.56 ( ( ord_less_eq_p_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_p_o @ B3 @ A5 )
% 2.87/1.56 => ( A5 = B3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_72_order__class_Oorder_Oantisym,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ B3 @ A5 )
% 2.87/1.56 => ( A5 = B3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_73_order__class_Oorder_Oantisym,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ B3 @ A5 )
% 2.87/1.56 => ( A5 = B3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_74_ord__le__eq__trans,axiom,
% 2.87/1.56 ! [A5: set_p,B3: set_p,C: set_p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ A5 @ B3 )
% 2.87/1.56 => ( ( B3 = C )
% 2.87/1.56 => ( ord_less_eq_set_p @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_75_ord__le__eq__trans,axiom,
% 2.87/1.56 ! [A5: $o > $o,B3: $o > $o,C: $o > $o] :
% 2.87/1.56 ( ( ord_less_eq_o_o @ A5 @ B3 )
% 2.87/1.56 => ( ( B3 = C )
% 2.87/1.56 => ( ord_less_eq_o_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_76_ord__le__eq__trans,axiom,
% 2.87/1.56 ! [A5: p > $o,B3: p > $o,C: p > $o] :
% 2.87/1.56 ( ( ord_less_eq_p_o @ A5 @ B3 )
% 2.87/1.56 => ( ( B3 = C )
% 2.87/1.56 => ( ord_less_eq_p_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_77_ord__le__eq__trans,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ( B3 = C )
% 2.87/1.56 => ( ord_less_eq_set_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_78_ord__le__eq__trans,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( ( B3 = C )
% 2.87/1.56 => ( ord_less_eq_nat @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_79_ord__eq__le__trans,axiom,
% 2.87/1.56 ! [A5: set_p,B3: set_p,C: set_p] :
% 2.87/1.56 ( ( A5 = B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_p @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_set_p @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_80_ord__eq__le__trans,axiom,
% 2.87/1.56 ! [A5: $o > $o,B3: $o > $o,C: $o > $o] :
% 2.87/1.56 ( ( A5 = B3 )
% 2.87/1.56 => ( ( ord_less_eq_o_o @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_o_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_81_ord__eq__le__trans,axiom,
% 2.87/1.56 ! [A5: p > $o,B3: p > $o,C: p > $o] :
% 2.87/1.56 ( ( A5 = B3 )
% 2.87/1.56 => ( ( ord_less_eq_p_o @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_p_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_82_ord__eq__le__trans,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o,C: set_o] :
% 2.87/1.56 ( ( A5 = B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_set_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_83_ord__eq__le__trans,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat,C: nat] :
% 2.87/1.56 ( ( A5 = B3 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_nat @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_84_mem__Collect__eq,axiom,
% 2.87/1.56 ! [A5: p,P2: p > $o] :
% 2.87/1.56 ( ( member_p @ A5 @ ( collect_p @ P2 ) )
% 2.87/1.56 = ( P2 @ A5 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_85_mem__Collect__eq,axiom,
% 2.87/1.56 ! [A5: $o,P2: $o > $o] :
% 2.87/1.56 ( ( member_o @ A5 @ ( collect_o @ P2 ) )
% 2.87/1.56 = ( P2 @ A5 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_86_Collect__mem__eq,axiom,
% 2.87/1.56 ! [A: set_p] :
% 2.87/1.56 ( ( collect_p
% 2.87/1.56 @ ^ [X3: p] : ( member_p @ X3 @ A ) )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_87_Collect__mem__eq,axiom,
% 2.87/1.56 ! [A: set_o] :
% 2.87/1.56 ( ( collect_o
% 2.87/1.56 @ ^ [X3: $o] : ( member_o @ X3 @ A ) )
% 2.87/1.56 = A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_88_Collect__cong,axiom,
% 2.87/1.56 ! [P2: p > $o,Q2: p > $o] :
% 2.87/1.56 ( ! [X: p] :
% 2.87/1.56 ( ( P2 @ X )
% 2.87/1.56 = ( Q2 @ X ) )
% 2.87/1.56 => ( ( collect_p @ P2 )
% 2.87/1.56 = ( collect_p @ Q2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_89_Collect__cong,axiom,
% 2.87/1.56 ! [P2: $o > $o,Q2: $o > $o] :
% 2.87/1.56 ( ! [X: $o] :
% 2.87/1.56 ( ( P2 @ X )
% 2.87/1.56 = ( Q2 @ X ) )
% 2.87/1.56 => ( ( collect_o @ P2 )
% 2.87/1.56 = ( collect_o @ Q2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_90_order__class_Oorder_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: set_p,Z: set_p] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: set_p,B4: set_p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ A6 @ B4 )
% 2.87/1.56 & ( ord_less_eq_set_p @ B4 @ A6 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_91_order__class_Oorder_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: $o > $o,Z: $o > $o] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: $o > $o,B4: $o > $o] :
% 2.87/1.56 ( ( ord_less_eq_o_o @ A6 @ B4 )
% 2.87/1.56 & ( ord_less_eq_o_o @ B4 @ A6 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_92_order__class_Oorder_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: p > $o,Z: p > $o] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: p > $o,B4: p > $o] :
% 2.87/1.56 ( ( ord_less_eq_p_o @ A6 @ B4 )
% 2.87/1.56 & ( ord_less_eq_p_o @ B4 @ A6 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_93_order__class_Oorder_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: set_o,Z: set_o] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: set_o,B4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A6 @ B4 )
% 2.87/1.56 & ( ord_less_eq_set_o @ B4 @ A6 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_94_order__class_Oorder_Oeq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A6: nat,B4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A6 @ B4 )
% 2.87/1.56 & ( ord_less_eq_nat @ B4 @ A6 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_95_antisym__conv,axiom,
% 2.87/1.56 ! [Y2: set_p,X2: set_p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ Y2 @ X2 )
% 2.87/1.56 => ( ( ord_less_eq_set_p @ X2 @ Y2 )
% 2.87/1.56 = ( X2 = Y2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_96_antisym__conv,axiom,
% 2.87/1.56 ! [Y2: $o > $o,X2: $o > $o] :
% 2.87/1.56 ( ( ord_less_eq_o_o @ Y2 @ X2 )
% 2.87/1.56 => ( ( ord_less_eq_o_o @ X2 @ Y2 )
% 2.87/1.56 = ( X2 = Y2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_97_antisym__conv,axiom,
% 2.87/1.56 ! [Y2: p > $o,X2: p > $o] :
% 2.87/1.56 ( ( ord_less_eq_p_o @ Y2 @ X2 )
% 2.87/1.56 => ( ( ord_less_eq_p_o @ X2 @ Y2 )
% 2.87/1.56 = ( X2 = Y2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_98_antisym__conv,axiom,
% 2.87/1.56 ! [Y2: set_o,X2: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ Y2 @ X2 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ X2 @ Y2 )
% 2.87/1.56 = ( X2 = Y2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_99_antisym__conv,axiom,
% 2.87/1.56 ! [Y2: nat,X2: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.87/1.56 = ( X2 = Y2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_100_le__cases3,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat,Z2: nat] :
% 2.87/1.56 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.87/1.56 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 2.87/1.56 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.87/1.56 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 2.87/1.56 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 2.87/1.56 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 2.87/1.56 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 2.87/1.56 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 2.87/1.56 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 2.87/1.56 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 2.87/1.56 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 2.87/1.56 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_101_order_Otrans,axiom,
% 2.87/1.56 ! [A5: set_p,B3: set_p,C: set_p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_p @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_set_p @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_102_order_Otrans,axiom,
% 2.87/1.56 ! [A5: $o > $o,B3: $o > $o,C: $o > $o] :
% 2.87/1.56 ( ( ord_less_eq_o_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_o_o @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_o_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_103_order_Otrans,axiom,
% 2.87/1.56 ! [A5: p > $o,B3: p > $o,C: p > $o] :
% 2.87/1.56 ( ( ord_less_eq_p_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_p_o @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_p_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_104_order_Otrans,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_set_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_105_order_Otrans,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ B3 @ C )
% 2.87/1.56 => ( ord_less_eq_nat @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_106_le__cases,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat] :
% 2.87/1.56 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 2.87/1.56 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_107_eq__refl,axiom,
% 2.87/1.56 ! [X2: $o > $o,Y2: $o > $o] :
% 2.87/1.56 ( ( X2 = Y2 )
% 2.87/1.56 => ( ord_less_eq_o_o @ X2 @ Y2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_108_eq__refl,axiom,
% 2.87/1.56 ! [X2: p > $o,Y2: p > $o] :
% 2.87/1.56 ( ( X2 = Y2 )
% 2.87/1.56 => ( ord_less_eq_p_o @ X2 @ Y2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_109_eq__refl,axiom,
% 2.87/1.56 ! [X2: set_o,Y2: set_o] :
% 2.87/1.56 ( ( X2 = Y2 )
% 2.87/1.56 => ( ord_less_eq_set_o @ X2 @ Y2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_110_eq__refl,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat] :
% 2.87/1.56 ( ( X2 = Y2 )
% 2.87/1.56 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_111_linear,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.87/1.56 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_112_antisym,axiom,
% 2.87/1.56 ! [X2: set_o,Y2: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X2 @ Y2 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ Y2 @ X2 )
% 2.87/1.56 => ( X2 = Y2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_113_antisym,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 2.87/1.56 => ( X2 = Y2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_114_eq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: set_o,Z: set_o] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [X3: set_o,Y3: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X3 @ Y3 )
% 2.87/1.56 & ( ord_less_eq_set_o @ Y3 @ X3 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_115_eq__iff,axiom,
% 2.87/1.56 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [X3: nat,Y3: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.87/1.56 & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_116_ord__le__eq__subst,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o,F: set_o > set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ( F @ B3 )
% 2.87/1.56 = C )
% 2.87/1.56 => ( ! [X: set_o,Y4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ A5 ) @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_117_ord__le__eq__subst,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o,F: set_o > nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ( F @ B3 )
% 2.87/1.56 = C )
% 2.87/1.56 => ( ! [X: set_o,Y4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ A5 ) @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_118_ord__le__eq__subst,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat,F: nat > set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( ( ( F @ B3 )
% 2.87/1.56 = C )
% 2.87/1.56 => ( ! [X: nat,Y4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ A5 ) @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_119_ord__le__eq__subst,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat,F: nat > nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( ( ( F @ B3 )
% 2.87/1.56 = C )
% 2.87/1.56 => ( ! [X: nat,Y4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ A5 ) @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_120_ord__eq__le__subst,axiom,
% 2.87/1.56 ! [A5: set_o,F: set_o > set_o,B3: set_o,C: set_o] :
% 2.87/1.56 ( ( A5
% 2.87/1.56 = ( F @ B3 ) )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ B3 @ C )
% 2.87/1.56 => ( ! [X: set_o,Y4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_set_o @ A5 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_121_ord__eq__le__subst,axiom,
% 2.87/1.56 ! [A5: nat,F: set_o > nat,B3: set_o,C: set_o] :
% 2.87/1.56 ( ( A5
% 2.87/1.56 = ( F @ B3 ) )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ B3 @ C )
% 2.87/1.56 => ( ! [X: set_o,Y4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_nat @ A5 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_122_ord__eq__le__subst,axiom,
% 2.87/1.56 ! [A5: set_o,F: nat > set_o,B3: nat,C: nat] :
% 2.87/1.56 ( ( A5
% 2.87/1.56 = ( F @ B3 ) )
% 2.87/1.56 => ( ( ord_less_eq_nat @ B3 @ C )
% 2.87/1.56 => ( ! [X: nat,Y4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_set_o @ A5 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_123_ord__eq__le__subst,axiom,
% 2.87/1.56 ! [A5: nat,F: nat > nat,B3: nat,C: nat] :
% 2.87/1.56 ( ( A5
% 2.87/1.56 = ( F @ B3 ) )
% 2.87/1.56 => ( ( ord_less_eq_nat @ B3 @ C )
% 2.87/1.56 => ( ! [X: nat,Y4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_nat @ A5 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_124_order__subst2,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o,F: set_o > set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ ( F @ B3 ) @ C )
% 2.87/1.56 => ( ! [X: set_o,Y4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ A5 ) @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_125_order__subst2,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o,F: set_o > nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C )
% 2.87/1.56 => ( ! [X: set_o,Y4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ A5 ) @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_126_order__subst2,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat,F: nat > set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ ( F @ B3 ) @ C )
% 2.87/1.56 => ( ! [X: nat,Y4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ A5 ) @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_127_order__subst2,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat,F: nat > nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ ( F @ B3 ) @ C )
% 2.87/1.56 => ( ! [X: nat,Y4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ A5 ) @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_128_order__subst1,axiom,
% 2.87/1.56 ! [A5: set_o,F: set_o > set_o,B3: set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ ( F @ B3 ) )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ B3 @ C )
% 2.87/1.56 => ( ! [X: set_o,Y4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_set_o @ A5 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_129_order__subst1,axiom,
% 2.87/1.56 ! [A5: set_o,F: nat > set_o,B3: nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ ( F @ B3 ) )
% 2.87/1.56 => ( ( ord_less_eq_nat @ B3 @ C )
% 2.87/1.56 => ( ! [X: nat,Y4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_set_o @ A5 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_130_order__subst1,axiom,
% 2.87/1.56 ! [A5: nat,F: set_o > nat,B3: set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ ( F @ B3 ) )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ B3 @ C )
% 2.87/1.56 => ( ! [X: set_o,Y4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_nat @ A5 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_131_order__subst1,axiom,
% 2.87/1.56 ! [A5: nat,F: nat > nat,B3: nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ ( F @ B3 ) )
% 2.87/1.56 => ( ( ord_less_eq_nat @ B3 @ C )
% 2.87/1.56 => ( ! [X: nat,Y4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X @ Y4 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 2.87/1.56 => ( ord_less_eq_nat @ A5 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_132_Collect__mono__iff,axiom,
% 2.87/1.56 ! [P2: $o > $o,Q2: $o > $o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q2 ) )
% 2.87/1.56 = ( ! [X3: $o] :
% 2.87/1.56 ( ( P2 @ X3 )
% 2.87/1.56 => ( Q2 @ X3 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_133_set__eq__subset,axiom,
% 2.87/1.56 ( ( ^ [Y: set_o,Z: set_o] : ( Y = Z ) )
% 2.87/1.56 = ( ^ [A4: set_o,B2: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A4 @ B2 )
% 2.87/1.56 & ( ord_less_eq_set_o @ B2 @ A4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_134_subset__trans,axiom,
% 2.87/1.56 ! [A: set_o,B: set_o,C3: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A @ B )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ B @ C3 )
% 2.87/1.56 => ( ord_less_eq_set_o @ A @ C3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_135_Collect__mono,axiom,
% 2.87/1.56 ! [P2: $o > $o,Q2: $o > $o] :
% 2.87/1.56 ( ! [X: $o] :
% 2.87/1.56 ( ( P2 @ X )
% 2.87/1.56 => ( Q2 @ X ) )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_136_subset__refl,axiom,
% 2.87/1.56 ! [A: set_o] : ( ord_less_eq_set_o @ A @ A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_137_subset__iff,axiom,
% 2.87/1.56 ( ord_less_eq_set_p
% 2.87/1.56 = ( ^ [A4: set_p,B2: set_p] :
% 2.87/1.56 ! [T: p] :
% 2.87/1.56 ( ( member_p @ T @ A4 )
% 2.87/1.56 => ( member_p @ T @ B2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_138_subset__iff,axiom,
% 2.87/1.56 ( ord_less_eq_set_o
% 2.87/1.56 = ( ^ [A4: set_o,B2: set_o] :
% 2.87/1.56 ! [T: $o] :
% 2.87/1.56 ( ( member_o @ T @ A4 )
% 2.87/1.56 => ( member_o @ T @ B2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_139_equalityD2,axiom,
% 2.87/1.56 ! [A: set_o,B: set_o] :
% 2.87/1.56 ( ( A = B )
% 2.87/1.56 => ( ord_less_eq_set_o @ B @ A ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_140_equalityD1,axiom,
% 2.87/1.56 ! [A: set_o,B: set_o] :
% 2.87/1.56 ( ( A = B )
% 2.87/1.56 => ( ord_less_eq_set_o @ A @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_141_subset__eq,axiom,
% 2.87/1.56 ( ord_less_eq_set_p
% 2.87/1.56 = ( ^ [A4: set_p,B2: set_p] :
% 2.87/1.56 ! [X3: p] :
% 2.87/1.56 ( ( member_p @ X3 @ A4 )
% 2.87/1.56 => ( member_p @ X3 @ B2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_142_subset__eq,axiom,
% 2.87/1.56 ( ord_less_eq_set_o
% 2.87/1.56 = ( ^ [A4: set_o,B2: set_o] :
% 2.87/1.56 ! [X3: $o] :
% 2.87/1.56 ( ( member_o @ X3 @ A4 )
% 2.87/1.56 => ( member_o @ X3 @ B2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_143_equalityE,axiom,
% 2.87/1.56 ! [A: set_o,B: set_o] :
% 2.87/1.56 ( ( A = B )
% 2.87/1.56 => ~ ( ( ord_less_eq_set_o @ A @ B )
% 2.87/1.56 => ~ ( ord_less_eq_set_o @ B @ A ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_144_subsetD,axiom,
% 2.87/1.56 ! [A: set_p,B: set_p,C: p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ A @ B )
% 2.87/1.56 => ( ( member_p @ C @ A )
% 2.87/1.56 => ( member_p @ C @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_145_subsetD,axiom,
% 2.87/1.56 ! [A: set_o,B: set_o,C: $o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A @ B )
% 2.87/1.56 => ( ( member_o @ C @ A )
% 2.87/1.56 => ( member_o @ C @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_146_in__mono,axiom,
% 2.87/1.56 ! [A: set_p,B: set_p,X2: p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ A @ B )
% 2.87/1.56 => ( ( member_p @ X2 @ A )
% 2.87/1.56 => ( member_p @ X2 @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_147_in__mono,axiom,
% 2.87/1.56 ! [A: set_o,B: set_o,X2: $o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A @ B )
% 2.87/1.56 => ( ( member_o @ X2 @ A )
% 2.87/1.56 => ( member_o @ X2 @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_148_Collect__subset,axiom,
% 2.87/1.56 ! [A: set_p,P2: p > $o] :
% 2.87/1.56 ( ord_less_eq_set_p
% 2.87/1.56 @ ( collect_p
% 2.87/1.56 @ ^ [X3: p] :
% 2.87/1.56 ( ( member_p @ X3 @ A )
% 2.87/1.56 & ( P2 @ X3 ) ) )
% 2.87/1.56 @ A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_149_Collect__subset,axiom,
% 2.87/1.56 ! [A: set_o,P2: $o > $o] :
% 2.87/1.56 ( ord_less_eq_set_o
% 2.87/1.56 @ ( collect_o
% 2.87/1.56 @ ^ [X3: $o] :
% 2.87/1.56 ( ( member_o @ X3 @ A )
% 2.87/1.56 & ( P2 @ X3 ) ) )
% 2.87/1.56 @ A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_150_flpSystem_OInactiveProcessSilentDecisionValuesDecrease,axiom,
% 2.87/1.56 ! [Sends: p > s > messageValue_v > message_p_v > nat,P: p,Q: p,Trans: p > s > messageValue_v > s,C: config256849571t_unit,Msg: message_p_v,C2: config256849571t_unit,Start: p > s] :
% 2.87/1.56 ( ( flpSystem_p_s_v @ Sends )
% 2.87/1.56 => ( ( P != Q )
% 2.87/1.56 => ( ( steps_p_s_v @ Trans @ Sends @ C @ Msg @ C2 )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ Msg )
% 2.87/1.56 => ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 2.87/1.56 => ( ord_less_eq_set_o
% 2.87/1.56 @ ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C2 ) )
% 2.87/1.56 @ ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C ) ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_151_flpSystem_OActiveProcessSilentDecisionValuesIncrease,axiom,
% 2.87/1.56 ! [Sends: p > s > messageValue_v > message_p_v > nat,P: p,Q: p,Trans: p > s > messageValue_v > s,C: config256849571t_unit,Msg: message_p_v,C2: config256849571t_unit,Start: p > s] :
% 2.87/1.56 ( ( flpSystem_p_s_v @ Sends )
% 2.87/1.56 => ( ( P = Q )
% 2.87/1.56 => ( ( steps_p_s_v @ Trans @ Sends @ C @ Msg @ C2 )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ Msg )
% 2.87/1.56 => ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 2.87/1.56 => ( ord_less_eq_set_o
% 2.87/1.56 @ ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C ) )
% 2.87/1.56 @ ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C2 ) ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_152_NotStepReachable,axiom,
% 2.87/1.56 ~ ( stepReachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ msg @ c ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_153_cMsgLastReachable,axiom,
% 2.87/1.56 reachable_p_s_v @ trans @ sends @ cMsg @ ( last_c571238084t_unit @ execMsga ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_154_NoReceivingNoChange,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,P: p] :
% 2.87/1.56 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.56 => ( ~ ( isReceiverOf_p_v @ P @ M )
% 2.87/1.56 => ( ( states1228886952t_unit @ Cfg1 @ P )
% 2.87/1.56 = ( states1228886952t_unit @ Cfg2 @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_155_initReachable__def,axiom,
% 2.87/1.56 ! [Cfg: config256849571t_unit] :
% 2.87/1.56 ( ( initReachable_p_s_v @ trans @ sends @ start @ Cfg )
% 2.87/1.56 = ( ? [Cfg0: config256849571t_unit] :
% 2.87/1.56 ( ( initial_p_s_v @ start @ Cfg0 )
% 2.87/1.56 & ( reachable_p_s_v @ trans @ sends @ Cfg0 @ Cfg ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_156_ReachableStepFirst,axiom,
% 2.87/1.56 ! [Cfg: config256849571t_unit,Cfg4: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ Cfg @ Cfg4 )
% 2.87/1.56 => ( ( Cfg = Cfg4 )
% 2.87/1.56 | ? [Cfg12: config256849571t_unit,Msg3: message_p_v,P3: p] :
% 2.87/1.56 ( ( steps_p_s_v @ trans @ sends @ Cfg @ Msg3 @ Cfg12 )
% 2.87/1.56 & ( enabled_p_v_s @ Cfg @ Msg3 )
% 2.87/1.56 & ( isReceiverOf_p_v @ P3 @ Msg3 )
% 2.87/1.56 & ( reachable_p_s_v @ trans @ sends @ Cfg12 @ Cfg4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_157_NotInQFrozenQReachability,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,P: p] :
% 2.87/1.56 ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.56 => ( ~ ( member_p @ P @ Q2 )
% 2.87/1.56 => ( ( states1228886952t_unit @ Cfg1 @ P )
% 2.87/1.56 = ( states1228886952t_unit @ Cfg2 @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_158_C_H_I2_J,axiom,
% 2.87/1.56 ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ c ) )
% 2.87/1.56 = ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_159_NoActivityNoMessageLoss,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,P: p,M2: message_p_v] :
% 2.87/1.56 ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.56 => ( ~ ( member_p @ P @ Q2 )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ M2 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_160_ReachableTrans,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,Cfg32: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg2 )
% 2.87/1.56 => ( ( reachable_p_s_v @ trans @ sends @ Cfg2 @ Cfg32 )
% 2.87/1.56 => ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg32 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_161_init,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit] : ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg1 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_162_empty__iff,axiom,
% 2.87/1.56 ! [C: p] :
% 2.87/1.56 ~ ( member_p @ C @ bot_bot_set_p ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_163_empty__iff,axiom,
% 2.87/1.56 ! [C: $o] :
% 2.87/1.56 ~ ( member_o @ C @ bot_bot_set_o ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_164_all__not__in__conv,axiom,
% 2.87/1.56 ! [A: set_p] :
% 2.87/1.56 ( ( ! [X3: p] :
% 2.87/1.56 ~ ( member_p @ X3 @ A ) )
% 2.87/1.56 = ( A = bot_bot_set_p ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_165_all__not__in__conv,axiom,
% 2.87/1.56 ! [A: set_o] :
% 2.87/1.56 ( ( ! [X3: $o] :
% 2.87/1.56 ~ ( member_o @ X3 @ A ) )
% 2.87/1.56 = ( A = bot_bot_set_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_166_Collect__empty__eq,axiom,
% 2.87/1.56 ! [P2: $o > $o] :
% 2.87/1.56 ( ( ( collect_o @ P2 )
% 2.87/1.56 = bot_bot_set_o )
% 2.87/1.56 = ( ! [X3: $o] :
% 2.87/1.56 ~ ( P2 @ X3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_167_empty__Collect__eq,axiom,
% 2.87/1.56 ! [P2: $o > $o] :
% 2.87/1.56 ( ( bot_bot_set_o
% 2.87/1.56 = ( collect_o @ P2 ) )
% 2.87/1.56 = ( ! [X3: $o] :
% 2.87/1.56 ~ ( P2 @ X3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_168_insertCI,axiom,
% 2.87/1.56 ! [A5: $o,B: set_o,B3: $o] :
% 2.87/1.56 ( ( ~ ( member_o @ A5 @ B )
% 2.87/1.56 => ( A5 = B3 ) )
% 2.87/1.56 => ( member_o @ A5 @ ( insert_o @ B3 @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_169_insertCI,axiom,
% 2.87/1.56 ! [A5: p,B: set_p,B3: p] :
% 2.87/1.56 ( ( ~ ( member_p @ A5 @ B )
% 2.87/1.56 => ( A5 = B3 ) )
% 2.87/1.56 => ( member_p @ A5 @ ( insert_p @ B3 @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_170_insert__iff,axiom,
% 2.87/1.56 ! [A5: $o,B3: $o,A: set_o] :
% 2.87/1.56 ( ( member_o @ A5 @ ( insert_o @ B3 @ A ) )
% 2.87/1.56 = ( ( A5 = B3 )
% 2.87/1.56 | ( member_o @ A5 @ A ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_171_insert__iff,axiom,
% 2.87/1.56 ! [A5: p,B3: p,A: set_p] :
% 2.87/1.56 ( ( member_p @ A5 @ ( insert_p @ B3 @ A ) )
% 2.87/1.56 = ( ( A5 = B3 )
% 2.87/1.56 | ( member_p @ A5 @ A ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_172_insert__absorb2,axiom,
% 2.87/1.56 ! [X2: $o,A: set_o] :
% 2.87/1.56 ( ( insert_o @ X2 @ ( insert_o @ X2 @ A ) )
% 2.87/1.56 = ( insert_o @ X2 @ A ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_173_C_H_I1_J,axiom,
% 2.87/1.56 reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ c ).
% 2.87/1.56
% 2.87/1.56 thf(fact_174_reachable_Ocases,axiom,
% 2.87/1.56 ! [A1: config256849571t_unit,A2: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ A1 @ A2 )
% 2.87/1.56 => ( ( A2 != A1 )
% 2.87/1.56 => ~ ! [Cfg23: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ A1 @ Cfg23 )
% 2.87/1.56 => ! [Msg3: message_p_v] :
% 2.87/1.56 ~ ( steps_p_s_v @ trans @ sends @ Cfg23 @ Msg3 @ A2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_175_reachable_Oinducts,axiom,
% 2.87/1.56 ! [X1: config256849571t_unit,X22: config256849571t_unit,P2: config256849571t_unit > config256849571t_unit > $o] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ X1 @ X22 )
% 2.87/1.56 => ( ! [Cfg12: config256849571t_unit] : ( P2 @ Cfg12 @ Cfg12 )
% 2.87/1.56 => ( ! [Cfg12: config256849571t_unit,Cfg23: config256849571t_unit,Msg3: message_p_v,Cfg33: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ Cfg12 @ Cfg23 )
% 2.87/1.56 => ( ( P2 @ Cfg12 @ Cfg23 )
% 2.87/1.56 => ( ( steps_p_s_v @ trans @ sends @ Cfg23 @ Msg3 @ Cfg33 )
% 2.87/1.56 => ( P2 @ Cfg12 @ Cfg33 ) ) ) )
% 2.87/1.56 => ( P2 @ X1 @ X22 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_176_reachable_Osimps,axiom,
% 2.87/1.56 ! [A1: config256849571t_unit,A2: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ A1 @ A2 )
% 2.87/1.56 = ( ? [Cfg13: config256849571t_unit] :
% 2.87/1.56 ( ( A1 = Cfg13 )
% 2.87/1.56 & ( A2 = Cfg13 ) )
% 2.87/1.56 | ? [Cfg13: config256849571t_unit,Cfg22: config256849571t_unit,Msg2: message_p_v,Cfg34: config256849571t_unit] :
% 2.87/1.56 ( ( A1 = Cfg13 )
% 2.87/1.56 & ( A2 = Cfg34 )
% 2.87/1.56 & ( reachable_p_s_v @ trans @ sends @ Cfg13 @ Cfg22 )
% 2.87/1.56 & ( steps_p_s_v @ trans @ sends @ Cfg22 @ Msg2 @ Cfg34 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_177_reachable_Ostep,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,Msg: message_p_v,Cfg32: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg2 )
% 2.87/1.56 => ( ( steps_p_s_v @ trans @ sends @ Cfg2 @ Msg @ Cfg32 )
% 2.87/1.56 => ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg32 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_178_QReachImplReach,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit] :
% 2.87/1.56 ( ( qReachable_p_s_v @ trans @ sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.56 => ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_179_isPrefixListExec,axiom,
% 2.87/1.56 prefix1615116500t_unit @ exec @ execMsga ).
% 2.87/1.56
% 2.87/1.56 thf(fact_180_OtherMessagesOnlyGrowing,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,M2: message_p_v] :
% 2.87/1.56 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.56 => ( ( M != M2 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_181_stepReachable__def,axiom,
% 2.87/1.56 ! [C1: config256849571t_unit,Msg: message_p_v,C22: config256849571t_unit] :
% 2.87/1.56 ( ( stepReachable_p_s_v @ trans @ sends @ C1 @ Msg @ C22 )
% 2.87/1.56 = ( ? [C4: config256849571t_unit,C5: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ C1 @ C4 )
% 2.87/1.56 & ( steps_p_s_v @ trans @ sends @ C4 @ Msg @ C5 )
% 2.87/1.56 & ( reachable_p_s_v @ trans @ sends @ C5 @ C22 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_182_StepReachable,axiom,
% 2.87/1.56 ! [Cfg: config256849571t_unit,Cfg4: config256849571t_unit,Msg: message_p_v] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ Cfg @ Cfg4 )
% 2.87/1.56 => ( ( enabled_p_v_s @ Cfg @ Msg )
% 2.87/1.56 => ( ~ ( enabled_p_v_s @ Cfg4 @ Msg )
% 2.87/1.56 => ( stepReachable_p_s_v @ trans @ sends @ Cfg @ Msg @ Cfg4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_183_NoMessageLossStep,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,P: p,M2: message_p_v] :
% 2.87/1.56 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ M )
% 2.87/1.56 => ( ~ ( isReceiverOf_p_v @ P @ M2 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_184_subset__empty,axiom,
% 2.87/1.56 ! [A: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 2.87/1.56 = ( A = bot_bot_set_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_185_empty__subsetI,axiom,
% 2.87/1.56 ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_186_singletonI,axiom,
% 2.87/1.56 ! [A5: p] : ( member_p @ A5 @ ( insert_p @ A5 @ bot_bot_set_p ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_187_singletonI,axiom,
% 2.87/1.56 ! [A5: $o] : ( member_o @ A5 @ ( insert_o @ A5 @ bot_bot_set_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_188_insert__subset,axiom,
% 2.87/1.56 ! [X2: p,A: set_p,B: set_p] :
% 2.87/1.56 ( ( ord_less_eq_set_p @ ( insert_p @ X2 @ A ) @ B )
% 2.87/1.56 = ( ( member_p @ X2 @ B )
% 2.87/1.56 & ( ord_less_eq_set_p @ A @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_189_insert__subset,axiom,
% 2.87/1.56 ! [X2: $o,A: set_o,B: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ ( insert_o @ X2 @ A ) @ B )
% 2.87/1.56 = ( ( member_o @ X2 @ B )
% 2.87/1.56 & ( ord_less_eq_set_o @ A @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_190_ExecMsg_I2_J,axiom,
% 2.87/1.56 prefix47729710ge_p_v @ trace2 @ traceMsga ).
% 2.87/1.56
% 2.87/1.56 thf(fact_191_lastExecExec_HReachable,axiom,
% 2.87/1.56 reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ ( last_c571238084t_unit @ exec2 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_192_singleton__conv,axiom,
% 2.87/1.56 ! [A5: $o] :
% 2.87/1.56 ( ( collect_o
% 2.87/1.56 @ ^ [X3: $o] : ( X3 = A5 ) )
% 2.87/1.56 = ( insert_o @ A5 @ bot_bot_set_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_193_singleton__conv2,axiom,
% 2.87/1.56 ! [A5: $o] :
% 2.87/1.56 ( ( collect_o
% 2.87/1.56 @ ( ^ [Y: $o,Z: $o] : ( Y = Z )
% 2.87/1.56 @ A5 ) )
% 2.87/1.56 = ( insert_o @ A5 @ bot_bot_set_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_194_ExecIsExecution,axiom,
% 2.87/1.56 execution_p_s_v @ trans @ sends @ start @ exec @ trace ).
% 2.87/1.56
% 2.87/1.56 thf(fact_195_vUniform__def,axiom,
% 2.87/1.56 ! [V2: $o,C: config256849571t_unit] :
% 2.87/1.56 ( ( vUniform_p_s_v @ trans @ sends @ start @ V2 @ C )
% 2.87/1.56 = ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 2.87/1.56 & ! [P4: p] :
% 2.87/1.56 ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ P4 @ C ) )
% 2.87/1.56 = ( insert_o @ V2 @ bot_bot_set_o ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_196_singleton__insert__inj__eq_H,axiom,
% 2.87/1.56 ! [A5: $o,A: set_o,B3: $o] :
% 2.87/1.56 ( ( ( insert_o @ A5 @ A )
% 2.87/1.56 = ( insert_o @ B3 @ bot_bot_set_o ) )
% 2.87/1.56 = ( ( A5 = B3 )
% 2.87/1.56 & ( ord_less_eq_set_o @ A @ ( insert_o @ B3 @ bot_bot_set_o ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_197_singleton__insert__inj__eq,axiom,
% 2.87/1.56 ! [B3: $o,A5: $o,A: set_o] :
% 2.87/1.56 ( ( ( insert_o @ B3 @ bot_bot_set_o )
% 2.87/1.56 = ( insert_o @ A5 @ A ) )
% 2.87/1.56 = ( ( A5 = B3 )
% 2.87/1.56 & ( ord_less_eq_set_o @ A @ ( insert_o @ B3 @ bot_bot_set_o ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_198_ExecMsg_I4_J,axiom,
% 2.87/1.56 ( ( last_message_p_v @ traceMsga )
% 2.87/1.56 = msg ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_199_isStepReachable,axiom,
% 2.87/1.56 stepReachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ msg @ ( last_c571238084t_unit @ execMsga ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_200_SilentDecisionValueNotInverting,axiom,
% 2.87/1.56 ! [Q: p,C: config256849571t_unit,V2: $o,Msg: message_p_v,C2: config256849571t_unit,P: p] :
% 2.87/1.56 ( ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C ) )
% 2.87/1.56 = ( insert_o @ V2 @ bot_bot_set_o ) )
% 2.87/1.56 => ( ( steps_p_s_v @ trans @ sends @ C @ Msg @ C2 )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ Msg )
% 2.87/1.56 => ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 2.87/1.56 => ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ Q @ C2 ) )
% 2.87/1.56 != ( insert_o @ ~ V2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_201__092_060open_062_092_060And_062p_O_A_092_060exists_062c_H_O_Areachable_A_Ilast_Aexec_J_Ac_H_A_092_060and_062_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060close_062,axiom,
% 2.87/1.56 ! [P: p] :
% 2.87/1.56 ? [C6: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ C6 )
% 2.87/1.56 & ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ P @ C6 ) )
% 2.87/1.56 = ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_202__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_H_O_A_092_060lbrakk_062reachable_A_Ilast_Aexec_J_Ac_H_059_Aval_091p_Mc_H_093_A_061_A_123True_M_AFalse_125_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.87/1.56 ~ ! [C6: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ C6 )
% 2.87/1.56 => ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ C6 ) )
% 2.87/1.56 != ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_203_Agree,axiom,
% 2.87/1.56 ! [Cfg: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ exec ) @ Cfg )
% 2.87/1.56 => ( agreement_p_v_s @ Cfg ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_204_emptyE,axiom,
% 2.87/1.56 ! [A5: p] :
% 2.87/1.56 ~ ( member_p @ A5 @ bot_bot_set_p ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_205_emptyE,axiom,
% 2.87/1.56 ! [A5: $o] :
% 2.87/1.56 ~ ( member_o @ A5 @ bot_bot_set_o ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_206_insertE,axiom,
% 2.87/1.56 ! [A5: $o,B3: $o,A: set_o] :
% 2.87/1.56 ( ( member_o @ A5 @ ( insert_o @ B3 @ A ) )
% 2.87/1.56 => ( ( A5 = ~ B3 )
% 2.87/1.56 => ( member_o @ A5 @ A ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_207_insertE,axiom,
% 2.87/1.56 ! [A5: p,B3: p,A: set_p] :
% 2.87/1.56 ( ( member_p @ A5 @ ( insert_p @ B3 @ A ) )
% 2.87/1.56 => ( ( A5 != B3 )
% 2.87/1.56 => ( member_p @ A5 @ A ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_208_equals0D,axiom,
% 2.87/1.56 ! [A: set_p,A5: p] :
% 2.87/1.56 ( ( A = bot_bot_set_p )
% 2.87/1.56 => ~ ( member_p @ A5 @ A ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_209_equals0D,axiom,
% 2.87/1.56 ! [A: set_o,A5: $o] :
% 2.87/1.56 ( ( A = bot_bot_set_o )
% 2.87/1.56 => ~ ( member_o @ A5 @ A ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_210_equals0I,axiom,
% 2.87/1.56 ! [A: set_p] :
% 2.87/1.56 ( ! [Y4: p] :
% 2.87/1.56 ~ ( member_p @ Y4 @ A )
% 2.87/1.56 => ( A = bot_bot_set_p ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_211_equals0I,axiom,
% 2.87/1.56 ! [A: set_o] :
% 2.87/1.56 ( ! [Y4: $o] :
% 2.87/1.56 ~ ( member_o @ Y4 @ A )
% 2.87/1.56 => ( A = bot_bot_set_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_212_insertI1,axiom,
% 2.87/1.56 ! [A5: $o,B: set_o] : ( member_o @ A5 @ ( insert_o @ A5 @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_213_insertI1,axiom,
% 2.87/1.56 ! [A5: p,B: set_p] : ( member_p @ A5 @ ( insert_p @ A5 @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_214_insertI2,axiom,
% 2.87/1.56 ! [A5: $o,B: set_o,B3: $o] :
% 2.87/1.56 ( ( member_o @ A5 @ B )
% 2.87/1.56 => ( member_o @ A5 @ ( insert_o @ B3 @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_215_insertI2,axiom,
% 2.87/1.56 ! [A5: p,B: set_p,B3: p] :
% 2.87/1.56 ( ( member_p @ A5 @ B )
% 2.87/1.56 => ( member_p @ A5 @ ( insert_p @ B3 @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_216_ex__in__conv,axiom,
% 2.87/1.56 ! [A: set_p] :
% 2.87/1.56 ( ( ? [X3: p] : ( member_p @ X3 @ A ) )
% 2.87/1.56 = ( A != bot_bot_set_p ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_217_ex__in__conv,axiom,
% 2.87/1.56 ! [A: set_o] :
% 2.87/1.56 ( ( ? [X3: $o] : ( member_o @ X3 @ A ) )
% 2.87/1.56 = ( A != bot_bot_set_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_218_Set_Oset__insert,axiom,
% 2.87/1.56 ! [X2: $o,A: set_o] :
% 2.87/1.56 ( ( member_o @ X2 @ A )
% 2.87/1.56 => ~ ! [B6: set_o] :
% 2.87/1.56 ( ( A
% 2.87/1.56 = ( insert_o @ X2 @ B6 ) )
% 2.87/1.56 => ( member_o @ X2 @ B6 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_219_Set_Oset__insert,axiom,
% 2.87/1.56 ! [X2: p,A: set_p] :
% 2.87/1.56 ( ( member_p @ X2 @ A )
% 2.87/1.56 => ~ ! [B6: set_p] :
% 2.87/1.56 ( ( A
% 2.87/1.56 = ( insert_p @ X2 @ B6 ) )
% 2.87/1.56 => ( member_p @ X2 @ B6 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_220_singletonD,axiom,
% 2.87/1.56 ! [B3: p,A5: p] :
% 2.87/1.56 ( ( member_p @ B3 @ ( insert_p @ A5 @ bot_bot_set_p ) )
% 2.87/1.56 => ( B3 = A5 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_221_singletonD,axiom,
% 2.87/1.56 ! [B3: $o,A5: $o] :
% 2.87/1.56 ( ( member_o @ B3 @ ( insert_o @ A5 @ bot_bot_set_o ) )
% 2.87/1.56 => ( B3 = A5 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_222_insert__ident,axiom,
% 2.87/1.56 ! [X2: $o,A: set_o,B: set_o] :
% 2.87/1.56 ( ~ ( member_o @ X2 @ A )
% 2.87/1.56 => ( ~ ( member_o @ X2 @ B )
% 2.87/1.56 => ( ( ( insert_o @ X2 @ A )
% 2.87/1.56 = ( insert_o @ X2 @ B ) )
% 2.87/1.56 = ( A = B ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_223_insert__ident,axiom,
% 2.87/1.56 ! [X2: p,A: set_p,B: set_p] :
% 2.87/1.56 ( ~ ( member_p @ X2 @ A )
% 2.87/1.56 => ( ~ ( member_p @ X2 @ B )
% 2.87/1.56 => ( ( ( insert_p @ X2 @ A )
% 2.87/1.56 = ( insert_p @ X2 @ B ) )
% 2.87/1.56 = ( A = B ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_224_insert__absorb,axiom,
% 2.87/1.56 ! [A5: $o,A: set_o] :
% 2.87/1.56 ( ( member_o @ A5 @ A )
% 2.87/1.56 => ( ( insert_o @ A5 @ A )
% 2.87/1.56 = A ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_225_insert__absorb,axiom,
% 2.87/1.56 ! [A5: p,A: set_p] :
% 2.87/1.56 ( ( member_p @ A5 @ A )
% 2.87/1.56 => ( ( insert_p @ A5 @ A )
% 2.87/1.56 = A ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_226_insert__eq__iff,axiom,
% 2.87/1.56 ! [A5: $o,A: set_o,B3: $o,B: set_o] :
% 2.87/1.56 ( ~ ( member_o @ A5 @ A )
% 2.87/1.56 => ( ~ ( member_o @ B3 @ B )
% 2.87/1.56 => ( ( ( insert_o @ A5 @ A )
% 2.87/1.56 = ( insert_o @ B3 @ B ) )
% 2.87/1.56 = ( ( ( A5 = B3 )
% 2.87/1.56 => ( A = B ) )
% 2.87/1.56 & ( ( A5 = ~ B3 )
% 2.87/1.56 => ? [C7: set_o] :
% 2.87/1.56 ( ( A
% 2.87/1.56 = ( insert_o @ B3 @ C7 ) )
% 2.87/1.56 & ~ ( member_o @ B3 @ C7 )
% 2.87/1.56 & ( B
% 2.87/1.56 = ( insert_o @ A5 @ C7 ) )
% 2.87/1.56 & ~ ( member_o @ A5 @ C7 ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_227_insert__eq__iff,axiom,
% 2.87/1.56 ! [A5: p,A: set_p,B3: p,B: set_p] :
% 2.87/1.56 ( ~ ( member_p @ A5 @ A )
% 2.87/1.56 => ( ~ ( member_p @ B3 @ B )
% 2.87/1.56 => ( ( ( insert_p @ A5 @ A )
% 2.87/1.56 = ( insert_p @ B3 @ B ) )
% 2.87/1.56 = ( ( ( A5 = B3 )
% 2.87/1.56 => ( A = B ) )
% 2.87/1.56 & ( ( A5 != B3 )
% 2.87/1.56 => ? [C7: set_p] :
% 2.87/1.56 ( ( A
% 2.87/1.56 = ( insert_p @ B3 @ C7 ) )
% 2.87/1.56 & ~ ( member_p @ B3 @ C7 )
% 2.87/1.56 & ( B
% 2.87/1.56 = ( insert_p @ A5 @ C7 ) )
% 2.87/1.56 & ~ ( member_p @ A5 @ C7 ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_228_singleton__iff,axiom,
% 2.87/1.56 ! [B3: p,A5: p] :
% 2.87/1.56 ( ( member_p @ B3 @ ( insert_p @ A5 @ bot_bot_set_p ) )
% 2.87/1.56 = ( B3 = A5 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_229_singleton__iff,axiom,
% 2.87/1.56 ! [B3: $o,A5: $o] :
% 2.87/1.56 ( ( member_o @ B3 @ ( insert_o @ A5 @ bot_bot_set_o ) )
% 2.87/1.56 = ( B3 = A5 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_230_insert__commute,axiom,
% 2.87/1.56 ! [X2: $o,Y2: $o,A: set_o] :
% 2.87/1.56 ( ( insert_o @ X2 @ ( insert_o @ Y2 @ A ) )
% 2.87/1.56 = ( insert_o @ Y2 @ ( insert_o @ X2 @ A ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_231_Collect__conv__if,axiom,
% 2.87/1.56 ! [P2: $o > $o,A5: $o] :
% 2.87/1.56 ( ( ( P2 @ A5 )
% 2.87/1.56 => ( ( collect_o
% 2.87/1.56 @ ^ [X3: $o] :
% 2.87/1.56 ( ( X3 = A5 )
% 2.87/1.56 & ( P2 @ X3 ) ) )
% 2.87/1.56 = ( insert_o @ A5 @ bot_bot_set_o ) ) )
% 2.87/1.56 & ( ~ ( P2 @ A5 )
% 2.87/1.56 => ( ( collect_o
% 2.87/1.56 @ ^ [X3: $o] :
% 2.87/1.56 ( ( X3 = A5 )
% 2.87/1.56 & ( P2 @ X3 ) ) )
% 2.87/1.56 = bot_bot_set_o ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_232_Collect__conv__if2,axiom,
% 2.87/1.56 ! [P2: $o > $o,A5: $o] :
% 2.87/1.56 ( ( ( P2 @ A5 )
% 2.87/1.56 => ( ( collect_o
% 2.87/1.56 @ ^ [X3: $o] :
% 2.87/1.56 ( ( A5 = X3 )
% 2.87/1.56 & ( P2 @ X3 ) ) )
% 2.87/1.56 = ( insert_o @ A5 @ bot_bot_set_o ) ) )
% 2.87/1.56 & ( ~ ( P2 @ A5 )
% 2.87/1.56 => ( ( collect_o
% 2.87/1.56 @ ^ [X3: $o] :
% 2.87/1.56 ( ( A5 = X3 )
% 2.87/1.56 & ( P2 @ X3 ) ) )
% 2.87/1.56 = bot_bot_set_o ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_233_doubleton__eq__iff,axiom,
% 2.87/1.56 ! [A5: $o,B3: $o,C: $o,D: $o] :
% 2.87/1.56 ( ( ( insert_o @ A5 @ ( insert_o @ B3 @ bot_bot_set_o ) )
% 2.87/1.56 = ( insert_o @ C @ ( insert_o @ D @ bot_bot_set_o ) ) )
% 2.87/1.56 = ( ( ( A5 = C )
% 2.87/1.56 & ( B3 = D ) )
% 2.87/1.56 | ( ( A5 = D )
% 2.87/1.56 & ( B3 = C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_234_insert__not__empty,axiom,
% 2.87/1.56 ! [A5: $o,A: set_o] :
% 2.87/1.56 ( ( insert_o @ A5 @ A )
% 2.87/1.56 != bot_bot_set_o ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_235_singleton__inject,axiom,
% 2.87/1.56 ! [A5: $o,B3: $o] :
% 2.87/1.56 ( ( ( insert_o @ A5 @ bot_bot_set_o )
% 2.87/1.56 = ( insert_o @ B3 @ bot_bot_set_o ) )
% 2.87/1.56 => ( A5 = B3 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_236_subset__singletonD,axiom,
% 2.87/1.56 ! [A: set_o,X2: $o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A @ ( insert_o @ X2 @ bot_bot_set_o ) )
% 2.87/1.56 => ( ( A = bot_bot_set_o )
% 2.87/1.56 | ( A
% 2.87/1.56 = ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_237_mk__disjoint__insert,axiom,
% 2.87/1.56 ! [A5: $o,A: set_o] :
% 2.87/1.56 ( ( member_o @ A5 @ A )
% 2.87/1.56 => ? [B6: set_o] :
% 2.87/1.56 ( ( A
% 2.87/1.56 = ( insert_o @ A5 @ B6 ) )
% 2.87/1.56 & ~ ( member_o @ A5 @ B6 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_238_mk__disjoint__insert,axiom,
% 2.87/1.56 ! [A5: p,A: set_p] :
% 2.87/1.56 ( ( member_p @ A5 @ A )
% 2.87/1.56 => ? [B6: set_p] :
% 2.87/1.56 ( ( A
% 2.87/1.56 = ( insert_p @ A5 @ B6 ) )
% 2.87/1.56 & ~ ( member_p @ A5 @ B6 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_239_subset__singleton__iff,axiom,
% 2.87/1.56 ! [X5: set_o,A5: $o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X5 @ ( insert_o @ A5 @ bot_bot_set_o ) )
% 2.87/1.56 = ( ( X5 = bot_bot_set_o )
% 2.87/1.56 | ( X5
% 2.87/1.56 = ( insert_o @ A5 @ bot_bot_set_o ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_240_insert__Collect,axiom,
% 2.87/1.56 ! [A5: $o,P2: $o > $o] :
% 2.87/1.56 ( ( insert_o @ A5 @ ( collect_o @ P2 ) )
% 2.87/1.56 = ( collect_o
% 2.87/1.56 @ ^ [U: $o] :
% 2.87/1.56 ( ( U != A5 )
% 2.87/1.56 => ( P2 @ U ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_241_insert__compr,axiom,
% 2.87/1.56 ( insert_p
% 2.87/1.56 = ( ^ [A6: p,B2: set_p] :
% 2.87/1.56 ( collect_p
% 2.87/1.56 @ ^ [X3: p] :
% 2.87/1.56 ( ( X3 = A6 )
% 2.87/1.56 | ( member_p @ X3 @ B2 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_242_insert__compr,axiom,
% 2.87/1.56 ( insert_o
% 2.87/1.56 = ( ^ [A6: $o,B2: set_o] :
% 2.87/1.56 ( collect_o
% 2.87/1.56 @ ^ [X3: $o] :
% 2.87/1.56 ( ( X3 = A6 )
% 2.87/1.56 | ( member_o @ X3 @ B2 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_243_empty__def,axiom,
% 2.87/1.56 ( bot_bot_set_o
% 2.87/1.56 = ( collect_o
% 2.87/1.56 @ ^ [X3: $o] : $false ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_244_bot_Oextremum,axiom,
% 2.87/1.56 ! [A5: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A5 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_245_bot_Oextremum,axiom,
% 2.87/1.56 ! [A5: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A5 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_246_bot_Oextremum__unique,axiom,
% 2.87/1.56 ! [A5: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ bot_bot_set_o )
% 2.87/1.56 = ( A5 = bot_bot_set_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_247_bot_Oextremum__unique,axiom,
% 2.87/1.56 ! [A5: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ bot_bot_nat )
% 2.87/1.56 = ( A5 = bot_bot_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_248_bot_Oextremum__uniqueI,axiom,
% 2.87/1.56 ! [A5: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ bot_bot_set_o )
% 2.87/1.56 => ( A5 = bot_bot_set_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_249_bot_Oextremum__uniqueI,axiom,
% 2.87/1.56 ! [A5: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ bot_bot_nat )
% 2.87/1.56 => ( A5 = bot_bot_nat ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_250_insert__mono,axiom,
% 2.87/1.56 ! [C3: set_o,D2: set_o,A5: $o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ C3 @ D2 )
% 2.87/1.56 => ( ord_less_eq_set_o @ ( insert_o @ A5 @ C3 ) @ ( insert_o @ A5 @ D2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_251_subset__insert,axiom,
% 2.87/1.56 ! [X2: p,A: set_p,B: set_p] :
% 2.87/1.56 ( ~ ( member_p @ X2 @ A )
% 2.87/1.56 => ( ( ord_less_eq_set_p @ A @ ( insert_p @ X2 @ B ) )
% 2.87/1.56 = ( ord_less_eq_set_p @ A @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_252_subset__insert,axiom,
% 2.87/1.56 ! [X2: $o,A: set_o,B: set_o] :
% 2.87/1.56 ( ~ ( member_o @ X2 @ A )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ A @ ( insert_o @ X2 @ B ) )
% 2.87/1.56 = ( ord_less_eq_set_o @ A @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_253_subset__insertI,axiom,
% 2.87/1.56 ! [B: set_o,A5: $o] : ( ord_less_eq_set_o @ B @ ( insert_o @ A5 @ B ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_254_subset__insertI2,axiom,
% 2.87/1.56 ! [A: set_o,B: set_o,B3: $o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A @ B )
% 2.87/1.56 => ( ord_less_eq_set_o @ A @ ( insert_o @ B3 @ B ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_255_flpSystem_OvUniform__def,axiom,
% 2.87/1.56 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s,V2: $o,C: config256849571t_unit] :
% 2.87/1.56 ( ( flpSystem_p_s_v @ Sends )
% 2.87/1.56 => ( ( vUniform_p_s_v @ Trans @ Sends @ Start @ V2 @ C )
% 2.87/1.56 = ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 2.87/1.56 & ! [P4: p] :
% 2.87/1.56 ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ P4 @ C ) )
% 2.87/1.56 = ( insert_o @ V2 @ bot_bot_set_o ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_256_flpSystem_OSilentDecisionValueNotInverting,axiom,
% 2.87/1.56 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s,Q: p,C: config256849571t_unit,V2: $o,Msg: message_p_v,C2: config256849571t_unit,P: p] :
% 2.87/1.56 ( ( flpSystem_p_s_v @ Sends )
% 2.87/1.56 => ( ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C ) )
% 2.87/1.56 = ( insert_o @ V2 @ bot_bot_set_o ) )
% 2.87/1.56 => ( ( steps_p_s_v @ Trans @ Sends @ C @ Msg @ C2 )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ Msg )
% 2.87/1.56 => ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 2.87/1.56 => ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ Q @ C2 ) )
% 2.87/1.56 != ( insert_o @ ~ V2 @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_257_flpSystem_OpSilDecVal_Ocong,axiom,
% 2.87/1.56 pSilDecVal_p_s_v = pSilDecVal_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_258_flpSystem_OvUniform_Ocong,axiom,
% 2.87/1.56 vUniform_p_s_v = vUniform_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_259_flpSystem_OagreementInit_Ocong,axiom,
% 2.87/1.56 agreementInit_p_s_v = agreementInit_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_260_expandExecutionReachable,axiom,
% 2.87/1.56 ! [CfgLast: config256849571t_unit,Cfg: config256849571t_unit,Exec: list_c1059388851t_unit,Trace: list_message_p_v] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ CfgLast @ Cfg )
% 2.87/1.56 => ( ( execution_p_s_v @ trans @ sends @ start @ Exec @ Trace )
% 2.87/1.56 => ( ( CfgLast
% 2.87/1.56 = ( last_c571238084t_unit @ Exec ) )
% 2.87/1.56 => ? [Exec2: list_c1059388851t_unit,Trace2: list_message_p_v] :
% 2.87/1.56 ( ( execution_p_s_v @ trans @ sends @ start @ Exec2 @ Trace2 )
% 2.87/1.56 & ( ( ( prefix1615116500t_unit @ Exec @ Exec2 )
% 2.87/1.56 & ( prefix47729710ge_p_v @ Trace @ Trace2 ) )
% 2.87/1.56 | ( ( Exec = Exec2 )
% 2.87/1.56 & ( Trace = Trace2 ) ) )
% 2.87/1.56 & ( ( last_c571238084t_unit @ Exec2 )
% 2.87/1.56 = Cfg ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_261_NewExec_I2_J,axiom,
% 2.87/1.56 ( ( ( prefix1615116500t_unit @ exec @ exec2 )
% 2.87/1.56 & ( prefix47729710ge_p_v @ trace @ trace2 ) )
% 2.87/1.56 | ( ( exec = exec2 )
% 2.87/1.56 & ( trace = trace2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_262_NoOutMessageLoss,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,V2: $o] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ Cfg1 @ Cfg2 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ ( outMsg_p_v @ V2 ) ) @ ( msgs_p1029620568t_unit @ Cfg2 @ ( outMsg_p_v @ V2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_263_asynchronousSystem_OReachableStepFirst,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg: config256849571t_unit,Cfg4: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg @ Cfg4 )
% 2.87/1.56 => ( ( Cfg = Cfg4 )
% 2.87/1.56 | ? [Cfg12: config256849571t_unit,Msg3: message_p_v,P3: p] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg @ Msg3 @ Cfg12 )
% 2.87/1.56 & ( enabled_p_v_s @ Cfg @ Msg3 )
% 2.87/1.56 & ( isReceiverOf_p_v @ P3 @ Msg3 )
% 2.87/1.56 & ( reachable_p_s_v @ Trans @ Sends @ Cfg12 @ Cfg4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_264_asynchronousSystem_ONoActivityNoMessageLoss,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,P: p,M2: message_p_v] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.56 => ( ~ ( member_p @ P @ Q2 )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ M2 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_265_asynchronousSystem_ONoMessageLossStep,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,P: p,M2: message_p_v] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ M )
% 2.87/1.56 => ( ~ ( isReceiverOf_p_v @ P @ M2 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_266_message_Oinject_I2_J,axiom,
% 2.87/1.56 ! [X22: $o,Y22: $o] :
% 2.87/1.56 ( ( ( outMsg_p_v @ X22 )
% 2.87/1.56 = ( outMsg_p_v @ Y22 ) )
% 2.87/1.56 = ( X22 = Y22 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_267_StepOutMsg,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,V2: $o,Cfg2: config256849571t_unit] :
% 2.87/1.56 ~ ( steps_p_s_v @ trans @ sends @ Cfg1 @ ( outMsg_p_v @ V2 ) @ Cfg2 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_268_isPrefixListTrace,axiom,
% 2.87/1.56 prefix47729710ge_p_v @ trace @ traceMsga ).
% 2.87/1.56
% 2.87/1.56 thf(fact_269_expandExecutionStep,axiom,
% 2.87/1.56 ! [Exec3: list_c1059388851t_unit,Msg: message_p_v,CMsg2: config256849571t_unit,Trace3: list_message_p_v] :
% 2.87/1.56 ( ( steps_p_s_v @ trans @ sends @ ( last_c571238084t_unit @ Exec3 ) @ Msg @ CMsg2 )
% 2.87/1.56 => ( ( execution_p_s_v @ trans @ sends @ start @ Exec3 @ Trace3 )
% 2.87/1.56 => ? [Exec4: list_c1059388851t_unit,Trace4: list_message_p_v] :
% 2.87/1.56 ( ( execution_p_s_v @ trans @ sends @ start @ Exec4 @ Trace4 )
% 2.87/1.56 & ( prefix1615116500t_unit @ Exec3 @ Exec4 )
% 2.87/1.56 & ( prefix47729710ge_p_v @ Trace3 @ Trace4 )
% 2.87/1.56 & ( ( last_c571238084t_unit @ Exec4 )
% 2.87/1.56 = CMsg2 )
% 2.87/1.56 & ( ( last_message_p_v @ Trace4 )
% 2.87/1.56 = Msg ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_270__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062exec_H_Atrace_H_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_Aexec_H_Atrace_H_059_AprefixList_Aexec_Aexec_H_A_092_060and_062_AprefixList_Atrace_Atrace_H_A_092_060or_062_Aexec_A_061_Aexec_H_A_092_060and_062_Atrace_A_061_Atrace_H_059_Alast_Aexec_H_A_061_Ac_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.87/1.56 ~ ! [Exec2: list_c1059388851t_unit,Trace2: list_message_p_v] :
% 2.87/1.56 ( ( execution_p_s_v @ trans @ sends @ start @ Exec2 @ Trace2 )
% 2.87/1.56 => ( ( ( ( prefix1615116500t_unit @ exec @ Exec2 )
% 2.87/1.56 & ( prefix47729710ge_p_v @ trace @ Trace2 ) )
% 2.87/1.56 | ( ( exec = Exec2 )
% 2.87/1.56 & ( trace = Trace2 ) ) )
% 2.87/1.56 => ( ( last_c571238084t_unit @ Exec2 )
% 2.87/1.56 != c ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_271__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062execMsg_AtraceMsg_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_AexecMsg_AtraceMsg_059_AprefixList_Aexec_H_AexecMsg_059_AprefixList_Atrace_H_AtraceMsg_059_Alast_AexecMsg_A_061_AcMsg_059_Alast_AtraceMsg_A_061_Amsg_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.87/1.56 ~ ! [ExecMsg: list_c1059388851t_unit,TraceMsg: list_message_p_v] :
% 2.87/1.56 ( ( execution_p_s_v @ trans @ sends @ start @ ExecMsg @ TraceMsg )
% 2.87/1.56 => ( ( prefix1615116500t_unit @ exec2 @ ExecMsg )
% 2.87/1.56 => ( ( prefix47729710ge_p_v @ trace2 @ TraceMsg )
% 2.87/1.56 => ( ( ( last_c571238084t_unit @ ExecMsg )
% 2.87/1.56 = cMsg )
% 2.87/1.56 => ( ( last_message_p_v @ TraceMsg )
% 2.87/1.56 != msg ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_272_bot__set__def,axiom,
% 2.87/1.56 ( bot_bot_set_o
% 2.87/1.56 = ( collect_o @ bot_bot_o_o ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_273_asynchronousSystem_OStepOutMsg,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,V2: $o,Cfg2: config256849571t_unit] :
% 2.87/1.56 ~ ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ ( outMsg_p_v @ V2 ) @ Cfg2 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_274_isReceiverOf_Osimps_I3_J,axiom,
% 2.87/1.56 ! [P1: p,V2: $o] :
% 2.87/1.56 ~ ( isReceiverOf_p_v @ P1 @ ( outMsg_p_v @ V2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_275_asynchronousSystem_ONoOutMessageLoss,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,V2: $o] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ ( outMsg_p_v @ V2 ) ) @ ( msgs_p1029620568t_unit @ Cfg2 @ ( outMsg_p_v @ V2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_276_asynchronousSystem_Osteps_Ocong,axiom,
% 2.87/1.56 steps_p_s_v = steps_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_277_asynchronousSystem_OReachableTrans,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,Cfg32: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 2.87/1.56 => ( ( reachable_p_s_v @ Trans @ Sends @ Cfg2 @ Cfg32 )
% 2.87/1.56 => ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg32 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_278_asynchronousSystem_Oreachable_Ocong,axiom,
% 2.87/1.56 reachable_p_s_v = reachable_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_279_asynchronousSystem_Oinit,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit] : ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg1 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_280_UniqueReceiverOf,axiom,
% 2.87/1.56 ! [Q: p,Msg: message_p_v,P: p] :
% 2.87/1.56 ( ( isReceiverOf_p_v @ Q @ Msg )
% 2.87/1.56 => ( ( P != Q )
% 2.87/1.56 => ~ ( isReceiverOf_p_v @ P @ Msg ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_281_asynchronousSystem_OQReachableTrans,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg2: config256849571t_unit,Q2: set_p,Cfg32: config256849571t_unit,Cfg1: config256849571t_unit] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg2 @ Q2 @ Cfg32 )
% 2.87/1.56 => ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.56 => ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_282_asynchronousSystem_OqReachable_Ocong,axiom,
% 2.87/1.56 qReachable_p_s_v = qReachable_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_283_asynchronousSystem_OInitQ,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p] : ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg1 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_284_asynchronousSystem_OinitReachable_Ocong,axiom,
% 2.87/1.56 initReachable_p_s_v = initReachable_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_285_asynchronousSystem_Oinitial_Ocong,axiom,
% 2.87/1.56 initial_p_s_v = initial_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_286_asynchronousSystem_OstepReachable_Ocong,axiom,
% 2.87/1.56 stepReachable_p_s_v = stepReachable_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_287_asynchronousSystem_Ostep,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Cfg2: config256849571t_unit,Msg: message_p_v,Cfg32: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg2 )
% 2.87/1.56 => ( ( steps_p_s_v @ Trans @ Sends @ Cfg2 @ Msg @ Cfg32 )
% 2.87/1.56 => ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg32 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_288_asynchronousSystem_Oreachable_Ocases,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,A1: config256849571t_unit,A2: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ A1 @ A2 )
% 2.87/1.56 => ( ( A2 != A1 )
% 2.87/1.56 => ~ ! [Cfg23: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ A1 @ Cfg23 )
% 2.87/1.56 => ! [Msg3: message_p_v] :
% 2.87/1.56 ~ ( steps_p_s_v @ Trans @ Sends @ Cfg23 @ Msg3 @ A2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_289_asynchronousSystem_Oreachable_Osimps,axiom,
% 2.87/1.56 ( reachable_p_s_v
% 2.87/1.56 = ( ^ [Trans2: p > s > messageValue_v > s,Sends2: p > s > messageValue_v > message_p_v > nat,A12: config256849571t_unit,A22: config256849571t_unit] :
% 2.87/1.56 ( ? [Cfg13: config256849571t_unit] :
% 2.87/1.56 ( ( A12 = Cfg13 )
% 2.87/1.56 & ( A22 = Cfg13 ) )
% 2.87/1.56 | ? [Cfg13: config256849571t_unit,Cfg22: config256849571t_unit,Msg2: message_p_v,Cfg34: config256849571t_unit] :
% 2.87/1.56 ( ( A12 = Cfg13 )
% 2.87/1.56 & ( A22 = Cfg34 )
% 2.87/1.56 & ( reachable_p_s_v @ Trans2 @ Sends2 @ Cfg13 @ Cfg22 )
% 2.87/1.56 & ( steps_p_s_v @ Trans2 @ Sends2 @ Cfg22 @ Msg2 @ Cfg34 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_290_asynchronousSystem_Oreachable_Oinducts,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,X1: config256849571t_unit,X22: config256849571t_unit,P2: config256849571t_unit > config256849571t_unit > $o] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ X1 @ X22 )
% 2.87/1.56 => ( ! [Cfg12: config256849571t_unit] : ( P2 @ Cfg12 @ Cfg12 )
% 2.87/1.56 => ( ! [Cfg12: config256849571t_unit,Cfg23: config256849571t_unit,Msg3: message_p_v,Cfg33: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg12 @ Cfg23 )
% 2.87/1.56 => ( ( P2 @ Cfg12 @ Cfg23 )
% 2.87/1.56 => ( ( steps_p_s_v @ Trans @ Sends @ Cfg23 @ Msg3 @ Cfg33 )
% 2.87/1.56 => ( P2 @ Cfg12 @ Cfg33 ) ) ) )
% 2.87/1.56 => ( P2 @ X1 @ X22 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_291_asynchronousSystem_ODiamondOne,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg: config256849571t_unit,M: message_p_v,Cfg1: config256849571t_unit,P: p,Q: p,M2: message_p_v,Cfg2: config256849571t_unit] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg @ M @ Cfg1 )
% 2.87/1.56 => ( ( P != Q )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ M )
% 2.87/1.56 => ( ~ ( isReceiverOf_p_v @ P @ M2 )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ Q @ M2 )
% 2.87/1.56 => ( ~ ( isReceiverOf_p_v @ Q @ M )
% 2.87/1.56 => ( ( steps_p_s_v @ Trans @ Sends @ Cfg @ M2 @ Cfg2 )
% 2.87/1.56 => ? [Cfg3: config256849571t_unit] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M2 @ Cfg3 )
% 2.87/1.56 & ( steps_p_s_v @ Trans @ Sends @ Cfg2 @ M @ Cfg3 ) ) ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_292_asynchronousSystem_OQReachImplReach,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.56 => ( reachable_p_s_v @ Trans @ Sends @ Cfg1 @ Cfg2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_293_asynchronousSystem_OOnlyOccurenceDisables,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,M2: message_p_v] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.56 => ( ( enabled_p_v_s @ Cfg1 @ M2 )
% 2.87/1.56 => ( ~ ( enabled_p_v_s @ Cfg2 @ M2 )
% 2.87/1.56 => ( M = M2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_294_asynchronousSystem_ONotInQFrozenQReachability,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,P: p] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.56 => ( ~ ( member_p @ P @ Q2 )
% 2.87/1.56 => ( ( states1228886952t_unit @ Cfg1 @ P )
% 2.87/1.56 = ( states1228886952t_unit @ Cfg2 @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_295_asynchronousSystem_OInitialIsInitReachable,axiom,
% 2.87/1.56 ! [Start: p > s,C: config256849571t_unit,Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat] :
% 2.87/1.56 ( ( initial_p_s_v @ Start @ C )
% 2.87/1.56 => ( initReachable_p_s_v @ Trans @ Sends @ Start @ C ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_296_asynchronousSystem_OOtherMessagesOnlyGrowing,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,M2: message_p_v] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.56 => ( ( M != M2 )
% 2.87/1.56 => ( ord_less_eq_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M2 ) @ ( msgs_p1029620568t_unit @ Cfg2 @ M2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_297_asynchronousSystem_OStepQ,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,Q2: set_p,Cfg2: config256849571t_unit,Msg: message_p_v,Cfg32: config256849571t_unit] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg2 )
% 2.87/1.56 => ( ( steps_p_s_v @ Trans @ Sends @ Cfg2 @ Msg @ Cfg32 )
% 2.87/1.56 => ( ? [X4: p] :
% 2.87/1.56 ( ( member_p @ X4 @ Q2 )
% 2.87/1.56 & ( isReceiverOf_p_v @ X4 @ Msg ) )
% 2.87/1.56 => ( qReachable_p_s_v @ Trans @ Sends @ Cfg1 @ Q2 @ Cfg32 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_298_asynchronousSystem_OqReachable_Ocases,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,A1: config256849571t_unit,A2: set_p,A3: config256849571t_unit] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans @ Sends @ A1 @ A2 @ A3 )
% 2.87/1.56 => ( ( A3 != A1 )
% 2.87/1.56 => ~ ! [Cfg23: config256849571t_unit] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans @ Sends @ A1 @ A2 @ Cfg23 )
% 2.87/1.56 => ! [Msg3: message_p_v] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg23 @ Msg3 @ A3 )
% 2.87/1.56 => ~ ? [X: p] :
% 2.87/1.56 ( ( member_p @ X @ A2 )
% 2.87/1.56 & ( isReceiverOf_p_v @ X @ Msg3 ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_299_asynchronousSystem_OqReachable_Osimps,axiom,
% 2.87/1.56 ( qReachable_p_s_v
% 2.87/1.56 = ( ^ [Trans2: p > s > messageValue_v > s,Sends2: p > s > messageValue_v > message_p_v > nat,A12: config256849571t_unit,A22: set_p,A32: config256849571t_unit] :
% 2.87/1.56 ( ( A32 = A12 )
% 2.87/1.56 | ? [Cfg22: config256849571t_unit] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans2 @ Sends2 @ A12 @ A22 @ Cfg22 )
% 2.87/1.56 & ? [Msg2: message_p_v] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans2 @ Sends2 @ Cfg22 @ Msg2 @ A32 )
% 2.87/1.56 & ? [X3: p] :
% 2.87/1.56 ( ( member_p @ X3 @ A22 )
% 2.87/1.56 & ( isReceiverOf_p_v @ X3 @ Msg2 ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_300_asynchronousSystem_OqReachable_Oinducts,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,X1: config256849571t_unit,X22: set_p,X32: config256849571t_unit,P2: config256849571t_unit > set_p > config256849571t_unit > $o] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans @ Sends @ X1 @ X22 @ X32 )
% 2.87/1.56 => ( ! [Cfg12: config256849571t_unit,Q3: set_p] : ( P2 @ Cfg12 @ Q3 @ Cfg12 )
% 2.87/1.56 => ( ! [Cfg12: config256849571t_unit,Q3: set_p,Cfg23: config256849571t_unit] :
% 2.87/1.56 ( ( qReachable_p_s_v @ Trans @ Sends @ Cfg12 @ Q3 @ Cfg23 )
% 2.87/1.56 => ( ( P2 @ Cfg12 @ Q3 @ Cfg23 )
% 2.87/1.56 => ! [Msg3: message_p_v,Cfg33: config256849571t_unit] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg23 @ Msg3 @ Cfg33 )
% 2.87/1.56 => ( ? [X: p] :
% 2.87/1.56 ( ( member_p @ X @ Q3 )
% 2.87/1.56 & ( isReceiverOf_p_v @ X @ Msg3 ) )
% 2.87/1.56 => ( P2 @ Cfg12 @ Q3 @ Cfg33 ) ) ) ) )
% 2.87/1.56 => ( P2 @ X1 @ X22 @ X32 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_301_asynchronousSystem_ONoReceivingNoChange,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit,P: p] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.56 => ( ~ ( isReceiverOf_p_v @ P @ M )
% 2.87/1.56 => ( ( states1228886952t_unit @ Cfg1 @ P )
% 2.87/1.56 = ( states1228886952t_unit @ Cfg2 @ P ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_302_asynchronousSystem_OinitReachable__def,axiom,
% 2.87/1.56 ( initReachable_p_s_v
% 2.87/1.56 = ( ^ [Trans2: p > s > messageValue_v > s,Sends2: p > s > messageValue_v > message_p_v > nat,Start2: p > s,Cfg5: config256849571t_unit] :
% 2.87/1.56 ? [Cfg0: config256849571t_unit] :
% 2.87/1.56 ( ( initial_p_s_v @ Start2 @ Cfg0 )
% 2.87/1.56 & ( reachable_p_s_v @ Trans2 @ Sends2 @ Cfg0 @ Cfg5 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_303_asynchronousSystem_OstepReachable__def,axiom,
% 2.87/1.56 ( stepReachable_p_s_v
% 2.87/1.56 = ( ^ [Trans2: p > s > messageValue_v > s,Sends2: p > s > messageValue_v > message_p_v > nat,C12: config256849571t_unit,Msg2: message_p_v,C23: config256849571t_unit] :
% 2.87/1.56 ? [C4: config256849571t_unit,C5: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans2 @ Sends2 @ C12 @ C4 )
% 2.87/1.56 & ( steps_p_s_v @ Trans2 @ Sends2 @ C4 @ Msg2 @ C5 )
% 2.87/1.56 & ( reachable_p_s_v @ Trans2 @ Sends2 @ C5 @ C23 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_304_asynchronousSystem_OStepReachable,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg: config256849571t_unit,Cfg4: config256849571t_unit,Msg: message_p_v] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ Cfg @ Cfg4 )
% 2.87/1.56 => ( ( enabled_p_v_s @ Cfg @ Msg )
% 2.87/1.56 => ( ~ ( enabled_p_v_s @ Cfg4 @ Msg )
% 2.87/1.56 => ( stepReachable_p_s_v @ Trans @ Sends @ Cfg @ Msg @ Cfg4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_305_asynchronousSystem_OexpandExecutionStep,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Exec3: list_c1059388851t_unit,Msg: message_p_v,CMsg2: config256849571t_unit,Start: p > s,Trace3: list_message_p_v] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ ( last_c571238084t_unit @ Exec3 ) @ Msg @ CMsg2 )
% 2.87/1.56 => ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec3 @ Trace3 )
% 2.87/1.56 => ? [Exec4: list_c1059388851t_unit,Trace4: list_message_p_v] :
% 2.87/1.56 ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec4 @ Trace4 )
% 2.87/1.56 & ( prefix1615116500t_unit @ Exec3 @ Exec4 )
% 2.87/1.56 & ( prefix47729710ge_p_v @ Trace3 @ Trace4 )
% 2.87/1.56 & ( ( last_c571238084t_unit @ Exec4 )
% 2.87/1.56 = CMsg2 )
% 2.87/1.56 & ( ( last_message_p_v @ Trace4 )
% 2.87/1.56 = Msg ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_306_asynchronousSystem_OexpandExecutionReachable,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,CfgLast: config256849571t_unit,Cfg: config256849571t_unit,Start: p > s,Exec: list_c1059388851t_unit,Trace: list_message_p_v] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ CfgLast @ Cfg )
% 2.87/1.56 => ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec @ Trace )
% 2.87/1.56 => ( ( CfgLast
% 2.87/1.56 = ( last_c571238084t_unit @ Exec ) )
% 2.87/1.56 => ? [Exec2: list_c1059388851t_unit,Trace2: list_message_p_v] :
% 2.87/1.56 ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec2 @ Trace2 )
% 2.87/1.56 & ( ( ( prefix1615116500t_unit @ Exec @ Exec2 )
% 2.87/1.56 & ( prefix47729710ge_p_v @ Trace @ Trace2 ) )
% 2.87/1.56 | ( ( Exec = Exec2 )
% 2.87/1.56 & ( Trace = Trace2 ) ) )
% 2.87/1.56 & ( ( last_c571238084t_unit @ Exec2 )
% 2.87/1.56 = Cfg ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_307_NonUniformCanReachSilentBivalence,axiom,
% 2.87/1.56 ! [C: config256849571t_unit,P: p] :
% 2.87/1.56 ( ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ C )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ C ) )
% 2.87/1.56 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 2.87/1.56 => ( ! [Cfg6: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ C @ Cfg6 )
% 2.87/1.56 => ( agreement_p_v_s @ Cfg6 ) )
% 2.87/1.56 => ? [C6: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ C @ C6 )
% 2.87/1.56 & ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ P @ C6 ) )
% 2.87/1.56 = ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_308_PseudoTermination,axiom,
% 2.87/1.56 ! [Cc2: config256849571t_unit,Q2: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc2 @ Q2 ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_309_DecisionValuesExist,axiom,
% 2.87/1.56 ! [C: config256849571t_unit,P: p] :
% 2.87/1.56 ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 2.87/1.56 => ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 2.87/1.56 => ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ P @ C ) )
% 2.87/1.56 != bot_bot_set_o ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_310_InitialNonUniformCfg,axiom,
% 2.87/1.56 ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 2.87/1.56 => ( ! [I2: config256849571t_unit,X_1: config256849571t_unit] : ( validity_p_s_v @ trans @ sends @ start @ I2 @ X_1 )
% 2.87/1.56 => ( ! [I2: config256849571t_unit,X_1: config256849571t_unit] : ( agreementInit_p_s_v @ trans @ sends @ start @ I2 @ X_1 )
% 2.87/1.56 => ? [Cfg6: config256849571t_unit] :
% 2.87/1.56 ( ( initial_p_s_v @ start @ Cfg6 )
% 2.87/1.56 & ( initReachable_p_s_v @ trans @ sends @ start @ Cfg6 )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ Cfg6 )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ Cfg6 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_311_flpPseudoConsensus_OPseudoTermination,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cc2: config256849571t_unit,Q2: set_p] :
% 2.87/1.56 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 2.87/1.56 => ( termin1618267753_p_s_v @ Trans @ Sends @ Start @ one_one_nat @ Cc2 @ Q2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_312_flpSystem_OterminationPseudo_Ocong,axiom,
% 2.87/1.56 termin1618267753_p_s_v = termin1618267753_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_313_flpSystem_ODecisionValuesExist,axiom,
% 2.87/1.56 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s,C: config256849571t_unit,P: p] :
% 2.87/1.56 ( ( flpSystem_p_s_v @ Sends )
% 2.87/1.56 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ Trans @ Sends @ Start @ one_one_nat @ Cc @ X_1 )
% 2.87/1.56 => ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 2.87/1.56 => ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ P @ C ) )
% 2.87/1.56 != bot_bot_set_o ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_314_flpSystem_ONonUniformCanReachSilentBivalence,axiom,
% 2.87/1.56 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s,C: config256849571t_unit,P: p] :
% 2.87/1.56 ( ( flpSystem_p_s_v @ Sends )
% 2.87/1.56 => ( ( ( initReachable_p_s_v @ Trans @ Sends @ Start @ C )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ Trans @ Sends @ Start @ $false @ C )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ Trans @ Sends @ Start @ $true @ C ) )
% 2.87/1.56 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ Trans @ Sends @ Start @ one_one_nat @ Cc @ X_1 )
% 2.87/1.56 => ( ! [Cfg6: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ C @ Cfg6 )
% 2.87/1.56 => ( agreement_p_v_s @ Cfg6 ) )
% 2.87/1.56 => ? [C6: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ Trans @ Sends @ C @ C6 )
% 2.87/1.56 & ( ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ Trans @ Sends @ Start @ V @ P @ C6 ) )
% 2.87/1.56 = ( insert_o @ $true @ ( insert_o @ $false @ bot_bot_set_o ) ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_315_flpSystem_OInitialNonUniformCfg,axiom,
% 2.87/1.56 ! [Sends: p > s > messageValue_v > message_p_v > nat,Trans: p > s > messageValue_v > s,Start: p > s] :
% 2.87/1.56 ( ( flpSystem_p_s_v @ Sends )
% 2.87/1.56 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ Trans @ Sends @ Start @ one_one_nat @ Cc @ X_1 )
% 2.87/1.56 => ( ! [I2: config256849571t_unit,X_1: config256849571t_unit] : ( validity_p_s_v @ Trans @ Sends @ Start @ I2 @ X_1 )
% 2.87/1.56 => ( ! [I2: config256849571t_unit,X_1: config256849571t_unit] : ( agreementInit_p_s_v @ Trans @ Sends @ Start @ I2 @ X_1 )
% 2.87/1.56 => ? [Cfg6: config256849571t_unit] :
% 2.87/1.56 ( ( initial_p_s_v @ Start @ Cfg6 )
% 2.87/1.56 & ( initReachable_p_s_v @ Trans @ Sends @ Start @ Cfg6 )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ Trans @ Sends @ Start @ $false @ Cfg6 )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ Trans @ Sends @ Start @ $true @ Cfg6 ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_316_execution_OExistImpliesMinEnabled,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Exec: list_c1059388851t_unit,Trace: list_message_p_v,P: p,Msg: message_p_v] :
% 2.87/1.56 ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec @ Trace )
% 2.87/1.56 => ( ( isReceiverOf_p_v @ P @ Msg )
% 2.87/1.56 => ( ( enabled_p_v_s @ ( last_c571238084t_unit @ Exec ) @ Msg )
% 2.87/1.56 => ? [X_1: message_p_v] : ( minimalEnabled_p_v_s @ Exec @ Trace @ X_1 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_317_flpSystem_Ovalidity_Ocong,axiom,
% 2.87/1.56 validity_p_s_v = validity_p_s_v ).
% 2.87/1.56
% 2.87/1.56 thf(fact_318_execution_OFirstOccurrenceExists,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Exec: list_c1059388851t_unit,Trace: list_message_p_v,Msg: message_p_v] :
% 2.87/1.56 ( ( execution_p_s_v @ Trans @ Sends @ Start @ Exec @ Trace )
% 2.87/1.56 => ( ( enabled_p_v_s @ ( last_c571238084t_unit @ Exec ) @ Msg )
% 2.87/1.56 => ( ? [P5: p] : ( isReceiverOf_p_v @ P5 @ Msg )
% 2.87/1.56 => ? [X_1: nat] : ( firstO1414030372_p_v_s @ Exec @ Trace @ Msg @ X_1 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_319_NonUniformImpliesNotDecided,axiom,
% 2.87/1.56 ! [C: config256849571t_unit,V2: $o] :
% 2.87/1.56 ( ! [Cfg6: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ C @ Cfg6 )
% 2.87/1.56 => ( agreement_p_v_s @ Cfg6 ) )
% 2.87/1.56 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 2.87/1.56 => ( ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $false @ C )
% 2.87/1.56 & ~ ( vUniform_p_s_v @ trans @ sends @ start @ $true @ C ) )
% 2.87/1.56 => ~ ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 2.87/1.56 & ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V2 ) ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_320_agreement__def,axiom,
% 2.87/1.56 ( agreement_p_v_s
% 2.87/1.56 = ( ^ [C8: config256849571t_unit] :
% 2.87/1.56 ! [V1: $o] :
% 2.87/1.56 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C8 @ ( outMsg_p_v @ V1 ) ) )
% 2.87/1.56 => ! [V22: $o] :
% 2.87/1.56 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C8 @ ( outMsg_p_v @ V22 ) ) )
% 2.87/1.56 = ( V22 = V1 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_321_ExistsMsg,axiom,
% 2.87/1.56 ! [Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit] :
% 2.87/1.56 ( ( steps_p_s_v @ trans @ sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.56 => ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_322_agreementInit__def,axiom,
% 2.87/1.56 ! [I: config256849571t_unit,C: config256849571t_unit] :
% 2.87/1.56 ( ( agreementInit_p_s_v @ trans @ sends @ start @ I @ C )
% 2.87/1.56 = ( ( ( initial_p_s_v @ start @ I )
% 2.87/1.56 & ( reachable_p_s_v @ trans @ sends @ I @ C ) )
% 2.87/1.56 => ! [V1: $o] :
% 2.87/1.56 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V1 ) ) )
% 2.87/1.56 => ! [V22: $o] :
% 2.87/1.56 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V22 ) ) )
% 2.87/1.56 = ( V22 = V1 ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_323_DecidedImpliesUniform,axiom,
% 2.87/1.56 ! [C: config256849571t_unit,V2: $o] :
% 2.87/1.56 ( ! [Cfg6: config256849571t_unit] :
% 2.87/1.56 ( ( reachable_p_s_v @ trans @ sends @ C @ Cfg6 )
% 2.87/1.56 => ( agreement_p_v_s @ Cfg6 ) )
% 2.87/1.56 => ( ! [Cc: config256849571t_unit,X_1: set_p] : ( termin1618267753_p_s_v @ trans @ sends @ start @ one_one_nat @ Cc @ X_1 )
% 2.87/1.56 => ( ( ( initReachable_p_s_v @ trans @ sends @ start @ C )
% 2.87/1.56 & ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V2 ) ) ) )
% 2.87/1.56 => ( vUniform_p_s_v @ trans @ sends @ start @ V2 @ C ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_324_flpSystem_Oagreement__def,axiom,
% 2.87/1.56 ! [Sends: p > s > messageValue_v > message_p_v > nat,C: config256849571t_unit] :
% 2.87/1.56 ( ( flpSystem_p_s_v @ Sends )
% 2.87/1.56 => ( ( agreement_p_v_s @ C )
% 2.87/1.56 = ( ! [V1: $o] :
% 2.87/1.56 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V1 ) ) )
% 2.87/1.56 => ! [V22: $o] :
% 2.87/1.56 ( ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ C @ ( outMsg_p_v @ V22 ) ) )
% 2.87/1.56 = ( V22 = V1 ) ) ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_325_enabled__def,axiom,
% 2.87/1.56 ( enabled_p_v_s
% 2.87/1.56 = ( ^ [Cfg5: config256849571t_unit,Msg2: message_p_v] : ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ Cfg5 @ Msg2 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_326_asynchronousSystem_OExistsMsg,axiom,
% 2.87/1.56 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Cfg1: config256849571t_unit,M: message_p_v,Cfg2: config256849571t_unit] :
% 2.87/1.56 ( ( steps_p_s_v @ Trans @ Sends @ Cfg1 @ M @ Cfg2 )
% 2.87/1.56 => ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ Cfg1 @ M ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_327_order_Onot__eq__order__implies__strict,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o] :
% 2.87/1.56 ( ( A5 != B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ord_less_set_o @ A5 @ B3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_328_order_Onot__eq__order__implies__strict,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat] :
% 2.87/1.56 ( ( A5 != B3 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( ord_less_nat @ A5 @ B3 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_329_dual__order_Ostrict__implies__order,axiom,
% 2.87/1.56 ! [B3: set_o,A5: set_o] :
% 2.87/1.56 ( ( ord_less_set_o @ B3 @ A5 )
% 2.87/1.56 => ( ord_less_eq_set_o @ B3 @ A5 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_330_dual__order_Ostrict__implies__order,axiom,
% 2.87/1.56 ! [B3: nat,A5: nat] :
% 2.87/1.56 ( ( ord_less_nat @ B3 @ A5 )
% 2.87/1.56 => ( ord_less_eq_nat @ B3 @ A5 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_331_dual__order_Ostrict__iff__order,axiom,
% 2.87/1.56 ( ord_less_set_o
% 2.87/1.56 = ( ^ [B4: set_o,A6: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ B4 @ A6 )
% 2.87/1.56 & ( A6 != B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_332_dual__order_Ostrict__iff__order,axiom,
% 2.87/1.56 ( ord_less_nat
% 2.87/1.56 = ( ^ [B4: nat,A6: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ B4 @ A6 )
% 2.87/1.56 & ( A6 != B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_333_dual__order_Oorder__iff__strict,axiom,
% 2.87/1.56 ( ord_less_eq_set_o
% 2.87/1.56 = ( ^ [B4: set_o,A6: set_o] :
% 2.87/1.56 ( ( ord_less_set_o @ B4 @ A6 )
% 2.87/1.56 | ( A6 = B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_334_dual__order_Oorder__iff__strict,axiom,
% 2.87/1.56 ( ord_less_eq_nat
% 2.87/1.56 = ( ^ [B4: nat,A6: nat] :
% 2.87/1.56 ( ( ord_less_nat @ B4 @ A6 )
% 2.87/1.56 | ( A6 = B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_335_order_Ostrict__implies__order,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o] :
% 2.87/1.56 ( ( ord_less_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ord_less_eq_set_o @ A5 @ B3 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_336_order_Ostrict__implies__order,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat] :
% 2.87/1.56 ( ( ord_less_nat @ A5 @ B3 )
% 2.87/1.56 => ( ord_less_eq_nat @ A5 @ B3 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_337_dual__order_Ostrict__trans2,axiom,
% 2.87/1.56 ! [B3: set_o,A5: set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_set_o @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ C @ B3 )
% 2.87/1.56 => ( ord_less_set_o @ C @ A5 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_338_dual__order_Ostrict__trans2,axiom,
% 2.87/1.56 ! [B3: nat,A5: nat,C: nat] :
% 2.87/1.56 ( ( ord_less_nat @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ C @ B3 )
% 2.87/1.56 => ( ord_less_nat @ C @ A5 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_339_dual__order_Ostrict__trans1,axiom,
% 2.87/1.56 ! [B3: set_o,A5: set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_set_o @ C @ B3 )
% 2.87/1.56 => ( ord_less_set_o @ C @ A5 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_340_dual__order_Ostrict__trans1,axiom,
% 2.87/1.56 ! [B3: nat,A5: nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ B3 @ A5 )
% 2.87/1.56 => ( ( ord_less_nat @ C @ B3 )
% 2.87/1.56 => ( ord_less_nat @ C @ A5 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_341_order_Ostrict__iff__order,axiom,
% 2.87/1.56 ( ord_less_set_o
% 2.87/1.56 = ( ^ [A6: set_o,B4: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A6 @ B4 )
% 2.87/1.56 & ( A6 != B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_342_order_Ostrict__iff__order,axiom,
% 2.87/1.56 ( ord_less_nat
% 2.87/1.56 = ( ^ [A6: nat,B4: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A6 @ B4 )
% 2.87/1.56 & ( A6 != B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_343_order_Oorder__iff__strict,axiom,
% 2.87/1.56 ( ord_less_eq_set_o
% 2.87/1.56 = ( ^ [A6: set_o,B4: set_o] :
% 2.87/1.56 ( ( ord_less_set_o @ A6 @ B4 )
% 2.87/1.56 | ( A6 = B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_344_order_Oorder__iff__strict,axiom,
% 2.87/1.56 ( ord_less_eq_nat
% 2.87/1.56 = ( ^ [A6: nat,B4: nat] :
% 2.87/1.56 ( ( ord_less_nat @ A6 @ B4 )
% 2.87/1.56 | ( A6 = B4 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_345_order_Ostrict__trans2,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_set_o @ B3 @ C )
% 2.87/1.56 => ( ord_less_set_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_346_order_Ostrict__trans2,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat,C: nat] :
% 2.87/1.56 ( ( ord_less_nat @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_eq_nat @ B3 @ C )
% 2.87/1.56 => ( ord_less_nat @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_347_order_Ostrict__trans1,axiom,
% 2.87/1.56 ! [A5: set_o,B3: set_o,C: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_set_o @ B3 @ C )
% 2.87/1.56 => ( ord_less_set_o @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_348_order_Ostrict__trans1,axiom,
% 2.87/1.56 ! [A5: nat,B3: nat,C: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ A5 @ B3 )
% 2.87/1.56 => ( ( ord_less_nat @ B3 @ C )
% 2.87/1.56 => ( ord_less_nat @ A5 @ C ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_349_not__le__imp__less,axiom,
% 2.87/1.56 ! [Y2: nat,X2: nat] :
% 2.87/1.56 ( ~ ( ord_less_eq_nat @ Y2 @ X2 )
% 2.87/1.56 => ( ord_less_nat @ X2 @ Y2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_350_less__le__not__le,axiom,
% 2.87/1.56 ( ord_less_set_o
% 2.87/1.56 = ( ^ [X3: set_o,Y3: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X3 @ Y3 )
% 2.87/1.56 & ~ ( ord_less_eq_set_o @ Y3 @ X3 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_351_less__le__not__le,axiom,
% 2.87/1.56 ( ord_less_nat
% 2.87/1.56 = ( ^ [X3: nat,Y3: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.87/1.56 & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_352_le__imp__less__or__eq,axiom,
% 2.87/1.56 ! [X2: set_o,Y2: set_o] :
% 2.87/1.56 ( ( ord_less_eq_set_o @ X2 @ Y2 )
% 2.87/1.56 => ( ( ord_less_set_o @ X2 @ Y2 )
% 2.87/1.56 | ( X2 = Y2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_353_le__imp__less__or__eq,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.87/1.56 => ( ( ord_less_nat @ X2 @ Y2 )
% 2.87/1.56 | ( X2 = Y2 ) ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(fact_354_le__less__linear,axiom,
% 2.87/1.56 ! [X2: nat,Y2: nat] :
% 2.87/1.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 2.87/1.56 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 2.87/1.56
% 2.87/1.56 thf(conj_0,conjecture,
% 2.87/1.56 ( ord_less_eq_set_o
% 2.87/1.56 @ ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ ( last_c571238084t_unit @ exec2 ) ) )
% 2.87/1.56 @ ( collect_o
% 2.87/1.56 @ ^ [V: $o] : ( pSilDecVal_p_s_v @ trans @ sends @ start @ V @ p2 @ cMsg ) ) ) ).
% 2.87/1.56 ------------------------
% 2.87/1.60 % (12920)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_12819 for (2999ds/27Mi)
% 2.96/1.60 % (12922)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_12819 for (2999ds/2Mi)
% 2.96/1.60 % (12923)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_12819 for (2999ds/275Mi)
% 2.96/1.60 % (12924)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/18Mi)
% 2.96/1.60 % (12922)Instruction limit reached!
% 2.96/1.60 % (12922)------------------------------
% 2.96/1.60 % (12922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.60 % (12922)Termination reason: Unknown
% 2.96/1.60 % (12922)Termination phase: shuffling
% 2.96/1.60
% 2.96/1.60 % (12922)Memory used [KB]: 1407
% 2.96/1.60 % (12922)Time elapsed: 0.002 s
% 2.96/1.60 % (12922)Instructions burned: 3 (million)
% 2.96/1.60 % (12922)------------------------------
% 2.96/1.60 % (12922)------------------------------
% 2.96/1.60 % (12918)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/183Mi)
% 2.96/1.60 % (12919)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_12819 for (2999ds/4Mi)
% 2.96/1.60 % (12921)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/2Mi)
% 2.96/1.60 % (12920)Instruction limit reached!
% 2.96/1.60 % (12920)------------------------------
% 2.96/1.60 % (12920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.60 % (12920)Termination reason: Unknown
% 2.96/1.60 % (12920)Termination phase: shuffling
% 2.96/1.60
% 2.96/1.60 % (12920)Memory used [KB]: 1791
% 2.96/1.60 % (12920)Time elapsed: 0.010 s
% 2.96/1.60 % (12920)Instructions burned: 27 (million)
% 2.96/1.60 % (12920)------------------------------
% 2.96/1.60 % (12920)------------------------------
% 2.96/1.60 % (12924)Instruction limit reached!
% 2.96/1.60 % (12924)------------------------------
% 2.96/1.60 % (12924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.60 % (12924)Termination reason: Unknown
% 2.96/1.60 % (12924)Termination phase: shuffling
% 2.96/1.60
% 2.96/1.60 % (12924)Memory used [KB]: 1791
% 2.96/1.60 % (12924)Time elapsed: 0.008 s
% 2.96/1.60 % (12924)Instructions burned: 20 (million)
% 2.96/1.60 % (12924)------------------------------
% 2.96/1.60 % (12924)------------------------------
% 2.96/1.61 % (12919)Instruction limit reached!
% 2.96/1.61 % (12919)------------------------------
% 2.96/1.61 % (12919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.61 % (12919)Termination reason: Unknown
% 2.96/1.61 % (12919)Termination phase: shuffling
% 2.96/1.61
% 2.96/1.61 % (12919)Memory used [KB]: 1535
% 2.96/1.61 % (12919)Time elapsed: 0.004 s
% 2.96/1.61 % (12919)Instructions burned: 4 (million)
% 2.96/1.61 % (12919)------------------------------
% 2.96/1.61 % (12919)------------------------------
% 2.96/1.61 % (12921)Instruction limit reached!
% 2.96/1.61 % (12921)------------------------------
% 2.96/1.61 % (12921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.61 % (12921)Termination reason: Unknown
% 2.96/1.61 % (12921)Termination phase: shuffling
% 2.96/1.61
% 2.96/1.61 % (12921)Memory used [KB]: 1407
% 2.96/1.61 % (12921)Time elapsed: 0.004 s
% 2.96/1.61 % (12921)Instructions burned: 3 (million)
% 2.96/1.61 % (12921)------------------------------
% 2.96/1.61 % (12921)------------------------------
% 2.96/1.61 % (12925)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/3Mi)
% 2.96/1.61 % (12925)Instruction limit reached!
% 2.96/1.61 % (12925)------------------------------
% 2.96/1.61 % (12925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.61 % (12925)Termination reason: Unknown
% 2.96/1.61 % (12925)Termination phase: shuffling
% 2.96/1.61
% 2.96/1.61 % (12925)Memory used [KB]: 1535
% 2.96/1.61 % (12925)Time elapsed: 0.003 s
% 2.96/1.61 % (12925)Instructions burned: 3 (million)
% 2.96/1.61 % (12925)------------------------------
% 2.96/1.61 % (12925)------------------------------
% 2.96/1.61 % (12926)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_12819 for (2999ds/37Mi)
% 2.96/1.61 % (12927)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_12819 for (2999ds/15Mi)
% 2.96/1.62 % (12930)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/7Mi)
% 2.96/1.62 % (12927)Instruction limit reached!
% 2.96/1.62 % (12927)------------------------------
% 2.96/1.62 % (12927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.62 % (12927)Termination reason: Unknown
% 2.96/1.62 % (12927)Termination phase: shuffling
% 2.96/1.62
% 2.96/1.62 % (12927)Memory used [KB]: 1663
% 2.96/1.62 % (12927)Time elapsed: 0.007 s
% 2.96/1.62 % (12927)Instructions burned: 16 (million)
% 2.96/1.62 % (12927)------------------------------
% 2.96/1.62 % (12927)------------------------------
% 2.96/1.62 % (12930)Instruction limit reached!
% 2.96/1.62 % (12930)------------------------------
% 2.96/1.62 % (12930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.62 % (12930)Termination reason: Unknown
% 2.96/1.62 % (12930)Termination phase: shuffling
% 2.96/1.62
% 2.96/1.62 % (12930)Memory used [KB]: 1535
% 2.96/1.62 % (12930)Time elapsed: 0.005 s
% 2.96/1.62 % (12930)Instructions burned: 9 (million)
% 2.96/1.62 % (12930)------------------------------
% 2.96/1.62 % (12930)------------------------------
% 2.96/1.62 % (12928)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_12819 for (2999ds/3Mi)
% 2.96/1.62 % (12929)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_12819 for (2999ds/1041Mi)
% 2.96/1.62 % (12926)Instruction limit reached!
% 2.96/1.62 % (12926)------------------------------
% 2.96/1.62 % (12926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.62 % (12926)Termination reason: Unknown
% 2.96/1.62 % (12926)Termination phase: shuffling
% 2.96/1.62
% 2.96/1.62 % (12926)Memory used [KB]: 2302
% 2.96/1.62 % (12926)Time elapsed: 0.011 s
% 2.96/1.62 % (12926)Instructions burned: 38 (million)
% 2.96/1.62 % (12926)------------------------------
% 2.96/1.62 % (12926)------------------------------
% 2.96/1.63 % (12928)Instruction limit reached!
% 2.96/1.63 % (12928)------------------------------
% 2.96/1.63 % (12928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.63 % (12928)Termination reason: Unknown
% 2.96/1.63 % (12928)Termination phase: shuffling
% 2.96/1.63
% 2.96/1.63 % (12928)Memory used [KB]: 1535
% 2.96/1.63 % (12928)Time elapsed: 0.004 s
% 2.96/1.63 % (12928)Instructions burned: 3 (million)
% 2.96/1.63 % (12928)------------------------------
% 2.96/1.63 % (12928)------------------------------
% 2.96/1.63 % (12931)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/16Mi)
% 2.96/1.63 % (12932)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_12819 for (2999ds/3Mi)
% 2.96/1.63 % (12933)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_12819 for (2999ds/3Mi)
% 2.96/1.63 % (12932)Instruction limit reached!
% 2.96/1.63 % (12932)------------------------------
% 2.96/1.63 % (12932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.63 % (12932)Termination reason: Unknown
% 2.96/1.63 % (12932)Termination phase: shuffling
% 2.96/1.63
% 2.96/1.63 % (12932)Memory used [KB]: 1535
% 2.96/1.63 % (12932)Time elapsed: 0.003 s
% 2.96/1.63 % (12932)Instructions burned: 3 (million)
% 2.96/1.63 % (12932)------------------------------
% 2.96/1.63 % (12932)------------------------------
% 2.96/1.63 % (12933)Instruction limit reached!
% 2.96/1.63 % (12933)------------------------------
% 2.96/1.63 % (12933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.63 % (12933)Termination reason: Unknown
% 2.96/1.63 % (12933)Termination phase: shuffling
% 2.96/1.63
% 2.96/1.63 % (12933)Memory used [KB]: 1535
% 2.96/1.63 % (12933)Time elapsed: 0.002 s
% 2.96/1.63 % (12933)Instructions burned: 3 (million)
% 2.96/1.63 % (12933)------------------------------
% 2.96/1.63 % (12933)------------------------------
% 2.96/1.63 % (12931)Instruction limit reached!
% 2.96/1.63 % (12931)------------------------------
% 2.96/1.63 % (12931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.63 % (12931)Termination reason: Unknown
% 2.96/1.63 % (12931)Termination phase: shuffling
% 2.96/1.63
% 2.96/1.63 % (12931)Memory used [KB]: 1663
% 2.96/1.63 % (12931)Time elapsed: 0.006 s
% 2.96/1.63 % (12931)Instructions burned: 16 (million)
% 2.96/1.63 % (12931)------------------------------
% 2.96/1.63 % (12931)------------------------------
% 2.96/1.64 % (12934)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/7Mi)
% 2.96/1.64 % (12935)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/3Mi)
% 2.96/1.64 % (12936)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/4Mi)
% 2.96/1.64 % (12937)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/18Mi)
% 2.96/1.65 % (12935)Instruction limit reached!
% 2.96/1.65 % (12935)------------------------------
% 2.96/1.65 % (12935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.65 % (12935)Termination reason: Unknown
% 2.96/1.65 % (12935)Termination phase: shuffling
% 2.96/1.65
% 2.96/1.65 % (12935)Memory used [KB]: 1535
% 2.96/1.65 % (12935)Time elapsed: 0.003 s
% 2.96/1.65 % (12935)Instructions burned: 6 (million)
% 2.96/1.65 % (12935)------------------------------
% 2.96/1.65 % (12935)------------------------------
% 2.96/1.65 % (12936)Instruction limit reached!
% 2.96/1.65 % (12936)------------------------------
% 2.96/1.65 % (12936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.65 % (12936)Termination reason: Unknown
% 2.96/1.65 % (12936)Termination phase: shuffling
% 2.96/1.65
% 2.96/1.65 % (12936)Memory used [KB]: 1535
% 2.96/1.65 % (12936)Time elapsed: 0.003 s
% 2.96/1.65 % (12936)Instructions burned: 6 (million)
% 2.96/1.65 % (12936)------------------------------
% 2.96/1.65 % (12936)------------------------------
% 2.96/1.65 % (12934)Instruction limit reached!
% 2.96/1.65 % (12934)------------------------------
% 2.96/1.65 % (12934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.65 % (12934)Termination reason: Unknown
% 2.96/1.65 % (12934)Termination phase: shuffling
% 2.96/1.65
% 2.96/1.65 % (12934)Memory used [KB]: 1535
% 2.96/1.65 % (12934)Time elapsed: 0.007 s
% 2.96/1.65 % (12934)Instructions burned: 8 (million)
% 2.96/1.65 % (12934)------------------------------
% 2.96/1.65 % (12934)------------------------------
% 2.96/1.65 % (12937)Instruction limit reached!
% 2.96/1.65 % (12937)------------------------------
% 2.96/1.65 % (12937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.65 % (12937)Termination reason: Unknown
% 2.96/1.65 % (12937)Termination phase: shuffling
% 2.96/1.65
% 2.96/1.65 % (12937)Memory used [KB]: 1791
% 2.96/1.65 % (12937)Time elapsed: 0.007 s
% 2.96/1.65 % (12937)Instructions burned: 19 (million)
% 2.96/1.65 % (12937)------------------------------
% 2.96/1.65 % (12937)------------------------------
% 2.96/1.65 % (12938)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/710Mi)
% 2.96/1.65 % (12939)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/6Mi)
% 2.96/1.66 % (12939)Instruction limit reached!
% 2.96/1.66 % (12939)------------------------------
% 2.96/1.66 % (12939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.66 % (12939)Termination reason: Unknown
% 2.96/1.66 % (12939)Termination phase: shuffling
% 2.96/1.66
% 2.96/1.66 % (12939)Memory used [KB]: 1535
% 2.96/1.66 % (12939)Time elapsed: 0.003 s
% 2.96/1.66 % (12939)Instructions burned: 6 (million)
% 2.96/1.66 % (12939)------------------------------
% 2.96/1.66 % (12939)------------------------------
% 2.96/1.66 % (12940)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_12819 for (2999ds/902Mi)
% 2.96/1.66 % (12918)Instruction limit reached!
% 2.96/1.66 % (12918)------------------------------
% 2.96/1.66 % (12918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.66 % (12941)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_12819 for (2999ds/21Mi)
% 2.96/1.66 % (12918)Termination reason: Unknown
% 2.96/1.66 % (12918)Termination phase: Saturation
% 2.96/1.66
% 2.96/1.66 % (12918)Memory used [KB]: 7291
% 2.96/1.66 % (12918)Time elapsed: 0.061 s
% 2.96/1.66 % (12918)Instructions burned: 184 (million)
% 2.96/1.66 % (12918)------------------------------
% 2.96/1.66 % (12918)------------------------------
% 2.96/1.67 % (12941)Instruction limit reached!
% 2.96/1.67 % (12941)------------------------------
% 2.96/1.67 % (12941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.67 % (12941)Termination reason: Unknown
% 2.96/1.67 % (12941)Termination phase: shuffling
% 2.96/1.67
% 2.96/1.67 % (12941)Memory used [KB]: 1791
% 2.96/1.67 % (12941)Time elapsed: 0.008 s
% 2.96/1.67 % (12941)Instructions burned: 23 (million)
% 2.96/1.67 % (12941)------------------------------
% 2.96/1.67 % (12941)------------------------------
% 2.96/1.67 % (12942)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/5Mi)
% 2.96/1.67 % (12942)Instruction limit reached!
% 2.96/1.67 % (12942)------------------------------
% 2.96/1.67 % (12942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.67 % (12942)Termination reason: Unknown
% 2.96/1.67 % (12942)Termination phase: shuffling
% 2.96/1.67
% 2.96/1.67 % (12942)Memory used [KB]: 1663
% 2.96/1.67 % (12942)Time elapsed: 0.003 s
% 2.96/1.67 % (12942)Instructions burned: 7 (million)
% 2.96/1.67 % (12942)------------------------------
% 2.96/1.67 % (12942)------------------------------
% 2.96/1.67 % (12943)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/6Mi)
% 2.96/1.67 % (12943)Instruction limit reached!
% 2.96/1.67 % (12943)------------------------------
% 2.96/1.67 % (12943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.67 % (12943)Termination reason: Unknown
% 2.96/1.67 % (12943)Termination phase: shuffling
% 2.96/1.67
% 2.96/1.67 % (12943)Memory used [KB]: 1663
% 2.96/1.67 % (12943)Time elapsed: 0.004 s
% 2.96/1.67 % (12943)Instructions burned: 7 (million)
% 2.96/1.67 % (12943)------------------------------
% 2.96/1.67 % (12943)------------------------------
% 2.96/1.68 % (12944)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/377Mi)
% 2.96/1.68 % (12945)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/779Mi)
% 2.96/1.68 % (12946)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_12819 for (2999ds/19Mi)
% 2.96/1.68 % (12923)Instruction limit reached!
% 2.96/1.68 % (12923)------------------------------
% 2.96/1.68 % (12923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.68 % (12923)Termination reason: Unknown
% 2.96/1.68 % (12923)Termination phase: Saturation
% 2.96/1.68
% 2.96/1.68 % (12923)Memory used [KB]: 7164
% 2.96/1.68 % (12923)Time elapsed: 0.087 s
% 2.96/1.68 % (12923)Instructions burned: 275 (million)
% 2.96/1.68 % (12938)First to succeed.
% 2.96/1.68 % (12923)------------------------------
% 2.96/1.68 % (12923)------------------------------
% 2.96/1.68 % (12938)Refutation found. Thanks to Tanya!
% 2.96/1.68 % SZS status Theorem for DTF2THF_12819
% 2.96/1.68 % SZS output start Proof for DTF2THF_12819
% 2.96/1.68 thf(type_def_5, type, p: $tType).
% 2.96/1.68 thf(type_def_6, type, s: $tType).
% 2.96/1.68 thf(type_def_7, type, messageValue_v: $tType).
% 2.96/1.68 thf(type_def_9, type, message_p_v: $tType).
% 2.96/1.68 thf(type_def_10, type, nat: $tType).
% 2.96/1.68 thf(type_def_11, type, config256849571t_unit: $tType).
% 2.96/1.68 thf(type_def_12, type, set_p: $tType).
% 2.96/1.68 thf(type_def_13, type, list_c1059388851t_unit: $tType).
% 2.96/1.68 thf(type_def_14, type, list_message_p_v: $tType).
% 2.96/1.68 thf(type_def_15, type, set_o: $tType).
% 2.96/1.68 thf(func_def_0, type, list_c1059388851t_unit: $tType).
% 2.96/1.68 thf(func_def_1, type, config256849571t_unit: $tType).
% 2.96/1.68 thf(func_def_2, type, list_message_p_v: $tType).
% 2.96/1.68 thf(func_def_3, type, message_p_v: $tType).
% 2.96/1.68 thf(func_def_4, type, messageValue_v: $tType).
% 2.96/1.68 thf(func_def_5, type, set_p: $tType).
% 2.96/1.68 thf(func_def_6, type, set_o: $tType).
% 2.96/1.68 thf(func_def_7, type, nat: $tType).
% 2.96/1.68 thf(func_def_8, type, s: $tType).
% 2.96/1.68 thf(func_def_9, type, p: $tType).
% 2.96/1.68 thf(func_def_10, type, initReachable_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > config256849571t_unit > $o).
% 2.96/1.68 thf(func_def_11, type, initial_p_s_v: (p > s) > config256849571t_unit > $o).
% 2.96/1.68 thf(func_def_12, type, qReachable_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > config256849571t_unit > set_p > config256849571t_unit > $o).
% 2.96/1.68 thf(func_def_13, type, reachable_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > config256849571t_unit > config256849571t_unit > $o).
% 2.96/1.68 thf(func_def_14, type, stepReachable_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > config256849571t_unit > message_p_v > config256849571t_unit > $o).
% 2.96/1.68 thf(func_def_15, type, steps_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > config256849571t_unit > message_p_v > config256849571t_unit > $o).
% 2.96/1.68 thf(func_def_16, type, msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat).
% 2.96/1.68 thf(func_def_17, type, states1228886952t_unit: config256849571t_unit > p > s).
% 2.96/1.69 thf(func_def_18, type, enabled_p_v_s: config256849571t_unit > message_p_v > $o).
% 2.96/1.69 thf(func_def_19, type, isReceiverOf_p_v: p > message_p_v > $o).
% 2.96/1.69 thf(func_def_20, type, outMsg_p_v: $o > message_p_v).
% 2.96/1.69 thf(func_def_21, type, execution_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > list_c1059388851t_unit > list_message_p_v > $o).
% 2.96/1.69 thf(func_def_22, type, firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o).
% 2.96/1.69 thf(func_def_23, type, minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o).
% 2.96/1.69 thf(func_def_24, type, flpSystem_p_s_v: (p > s > messageValue_v > message_p_v > nat) > $o).
% 2.96/1.69 thf(func_def_25, type, agreementInit_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > config256849571t_unit > config256849571t_unit > $o).
% 2.96/1.69 thf(func_def_26, type, agreement_p_v_s: config256849571t_unit > $o).
% 2.96/1.69 thf(func_def_27, type, pSilDecVal_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > $o > p > config256849571t_unit > $o).
% 2.96/1.69 thf(func_def_28, type, termin1618267753_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > nat > config256849571t_unit > set_p > $o).
% 2.96/1.69 thf(func_def_29, type, vUniform_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > $o > config256849571t_unit > $o).
% 2.96/1.69 thf(func_def_30, type, validity_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > config256849571t_unit > config256849571t_unit > $o).
% 2.96/1.69 thf(func_def_31, type, fLPThe9398366_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > $o).
% 2.96/1.69 thf(func_def_32, type, one_one_nat: nat).
% 2.96/1.69 thf(func_def_33, type, zero_zero_nat: nat).
% 2.96/1.69 thf(func_def_34, type, prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o).
% 2.96/1.69 thf(func_def_35, type, prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o).
% 2.96/1.69 thf(func_def_36, type, last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit).
% 2.96/1.69 thf(func_def_37, type, last_message_p_v: list_message_p_v > message_p_v).
% 2.96/1.69 thf(func_def_38, type, bot_bot_o_o: $o > $o).
% 2.96/1.69 thf(func_def_39, type, bot_bot_nat: nat).
% 2.96/1.69 thf(func_def_40, type, bot_bot_set_o: set_o).
% 2.96/1.69 thf(func_def_41, type, bot_bot_set_p: set_p).
% 2.96/1.69 thf(func_def_42, type, ord_less_nat: nat > nat > $o).
% 2.96/1.69 thf(func_def_43, type, ord_less_set_o: set_o > set_o > $o).
% 2.96/1.69 thf(func_def_44, type, ord_less_eq_o_o: ($o > $o) > ($o > $o) > $o).
% 2.96/1.69 thf(func_def_45, type, ord_less_eq_p_o: (p > $o) > (p > $o) > $o).
% 2.96/1.69 thf(func_def_46, type, ord_less_eq_nat: nat > nat > $o).
% 2.96/1.69 thf(func_def_47, type, ord_less_eq_set_o: set_o > set_o > $o).
% 2.96/1.69 thf(func_def_48, type, ord_less_eq_set_p: set_p > set_p > $o).
% 2.96/1.69 thf(func_def_49, type, collect_o: ($o > $o) > set_o).
% 2.96/1.69 thf(func_def_50, type, collect_p: (p > $o) > set_p).
% 2.96/1.69 thf(func_def_51, type, insert_o: $o > set_o > set_o).
% 2.96/1.69 thf(func_def_52, type, insert_p: p > set_p > set_p).
% 2.96/1.69 thf(func_def_53, type, member_o: $o > set_o > $o).
% 2.96/1.69 thf(func_def_54, type, member_p: p > set_p > $o).
% 2.96/1.69 thf(func_def_55, type, cMsg: config256849571t_unit).
% 2.96/1.69 thf(func_def_56, type, c: config256849571t_unit).
% 2.96/1.69 thf(func_def_57, type, exec: list_c1059388851t_unit).
% 2.96/1.69 thf(func_def_58, type, execMsga: list_c1059388851t_unit).
% 2.96/1.69 thf(func_def_59, type, exec2: list_c1059388851t_unit).
% 2.96/1.69 thf(func_def_60, type, msg: message_p_v).
% 2.96/1.69 thf(func_def_61, type, p2: p).
% 2.96/1.69 thf(func_def_62, type, sends: p > s > messageValue_v > message_p_v > nat).
% 2.96/1.69 thf(func_def_63, type, start: p > s).
% 2.96/1.69 thf(func_def_64, type, trace: list_message_p_v).
% 2.96/1.69 thf(func_def_65, type, traceMsga: list_message_p_v).
% 2.96/1.69 thf(func_def_66, type, trace2: list_message_p_v).
% 2.96/1.69 thf(func_def_67, type, trans: p > s > messageValue_v > s).
% 2.96/1.69 thf(func_def_87, type, sK0: list_message_p_v).
% 2.96/1.69 thf(func_def_88, type, sK1: list_c1059388851t_unit).
% 2.96/1.69 thf(func_def_89, type, sK2: (set_o > set_o) > set_o).
% 2.96/1.69 thf(func_def_90, type, sK3: (set_o > set_o) > set_o).
% 2.96/1.69 thf(func_def_91, type, sK4: ($o > $o) > ($o > $o) > $o).
% 2.96/1.69 thf(func_def_92, type, sK5: (set_o > set_o) > set_o).
% 2.96/1.69 thf(func_def_93, type, sK6: (set_o > set_o) > set_o).
% 2.96/1.69 thf(func_def_94, type, sK7: ($o > $o) > ($o > $o) > $o).
% 2.96/1.69 thf(func_def_95, type, sK8: ($o > $o) > $o).
% 2.96/1.69 thf(func_def_96, type, sK9: ($o > $o) > ($o > $o) > $o).
% 2.96/1.69 thf(func_def_97, type, sK10: (set_o > set_o) > set_o).
% 2.96/1.69 thf(func_def_98, type, sK11: (set_o > set_o) > set_o).
% 2.96/1.69 thf(func_def_99, type, sK12: config256849571t_unit).
% 2.96/1.69 thf(func_def_100, type, sK13: ($o > $o) > $o).
% 2.96/1.69 thf(func_def_101, type, sK14: (set_o > set_o) > set_o).
% 2.96/1.69 thf(func_def_102, type, sK15: (set_o > set_o) > set_o).
% 2.96/1.69 thf(f1199,plain,(
% 2.96/1.69 $false),
% 2.96/1.69 inference(avatar_sat_refutation,[status(thm)],[f1194,f1195,f1196,f1198])).
% 2.96/1.69 thf(f1198,plain,(
% 2.96/1.69 spl16_2),
% 2.96/1.69 inference(avatar_split_clause,[status(thm)],[f1149,f1187])).
% 2.96/1.69 thf(f1187,definition,(
% 2.96/1.69 spl16_2 <=> ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) = $true)),
% 2.96/1.69 introduced(definition,[new_symbols(naming,[spl16_2])],[avatar_definition])).
% 2.96/1.69 thf(f1149,plain,(
% 2.96/1.69 ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) = $true)),
% 2.96/1.69 inference(cnf_transformation,[status(thm)],[f857])).
% 2.96/1.69 thf(f857,plain,(
% 2.96/1.69 ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) = $true)),
% 2.96/1.69 inference(fool_elimination,[status(thm)],[f856])).
% 2.96/1.69 thf(f856,plain,(
% 2.96/1.69 (initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2))),
% 2.96/1.69 inference(rectify,[status(thm)],[f2])).
% 2.96/1.69 thf(f2,axiom,(
% 2.96/1.69 (initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2))),
% 2.96/1.69 file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_1_InitReachLastExec_H)).
% 2.96/1.69 thf(f1196,plain,(
% 2.96/1.69 spl16_3),
% 2.96/1.69 inference(avatar_split_clause,[status(thm)],[f1160,f1191])).
% 2.96/1.69 thf(f1191,definition,(
% 2.96/1.69 spl16_3 <=> ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ (last_message_p_v @ sK0) @ (last_c571238084t_unit @ sK1)) = $true)),
% 2.96/1.69 introduced(definition,[new_symbols(naming,[spl16_3])],[avatar_definition])).
% 2.96/1.69 thf(f1160,plain,(
% 2.96/1.69 ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ (last_message_p_v @ sK0) @ (last_c571238084t_unit @ sK1)) = $true)),
% 2.96/1.69 inference(definition_unfolding,[status(thm)],[f1120,f1111,f1110])).
% 2.96/1.69 thf(f1110,plain,(
% 2.96/1.69 (cMsg = (last_c571238084t_unit @ sK1))),
% 2.96/1.69 inference(cnf_transformation,[status(thm)],[f1076])).
% 2.96/1.69 thf(f1076,plain,(
% 2.96/1.69 ((prefix47729710ge_p_v @ trace2 @ sK0) = $true) & (msg = (last_message_p_v @ sK0)) & (cMsg = (last_c571238084t_unit @ sK1)) & ((prefix1615116500t_unit @ exec2 @ sK1) = $true) & ((execution_p_s_v @ trans @ sends @ start @ sK1 @ sK0) = $true)),
% 2.96/1.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f1032,f1075])).
% 2.96/1.69 thf(f1075,plain,(
% 2.96/1.69 ? [X0 : list_message_p_v,X1 : list_c1059388851t_unit] : (((prefix47729710ge_p_v @ trace2 @ X0) = $true) & (msg = (last_message_p_v @ X0)) & (cMsg = (last_c571238084t_unit @ X1)) & ($true = (prefix1615116500t_unit @ exec2 @ X1)) & ($true = (execution_p_s_v @ trans @ sends @ start @ X1 @ X0))) => (((prefix47729710ge_p_v @ trace2 @ sK0) = $true) & (msg = (last_message_p_v @ sK0)) & (cMsg = (last_c571238084t_unit @ sK1)) & ((prefix1615116500t_unit @ exec2 @ sK1) = $true) & ((execution_p_s_v @ trans @ sends @ start @ sK1 @ sK0) = $true))),
% 2.96/1.69 introduced(definition,[],[choice_axiom])).
% 2.96/1.69 thf(f1032,plain,(
% 2.96/1.69 ? [X0 : list_message_p_v,X1 : list_c1059388851t_unit] : (((prefix47729710ge_p_v @ trace2 @ X0) = $true) & (msg = (last_message_p_v @ X0)) & (cMsg = (last_c571238084t_unit @ X1)) & ($true = (prefix1615116500t_unit @ exec2 @ X1)) & ($true = (execution_p_s_v @ trans @ sends @ start @ X1 @ X0)))),
% 2.96/1.69 inference(flattening,[status(thm)],[f1031])).
% 2.96/1.69 thf(f1031,plain,(
% 2.96/1.69 ? [X0 : list_message_p_v,X1 : list_c1059388851t_unit] : (((((msg = (last_message_p_v @ X0)) & (cMsg = (last_c571238084t_unit @ X1))) & ((prefix47729710ge_p_v @ trace2 @ X0) = $true)) & ($true = (prefix1615116500t_unit @ exec2 @ X1))) & ($true = (execution_p_s_v @ trans @ sends @ start @ X1 @ X0)))),
% 2.96/1.69 inference(ennf_transformation,[status(thm)],[f1013])).
% 2.96/1.69 thf(f1013,plain,(
% 2.96/1.69 ~! [X0 : list_message_p_v,X1 : list_c1059388851t_unit] : (($true = (execution_p_s_v @ trans @ sends @ start @ X1 @ X0)) => (($true = (prefix1615116500t_unit @ exec2 @ X1)) => (((prefix47729710ge_p_v @ trace2 @ X0) = $true) => ((cMsg = (last_c571238084t_unit @ X1)) => (msg != (last_message_p_v @ X0))))))),
% 2.96/1.69 inference(fool_elimination,[status(thm)],[f1012])).
% 2.96/1.69 thf(f1012,plain,(
% 2.96/1.69 ~! [X0 : list_message_p_v,X1 : list_c1059388851t_unit] : ((execution_p_s_v @ trans @ sends @ start @ X1 @ X0) => ((prefix1615116500t_unit @ exec2 @ X1) => ((prefix47729710ge_p_v @ trace2 @ X0) => ((cMsg = (last_c571238084t_unit @ X1)) => (msg != (last_message_p_v @ X0))))))),
% 2.96/1.69 inference(rectify,[status(thm)],[f272])).
% 2.96/1.69 thf(f272,axiom,(
% 2.96/1.69 ~! [X87 : list_message_p_v,X86 : list_c1059388851t_unit] : ((execution_p_s_v @ trans @ sends @ start @ X86 @ X87) => ((prefix1615116500t_unit @ exec2 @ X86) => ((prefix47729710ge_p_v @ trace2 @ X87) => ((cMsg = (last_c571238084t_unit @ X86)) => (msg != (last_message_p_v @ X87))))))),
% 2.96/1.69 file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_271__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062execMsg_AtraceMsg_O_A_092_060lbrakk_062execution_Atrans_Asends_Astart_AexecMsg_AtraceMsg_059_AprefixList_Aexec_H_AexecMsg_059_AprefixList_Atrace_H_AtraceMsg_059_Alast_AexecMsg_A_061_AcMsg_059_Alast_AtraceMsg_A_061_Amsg_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 2.96/1.69 thf(f1111,plain,(
% 2.96/1.69 (msg = (last_message_p_v @ sK0))),
% 2.96/1.69 inference(cnf_transformation,[status(thm)],[f1076])).
% 2.96/1.69 thf(f1120,plain,(
% 2.96/1.69 ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg) = $true)),
% 2.96/1.69 inference(cnf_transformation,[status(thm)],[f558])).
% 2.96/1.69 thf(f558,plain,(
% 2.96/1.69 ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg) = $true)),
% 2.96/1.69 inference(fool_elimination,[status(thm)],[f557])).
% 2.96/1.69 thf(f557,plain,(
% 2.96/1.69 (steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg)),
% 2.96/1.69 inference(rectify,[status(thm)],[f4])).
% 2.96/1.69 thf(f4,axiom,(
% 2.96/1.69 (steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg)),
% 2.96/1.69 file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_3_CMsg)).
% 2.96/1.69 thf(f1195,plain,(
% 2.96/1.69 ~spl16_1),
% 2.96/1.69 inference(avatar_split_clause,[status(thm)],[f1161,f1183])).
% 2.96/1.69 thf(f1183,definition,(
% 2.96/1.69 spl16_1 <=> ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ sK1))))) = $true)),
% 2.96/1.69 introduced(definition,[new_symbols(naming,[spl16_1])],[avatar_definition])).
% 2.96/1.69 thf(f1161,plain,(
% 2.96/1.69 ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ sK1))))) != $true)),
% 2.96/1.69 inference(definition_unfolding,[status(thm)],[f1150,f1110])).
% 2.96/1.69 thf(f1150,plain,(
% 2.96/1.69 ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))) != $true)),
% 2.96/1.69 inference(cnf_transformation,[status(thm)],[f1024])).
% 2.96/1.69 thf(f1024,plain,(
% 2.96/1.69 ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))) != $true)),
% 2.96/1.69 inference(flattening,[status(thm)],[f402])).
% 2.96/1.69 thf(f402,plain,(
% 2.96/1.69 ~((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))) = $true)),
% 2.96/1.69 inference(fool_elimination,[status(thm)],[f401])).
% 2.96/1.69 thf(f401,plain,(
% 2.96/1.69 ~(ord_less_eq_set_o @ (collect_o @ (^[X0 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[X1 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X1 @ p2 @ cMsg))))),
% 2.96/1.69 inference(rectify,[status(thm)],[f357])).
% 2.96/1.69 thf(f357,negated_conjecture,(
% 2.96/1.69 ~(ord_less_eq_set_o @ (collect_o @ (^[X0 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[X0 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ cMsg))))),
% 2.96/1.69 inference(negated_conjecture,[status(cth)],[f356])).
% 2.96/1.69 thf(f356,conjecture,(
% 2.96/1.69 (ord_less_eq_set_o @ (collect_o @ (^[X0 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[X0 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ cMsg))))),
% 2.96/1.69 file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',conj_0)).
% 2.96/1.69 thf(f1194,plain,(
% 2.96/1.69 spl16_1 | ~spl16_2 | ~spl16_3),
% 2.96/1.69 inference(avatar_split_clause,[status(thm)],[f1181,f1191,f1187,f1183])).
% 2.96/1.69 thf(f1181,plain,(
% 2.96/1.69 ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ sK1))))) = $true) | ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ (last_message_p_v @ sK0) @ (last_c571238084t_unit @ sK1)) != $true) | ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) != $true)),
% 2.96/1.69 inference(subsumption_resolution,[status(thm)],[f1178,f1164])).
% 2.96/1.69 thf(f1164,plain,(
% 2.96/1.69 ((isReceiverOf_p_v @ p2 @ (last_message_p_v @ sK0)) = $true)),
% 2.96/1.69 inference(definition_unfolding,[status(thm)],[f1157,f1111])).
% 2.96/1.69 thf(f1157,plain,(
% 2.96/1.69 ((isReceiverOf_p_v @ p2 @ msg) = $true)),
% 2.96/1.69 inference(cnf_transformation,[status(thm)],[f534])).
% 2.96/1.69 thf(f534,plain,(
% 2.96/1.69 ((isReceiverOf_p_v @ p2 @ msg) = $true)),
% 2.96/1.69 inference(fool_elimination,[status(thm)],[f533])).
% 2.96/1.69 thf(f533,plain,(
% 2.96/1.69 (isReceiverOf_p_v @ p2 @ msg)),
% 2.96/1.69 inference(rectify,[status(thm)],[f1])).
% 2.96/1.69 thf(f1,axiom,(
% 2.96/1.69 (isReceiverOf_p_v @ p2 @ msg)),
% 2.96/1.69 file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_0_PisReceiverOf)).
% 2.96/1.69 thf(f1178,plain,(
% 2.96/1.69 ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ (last_message_p_v @ sK0) @ (last_c571238084t_unit @ sK1)) != $true) | ((isReceiverOf_p_v @ p2 @ (last_message_p_v @ sK0)) != $true) | ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ sK1))))) = $true) | ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) != $true)),
% 2.96/1.69 inference(trivial_inequality_removal,[status(thm)],[f1162])).
% 2.96/1.69 thf(f1162,plain,(
% 2.96/1.69 ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ (last_message_p_v @ sK0) @ (last_c571238084t_unit @ sK1)) != $true) | ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) != $true) | ((isReceiverOf_p_v @ p2 @ (last_message_p_v @ sK0)) != $true) | (p2 != p2) | ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ sK1))))) = $true)),
% 2.96/1.69 inference(definition_unfolding,[status(thm)],[f1154,f1111,f1110,f1111,f1110])).
% 2.96/1.69 thf(f1154,plain,(
% 2.96/1.69 ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg) != $true) | ((isReceiverOf_p_v @ p2 @ msg) != $true) | ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) != $true) | (p2 != p2) | ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))) = $true)),
% 2.96/1.69 inference(cnf_transformation,[status(thm)],[f1044])).
% 2.96/1.69 thf(f1044,plain,(
% 2.96/1.69 ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg) != $true) | ((isReceiverOf_p_v @ p2 @ msg) != $true) | ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) != $true) | (p2 != p2) | ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))) = $true)),
% 2.96/1.69 inference(flattening,[status(thm)],[f1043])).
% 2.96/1.69 thf(f1043,plain,(
% 2.96/1.69 (((((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))) = $true) | ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) != $true)) | ((isReceiverOf_p_v @ p2 @ msg) != $true)) | ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg) != $true)) | (p2 != p2)),
% 2.96/1.69 inference(ennf_transformation,[status(thm)],[f747])).
% 2.96/1.69 thf(f747,plain,(
% 2.96/1.69 (p2 = p2) => (((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg) = $true) => (((isReceiverOf_p_v @ p2 @ msg) = $true) => (((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) = $true) => ((ord_less_eq_set_o @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[Y0 : $o]: (pSilDecVal_p_s_v @ trans @ sends @ start @ Y0 @ p2 @ cMsg)))) = $true))))),
% 2.96/1.69 inference(fool_elimination,[status(thm)],[f746])).
% 2.96/1.69 thf(f746,plain,(
% 2.96/1.69 (p2 = p2) => ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg) => ((isReceiverOf_p_v @ p2 @ msg) => ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) => (ord_less_eq_set_o @ (collect_o @ (^[X0 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[X1 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X1 @ p2 @ cMsg)))))))),
% 2.96/1.69 inference(rectify,[status(thm)],[f7])).
% 2.96/1.69 thf(f7,axiom,(
% 2.96/1.69 (p2 = p2) => ((steps_p_s_v @ trans @ sends @ (last_c571238084t_unit @ exec2) @ msg @ cMsg) => ((isReceiverOf_p_v @ p2 @ msg) => ((initReachable_p_s_v @ trans @ sends @ start @ (last_c571238084t_unit @ exec2)) => (ord_less_eq_set_o @ (collect_o @ (^[X0 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ (last_c571238084t_unit @ exec2)))) @ (collect_o @ (^[X0 : $o] : (pSilDecVal_p_s_v @ trans @ sends @ start @ X0 @ p2 @ cMsg)))))))),
% 2.96/1.69 file('/export/starexec/sandbox2/tmp/tmp.jNGi28GK9N/DTF2THF_12819.p',fact_6__092_060open_062_092_060lbrakk_062p_A_061_Ap_059_Alast_Aexec_H_A_092_060turnstile_062_Amsg_A_092_060mapsto_062_AcMsg_059_AisReceiverOf_Ap_Amsg_059_AinitReachable_A_Ilast_Aexec_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Aval_091p_Mlast_Aexec_H_093_A_092_060subseteq_062_Aval_091p_McMsg_093_092_060close_062)).
% 2.96/1.69 % SZS output end Proof for DTF2THF_12819
% 2.96/1.69 % (12938)------------------------------
% 2.96/1.69 % (12938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.69 % (12938)Termination reason: Refutation
% 2.96/1.69
% 2.96/1.69 % (12938)Memory used [KB]: 6780
% 2.96/1.69 % (12938)Time elapsed: 0.030 s
% 2.96/1.69 % (12938)Instructions burned: 94 (million)
% 2.96/1.69 % (12938)------------------------------
% 2.96/1.69 % (12938)------------------------------
% 2.96/1.69 % (12917)Success in time 0.105 s
%------------------------------------------------------------------------------