TSTP Solution File: ITP057^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP057^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 : Tue May 7 07:47:28 EDT 2024
% Result : Theorem 136.71s 115.02s
% Output : Refutation 137.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 341
% Syntax : Number of formulae : 627 ( 189 unt; 57 typ; 0 def)
% Number of atoms : 2215 ( 433 equ; 10 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 12953 ( 218 ~; 40 |; 212 &;11678 @)
% ( 0 <=>; 805 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 10 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 942 ( 942 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 57 usr; 18 con; 0-9 aty)
% Number of variables : 2341 ( 178 ^1968 !; 112 ?;2341 :)
% ( 83 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(v_type,type,
v: $tType ).
thf(s_type,type,
s: $tType ).
thf(p_type,type,
p: $tType ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(order_bot_type,type,
order_bot:
!>[TA: $tType] : $o ).
thf(dense_linorder_type,type,
dense_linorder:
!>[TA: $tType] : $o ).
thf(initReachable_type,type,
initReachable:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( TC > TB ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(initial_type,type,
initial:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(qReachable_type,type,
qReachable:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > ( set @ TC ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(reachable_type,type,
reachable:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(stepReachable_type,type,
stepReachable:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > ( message @ TC @ TA ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(steps_type,type,
steps:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > ( message @ TC @ TA ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(msgs_type,type,
msgs:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( configuration_ext @ TD @ TC @ TB @ TA ) > ( message @ TD @ TC ) > nat ) ).
thf(states_type,type,
states:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( configuration_ext @ TD @ TC @ TB @ TA ) > TD > TB ) ).
thf(enabled_type,type,
enabled:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( message @ TC @ TB ) > $o ) ).
thf(isReceiverOf_type,type,
isReceiverOf:
!>[TA: $tType,TB: $tType] : ( TB > ( message @ TB @ TA ) > $o ) ).
thf(outMsg_type,type,
outMsg:
!>[TA: $tType,TB: $tType] : ( $o > ( message @ TB @ TA ) ) ).
thf(execution_type,type,
execution:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( TC > TB ) > ( list @ ( configuration_ext @ TC @ TA @ TB @ product_unit ) ) > ( list @ ( message @ TC @ TA ) ) > $o ) ).
thf(firstOccurrence_type,type,
firstOccurrence:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( message @ TC @ TB ) > nat > $o ) ).
thf(minimalEnabled_type,type,
minimalEnabled:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( message @ TC @ TB ) > $o ) ).
thf(flpSystem_type,type,
flpSystem:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > $o ) ).
thf(agreement_type,type,
agreement:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( configuration_ext @ TC @ TB @ TA @ product_unit ) > $o ) ).
thf(agreementInit_type,type,
agreementInit:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( TC > TB ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(pSilDecVal_type,type,
pSilDecVal:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( TC > TB ) > $o > TC > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(terminationPseudo_type,type,
terminationPseudo:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( TC > TB ) > nat > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > ( set @ TC ) > $o ) ).
thf(vUniform_type,type,
vUniform:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( TC > TB ) > $o > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(validity_type,type,
validity:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( TC > TB ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > ( configuration_ext @ TC @ TA @ TB @ product_unit ) > $o ) ).
thf(fLPThe1922692578sensus_type,type,
fLPThe1922692578sensus:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( TC > TB ) > $o ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(prefixList_type,type,
prefixList:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(last_type,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(cMsg_type,type,
cMsg: configuration_ext @ p @ v @ s @ product_unit ).
thf(c_type,type,
c: configuration_ext @ p @ v @ s @ product_unit ).
thf(exec_type,type,
exec: list @ ( configuration_ext @ p @ v @ s @ product_unit ) ).
thf(execMsga_type,type,
execMsga: list @ ( configuration_ext @ p @ v @ s @ product_unit ) ).
thf(exec2_type,type,
exec2: list @ ( configuration_ext @ p @ v @ s @ product_unit ) ).
thf(msg_type,type,
msg: message @ p @ v ).
thf(p2_type,type,
p2: p ).
thf(sends_type,type,
sends: p > s > ( messageValue @ v ) > ( message @ p @ v ) > nat ).
thf(start_type,type,
start: p > s ).
thf(trace_type,type,
trace: list @ ( message @ p @ v ) ).
thf(traceMsga_type,type,
traceMsga: list @ ( message @ p @ v ) ).
thf(trace2_type,type,
trace2: list @ ( message @ p @ v ) ).
thf(trans_type,type,
trans: p > s > ( messageValue @ v ) > s ).
thf(116,axiom,
flpSystem @ p @ s @ v @ sends,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_flpSystem__axioms) ).
thf(629,plain,
flpSystem @ p @ s @ v @ sends,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(115,axiom,
bot @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Obot_22) ).
thf(628,plain,
bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(86,axiom,
isReceiverOf @ p @ v @ p2 @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_PisReceiverOf) ).
thf(518,plain,
isReceiverOf @ p @ v @ p2 @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(212,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_dense__le) ).
thf(941,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(132,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_set__eq__subset) ).
thf(666,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(256,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_subset__iff) ).
thf(1083,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(220,axiom,
( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_NewExec_I3_J) ).
thf(962,plain,
( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(69,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_dual__order_Oantisym) ).
thf(468,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(170,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: list @ ( configuration_ext @ p @ v @ s @ product_unit ),D: list @ ( message @ p @ v )] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( execution @ p @ s @ v @ trans @ sends @ start @ C @ D )
=> ( ( A
= ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ C ) )
=> ? [E: list @ ( configuration_ext @ p @ v @ s @ product_unit ),F: list @ ( message @ p @ v )] :
( ( execution @ p @ s @ v @ trans @ sends @ start @ E @ F )
& ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ C @ E )
& ( prefixList @ ( message @ p @ v ) @ D @ F ) )
| ( ( C = E )
& ( D = F ) ) )
& ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ E )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_expandExecutionReachable) ).
thf(777,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: list @ ( configuration_ext @ p @ v @ s @ product_unit ),D: list @ ( message @ p @ v )] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( execution @ p @ s @ v @ trans @ sends @ start @ C @ D )
=> ( ( A
= ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ C ) )
=> ? [E: list @ ( configuration_ext @ p @ v @ s @ product_unit ),F: list @ ( message @ p @ v )] :
( ( execution @ p @ s @ v @ trans @ sends @ start @ E @ F )
& ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ C @ E )
& ( prefixList @ ( message @ p @ v ) @ D @ F ) )
| ( ( C = E )
& ( D = F ) ) )
& ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ E )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(95,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_insert__subset) ).
thf(555,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(236,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ A )
=> ( agreement @ p @ v @ s @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Agree) ).
thf(1005,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ A )
=> ( agreement @ p @ v @ s @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(140,axiom,
execution @ p @ s @ v @ trans @ sends @ start @ execMsga @ traceMsga,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_isExecution) ).
thf(683,plain,
execution @ p @ s @ v @ trans @ sends @ start @ execMsga @ traceMsga,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(154,axiom,
! [A: p,B: p,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v,E: configuration_ext @ p @ v @ s @ product_unit] :
( ( A = B )
=> ( ( steps @ p @ s @ v @ trans @ sends @ C @ D @ E )
=> ( ( isReceiverOf @ p @ v @ A @ D )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ F @ B @ C ) )
@ ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ F @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_ActiveProcessSilentDecisionValuesIncrease) ).
thf(730,plain,
! [A: p,B: p,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v,E: configuration_ext @ p @ v @ s @ product_unit] :
( ( A = B )
=> ( ( steps @ p @ s @ v @ trans @ sends @ C @ D @ E )
=> ( ( isReceiverOf @ p @ v @ A @ D )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ F @ B @ C ) )
@ ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ F @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(232,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Collect__mono) ).
thf(994,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(157,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_PseudoTermination) ).
thf(741,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(276,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > ( messageValue @ TA ) > TC,B: TB > TC > ( messageValue @ TA ) > ( message @ TB @ TA ) > nat,C: configuration_ext @ TB @ TA @ TC @ product_unit,D: configuration_ext @ TB @ TA @ TC @ product_unit,E: $o] :
( ( reachable @ TB @ TC @ TA @ A @ B @ C @ D )
=> ( ord_less_eq @ nat @ ( msgs @ TB @ TA @ TC @ product_unit @ C @ ( outMsg @ TB @ TA @ E ) ) @ ( msgs @ TB @ TA @ TC @ product_unit @ D @ ( outMsg @ TB @ TA @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_asynchronousSystem_ONoOutMessageLoss) ).
thf(1142,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > ( messageValue @ TA ) > TC,B: TB > TC > ( messageValue @ TA ) > ( message @ TB @ TA ) > nat,C: configuration_ext @ TB @ TA @ TC @ product_unit,D: configuration_ext @ TB @ TA @ TC @ product_unit,E: $o] :
( ( reachable @ TB @ TC @ TA @ A @ B @ C @ D )
=> ( ord_less_eq @ nat @ ( msgs @ TB @ TA @ TC @ product_unit @ C @ ( outMsg @ TB @ TA @ E ) ) @ ( msgs @ TB @ TA @ TC @ product_unit @ D @ ( outMsg @ TB @ TA @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(110,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: $o] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ C ) ) @ ( msgs @ p @ v @ s @ product_unit @ B @ ( outMsg @ p @ v @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_NoOutMessageLoss) ).
thf(614,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: $o] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ C ) ) @ ( msgs @ p @ v @ s @ product_unit @ B @ ( outMsg @ p @ v @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(247,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
= ( ? [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( A = C )
& ( B = C ) )
| ? [C: configuration_ext @ p @ v @ s @ product_unit,D: configuration_ext @ p @ v @ s @ product_unit,E: message @ p @ v,F: configuration_ext @ p @ v @ s @ product_unit] :
( ( A = C )
& ( B = F )
& ( reachable @ p @ s @ v @ trans @ sends @ C @ D )
& ( steps @ p @ s @ v @ trans @ sends @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_reachable_Osimps) ).
thf(1041,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
= ( ? [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( A = C )
& ( B = C ) )
| ? [C: configuration_ext @ p @ v @ s @ product_unit,D: configuration_ext @ p @ v @ s @ product_unit,E: message @ p @ v,F: configuration_ext @ p @ v @ s @ product_unit] :
( ( A = C )
& ( B = F )
& ( reachable @ p @ s @ v @ trans @ sends @ C @ D )
& ( steps @ p @ s @ v @ trans @ sends @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(282,axiom,
reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_C_H_I1_J) ).
thf(1158,plain,
reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,B: TA > TC > ( messageValue @ TB ) > TC,C: TA > TC,D: TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: $o,G: message @ TA @ TB,H: configuration_ext @ TA @ TB @ TC @ product_unit,I: TA] :
( ( flpSystem @ TA @ TC @ TB @ A )
=> ( ( ( collect @ $o
@ ^ [J: $o] : ( pSilDecVal @ TA @ TC @ TB @ B @ A @ C @ J @ D @ E ) )
= ( insert @ $o @ F @ ( bot_bot @ ( set @ $o ) ) ) )
=> ( ( steps @ TA @ TC @ TB @ B @ A @ E @ G @ H )
=> ( ( isReceiverOf @ TA @ TB @ I @ G )
=> ( ( initReachable @ TA @ TC @ TB @ B @ A @ C @ E )
=> ( ( collect @ $o
@ ^ [J: $o] : ( pSilDecVal @ TA @ TC @ TB @ B @ A @ C @ J @ D @ H ) )
!= ( insert @ $o @ ~ F @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_flpSystem_OSilentDecisionValueNotInverting) ).
thf(762,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,B: TA > TC > ( messageValue @ TB ) > TC,C: TA > TC,D: TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: $o,G: message @ TA @ TB,H: configuration_ext @ TA @ TB @ TC @ product_unit,I: TA] :
( ( flpSystem @ TA @ TC @ TB @ A )
=> ( ( ( collect @ $o
@ ^ [J: $o] : ( pSilDecVal @ TA @ TC @ TB @ B @ A @ C @ J @ D @ E ) )
= ( insert @ $o @ F @ ( bot_bot @ ( set @ $o ) ) ) )
=> ( ( steps @ TA @ TC @ TB @ B @ A @ E @ G @ H )
=> ( ( isReceiverOf @ TA @ TB @ I @ G )
=> ( ( initReachable @ TA @ TC @ TB @ B @ A @ C @ E )
=> ( ( collect @ $o
@ ^ [J: $o] : ( pSilDecVal @ TA @ TC @ TB @ B @ A @ C @ J @ D @ H ) )
!= ( insert @ $o @ ~ F @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(272,axiom,
initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_InitReachLastExecMsg) ).
thf(1137,plain,
initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(171,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_le__cases3) ).
thf(797,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(207,axiom,
order_bot @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__bot_17) ).
thf(930,plain,
order_bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(160,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_subset__singletonD) ).
thf(747,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(201,axiom,
execution @ p @ s @ v @ trans @ sends @ start @ exec2 @ trace2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_NewExec_I1_J) ).
thf(913,plain,
execution @ p @ s @ v @ trans @ sends @ start @ exec2 @ trace2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(260,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( reachable @ p @ s @ v @ trans @ sends @ B @ C )
=> ( reachable @ p @ s @ v @ trans @ sends @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_ReachableTrans) ).
thf(1095,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( reachable @ p @ s @ v @ trans @ sends @ B @ C )
=> ( reachable @ p @ s @ v @ trans @ sends @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(269,axiom,
! [A: p,B: configuration_ext @ p @ v @ s @ product_unit,C: $o,D: message @ p @ v,E: configuration_ext @ p @ v @ s @ product_unit,F: p] :
( ( ( collect @ $o
@ ^ [G: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ G @ A @ B ) )
= ( insert @ $o @ C @ ( bot_bot @ ( set @ $o ) ) ) )
=> ( ( steps @ p @ s @ v @ trans @ sends @ B @ D @ E )
=> ( ( isReceiverOf @ p @ v @ F @ D )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ B )
=> ( ( collect @ $o
@ ^ [G: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ G @ A @ E ) )
!= ( insert @ $o @ ~ C @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_SilentDecisionValueNotInverting) ).
thf(1127,plain,
! [A: p,B: configuration_ext @ p @ v @ s @ product_unit,C: $o,D: message @ p @ v,E: configuration_ext @ p @ v @ s @ product_unit,F: p] :
( ( ( collect @ $o
@ ^ [G: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ G @ A @ B ) )
= ( insert @ $o @ C @ ( bot_bot @ ( set @ $o ) ) ) )
=> ( ( steps @ p @ s @ v @ trans @ sends @ B @ D @ E )
=> ( ( isReceiverOf @ p @ v @ F @ D )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ B )
=> ( ( collect @ $o
@ ^ [G: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ G @ A @ E ) )
!= ( insert @ $o @ ~ C @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_le__funD) ).
thf(709,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( agreementInit @ TA @ TB @ TC )
= ( agreementInit @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_flpSystem_OagreementInit_Ocong) ).
thf(417,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(224,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( stepReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
= ( ? [D: configuration_ext @ p @ v @ s @ product_unit,E: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ D )
& ( steps @ p @ s @ v @ trans @ sends @ D @ B @ E )
& ( reachable @ p @ s @ v @ trans @ sends @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_stepReachable__def) ).
thf(973,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( stepReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
= ( ? [D: configuration_ext @ p @ v @ s @ product_unit,E: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ D )
& ( steps @ p @ s @ v @ trans @ sends @ D @ B @ E )
& ( reachable @ p @ s @ v @ trans @ sends @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(301,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(98,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Collect__mono__iff) ).
thf(565,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: TB,B: $o] :
~ ( isReceiverOf @ TB @ TA @ A @ ( outMsg @ TB @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_isReceiverOf_Osimps_I3_J) ).
thf(436,plain,
! [TA: $tType,TB: $tType,A: TB,B: $o] :
~ ( isReceiverOf @ TB @ TA @ A @ ( outMsg @ TB @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( pSilDecVal @ TA @ TB @ TC )
= ( pSilDecVal @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_flpSystem_OpSilDecVal_Ocong) ).
thf(504,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_order__subst1) ).
thf(917,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(209,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_order__refl) ).
thf(934,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(106,axiom,
( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ exec2 )
& ( prefixList @ ( message @ p @ v ) @ trace @ trace2 ) )
| ( ( exec = exec2 )
& ( trace = trace2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_NewExec_I2_J) ).
thf(587,plain,
( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ exec2 )
& ( prefixList @ ( message @ p @ v ) @ trace @ trace2 ) )
| ( ( exec = exec2 )
& ( trace = trace2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(112,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_rev__predicate1D) ).
thf(619,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(174,axiom,
prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ execMsga,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_isPrefixListExec) ).
thf(817,plain,
prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ execMsga,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(278,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_singleton__conv2) ).
thf(1147,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( reachable @ TA @ TB @ TC )
= ( ^ [A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ? [E: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( C = E )
& ( D = E ) )
| ? [E: configuration_ext @ TA @ TC @ TB @ product_unit,F: configuration_ext @ TA @ TC @ TB @ product_unit,G: message @ TA @ TC,H: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( C = E )
& ( D = H )
& ( reachable @ TA @ TB @ TC @ A @ B @ E @ F )
& ( steps @ TA @ TB @ TC @ A @ B @ F @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_asynchronousSystem_Oreachable_Osimps) ).
thf(421,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( reachable @ TA @ TB @ TC )
= ( ^ [A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ? [E: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( C = E )
& ( D = E ) )
| ? [E: configuration_ext @ TA @ TC @ TB @ product_unit,F: configuration_ext @ TA @ TC @ TB @ product_unit,G: message @ TA @ TC,H: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( C = E )
& ( D = H )
& ( reachable @ TA @ TB @ TC @ A @ B @ E @ F )
& ( steps @ TA @ TB @ TC @ A @ B @ F @ G @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(240,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_equals0D) ).
thf(1013,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( terminationPseudo @ TA @ TB @ TC )
= ( terminationPseudo @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_flpSystem_OterminationPseudo_Ocong) ).
thf(416,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(316,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(262,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: message @ p @ v,D: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( steps @ p @ s @ v @ trans @ sends @ B @ C @ D )
=> ( reachable @ p @ s @ v @ trans @ sends @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_reachable_Ostep) ).
thf(1100,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: message @ p @ v,D: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( steps @ p @ s @ v @ trans @ sends @ B @ C @ D )
=> ( reachable @ p @ s @ v @ trans @ sends @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(78,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: p,E: p,F: message @ p @ v,G: configuration_ext @ p @ v @ s @ product_unit] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( D != E )
=> ( ( isReceiverOf @ p @ v @ D @ B )
=> ( ~ ( isReceiverOf @ p @ v @ D @ F )
=> ( ( isReceiverOf @ p @ v @ E @ F )
=> ( ~ ( isReceiverOf @ p @ v @ E @ B )
=> ( ( steps @ p @ s @ v @ trans @ sends @ A @ F @ G )
=> ? [H: configuration_ext @ p @ v @ s @ product_unit] :
( ( steps @ p @ s @ v @ trans @ sends @ C @ F @ H )
& ( steps @ p @ s @ v @ trans @ sends @ G @ B @ H ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_DiamondOne) ).
thf(492,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: p,E: p,F: message @ p @ v,G: configuration_ext @ p @ v @ s @ product_unit] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( D != E )
=> ( ( isReceiverOf @ p @ v @ D @ B )
=> ( ~ ( isReceiverOf @ p @ v @ D @ F )
=> ( ( isReceiverOf @ p @ v @ E @ F )
=> ( ~ ( isReceiverOf @ p @ v @ E @ B )
=> ( ( steps @ p @ s @ v @ trans @ sends @ A @ F @ G )
=> ? [H: configuration_ext @ p @ v @ s @ product_unit] :
( ( steps @ p @ s @ v @ trans @ sends @ C @ F @ H )
& ( steps @ p @ s @ v @ trans @ sends @ G @ B @ H ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(163,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_less__eq__set__def) ).
thf(756,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(443,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(124,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
= ( ? [B: configuration_ext @ p @ v @ s @ product_unit] :
( ( initial @ p @ s @ v @ start @ B )
& ( reachable @ p @ s @ v @ trans @ sends @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_initReachable__def) ).
thf(646,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
= ( ? [B: configuration_ext @ p @ v @ s @ product_unit] :
( ( initial @ p @ s @ v @ start @ B )
& ( reachable @ p @ s @ v @ trans @ sends @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: TA > TC,D: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),E: list @ ( message @ TA @ TB ),F: TA,G: message @ TA @ TB] :
( ( execution @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( isReceiverOf @ TA @ TB @ F @ G )
=> ( ( enabled @ TA @ TB @ TC @ ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ D ) @ G )
=> ? [H: message @ TA @ TB] : ( minimalEnabled @ TA @ TB @ TC @ D @ E @ H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_execution_OExistImpliesMinEnabled) ).
thf(834,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: TA > TC,D: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),E: list @ ( message @ TA @ TB ),F: TA,G: message @ TA @ TB] :
( ( execution @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( isReceiverOf @ TA @ TB @ F @ G )
=> ( ( enabled @ TA @ TB @ TC @ ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ D ) @ G )
=> ? [H: message @ TA @ TB] : ( minimalEnabled @ TA @ TB @ TC @ D @ E @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( qReachable @ TA @ TB @ TC )
= ( qReachable @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_asynchronousSystem_OqReachable_Ocong) ).
thf(348,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_insert__commute) ).
thf(353,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(176,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_subsetI) ).
thf(821,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(199,axiom,
! [A: $o,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( vUniform @ p @ s @ v @ trans @ sends @ start @ A @ B )
= ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ B )
& ! [C: p] :
( ( collect @ $o
@ ^ [D: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ D @ C @ B ) )
= ( insert @ $o @ A @ ( bot_bot @ ( set @ $o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_vUniform__def) ).
thf(905,plain,
! [A: $o,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( vUniform @ p @ s @ v @ trans @ sends @ start @ A @ B )
= ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ B )
& ! [C: p] :
( ( collect @ $o
@ ^ [D: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ D @ C @ B ) )
= ( insert @ $o @ A @ ( bot_bot @ ( set @ $o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(72,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_dual__order_Oeq__iff) ).
thf(475,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(206,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: $o] :
( ! [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
=> ( agreement @ p @ v @ s @ C ) )
=> ( ! [C: configuration_ext @ p @ v @ s @ product_unit,D: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ C @ D )
=> ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ A ) )
=> ~ ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_NonUniformImpliesNotDecided) ).
thf(924,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: $o] :
( ! [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
=> ( agreement @ p @ v @ s @ C ) )
=> ( ! [C: configuration_ext @ p @ v @ s @ product_unit,D: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ C @ D )
=> ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ A ) )
=> ~ ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_singleton__insert__inj__eq_H) ).
thf(660,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(230,axiom,
~ ! [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ A )
=> ( ( collect @ $o
@ ^ [B: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ B @ p2 @ A ) )
!= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127__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) ).
thf(988,plain,
~ ! [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ A )
=> ( ( collect @ $o
@ ^ [B: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ B @ p2 @ A ) )
!= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( fLPThe1922692578sensus @ TA @ TC @ TB @ A @ B @ C )
=> ( agreementInit @ TA @ TC @ TB @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_flpPseudoConsensus_OAgreement) ).
thf(428,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( fLPThe1922692578sensus @ TA @ TC @ TB @ A @ B @ C )
=> ( agreementInit @ TA @ TC @ TB @ A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( reachable @ TA @ TC @ TB @ A @ B @ D @ E )
=> ( reachable @ TA @ TC @ TB @ A @ B @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_asynchronousSystem_OReachableTrans) ).
thf(312,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( reachable @ TA @ TC @ TB @ A @ B @ D @ E )
=> ( reachable @ TA @ TC @ TB @ A @ B @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(254,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_ord__le__eq__subst) ).
thf(1074,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(292,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(204,axiom,
( ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ c ) )
= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_C_H_I2_J) ).
thf(920,plain,
( ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ c ) )
= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(136,axiom,
linorder @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Olinorder_19) ).
thf(678,plain,
linorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(280,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_linear) ).
thf(1153,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(284,axiom,
! [A: list @ ( configuration_ext @ p @ v @ s @ product_unit ),B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: list @ ( message @ p @ v )] :
( ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A ) @ B @ C )
=> ( ( execution @ p @ s @ v @ trans @ sends @ start @ A @ D )
=> ? [E: list @ ( configuration_ext @ p @ v @ s @ product_unit ),F: list @ ( message @ p @ v )] :
( ( execution @ p @ s @ v @ trans @ sends @ start @ E @ F )
& ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A @ E )
& ( prefixList @ ( message @ p @ v ) @ D @ F )
& ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ E )
= C )
& ( ( last @ ( message @ p @ v ) @ F )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_expandExecutionStep) ).
thf(1163,plain,
! [A: list @ ( configuration_ext @ p @ v @ s @ product_unit ),B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: list @ ( message @ p @ v )] :
( ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A ) @ B @ C )
=> ( ( execution @ p @ s @ v @ trans @ sends @ start @ A @ D )
=> ? [E: list @ ( configuration_ext @ p @ v @ s @ product_unit ),F: list @ ( message @ p @ v )] :
( ( execution @ p @ s @ v @ trans @ sends @ start @ E @ F )
& ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A @ E )
& ( prefixList @ ( message @ p @ v ) @ D @ F )
& ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ E )
= C )
& ( ( last @ ( message @ p @ v ) @ F )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( initReachable @ TA @ TB @ TC )
= ( initReachable @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_asynchronousSystem_OinitReachable_Ocong) ).
thf(334,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(216,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Collect__conv__if2) ).
thf(952,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit] : ( reachable @ TA @ TC @ TB @ A @ B @ C @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_asynchronousSystem_Oinit) ).
thf(297,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit] : ( reachable @ TA @ TC @ TB @ A @ B @ C @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: message @ TA @ TB] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( enabled @ TA @ TB @ TC @ C @ E )
=> ( ~ ( enabled @ TA @ TB @ TC @ D @ E )
=> ( stepReachable @ TA @ TC @ TB @ A @ B @ C @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_asynchronousSystem_OStepReachable) ).
thf(424,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: message @ TA @ TB] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( enabled @ TA @ TB @ TC @ C @ E )
=> ( ~ ( enabled @ TA @ TB @ TC @ D @ E )
=> ( stepReachable @ TA @ TC @ TB @ A @ B @ C @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(117,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: p,E: message @ p @ v] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ~ ( member @ p @ D @ B )
=> ( ( isReceiverOf @ p @ v @ D @ E )
=> ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ A @ E ) @ ( msgs @ p @ v @ s @ product_unit @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_NoActivityNoMessageLoss) ).
thf(630,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: p,E: message @ p @ v] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ~ ( member @ p @ D @ B )
=> ( ( isReceiverOf @ p @ v @ D @ E )
=> ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ A @ E ) @ ( msgs @ p @ v @ s @ product_unit @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(217,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_singleton__insert__inj__eq) ).
thf(957,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(196,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( B != A )
=> ~ ! [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
=> ! [D: message @ p @ v] :
~ ( steps @ p @ s @ v @ trans @ sends @ C @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_reachable_Ocases) ).
thf(894,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( B != A )
=> ~ ! [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
=> ! [D: message @ p @ v] :
~ ( steps @ p @ s @ v @ trans @ sends @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(267,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p] : ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_InitQ) ).
thf(1123,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p] : ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Set_Oset__insert) ).
thf(349,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(75,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_dual__order_Oorder__iff__strict) ).
thf(484,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(114,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( qReachable @ p @ s @ v @ trans @ sends @ D @ B @ A )
=> ( qReachable @ p @ s @ v @ trans @ sends @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_QReachableTrans) ).
thf(625,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( qReachable @ p @ s @ v @ trans @ sends @ D @ B @ A )
=> ( qReachable @ p @ s @ v @ trans @ sends @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: message @ TA @ TB] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( D != F )
=> ( ord_less_eq @ nat @ ( msgs @ TA @ TB @ TC @ product_unit @ C @ F ) @ ( msgs @ TA @ TB @ TC @ product_unit @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_asynchronousSystem_OOtherMessagesOnlyGrowing) ).
thf(879,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: message @ TA @ TB] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( D != F )
=> ( ord_less_eq @ nat @ ( msgs @ TA @ TB @ TC @ product_unit @ C @ F ) @ ( msgs @ TA @ TB @ TC @ product_unit @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(185,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_order_Ostrict__trans2) ).
thf(852,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( qReachable @ TA @ TB @ TC )
= ( ^ [A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( E = C )
| ? [F: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( qReachable @ TA @ TB @ TC @ A @ B @ C @ D @ F )
& ? [G: message @ TA @ TC] :
( ( steps @ TA @ TB @ TC @ A @ B @ F @ G @ E )
& ? [H: TA] :
( ( member @ TA @ H @ D )
& ( isReceiverOf @ TA @ TC @ H @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_asynchronousSystem_OqReachable_Osimps) ).
thf(329,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( qReachable @ TA @ TB @ TC )
= ( ^ [A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( E = C )
| ? [F: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( qReachable @ TA @ TB @ TC @ A @ B @ C @ D @ F )
& ? [G: message @ TA @ TC] :
( ( steps @ TA @ TB @ TC @ A @ B @ F @ G @ E )
& ? [H: TA] :
( ( member @ TA @ H @ D )
& ( isReceiverOf @ TA @ TC @ H @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(283,axiom,
( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_NonUniformLexec) ).
thf(1159,plain,
( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(139,axiom,
fLPThe1922692578sensus @ p @ s @ v @ trans @ sends @ start,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_flpPseudoConsensus__axioms) ).
thf(682,plain,
fLPThe1922692578sensus @ p @ s @ v @ trans @ sends @ start,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(93,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_9) ).
thf(551,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(239,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_13) ).
thf(1012,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(264,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_in__mono) ).
thf(1106,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,B: TC,C: TC,D: TC > TA > ( messageValue @ TB ) > TA,E: configuration_ext @ TC @ TB @ TA @ product_unit,F: message @ TC @ TB,G: configuration_ext @ TC @ TB @ TA @ product_unit,H: TC > TA] :
( ( flpSystem @ TC @ TA @ TB @ A )
=> ( ( B = C )
=> ( ( steps @ TC @ TA @ TB @ D @ A @ E @ F @ G )
=> ( ( isReceiverOf @ TC @ TB @ B @ F )
=> ( ( initReachable @ TC @ TA @ TB @ D @ A @ H @ E )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [I: $o] : ( pSilDecVal @ TC @ TA @ TB @ D @ A @ H @ I @ C @ E ) )
@ ( collect @ $o
@ ^ [I: $o] : ( pSilDecVal @ TC @ TA @ TB @ D @ A @ H @ I @ C @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_flpSystem_OActiveProcessSilentDecisionValuesIncrease) ).
thf(583,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,B: TC,C: TC,D: TC > TA > ( messageValue @ TB ) > TA,E: configuration_ext @ TC @ TB @ TA @ product_unit,F: message @ TC @ TB,G: configuration_ext @ TC @ TB @ TA @ product_unit,H: TC > TA] :
( ( flpSystem @ TC @ TA @ TB @ A )
=> ( ( B = C )
=> ( ( steps @ TC @ TA @ TB @ D @ A @ E @ F @ G )
=> ( ( isReceiverOf @ TC @ TB @ B @ F )
=> ( ( initReachable @ TC @ TA @ TB @ D @ A @ H @ E )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [I: $o] : ( pSilDecVal @ TC @ TA @ TB @ D @ A @ H @ I @ C @ E ) )
@ ( collect @ $o
@ ^ [I: $o] : ( pSilDecVal @ TC @ TA @ TB @ D @ A @ H @ I @ C @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(88,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_order_Oorder__iff__strict) ).
thf(522,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(179,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_dense__le__bounded) ).
thf(830,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(87,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(519,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(241,axiom,
( ! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ A @ B )
=> ( ! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] : ( validity @ p @ s @ v @ trans @ sends @ start @ A @ B )
=> ( ! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] : ( agreementInit @ p @ s @ v @ trans @ sends @ start @ A @ B )
=> ? [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( initial @ p @ s @ v @ start @ A )
& ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_InitialNonUniformCfg) ).
thf(1017,plain,
( ! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ A @ B )
=> ( ! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] : ( validity @ p @ s @ v @ trans @ sends @ start @ A @ B )
=> ( ! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] : ( agreementInit @ p @ s @ v @ trans @ sends @ start @ A @ B )
=> ? [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( initial @ p @ s @ v @ start @ A )
& ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(152,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_dual__order_Ostrict__iff__order) ).
thf(725,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,B: TA > TC > ( messageValue @ TB ) > TC,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: TA] :
( ( flpSystem @ TA @ TC @ TB @ A )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit,G: set @ TA] : ( terminationPseudo @ TA @ TC @ TB @ B @ A @ C @ ( one_one @ nat ) @ F @ G )
=> ( ( initReachable @ TA @ TC @ TB @ B @ A @ C @ D )
=> ( ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ TA @ TC @ TB @ B @ A @ C @ F @ E @ D ) )
!= ( bot_bot @ ( set @ $o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_flpSystem_ODecisionValuesExist) ).
thf(980,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,B: TA > TC > ( messageValue @ TB ) > TC,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: TA] :
( ( flpSystem @ TA @ TC @ TB @ A )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit,G: set @ TA] : ( terminationPseudo @ TA @ TC @ TB @ B @ A @ C @ ( one_one @ nat ) @ F @ G )
=> ( ( initReachable @ TA @ TC @ TB @ B @ A @ C @ D )
=> ( ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ TA @ TC @ TB @ B @ A @ C @ F @ E @ D ) )
!= ( bot_bot @ ( set @ $o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: ( configuration_ext @ TA @ TB @ TC @ product_unit ) > ( configuration_ext @ TA @ TB @ TC @ product_unit ) > $o] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit] : ( E @ F @ F )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit,G: configuration_ext @ TA @ TB @ TC @ product_unit,H: message @ TA @ TB,I: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ F @ G )
=> ( ( E @ F @ G )
=> ( ( steps @ TA @ TC @ TB @ A @ B @ G @ H @ I )
=> ( E @ F @ I ) ) ) )
=> ( E @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_asynchronousSystem_Oreachable_Oinducts) ).
thf(388,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: ( configuration_ext @ TA @ TB @ TC @ product_unit ) > ( configuration_ext @ TA @ TB @ TC @ product_unit ) > $o] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit] : ( E @ F @ F )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit,G: configuration_ext @ TA @ TB @ TC @ product_unit,H: message @ TA @ TB,I: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ F @ G )
=> ( ( E @ F @ G )
=> ( ( steps @ TA @ TC @ TB @ A @ B @ G @ H @ I )
=> ( E @ F @ I ) ) ) )
=> ( E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(187,axiom,
stepReachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_isStepReachable) ).
thf(857,plain,
stepReachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(273,axiom,
bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_16) ).
thf(1138,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_insert__absorb2) ).
thf(356,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(244,axiom,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_MsgEnabled) ).
thf(1028,plain,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(162,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_singleton__inject) ).
thf(753,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(133,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_subset__insertI) ).
thf(669,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: TA > TC,F: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),G: list @ ( message @ TA @ TB )] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( execution @ TA @ TC @ TB @ A @ B @ E @ F @ G )
=> ( ( C
= ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ F ) )
=> ? [H: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),I: list @ ( message @ TA @ TB )] :
( ( execution @ TA @ TC @ TB @ A @ B @ E @ H @ I )
& ( ( ( prefixList @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ F @ H )
& ( prefixList @ ( message @ TA @ TB ) @ G @ I ) )
| ( ( F = H )
& ( G = I ) ) )
& ( ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ H )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_asynchronousSystem_OexpandExecutionReachable) ).
thf(526,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: TA > TC,F: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),G: list @ ( message @ TA @ TB )] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( execution @ TA @ TC @ TB @ A @ B @ E @ F @ G )
=> ( ( C
= ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ F ) )
=> ? [H: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),I: list @ ( message @ TA @ TB )] :
( ( execution @ TA @ TC @ TB @ A @ B @ E @ H @ I )
& ( ( ( prefixList @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ F @ H )
& ( prefixList @ ( message @ TA @ TB ) @ G @ I ) )
| ( ( F = H )
& ( G = I ) ) )
& ( ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ H )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(119,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_not__le__imp__less) ).
thf(637,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(281,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_bot__set__def) ).
thf(1155,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(147,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_subset__empty) ).
thf(706,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( stepReachable @ TA @ TB @ TC )
= ( stepReachable @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_asynchronousSystem_OstepReachable_Ocong) ).
thf(328,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(70,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_empty__subsetI) ).
thf(471,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(198,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_dense__ge__bounded) ).
thf(901,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(142,axiom,
! [A: p] :
? [B: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ B )
& ( ( collect @ $o
@ ^ [C: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ C @ A @ B ) )
= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126__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) ).
thf(686,plain,
! [A: p] :
? [B: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ B )
& ( ( collect @ $o
@ ^ [C: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ C @ A @ B ) )
= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TA @ TB @ TC @ product_unit @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_asynchronousSystem_OExistsMsg) ).
thf(679,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TA @ TB @ TC @ product_unit @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(246,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_subset__insertI2) ).
thf(1039,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(223,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_dense__ge) ).
thf(970,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(233,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_order__subst2) ).
thf(997,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(229,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_subset__antisym) ).
thf(985,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(145,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_emptyE) ).
thf(701,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( minimalEnabled @ TA @ TB @ TC )
= ( minimalEnabled @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_execution_OminimalEnabled_Ocong) ).
thf(457,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(235,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(1002,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: TA > TB,D: configuration_ext @ TA @ TC @ TB @ product_unit,E: set @ TA] :
( ( fLPThe1922692578sensus @ TA @ TB @ TC @ A @ B @ C )
=> ( terminationPseudo @ TA @ TB @ TC @ A @ B @ C @ ( one_one @ nat ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_flpPseudoConsensus_OPseudoTermination) ).
thf(371,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: TA > TB,D: configuration_ext @ TA @ TC @ TB @ product_unit,E: set @ TA] :
( ( fLPThe1922692578sensus @ TA @ TB @ TC @ A @ B @ C )
=> ( terminationPseudo @ TA @ TB @ TC @ A @ B @ C @ ( one_one @ nat ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(85,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_le__imp__less__or__eq) ).
thf(515,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(279,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_order_Ostrict__iff__order) ).
thf(1150,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(270,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_equalityD2) ).
thf(1131,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(127,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_empty__def) ).
thf(654,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(257,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: p] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ~ ( isReceiverOf @ p @ v @ D @ B )
=> ( ( states @ p @ v @ s @ product_unit @ A @ D )
= ( states @ p @ v @ s @ product_unit @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_NoReceivingNoChange) ).
thf(1086,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: p] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ~ ( isReceiverOf @ p @ v @ D @ B )
=> ( ( states @ p @ v @ s @ product_unit @ A @ D )
= ( states @ p @ v @ s @ product_unit @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(83,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_empty__iff) ).
thf(508,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(128,axiom,
reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_lastExecExec_HReachable) ).
thf(657,plain,
reachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(166,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
= ( ( C = A )
| ? [D: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ D )
& ? [E: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ D @ E @ C )
& ? [F: p] :
( ( member @ p @ F @ B )
& ( isReceiverOf @ p @ v @ F @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_qReachable_Osimps) ).
thf(765,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
= ( ( C = A )
| ? [D: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ D )
& ? [E: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ D @ E @ C )
& ? [F: p] :
( ( member @ p @ F @ B )
& ( isReceiverOf @ p @ v @ F @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(135,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: p] :
( ! [C: configuration_ext @ p @ v @ s @ product_unit,D: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ C @ D )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
=> ( ( collect @ $o
@ ^ [C: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ C @ B @ A ) )
!= ( bot_bot @ ( set @ $o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_DecisionValuesExist) ).
thf(674,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: p] :
( ! [C: configuration_ext @ p @ v @ s @ product_unit,D: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ C @ D )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
=> ( ( collect @ $o
@ ^ [C: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ C @ B @ A ) )
!= ( bot_bot @ ( set @ $o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(243,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_le__funE) ).
thf(1026,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(169,axiom,
! [A: p,B: p,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v,E: configuration_ext @ p @ v @ s @ product_unit] :
( ( A != B )
=> ( ( steps @ p @ s @ v @ trans @ sends @ C @ D @ E )
=> ( ( isReceiverOf @ p @ v @ A @ D )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ F @ B @ E ) )
@ ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ F @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_InactiveProcessSilentDecisionValuesDecrease) ).
thf(773,plain,
! [A: p,B: p,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v,E: configuration_ext @ p @ v @ s @ product_unit] :
( ( A != B )
=> ( ( steps @ p @ s @ v @ trans @ sends @ C @ D @ E )
=> ( ( isReceiverOf @ p @ v @ A @ D )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ C )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ F @ B @ E ) )
@ ( collect @ $o
@ ^ [F: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ F @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(118,axiom,
~ ! [A: configuration_ext @ p @ v @ s @ product_unit] :
~ ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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) ).
thf(633,plain,
~ ! [A: configuration_ext @ p @ v @ s @ product_unit] :
~ ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: ( configuration_ext @ TA @ TB @ TC @ product_unit ) > ( set @ TA ) > ( configuration_ext @ TA @ TB @ TC @ product_unit ) > $o] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ! [G: configuration_ext @ TA @ TB @ TC @ product_unit,H: set @ TA] : ( F @ G @ H @ G )
=> ( ! [G: configuration_ext @ TA @ TB @ TC @ product_unit,H: set @ TA,I: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ G @ H @ I )
=> ( ( F @ G @ H @ I )
=> ! [J: message @ TA @ TB,K: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( steps @ TA @ TC @ TB @ A @ B @ I @ J @ K )
=> ( ? [L: TA] :
( ( member @ TA @ L @ H )
& ( isReceiverOf @ TA @ TB @ L @ J ) )
=> ( F @ G @ H @ K ) ) ) ) )
=> ( F @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_asynchronousSystem_OqReachable_Oinducts) ).
thf(360,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: ( configuration_ext @ TA @ TB @ TC @ product_unit ) > ( set @ TA ) > ( configuration_ext @ TA @ TB @ TC @ product_unit ) > $o] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ! [G: configuration_ext @ TA @ TB @ TC @ product_unit,H: set @ TA] : ( F @ G @ H @ G )
=> ( ! [G: configuration_ext @ TA @ TB @ TC @ product_unit,H: set @ TA,I: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ G @ H @ I )
=> ( ( F @ G @ H @ I )
=> ! [J: message @ TA @ TB,K: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( steps @ TA @ TC @ TB @ A @ B @ I @ J @ K )
=> ( ? [L: TA] :
( ( member @ TA @ L @ H )
& ( isReceiverOf @ TA @ TB @ L @ J ) )
=> ( F @ G @ H @ K ) ) ) ) )
=> ( F @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(96,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_dual__order_Ostrict__trans1) ).
thf(558,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(253,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_ex__in__conv) ).
thf(1071,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(271,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_order__trans) ).
thf(1135,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(161,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v,E: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( steps @ p @ s @ v @ trans @ sends @ C @ D @ E )
=> ( ? [F: p] :
( ( member @ p @ F @ B )
& ( isReceiverOf @ p @ v @ F @ D ) )
=> ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_StepQ) ).
thf(750,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v,E: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( steps @ p @ s @ v @ trans @ sends @ C @ D @ E )
=> ( ? [F: p] :
( ( member @ p @ F @ B )
& ( isReceiverOf @ p @ v @ F @ D ) )
=> ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(55,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_insert__eq__iff) ).
thf(430,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(263,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_subset__insert) ).
thf(1103,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(177,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_doubleton__eq__iff) ).
thf(824,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(159,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_le__less__linear) ).
thf(745,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_le__fun__def) ).
thf(573,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( steps @ TA @ TB @ TC )
= ( steps @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_asynchronousSystem_Osteps_Ocong) ).
thf(296,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_insert__iff) ).
thf(375,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(237,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TC @ TB @ product_unit,F: TA] :
( ( qReachable @ TA @ TB @ TC @ A @ B @ C @ D @ E )
=> ( ~ ( member @ TA @ F @ D )
=> ( ( states @ TA @ TC @ TB @ product_unit @ C @ F )
= ( states @ TA @ TC @ TB @ product_unit @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_asynchronousSystem_ONotInQFrozenQReachability) ).
thf(1007,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TC @ TB @ product_unit,F: TA] :
( ( qReachable @ TA @ TB @ TC @ A @ B @ C @ D @ E )
=> ( ~ ( member @ TA @ F @ D )
=> ( ( states @ TA @ TC @ TB @ product_unit @ C @ F )
= ( states @ TA @ TC @ TB @ product_unit @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1,conjecture,
( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ cMsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ cMsg ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(286,plain,
~ ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ cMsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(158,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_8) ).
thf(743,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( validity @ TA @ TB @ TC )
= ( validity @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_flpSystem_Ovalidity_Ocong) ).
thf(291,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(91,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_insert__Collect) ).
thf(545,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: TA > TC,G: list @ ( message @ TA @ TB )] :
( ( steps @ TA @ TC @ TB @ A @ B @ ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ C ) @ D @ E )
=> ( ( execution @ TA @ TC @ TB @ A @ B @ F @ C @ G )
=> ? [H: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),I: list @ ( message @ TA @ TB )] :
( ( execution @ TA @ TC @ TB @ A @ B @ F @ H @ I )
& ( prefixList @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ C @ H )
& ( prefixList @ ( message @ TA @ TB ) @ G @ I )
& ( ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ H )
= E )
& ( ( last @ ( message @ TA @ TB ) @ I )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_asynchronousSystem_OexpandExecutionStep) ).
thf(843,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: TA > TC,G: list @ ( message @ TA @ TB )] :
( ( steps @ TA @ TC @ TB @ A @ B @ ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ C ) @ D @ E )
=> ( ( execution @ TA @ TC @ TB @ A @ B @ F @ C @ G )
=> ? [H: list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ),I: list @ ( message @ TA @ TB )] :
( ( execution @ TA @ TC @ TB @ A @ B @ F @ H @ I )
& ( prefixList @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ C @ H )
& ( prefixList @ ( message @ TA @ TB ) @ G @ I )
& ( ( last @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ H )
= E )
& ( ( last @ ( message @ TA @ TB ) @ I )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(268,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_order_Ostrict__implies__order) ).
thf(1125,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(103,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( enabled @ p @ v @ s @ A @ D )
=> ( ~ ( enabled @ p @ v @ s @ C @ D )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_OnlyOccurenceDisables) ).
thf(577,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( enabled @ p @ v @ s @ A @ D )
=> ( ~ ( enabled @ p @ v @ s @ C @ D )
=> ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(149,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( C != A )
=> ~ ! [D: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ D )
=> ! [E: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ D @ E @ C )
=> ~ ? [F: p] :
( ( member @ p @ F @ B )
& ( isReceiverOf @ p @ v @ F @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_qReachable_Ocases) ).
thf(711,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( C != A )
=> ~ ! [D: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ D )
=> ! [E: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ D @ E @ C )
=> ~ ? [F: p] :
( ( member @ p @ F @ B )
& ( isReceiverOf @ p @ v @ F @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(122,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_order__class_Oorder_Oantisym) ).
thf(641,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(274,axiom,
prefixList @ ( message @ p @ v ) @ trace2 @ traceMsga,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_ExecMsg_I2_J) ).
thf(1139,plain,
prefixList @ ( message @ p @ v ) @ trace2 @ traceMsga,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,B: TA > TB > ( messageValue @ TC ) > TB,C: TA > TB,D: $o,E: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( flpSystem @ TA @ TB @ TC @ A )
=> ( ( vUniform @ TA @ TB @ TC @ B @ A @ C @ D @ E )
= ( ( initReachable @ TA @ TB @ TC @ B @ A @ C @ E )
& ! [F: TA] :
( ( collect @ $o
@ ^ [G: $o] : ( pSilDecVal @ TA @ TB @ TC @ B @ A @ C @ G @ F @ E ) )
= ( insert @ $o @ D @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_flpSystem_OvUniform__def) ).
thf(611,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,B: TA > TB > ( messageValue @ TC ) > TB,C: TA > TB,D: $o,E: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( flpSystem @ TA @ TB @ TC @ A )
=> ( ( vUniform @ TA @ TB @ TC @ B @ A @ C @ D @ E )
= ( ( initReachable @ TA @ TB @ TC @ B @ A @ C @ E )
& ! [F: TA] :
( ( collect @ $o
@ ^ [G: $o] : ( pSilDecVal @ TA @ TB @ TC @ B @ A @ C @ G @ F @ E ) )
= ( insert @ $o @ D @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(79,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_ord__le__eq__trans) ).
thf(498,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(259,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_eq__iff) ).
thf(1092,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: $o,B: $o] :
( ( ( outMsg @ TA @ TB @ A )
= ( outMsg @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_message_Oinject_I2_J) ).
thf(335,plain,
! [TA: $tType,TB: $tType,A: $o,B: $o] :
( ( ( outMsg @ TA @ TB @ A )
= ( outMsg @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(258,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__cases) ).
thf(1090,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,B: TC,C: TC,D: TC > TA > ( messageValue @ TB ) > TA,E: configuration_ext @ TC @ TB @ TA @ product_unit,F: message @ TC @ TB,G: configuration_ext @ TC @ TB @ TA @ product_unit,H: TC > TA] :
( ( flpSystem @ TC @ TA @ TB @ A )
=> ( ( B != C )
=> ( ( steps @ TC @ TA @ TB @ D @ A @ E @ F @ G )
=> ( ( isReceiverOf @ TC @ TB @ B @ F )
=> ( ( initReachable @ TC @ TA @ TB @ D @ A @ H @ E )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [I: $o] : ( pSilDecVal @ TC @ TA @ TB @ D @ A @ H @ I @ C @ G ) )
@ ( collect @ $o
@ ^ [I: $o] : ( pSilDecVal @ TC @ TA @ TB @ D @ A @ H @ I @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_flpSystem_OInactiveProcessSilentDecisionValuesDecrease) ).
thf(947,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,B: TC,C: TC,D: TC > TA > ( messageValue @ TB ) > TA,E: configuration_ext @ TC @ TB @ TA @ product_unit,F: message @ TC @ TB,G: configuration_ext @ TC @ TB @ TA @ product_unit,H: TC > TA] :
( ( flpSystem @ TC @ TA @ TB @ A )
=> ( ( B != C )
=> ( ( steps @ TC @ TA @ TB @ D @ A @ E @ F @ G )
=> ( ( isReceiverOf @ TC @ TB @ B @ F )
=> ( ( initReachable @ TC @ TA @ TB @ D @ A @ H @ E )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [I: $o] : ( pSilDecVal @ TC @ TA @ TB @ D @ A @ H @ I @ C @ G ) )
@ ( collect @ $o
@ ^ [I: $o] : ( pSilDecVal @ TC @ TA @ TB @ D @ A @ H @ I @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( D != C )
=> ~ ! [E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ E )
=> ! [F: message @ TA @ TB] :
~ ( steps @ TA @ TC @ TB @ A @ B @ E @ F @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_asynchronousSystem_Oreachable_Ocases) ).
thf(445,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( D != C )
=> ~ ! [E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ E )
=> ! [F: message @ TA @ TB] :
~ ( steps @ TA @ TC @ TB @ A @ B @ E @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(210,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: $o,C: configuration_ext @ p @ v @ s @ product_unit] :
~ ( steps @ p @ s @ v @ trans @ sends @ A @ ( outMsg @ p @ v @ B ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_StepOutMsg) ).
thf(936,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: $o,C: configuration_ext @ p @ v @ s @ product_unit] :
~ ( steps @ p @ s @ v @ trans @ sends @ A @ ( outMsg @ p @ v @ B ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(197,axiom,
order_bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_11) ).
thf(900,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(138,axiom,
initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_InitReachLastExec_H) ).
thf(681,plain,
initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(250,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: ( configuration_ext @ p @ v @ s @ product_unit ) > ( configuration_ext @ p @ v @ s @ product_unit ) > $o] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ! [D: configuration_ext @ p @ v @ s @ product_unit] : ( C @ D @ D )
=> ( ! [D: configuration_ext @ p @ v @ s @ product_unit,E: configuration_ext @ p @ v @ s @ product_unit,F: message @ p @ v,G: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ D @ E )
=> ( ( C @ D @ E )
=> ( ( steps @ p @ s @ v @ trans @ sends @ E @ F @ G )
=> ( C @ D @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_reachable_Oinducts) ).
thf(1048,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: ( configuration_ext @ p @ v @ s @ product_unit ) > ( configuration_ext @ p @ v @ s @ product_unit ) > $o] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ! [D: configuration_ext @ p @ v @ s @ product_unit] : ( C @ D @ D )
=> ( ! [D: configuration_ext @ p @ v @ s @ product_unit,E: configuration_ext @ p @ v @ s @ product_unit,F: message @ p @ v,G: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ D @ E )
=> ( ( C @ D @ E )
=> ( ( steps @ p @ s @ v @ trans @ sends @ E @ F @ G )
=> ( C @ D @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(277,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_subset__singleton__iff) ).
thf(1144,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(18,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(318,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(125,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_insert__not__empty) ).
thf(649,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_insert__ident) ).
thf(303,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(190,axiom,
~ ! [A: list @ ( configuration_ext @ p @ v @ s @ product_unit ),B: list @ ( message @ p @ v )] :
( ( execution @ p @ s @ v @ trans @ sends @ start @ A @ B )
=> ( ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ A )
& ( prefixList @ ( message @ p @ v ) @ trace @ B ) )
| ( ( exec = A )
& ( trace = B ) ) )
=> ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A )
!= c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179__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) ).
thf(863,plain,
~ ! [A: list @ ( configuration_ext @ p @ v @ s @ product_unit ),B: list @ ( message @ p @ v )] :
( ( execution @ p @ s @ v @ trans @ sends @ start @ A @ B )
=> ( ( ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec @ A )
& ( prefixList @ ( message @ p @ v ) @ trace @ B ) )
| ( ( exec = A )
& ( trace = B ) ) )
=> ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A )
!= c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(195,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_equalityD1) ).
thf(890,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(172,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_order_Ostrict__trans1) ).
thf(811,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(113,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: $o] :
( ! [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
=> ( agreement @ p @ v @ s @ C ) )
=> ( ! [C: configuration_ext @ p @ v @ s @ product_unit,D: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ C @ D )
=> ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ B ) ) ) )
=> ( vUniform @ p @ s @ v @ trans @ sends @ start @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_DecidedImpliesUniform) ).
thf(621,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: $o] :
( ! [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
=> ( agreement @ p @ v @ s @ C ) )
=> ( ! [C: configuration_ext @ p @ v @ s @ product_unit,D: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ C @ D )
=> ( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ B ) ) ) )
=> ( vUniform @ p @ s @ v @ trans @ sends @ start @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(245,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( A = B )
| ? [C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v,E: p] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ D @ C )
& ( enabled @ p @ v @ s @ A @ D )
& ( isReceiverOf @ p @ v @ E @ D )
& ( reachable @ p @ s @ v @ trans @ sends @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_ReachableStepFirst) ).
thf(1029,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( A = B )
| ? [C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v,E: p] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ D @ C )
& ( enabled @ p @ v @ s @ A @ D )
& ( isReceiverOf @ p @ v @ E @ D )
& ( reachable @ p @ s @ v @ trans @ sends @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(221,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_predicate1I) ).
thf(964,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(242,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_eq__refl) ).
thf(1022,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: TA > TB] :
( ( fLPThe1922692578sensus @ TA @ TB @ TC @ A @ B @ C )
=> ( flpSystem @ TA @ TB @ TC @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_flpPseudoConsensus_Oaxioms_I1_J) ).
thf(462,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: TA > TB] :
( ( fLPThe1922692578sensus @ TA @ TB @ TC @ A @ B @ C )
=> ( flpSystem @ TA @ TB @ TC @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(188,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_10) ).
thf(858,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(34,axiom,
bot @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Obot_5) ).
thf(367,plain,
bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(200,axiom,
order @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_20) ).
thf(912,plain,
order @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(228,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_7) ).
thf(983,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(248,axiom,
reachable @ p @ s @ v @ trans @ sends @ cMsg @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_cMsgLastReachable) ).
thf(1044,plain,
reachable @ p @ s @ v @ trans @ sends @ cMsg @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(251,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: message @ TA @ TC,E: configuration_ext @ TA @ TC @ TB @ product_unit,F: TA] :
( ( steps @ TA @ TB @ TC @ A @ B @ C @ D @ E )
=> ( ~ ( isReceiverOf @ TA @ TC @ F @ D )
=> ( ( states @ TA @ TC @ TB @ product_unit @ C @ F )
= ( states @ TA @ TC @ TB @ product_unit @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_asynchronousSystem_ONoReceivingNoChange) ).
thf(1066,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: message @ TA @ TC,E: configuration_ext @ TA @ TC @ TB @ product_unit,F: TA] :
( ( steps @ TA @ TB @ TC @ A @ B @ C @ D @ E )
=> ( ~ ( isReceiverOf @ TA @ TC @ F @ D )
=> ( ( states @ TA @ TC @ TB @ product_unit @ C @ F )
= ( states @ TA @ TC @ TB @ product_unit @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( initReachable @ TA @ TB @ TC )
= ( ^ [A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: TA > TB,D: configuration_ext @ TA @ TC @ TB @ product_unit] :
? [E: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( initial @ TA @ TB @ TC @ C @ E )
& ( reachable @ TA @ TB @ TC @ A @ B @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_asynchronousSystem_OinitReachable__def) ).
thf(306,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( initReachable @ TA @ TB @ TC )
= ( ^ [A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: TA > TB,D: configuration_ext @ TA @ TC @ TB @ product_unit] :
? [E: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( initial @ TA @ TB @ TC @ C @ E )
& ( reachable @ TA @ TB @ TC @ A @ B @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(234,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_subsetD) ).
thf(1000,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_insertI2) ).
thf(299,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(184,axiom,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_True) ).
thf(851,plain,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(205,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_dual__order_Otrans) ).
thf(922,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(129,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_dual__order_Orefl) ).
thf(658,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(167,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_bot_Oextremum__unique) ).
thf(768,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(178,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_antisym) ).
thf(827,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( reachable @ TA @ TC @ TB @ A @ B @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_asynchronousSystem_OQReachImplReach) ).
thf(455,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( reachable @ TA @ TC @ TB @ A @ B @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(194,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_equalityE) ).
thf(883,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(82,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: p,E: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( isReceiverOf @ p @ v @ D @ B )
=> ( ~ ( isReceiverOf @ p @ v @ D @ E )
=> ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ A @ E ) @ ( msgs @ p @ v @ s @ product_unit @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_NoMessageLossStep) ).
thf(505,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: p,E: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( isReceiverOf @ p @ v @ D @ B )
=> ( ~ ( isReceiverOf @ p @ v @ D @ E )
=> ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ A @ E ) @ ( msgs @ p @ v @ s @ product_unit @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( stepReachable @ TA @ TB @ TC )
= ( ^ [A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: message @ TA @ TC,E: configuration_ext @ TA @ TC @ TB @ product_unit] :
? [F: configuration_ext @ TA @ TC @ TB @ product_unit,G: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( reachable @ TA @ TB @ TC @ A @ B @ C @ F )
& ( steps @ TA @ TB @ TC @ A @ B @ F @ D @ G )
& ( reachable @ TA @ TB @ TC @ A @ B @ G @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_asynchronousSystem_OstepReachable__def) ).
thf(438,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( stepReachable @ TA @ TB @ TC )
= ( ^ [A: TA > TB > ( messageValue @ TC ) > TB,B: TA > TB > ( messageValue @ TC ) > ( message @ TA @ TC ) > nat,C: configuration_ext @ TA @ TC @ TB @ product_unit,D: message @ TA @ TC,E: configuration_ext @ TA @ TC @ TB @ product_unit] :
? [F: configuration_ext @ TA @ TC @ TB @ product_unit,G: configuration_ext @ TA @ TC @ TB @ product_unit] :
( ( reachable @ TA @ TB @ TC @ A @ B @ C @ F )
& ( steps @ TA @ TB @ TC @ A @ B @ F @ D @ G )
& ( reachable @ TA @ TB @ TC @ A @ B @ G @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(71,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_subset__trans) ).
thf(473,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(77,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_6) ).
thf(490,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: message @ TA @ TB,G: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( steps @ TA @ TC @ TB @ A @ B @ E @ F @ G )
=> ( ? [H: TA] :
( ( member @ TA @ H @ D )
& ( isReceiverOf @ TA @ TB @ H @ F ) )
=> ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_asynchronousSystem_OStepQ) ).
thf(426,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: message @ TA @ TB,G: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( steps @ TA @ TC @ TB @ A @ B @ E @ F @ G )
=> ( ? [H: TA] :
( ( member @ TA @ H @ D )
& ( isReceiverOf @ TA @ TB @ H @ F ) )
=> ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(213,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_all__not__in__conv) ).
thf(944,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( initial @ TA @ TB @ TC )
= ( initial @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_asynchronousSystem_Oinitial_Ocong) ).
thf(374,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(76,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_empty__Collect__eq) ).
thf(487,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(255,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_predicate1D) ).
thf(1081,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(111,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_dual__order_Ostrict__trans2) ).
thf(617,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(211,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_bot_Oextremum) ).
thf(939,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(94,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] : ( agreementInit @ p @ s @ v @ trans @ sends @ start @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Agreement) ).
thf(553,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] : ( agreementInit @ p @ s @ v @ trans @ sends @ start @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(65,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_mk__disjoint__insert) ).
thf(458,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(181,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_ExistsMsg) ).
thf(836,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(131,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_order__class_Oorder_Oeq__iff) ).
thf(663,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > ( messageValue @ TC ) > ( message @ TB @ TC ) > nat,B: configuration_ext @ TB @ TC @ TA @ product_unit] :
( ( flpSystem @ TB @ TA @ TC @ A )
=> ( ( agreement @ TB @ TC @ TA @ B )
= ( ! [C: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TB @ TC @ TA @ product_unit @ B @ ( outMsg @ TB @ TC @ C ) ) )
=> ! [D: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TB @ TC @ TA @ product_unit @ B @ ( outMsg @ TB @ TC @ D ) ) )
= ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_flpSystem_Oagreement__def) ).
thf(548,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > ( messageValue @ TC ) > ( message @ TB @ TC ) > nat,B: configuration_ext @ TB @ TC @ TA @ product_unit] :
( ( flpSystem @ TB @ TA @ TC @ A )
=> ( ( agreement @ TB @ TC @ TA @ B )
= ( ! [C: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TB @ TC @ TA @ product_unit @ B @ ( outMsg @ TB @ TC @ C ) ) )
=> ! [D: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TB @ TC @ TA @ product_unit @ B @ ( outMsg @ TB @ TC @ D ) ) )
= ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(89,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_14) ).
thf(525,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(143,axiom,
~ ! [A: list @ ( configuration_ext @ p @ v @ s @ product_unit ),B: list @ ( message @ p @ v )] :
( ( execution @ p @ s @ v @ trans @ sends @ start @ A @ B )
=> ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 @ A )
=> ( ( prefixList @ ( message @ p @ v ) @ trace2 @ B )
=> ( ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A )
= cMsg )
=> ( ( last @ ( message @ p @ v ) @ B )
!= msg ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180__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(690,plain,
~ ! [A: list @ ( configuration_ext @ p @ v @ s @ product_unit ),B: list @ ( message @ p @ v )] :
( ( execution @ p @ s @ v @ trans @ sends @ start @ A @ B )
=> ( ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 @ A )
=> ( ( prefixList @ ( message @ p @ v ) @ trace2 @ B )
=> ( ( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A )
= cMsg )
=> ( ( last @ ( message @ p @ v ) @ B )
!= msg ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(121,axiom,
execution @ p @ s @ v @ trans @ sends @ start @ exec @ trace,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_ExecIsExecution) ).
thf(640,plain,
execution @ p @ s @ v @ trans @ sends @ start @ exec @ trace,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_insertI1) ).
thf(414,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(156,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( reachable @ p @ s @ v @ trans @ sends @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_QReachImplReach) ).
thf(739,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( reachable @ p @ s @ v @ trans @ sends @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(261,axiom,
( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga )
= cMsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ExecMsg_I3_J) ).
thf(1098,plain,
( ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ execMsga )
= cMsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(231,axiom,
steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ cMsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_CMsg) ).
thf(993,plain,
steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ cMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: configuration_ext @ TA @ TB @ TC @ product_unit,C: TA > TC > ( messageValue @ TB ) > TC,D: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat] :
( ( initial @ TA @ TC @ TB @ A @ B )
=> ( initReachable @ TA @ TC @ TB @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_asynchronousSystem_OInitialIsInitReachable) ).
thf(441,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: configuration_ext @ TA @ TB @ TC @ product_unit,C: TA > TC > ( messageValue @ TB ) > TC,D: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat] :
( ( initial @ TA @ TC @ TB @ A @ B )
=> ( initReachable @ TA @ TC @ TB @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(37,axiom,
order_bot @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder__bot_1) ).
thf(370,plain,
order_bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(80,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_subset__refl) ).
thf(502,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_bot__apply) ).
thf(338,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(102,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_15) ).
thf(576,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( reachable @ TA @ TB @ TC )
= ( reachable @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_asynchronousSystem_Oreachable_Ocong) ).
thf(359,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(146,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_singleton__iff) ).
thf(703,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA] : ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_asynchronousSystem_OInitQ) ).
thf(314,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA] : ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: TA,G: message @ TA @ TB] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ~ ( member @ TA @ F @ D )
=> ( ( isReceiverOf @ TA @ TB @ F @ G )
=> ( ord_less_eq @ nat @ ( msgs @ TA @ TB @ TC @ product_unit @ C @ G ) @ ( msgs @ TA @ TB @ TC @ product_unit @ E @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_asynchronousSystem_ONoActivityNoMessageLoss) ).
thf(571,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: TA,G: message @ TA @ TB] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ~ ( member @ TA @ F @ D )
=> ( ( isReceiverOf @ TA @ TB @ F @ G )
=> ( ord_less_eq @ nat @ ( msgs @ TA @ TB @ TC @ product_unit @ C @ G ) @ ( msgs @ TA @ TB @ TC @ product_unit @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(191,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ~ ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_less__le__not__le) ).
thf(876,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ~ ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: $o,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
~ ( steps @ TA @ TC @ TB @ A @ B @ C @ ( outMsg @ TA @ TB @ D ) @ E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_asynchronousSystem_OStepOutMsg) ).
thf(386,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: $o,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
~ ( steps @ TA @ TC @ TB @ A @ B @ C @ ( outMsg @ TA @ TB @ D ) @ E ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(226,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit] : ( reachable @ p @ s @ v @ trans @ sends @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_init) ).
thf(978,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit] : ( reachable @ p @ s @ v @ trans @ sends @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(275,axiom,
( ( agreement @ p @ v @ s )
= ( ^ [A: configuration_ext @ p @ v @ s @ product_unit] :
! [B: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ B ) ) )
=> ! [C: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ C ) ) )
= ( C = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_agreement__def) ).
thf(1140,plain,
( ( agreement @ p @ v @ s )
= ( ^ [A: configuration_ext @ p @ v @ s @ product_unit] :
! [B: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ B ) ) )
=> ! [C: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ A @ ( outMsg @ p @ v @ C ) ) )
= ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(68,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( agreementInit @ p @ s @ v @ trans @ sends @ start @ A @ B )
= ( ( ( initial @ p @ s @ v @ start @ A )
& ( reachable @ p @ s @ v @ trans @ sends @ A @ B ) )
=> ! [C: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ B @ ( outMsg @ p @ v @ C ) ) )
=> ! [D: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ B @ ( outMsg @ p @ v @ D ) ) )
= ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_agreementInit__def) ).
thf(465,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit] :
( ( agreementInit @ p @ s @ v @ trans @ sends @ start @ A @ B )
= ( ( ( initial @ p @ s @ v @ start @ A )
& ( reachable @ p @ s @ v @ trans @ sends @ A @ B ) )
=> ! [C: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ B @ ( outMsg @ p @ v @ C ) ) )
=> ! [D: $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ B @ ( outMsg @ p @ v @ D ) ) )
= ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: TA,G: TA,H: message @ TA @ TB,I: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( F != G )
=> ( ( isReceiverOf @ TA @ TB @ F @ D )
=> ( ~ ( isReceiverOf @ TA @ TB @ F @ H )
=> ( ( isReceiverOf @ TA @ TB @ G @ H )
=> ( ~ ( isReceiverOf @ TA @ TB @ G @ D )
=> ( ( steps @ TA @ TC @ TB @ A @ B @ C @ H @ I )
=> ? [J: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( steps @ TA @ TC @ TB @ A @ B @ E @ H @ J )
& ( steps @ TA @ TC @ TB @ A @ B @ I @ D @ J ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_asynchronousSystem_ODiamondOne) ).
thf(450,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: TA,G: TA,H: message @ TA @ TB,I: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( F != G )
=> ( ( isReceiverOf @ TA @ TB @ F @ D )
=> ( ~ ( isReceiverOf @ TA @ TB @ F @ H )
=> ( ( isReceiverOf @ TA @ TB @ G @ H )
=> ( ~ ( isReceiverOf @ TA @ TB @ G @ D )
=> ( ( steps @ TA @ TC @ TB @ A @ B @ C @ H @ I )
=> ? [J: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( steps @ TA @ TC @ TB @ A @ B @ E @ H @ J )
& ( steps @ TA @ TC @ TB @ A @ B @ I @ D @ J ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(208,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_subset__eq) ).
thf(931,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(74,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Collect__subset) ).
thf(482,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(134,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_equals0I) ).
thf(671,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(225,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_dual__order_Ostrict__implies__order) ).
thf(976,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: TA,G: message @ TA @ TB] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( isReceiverOf @ TA @ TB @ F @ D )
=> ( ~ ( isReceiverOf @ TA @ TB @ F @ G )
=> ( ord_less_eq @ nat @ ( msgs @ TA @ TB @ TC @ product_unit @ C @ G ) @ ( msgs @ TA @ TB @ TC @ product_unit @ E @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_asynchronousSystem_ONoMessageLossStep) ).
thf(581,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: TA,G: message @ TA @ TB] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( isReceiverOf @ TA @ TB @ F @ D )
=> ( ~ ( isReceiverOf @ TA @ TB @ F @ G )
=> ( ord_less_eq @ nat @ ( msgs @ TA @ TB @ TC @ product_unit @ C @ G ) @ ( msgs @ TA @ TB @ TC @ product_unit @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(164,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_antisym__conv) ).
thf(759,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(238,axiom,
( ( p2 = p2 )
=> ( ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ cMsg )
=> ( ( isReceiverOf @ p @ v @ p2 @ msg )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ cMsg ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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) ).
thf(1010,plain,
( ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ cMsg )
=> ( ( isReceiverOf @ p @ v @ p2 @ msg )
=> ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
=> ( ord_less_eq @ ( set @ $o )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) )
@ ( collect @ $o
@ ^ [A: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ A @ p2 @ cMsg ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(35,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_3) ).
thf(368,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(168,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_singletonI) ).
thf(771,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(265,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: p] :
( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ A ) )
=> ( ! [C: configuration_ext @ p @ v @ s @ product_unit,D: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ C @ D )
=> ( ! [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
=> ( agreement @ p @ v @ s @ C ) )
=> ? [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
& ( ( collect @ $o
@ ^ [D: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ D @ B @ C ) )
= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_NonUniformCanReachSilentBivalence) ).
thf(1108,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: p] :
( ( ( initReachable @ p @ s @ v @ trans @ sends @ start @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ A )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ A ) )
=> ( ! [C: configuration_ext @ p @ v @ s @ product_unit,D: set @ p] : ( terminationPseudo @ p @ s @ v @ trans @ sends @ start @ ( one_one @ nat ) @ C @ D )
=> ( ! [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
=> ( agreement @ p @ v @ s @ C ) )
=> ? [C: configuration_ext @ p @ v @ s @ product_unit] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ C )
& ( ( collect @ $o
@ ^ [D: $o] : ( pSilDecVal @ p @ s @ v @ trans @ sends @ start @ D @ B @ C ) )
= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(144,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_insert__mono) ).
thf(699,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( E != C )
=> ~ ! [F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ F )
=> ! [G: message @ TA @ TB] :
( ( steps @ TA @ TC @ TB @ A @ B @ F @ G @ E )
=> ~ ? [H: TA] :
( ( member @ TA @ H @ D )
& ( isReceiverOf @ TA @ TB @ H @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_asynchronousSystem_OqReachable_Ocases) ).
thf(319,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( E != C )
=> ~ ! [F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ F )
=> ! [G: message @ TA @ TB] :
( ( steps @ TA @ TC @ TB @ A @ B @ F @ G @ E )
=> ~ ? [H: TA] :
( ( member @ TA @ H @ D )
& ( isReceiverOf @ TA @ TB @ H @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ),E: list @ ( message @ TC @ TB ),F: message @ TC @ TB] :
( ( execution @ TC @ TA @ TB @ A @ B @ C @ D @ E )
=> ( ( enabled @ TC @ TB @ TA @ ( last @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) @ D ) @ F )
=> ( ? [G: TC] : ( isReceiverOf @ TC @ TB @ G @ F )
=> ? [G: nat] : ( firstOccurrence @ TC @ TB @ TA @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_execution_OFirstOccurrenceExists) ).
thf(652,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ),E: list @ ( message @ TC @ TB ),F: message @ TC @ TB] :
( ( execution @ TC @ TA @ TB @ A @ B @ C @ D @ E )
=> ( ( enabled @ TC @ TB @ TA @ ( last @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) @ D ) @ F )
=> ( ? [G: TC] : ( isReceiverOf @ TC @ TB @ G @ F )
=> ? [G: nat] : ( firstOccurrence @ TC @ TB @ TA @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: message @ TA @ TB] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( enabled @ TA @ TB @ TC @ C @ F )
=> ( ~ ( enabled @ TA @ TB @ TC @ E @ F )
=> ( D = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_asynchronousSystem_OOnlyOccurenceDisables) ).
thf(418,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: message @ TA @ TB,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: message @ TA @ TB] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( enabled @ TA @ TB @ TC @ C @ F )
=> ( ~ ( enabled @ TA @ TB @ TC @ E @ F )
=> ( D = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(219,axiom,
prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 @ execMsga,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_ExecMsg_I1_J) ).
thf(961,plain,
prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 @ execMsga,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(173,axiom,
( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_nonUniformC_H) ).
thf(813,plain,
( ( initReachable @ p @ s @ v @ trans @ sends @ start @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $false @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) )
& ~ ( vUniform @ p @ s @ v @ trans @ sends @ start @ $true @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(99,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: message @ p @ v] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( enabled @ p @ v @ s @ A @ C )
=> ( ~ ( enabled @ p @ v @ s @ B @ C )
=> ( stepReachable @ p @ s @ v @ trans @ sends @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_StepReachable) ).
thf(568,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: configuration_ext @ p @ v @ s @ product_unit,C: message @ p @ v] :
( ( reachable @ p @ s @ v @ trans @ sends @ A @ B )
=> ( ( enabled @ p @ v @ s @ A @ C )
=> ( ~ ( enabled @ p @ v @ s @ B @ C )
=> ( stepReachable @ p @ s @ v @ trans @ sends @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(73,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: p] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ~ ( member @ p @ D @ B )
=> ( ( states @ p @ v @ s @ product_unit @ A @ D )
= ( states @ p @ v @ s @ product_unit @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_NotInQFrozenQReachability) ).
thf(478,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: p] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ~ ( member @ p @ D @ B )
=> ( ( states @ p @ v @ s @ product_unit @ A @ D )
= ( states @ p @ v @ s @ product_unit @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TA,B: message @ TA @ TB,C: TA] :
( ( isReceiverOf @ TA @ TB @ A @ B )
=> ( ( C != A )
=> ~ ( isReceiverOf @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_UniqueReceiverOf) ).
thf(383,plain,
! [TA: $tType,TB: $tType,A: TA,B: message @ TA @ TB,C: TA] :
( ( isReceiverOf @ TA @ TB @ A @ B )
=> ( ( C != A )
=> ~ ( isReceiverOf @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(141,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( initial @ p @ s @ v @ start @ A )
=> ( initReachable @ p @ s @ v @ trans @ sends @ start @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_InitialIsInitReachable) ).
thf(684,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit] :
( ( initial @ p @ s @ v @ start @ A )
=> ( initReachable @ p @ s @ v @ trans @ sends @ start @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( qReachable @ TA @ TC @ TB @ A @ B @ F @ D @ C )
=> ( qReachable @ TA @ TC @ TB @ A @ B @ F @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_asynchronousSystem_OQReachableTrans) ).
thf(346,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: set @ TA,E: configuration_ext @ TA @ TB @ TC @ product_unit,F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( qReachable @ TA @ TC @ TB @ A @ B @ C @ D @ E )
=> ( ( qReachable @ TA @ TC @ TB @ A @ B @ F @ D @ C )
=> ( qReachable @ TA @ TC @ TB @ A @ B @ F @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(249,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Collect__empty__eq) ).
thf(1045,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_insertE) ).
thf(287,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( vUniform @ TA @ TB @ TC )
= ( vUniform @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_flpSystem_OvUniform_Ocong) ).
thf(290,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(202,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_bot_Oextremum__uniqueI) ).
thf(914,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_insertCI) ).
thf(378,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_bot__fun__def) ).
thf(433,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(84,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_linorder__wlog) ).
thf(510,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(266,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_ord__eq__le__subst) ).
thf(1116,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(222,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_order_Onot__eq__order__implies__strict) ).
thf(967,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(215,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_order_Otrans) ).
thf(950,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(175,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(818,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( C = D )
| ? [E: configuration_ext @ TA @ TB @ TC @ product_unit,F: message @ TA @ TB,G: TA] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ F @ E )
& ( enabled @ TA @ TB @ TC @ C @ F )
& ( isReceiverOf @ TA @ TB @ G @ F )
& ( reachable @ TA @ TC @ TB @ A @ B @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_asynchronousSystem_OReachableStepFirst) ).
thf(405,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( C = D )
| ? [E: configuration_ext @ TA @ TB @ TC @ product_unit,F: message @ TA @ TB,G: TA] :
( ( steps @ TA @ TC @ TB @ A @ B @ C @ F @ E )
& ( enabled @ TA @ TB @ TC @ C @ F )
& ( isReceiverOf @ TA @ TB @ G @ F )
& ( reachable @ TA @ TC @ TB @ A @ B @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(186,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_insert__compr) ).
thf(854,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(155,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( B != D )
=> ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ A @ D ) @ ( msgs @ p @ v @ s @ product_unit @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_OtherMessagesOnlyGrowing) ).
thf(735,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: message @ p @ v,C: configuration_ext @ p @ v @ s @ product_unit,D: message @ p @ v] :
( ( steps @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ( B != D )
=> ( ord_less_eq @ nat @ ( msgs @ p @ v @ s @ product_unit @ A @ D ) @ ( msgs @ p @ v @ s @ product_unit @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(39,axiom,
ord @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_4) ).
thf(373,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(108,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: ( configuration_ext @ p @ v @ s @ product_unit ) > ( set @ p ) > ( configuration_ext @ p @ v @ s @ product_unit ) > $o] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ! [E: configuration_ext @ p @ v @ s @ product_unit,F: set @ p] : ( D @ E @ F @ E )
=> ( ! [E: configuration_ext @ p @ v @ s @ product_unit,F: set @ p,G: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ E @ F @ G )
=> ( ( D @ E @ F @ G )
=> ! [H: message @ p @ v,I: configuration_ext @ p @ v @ s @ product_unit] :
( ( steps @ p @ s @ v @ trans @ sends @ G @ H @ I )
=> ( ? [J: p] :
( ( member @ p @ J @ F )
& ( isReceiverOf @ p @ v @ J @ H ) )
=> ( D @ E @ F @ I ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_qReachable_Oinducts) ).
thf(603,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: set @ p,C: configuration_ext @ p @ v @ s @ product_unit,D: ( configuration_ext @ p @ v @ s @ product_unit ) > ( set @ p ) > ( configuration_ext @ p @ v @ s @ product_unit ) > $o] :
( ( qReachable @ p @ s @ v @ trans @ sends @ A @ B @ C )
=> ( ! [E: configuration_ext @ p @ v @ s @ product_unit,F: set @ p] : ( D @ E @ F @ E )
=> ( ! [E: configuration_ext @ p @ v @ s @ product_unit,F: set @ p,G: configuration_ext @ p @ v @ s @ product_unit] :
( ( qReachable @ p @ s @ v @ trans @ sends @ E @ F @ G )
=> ( ( D @ E @ F @ G )
=> ! [H: message @ p @ v,I: configuration_ext @ p @ v @ s @ product_unit] :
( ( steps @ p @ s @ v @ trans @ sends @ G @ H @ I )
=> ( ? [J: p] :
( ( member @ p @ J @ F )
& ( isReceiverOf @ p @ v @ J @ H ) )
=> ( D @ E @ F @ I ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: message @ TA @ TB,F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( steps @ TA @ TC @ TB @ A @ B @ D @ E @ F )
=> ( reachable @ TA @ TC @ TB @ A @ B @ C @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_asynchronousSystem_Ostep) ).
thf(294,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: configuration_ext @ TA @ TB @ TC @ product_unit,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: message @ TA @ TB,F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( steps @ TA @ TC @ TB @ A @ B @ D @ E @ F )
=> ( reachable @ TA @ TC @ TB @ A @ B @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,B: TA > TC > ( messageValue @ TB ) > TC,C: TA > TC] :
( ( flpSystem @ TA @ TC @ TB @ A )
=> ( ! [D: configuration_ext @ TA @ TB @ TC @ product_unit,E: set @ TA] : ( terminationPseudo @ TA @ TC @ TB @ B @ A @ C @ ( one_one @ nat ) @ D @ E )
=> ( ! [D: configuration_ext @ TA @ TB @ TC @ product_unit,E: configuration_ext @ TA @ TB @ TC @ product_unit] : ( validity @ TA @ TC @ TB @ B @ A @ C @ D @ E )
=> ( ! [D: configuration_ext @ TA @ TB @ TC @ product_unit,E: configuration_ext @ TA @ TB @ TC @ product_unit] : ( agreementInit @ TA @ TC @ TB @ B @ A @ C @ D @ E )
=> ? [D: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( initial @ TA @ TC @ TB @ C @ D )
& ( initReachable @ TA @ TC @ TB @ B @ A @ C @ D )
& ~ ( vUniform @ TA @ TC @ TB @ B @ A @ C @ $false @ D )
& ~ ( vUniform @ TA @ TC @ TB @ B @ A @ C @ $true @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_flpSystem_OInitialNonUniformCfg) ).
thf(341,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,B: TA > TC > ( messageValue @ TB ) > TC,C: TA > TC] :
( ( flpSystem @ TA @ TC @ TB @ A )
=> ( ! [D: configuration_ext @ TA @ TB @ TC @ product_unit,E: set @ TA] : ( terminationPseudo @ TA @ TC @ TB @ B @ A @ C @ ( one_one @ nat ) @ D @ E )
=> ( ! [D: configuration_ext @ TA @ TB @ TC @ product_unit,E: configuration_ext @ TA @ TB @ TC @ product_unit] : ( validity @ TA @ TC @ TB @ B @ A @ C @ D @ E )
=> ( ! [D: configuration_ext @ TA @ TB @ TC @ product_unit,E: configuration_ext @ TA @ TB @ TC @ product_unit] : ( agreementInit @ TA @ TC @ TB @ B @ A @ C @ D @ E )
=> ? [D: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( initial @ TA @ TC @ TB @ C @ D )
& ( initReachable @ TA @ TC @ TB @ B @ A @ C @ D )
& ~ ( vUniform @ TA @ TC @ TB @ B @ A @ C @ $false @ D )
& ~ ( vUniform @ TA @ TC @ TB @ B @ A @ C @ $true @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(285,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( enabled @ TA @ TB @ TC )
= ( ^ [A: configuration_ext @ TA @ TB @ TC @ product_unit,B: message @ TA @ TB] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TA @ TB @ TC @ product_unit @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_enabled__def) ).
thf(1172,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( enabled @ TA @ TB @ TC )
= ( ^ [A: configuration_ext @ TA @ TB @ TC @ product_unit,B: message @ TA @ TB] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TA @ TB @ TC @ product_unit @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(218,axiom,
ord @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oord_21) ).
thf(960,plain,
ord @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_singletonD) ).
thf(720,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(182,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_ord__eq__le__trans) ).
thf(839,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(153,axiom,
? [A: configuration_ext @ p @ v @ s @ product_unit] : ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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) ).
thf(728,plain,
? [A: configuration_ext @ p @ v @ s @ product_unit] : ( steps @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec2 ) @ msg @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(67,axiom,
prefixList @ ( message @ p @ v ) @ trace @ traceMsga,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_isPrefixListTrace) ).
thf(464,plain,
prefixList @ ( message @ p @ v ) @ trace @ traceMsga,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(332,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(189,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_singleton__conv) ).
thf(860,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,B: TA > TC > ( messageValue @ TB ) > TC,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: TA] :
( ( flpSystem @ TA @ TC @ TB @ A )
=> ( ( ( initReachable @ TA @ TC @ TB @ B @ A @ C @ D )
& ~ ( vUniform @ TA @ TC @ TB @ B @ A @ C @ $false @ D )
& ~ ( vUniform @ TA @ TC @ TB @ B @ A @ C @ $true @ D ) )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit,G: set @ TA] : ( terminationPseudo @ TA @ TC @ TB @ B @ A @ C @ ( one_one @ nat ) @ F @ G )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ B @ A @ D @ F )
=> ( agreement @ TA @ TB @ TC @ F ) )
=> ? [F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ B @ A @ D @ F )
& ( ( collect @ $o
@ ^ [G: $o] : ( pSilDecVal @ TA @ TC @ TB @ B @ A @ C @ G @ E @ F ) )
= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_flpSystem_ONonUniformCanReachSilentBivalence) ).
thf(596,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,B: TA > TC > ( messageValue @ TB ) > TC,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: TA] :
( ( flpSystem @ TA @ TC @ TB @ A )
=> ( ( ( initReachable @ TA @ TC @ TB @ B @ A @ C @ D )
& ~ ( vUniform @ TA @ TC @ TB @ B @ A @ C @ $false @ D )
& ~ ( vUniform @ TA @ TC @ TB @ B @ A @ C @ $true @ D ) )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit,G: set @ TA] : ( terminationPseudo @ TA @ TC @ TB @ B @ A @ C @ ( one_one @ nat ) @ F @ G )
=> ( ! [F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ B @ A @ D @ F )
=> ( agreement @ TA @ TB @ TC @ F ) )
=> ? [F: configuration_ext @ TA @ TB @ TC @ product_unit] :
( ( reachable @ TA @ TC @ TB @ B @ A @ D @ F )
& ( ( collect @ $o
@ ^ [G: $o] : ( pSilDecVal @ TA @ TC @ TB @ B @ A @ C @ G @ E @ F ) )
= ( insert @ $o @ $true @ ( insert @ $o @ $false @ ( bot_bot @ ( set @ $o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_le__funI) ).
thf(644,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(151,axiom,
( ( last @ ( message @ p @ v ) @ traceMsga )
= msg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_ExecMsg_I4_J) ).
thf(723,plain,
( ( last @ ( message @ p @ v ) @ traceMsga )
= msg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(36,axiom,
preorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_2) ).
thf(369,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_insert__absorb) ).
thf(309,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(97,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Collect__conv__if) ).
thf(560,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(120,axiom,
preorder @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Opreorder_18) ).
thf(639,plain,
preorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(252,axiom,
~ ( stepReachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_NotStepReachable) ).
thf(1069,plain,
~ ( stepReachable @ p @ s @ v @ trans @ sends @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ exec ) @ msg @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(193,axiom,
preorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12) ).
thf(882,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1175,plain,
$false,
inference(e,[status(thm)],[629,628,518,941,666,1083,962,468,777,555,1005,683,730,994,741,1142,614,1041,1158,762,1137,797,930,747,913,1095,1127,709,417,973,301,565,436,504,917,934,587,619,817,1147,421,1013,416,316,1100,492,756,443,646,834,348,353,821,905,475,924,660,988,428,312,1074,292,920,678,1153,1163,334,952,297,424,630,957,894,1123,349,484,625,879,852,329,1159,682,551,1012,1106,583,522,830,519,1017,725,980,388,857,1138,356,1028,753,669,526,637,1155,706,328,471,901,686,679,1039,970,997,985,701,457,1002,371,515,1150,1131,654,1086,508,657,765,674,1026,773,633,360,558,1071,1135,750,430,1103,824,745,573,296,375,1007,286,743,291,545,843,1125,577,711,641,1139,611,498,1092,335,1090,947,445,936,900,681,1048,1144,318,649,303,863,890,811,621,1029,964,1022,462,858,367,912,983,1044,1066,306,1000,299,851,922,658,768,827,455,883,505,438,473,490,426,944,374,487,1081,617,939,553,458,836,663,548,525,690,640,414,739,1098,993,441,370,502,338,576,359,703,314,571,876,386,978,1140,465,450,931,482,671,976,581,759,1010,368,771,1108,699,319,652,418,961,813,568,478,383,684,346,1045,287,290,914,378,433,510,1116,967,950,818,405,854,735,373,603,294,341,1172,960,720,839,728,464,332,860,596,644,723,369,309,560,639,1069,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP057^2 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n008.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 14:24:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/1.13 % [INFO] Parsing done (272ms).
% 1.74/1.14 % [INFO] Running in sequential loop mode.
% 2.63/1.35 % [INFO] eprover registered as external prover.
% 2.63/1.36 % [INFO] cvc4 registered as external prover.
% 2.63/1.36 % [INFO] Scanning for conjecture ...
% 2.97/1.49 % [INFO] Found a conjecture and 284 axioms. Running axiom selection ...
% 3.24/1.59 % [INFO] Axiom selection finished. Selected 283 axioms (removed 1 axioms).
% 4.40/1.87 % [INFO] Problem is higher-order (TPTP THF).
% 4.40/1.89 % [INFO] Type checking passed.
% 4.40/1.89 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 136.71/115.01 % External prover 'e' found a proof!
% 136.71/115.02 % [INFO] Killing All external provers ...
% 136.71/115.02 % Time passed: 114484ms (effective reasoning time: 113873ms)
% 136.71/115.02 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 136.71/115.02 % Axioms used in derivation (283): fact_123_ExecMsg_I4_J, tcon_fun___Orderings_Obot, fact_37_dual__order_Oeq__iff, fact_212_asynchronousSystem_OstepReachable__def, fact_159_bot_Oextremum__uniqueI, fact_220_flpPseudoConsensus_OPseudoTermination, tcon_HOL_Obool___Orderings_Oorder_14, fact_133_insertI1, fact_172_asynchronousSystem_OReachableStepFirst, fact_68_subset__trans, tcon_Product__Type_Ounit___Orderings_Opreorder_18, fact_185_asynchronousSystem_Osteps_Ocong, fact_170_NewExec_I2_J, fact_221_flpSystem_OterminationPseudo_Ocong, fact_245_dual__order_Ostrict__trans1, fact_228_execution_OFirstOccurrenceExists, fact_120_vUniform__def, fact_176_StepOutMsg, fact_103_reachable_Osimps, fact_16_NewExec_I1_J, fact_79_flpSystem_OInactiveProcessSilentDecisionValuesDecrease, fact_250_not__le__imp__less, fact_178_expandExecutionStep, fact_157_bot_Oextremum, fact_126__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, fact_173_asynchronousSystem_ONoActivityNoMessageLoss, fact_244_dual__order_Ostrict__trans2, fact_13_InactiveProcessSilentDecisionValuesDecrease, tcon_Nat_Onat___Orderings_Olinorder, fact_60_order__subst2, fact_28_StepQ, fact_230_agreement__def, fact_131_equals0D, fact_11_Agreement, fact_208_asynchronousSystem_OqReachable_Osimps, fact_90_init, fact_92_empty__iff, tcon_HOL_Obool___Orderings_Opreorder_12, fact_225_execution_OExistImpliesMinEnabled, fact_87_C_H_I2_J, fact_2_NewExec_I3_J, fact_12_ActiveProcessSilentDecisionValuesIncrease, fact_61_order__subst1, 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, tcon_HOL_Obool___Orderings_Obot_16, fact_64_le__funE, fact_249_order_Ostrict__trans1, fact_149_predicate1D, fact_204_asynchronousSystem_OInitialIsInitReachable, tcon_fun___Orderings_Oord, fact_191_asynchronousSystem_OqReachable_Ocong, fact_234_flpSystem_Oagreement__def, fact_177_isPrefixListTrace, fact_80_flpSystem_OActiveProcessSilentDecisionValuesIncrease, fact_164_flpSystem_OvUniform__def, fact_229_NonUniformImpliesNotDecided, fact_75_equalityE, fact_233_DecidedImpliesUniform, fact_53_le__cases, fact_102_reachable_Oinducts, fact_24_OnlyOccurenceDisables, fact_195_asynchronousSystem_OstepReachable_Ocong, tcon_HOL_Obool___Orderings_Oord_15, fact_17_InitialIsInitReachable, fact_180__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, fact_203_asynchronousSystem_ONotInQFrozenQReachability, fact_71_subset__iff, fact_247_order_Oorder__iff__strict, fact_32_NonUniformLexec, fact_26_qReachable_Oinducts, fact_153_rev__predicate1D, fact_113_singletonI, fact_232_agreementInit__def, fact_181_bot__set__def, fact_1_InitReachLastExec_H, fact_36_dual__order_Oantisym, fact_77_in__mono, fact_125_SilentDecisionValueNotInverting, fact_214_asynchronousSystem_OexpandExecutionStep, tcon_HOL_Obool___Orderings_Oorder__bot_11, fact_186_asynchronousSystem_OReachableTrans, fact_121_singleton__insert__inj__eq_H, fact_184_asynchronousSystem_ONoOutMessageLoss, fact_168_flpSystem_OagreementInit_Ocong, fact_85_ReachableStepFirst, fact_7_DiamondOne, fact_146_insert__not__empty, tcon_Set_Oset___Orderings_Obot_10, fact_163_subset__insertI2, fact_67_set__eq__subset, fact_223_flpSystem_ONonUniformCanReachSilentBivalence, fact_46_Collect__mem__eq, fact_198_asynchronousSystem_Oreachable_Osimps, fact_187_asynchronousSystem_Oreachable_Ocong, fact_107_OtherMessagesOnlyGrowing, fact_58_ord__le__eq__subst, fact_74_subset__eq, fact_139_insert__absorb, fact_205_asynchronousSystem_OOtherMessagesOnlyGrowing, fact_23_order__refl, fact_119_ExecIsExecution, fact_243_dense__ge__bounded, fact_78_Collect__subset, fact_38_dual__order_Otrans, fact_192_asynchronousSystem_OInitQ, fact_142_insert__commute, fact_242_dense__le__bounded, fact_66_Collect__mono__iff, fact_196_asynchronousSystem_Ostep, fact_52_order_Otrans, tcon_Set_Oset___Orderings_Oord_9, fact_98_insert__absorb2, fact_158_bot_Oextremum__unique, fact_8_True, fact_154_insert__Collect, fact_255_dense__ge, fact_65_le__funD, fact_15_InitReachLastExecMsg, fact_218_DecisionValuesExist, fact_127__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, fact_201_asynchronousSystem_OQReachImplReach, fact_128_Agree, fact_183_isReceiverOf_Osimps_I3_J, fact_86_NotInQFrozenQReachability, fact_57_eq__iff, fact_151_mk__disjoint__insert, fact_116_lastExecExec_HReachable, fact_217_PseudoTermination, 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, fact_63_le__funI, fact_231_ExistsMsg, fact_3_CMsg, fact_141_singleton__iff, fact_110_NoMessageLossStep, fact_160_insert__mono, tcon_Product__Type_Ounit___Orderings_Oord_21, fact_118_singleton__conv2, fact_43_ord__le__eq__trans, fact_227_flpSystem_Ovalidity_Ocong, fact_51_le__cases3, fact_45_mem__Collect__eq, fact_165_flpSystem_OSilentDecisionValueNotInverting, fact_105_QReachImplReach, tcon_Product__Type_Ounit___Orderings_Oorder_20, fact_29_ExecMsg_I1_J, fact_117_singleton__conv, fact_199_asynchronousSystem_Oreachable_Oinducts, fact_33_flpPseudoConsensus_Oaxioms_I1_J, fact_5_ExecMsg_I3_J, fact_197_asynchronousSystem_Oreachable_Ocases, fact_20_subset__antisym, fact_202_asynchronousSystem_OOnlyOccurenceDisables, fact_25_qReachable_Osimps, fact_132_equals0I, fact_167_flpSystem_OvUniform_Ocong, fact_138_insert__ident, fact_94_Collect__empty__eq, fact_82_cMsgLastReachable, fact_236_asynchronousSystem_OExistsMsg, fact_152_subset__singleton__iff, fact_211_asynchronousSystem_OinitReachable__def, fact_175_message_Oinject_I2_J, fact_144_Collect__conv__if2, fact_42_order__class_Oorder_Oantisym, fact_39_linorder__wlog, fact_206_asynchronousSystem_OStepQ, tcon_Nat_Onat___Orderings_Opreorder_2, fact_122_singleton__insert__inj__eq, fact_155_insert__compr, fact_115_ExecMsg_I2_J, fact_162_subset__insertI, tcon_Nat_Onat___Orderings_Oorder__bot_1, fact_238_dual__order_Ostrict__implies__order, fact_209_asynchronousSystem_OqReachable_Oinducts, fact_47_Collect__cong, fact_34_flpPseudoConsensus_OAgreement, fact_194_asynchronousSystem_Oinitial_Ocong, fact_35_less__eq__set__def, fact_145_doubleton__eq__iff, fact_189_UniqueReceiverOf, fact_89_ReachableTrans, tcon_fun___Orderings_Oorder__bot, fact_166_flpSystem_OpSilDecVal_Ocong, tcon_HOL_Obool___Orderings_Olinorder_13, fact_193_asynchronousSystem_OinitReachable_Ocong, fact_49_order__class_Oorder_Oeq__iff, fact_179__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, fact_235_enabled__def, fact_134_insertI2, fact_124_isStepReachable, fact_207_asynchronousSystem_OqReachable_Ocases, fact_91_bot__apply, fact_22_InitQ, fact_148_bot__fun__def, fact_69_Collect__mono, fact_41_order__trans, tcon_Nat_Onat___Orderings_Oorder_3, fact_213_asynchronousSystem_OStepReachable, fact_44_ord__eq__le__trans, fact_143_Collect__conv__if, fact_99_C_H_I1_J, fact_4_flpPseudoConsensus__axioms, fact_174_asynchronousSystem_ONoMessageLossStep, fact_215_asynchronousSystem_OexpandExecutionReachable, fact_31_MsgEnabled, tcon_Product__Type_Ounit___Orderings_Olinorder_19, fact_93_all__not__in__conv, tcon_fun___Orderings_Opreorder, fact_14_nonUniformC_H, fact_182_asynchronousSystem_OStepOutMsg, fact_30_isExecution, fact_109_StepReachable, fact_112_empty__subsetI, fact_222_flpSystem_ODecisionValuesExist, fact_190_asynchronousSystem_OQReachableTrans, fact_156_empty__def, fact_40_dual__order_Orefl, tcon_Set_Oset___Orderings_Oorder_8, fact_137_singletonD, fact_56_antisym, fact_135_ex__in__conv, fact_216_NonUniformCanReachSilentBivalence, fact_97_insert__iff, fact_106_isPrefixListExec, fact_239_dual__order_Ostrict__iff__order, fact_237_order_Onot__eq__order__implies__strict, tcon_Product__Type_Ounit___Orderings_Obot_22, fact_111_subset__empty, fact_129_emptyE, tcon_fun___Orderings_Oorder, fact_248_order_Ostrict__trans2, fact_251_less__le__not__le, fact_254_dense__le, fact_161_subset__insert, fact_54_eq__refl, fact_224_flpSystem_OInitialNonUniformCfg, fact_81_NotStepReachable, fact_95_empty__Collect__eq, fact_101_reachable_Ocases, fact_226_execution_OminimalEnabled_Ocong, fact_136_Set_Oset__insert, fact_252_le__imp__less__or__eq, 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, fact_83_NoReceivingNoChange, fact_100_predicate1I, fact_114_insert__subset, tcon_Nat_Onat___Orderings_Oord_4, fact_84_initReachable__def, tcon_Set_Oset___Orderings_Opreorder_7, fact_246_order_Ostrict__iff__order, fact_169_expandExecutionReachable, fact_171_NoOutMessageLoss, fact_0_PisReceiverOf, fact_147_singleton__inject, fact_130_insertE, fact_55_linear, tcon_Set_Oset___Orderings_Oorder__bot_6, fact_19_subsetI, fact_240_dual__order_Oorder__iff__strict, fact_73_equalityD1, fact_200_asynchronousSystem_ODiamondOne, fact_27_qReachable_Ocases, fact_62_le__fun__def, fact_72_equalityD2, fact_50_antisym__conv, fact_210_asynchronousSystem_ONoReceivingNoChange, fact_241_order_Ostrict__implies__order, fact_70_subset__refl, fact_150_subset__singletonD, fact_140_insert__eq__iff, fact_21_QReachableTrans, fact_96_insertCI, fact_104_reachable_Ostep, fact_219_InitialNonUniformCfg, fact_188_asynchronousSystem_Oinit, tcon_Nat_Onat___Orderings_Obot_5, fact_88_NoActivityNoMessageLoss, tcon_Product__Type_Ounit___Orderings_Oorder__bot_17, fact_108_stepReachable__def, fact_76_subsetD, fact_18_flpSystem__axioms, fact_59_ord__eq__le__subst, fact_253_le__less__linear
% 136.71/115.02 % No. of inferences in proof: 570
% 136.71/115.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 114484 ms resp. 113873 ms w/o parsing
% 137.46/115.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 137.46/115.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------