TPTP Problem File: SWV463+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWV463+1 : TPTP v8.2.0. Released v4.0.0.
% Domain : Software Verification
% Problem : Establishing that there cannot be two leaders, part i52_p38
% Version : [Sve07] axioms : Especial.
% English :
% Refs : [Sto97] Stoller (1997), Leader Election in Distributed Systems
% : [Sve07] Svensson (2007), Email to Koen Claessen
% : [Sve08] Svensson (2008), A Semi-Automatic Correctness Proof Pr
% Source : [Sve07]
% Names : stoller_i52_p38 [Sve07]
% Status : Theorem
% Rating : 0.28 v8.2.0, 0.31 v8.1.0, 0.28 v7.4.0, 0.23 v7.3.0, 0.24 v7.2.0, 0.21 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.31 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.40 v6.0.0, 0.35 v5.5.0, 0.41 v5.4.0, 0.46 v5.3.0, 0.52 v5.2.0, 0.35 v5.1.0, 0.48 v5.0.0, 0.46 v4.1.0, 0.48 v4.0.0
% Syntax : Number of formulae : 67 ( 40 unt; 0 def)
% Number of atoms : 205 ( 104 equ)
% Maximal formula atoms : 94 ( 3 avg)
% Number of connectives : 203 ( 65 ~; 11 |; 78 &)
% ( 13 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% Number of functors : 34 ( 34 usr; 17 con; 0-2 aty)
% Number of variables : 166 ( 165 !; 1 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
%----Include axioms for verification of Stoller's leader election algorithm
include('Axioms/SWV011+0.ax').
%------------------------------------------------------------------------------
fof(conj,conjecture,
! [V,W,X,Y] :
( ( ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> host(Pid0) != host(Z) )
& ! [Z,Pid0] :
( elem(m_Halt(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid20,Pid0] :
( elem(m_Ack(Pid0,Z),queue(host(Pid20)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( ( Pid0 != Z
& host(Pid0) = host(Z) )
=> ( ~ setIn(Z,alive)
| ~ setIn(Pid0,alive) ) )
& ! [Z,Pid0] :
( ( setIn(Pid0,alive)
& elem(m_Ack(Pid0,Z),queue(host(Pid0))) )
=> leq(host(Z),index(pendack,host(Pid0))) )
& ! [Z,Pid0] :
( ( setIn(Pid0,alive)
& index(status,host(Pid0)) = elec_1 )
=> ~ elem(m_Ack(Pid0,Z),queue(host(Pid0))) )
& ! [Z] :
( ( ( index(status,host(Z)) = elec_1
| index(status,host(Z)) = elec_2 )
& setIn(Z,alive) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid20,Pid0] :
( ( setIn(Pid0,alive)
& elem(m_Down(Pid20),queue(host(Pid0)))
& host(Pid20) = host(Z) )
=> ~ ( setIn(Z,alive)
& index(ldr,host(Z)) = host(Z)
& index(status,host(Z)) = norm ) )
& ! [Z,Pid0] :
( ( ~ leq(host(Z),host(Pid0))
& setIn(Z,alive)
& setIn(Pid0,alive)
& index(status,host(Z)) = elec_2
& index(status,host(Pid0)) = elec_2 )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,Pid20,Pid0] :
( ( setIn(Z,alive)
& setIn(Pid0,alive)
& host(Pid0) = host(Pid20)
& index(status,host(Z)) = elec_2
& index(status,host(Pid0)) = elec_2 )
=> ~ elem(m_Ack(Z,Pid20),queue(host(Z))) )
& ! [Z,Pid0] :
( ( ~ leq(host(Z),host(Pid0))
& setIn(Z,alive)
& setIn(Pid0,alive)
& index(status,host(Z)) = elec_2
& index(status,host(Pid0)) = elec_2 )
=> ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0))) )
& ! [Z,Pid20,Pid0] :
( ( ~ leq(index(pendack,host(Pid0)),host(Z))
& setIn(Pid0,alive)
& elem(m_Halt(Pid0),queue(host(Pid20)))
& index(status,host(Pid0)) = elec_2 )
=> ~ ( setIn(Z,alive)
& index(ldr,host(Z)) = host(Z)
& index(status,host(Z)) = norm ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( ! [V0] :
( ( ~ leq(host(Pid0),V0)
& leq(s(zero),V0) )
=> ( setIn(V0,index(down,host(Pid0)))
| V0 = host(Pid20) ) )
& elem(m_Down(Pid20),queue(host(Pid0)))
& host(Pid0) = nbr_proc
& host(Pid0) = host(Pid30)
& index(status,host(Pid0)) = elec_1 )
=> ~ ( setIn(Z,alive)
& elem(m_Down(Pid30),queue(host(Z))) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( setIn(Pid0,alive)
& elem(m_Down(Pid20),queue(host(Pid0)))
& elem(m_Ack(Pid0,Pid30),queue(host(Pid0)))
& leq(nbr_proc,s(index(pendack,host(Pid0))))
& index(status,host(Pid0)) = elec_2
& host(Pid30) = index(pendack,host(Pid0))
& host(Pid20) = s(index(pendack,host(Pid0))) )
=> ~ ( setIn(Z,alive)
& index(ldr,host(Z)) = host(Z)
& index(status,host(Z)) = norm ) )
& queue(host(X)) = cons(m_Ack(W,Y),V) )
=> ( setIn(X,alive)
=> ( ( index(elid,host(X)) = W
& index(status,host(X)) = elec_2
& host(Y) = index(pendack,host(X)) )
=> ( leq(nbr_proc,index(pendack,host(X)))
=> ! [Z] :
( ( setIn(host(Z),index(acks,host(X)))
| host(Z) = host(Y) )
=> ! [V0] :
( host(X) != host(V0)
=> ! [W0,X0,Y0] :
( host(Z) = host(Y0)
=> ( host(X) != host(Y0)
=> ( ( setIn(Y0,alive)
& leq(nbr_proc,s(index(pendack,host(Y0))))
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X)))
& elem(m_Ack(Y0,W0),snoc(queue(host(Y0)),m_Ldr(X)))
& index(status,host(Y0)) = elec_2
& host(W0) = index(pendack,host(Y0))
& host(X0) = s(index(pendack,host(Y0))) )
=> ~ ( setIn(V0,alive)
& index(ldr,host(V0)) = host(V0)
& index(status,host(V0)) = norm ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------