TPTP Problem File: SWV465+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV465+1 : TPTP v8.2.0. Released v4.0.0.
% Domain : Software Verification
% Problem : Establishing that there cannot be two leaders, part i52_p59
% 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_p59 [Sve07]
% Status : Theorem
% Rating : 0.53 v8.2.0, 0.58 v8.1.0, 0.50 v7.5.0, 0.53 v7.4.0, 0.40 v7.3.0, 0.52 v7.1.0, 0.48 v7.0.0, 0.53 v6.4.0, 0.54 v6.3.0, 0.50 v6.2.0, 0.56 v6.1.0, 0.70 v6.0.0, 0.57 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0, 0.65 v5.1.0, 0.71 v5.0.0, 0.75 v4.1.0, 0.74 v4.0.1, 0.78 v4.0.0
% Syntax : Number of formulae : 67 ( 40 unt; 0 def)
% Number of atoms : 199 ( 100 equ)
% Maximal formula atoms : 88 ( 2 avg)
% Number of connectives : 196 ( 64 ~; 10 |; 76 &)
% ( 13 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% Number of functors : 33 ( 33 usr; 16 con; 0-2 aty)
% Number of variables : 164 ( 163 !; 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] :
( elem(m_Ldr(Z),queue(host(Y)))
=> ~ leq(host(Y),host(Z)) )
& ! [Y,Z] :
( elem(m_Down(Z),queue(host(Y)))
=> host(Z) != host(Y) )
& ! [Y,Z] :
( elem(m_Halt(Z),queue(host(Y)))
=> ~ leq(host(Y),host(Z)) )
& ! [Y,Z,Pid0] :
( elem(m_Ack(Pid0,Y),queue(host(Z)))
=> ~ leq(host(Y),host(Pid0)) )
& ! [Y,Z] :
( ( Z != Y
& host(Z) = host(Y) )
=> ( ~ setIn(Y,alive)
| ~ setIn(Z,alive) ) )
& ! [Y,Z] :
( ( setIn(Z,alive)
& elem(m_Ack(Z,Y),queue(host(Z))) )
=> leq(host(Y),index(pendack,host(Z))) )
& ! [Y,Z] :
( ( setIn(Z,alive)
& index(status,host(Z)) = elec_1 )
=> ~ elem(m_Ack(Z,Y),queue(host(Z))) )
& ! [Y] :
( ( ( index(status,host(Y)) = elec_1
| index(status,host(Y)) = elec_2 )
& setIn(Y,alive) )
=> index(elid,host(Y)) = Y )
& ! [Y,Z] :
( ( ~ leq(host(Y),host(Z))
& setIn(Y,alive)
& setIn(Z,alive)
& index(status,host(Y)) = elec_2
& index(status,host(Z)) = elec_2 )
=> leq(index(pendack,host(Z)),host(Y)) )
& ! [Y,Z,Pid0] :
( ( setIn(Pid0,alive)
& elem(m_Down(Z),queue(host(Pid0)))
& host(Z) = host(Y) )
=> ~ ( setIn(Y,alive)
& index(ldr,host(Y)) = host(Y)
& index(status,host(Y)) = norm ) )
& ! [Y,Z,Pid0] :
( ( setIn(Y,alive)
& setIn(Pid0,alive)
& host(Pid0) = host(Z)
& index(status,host(Y)) = elec_2
& index(status,host(Pid0)) = elec_2 )
=> ~ elem(m_Ack(Y,Z),queue(host(Y))) )
& ! [Y,Z] :
( ( ~ leq(host(Y),host(Z))
& setIn(Y,alive)
& setIn(Z,alive)
& index(status,host(Y)) = elec_2
& index(status,host(Z)) = elec_2 )
=> ~ leq(index(pendack,host(Y)),index(pendack,host(Z))) )
& ! [Y,Z,Pid0] :
( ( ~ leq(index(pendack,host(Pid0)),host(Y))
& setIn(Pid0,alive)
& elem(m_Halt(Pid0),queue(host(Z)))
& index(status,host(Pid0)) = elec_2 )
=> ~ ( setIn(Y,alive)
& index(ldr,host(Y)) = host(Y)
& index(status,host(Y)) = norm ) )
& ! [Y,Z,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) = host(Z)
& host(Pid0) = nbr_proc
& index(status,host(Pid0)) = elec_1 )
=> ~ ( setIn(Y,alive)
& elem(m_Down(Z),queue(host(Y))) ) )
& ! [Y,Z,Pid20,Pid0] :
( ( setIn(Pid0,alive)
& elem(m_Ack(Pid0,Z),queue(host(Pid0)))
& elem(m_Down(Pid20),queue(host(Pid0)))
& leq(nbr_proc,s(index(pendack,host(Pid0))))
& index(status,host(Pid0)) = elec_2
& host(Z) = index(pendack,host(Pid0))
& host(Pid20) = s(index(pendack,host(Pid0))) )
=> ~ ( setIn(Y,alive)
& index(ldr,host(Y)) = host(Y)
& index(status,host(Y)) = norm ) )
& queue(host(X)) = cons(m_NormQ(W),V) )
=> ( setIn(X,alive)
=> ( index(status,host(X)) != norm
=> ! [Y,Z,X0,Y0] :
( host(W) = host(Y0)
=> ( host(X) = host(Y0)
=> ( ( setIn(Y0,alive)
& elem(m_Down(X0),snoc(V,m_NotNorm(W)))
& elem(m_Ack(Y0,Z),snoc(V,m_NotNorm(W)))
& leq(nbr_proc,s(index(pendack,host(Y0))))
& index(status,host(Y0)) = elec_2
& host(Z) = index(pendack,host(Y0))
& host(X0) = s(index(pendack,host(Y0))) )
=> ~ ( setIn(Y,alive)
& index(ldr,host(Y)) = host(Y)
& index(status,host(Y)) = norm ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------