%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV480+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:08:03 AM UTC 2026
% Result : Theorem 15.65s 2.70s
% Output : CNFRefutation 15.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 86 ( 39 unt; 0 def)
% Number of atoms : 855 ( 376 equ)
% Maximal formula atoms : 174 ( 9 avg)
% Number of connectives : 1244 ( 475 ~; 408 |; 302 &)
% ( 3 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 21 con; 0-4 aty)
% Number of variables : 347 ( 10 sgn 284 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_02,axiom,
! [P] : leq(s(zero),host(P)),
file('theBenchmark.p',axiom_02) ).
fof(axiom_04,axiom,
! [P] : leq(host(P),nbr_proc),
file('theBenchmark.p',axiom_04) ).
fof(axiom_38,axiom,
! [Y,Q] : init(snoc(Q,Y)) = Q,
file('theBenchmark.p',axiom_38) ).
fof(axiom_46,axiom,
! [X,Y,Q] :
( elem(X,cons(Y,Q))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_46) ).
fof(axiom_58,axiom,
! [X] : ~ leq(s(X),X),
file('theBenchmark.p',axiom_58) ).
fof(axiom_61,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
<=> X = Y ),
file('theBenchmark.p',axiom_61) ).
fof(axiom_64,axiom,
! [X,Y] :
( leq(X,s(Y))
<=> ( leq(X,Y)
| X = s(Y) ) ),
file('theBenchmark.p',axiom_64) ).
fof(conj,conjecture,
! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Down(Y),V)
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid30) = s(host(Pid0))
& elem(m_Down(Pid30),queue(host(Pid0)))
& elem(m_Down(Pid20),queue(host(Pid0)))
& leq(nbr_proc,s(host(Pid0)))
& setIn(Pid0,alive)
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& index(status,host(Z)) = elec_2
& host(Pid30) = host(Pid0)
& elem(m_Down(Pid20),queue(host(Pid0)))
& leq(host(Z),host(Pid0))
& setIn(Z,alive)
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ elem(m_Ack(Z,Pid30),queue(host(Z))) )
& ! [Z,Pid20,Pid0] :
( ( host(index(elid,host(Pid0))) = host(Pid20)
& index(status,host(Pid0)) = wait
& host(Pid20) = host(Z)
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ ( index(ldr,host(Pid20)) = host(Pid20)
& index(status,host(Pid20)) = norm
& setIn(Pid20,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid20)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Z)
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ ( index(ldr,host(Pid20)) = host(Pid20)
& index(status,host(Pid20)) = norm
& setIn(Pid20,alive) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Pid30) = host(Z)
& setIn(Pid20,alive)
& setIn(Z,alive)
& host(Pid20) != host(Z) )
=> ~ ( setIn(host(Pid30),index(down,host(Pid20)))
& elem(m_Down(Pid0),queue(host(Z))) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Pid30) = host(Z)
& setIn(Pid20,alive)
& setIn(Z,alive)
& host(Pid20) != host(Z) )
=> ~ ( elem(m_Down(Pid30),queue(host(Pid20)))
& elem(m_Down(Pid0),queue(host(Z))) ) )
& ! [Z,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive)
& ~ leq(host(Pid20),host(Pid0)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> Pid0 = Z )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Pid0)
& setIn(Pid0,alive) )
=> ~ ( elem(m_Down(Pid20),queue(host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& elem(m_Down(Pid20),queue(host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& setIn(Pid0,alive) )
=> ~ ( setIn(host(Pid0),index(down,host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(host(Pid0),index(down,host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> host(Pid0) != host(Z) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( leq(host(X),host(Y))
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2 )
=> ( leq(nbr_proc,index(pendack,host(X)))
=> ! [Z] :
( ~ setIn(host(Z),index(acks,host(X)))
=> ! [V0] :
( host(X) = host(V0)
=> ! [W0,X0,Y0] :
( host(X) != host(Y0)
=> ( ( index(status,host(Y0)) = elec_1
& host(W0) = s(host(Y0))
& elem(m_Down(X0),queue(host(Y0)))
& elem(m_Down(W0),queue(host(Y0)))
& leq(nbr_proc,s(host(Y0)))
& setIn(Y0,alive)
& ! [V1] :
( ( leq(s(zero),V1)
& ~ leq(host(Y0),V1) )
=> ( V1 = host(X0)
| setIn(V1,index(down,host(Y0))) ) ) )
=> ~ ( host(X) = host(V0)
& setIn(V0,alive) ) ) ) ) ) ) ) ) ) ),
file('theBenchmark.p',conj) ).
fof(conj_neg,negated_conjecture,
~ ! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Down(Y),V)
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid30) = s(host(Pid0))
& elem(m_Down(Pid30),queue(host(Pid0)))
& elem(m_Down(Pid20),queue(host(Pid0)))
& leq(nbr_proc,s(host(Pid0)))
& setIn(Pid0,alive)
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& index(status,host(Z)) = elec_2
& host(Pid30) = host(Pid0)
& elem(m_Down(Pid20),queue(host(Pid0)))
& leq(host(Z),host(Pid0))
& setIn(Z,alive)
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ elem(m_Ack(Z,Pid30),queue(host(Z))) )
& ! [Z,Pid20,Pid0] :
( ( host(index(elid,host(Pid0))) = host(Pid20)
& index(status,host(Pid0)) = wait
& host(Pid20) = host(Z)
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ ( index(ldr,host(Pid20)) = host(Pid20)
& index(status,host(Pid20)) = norm
& setIn(Pid20,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid20)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Z)
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ ( index(ldr,host(Pid20)) = host(Pid20)
& index(status,host(Pid20)) = norm
& setIn(Pid20,alive) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Pid30) = host(Z)
& setIn(Pid20,alive)
& setIn(Z,alive)
& host(Pid20) != host(Z) )
=> ~ ( setIn(host(Pid30),index(down,host(Pid20)))
& elem(m_Down(Pid0),queue(host(Z))) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Pid30) = host(Z)
& setIn(Pid20,alive)
& setIn(Z,alive)
& host(Pid20) != host(Z) )
=> ~ ( elem(m_Down(Pid30),queue(host(Pid20)))
& elem(m_Down(Pid0),queue(host(Z))) ) )
& ! [Z,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive)
& ~ leq(host(Pid20),host(Pid0)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> Pid0 = Z )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Pid0)
& setIn(Pid0,alive) )
=> ~ ( elem(m_Down(Pid20),queue(host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& elem(m_Down(Pid20),queue(host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& setIn(Pid0,alive) )
=> ~ ( setIn(host(Pid0),index(down,host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(host(Pid0),index(down,host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> host(Pid0) != host(Z) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( leq(host(X),host(Y))
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2 )
=> ( leq(nbr_proc,index(pendack,host(X)))
=> ! [Z] :
( ~ setIn(host(Z),index(acks,host(X)))
=> ! [V0] :
( host(X) = host(V0)
=> ! [W0,X0,Y0] :
( host(X) != host(Y0)
=> ( ( index(status,host(Y0)) = elec_1
& host(W0) = s(host(Y0))
& elem(m_Down(X0),queue(host(Y0)))
& elem(m_Down(W0),queue(host(Y0)))
& leq(nbr_proc,s(host(Y0)))
& setIn(Y0,alive)
& ! [V1] :
( ( leq(s(zero),V1)
& ~ leq(host(Y0),V1) )
=> ( V1 = host(X0)
| setIn(V1,index(down,host(Y0))) ) ) )
=> ~ ( host(X) = host(V0)
& setIn(V0,alive) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_62,plain,
leq(s(zero),host(A)),
inference(clausify,[status(thm)],[axiom_02]) ).
cnf(c_64,plain,
leq(host(A),nbr_proc),
inference(clausify,[status(thm)],[axiom_04]) ).
cnf(c_106,plain,
init(snoc(A,B)) = A,
inference(clausify,[status(thm)],[axiom_38]) ).
cnf(c_115,plain,
( B != A
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
cnf(c_145,plain,
~ leq(s(A),A),
inference(clausify,[status(thm)],[axiom_58]) ).
cnf(c_148,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[axiom_61]) ).
cnf(c_154,plain,
( leq(A,B)
| s(B) = A
| ~ leq(A,s(B)) ),
inference(clausify,[status(thm)],[axiom_64]) ).
fof(nnf_58,plain,
? [V,W,X,Y] :
( ? [Z] :
( ? [V0] :
( ? [W0,X0,Y0] :
( host(V0) = host(X)
& setIn(V0,alive)
& index(status,host(Y0)) = elec_1
& s(host(Y0)) = host(W0)
& elem(m_Down(X0),queue(host(Y0)))
& elem(m_Down(W0),queue(host(Y0)))
& leq(nbr_proc,s(host(Y0)))
& setIn(Y0,alive)
& ! [V1] :
( host(X0) = V1
| setIn(V1,index(down,host(Y0)))
| ~ leq(s(zero),V1)
| leq(host(Y0),V1) )
& host(Y0) != host(X) )
& host(V0) = host(X) )
& ~ setIn(host(Z),index(acks,host(X))) )
& leq(nbr_proc,index(pendack,host(X)))
& index(pendack,host(X)) = host(Y)
& index(status,host(X)) = elec_2
& leq(host(X),host(Y))
& setIn(X,alive)
& cons(m_Down(Y),V) = queue(host(X))
& ! [X44,Pid30,Pid20,Pid0] :
( index(status,host(X44)) != norm
| index(ldr,host(X44)) != host(X44)
| ~ setIn(X44,alive)
| index(status,host(Pid0)) != elec_1
| s(host(Pid0)) != host(Pid30)
| ~ elem(m_Down(Pid30),queue(host(Pid0)))
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ leq(nbr_proc,s(host(Pid0)))
| ~ setIn(Pid0,alive)
| ? [X45] :
( host(Pid20) != X45
& ~ setIn(X45,index(down,host(Pid0)))
& leq(s(zero),X45)
& ~ leq(host(Pid0),X45) ) )
& ! [X39,X40,X41,X42] :
( ~ elem(m_Ack(X39,X40),queue(host(X39)))
| index(status,host(X42)) != elec_1
| index(status,host(X39)) != elec_2
| host(X40) != host(X42)
| ~ elem(m_Down(X41),queue(host(X42)))
| ~ leq(host(X39),host(X42))
| ~ setIn(X39,alive)
| ? [X43] :
( host(X41) != X43
& ~ setIn(X43,index(down,host(X42)))
& leq(s(zero),X43)
& ~ leq(host(X42),X43) ) )
& ! [X36,X37,X38] :
( index(ldr,host(X37)) != host(X37)
| index(status,host(X37)) != norm
| ~ setIn(X37,alive)
| host(index(elid,host(X38))) != host(X37)
| index(status,host(X38)) != wait
| host(X37) != host(X36)
| ~ elem(m_Down(X36),queue(host(X38)))
| ~ setIn(X38,alive)
| host(X37) = host(X38) )
& ! [X33,X34,X35] :
( index(ldr,host(X34)) != host(X34)
| index(status,host(X34)) != norm
| ~ setIn(X34,alive)
| index(ldr,host(X35)) != host(X34)
| index(status,host(X35)) != norm
| host(X34) != host(X33)
| ~ elem(m_Down(X33),queue(host(X35)))
| ~ setIn(X35,alive)
| host(X34) = host(X35) )
& ! [X29,X30,X31,X32] :
( ~ setIn(host(X30),index(down,host(X31)))
| ~ elem(m_Down(X32),queue(host(X29)))
| host(X31) != host(X32)
| host(X30) != host(X29)
| ~ setIn(X31,alive)
| ~ setIn(X29,alive)
| host(X31) = host(X29) )
& ! [X25,X26,X27,X28] :
( ~ elem(m_Down(X26),queue(host(X27)))
| ~ elem(m_Down(X28),queue(host(X25)))
| host(X27) != host(X28)
| host(X26) != host(X25)
| ~ setIn(X27,alive)
| ~ setIn(X25,alive)
| host(X27) = host(X25) )
& ! [X22,X23,X24] :
( index(status,host(X22)) != norm
| index(ldr,host(X22)) != host(X22)
| ~ setIn(X22,alive)
| host(X23) != host(X22)
| ~ elem(m_Down(X23),queue(host(X24)))
| ~ setIn(X24,alive)
| leq(host(X23),host(X24)) )
& ! [X20,X21] :
( X21 = X20
| index(ldr,host(X21)) != host(X21)
| index(status,host(X21)) != norm
| index(status,host(X20)) != norm
| index(ldr,host(X20)) != host(X20)
| ~ setIn(X21,alive)
| ~ setIn(X20,alive) )
& ! [X17,X18,X19] :
( ~ elem(m_Down(X18),queue(host(X17)))
| ~ setIn(X17,alive)
| index(ldr,host(X19)) != host(X19)
| index(status,host(X19)) != norm
| host(X18) != host(X19)
| ~ setIn(X19,alive) )
& ! [X14,X15,X16] :
( leq(index(pendack,host(X16)),host(X14))
| index(status,host(X16)) != elec_2
| host(X15) != host(X16)
| ~ elem(m_Down(X15),queue(host(X14)))
| ~ setIn(X16,alive)
| ~ setIn(X14,alive) )
& ! [X12,X13] :
( ~ setIn(host(X13),index(down,host(X12)))
| ~ setIn(X12,alive)
| index(ldr,host(X13)) != host(X13)
| index(status,host(X13)) != norm
| ~ setIn(X13,alive) )
& ! [X10,X11] :
( leq(index(pendack,host(X11)),host(X10))
| index(status,host(X11)) != elec_2
| ~ setIn(host(X11),index(down,host(X10)))
| ~ setIn(X11,alive)
| ~ setIn(X10,alive) )
& ! [X9] :
( index(elid,host(X9)) = X9
| ~ setIn(X9,alive)
| ( index(status,host(X9)) != elec_2
& index(status,host(X9)) != elec_1 ) )
& ! [X7,X8] :
( ~ setIn(X8,alive)
| ~ setIn(X7,alive)
| host(X8) != host(X7)
| X8 = X7 )
& ! [X5,X6] :
( host(X6) != host(X5)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( ~ leq(host(X3),host(X4))
| ~ elem(m_Ldr(X4),queue(host(X3))) ) ),
inference(fof_nnf,[status(thm)],[conj_neg]) ).
fof(sk_conj_neg_sk,plain,
( host(sK3) = host(sK2)
& setIn(sK3,alive)
& index(status,host(sK4)) = elec_1
& s(host(sK4)) = host(sK6)
& elem(m_Down(sK5),queue(host(sK4)))
& elem(m_Down(sK6),queue(host(sK4)))
& leq(nbr_proc,s(host(sK4)))
& setIn(sK4,alive)
& ! [V1] :
( host(sK5) = V1
| setIn(V1,index(down,host(sK4)))
| ~ leq(s(zero),V1)
| leq(host(sK4),V1) )
& host(sK4) != host(sK2)
& host(sK3) = host(sK2)
& ~ setIn(host(sK9),index(acks,host(sK2)))
& leq(nbr_proc,index(pendack,host(sK2)))
& index(pendack,host(sK2)) = host(sK0)
& index(status,host(sK2)) = elec_2
& leq(host(sK2),host(sK0))
& setIn(sK2,alive)
& cons(m_Down(sK0),sK1) = queue(host(sK2))
& ! [X44,Pid30,Pid20,Pid0] :
( index(status,host(X44)) != norm
| index(ldr,host(X44)) != host(X44)
| ~ setIn(X44,alive)
| index(status,host(Pid0)) != elec_1
| s(host(Pid0)) != host(Pid30)
| ~ elem(m_Down(Pid30),queue(host(Pid0)))
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ leq(nbr_proc,s(host(Pid0)))
| ~ setIn(Pid0,alive)
| ( host(Pid20) != sK8(X44,Pid30,Pid20,Pid0)
& ~ setIn(sK8(X44,Pid30,Pid20,Pid0),index(down,host(Pid0)))
& leq(s(zero),sK8(X44,Pid30,Pid20,Pid0))
& ~ leq(host(Pid0),sK8(X44,Pid30,Pid20,Pid0)) ) )
& ! [X39,X40,X41,X42] :
( ~ elem(m_Ack(X39,X40),queue(host(X39)))
| index(status,host(X42)) != elec_1
| index(status,host(X39)) != elec_2
| host(X40) != host(X42)
| ~ elem(m_Down(X41),queue(host(X42)))
| ~ leq(host(X39),host(X42))
| ~ setIn(X39,alive)
| ( host(X41) != sK7(X39,X40,X41,X42)
& ~ setIn(sK7(X39,X40,X41,X42),index(down,host(X42)))
& leq(s(zero),sK7(X39,X40,X41,X42))
& ~ leq(host(X42),sK7(X39,X40,X41,X42)) ) )
& ! [X36,X37,X38] :
( index(ldr,host(X37)) != host(X37)
| index(status,host(X37)) != norm
| ~ setIn(X37,alive)
| host(index(elid,host(X38))) != host(X37)
| index(status,host(X38)) != wait
| host(X37) != host(X36)
| ~ elem(m_Down(X36),queue(host(X38)))
| ~ setIn(X38,alive)
| host(X37) = host(X38) )
& ! [X33,X34,X35] :
( index(ldr,host(X34)) != host(X34)
| index(status,host(X34)) != norm
| ~ setIn(X34,alive)
| index(ldr,host(X35)) != host(X34)
| index(status,host(X35)) != norm
| host(X34) != host(X33)
| ~ elem(m_Down(X33),queue(host(X35)))
| ~ setIn(X35,alive)
| host(X34) = host(X35) )
& ! [X29,X30,X31,X32] :
( ~ setIn(host(X30),index(down,host(X31)))
| ~ elem(m_Down(X32),queue(host(X29)))
| host(X31) != host(X32)
| host(X30) != host(X29)
| ~ setIn(X31,alive)
| ~ setIn(X29,alive)
| host(X31) = host(X29) )
& ! [X25,X26,X27,X28] :
( ~ elem(m_Down(X26),queue(host(X27)))
| ~ elem(m_Down(X28),queue(host(X25)))
| host(X27) != host(X28)
| host(X26) != host(X25)
| ~ setIn(X27,alive)
| ~ setIn(X25,alive)
| host(X27) = host(X25) )
& ! [X22,X23,X24] :
( index(status,host(X22)) != norm
| index(ldr,host(X22)) != host(X22)
| ~ setIn(X22,alive)
| host(X23) != host(X22)
| ~ elem(m_Down(X23),queue(host(X24)))
| ~ setIn(X24,alive)
| leq(host(X23),host(X24)) )
& ! [X20,X21] :
( X21 = X20
| index(ldr,host(X21)) != host(X21)
| index(status,host(X21)) != norm
| index(status,host(X20)) != norm
| index(ldr,host(X20)) != host(X20)
| ~ setIn(X21,alive)
| ~ setIn(X20,alive) )
& ! [X17,X18,X19] :
( ~ elem(m_Down(X18),queue(host(X17)))
| ~ setIn(X17,alive)
| index(ldr,host(X19)) != host(X19)
| index(status,host(X19)) != norm
| host(X18) != host(X19)
| ~ setIn(X19,alive) )
& ! [X14,X15,X16] :
( leq(index(pendack,host(X16)),host(X14))
| index(status,host(X16)) != elec_2
| host(X15) != host(X16)
| ~ elem(m_Down(X15),queue(host(X14)))
| ~ setIn(X16,alive)
| ~ setIn(X14,alive) )
& ! [X12,X13] :
( ~ setIn(host(X13),index(down,host(X12)))
| ~ setIn(X12,alive)
| index(ldr,host(X13)) != host(X13)
| index(status,host(X13)) != norm
| ~ setIn(X13,alive) )
& ! [X10,X11] :
( leq(index(pendack,host(X11)),host(X10))
| index(status,host(X11)) != elec_2
| ~ setIn(host(X11),index(down,host(X10)))
| ~ setIn(X11,alive)
| ~ setIn(X10,alive) )
& ! [X9] :
( index(elid,host(X9)) = X9
| ~ setIn(X9,alive)
| ( index(status,host(X9)) != elec_2
& index(status,host(X9)) != elec_1 ) )
& ! [X7,X8] :
( ~ setIn(X8,alive)
| ~ setIn(X7,alive)
| host(X8) != host(X7)
| X8 = X7 )
& ! [X5,X6] :
( host(X6) != host(X5)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( ~ leq(host(X3),host(X4))
| ~ elem(m_Ldr(X4),queue(host(X3))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK0,sK1,sK2,sK9,sK3,sK4,sK5,sK6]),skolemize(V,sK1),skolemize(W,sK10),skolemize(X,sK2),skolemize(Y,sK0),skolemize(X43,sK7(X39,X40,X41,X42)),skolemize(X45,sK8(X44,Pid30,Pid20,Pid0)),skolemize(Z,sK9),skolemize(V0,sK3),skolemize(W0,sK6),skolemize(X0,sK5),skolemize(Y0,sK4)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( setIn(sK3,alive)
& index(status,host(sK4)) = elec_1
& s(host(sK4)) = host(sK6)
& elem(m_Down(sK5),queue(host(sK4)))
& elem(m_Down(sK6),queue(host(sK4)))
& leq(nbr_proc,s(host(sK4)))
& setIn(sK4,alive)
& ! [VAR_0] :
( host(sK5) = VAR_0
| setIn(VAR_0,index(down,host(sK4)))
| ~ leq(s(zero),VAR_0)
| leq(host(sK4),VAR_0) )
& host(sK4) != host(sK2)
& host(sK3) = host(sK2)
& ~ setIn(host(sK9),index(acks,host(sK2)))
& leq(nbr_proc,index(pendack,host(sK2)))
& index(pendack,host(sK2)) = host(sK0)
& index(status,host(sK2)) = elec_2
& leq(host(sK2),host(sK0))
& setIn(sK2,alive)
& cons(m_Down(sK0),sK1) = queue(host(sK2))
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( index(status,host(VAR_1)) != norm
| index(ldr,host(VAR_1)) != host(VAR_1)
| ~ setIn(VAR_1,alive)
| index(status,host(VAR_3)) != elec_1
| s(host(VAR_3)) != host(VAR_2)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ elem(m_Down(VAR_0),queue(host(VAR_3)))
| ~ leq(nbr_proc,s(host(VAR_3)))
| ~ setIn(VAR_3,alive)
| host(VAR_0) != sK8(VAR_1,VAR_2,VAR_0,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( index(status,host(VAR_0)) != norm
| index(ldr,host(VAR_0)) != host(VAR_0)
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_3)) != elec_1
| s(host(VAR_3)) != host(VAR_1)
| ~ elem(m_Down(VAR_1),queue(host(VAR_3)))
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ leq(nbr_proc,s(host(VAR_3)))
| ~ setIn(VAR_3,alive)
| ~ setIn(sK8(VAR_0,VAR_1,VAR_2,VAR_3),index(down,host(VAR_3))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( index(status,host(VAR_0)) != norm
| index(ldr,host(VAR_0)) != host(VAR_0)
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_3)) != elec_1
| s(host(VAR_3)) != host(VAR_1)
| ~ elem(m_Down(VAR_1),queue(host(VAR_3)))
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ leq(nbr_proc,s(host(VAR_3)))
| ~ setIn(VAR_3,alive)
| leq(s(zero),sK8(VAR_0,VAR_1,VAR_2,VAR_3)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( index(status,host(VAR_1)) != norm
| index(ldr,host(VAR_1)) != host(VAR_1)
| ~ setIn(VAR_1,alive)
| index(status,host(VAR_0)) != elec_1
| s(host(VAR_0)) != host(VAR_2)
| ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| ~ elem(m_Down(VAR_3),queue(host(VAR_0)))
| ~ leq(nbr_proc,s(host(VAR_0)))
| ~ setIn(VAR_0,alive)
| ~ leq(host(VAR_0),sK8(VAR_1,VAR_2,VAR_3,VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Ack(VAR_1,VAR_2),queue(host(VAR_1)))
| index(status,host(VAR_3)) != elec_1
| index(status,host(VAR_1)) != elec_2
| host(VAR_2) != host(VAR_3)
| ~ elem(m_Down(VAR_0),queue(host(VAR_3)))
| ~ leq(host(VAR_1),host(VAR_3))
| ~ setIn(VAR_1,alive)
| host(VAR_0) != sK7(VAR_1,VAR_2,VAR_0,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_0)))
| index(status,host(VAR_3)) != elec_1
| index(status,host(VAR_0)) != elec_2
| host(VAR_1) != host(VAR_3)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ leq(host(VAR_0),host(VAR_3))
| ~ setIn(VAR_0,alive)
| ~ setIn(sK7(VAR_0,VAR_1,VAR_2,VAR_3),index(down,host(VAR_3))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_0)))
| index(status,host(VAR_3)) != elec_1
| index(status,host(VAR_0)) != elec_2
| host(VAR_1) != host(VAR_3)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ leq(host(VAR_0),host(VAR_3))
| ~ setIn(VAR_0,alive)
| leq(s(zero),sK7(VAR_0,VAR_1,VAR_2,VAR_3)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Ack(VAR_1,VAR_2),queue(host(VAR_1)))
| index(status,host(VAR_0)) != elec_1
| index(status,host(VAR_1)) != elec_2
| host(VAR_2) != host(VAR_0)
| ~ elem(m_Down(VAR_3),queue(host(VAR_0)))
| ~ leq(host(VAR_1),host(VAR_0))
| ~ setIn(VAR_1,alive)
| ~ leq(host(VAR_0),sK7(VAR_1,VAR_2,VAR_3,VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(ldr,host(VAR_0)) != host(VAR_0)
| index(status,host(VAR_0)) != norm
| ~ setIn(VAR_0,alive)
| host(index(elid,host(VAR_1))) != host(VAR_0)
| index(status,host(VAR_1)) != wait
| host(VAR_0) != host(VAR_2)
| ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(ldr,host(VAR_0)) != host(VAR_0)
| index(status,host(VAR_0)) != norm
| ~ setIn(VAR_0,alive)
| index(ldr,host(VAR_1)) != host(VAR_0)
| index(status,host(VAR_1)) != norm
| host(VAR_0) != host(VAR_2)
| ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ setIn(host(VAR_2),index(down,host(VAR_0)))
| ~ elem(m_Down(VAR_3),queue(host(VAR_1)))
| host(VAR_0) != host(VAR_3)
| host(VAR_2) != host(VAR_1)
| ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| ~ elem(m_Down(VAR_3),queue(host(VAR_1)))
| host(VAR_0) != host(VAR_3)
| host(VAR_2) != host(VAR_1)
| ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(status,host(VAR_2)) != norm
| index(ldr,host(VAR_2)) != host(VAR_2)
| ~ setIn(VAR_2,alive)
| host(VAR_0) != host(VAR_2)
| ~ elem(m_Down(VAR_0),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| leq(host(VAR_0),host(VAR_1)) )
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| index(ldr,host(VAR_1)) != host(VAR_1)
| index(status,host(VAR_1)) != norm
| index(status,host(VAR_0)) != norm
| index(ldr,host(VAR_0)) != host(VAR_0)
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ elem(m_Down(VAR_1),queue(host(VAR_2)))
| ~ setIn(VAR_2,alive)
| index(ldr,host(VAR_0)) != host(VAR_0)
| index(status,host(VAR_0)) != norm
| host(VAR_1) != host(VAR_0)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1,VAR_2] :
( leq(index(pendack,host(VAR_1)),host(VAR_0))
| index(status,host(VAR_1)) != elec_2
| host(VAR_2) != host(VAR_1)
| ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1] :
( ~ setIn(host(VAR_0),index(down,host(VAR_1)))
| ~ setIn(VAR_1,alive)
| index(ldr,host(VAR_0)) != host(VAR_0)
| index(status,host(VAR_0)) != norm
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1] :
( leq(index(pendack,host(VAR_1)),host(VAR_0))
| index(status,host(VAR_1)) != elec_2
| ~ setIn(host(VAR_1),index(down,host(VAR_0)))
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_2 )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_1 )
& ! [VAR_0,VAR_1] :
( ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) != host(VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( host(VAR_0) != host(VAR_1)
| ~ elem(m_Down(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Ldr(VAR_0),queue(host(VAR_1))) ) ),
inference(cnf_transformation,[status(thm)],[sk_conj_neg_sk]) ).
cnf(c_158,negated_conjecture,
( host(A) != host(B)
| ~ elem(m_Down(A),queue(host(B))) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_162,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != elec_2
| ~ setIn(host(B),index(down,host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_164,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != elec_2
| host(C) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_181,negated_conjecture,
cons(m_Down(sK0),sK1) = queue(host(sK2)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_182,negated_conjecture,
queue(host(sK2)) = cons(m_Down(sK0),sK1),
inference(copy,[status(thm)],[c_181]) ).
cnf(c_183,negated_conjecture,
setIn(sK2,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_185,negated_conjecture,
index(status,host(sK2)) = elec_2,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_186,negated_conjecture,
elec_2 = index(status,host(sK2)),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_187,negated_conjecture,
index(pendack,host(sK2)) = host(sK0),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_188,negated_conjecture,
host(sK0) = index(pendack,host(sK2)),
inference(copy,[status(thm)],[c_187]) ).
cnf(c_189,negated_conjecture,
leq(nbr_proc,index(pendack,host(sK2))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_191,negated_conjecture,
host(sK3) = host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_192,negated_conjecture,
host(sK4) != host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_193,negated_conjecture,
( host(sK5) = A
| setIn(A,index(down,host(sK4)))
| ~ leq(s(zero),A)
| leq(host(sK4),A) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_194,negated_conjecture,
setIn(sK4,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_195,negated_conjecture,
leq(nbr_proc,s(host(sK4))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_197,negated_conjecture,
elem(m_Down(sK5),queue(host(sK4))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_198,negated_conjecture,
s(host(sK4)) = host(sK6),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_201,negated_conjecture,
setIn(sK3,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_4182,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != index(status,host(sK2))
| host(C) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_186,c_164]) ).
cnf(c_217,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(sK2)) != index(status,host(B))
| host(C) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_4182]) ).
cnf(c_4183,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != index(status,host(sK2))
| ~ setIn(host(B),index(down,host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_186,c_162]) ).
cnf(c_218,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(sK2)) != index(status,host(B))
| ~ setIn(host(B),index(down,host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_4183]) ).
cnf(c_224,negated_conjecture,
leq(nbr_proc,host(sK6)),
inference(paramod,[status(thm)],[c_198,c_195]) ).
cnf(c_4184,plain,
elem(A,cons(init(snoc(A,B)),C)),
inference(resolve,[status(thm)],[c_115,c_106]) ).
cnf(c_259,plain,
elem(A,cons(A,B)),
inference(paramod,[status(thm)],[c_106,c_4184]) ).
cnf(c_4185,plain,
( host(A) != host(sK2)
| ~ elem(m_Down(A),cons(m_Down(sK0),sK1)) ),
inference(paramod,[status(thm)],[c_182,c_158]) ).
cnf(c_324,plain,
( host(sK2) != host(A)
| ~ elem(m_Down(A),cons(m_Down(sK0),sK1)) ),
inference(copy,[status(thm)],[c_4185]) ).
cnf(c_336,plain,
leq(index(pendack,host(sK2)),nbr_proc),
inference(paramod,[status(thm)],[c_188,c_64]) ).
cnf(c_4186,negated_conjecture,
( nbr_proc = index(pendack,host(sK2))
| ~ leq(index(pendack,host(sK2)),nbr_proc) ),
inference(resolve,[status(thm)],[c_189,c_148]) ).
cnf(c_4187,negated_conjecture,
( index(pendack,host(sK2)) = nbr_proc
| ~ leq(index(pendack,host(sK2)),nbr_proc) ),
inference(copy,[status(thm)],[c_4186]) ).
cnf(c_353,negated_conjecture,
index(pendack,host(sK2)) = nbr_proc,
inference(resolve,[status(thm)],[c_336,c_4187]) ).
cnf(c_370,negated_conjecture,
host(sK0) = nbr_proc,
inference(paramod,[status(thm)],[c_353,c_188]) ).
cnf(c_376,plain,
( host(sK5) = host(A)
| setIn(host(A),index(down,host(sK4)))
| leq(host(sK4),host(A)) ),
inference(resolve,[status(thm)],[c_193,c_62]) ).
cnf(c_398,plain,
~ leq(host(sK6),host(sK4)),
inference(paramod,[status(thm)],[c_198,c_145]) ).
cnf(c_4188,plain,
( leq(A,host(sK4))
| s(host(sK4)) = A
| ~ leq(A,host(sK6)) ),
inference(paramod,[status(thm)],[c_198,c_154]) ).
cnf(c_401,plain,
( leq(A,host(sK4))
| host(sK6) = A
| ~ leq(A,host(sK6)) ),
inference(paramod,[status(thm)],[c_198,c_4188]) ).
cnf(c_4189,negated_conjecture,
( leq(index(pendack,host(A)),host(sK4))
| index(status,host(sK2)) != index(status,host(A))
| host(sK5) != host(A)
| ~ setIn(A,alive)
| ~ setIn(sK4,alive) ),
inference(resolve,[status(thm)],[c_217,c_197]) ).
cnf(c_428,negated_conjecture,
( leq(index(pendack,host(A)),host(sK4))
| index(status,host(sK2)) != index(status,host(A))
| host(sK5) != host(A)
| ~ setIn(A,alive) ),
inference(resolve,[status(thm)],[c_194,c_4189]) ).
cnf(c_4190,plain,
( leq(index(pendack,host(sK3)),host(A))
| index(status,host(sK2)) != index(status,host(sK3))
| ~ setIn(host(sK2),index(down,host(A)))
| ~ setIn(sK3,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_191,c_218]) ).
cnf(c_4191,plain,
( leq(index(pendack,host(sK3)),host(A))
| index(status,host(sK2)) != index(status,host(sK2))
| ~ setIn(host(sK2),index(down,host(A)))
| ~ setIn(sK3,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_191,c_4190]) ).
cnf(c_4192,plain,
( leq(index(pendack,host(sK2)),host(A))
| index(status,host(sK2)) != index(status,host(sK2))
| ~ setIn(host(sK2),index(down,host(A)))
| ~ setIn(sK3,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_191,c_4191]) ).
cnf(c_4193,plain,
( leq(nbr_proc,host(A))
| index(status,host(sK2)) != index(status,host(sK2))
| ~ setIn(host(sK2),index(down,host(A)))
| ~ setIn(sK3,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_353,c_4192]) ).
cnf(c_4194,plain,
( leq(nbr_proc,host(A))
| ~ setIn(host(sK2),index(down,host(A)))
| ~ setIn(sK3,alive)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_4193]) ).
cnf(c_433,negated_conjecture,
( leq(nbr_proc,host(A))
| ~ setIn(host(sK2),index(down,host(A)))
| ~ setIn(A,alive) ),
inference(resolve,[status(thm)],[c_201,c_4194]) ).
cnf(c_4195,negated_conjecture,
( nbr_proc = host(sK6)
| ~ leq(host(sK6),nbr_proc) ),
inference(resolve,[status(thm)],[c_224,c_148]) ).
cnf(c_4196,negated_conjecture,
( host(sK6) = nbr_proc
| ~ leq(host(sK6),nbr_proc) ),
inference(copy,[status(thm)],[c_4195]) ).
cnf(c_441,negated_conjecture,
host(sK6) = nbr_proc,
inference(resolve,[status(thm)],[c_64,c_4196]) ).
cnf(c_4197,plain,
( leq(A,host(sK4))
| host(sK6) = A
| ~ leq(A,nbr_proc) ),
inference(paramod,[status(thm)],[c_441,c_401]) ).
cnf(c_449,plain,
( leq(A,host(sK4))
| nbr_proc = A
| ~ leq(A,nbr_proc) ),
inference(paramod,[status(thm)],[c_441,c_4197]) ).
cnf(c_452,plain,
~ leq(nbr_proc,host(sK4)),
inference(paramod,[status(thm)],[c_441,c_398]) ).
cnf(c_4198,plain,
host(sK2) != host(sK0),
inference(resolve,[status(thm)],[c_324,c_259]) ).
cnf(c_716,plain,
host(sK2) != nbr_proc,
inference(paramod,[status(thm)],[c_370,c_4198]) ).
cnf(c_4199,plain,
( leq(host(A),host(sK4))
| nbr_proc = host(A) ),
inference(resolve,[status(thm)],[c_449,c_64]) ).
cnf(c_2817,plain,
( leq(host(A),host(sK4))
| host(A) = nbr_proc ),
inference(copy,[status(thm)],[c_4199]) ).
cnf(c_4200,negated_conjecture,
( leq(index(pendack,host(sK2)),host(sK4))
| index(status,host(sK2)) != index(status,host(sK2))
| host(sK5) != host(sK2) ),
inference(resolve,[status(thm)],[c_428,c_183]) ).
cnf(c_4201,negated_conjecture,
( leq(nbr_proc,host(sK4))
| index(status,host(sK2)) != index(status,host(sK2))
| host(sK5) != host(sK2) ),
inference(paramod,[status(thm)],[c_353,c_4200]) ).
cnf(c_4202,negated_conjecture,
( leq(nbr_proc,host(sK4))
| host(sK5) != host(sK2) ),
inference(copy,[status(thm)],[c_4201]) ).
cnf(c_3893,negated_conjecture,
host(sK5) != host(sK2),
inference(resolve,[status(thm)],[c_452,c_4202]) ).
cnf(c_4203,plain,
( host(sK5) = host(sK2)
| leq(host(sK4),host(sK2))
| leq(nbr_proc,host(sK4))
| ~ setIn(sK4,alive) ),
inference(resolve,[status(thm)],[c_433,c_376]) ).
cnf(c_4204,negated_conjecture,
( host(sK5) = host(sK2)
| leq(host(sK4),host(sK2))
| leq(nbr_proc,host(sK4)) ),
inference(resolve,[status(thm)],[c_194,c_4203]) ).
cnf(c_4205,negated_conjecture,
( host(sK5) = host(sK2)
| leq(host(sK4),host(sK2)) ),
inference(resolve,[status(thm)],[c_452,c_4204]) ).
cnf(c_4136,negated_conjecture,
leq(host(sK4),host(sK2)),
inference(resolve,[status(thm)],[c_3893,c_4205]) ).
cnf(c_4206,plain,
( host(sK4) = host(sK2)
| ~ leq(host(sK2),host(sK4)) ),
inference(resolve,[status(thm)],[c_4136,c_148]) ).
cnf(c_4149,negated_conjecture,
~ leq(host(sK2),host(sK4)),
inference(resolve,[status(thm)],[c_192,c_4206]) ).
cnf(c_4207,plain,
host(sK2) = nbr_proc,
inference(resolve,[status(thm)],[c_4149,c_2817]) ).
cnf(c_4181,plain,
$false,
inference(resolve,[status(thm)],[c_716,c_4207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV480+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n003.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 13:58:54 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.41 % Process 3068113 was started by sandbox2 on n003,
% 0.15/0.41 % Sat Sep 26 13:58:54 2026
% 0.15/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 15.65/2.70
% 15.65/2.70 % given #500 (T,wt=9): 1294 leq(host(A),B) | leq(s(B),s(nbr_proc)). [resolve(1038,b,152,a)].
% 15.65/2.70
% 15.65/2.70 % SZS status Theorem for theBenchmark
% 15.65/2.70
% 15.65/2.70 % Proof 1 at 1.69 (+ 0.51) seconds.
% 15.65/2.70 % Length of proof is 56.
% 15.65/2.70 % Level of proof is 8.
% 15.65/2.70 % Maximum clause weight is 33.000.
% 15.65/2.70 % Given clauses 707.
% 15.65/2.70
% 15.65/2.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------