%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV466+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 09:08:01 AM UTC 2026
% Result : Theorem 8.06s 1.55s
% Output : CNFRefutation 8.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 9
% Syntax : Number of formulae : 129 ( 54 unt; 0 def)
% Number of atoms : 795 ( 342 equ)
% Maximal formula atoms : 111 ( 6 avg)
% Number of connectives : 1108 ( 442 ~; 375 |; 235 &)
% ( 4 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 20 con; 0-4 aty)
% Number of variables : 336 ( 12 sgn 236 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_04,axiom,
! [P] : leq(host(P),nbr_proc),
file('theBenchmark.p',axiom_04) ).
fof(axiom_14,axiom,
! [X,Y,Z] : m_Ack(X,Y) != m_Ldr(Z),
file('theBenchmark.p',axiom_14) ).
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_47,axiom,
! [X,Y,Q] :
( elem(X,snoc(Q,Y))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_47) ).
fof(axiom_60,axiom,
! [X,Y] :
( leq(Y,X)
| leq(X,Y) ),
file('theBenchmark.p',axiom_60) ).
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] :
( ( host(Pid20) = s(index(pendack,host(Pid0)))
& host(Pid30) = index(pendack,host(Pid0))
& index(status,host(Pid0)) = elec_2
& leq(nbr_proc,s(index(pendack,host(Pid0))))
& elem(m_Ack(Pid0,Pid30),queue(host(Pid0)))
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid0) = host(Pid30)
& host(Pid0) = nbr_proc
& elem(m_Down(Pid20),queue(host(Pid0)))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( elem(m_Down(Pid30),queue(host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& elem(m_Halt(Pid0),queue(host(Pid20)))
& setIn(Pid0,alive)
& ~ leq(index(pendack,host(Pid0)),host(Z)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0))) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& host(Pid0) = host(Pid20)
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> ~ elem(m_Ack(Z,Pid20),queue(host(Z))) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& setIn(Pid0,alive) )
=> ~ elem(m_Ack(Pid0,Z),queue(host(Pid0))) )
& ! [Z,Pid0] :
( ( elem(m_Ack(Pid0,Z),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> leq(host(Z),index(pendack,host(Pid0))) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( elem(m_Ack(Pid0,Z),queue(host(Pid20)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Halt(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_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(Z) = host(Y0)
=> ( host(X) != host(Y0)
=> ( ( host(X0) = s(index(pendack,host(Y0)))
& host(W0) = index(pendack,host(Y0))
& index(status,host(Y0)) = elec_2
& elem(m_Ack(Y0,W0),snoc(queue(host(Y0)),m_Ldr(X)))
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X)))
& leq(nbr_proc,s(index(pendack,host(Y0))))
& setIn(Y0,alive) )
=> ~ ( 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] :
( ( host(Pid20) = s(index(pendack,host(Pid0)))
& host(Pid30) = index(pendack,host(Pid0))
& index(status,host(Pid0)) = elec_2
& leq(nbr_proc,s(index(pendack,host(Pid0))))
& elem(m_Ack(Pid0,Pid30),queue(host(Pid0)))
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid0) = host(Pid30)
& host(Pid0) = nbr_proc
& elem(m_Down(Pid20),queue(host(Pid0)))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( elem(m_Down(Pid30),queue(host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& elem(m_Halt(Pid0),queue(host(Pid20)))
& setIn(Pid0,alive)
& ~ leq(index(pendack,host(Pid0)),host(Z)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0))) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& host(Pid0) = host(Pid20)
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> ~ elem(m_Ack(Z,Pid20),queue(host(Z))) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& setIn(Pid0,alive) )
=> ~ elem(m_Ack(Pid0,Z),queue(host(Pid0))) )
& ! [Z,Pid0] :
( ( elem(m_Ack(Pid0,Z),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> leq(host(Z),index(pendack,host(Pid0))) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( elem(m_Ack(Pid0,Z),queue(host(Pid20)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Halt(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_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(Z) = host(Y0)
=> ( host(X) != host(Y0)
=> ( ( host(X0) = s(index(pendack,host(Y0)))
& host(W0) = index(pendack,host(Y0))
& index(status,host(Y0)) = elec_2
& elem(m_Ack(Y0,W0),snoc(queue(host(Y0)),m_Ldr(X)))
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X)))
& leq(nbr_proc,s(index(pendack,host(Y0))))
& setIn(Y0,alive) )
=> ~ ( host(X) = host(V0)
& setIn(V0,alive) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_64,plain,
leq(host(A),nbr_proc),
inference(clausify,[status(thm)],[axiom_04]) ).
cnf(c_79,plain,
m_Ldr(A) != m_Ack(B,C),
inference(clausify,[status(thm)],[axiom_14]) ).
cnf(c_108,plain,
init(snoc(A,B)) = A,
inference(clausify,[status(thm)],[axiom_38]) ).
cnf(c_119,plain,
( B != A
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
cnf(c_121,plain,
( elem(A,B)
| C = A
| ~ elem(A,snoc(B,C)) ),
inference(clausify,[status(thm)],[axiom_47]) ).
cnf(c_151,plain,
( leq(B,A)
| leq(A,B) ),
inference(clausify,[status(thm)],[axiom_60]) ).
cnf(c_152,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[axiom_61]) ).
cnf(c_158,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)
& s(index(pendack,host(Y0))) = host(X0)
& index(pendack,host(Y0)) = host(W0)
& index(status,host(Y0)) = elec_2
& elem(m_Ack(Y0,W0),snoc(queue(host(Y0)),m_Ldr(X)))
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X)))
& leq(nbr_proc,s(index(pendack,host(Y0))))
& setIn(Y0,alive)
& host(Y0) != host(X)
& host(Y0) = host(Z) )
& 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))
& ! [X37,Pid30,Pid20,Pid0] :
( index(status,host(X37)) != norm
| index(ldr,host(X37)) != host(X37)
| ~ setIn(X37,alive)
| s(index(pendack,host(Pid0))) != host(Pid20)
| index(pendack,host(Pid0)) != host(Pid30)
| index(status,host(Pid0)) != elec_2
| ~ leq(nbr_proc,s(index(pendack,host(Pid0))))
| ~ elem(m_Ack(Pid0,Pid30),queue(host(Pid0)))
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive) )
& ! [X32,X33,X34,X35] :
( ~ elem(m_Down(X33),queue(host(X32)))
| ~ setIn(X32,alive)
| index(status,host(X35)) != elec_1
| host(X33) != host(X35)
| host(X35) != nbr_proc
| ~ elem(m_Down(X34),queue(host(X35)))
| ? [X36] :
( host(X34) != X36
& ~ setIn(X36,index(down,host(X35)))
& leq(s(zero),X36)
& ~ leq(host(X35),X36) ) )
& ! [X29,X30,X31] :
( index(status,host(X29)) != norm
| index(ldr,host(X29)) != host(X29)
| ~ setIn(X29,alive)
| index(status,host(X31)) != elec_2
| ~ elem(m_Halt(X31),queue(host(X30)))
| ~ setIn(X31,alive)
| leq(index(pendack,host(X31)),host(X29)) )
& ! [X27,X28] :
( ~ leq(index(pendack,host(X27)),index(pendack,host(X28)))
| index(status,host(X28)) != elec_2
| index(status,host(X27)) != elec_2
| ~ setIn(X28,alive)
| ~ setIn(X27,alive)
| leq(host(X27),host(X28)) )
& ! [X24,X25,X26] :
( ~ elem(m_Ack(X24,X25),queue(host(X24)))
| index(status,host(X26)) != elec_2
| index(status,host(X24)) != elec_2
| host(X25) != host(X26)
| ~ setIn(X26,alive)
| ~ setIn(X24,alive) )
& ! [X22,X23] :
( leq(index(pendack,host(X23)),host(X22))
| index(status,host(X23)) != elec_2
| index(status,host(X22)) != elec_2
| ~ setIn(X23,alive)
| ~ setIn(X22,alive)
| leq(host(X22),host(X23)) )
& ! [X19,X20,X21] :
( index(status,host(X19)) != norm
| index(ldr,host(X19)) != host(X19)
| ~ setIn(X19,alive)
| host(X20) != host(X19)
| ~ elem(m_Down(X20),queue(host(X21)))
| ~ setIn(X21,alive) )
& ! [X18] :
( index(elid,host(X18)) = X18
| ~ setIn(X18,alive)
| ( index(status,host(X18)) != elec_2
& index(status,host(X18)) != elec_1 ) )
& ! [X16,X17] :
( ~ elem(m_Ack(X17,X16),queue(host(X17)))
| index(status,host(X17)) != elec_1
| ~ setIn(X17,alive) )
& ! [X14,X15] :
( leq(host(X14),index(pendack,host(X15)))
| ~ elem(m_Ack(X15,X14),queue(host(X15)))
| ~ setIn(X15,alive) )
& ! [X12,X13] :
( ~ setIn(X13,alive)
| ~ setIn(X12,alive)
| host(X13) != host(X12)
| X13 = X12 )
& ! [X9,X10,X11] :
( ~ leq(host(X9),host(X11))
| ~ elem(m_Ack(X11,X9),queue(host(X10))) )
& ! [X7,X8] :
( ~ leq(host(X7),host(X8))
| ~ elem(m_Halt(X8),queue(host(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)
& s(index(pendack,host(sK4))) = host(sK7)
& index(pendack,host(sK4)) = host(sK6)
& index(status,host(sK4)) = elec_2
& elem(m_Ack(sK4,sK6),snoc(queue(host(sK4)),m_Ldr(sK2)))
& elem(m_Down(sK7),snoc(queue(host(sK4)),m_Ldr(sK2)))
& leq(nbr_proc,s(index(pendack,host(sK4))))
& setIn(sK4,alive)
& host(sK4) != host(sK2)
& host(sK4) = host(sK5)
& host(sK3) = host(sK2)
& setIn(host(sK5),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))
& ! [X37,Pid30,Pid20,Pid0] :
( index(status,host(X37)) != norm
| index(ldr,host(X37)) != host(X37)
| ~ setIn(X37,alive)
| s(index(pendack,host(Pid0))) != host(Pid20)
| index(pendack,host(Pid0)) != host(Pid30)
| index(status,host(Pid0)) != elec_2
| ~ leq(nbr_proc,s(index(pendack,host(Pid0))))
| ~ elem(m_Ack(Pid0,Pid30),queue(host(Pid0)))
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive) )
& ! [X32,X33,X34,X35] :
( ~ elem(m_Down(X33),queue(host(X32)))
| ~ setIn(X32,alive)
| index(status,host(X35)) != elec_1
| host(X33) != host(X35)
| host(X35) != nbr_proc
| ~ elem(m_Down(X34),queue(host(X35)))
| ( host(X34) != sK8(X32,X33,X34,X35)
& ~ setIn(sK8(X32,X33,X34,X35),index(down,host(X35)))
& leq(s(zero),sK8(X32,X33,X34,X35))
& ~ leq(host(X35),sK8(X32,X33,X34,X35)) ) )
& ! [X29,X30,X31] :
( index(status,host(X29)) != norm
| index(ldr,host(X29)) != host(X29)
| ~ setIn(X29,alive)
| index(status,host(X31)) != elec_2
| ~ elem(m_Halt(X31),queue(host(X30)))
| ~ setIn(X31,alive)
| leq(index(pendack,host(X31)),host(X29)) )
& ! [X27,X28] :
( ~ leq(index(pendack,host(X27)),index(pendack,host(X28)))
| index(status,host(X28)) != elec_2
| index(status,host(X27)) != elec_2
| ~ setIn(X28,alive)
| ~ setIn(X27,alive)
| leq(host(X27),host(X28)) )
& ! [X24,X25,X26] :
( ~ elem(m_Ack(X24,X25),queue(host(X24)))
| index(status,host(X26)) != elec_2
| index(status,host(X24)) != elec_2
| host(X25) != host(X26)
| ~ setIn(X26,alive)
| ~ setIn(X24,alive) )
& ! [X22,X23] :
( leq(index(pendack,host(X23)),host(X22))
| index(status,host(X23)) != elec_2
| index(status,host(X22)) != elec_2
| ~ setIn(X23,alive)
| ~ setIn(X22,alive)
| leq(host(X22),host(X23)) )
& ! [X19,X20,X21] :
( index(status,host(X19)) != norm
| index(ldr,host(X19)) != host(X19)
| ~ setIn(X19,alive)
| host(X20) != host(X19)
| ~ elem(m_Down(X20),queue(host(X21)))
| ~ setIn(X21,alive) )
& ! [X18] :
( index(elid,host(X18)) = X18
| ~ setIn(X18,alive)
| ( index(status,host(X18)) != elec_2
& index(status,host(X18)) != elec_1 ) )
& ! [X16,X17] :
( ~ elem(m_Ack(X17,X16),queue(host(X17)))
| index(status,host(X17)) != elec_1
| ~ setIn(X17,alive) )
& ! [X14,X15] :
( leq(host(X14),index(pendack,host(X15)))
| ~ elem(m_Ack(X15,X14),queue(host(X15)))
| ~ setIn(X15,alive) )
& ! [X12,X13] :
( ~ setIn(X13,alive)
| ~ setIn(X12,alive)
| host(X13) != host(X12)
| X13 = X12 )
& ! [X9,X10,X11] :
( ~ leq(host(X9),host(X11))
| ~ elem(m_Ack(X11,X9),queue(host(X10))) )
& ! [X7,X8] :
( ~ leq(host(X7),host(X8))
| ~ elem(m_Halt(X8),queue(host(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,[sK8,sK0,sK1,sK2,sK5,sK3,sK4,sK7,sK6]),skolemize(V,sK1),skolemize(W,sK9),skolemize(X,sK2),skolemize(Y,sK0),skolemize(X36,sK8(X32,X33,X34,X35)),skolemize(Z,sK5),skolemize(V0,sK3),skolemize(W0,sK6),skolemize(X0,sK7),skolemize(Y0,sK4)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( setIn(sK3,alive)
& s(index(pendack,host(sK4))) = host(sK7)
& index(pendack,host(sK4)) = host(sK6)
& index(status,host(sK4)) = elec_2
& elem(m_Ack(sK4,sK6),snoc(queue(host(sK4)),m_Ldr(sK2)))
& elem(m_Down(sK7),snoc(queue(host(sK4)),m_Ldr(sK2)))
& leq(nbr_proc,s(index(pendack,host(sK4))))
& setIn(sK4,alive)
& host(sK4) != host(sK2)
& host(sK4) = host(sK5)
& host(sK3) = host(sK2)
& setIn(host(sK5),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_3)) != norm
| index(ldr,host(VAR_3)) != host(VAR_3)
| ~ setIn(VAR_3,alive)
| s(index(pendack,host(VAR_0))) != host(VAR_1)
| index(pendack,host(VAR_0)) != host(VAR_2)
| index(status,host(VAR_0)) != elec_2
| ~ leq(nbr_proc,s(index(pendack,host(VAR_0))))
| ~ elem(m_Ack(VAR_0,VAR_2),queue(host(VAR_0)))
| ~ elem(m_Down(VAR_1),queue(host(VAR_0)))
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| index(status,host(VAR_3)) != elec_1
| host(VAR_2) != host(VAR_3)
| host(VAR_3) != nbr_proc
| ~ elem(m_Down(VAR_0),queue(host(VAR_3)))
| host(VAR_0) != sK8(VAR_1,VAR_2,VAR_0,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_1),queue(host(VAR_0)))
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_3)) != elec_1
| host(VAR_1) != host(VAR_3)
| host(VAR_3) != nbr_proc
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ setIn(sK8(VAR_0,VAR_1,VAR_2,VAR_3),index(down,host(VAR_3))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_1),queue(host(VAR_0)))
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_3)) != elec_1
| host(VAR_1) != host(VAR_3)
| host(VAR_3) != nbr_proc
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| leq(s(zero),sK8(VAR_0,VAR_1,VAR_2,VAR_3)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| index(status,host(VAR_0)) != elec_1
| host(VAR_2) != host(VAR_0)
| host(VAR_0) != nbr_proc
| ~ elem(m_Down(VAR_3),queue(host(VAR_0)))
| ~ leq(host(VAR_0),sK8(VAR_1,VAR_2,VAR_3,VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(status,host(VAR_1)) != norm
| index(ldr,host(VAR_1)) != host(VAR_1)
| ~ setIn(VAR_1,alive)
| index(status,host(VAR_0)) != elec_2
| ~ elem(m_Halt(VAR_0),queue(host(VAR_2)))
| ~ setIn(VAR_0,alive)
| leq(index(pendack,host(VAR_0)),host(VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ leq(index(pendack,host(VAR_0)),index(pendack,host(VAR_1)))
| index(status,host(VAR_1)) != elec_2
| index(status,host(VAR_0)) != elec_2
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive)
| leq(host(VAR_0),host(VAR_1)) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ elem(m_Ack(VAR_0,VAR_2),queue(host(VAR_0)))
| index(status,host(VAR_1)) != elec_2
| index(status,host(VAR_0)) != elec_2
| host(VAR_2) != host(VAR_1)
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1] :
( leq(index(pendack,host(VAR_1)),host(VAR_0))
| index(status,host(VAR_1)) != elec_2
| index(status,host(VAR_0)) != elec_2
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive)
| leq(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_1) != host(VAR_2)
| ~ elem(m_Down(VAR_1),queue(host(VAR_0)))
| ~ 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] :
( ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_0)))
| index(status,host(VAR_0)) != elec_1
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1] :
( leq(host(VAR_1),index(pendack,host(VAR_0)))
| ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_0)))
| ~ setIn(VAR_0,alive) )
& ! [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,VAR_2] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_2))) )
& ! [VAR_0,VAR_1] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Halt(VAR_0),queue(host(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_162,negated_conjecture,
( host(A) != host(B)
| ~ elem(m_Down(A),queue(host(B))) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_171,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != elec_2
| index(status,host(A)) != elec_2
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_172,negated_conjecture,
( ~ elem(m_Ack(A,C),queue(host(A)))
| index(status,host(B)) != elec_2
| index(status,host(A)) != elec_2
| host(C) != host(B)
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_173,negated_conjecture,
( ~ leq(index(pendack,host(A)),index(pendack,host(B)))
| index(status,host(B)) != elec_2
| index(status,host(A)) != elec_2
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
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(sK5),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_193,negated_conjecture,
host(sK4) != host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_194,negated_conjecture,
host(sK5) != host(sK2),
inference(paramod,[status(thm)],[c_192,c_193]) ).
cnf(c_195,negated_conjecture,
setIn(sK4,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_196,negated_conjecture,
leq(nbr_proc,s(index(pendack,host(sK4)))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_197,negated_conjecture,
leq(nbr_proc,s(index(pendack,host(sK5)))),
inference(paramod,[status(thm)],[c_192,c_196]) ).
cnf(c_200,negated_conjecture,
elem(m_Ack(sK4,sK6),snoc(queue(host(sK4)),m_Ldr(sK2))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_201,negated_conjecture,
elem(m_Ack(sK4,sK6),snoc(queue(host(sK5)),m_Ldr(sK2))),
inference(paramod,[status(thm)],[c_192,c_200]) ).
cnf(c_202,negated_conjecture,
index(status,host(sK4)) = elec_2,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_2858,negated_conjecture,
index(status,host(sK5)) = elec_2,
inference(paramod,[status(thm)],[c_192,c_202]) ).
cnf(c_203,negated_conjecture,
index(status,host(sK5)) = index(status,host(sK2)),
inference(paramod,[status(thm)],[c_186,c_2858]) ).
cnf(c_204,negated_conjecture,
index(pendack,host(sK4)) = host(sK6),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_2859,negated_conjecture,
index(pendack,host(sK5)) = host(sK6),
inference(paramod,[status(thm)],[c_192,c_204]) ).
cnf(c_205,negated_conjecture,
host(sK6) = index(pendack,host(sK5)),
inference(copy,[status(thm)],[c_2859]) ).
cnf(c_206,negated_conjecture,
s(index(pendack,host(sK4))) = host(sK7),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_207,negated_conjecture,
s(index(pendack,host(sK5))) = host(sK7),
inference(paramod,[status(thm)],[c_192,c_206]) ).
cnf(c_208,negated_conjecture,
setIn(sK3,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_2860,negated_conjecture,
( ~ leq(index(pendack,host(A)),index(pendack,host(B)))
| index(status,host(B)) != elec_2
| index(status,host(A)) != index(status,host(sK2))
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
inference(paramod,[status(thm)],[c_186,c_173]) ).
cnf(c_2861,negated_conjecture,
( ~ leq(index(pendack,host(A)),index(pendack,host(B)))
| index(status,host(B)) != index(status,host(sK2))
| index(status,host(A)) != index(status,host(sK2))
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
inference(paramod,[status(thm)],[c_186,c_2860]) ).
cnf(c_2862,negated_conjecture,
( ~ leq(index(pendack,host(A)),index(pendack,host(B)))
| index(status,host(B)) != index(status,host(sK2))
| index(status,host(sK2)) != index(status,host(A))
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
inference(copy,[status(thm)],[c_2861]) ).
cnf(c_214,negated_conjecture,
( ~ leq(index(pendack,host(A)),index(pendack,host(B)))
| index(status,host(sK2)) != index(status,host(B))
| index(status,host(sK2)) != index(status,host(A))
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
inference(copy,[status(thm)],[c_2862]) ).
cnf(c_2863,negated_conjecture,
( ~ elem(m_Ack(A,C),queue(host(A)))
| index(status,host(B)) != elec_2
| index(status,host(A)) != index(status,host(sK2))
| host(C) != host(B)
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_186,c_172]) ).
cnf(c_2864,negated_conjecture,
( ~ elem(m_Ack(A,C),queue(host(A)))
| index(status,host(B)) != index(status,host(sK2))
| index(status,host(A)) != index(status,host(sK2))
| host(C) != host(B)
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_186,c_2863]) ).
cnf(c_2865,negated_conjecture,
( ~ elem(m_Ack(A,C),queue(host(A)))
| index(status,host(B)) != index(status,host(sK2))
| index(status,host(sK2)) != index(status,host(A))
| host(C) != host(B)
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_2864]) ).
cnf(c_215,negated_conjecture,
( ~ elem(m_Ack(A,C),queue(host(A)))
| index(status,host(sK2)) != index(status,host(B))
| index(status,host(sK2)) != index(status,host(A))
| host(C) != host(B)
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_2865]) ).
cnf(c_2866,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != elec_2
| index(status,host(A)) != index(status,host(sK2))
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
inference(paramod,[status(thm)],[c_186,c_171]) ).
cnf(c_2867,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != index(status,host(sK2))
| index(status,host(A)) != index(status,host(sK2))
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
inference(paramod,[status(thm)],[c_186,c_2866]) ).
cnf(c_2868,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != index(status,host(sK2))
| index(status,host(sK2)) != index(status,host(A))
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
inference(copy,[status(thm)],[c_2867]) ).
cnf(c_216,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(sK2)) != index(status,host(B))
| index(status,host(sK2)) != index(status,host(A))
| ~ setIn(B,alive)
| ~ setIn(A,alive)
| leq(host(A),host(B)) ),
inference(copy,[status(thm)],[c_2868]) ).
cnf(c_222,negated_conjecture,
leq(nbr_proc,host(sK7)),
inference(paramod,[status(thm)],[c_207,c_197]) ).
cnf(c_2869,plain,
elem(A,cons(init(snoc(A,B)),C)),
inference(resolve,[status(thm)],[c_119,c_108]) ).
cnf(c_248,plain,
elem(A,cons(A,B)),
inference(paramod,[status(thm)],[c_108,c_2869]) ).
cnf(c_2870,plain,
( nbr_proc = host(A)
| ~ leq(nbr_proc,host(A)) ),
inference(resolve,[status(thm)],[c_152,c_64]) ).
cnf(c_285,plain,
( host(A) = nbr_proc
| ~ leq(nbr_proc,host(A)) ),
inference(copy,[status(thm)],[c_2870]) ).
cnf(c_303,plain,
( leq(s(A),B)
| leq(B,A)
| s(A) = B ),
inference(resolve,[status(thm)],[c_158,c_151]) ).
cnf(c_2871,plain,
( host(A) != host(sK2)
| ~ elem(m_Down(A),cons(m_Down(sK0),sK1)) ),
inference(paramod,[status(thm)],[c_182,c_162]) ).
cnf(c_311,plain,
( host(sK2) != host(A)
| ~ elem(m_Down(A),cons(m_Down(sK0),sK1)) ),
inference(copy,[status(thm)],[c_2871]) ).
cnf(c_325,plain,
leq(index(pendack,host(sK2)),nbr_proc),
inference(paramod,[status(thm)],[c_188,c_64]) ).
cnf(c_2872,negated_conjecture,
( nbr_proc = index(pendack,host(sK2))
| ~ leq(index(pendack,host(sK2)),nbr_proc) ),
inference(resolve,[status(thm)],[c_189,c_152]) ).
cnf(c_2873,negated_conjecture,
( index(pendack,host(sK2)) = nbr_proc
| ~ leq(index(pendack,host(sK2)),nbr_proc) ),
inference(copy,[status(thm)],[c_2872]) ).
cnf(c_335,negated_conjecture,
index(pendack,host(sK2)) = nbr_proc,
inference(resolve,[status(thm)],[c_325,c_2873]) ).
cnf(c_345,negated_conjecture,
host(sK0) = nbr_proc,
inference(paramod,[status(thm)],[c_335,c_188]) ).
cnf(c_2874,negated_conjecture,
( elem(m_Ack(sK4,sK6),queue(host(sK5)))
| m_Ldr(sK2) = m_Ack(sK4,sK6) ),
inference(resolve,[status(thm)],[c_201,c_121]) ).
cnf(c_368,negated_conjecture,
elem(m_Ack(sK4,sK6),queue(host(sK5))),
inference(resolve,[status(thm)],[c_79,c_2874]) ).
cnf(c_375,plain,
leq(index(pendack,host(sK5)),nbr_proc),
inference(paramod,[status(thm)],[c_205,c_64]) ).
cnf(c_2875,negated_conjecture,
( ~ leq(index(pendack,host(sK4)),index(pendack,host(A)))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK4))
| ~ setIn(A,alive)
| leq(host(sK4),host(A)) ),
inference(resolve,[status(thm)],[c_214,c_195]) ).
cnf(c_2876,negated_conjecture,
( ~ leq(index(pendack,host(sK4)),index(pendack,host(A)))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK4))
| ~ setIn(A,alive)
| leq(host(sK5),host(A)) ),
inference(paramod,[status(thm)],[c_192,c_2875]) ).
cnf(c_2877,negated_conjecture,
( ~ leq(index(pendack,host(sK4)),index(pendack,host(A)))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK5))
| ~ setIn(A,alive)
| leq(host(sK5),host(A)) ),
inference(paramod,[status(thm)],[c_192,c_2876]) ).
cnf(c_2878,negated_conjecture,
( ~ leq(index(pendack,host(sK4)),index(pendack,host(A)))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK2))
| ~ setIn(A,alive)
| leq(host(sK5),host(A)) ),
inference(paramod,[status(thm)],[c_203,c_2877]) ).
cnf(c_2879,negated_conjecture,
( ~ leq(index(pendack,host(sK5)),index(pendack,host(A)))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK2))
| ~ setIn(A,alive)
| leq(host(sK5),host(A)) ),
inference(paramod,[status(thm)],[c_192,c_2878]) ).
cnf(c_399,negated_conjecture,
( ~ leq(index(pendack,host(sK5)),index(pendack,host(A)))
| index(status,host(sK2)) != index(status,host(A))
| ~ setIn(A,alive)
| leq(host(sK5),host(A)) ),
inference(copy,[status(thm)],[c_2879]) ).
cnf(c_2880,negated_conjecture,
( ~ elem(m_Ack(sK4,B),queue(host(sK4)))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK4))
| host(B) != host(A)
| ~ setIn(A,alive) ),
inference(resolve,[status(thm)],[c_215,c_195]) ).
cnf(c_2881,negated_conjecture,
( ~ elem(m_Ack(sK4,B),queue(host(sK4)))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK5))
| host(B) != host(A)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_192,c_2880]) ).
cnf(c_2882,negated_conjecture,
( ~ elem(m_Ack(sK4,B),queue(host(sK4)))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK2))
| host(B) != host(A)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_203,c_2881]) ).
cnf(c_2883,negated_conjecture,
( ~ elem(m_Ack(sK4,B),queue(host(sK5)))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK2))
| host(B) != host(A)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_192,c_2882]) ).
cnf(c_403,negated_conjecture,
( ~ elem(m_Ack(sK4,B),queue(host(sK5)))
| index(status,host(sK2)) != index(status,host(A))
| host(B) != host(A)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_2883]) ).
cnf(c_2884,negated_conjecture,
( leq(index(pendack,host(A)),host(sK3))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK3))
| ~ setIn(A,alive)
| leq(host(sK3),host(A)) ),
inference(resolve,[status(thm)],[c_216,c_208]) ).
cnf(c_2885,negated_conjecture,
( leq(index(pendack,host(A)),host(sK3))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK3))
| ~ setIn(A,alive)
| leq(host(sK2),host(A)) ),
inference(paramod,[status(thm)],[c_191,c_2884]) ).
cnf(c_2886,negated_conjecture,
( leq(index(pendack,host(A)),host(sK3))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK2))
| ~ setIn(A,alive)
| leq(host(sK2),host(A)) ),
inference(paramod,[status(thm)],[c_191,c_2885]) ).
cnf(c_2887,negated_conjecture,
( leq(index(pendack,host(A)),host(sK2))
| index(status,host(sK2)) != index(status,host(A))
| index(status,host(sK2)) != index(status,host(sK2))
| ~ setIn(A,alive)
| leq(host(sK2),host(A)) ),
inference(paramod,[status(thm)],[c_191,c_2886]) ).
cnf(c_407,negated_conjecture,
( leq(index(pendack,host(A)),host(sK2))
| index(status,host(sK2)) != index(status,host(A))
| ~ setIn(A,alive)
| leq(host(sK2),host(A)) ),
inference(copy,[status(thm)],[c_2887]) ).
cnf(c_2888,negated_conjecture,
( nbr_proc = host(sK7)
| ~ leq(host(sK7),nbr_proc) ),
inference(resolve,[status(thm)],[c_222,c_152]) ).
cnf(c_2889,negated_conjecture,
( host(sK7) = nbr_proc
| ~ leq(host(sK7),nbr_proc) ),
inference(copy,[status(thm)],[c_2888]) ).
cnf(c_419,negated_conjecture,
host(sK7) = nbr_proc,
inference(resolve,[status(thm)],[c_64,c_2889]) ).
cnf(c_429,negated_conjecture,
s(index(pendack,host(sK5))) = nbr_proc,
inference(paramod,[status(thm)],[c_419,c_207]) ).
cnf(c_2890,plain,
host(sK2) != host(sK0),
inference(resolve,[status(thm)],[c_311,c_248]) ).
cnf(c_547,plain,
host(sK2) != nbr_proc,
inference(paramod,[status(thm)],[c_345,c_2890]) ).
cnf(c_2891,negated_conjecture,
( ~ elem(m_Ack(sK4,A),queue(host(sK5)))
| index(status,host(sK2)) != index(status,host(sK2))
| host(A) != host(sK2) ),
inference(resolve,[status(thm)],[c_403,c_183]) ).
cnf(c_2892,negated_conjecture,
( ~ elem(m_Ack(sK4,A),queue(host(sK5)))
| index(status,host(sK2)) != index(status,host(sK2))
| host(sK2) != host(A) ),
inference(copy,[status(thm)],[c_2891]) ).
cnf(c_657,negated_conjecture,
( ~ elem(m_Ack(sK4,A),queue(host(sK5)))
| host(sK2) != host(A) ),
inference(copy,[status(thm)],[c_2892]) ).
cnf(c_2893,plain,
host(sK2) != host(sK6),
inference(resolve,[status(thm)],[c_368,c_657]) ).
cnf(c_2894,plain,
host(sK2) != index(pendack,host(sK5)),
inference(paramod,[status(thm)],[c_205,c_2893]) ).
cnf(c_875,plain,
index(pendack,host(sK5)) != host(sK2),
inference(copy,[status(thm)],[c_2894]) ).
cnf(c_2895,negated_conjecture,
( ~ leq(index(pendack,host(sK5)),index(pendack,host(sK2)))
| index(status,host(sK2)) != index(status,host(sK2))
| leq(host(sK5),host(sK2)) ),
inference(resolve,[status(thm)],[c_399,c_183]) ).
cnf(c_2896,negated_conjecture,
( ~ leq(index(pendack,host(sK5)),nbr_proc)
| index(status,host(sK2)) != index(status,host(sK2))
| leq(host(sK5),host(sK2)) ),
inference(paramod,[status(thm)],[c_335,c_2895]) ).
cnf(c_2897,negated_conjecture,
( ~ leq(index(pendack,host(sK5)),nbr_proc)
| leq(host(sK5),host(sK2)) ),
inference(copy,[status(thm)],[c_2896]) ).
cnf(c_2706,negated_conjecture,
leq(host(sK5),host(sK2)),
inference(resolve,[status(thm)],[c_375,c_2897]) ).
cnf(c_2898,plain,
( host(sK5) = host(sK2)
| ~ leq(host(sK2),host(sK5)) ),
inference(resolve,[status(thm)],[c_2706,c_152]) ).
cnf(c_2716,negated_conjecture,
~ leq(host(sK2),host(sK5)),
inference(resolve,[status(thm)],[c_194,c_2898]) ).
cnf(c_2899,negated_conjecture,
( leq(index(pendack,host(sK4)),host(sK2))
| index(status,host(sK2)) != index(status,host(sK4))
| leq(host(sK2),host(sK4)) ),
inference(resolve,[status(thm)],[c_407,c_195]) ).
cnf(c_2900,negated_conjecture,
( leq(index(pendack,host(sK4)),host(sK2))
| index(status,host(sK2)) != index(status,host(sK4))
| leq(host(sK2),host(sK5)) ),
inference(paramod,[status(thm)],[c_192,c_2899]) ).
cnf(c_2901,negated_conjecture,
( leq(index(pendack,host(sK4)),host(sK2))
| index(status,host(sK2)) != index(status,host(sK5))
| leq(host(sK2),host(sK5)) ),
inference(paramod,[status(thm)],[c_192,c_2900]) ).
cnf(c_2902,negated_conjecture,
( leq(index(pendack,host(sK4)),host(sK2))
| index(status,host(sK2)) != index(status,host(sK2))
| leq(host(sK2),host(sK5)) ),
inference(paramod,[status(thm)],[c_203,c_2901]) ).
cnf(c_2903,negated_conjecture,
( leq(index(pendack,host(sK5)),host(sK2))
| index(status,host(sK2)) != index(status,host(sK2))
| leq(host(sK2),host(sK5)) ),
inference(paramod,[status(thm)],[c_192,c_2902]) ).
cnf(c_2904,negated_conjecture,
( leq(index(pendack,host(sK5)),host(sK2))
| leq(host(sK2),host(sK5)) ),
inference(copy,[status(thm)],[c_2903]) ).
cnf(c_2810,negated_conjecture,
leq(index(pendack,host(sK5)),host(sK2)),
inference(resolve,[status(thm)],[c_2716,c_2904]) ).
cnf(c_2905,plain,
( index(pendack,host(sK5)) = host(sK2)
| ~ leq(host(sK2),index(pendack,host(sK5))) ),
inference(resolve,[status(thm)],[c_2810,c_152]) ).
cnf(c_2820,plain,
~ leq(host(sK2),index(pendack,host(sK5))),
inference(resolve,[status(thm)],[c_875,c_2905]) ).
cnf(c_2906,plain,
( leq(s(index(pendack,host(sK5))),host(sK2))
| s(index(pendack,host(sK5))) = host(sK2) ),
inference(resolve,[status(thm)],[c_2820,c_303]) ).
cnf(c_2907,plain,
( leq(s(index(pendack,host(sK5))),host(sK2))
| nbr_proc = host(sK2) ),
inference(paramod,[status(thm)],[c_429,c_2906]) ).
cnf(c_2908,plain,
( leq(nbr_proc,host(sK2))
| nbr_proc = host(sK2) ),
inference(paramod,[status(thm)],[c_429,c_2907]) ).
cnf(c_2909,plain,
( leq(nbr_proc,host(sK2))
| host(sK2) = nbr_proc ),
inference(copy,[status(thm)],[c_2908]) ).
cnf(c_2851,plain,
leq(nbr_proc,host(sK2)),
inference(resolve,[status(thm)],[c_547,c_2909]) ).
cnf(c_2910,plain,
host(sK2) = nbr_proc,
inference(resolve,[status(thm)],[c_2851,c_285]) ).
cnf(c_2857,plain,
$false,
inference(resolve,[status(thm)],[c_547,c_2910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV466+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:55:49 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1732058 was started by sandbox on n020,
% 0.13/0.36 % Sat Sep 26 13:55:49 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 8.06/1.55
% 8.06/1.55 % given #500 (A,wt=14): 357 -elem(m_Ack(c9,A),queue(host(c5))) | leq(host(A),index(pendack,host(c5))). [resolve(195,a,166,a),rewrite([192(4),192(10)])].
% 8.06/1.55
% 8.06/1.55 % SZS status Theorem for theBenchmark
% 8.06/1.55
% 8.06/1.55 % Proof 1 at 0.71 (+ 0.21) seconds.
% 8.06/1.55 % Length of proof is 72.
% 8.06/1.55 % Level of proof is 10.
% 8.06/1.55 % Maximum clause weight is 38.000.
% 8.06/1.55 % Given clauses 553.
% 8.06/1.55
% 8.06/1.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------