%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV464+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 : n002.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 0.14s 10.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 28 unt; 0 def)
% Number of atoms : 678 ( 310 equ)
% Maximal formula atoms : 111 ( 10 avg)
% Number of connectives : 1041 ( 426 ~; 330 |; 237 &)
% ( 2 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 19 con; 0-4 aty)
% Number of variables : 295 ( 6 sgn 227 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_04,axiom,
! [P] : leq(host(P),nbr_proc),
file('theBenchmark.p',axiom_04) ).
fof(axiom_11,axiom,
! [X,Y,Z] : m_Ack(X,Y) != m_Halt(Z),
file('theBenchmark.p',axiom_11) ).
fof(axiom_17,axiom,
! [X,Y] : m_Down(X) != m_Halt(Y),
file('theBenchmark.p',axiom_17) ).
fof(axiom_47,axiom,
! [X,Y,Q] :
( elem(X,snoc(Q,Y))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_47) ).
fof(axiom_61,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
<=> X = Y ),
file('theBenchmark.p',axiom_61) ).
fof(conj,conjecture,
! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Ack(W,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)
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W )
=> ( ~ leq(nbr_proc,index(pendack,host(X)))
=> ! [Z,W0,X0,Y0] :
( s(index(pendack,host(X))) = 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_Halt(X)))
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Halt(X)))
& leq(nbr_proc,s(index(pendack,host(Y0))))
& setIn(Y0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) ) ) ) ) ) ) ),
file('theBenchmark.p',conj) ).
fof(conj_neg,negated_conjecture,
~ ! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Ack(W,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)
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W )
=> ( ~ leq(nbr_proc,index(pendack,host(X)))
=> ! [Z,W0,X0,Y0] :
( s(index(pendack,host(X))) = 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_Halt(X)))
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Halt(X)))
& leq(nbr_proc,s(index(pendack,host(Y0))))
& setIn(Y0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_64,plain,
leq(host(A),nbr_proc),
inference(clausify,[status(thm)],[axiom_04]) ).
cnf(c_76,plain,
m_Halt(A) != m_Ack(B,C),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_82,plain,
m_Down(A) != m_Halt(B),
inference(clausify,[status(thm)],[axiom_17]) ).
cnf(c_121,plain,
( elem(A,B)
| C = A
| ~ elem(A,snoc(B,C)) ),
inference(clausify,[status(thm)],[axiom_47]) ).
cnf(c_152,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[axiom_61]) ).
fof(nnf_58,plain,
? [V,W,X,Y] :
( ? [Z,W0,X0,Y0] :
( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,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_Halt(X)))
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Halt(X)))
& leq(nbr_proc,s(index(pendack,host(Y0))))
& setIn(Y0,alive)
& host(Y0) != host(X)
& s(index(pendack,host(X))) = host(Y0) )
& ~ leq(nbr_proc,index(pendack,host(X)))
& index(pendack,host(X)) = host(Y)
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W
& setIn(X,alive)
& cons(m_Ack(W,Y),V) = queue(host(X))
& ! [X36,Pid30,Pid20,Pid0] :
( index(status,host(X36)) != norm
| index(ldr,host(X36)) != host(X36)
| ~ setIn(X36,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)))
| ? [V0] :
( host(X34) != V0
& ~ setIn(V0,index(down,host(X35)))
& leq(s(zero),V0)
& ~ leq(host(X35),V0) ) )
& ! [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,
( index(status,host(sK4)) = norm
& index(ldr,host(sK4)) = host(sK4)
& setIn(sK4,alive)
& s(index(pendack,host(sK1))) = host(sK2)
& index(pendack,host(sK1)) = host(sK3)
& index(status,host(sK1)) = elec_2
& elem(m_Ack(sK1,sK3),snoc(queue(host(sK1)),m_Halt(sK0)))
& elem(m_Down(sK2),snoc(queue(host(sK1)),m_Halt(sK0)))
& leq(nbr_proc,s(index(pendack,host(sK1))))
& setIn(sK1,alive)
& host(sK1) != host(sK0)
& s(index(pendack,host(sK0))) = host(sK1)
& ~ leq(nbr_proc,index(pendack,host(sK0)))
& index(pendack,host(sK0)) = host(sK7)
& index(status,host(sK0)) = elec_2
& index(elid,host(sK0)) = sK6
& setIn(sK0,alive)
& cons(m_Ack(sK6,sK7),sK8) = queue(host(sK0))
& ! [X36,Pid30,Pid20,Pid0] :
( index(status,host(X36)) != norm
| index(ldr,host(X36)) != host(X36)
| ~ setIn(X36,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) != sK5(X32,X33,X34,X35)
& ~ setIn(sK5(X32,X33,X34,X35),index(down,host(X35)))
& leq(s(zero),sK5(X32,X33,X34,X35))
& ~ leq(host(X35),sK5(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,[sK5,sK6,sK7,sK8,sK0,sK1,sK2,sK3,sK4]),skolemize(V,sK8),skolemize(W,sK6),skolemize(X,sK0),skolemize(Y,sK7),skolemize(V0,sK5(X32,X33,X34,X35)),skolemize(Z,sK4),skolemize(W0,sK3),skolemize(X0,sK2),skolemize(Y0,sK1)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( index(status,host(sK4)) = norm
& index(ldr,host(sK4)) = host(sK4)
& setIn(sK4,alive)
& s(index(pendack,host(sK1))) = host(sK2)
& index(pendack,host(sK1)) = host(sK3)
& index(status,host(sK1)) = elec_2
& elem(m_Ack(sK1,sK3),snoc(queue(host(sK1)),m_Halt(sK0)))
& elem(m_Down(sK2),snoc(queue(host(sK1)),m_Halt(sK0)))
& leq(nbr_proc,s(index(pendack,host(sK1))))
& setIn(sK1,alive)
& host(sK1) != host(sK0)
& s(index(pendack,host(sK0))) = host(sK1)
& ~ leq(nbr_proc,index(pendack,host(sK0)))
& index(pendack,host(sK0)) = host(sK7)
& index(status,host(sK0)) = elec_2
& index(elid,host(sK0)) = sK6
& setIn(sK0,alive)
& cons(m_Ack(sK6,sK7),sK8) = queue(host(sK0))
& ! [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) != sK5(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(sK5(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),sK5(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),sK5(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_180,negated_conjecture,
( index(status,host(D)) != norm
| index(ldr,host(D)) != host(D)
| ~ setIn(D,alive)
| s(index(pendack,host(A))) != host(B)
| index(pendack,host(A)) != host(C)
| index(status,host(A)) != elec_2
| ~ leq(nbr_proc,s(index(pendack,host(A))))
| ~ elem(m_Ack(A,C),queue(host(A)))
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_184,negated_conjecture,
index(status,host(sK0)) = elec_2,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_185,negated_conjecture,
elec_2 = index(status,host(sK0)),
inference(copy,[status(thm)],[c_184]) ).
cnf(c_192,negated_conjecture,
setIn(sK1,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_193,negated_conjecture,
leq(nbr_proc,s(index(pendack,host(sK1)))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_194,negated_conjecture,
elem(m_Down(sK2),snoc(queue(host(sK1)),m_Halt(sK0))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_195,negated_conjecture,
elem(m_Ack(sK1,sK3),snoc(queue(host(sK1)),m_Halt(sK0))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_196,negated_conjecture,
index(status,host(sK1)) = elec_2,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_197,negated_conjecture,
index(status,host(sK1)) = index(status,host(sK0)),
inference(paramod,[status(thm)],[c_185,c_196]) ).
cnf(c_198,negated_conjecture,
index(pendack,host(sK1)) = host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_199,negated_conjecture,
s(index(pendack,host(sK1))) = host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_200,negated_conjecture,
s(host(sK3)) = host(sK2),
inference(paramod,[status(thm)],[c_198,c_199]) ).
cnf(c_201,negated_conjecture,
setIn(sK4,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_202,negated_conjecture,
index(ldr,host(sK4)) = host(sK4),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_203,negated_conjecture,
index(status,host(sK4)) = norm,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_204,negated_conjecture,
norm = index(status,host(sK4)),
inference(copy,[status(thm)],[c_203]) ).
cnf(c_996,negated_conjecture,
( index(status,host(D)) != norm
| index(ldr,host(D)) != host(D)
| ~ setIn(D,alive)
| s(index(pendack,host(A))) != host(B)
| index(pendack,host(A)) != host(C)
| index(status,host(A)) != index(status,host(sK0))
| ~ leq(nbr_proc,s(index(pendack,host(A))))
| ~ elem(m_Ack(A,C),queue(host(A)))
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_185,c_180]) ).
cnf(c_997,negated_conjecture,
( index(status,host(D)) != index(status,host(sK4))
| index(ldr,host(D)) != host(D)
| ~ setIn(D,alive)
| s(index(pendack,host(A))) != host(B)
| index(pendack,host(A)) != host(C)
| index(status,host(A)) != index(status,host(sK0))
| ~ leq(nbr_proc,s(index(pendack,host(A))))
| ~ elem(m_Ack(A,C),queue(host(A)))
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_204,c_996]) ).
cnf(c_998,negated_conjecture,
( index(status,host(D)) != index(status,host(sK4))
| index(ldr,host(D)) != host(D)
| ~ setIn(D,alive)
| s(index(pendack,host(A))) != host(B)
| index(pendack,host(A)) != host(C)
| index(status,host(sK0)) != index(status,host(A))
| ~ leq(nbr_proc,s(index(pendack,host(A))))
| ~ elem(m_Ack(A,C),queue(host(A)))
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_997]) ).
cnf(c_208,negated_conjecture,
( index(status,host(sK4)) != index(status,host(D))
| index(ldr,host(D)) != host(D)
| ~ setIn(D,alive)
| s(index(pendack,host(A))) != host(B)
| index(pendack,host(A)) != host(C)
| index(status,host(sK0)) != index(status,host(A))
| ~ leq(nbr_proc,s(index(pendack,host(A))))
| ~ elem(m_Ack(A,C),queue(host(A)))
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_998]) ).
cnf(c_999,negated_conjecture,
leq(nbr_proc,s(host(sK3))),
inference(paramod,[status(thm)],[c_198,c_193]) ).
cnf(c_217,negated_conjecture,
leq(nbr_proc,host(sK2)),
inference(paramod,[status(thm)],[c_200,c_999]) ).
cnf(c_1000,negated_conjecture,
( elem(m_Down(sK2),queue(host(sK1)))
| m_Halt(sK0) = m_Down(sK2) ),
inference(resolve,[status(thm)],[c_194,c_121]) ).
cnf(c_329,negated_conjecture,
elem(m_Down(sK2),queue(host(sK1))),
inference(resolve,[status(thm)],[c_82,c_1000]) ).
cnf(c_1001,negated_conjecture,
( elem(m_Ack(sK1,sK3),queue(host(sK1)))
| m_Halt(sK0) = m_Ack(sK1,sK3) ),
inference(resolve,[status(thm)],[c_195,c_121]) ).
cnf(c_1002,negated_conjecture,
( elem(m_Ack(sK1,sK3),queue(host(sK1)))
| m_Ack(sK1,sK3) = m_Halt(sK0) ),
inference(copy,[status(thm)],[c_1001]) ).
cnf(c_334,negated_conjecture,
elem(m_Ack(sK1,sK3),queue(host(sK1))),
inference(resolve,[status(thm)],[c_76,c_1002]) ).
cnf(c_1003,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| s(index(pendack,host(sK1))) != host(A)
| index(status,host(sK0)) != index(status,host(sK1))
| ~ leq(nbr_proc,s(index(pendack,host(sK1))))
| ~ elem(m_Ack(sK1,sK3),queue(host(sK1)))
| ~ elem(m_Down(A),queue(host(sK1)))
| ~ setIn(sK1,alive) ),
inference(resolve,[status(thm)],[c_208,c_198]) ).
cnf(c_1004,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| s(index(pendack,host(sK1))) != host(A)
| index(status,host(sK0)) != index(status,host(sK1))
| ~ leq(nbr_proc,s(host(sK3)))
| ~ elem(m_Ack(sK1,sK3),queue(host(sK1)))
| ~ elem(m_Down(A),queue(host(sK1)))
| ~ setIn(sK1,alive) ),
inference(paramod,[status(thm)],[c_198,c_1003]) ).
cnf(c_1005,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| s(index(pendack,host(sK1))) != host(A)
| index(status,host(sK0)) != index(status,host(sK1))
| ~ leq(nbr_proc,host(sK2))
| ~ elem(m_Ack(sK1,sK3),queue(host(sK1)))
| ~ elem(m_Down(A),queue(host(sK1)))
| ~ setIn(sK1,alive) ),
inference(paramod,[status(thm)],[c_200,c_1004]) ).
cnf(c_1006,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| s(index(pendack,host(sK1))) != host(A)
| index(status,host(sK0)) != index(status,host(sK0))
| ~ leq(nbr_proc,host(sK2))
| ~ elem(m_Ack(sK1,sK3),queue(host(sK1)))
| ~ elem(m_Down(A),queue(host(sK1)))
| ~ setIn(sK1,alive) ),
inference(paramod,[status(thm)],[c_197,c_1005]) ).
cnf(c_1007,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| s(host(sK3)) != host(A)
| index(status,host(sK0)) != index(status,host(sK0))
| ~ leq(nbr_proc,host(sK2))
| ~ elem(m_Ack(sK1,sK3),queue(host(sK1)))
| ~ elem(m_Down(A),queue(host(sK1)))
| ~ setIn(sK1,alive) ),
inference(paramod,[status(thm)],[c_198,c_1006]) ).
cnf(c_1008,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(sK2) != host(A)
| index(status,host(sK0)) != index(status,host(sK0))
| ~ leq(nbr_proc,host(sK2))
| ~ elem(m_Ack(sK1,sK3),queue(host(sK1)))
| ~ elem(m_Down(A),queue(host(sK1)))
| ~ setIn(sK1,alive) ),
inference(paramod,[status(thm)],[c_200,c_1007]) ).
cnf(c_1009,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(sK2) != host(A)
| ~ leq(nbr_proc,host(sK2))
| ~ elem(m_Ack(sK1,sK3),queue(host(sK1)))
| ~ elem(m_Down(A),queue(host(sK1)))
| ~ setIn(sK1,alive) ),
inference(copy,[status(thm)],[c_1008]) ).
cnf(c_1010,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(sK2) != host(A)
| ~ leq(nbr_proc,host(sK2))
| ~ elem(m_Ack(sK1,sK3),queue(host(sK1)))
| ~ elem(m_Down(A),queue(host(sK1))) ),
inference(resolve,[status(thm)],[c_192,c_1009]) ).
cnf(c_1011,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(sK2) != host(A)
| ~ leq(nbr_proc,host(sK2))
| ~ elem(m_Down(A),queue(host(sK1))) ),
inference(resolve,[status(thm)],[c_334,c_1010]) ).
cnf(c_350,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(sK2) != host(A)
| ~ elem(m_Down(A),queue(host(sK1))) ),
inference(resolve,[status(thm)],[c_217,c_1011]) ).
cnf(c_1012,negated_conjecture,
( nbr_proc = host(sK2)
| ~ leq(host(sK2),nbr_proc) ),
inference(resolve,[status(thm)],[c_217,c_152]) ).
cnf(c_1013,negated_conjecture,
( host(sK2) = nbr_proc
| ~ leq(host(sK2),nbr_proc) ),
inference(copy,[status(thm)],[c_1012]) ).
cnf(c_436,negated_conjecture,
host(sK2) = nbr_proc,
inference(resolve,[status(thm)],[c_64,c_1013]) ).
cnf(c_1014,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| nbr_proc != host(A)
| ~ elem(m_Down(A),queue(host(sK1))) ),
inference(paramod,[status(thm)],[c_436,c_350]) ).
cnf(c_440,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(A) != nbr_proc
| ~ elem(m_Down(A),queue(host(sK1))) ),
inference(copy,[status(thm)],[c_1014]) ).
cnf(c_1015,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| index(ldr,host(sK4)) != host(sK4)
| host(A) != nbr_proc
| ~ elem(m_Down(A),queue(host(sK1))) ),
inference(resolve,[status(thm)],[c_440,c_201]) ).
cnf(c_1016,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| host(sK4) != host(sK4)
| host(A) != nbr_proc
| ~ elem(m_Down(A),queue(host(sK1))) ),
inference(paramod,[status(thm)],[c_202,c_1015]) ).
cnf(c_1017,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| host(A) != nbr_proc
| ~ elem(m_Down(A),queue(host(sK1))) ),
inference(copy,[status(thm)],[c_1016]) ).
cnf(c_994,negated_conjecture,
( host(A) != nbr_proc
| ~ elem(m_Down(A),queue(host(sK1))) ),
inference(copy,[status(thm)],[c_1017]) ).
cnf(c_1018,plain,
~ elem(m_Down(sK2),queue(host(sK1))),
inference(resolve,[status(thm)],[c_994,c_436]) ).
cnf(c_995,plain,
$false,
inference(resolve,[status(thm)],[c_329,c_1018]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV464+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n002.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Sat Sep 26 13:58:02 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.39 % Process 1907144 was started by sandbox2 on n002,
% 0.11/10.39 % Sat Sep 26 13:58:02 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/10.41
% 0.14/10.41 % From the command line: assign(max_seconds, 300).
% 0.14/10.61
% 0.14/10.61 % SZS status Theorem for theBenchmark
% 0.14/10.61
% 0.14/10.61 % Proof 1 at 0.11 (+ 0.06) seconds.
% 0.14/10.61 % Length of proof is 36.
% 0.14/10.61 % Level of proof is 7.
% 0.14/10.61 % Maximum clause weight is 86.000.
% 0.14/10.61 % Given clauses 267.
% 0.14/10.61
% 0.14/10.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------