%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV461+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 : n014.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 09:08:00 AM UTC 2026
% Result : Theorem 0.12s 5.90s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 28 unt; 0 def)
% Number of atoms : 713 ( 332 equ)
% Maximal formula atoms : 117 ( 10 avg)
% Number of connectives : 1087 ( 443 ~; 344 |; 243 &)
% ( 2 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 19 con; 0-4 aty)
% Number of variables : 297 ( 6 sgn 235 !; 7 ?)
% 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_33,axiom,
! [Pid,Pid2] :
( host(Pid) != host(Pid2)
=> Pid != Pid2 ),
file('theBenchmark.p',axiom_33) ).
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,Z,Pid0] :
( ( host(Z) = s(index(pendack,host(Pid0)))
& host(Y) = index(pendack,host(Pid0))
& index(status,host(Pid0)) = elec_2
& leq(nbr_proc,s(index(pendack,host(Pid0))))
& elem(m_Ack(Pid0,Y),queue(host(Pid0)))
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(X)
& setIn(X,alive) ) )
& ! [X,Y,Z,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid0) = nbr_proc
& host(Pid0) = host(Y)
& elem(m_Down(Z),queue(host(Pid0)))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Z)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( elem(m_Down(Y),queue(host(X)))
& setIn(X,alive) ) )
& ! [X,Y,Z] :
( ( index(status,host(Z)) = elec_2
& elem(m_Halt(Z),queue(host(Y)))
& setIn(Z,alive)
& ~ leq(index(pendack,host(Z)),host(X)) )
=> ~ ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(X)
& setIn(X,alive) ) )
& ! [X,Y] :
( ( index(status,host(Y)) = elec_2
& index(status,host(X)) = elec_2
& setIn(Y,alive)
& setIn(X,alive)
& ~ leq(host(X),host(Y)) )
=> ~ leq(index(pendack,host(X)),index(pendack,host(Y))) )
& ! [X,Y] :
( ( index(status,host(Y)) = elec_2
& index(status,host(X)) = elec_2
& setIn(Y,alive)
& setIn(X,alive)
& ~ leq(host(X),host(Y)) )
=> leq(index(pendack,host(Y)),host(X)) )
& ! [X,Y,Z] :
( ( index(status,host(Z)) = elec_2
& index(status,host(X)) = elec_2
& host(Z) = host(Y)
& setIn(Z,alive)
& setIn(X,alive) )
=> ~ elem(m_Ack(X,Y),queue(host(X))) )
& ! [X,Y,Z] :
( ( host(Y) = host(X)
& elem(m_Down(Y),queue(host(Z)))
& setIn(Z,alive) )
=> ~ ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(X)
& setIn(X,alive) ) )
& ! [X] :
( ( setIn(X,alive)
& ( index(status,host(X)) = elec_2
| index(status,host(X)) = elec_1 ) )
=> index(elid,host(X)) = X )
& ! [X,Y] :
( ( index(status,host(Y)) = elec_1
& setIn(Y,alive) )
=> ~ elem(m_Ack(Y,X),queue(host(Y))) )
& ! [X,Y] :
( ( elem(m_Ack(Y,X),queue(host(Y)))
& setIn(Y,alive) )
=> leq(host(X),index(pendack,host(Y))) )
& ! [X,Y] :
( ( host(Y) = host(X)
& Y != X )
=> ( ~ setIn(Y,alive)
| ~ setIn(X,alive) ) )
& ! [X,Y,Z] :
( elem(m_Ack(Z,X),queue(host(Y)))
=> ~ leq(host(X),host(Z)) )
& ! [X,Y] :
( elem(m_Halt(Y),queue(host(X)))
=> ~ leq(host(X),host(Y)) )
& ! [X,Y] :
( elem(m_Down(Y),queue(host(X)))
=> host(Y) != host(X) )
& ! [X,Y] :
( elem(m_Ldr(Y),queue(host(X)))
=> ~ leq(host(X),host(Y)) )
& ! [X] :
( host(W) = host(X)
=> ~ setIn(X,alive) ) )
=> ( queue(host(W)) = q_nil
=> ( ( host(W) = host(V)
& ~ setIn(V,pids)
& ! [X] :
( host(W) = host(X)
=> leq(X,V) ) )
=> ( host(V) = s(zero)
=> ( ~ leq(nbr_proc,host(V))
=> ! [X] :
( host(V) != host(X)
=> ! [Y,Z,Z0] :
( s(host(V)) = host(Z0)
=> ( host(V) != host(Z0)
=> ( ( host(Z) = s(index(pendack,host(Z0)))
& host(Y) = index(pendack,host(Z0))
& index(status,host(Z0)) = elec_2
& elem(m_Ack(Z0,Y),snoc(queue(host(Z0)),m_Halt(V)))
& elem(m_Down(Z),snoc(queue(host(Z0)),m_Halt(V)))
& leq(nbr_proc,s(index(pendack,host(Z0))))
& ( Z0 = V
| setIn(Z0,alive) ) )
=> ~ ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(X)
& ( X = V
| setIn(X,alive) ) ) ) ) ) ) ) ) ) ) ),
file('theBenchmark.p',conj) ).
fof(conj_neg,negated_conjecture,
~ ! [V,W] :
( ( ! [X,Y,Z,Pid0] :
( ( host(Z) = s(index(pendack,host(Pid0)))
& host(Y) = index(pendack,host(Pid0))
& index(status,host(Pid0)) = elec_2
& leq(nbr_proc,s(index(pendack,host(Pid0))))
& elem(m_Ack(Pid0,Y),queue(host(Pid0)))
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(X)
& setIn(X,alive) ) )
& ! [X,Y,Z,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid0) = nbr_proc
& host(Pid0) = host(Y)
& elem(m_Down(Z),queue(host(Pid0)))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Z)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( elem(m_Down(Y),queue(host(X)))
& setIn(X,alive) ) )
& ! [X,Y,Z] :
( ( index(status,host(Z)) = elec_2
& elem(m_Halt(Z),queue(host(Y)))
& setIn(Z,alive)
& ~ leq(index(pendack,host(Z)),host(X)) )
=> ~ ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(X)
& setIn(X,alive) ) )
& ! [X,Y] :
( ( index(status,host(Y)) = elec_2
& index(status,host(X)) = elec_2
& setIn(Y,alive)
& setIn(X,alive)
& ~ leq(host(X),host(Y)) )
=> ~ leq(index(pendack,host(X)),index(pendack,host(Y))) )
& ! [X,Y] :
( ( index(status,host(Y)) = elec_2
& index(status,host(X)) = elec_2
& setIn(Y,alive)
& setIn(X,alive)
& ~ leq(host(X),host(Y)) )
=> leq(index(pendack,host(Y)),host(X)) )
& ! [X,Y,Z] :
( ( index(status,host(Z)) = elec_2
& index(status,host(X)) = elec_2
& host(Z) = host(Y)
& setIn(Z,alive)
& setIn(X,alive) )
=> ~ elem(m_Ack(X,Y),queue(host(X))) )
& ! [X,Y,Z] :
( ( host(Y) = host(X)
& elem(m_Down(Y),queue(host(Z)))
& setIn(Z,alive) )
=> ~ ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(X)
& setIn(X,alive) ) )
& ! [X] :
( ( setIn(X,alive)
& ( index(status,host(X)) = elec_2
| index(status,host(X)) = elec_1 ) )
=> index(elid,host(X)) = X )
& ! [X,Y] :
( ( index(status,host(Y)) = elec_1
& setIn(Y,alive) )
=> ~ elem(m_Ack(Y,X),queue(host(Y))) )
& ! [X,Y] :
( ( elem(m_Ack(Y,X),queue(host(Y)))
& setIn(Y,alive) )
=> leq(host(X),index(pendack,host(Y))) )
& ! [X,Y] :
( ( host(Y) = host(X)
& Y != X )
=> ( ~ setIn(Y,alive)
| ~ setIn(X,alive) ) )
& ! [X,Y,Z] :
( elem(m_Ack(Z,X),queue(host(Y)))
=> ~ leq(host(X),host(Z)) )
& ! [X,Y] :
( elem(m_Halt(Y),queue(host(X)))
=> ~ leq(host(X),host(Y)) )
& ! [X,Y] :
( elem(m_Down(Y),queue(host(X)))
=> host(Y) != host(X) )
& ! [X,Y] :
( elem(m_Ldr(Y),queue(host(X)))
=> ~ leq(host(X),host(Y)) )
& ! [X] :
( host(W) = host(X)
=> ~ setIn(X,alive) ) )
=> ( queue(host(W)) = q_nil
=> ( ( host(W) = host(V)
& ~ setIn(V,pids)
& ! [X] :
( host(W) = host(X)
=> leq(X,V) ) )
=> ( host(V) = s(zero)
=> ( ~ leq(nbr_proc,host(V))
=> ! [X] :
( host(V) != host(X)
=> ! [Y,Z,Z0] :
( s(host(V)) = host(Z0)
=> ( host(V) != host(Z0)
=> ( ( host(Z) = s(index(pendack,host(Z0)))
& host(Y) = index(pendack,host(Z0))
& index(status,host(Z0)) = elec_2
& elem(m_Ack(Z0,Y),snoc(queue(host(Z0)),m_Halt(V)))
& elem(m_Down(Z),snoc(queue(host(Z0)),m_Halt(V)))
& leq(nbr_proc,s(index(pendack,host(Z0))))
& ( Z0 = V
| setIn(Z0,alive) ) )
=> ~ ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(X)
& ( X = V
| setIn(X,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_103,plain,
( A != B
| host(A) = host(B) ),
inference(clausify,[status(thm)],[axiom_33]) ).
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,Z0] :
( index(status,host(X)) = norm
& index(ldr,host(X)) = host(X)
& ( V = X
| setIn(X,alive) )
& s(index(pendack,host(Z0))) = host(Z)
& index(pendack,host(Z0)) = host(Y)
& index(status,host(Z0)) = elec_2
& elem(m_Ack(Z0,Y),snoc(queue(host(Z0)),m_Halt(V)))
& elem(m_Down(Z),snoc(queue(host(Z0)),m_Halt(V)))
& leq(nbr_proc,s(index(pendack,host(Z0))))
& ( Z0 = V
| setIn(Z0,alive) )
& host(Z0) != host(V)
& s(host(V)) = host(Z0) )
& host(V) != host(X) )
& ~ leq(nbr_proc,host(V))
& s(zero) = host(V)
& host(V) = host(W)
& ~ setIn(V,pids)
& ! [X39] :
( leq(X39,V)
| host(W) != host(X39) )
& queue(host(W)) = q_nil
& ! [X36,X37,X38,Pid0] :
( index(status,host(X36)) != norm
| index(ldr,host(X36)) != host(X36)
| ~ setIn(X36,alive)
| s(index(pendack,host(Pid0))) != host(X38)
| index(pendack,host(Pid0)) != host(X37)
| index(status,host(Pid0)) != elec_2
| ~ leq(nbr_proc,s(index(pendack,host(Pid0))))
| ~ elem(m_Ack(Pid0,X37),queue(host(Pid0)))
| ~ elem(m_Down(X38),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(X35) != nbr_proc
| host(X35) != host(X33)
| ~ 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)) )
& ! [X25,X26] :
( leq(index(pendack,host(X26)),host(X25))
| index(status,host(X26)) != elec_2
| index(status,host(X25)) != elec_2
| ~ setIn(X26,alive)
| ~ setIn(X25,alive)
| leq(host(X25),host(X26)) )
& ! [X22,X23,X24] :
( ~ elem(m_Ack(X22,X23),queue(host(X22)))
| index(status,host(X24)) != elec_2
| index(status,host(X22)) != elec_2
| host(X24) != host(X23)
| ~ setIn(X24,alive)
| ~ setIn(X22,alive) )
& ! [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))) )
& ! [X0] :
( ~ setIn(X0,alive)
| host(W) != host(X0) ) ),
inference(fof_nnf,[status(thm)],[conj_neg]) ).
fof(sk_conj_neg_sk,plain,
( index(status,host(sK1)) = norm
& index(ldr,host(sK1)) = host(sK1)
& ( sK0 = sK1
| setIn(sK1,alive) )
& s(index(pendack,host(sK2))) = host(sK3)
& index(pendack,host(sK2)) = host(sK4)
& index(status,host(sK2)) = elec_2
& elem(m_Ack(sK2,sK4),snoc(queue(host(sK2)),m_Halt(sK0)))
& elem(m_Down(sK3),snoc(queue(host(sK2)),m_Halt(sK0)))
& leq(nbr_proc,s(index(pendack,host(sK2))))
& ( sK2 = sK0
| setIn(sK2,alive) )
& host(sK2) != host(sK0)
& s(host(sK0)) = host(sK2)
& host(sK0) != host(sK1)
& ~ leq(nbr_proc,host(sK0))
& s(zero) = host(sK0)
& host(sK0) = host(sK5)
& ~ setIn(sK0,pids)
& ! [X39] :
( leq(X39,sK0)
| host(sK5) != host(X39) )
& queue(host(sK5)) = q_nil
& ! [X36,X37,X38,Pid0] :
( index(status,host(X36)) != norm
| index(ldr,host(X36)) != host(X36)
| ~ setIn(X36,alive)
| s(index(pendack,host(Pid0))) != host(X38)
| index(pendack,host(Pid0)) != host(X37)
| index(status,host(Pid0)) != elec_2
| ~ leq(nbr_proc,s(index(pendack,host(Pid0))))
| ~ elem(m_Ack(Pid0,X37),queue(host(Pid0)))
| ~ elem(m_Down(X38),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(X35) != nbr_proc
| host(X35) != host(X33)
| ~ elem(m_Down(X34),queue(host(X35)))
| ( host(X34) != sK6(X32,X33,X34,X35)
& ~ setIn(sK6(X32,X33,X34,X35),index(down,host(X35)))
& leq(s(zero),sK6(X32,X33,X34,X35))
& ~ leq(host(X35),sK6(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)) )
& ! [X25,X26] :
( leq(index(pendack,host(X26)),host(X25))
| index(status,host(X26)) != elec_2
| index(status,host(X25)) != elec_2
| ~ setIn(X26,alive)
| ~ setIn(X25,alive)
| leq(host(X25),host(X26)) )
& ! [X22,X23,X24] :
( ~ elem(m_Ack(X22,X23),queue(host(X22)))
| index(status,host(X24)) != elec_2
| index(status,host(X22)) != elec_2
| host(X24) != host(X23)
| ~ setIn(X24,alive)
| ~ setIn(X22,alive) )
& ! [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))) )
& ! [X0] :
( ~ setIn(X0,alive)
| host(sK5) != host(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK0,sK1,sK2,sK3,sK4]),skolemize(V,sK0),skolemize(W,sK5),skolemize(V0,sK6(X32,X33,X34,X35)),skolemize(X,sK1),skolemize(Y,sK4),skolemize(Z,sK3),skolemize(Z0,sK2)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( index(status,host(sK1)) = norm
& index(ldr,host(sK1)) = host(sK1)
& ( sK0 = sK1
| setIn(sK1,alive) )
& s(index(pendack,host(sK2))) = host(sK3)
& index(pendack,host(sK2)) = host(sK4)
& index(status,host(sK2)) = elec_2
& elem(m_Ack(sK2,sK4),snoc(queue(host(sK2)),m_Halt(sK0)))
& elem(m_Down(sK3),snoc(queue(host(sK2)),m_Halt(sK0)))
& leq(nbr_proc,s(index(pendack,host(sK2))))
& ( sK2 = sK0
| setIn(sK2,alive) )
& host(sK2) != host(sK0)
& s(host(sK0)) = host(sK2)
& host(sK0) != host(sK1)
& ~ leq(nbr_proc,host(sK0))
& s(zero) = host(sK0)
& host(sK0) = host(sK5)
& ~ setIn(sK0,pids)
& ! [VAR_0] :
( leq(VAR_0,sK0)
| host(sK5) != host(VAR_0) )
& queue(host(sK5)) = q_nil
& ! [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_3) != nbr_proc
| host(VAR_3) != host(VAR_2)
| ~ elem(m_Down(VAR_0),queue(host(VAR_3)))
| host(VAR_0) != sK6(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_3) != nbr_proc
| host(VAR_3) != host(VAR_1)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ setIn(sK6(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_3) != nbr_proc
| host(VAR_3) != host(VAR_1)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| leq(s(zero),sK6(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_0) != nbr_proc
| host(VAR_0) != host(VAR_2)
| ~ elem(m_Down(VAR_3),queue(host(VAR_0)))
| ~ leq(host(VAR_0),sK6(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] :
( 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] :
( ~ 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_1) != host(VAR_2)
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [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))) )
& ! [VAR_0] :
( ~ setIn(VAR_0,alive)
| host(sK5) != host(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_conj_neg_sk]) ).
cnf(c_181,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_190,negated_conjecture,
host(sK0) != host(sK1),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_191,negated_conjecture,
host(sK1) != host(sK0),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_193,negated_conjecture,
host(sK2) != host(sK0),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_194,negated_conjecture,
( sK2 = sK0
| setIn(sK2,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_195,negated_conjecture,
leq(nbr_proc,s(index(pendack,host(sK2)))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_196,negated_conjecture,
elem(m_Down(sK3),snoc(queue(host(sK2)),m_Halt(sK0))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_197,negated_conjecture,
elem(m_Ack(sK2,sK4),snoc(queue(host(sK2)),m_Halt(sK0))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_198,negated_conjecture,
index(status,host(sK2)) = elec_2,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_199,negated_conjecture,
elec_2 = index(status,host(sK2)),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_200,negated_conjecture,
index(pendack,host(sK2)) = host(sK4),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_201,negated_conjecture,
s(index(pendack,host(sK2))) = host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_202,negated_conjecture,
s(host(sK4)) = host(sK3),
inference(paramod,[status(thm)],[c_200,c_201]) ).
cnf(c_203,negated_conjecture,
( sK0 = sK1
| setIn(sK1,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_204,negated_conjecture,
( sK1 = sK0
| setIn(sK1,alive) ),
inference(copy,[status(thm)],[c_203]) ).
cnf(c_205,negated_conjecture,
index(ldr,host(sK1)) = host(sK1),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_206,negated_conjecture,
index(status,host(sK1)) = norm,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_207,negated_conjecture,
norm = index(status,host(sK1)),
inference(copy,[status(thm)],[c_206]) ).
cnf(c_826,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(sK2))
| ~ 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_199,c_181]) ).
cnf(c_827,negated_conjecture,
( index(status,host(D)) != index(status,host(sK1))
| 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(sK2))
| ~ 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_207,c_826]) ).
cnf(c_828,negated_conjecture,
( index(status,host(D)) != index(status,host(sK1))
| 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(sK2)) != 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_827]) ).
cnf(c_228,negated_conjecture,
( index(status,host(sK1)) != 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(sK2)) != 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_828]) ).
cnf(c_829,negated_conjecture,
leq(nbr_proc,s(host(sK4))),
inference(paramod,[status(thm)],[c_200,c_195]) ).
cnf(c_237,negated_conjecture,
leq(nbr_proc,host(sK3)),
inference(paramod,[status(thm)],[c_202,c_829]) ).
cnf(c_830,negated_conjecture,
( elem(m_Down(sK3),queue(host(sK2)))
| m_Halt(sK0) = m_Down(sK3) ),
inference(resolve,[status(thm)],[c_196,c_121]) ).
cnf(c_288,negated_conjecture,
elem(m_Down(sK3),queue(host(sK2))),
inference(resolve,[status(thm)],[c_82,c_830]) ).
cnf(c_831,negated_conjecture,
( elem(m_Ack(sK2,sK4),queue(host(sK2)))
| m_Halt(sK0) = m_Ack(sK2,sK4) ),
inference(resolve,[status(thm)],[c_197,c_121]) ).
cnf(c_832,negated_conjecture,
( elem(m_Ack(sK2,sK4),queue(host(sK2)))
| m_Ack(sK2,sK4) = m_Halt(sK0) ),
inference(copy,[status(thm)],[c_831]) ).
cnf(c_293,negated_conjecture,
elem(m_Ack(sK2,sK4),queue(host(sK2))),
inference(resolve,[status(thm)],[c_76,c_832]) ).
cnf(c_833,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| s(index(pendack,host(sK2))) != host(A)
| index(status,host(sK2)) != index(status,host(sK2))
| ~ leq(nbr_proc,s(index(pendack,host(sK2))))
| ~ elem(m_Ack(sK2,sK4),queue(host(sK2)))
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(resolve,[status(thm)],[c_228,c_200]) ).
cnf(c_834,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| s(index(pendack,host(sK2))) != host(A)
| index(status,host(sK2)) != index(status,host(sK2))
| ~ leq(nbr_proc,s(host(sK4)))
| ~ elem(m_Ack(sK2,sK4),queue(host(sK2)))
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(paramod,[status(thm)],[c_200,c_833]) ).
cnf(c_835,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| s(index(pendack,host(sK2))) != host(A)
| index(status,host(sK2)) != index(status,host(sK2))
| ~ leq(nbr_proc,host(sK3))
| ~ elem(m_Ack(sK2,sK4),queue(host(sK2)))
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(paramod,[status(thm)],[c_202,c_834]) ).
cnf(c_836,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| s(host(sK4)) != host(A)
| index(status,host(sK2)) != index(status,host(sK2))
| ~ leq(nbr_proc,host(sK3))
| ~ elem(m_Ack(sK2,sK4),queue(host(sK2)))
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(paramod,[status(thm)],[c_200,c_835]) ).
cnf(c_837,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(sK3) != host(A)
| index(status,host(sK2)) != index(status,host(sK2))
| ~ leq(nbr_proc,host(sK3))
| ~ elem(m_Ack(sK2,sK4),queue(host(sK2)))
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(paramod,[status(thm)],[c_202,c_836]) ).
cnf(c_838,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(sK3) != host(A)
| ~ leq(nbr_proc,host(sK3))
| ~ elem(m_Ack(sK2,sK4),queue(host(sK2)))
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(copy,[status(thm)],[c_837]) ).
cnf(c_839,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(sK3) != host(A)
| ~ leq(nbr_proc,host(sK3))
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(resolve,[status(thm)],[c_293,c_838]) ).
cnf(c_362,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(sK3) != host(A)
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(resolve,[status(thm)],[c_237,c_839]) ).
cnf(c_840,negated_conjecture,
( nbr_proc = host(sK3)
| ~ leq(host(sK3),nbr_proc) ),
inference(resolve,[status(thm)],[c_237,c_152]) ).
cnf(c_841,negated_conjecture,
( host(sK3) = nbr_proc
| ~ leq(host(sK3),nbr_proc) ),
inference(copy,[status(thm)],[c_840]) ).
cnf(c_389,negated_conjecture,
host(sK3) = nbr_proc,
inference(resolve,[status(thm)],[c_64,c_841]) ).
cnf(c_842,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| nbr_proc != host(A)
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(paramod,[status(thm)],[c_389,c_362]) ).
cnf(c_390,negated_conjecture,
( index(status,host(sK1)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(A) != nbr_proc
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(copy,[status(thm)],[c_842]) ).
cnf(c_843,negated_conjecture,
( index(status,host(sK1)) != index(status,host(sK1))
| ~ setIn(sK1,alive)
| host(A) != nbr_proc
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(resolve,[status(thm)],[c_390,c_205]) ).
cnf(c_788,negated_conjecture,
( ~ setIn(sK1,alive)
| host(A) != nbr_proc
| ~ elem(m_Down(A),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(copy,[status(thm)],[c_843]) ).
cnf(c_844,plain,
( ~ setIn(sK1,alive)
| ~ elem(m_Down(sK3),queue(host(sK2)))
| ~ setIn(sK2,alive) ),
inference(resolve,[status(thm)],[c_788,c_389]) ).
cnf(c_790,plain,
( ~ setIn(sK1,alive)
| ~ setIn(sK2,alive) ),
inference(resolve,[status(thm)],[c_288,c_844]) ).
cnf(c_791,plain,
( sK2 = sK0
| ~ setIn(sK1,alive) ),
inference(resolve,[status(thm)],[c_790,c_194]) ).
cnf(c_794,plain,
( sK1 = sK0
| sK2 = sK0 ),
inference(resolve,[status(thm)],[c_791,c_204]) ).
cnf(c_845,plain,
( host(sK2) = host(sK0)
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_794,c_103]) ).
cnf(c_799,negated_conjecture,
sK1 = sK0,
inference(resolve,[status(thm)],[c_193,c_845]) ).
cnf(c_846,negated_conjecture,
host(sK0) != host(sK0),
inference(paramod,[status(thm)],[c_799,c_191]) ).
cnf(c_825,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV461+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.41 % Computer : n014.cluster.edu
% 0.10/5.41 % Model : x86_64 x86_64
% 0.10/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.41 % Memory : 8046.5625MB
% 0.10/5.41 % OS : Linux 6.8.0-71-generic
% 0.10/5.41 % CPULimit : 300
% 0.10/5.41 % WCLimit : 300
% 0.10/5.41 % DateTime : Sat Sep 26 13:55:23 UTC 2026
% 0.10/5.41 % CPUTime :
% 0.10/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.41 % Process 3321216 was started by sandbox on n014,
% 0.10/5.41 % Sat Sep 26 13:55:23 2026
% 0.10/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.43
% 0.10/5.43 % From the command line: assign(max_seconds, 300).
% 0.12/5.90
% 0.12/5.90 % SZS status Theorem for theBenchmark
% 0.12/5.90
% 0.12/5.90 % Proof 1 at 0.12 (+ 0.06) seconds.
% 0.12/5.90 % Length of proof is 44.
% 0.12/5.90 % Level of proof is 11.
% 0.12/5.90 % Maximum clause weight is 86.000.
% 0.12/5.90 % Given clauses 246.
% 0.12/5.90
% 0.12/5.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------