%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV457+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 : n007.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 17.74s 2.78s
% Output : CNFRefutation 17.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 9
% Syntax : Number of formulae : 97 ( 41 unt; 0 def)
% Number of atoms : 632 ( 278 equ)
% Maximal formula atoms : 74 ( 6 avg)
% Number of connectives : 932 ( 397 ~; 307 |; 181 &)
% ( 3 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 17 con; 0-2 aty)
% Number of variables : 301 ( 22 sgn 203 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_04,axiom,
! [P] : leq(host(P),nbr_proc),
file('theBenchmark.p',axiom_04) ).
fof(axiom_31,axiom,
! [X1,X2,Y1,Y2] :
( X1 != X2
=> m_Ack(X1,Y1) != m_Ack(X2,Y2) ),
file('theBenchmark.p',axiom_31) ).
fof(axiom_32,axiom,
! [X1,X2,Y1,Y2] :
( Y1 != Y2
=> m_Ack(X1,Y1) != m_Ack(X2,Y2) ),
file('theBenchmark.p',axiom_32) ).
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_59,axiom,
! [X] : leq(X,X),
file('theBenchmark.p',axiom_59) ).
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] :
( ( queue(host(W)) = cons(m_Halt(X),V)
& ! [Y,Z,Pid0] :
( ( host(Z) = index(pendack,host(Pid0))
& index(status,host(Pid0)) = elec_2
& leq(nbr_proc,index(pendack,host(Pid0)))
& elem(m_Ack(Pid0,Z),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Y)) = norm
& index(ldr,host(Y)) = host(Y)
& setIn(Y,alive) ) )
& ! [Y,Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& elem(m_Halt(Pid0),queue(host(Z)))
& setIn(Pid0,alive)
& ~ leq(index(pendack,host(Pid0)),host(Y)) )
=> ~ ( index(status,host(Y)) = norm
& index(ldr,host(Y)) = host(Y)
& setIn(Y,alive) ) )
& ! [Y,Z] :
( ( index(status,host(Z)) = elec_2
& index(status,host(Y)) = elec_2
& setIn(Z,alive)
& setIn(Y,alive)
& ~ leq(host(Y),host(Z)) )
=> ~ leq(index(pendack,host(Y)),index(pendack,host(Z))) )
& ! [Y,Z,Pid0] :
( ( host(Z) = host(Y)
& elem(m_Ack(Pid0,Y),queue(host(Pid0)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> ~ setIn(host(Pid0),index(down,host(Z))) )
& ! [Y,Z,Pid0] :
( ( host(Pid0) = host(Y)
& elem(m_Ack(Pid0,Z),queue(host(Pid0)))
& elem(m_Down(Y),queue(host(Z))) )
=> ~ setIn(Pid0,alive) )
& ! [Y] :
( ( setIn(Y,alive)
& ( index(status,host(Y)) = elec_2
| index(status,host(Y)) = elec_1 ) )
=> index(elid,host(Y)) = Y )
& ! [Y,Z] :
( ( index(status,host(Z)) = elec_1
& setIn(Z,alive) )
=> ~ elem(m_Ack(Z,Y),queue(host(Z))) )
& ! [Y,Z] :
( ( index(status,host(Z)) = elec_1
& setIn(Z,alive) )
=> ~ elem(m_Ack(Y,Z),queue(host(Y))) )
& ! [Y,Z] :
( ( elem(m_Ack(Z,Y),queue(host(Z)))
& setIn(Z,alive) )
=> leq(host(Y),index(pendack,host(Z))) )
& ! [Y,Z] :
( ( host(Z) = host(Y)
& Z != Y )
=> ( ~ setIn(Z,alive)
| ~ setIn(Y,alive) ) )
& ! [Y,Z] :
( ( host(Z) = host(Y)
& leq(Z,Y)
& ~ setIn(Y,alive) )
=> ~ setIn(Z,alive) )
& ! [Y,Z,Pid0] :
( elem(m_Ack(Pid0,Y),queue(host(Z)))
=> ~ leq(host(Y),host(Pid0)) )
& ! [Y,Z] :
( elem(m_Ldr(Z),queue(host(Y)))
=> ~ leq(host(Y),host(Z)) )
& ! [Y,Z] :
( elem(m_Down(Z),queue(host(Y)))
=> ~ setIn(Z,alive) )
& ! [Y,Z] :
( elem(m_Ack(Z,Y),queue(host(Z)))
=> setIn(Z,pids) ) )
=> ( setIn(W,alive)
=> ! [Y] :
( host(W) != host(Y)
=> ! [Z,X0] :
( host(X) = host(X0)
=> ( host(W) != host(X0)
=> ( ( host(Z) = index(pendack,host(X0))
& index(status,host(X0)) = elec_2
& elem(m_Ack(X0,Z),snoc(queue(host(X0)),m_Ack(X,W)))
& leq(nbr_proc,index(pendack,host(X0)))
& setIn(X0,alive) )
=> ~ ( index(status,host(Y)) = norm
& index(ldr,host(Y)) = host(Y)
& setIn(Y,alive) ) ) ) ) ) ) ),
file('theBenchmark.p',conj) ).
fof(conj_neg,negated_conjecture,
~ ! [V,W,X] :
( ( queue(host(W)) = cons(m_Halt(X),V)
& ! [Y,Z,Pid0] :
( ( host(Z) = index(pendack,host(Pid0))
& index(status,host(Pid0)) = elec_2
& leq(nbr_proc,index(pendack,host(Pid0)))
& elem(m_Ack(Pid0,Z),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Y)) = norm
& index(ldr,host(Y)) = host(Y)
& setIn(Y,alive) ) )
& ! [Y,Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& elem(m_Halt(Pid0),queue(host(Z)))
& setIn(Pid0,alive)
& ~ leq(index(pendack,host(Pid0)),host(Y)) )
=> ~ ( index(status,host(Y)) = norm
& index(ldr,host(Y)) = host(Y)
& setIn(Y,alive) ) )
& ! [Y,Z] :
( ( index(status,host(Z)) = elec_2
& index(status,host(Y)) = elec_2
& setIn(Z,alive)
& setIn(Y,alive)
& ~ leq(host(Y),host(Z)) )
=> ~ leq(index(pendack,host(Y)),index(pendack,host(Z))) )
& ! [Y,Z,Pid0] :
( ( host(Z) = host(Y)
& elem(m_Ack(Pid0,Y),queue(host(Pid0)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> ~ setIn(host(Pid0),index(down,host(Z))) )
& ! [Y,Z,Pid0] :
( ( host(Pid0) = host(Y)
& elem(m_Ack(Pid0,Z),queue(host(Pid0)))
& elem(m_Down(Y),queue(host(Z))) )
=> ~ setIn(Pid0,alive) )
& ! [Y] :
( ( setIn(Y,alive)
& ( index(status,host(Y)) = elec_2
| index(status,host(Y)) = elec_1 ) )
=> index(elid,host(Y)) = Y )
& ! [Y,Z] :
( ( index(status,host(Z)) = elec_1
& setIn(Z,alive) )
=> ~ elem(m_Ack(Z,Y),queue(host(Z))) )
& ! [Y,Z] :
( ( index(status,host(Z)) = elec_1
& setIn(Z,alive) )
=> ~ elem(m_Ack(Y,Z),queue(host(Y))) )
& ! [Y,Z] :
( ( elem(m_Ack(Z,Y),queue(host(Z)))
& setIn(Z,alive) )
=> leq(host(Y),index(pendack,host(Z))) )
& ! [Y,Z] :
( ( host(Z) = host(Y)
& Z != Y )
=> ( ~ setIn(Z,alive)
| ~ setIn(Y,alive) ) )
& ! [Y,Z] :
( ( host(Z) = host(Y)
& leq(Z,Y)
& ~ setIn(Y,alive) )
=> ~ setIn(Z,alive) )
& ! [Y,Z,Pid0] :
( elem(m_Ack(Pid0,Y),queue(host(Z)))
=> ~ leq(host(Y),host(Pid0)) )
& ! [Y,Z] :
( elem(m_Ldr(Z),queue(host(Y)))
=> ~ leq(host(Y),host(Z)) )
& ! [Y,Z] :
( elem(m_Down(Z),queue(host(Y)))
=> ~ setIn(Z,alive) )
& ! [Y,Z] :
( elem(m_Ack(Z,Y),queue(host(Z)))
=> setIn(Z,pids) ) )
=> ( setIn(W,alive)
=> ! [Y] :
( host(W) != host(Y)
=> ! [Z,X0] :
( host(X) = host(X0)
=> ( host(W) != host(X0)
=> ( ( host(Z) = index(pendack,host(X0))
& index(status,host(X0)) = elec_2
& elem(m_Ack(X0,Z),snoc(queue(host(X0)),m_Ack(X,W)))
& leq(nbr_proc,index(pendack,host(X0)))
& setIn(X0,alive) )
=> ~ ( index(status,host(Y)) = norm
& index(ldr,host(Y)) = host(Y)
& setIn(Y,alive) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_64,plain,
leq(host(A),nbr_proc),
inference(clausify,[status(thm)],[axiom_04]) ).
cnf(c_100,plain,
( m_Ack(A,C) != m_Ack(B,D)
| A = B ),
inference(clausify,[status(thm)],[axiom_31]) ).
cnf(c_101,plain,
( m_Ack(C,A) != m_Ack(D,B)
| A = B ),
inference(clausify,[status(thm)],[axiom_32]) ).
cnf(c_107,plain,
init(snoc(A,B)) = A,
inference(clausify,[status(thm)],[axiom_38]) ).
cnf(c_118,plain,
( B != A
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
cnf(c_120,plain,
( elem(A,B)
| C = A
| ~ elem(A,snoc(B,C)) ),
inference(clausify,[status(thm)],[axiom_47]) ).
cnf(c_149,plain,
leq(A,A),
inference(clausify,[status(thm)],[axiom_59]) ).
cnf(c_151,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[axiom_61]) ).
fof(nnf_58,plain,
? [V,W,X] :
( ? [Y] :
( ? [Z,X0] :
( index(status,host(Y)) = norm
& index(ldr,host(Y)) = host(Y)
& setIn(Y,alive)
& index(pendack,host(X0)) = host(Z)
& index(status,host(X0)) = elec_2
& elem(m_Ack(X0,Z),snoc(queue(host(X0)),m_Ack(X,W)))
& leq(nbr_proc,index(pendack,host(X0)))
& setIn(X0,alive)
& host(X0) != host(W)
& host(X0) = host(X) )
& host(W) != host(Y) )
& setIn(W,alive)
& cons(m_Halt(X),V) = queue(host(W))
& ! [X34,X35,Pid0] :
( index(status,host(X34)) != norm
| index(ldr,host(X34)) != host(X34)
| ~ setIn(X34,alive)
| index(pendack,host(Pid0)) != host(X35)
| index(status,host(Pid0)) != elec_2
| ~ leq(nbr_proc,index(pendack,host(Pid0)))
| ~ elem(m_Ack(Pid0,X35),queue(host(Pid0)))
| ~ setIn(Pid0,alive) )
& ! [X31,X32,X33] :
( index(status,host(X31)) != norm
| index(ldr,host(X31)) != host(X31)
| ~ setIn(X31,alive)
| index(status,host(X33)) != elec_2
| ~ elem(m_Halt(X33),queue(host(X32)))
| ~ setIn(X33,alive)
| leq(index(pendack,host(X33)),host(X31)) )
& ! [X29,X30] :
( ~ leq(index(pendack,host(X29)),index(pendack,host(X30)))
| index(status,host(X30)) != elec_2
| index(status,host(X29)) != elec_2
| ~ setIn(X30,alive)
| ~ setIn(X29,alive)
| leq(host(X29),host(X30)) )
& ! [X26,X27,X28] :
( ~ setIn(host(X28),index(down,host(X27)))
| host(X27) != host(X26)
| ~ elem(m_Ack(X28,X26),queue(host(X28)))
| ~ setIn(X28,alive)
| ~ setIn(X27,alive) )
& ! [X23,X24,X25] :
( ~ setIn(X25,alive)
| host(X25) != host(X23)
| ~ elem(m_Ack(X25,X24),queue(host(X25)))
| ~ elem(m_Down(X23),queue(host(X24))) )
& ! [X22] :
( index(elid,host(X22)) = X22
| ~ setIn(X22,alive)
| ( index(status,host(X22)) != elec_2
& index(status,host(X22)) != elec_1 ) )
& ! [X20,X21] :
( ~ elem(m_Ack(X21,X20),queue(host(X21)))
| index(status,host(X21)) != elec_1
| ~ setIn(X21,alive) )
& ! [X18,X19] :
( ~ elem(m_Ack(X18,X19),queue(host(X18)))
| index(status,host(X19)) != elec_1
| ~ setIn(X19,alive) )
& ! [X16,X17] :
( leq(host(X16),index(pendack,host(X17)))
| ~ elem(m_Ack(X17,X16),queue(host(X17)))
| ~ setIn(X17,alive) )
& ! [X14,X15] :
( ~ setIn(X15,alive)
| ~ setIn(X14,alive)
| host(X15) != host(X14)
| X15 = X14 )
& ! [X12,X13] :
( ~ setIn(X13,alive)
| host(X13) != host(X12)
| ~ leq(X13,X12)
| setIn(X12,alive) )
& ! [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_Ldr(X8),queue(host(X7))) )
& ! [X5,X6] :
( ~ setIn(X6,alive)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( setIn(X4,pids)
| ~ elem(m_Ack(X4,X3),queue(host(X4))) ) ),
inference(fof_nnf,[status(thm)],[conj_neg]) ).
fof(sk_conj_neg_sk,plain,
( index(status,host(sK3)) = norm
& index(ldr,host(sK3)) = host(sK3)
& setIn(sK3,alive)
& index(pendack,host(sK4)) = host(sK5)
& index(status,host(sK4)) = elec_2
& elem(m_Ack(sK4,sK5),snoc(queue(host(sK4)),m_Ack(sK0,sK2)))
& leq(nbr_proc,index(pendack,host(sK4)))
& setIn(sK4,alive)
& host(sK4) != host(sK2)
& host(sK4) = host(sK0)
& host(sK2) != host(sK3)
& setIn(sK2,alive)
& cons(m_Halt(sK0),sK1) = queue(host(sK2))
& ! [X34,X35,Pid0] :
( index(status,host(X34)) != norm
| index(ldr,host(X34)) != host(X34)
| ~ setIn(X34,alive)
| index(pendack,host(Pid0)) != host(X35)
| index(status,host(Pid0)) != elec_2
| ~ leq(nbr_proc,index(pendack,host(Pid0)))
| ~ elem(m_Ack(Pid0,X35),queue(host(Pid0)))
| ~ setIn(Pid0,alive) )
& ! [X31,X32,X33] :
( index(status,host(X31)) != norm
| index(ldr,host(X31)) != host(X31)
| ~ setIn(X31,alive)
| index(status,host(X33)) != elec_2
| ~ elem(m_Halt(X33),queue(host(X32)))
| ~ setIn(X33,alive)
| leq(index(pendack,host(X33)),host(X31)) )
& ! [X29,X30] :
( ~ leq(index(pendack,host(X29)),index(pendack,host(X30)))
| index(status,host(X30)) != elec_2
| index(status,host(X29)) != elec_2
| ~ setIn(X30,alive)
| ~ setIn(X29,alive)
| leq(host(X29),host(X30)) )
& ! [X26,X27,X28] :
( ~ setIn(host(X28),index(down,host(X27)))
| host(X27) != host(X26)
| ~ elem(m_Ack(X28,X26),queue(host(X28)))
| ~ setIn(X28,alive)
| ~ setIn(X27,alive) )
& ! [X23,X24,X25] :
( ~ setIn(X25,alive)
| host(X25) != host(X23)
| ~ elem(m_Ack(X25,X24),queue(host(X25)))
| ~ elem(m_Down(X23),queue(host(X24))) )
& ! [X22] :
( index(elid,host(X22)) = X22
| ~ setIn(X22,alive)
| ( index(status,host(X22)) != elec_2
& index(status,host(X22)) != elec_1 ) )
& ! [X20,X21] :
( ~ elem(m_Ack(X21,X20),queue(host(X21)))
| index(status,host(X21)) != elec_1
| ~ setIn(X21,alive) )
& ! [X18,X19] :
( ~ elem(m_Ack(X18,X19),queue(host(X18)))
| index(status,host(X19)) != elec_1
| ~ setIn(X19,alive) )
& ! [X16,X17] :
( leq(host(X16),index(pendack,host(X17)))
| ~ elem(m_Ack(X17,X16),queue(host(X17)))
| ~ setIn(X17,alive) )
& ! [X14,X15] :
( ~ setIn(X15,alive)
| ~ setIn(X14,alive)
| host(X15) != host(X14)
| X15 = X14 )
& ! [X12,X13] :
( ~ setIn(X13,alive)
| host(X13) != host(X12)
| ~ leq(X13,X12)
| setIn(X12,alive) )
& ! [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_Ldr(X8),queue(host(X7))) )
& ! [X5,X6] :
( ~ setIn(X6,alive)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( setIn(X4,pids)
| ~ elem(m_Ack(X4,X3),queue(host(X4))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK0),skolemize(Y,sK3),skolemize(Z,sK5),skolemize(X0,sK4)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( index(status,host(sK3)) = norm
& index(ldr,host(sK3)) = host(sK3)
& setIn(sK3,alive)
& index(pendack,host(sK4)) = host(sK5)
& index(status,host(sK4)) = elec_2
& elem(m_Ack(sK4,sK5),snoc(queue(host(sK4)),m_Ack(sK0,sK2)))
& leq(nbr_proc,index(pendack,host(sK4)))
& setIn(sK4,alive)
& host(sK4) != host(sK2)
& host(sK4) = host(sK0)
& host(sK2) != host(sK3)
& setIn(sK2,alive)
& cons(m_Halt(sK0),sK1) = queue(host(sK2))
& ! [VAR_0,VAR_1,VAR_2] :
( index(status,host(VAR_2)) != norm
| index(ldr,host(VAR_2)) != host(VAR_2)
| ~ setIn(VAR_2,alive)
| index(pendack,host(VAR_0)) != host(VAR_1)
| index(status,host(VAR_0)) != elec_2
| ~ leq(nbr_proc,index(pendack,host(VAR_0)))
| ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_0)))
| ~ setIn(VAR_0,alive) )
& ! [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] :
( ~ setIn(host(VAR_1),index(down,host(VAR_0)))
| host(VAR_0) != host(VAR_2)
| ~ elem(m_Ack(VAR_1,VAR_2),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ setIn(VAR_2,alive)
| host(VAR_2) != host(VAR_0)
| ~ elem(m_Ack(VAR_2,VAR_1),queue(host(VAR_2)))
| ~ elem(m_Down(VAR_0),queue(host(VAR_1))) )
& ! [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] :
( ~ elem(m_Ack(VAR_1,VAR_0),queue(host(VAR_1)))
| 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] :
( ~ setIn(VAR_1,alive)
| host(VAR_1) != host(VAR_0)
| ~ leq(VAR_1,VAR_0)
| setIn(VAR_0,alive) )
& ! [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_Ldr(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( ~ setIn(VAR_0,alive)
| ~ elem(m_Down(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( setIn(VAR_0,pids)
| ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_0))) ) ),
inference(cnf_transformation,[status(thm)],[sk_conj_neg_sk]) ).
cnf(c_173,negated_conjecture,
( index(status,host(B)) != norm
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(A)) != elec_2
| ~ elem(m_Halt(A),queue(host(C)))
| ~ setIn(A,alive)
| leq(index(pendack,host(A)),host(B)) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_174,negated_conjecture,
( index(status,host(C)) != norm
| index(ldr,host(C)) != host(C)
| ~ setIn(C,alive)
| index(pendack,host(A)) != host(B)
| index(status,host(A)) != elec_2
| ~ leq(nbr_proc,index(pendack,host(A)))
| ~ elem(m_Ack(A,B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_175,negated_conjecture,
cons(m_Halt(sK0),sK1) = queue(host(sK2)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_176,negated_conjecture,
queue(host(sK2)) = cons(m_Halt(sK0),sK1),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_178,negated_conjecture,
host(sK2) != host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_179,negated_conjecture,
host(sK3) != host(sK2),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_180,negated_conjecture,
host(sK4) = host(sK0),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_183,negated_conjecture,
setIn(sK4,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_184,negated_conjecture,
leq(nbr_proc,index(pendack,host(sK4))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_185,negated_conjecture,
leq(nbr_proc,index(pendack,host(sK0))),
inference(paramod,[status(thm)],[c_180,c_184]) ).
cnf(c_186,negated_conjecture,
elem(m_Ack(sK4,sK5),snoc(queue(host(sK4)),m_Ack(sK0,sK2))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_187,negated_conjecture,
elem(m_Ack(sK4,sK5),snoc(queue(host(sK0)),m_Ack(sK0,sK2))),
inference(paramod,[status(thm)],[c_180,c_186]) ).
cnf(c_188,negated_conjecture,
index(status,host(sK4)) = elec_2,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_4322,negated_conjecture,
index(status,host(sK0)) = elec_2,
inference(paramod,[status(thm)],[c_180,c_188]) ).
cnf(c_189,negated_conjecture,
elec_2 = index(status,host(sK0)),
inference(copy,[status(thm)],[c_4322]) ).
cnf(c_190,negated_conjecture,
index(pendack,host(sK4)) = host(sK5),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_4323,negated_conjecture,
index(pendack,host(sK0)) = host(sK5),
inference(paramod,[status(thm)],[c_180,c_190]) ).
cnf(c_191,negated_conjecture,
host(sK5) = index(pendack,host(sK0)),
inference(copy,[status(thm)],[c_4323]) ).
cnf(c_192,negated_conjecture,
setIn(sK3,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_193,negated_conjecture,
index(ldr,host(sK3)) = host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_194,negated_conjecture,
index(status,host(sK3)) = norm,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_195,negated_conjecture,
norm = index(status,host(sK3)),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_4324,negated_conjecture,
( index(status,host(C)) != norm
| index(ldr,host(C)) != host(C)
| ~ setIn(C,alive)
| index(pendack,host(A)) != host(B)
| index(status,host(A)) != index(status,host(sK0))
| ~ leq(nbr_proc,index(pendack,host(A)))
| ~ elem(m_Ack(A,B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_189,c_174]) ).
cnf(c_4325,negated_conjecture,
( index(status,host(C)) != index(status,host(sK3))
| index(ldr,host(C)) != host(C)
| ~ setIn(C,alive)
| index(pendack,host(A)) != host(B)
| index(status,host(A)) != index(status,host(sK0))
| ~ leq(nbr_proc,index(pendack,host(A)))
| ~ elem(m_Ack(A,B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_195,c_4324]) ).
cnf(c_4326,negated_conjecture,
( index(status,host(C)) != index(status,host(sK3))
| index(ldr,host(C)) != host(C)
| ~ setIn(C,alive)
| index(pendack,host(A)) != host(B)
| index(status,host(sK0)) != index(status,host(A))
| ~ leq(nbr_proc,index(pendack,host(A)))
| ~ elem(m_Ack(A,B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_4325]) ).
cnf(c_199,negated_conjecture,
( index(status,host(sK3)) != index(status,host(C))
| index(ldr,host(C)) != host(C)
| ~ setIn(C,alive)
| index(pendack,host(A)) != host(B)
| index(status,host(sK0)) != index(status,host(A))
| ~ leq(nbr_proc,index(pendack,host(A)))
| ~ elem(m_Ack(A,B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_4326]) ).
cnf(c_4327,negated_conjecture,
( index(status,host(B)) != norm
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(A)) != index(status,host(sK0))
| ~ elem(m_Halt(A),queue(host(C)))
| ~ setIn(A,alive)
| leq(index(pendack,host(A)),host(B)) ),
inference(paramod,[status(thm)],[c_189,c_173]) ).
cnf(c_4328,negated_conjecture,
( index(status,host(B)) != index(status,host(sK3))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(A)) != index(status,host(sK0))
| ~ elem(m_Halt(A),queue(host(C)))
| ~ setIn(A,alive)
| leq(index(pendack,host(A)),host(B)) ),
inference(paramod,[status(thm)],[c_195,c_4327]) ).
cnf(c_4329,negated_conjecture,
( index(status,host(B)) != index(status,host(sK3))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(sK0)) != index(status,host(A))
| ~ elem(m_Halt(A),queue(host(C)))
| ~ setIn(A,alive)
| leq(index(pendack,host(A)),host(B)) ),
inference(copy,[status(thm)],[c_4328]) ).
cnf(c_200,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(sK0)) != index(status,host(A))
| ~ elem(m_Halt(A),queue(host(C)))
| ~ setIn(A,alive)
| leq(index(pendack,host(A)),host(B)) ),
inference(copy,[status(thm)],[c_4329]) ).
cnf(c_4330,plain,
elem(A,cons(init(snoc(A,B)),C)),
inference(resolve,[status(thm)],[c_118,c_107]) ).
cnf(c_233,plain,
elem(A,cons(A,B)),
inference(paramod,[status(thm)],[c_107,c_4330]) ).
cnf(c_4331,plain,
( nbr_proc = host(A)
| ~ leq(nbr_proc,host(A)) ),
inference(resolve,[status(thm)],[c_151,c_64]) ).
cnf(c_270,plain,
( host(A) = nbr_proc
| ~ leq(nbr_proc,host(A)) ),
inference(copy,[status(thm)],[c_4331]) ).
cnf(c_4332,negated_conjecture,
( nbr_proc = index(pendack,host(sK0))
| ~ leq(index(pendack,host(sK0)),nbr_proc) ),
inference(resolve,[status(thm)],[c_185,c_151]) ).
cnf(c_320,negated_conjecture,
( index(pendack,host(sK0)) = nbr_proc
| ~ leq(index(pendack,host(sK0)),nbr_proc) ),
inference(copy,[status(thm)],[c_4332]) ).
cnf(c_4333,negated_conjecture,
( elem(m_Ack(sK4,sK5),queue(host(sK0)))
| m_Ack(sK0,sK2) = m_Ack(sK4,sK5) ),
inference(resolve,[status(thm)],[c_187,c_120]) ).
cnf(c_324,negated_conjecture,
( elem(m_Ack(sK4,sK5),queue(host(sK0)))
| m_Ack(sK4,sK5) = m_Ack(sK0,sK2) ),
inference(copy,[status(thm)],[c_4333]) ).
cnf(c_331,plain,
leq(index(pendack,host(sK0)),nbr_proc),
inference(paramod,[status(thm)],[c_191,c_64]) ).
cnf(c_336,negated_conjecture,
index(pendack,host(sK0)) = nbr_proc,
inference(resolve,[status(thm)],[c_331,c_320]) ).
cnf(c_346,negated_conjecture,
host(sK5) = nbr_proc,
inference(paramod,[status(thm)],[c_336,c_191]) ).
cnf(c_4334,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(pendack,host(sK4)) != host(A)
| index(status,host(sK0)) != index(status,host(sK4))
| ~ leq(nbr_proc,index(pendack,host(sK4)))
| ~ elem(m_Ack(sK4,A),queue(host(sK4))) ),
inference(resolve,[status(thm)],[c_199,c_183]) ).
cnf(c_4335,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(pendack,host(sK4)) != host(A)
| index(status,host(sK0)) != index(status,host(sK4))
| ~ leq(nbr_proc,index(pendack,host(sK4)))
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(paramod,[status(thm)],[c_180,c_4334]) ).
cnf(c_4336,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(pendack,host(sK4)) != host(A)
| index(status,host(sK0)) != index(status,host(sK4))
| ~ leq(nbr_proc,index(pendack,host(sK0)))
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(paramod,[status(thm)],[c_180,c_4335]) ).
cnf(c_4337,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(pendack,host(sK4)) != host(A)
| index(status,host(sK0)) != index(status,host(sK4))
| ~ leq(nbr_proc,nbr_proc)
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(paramod,[status(thm)],[c_336,c_4336]) ).
cnf(c_4338,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(pendack,host(sK4)) != host(A)
| index(status,host(sK0)) != index(status,host(sK0))
| ~ leq(nbr_proc,nbr_proc)
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(paramod,[status(thm)],[c_180,c_4337]) ).
cnf(c_4339,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(pendack,host(sK0)) != host(A)
| index(status,host(sK0)) != index(status,host(sK0))
| ~ leq(nbr_proc,nbr_proc)
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(paramod,[status(thm)],[c_180,c_4338]) ).
cnf(c_4340,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| nbr_proc != host(A)
| index(status,host(sK0)) != index(status,host(sK0))
| ~ leq(nbr_proc,nbr_proc)
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(paramod,[status(thm)],[c_336,c_4339]) ).
cnf(c_4341,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(A) != nbr_proc
| index(status,host(sK0)) != index(status,host(sK0))
| ~ leq(nbr_proc,nbr_proc)
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(copy,[status(thm)],[c_4340]) ).
cnf(c_4342,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(A) != nbr_proc
| ~ leq(nbr_proc,nbr_proc)
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(copy,[status(thm)],[c_4341]) ).
cnf(c_356,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| host(A) != nbr_proc
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(resolve,[status(thm)],[c_149,c_4342]) ).
cnf(c_4343,negated_conjecture,
( index(status,host(sK3)) != index(status,host(sK3))
| index(ldr,host(sK3)) != host(sK3)
| index(status,host(sK0)) != index(status,host(A))
| ~ elem(m_Halt(A),queue(host(B)))
| ~ setIn(A,alive)
| leq(index(pendack,host(A)),host(sK3)) ),
inference(resolve,[status(thm)],[c_200,c_192]) ).
cnf(c_4344,negated_conjecture,
( index(status,host(sK3)) != index(status,host(sK3))
| host(sK3) != host(sK3)
| index(status,host(sK0)) != index(status,host(A))
| ~ elem(m_Halt(A),queue(host(B)))
| ~ setIn(A,alive)
| leq(index(pendack,host(A)),host(sK3)) ),
inference(paramod,[status(thm)],[c_193,c_4343]) ).
cnf(c_4345,negated_conjecture,
( index(status,host(sK3)) != index(status,host(sK3))
| index(status,host(sK0)) != index(status,host(A))
| ~ elem(m_Halt(A),queue(host(B)))
| ~ setIn(A,alive)
| leq(index(pendack,host(A)),host(sK3)) ),
inference(copy,[status(thm)],[c_4344]) ).
cnf(c_361,negated_conjecture,
( index(status,host(sK0)) != index(status,host(A))
| ~ elem(m_Halt(A),queue(host(B)))
| ~ setIn(A,alive)
| leq(index(pendack,host(A)),host(sK3)) ),
inference(copy,[status(thm)],[c_4345]) ).
cnf(c_4346,negated_conjecture,
( index(status,host(sK3)) != index(status,host(sK3))
| index(ldr,host(sK3)) != host(sK3)
| host(A) != nbr_proc
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(resolve,[status(thm)],[c_356,c_192]) ).
cnf(c_4347,negated_conjecture,
( index(status,host(sK3)) != index(status,host(sK3))
| host(sK3) != host(sK3)
| host(A) != nbr_proc
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(paramod,[status(thm)],[c_193,c_4346]) ).
cnf(c_4348,negated_conjecture,
( index(status,host(sK3)) != index(status,host(sK3))
| host(A) != nbr_proc
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(copy,[status(thm)],[c_4347]) ).
cnf(c_807,negated_conjecture,
( host(A) != nbr_proc
| ~ elem(m_Ack(sK4,A),queue(host(sK0))) ),
inference(copy,[status(thm)],[c_4348]) ).
cnf(c_4349,plain,
( host(sK5) != nbr_proc
| m_Ack(sK4,sK5) = m_Ack(sK0,sK2) ),
inference(resolve,[status(thm)],[c_324,c_807]) ).
cnf(c_4350,plain,
( nbr_proc != nbr_proc
| m_Ack(sK4,sK5) = m_Ack(sK0,sK2) ),
inference(paramod,[status(thm)],[c_346,c_4349]) ).
cnf(c_2568,plain,
m_Ack(sK4,sK5) = m_Ack(sK0,sK2),
inference(copy,[status(thm)],[c_4350]) ).
cnf(c_2594,plain,
sK5 = sK2,
inference(resolve,[status(thm)],[c_2568,c_101]) ).
cnf(c_2595,plain,
sK4 = sK0,
inference(resolve,[status(thm)],[c_2568,c_100]) ).
cnf(c_2614,negated_conjecture,
host(sK2) = nbr_proc,
inference(paramod,[status(thm)],[c_2594,c_346]) ).
cnf(c_2709,negated_conjecture,
setIn(sK0,alive),
inference(paramod,[status(thm)],[c_2595,c_183]) ).
cnf(c_2800,negated_conjecture,
host(sK3) != nbr_proc,
inference(paramod,[status(thm)],[c_2614,c_179]) ).
cnf(c_2801,negated_conjecture,
queue(nbr_proc) = cons(m_Halt(sK0),sK1),
inference(paramod,[status(thm)],[c_2614,c_176]) ).
cnf(c_4351,negated_conjecture,
( index(status,host(sK0)) != index(status,host(sK0))
| ~ elem(m_Halt(sK0),queue(host(A)))
| leq(index(pendack,host(sK0)),host(sK3)) ),
inference(resolve,[status(thm)],[c_361,c_2709]) ).
cnf(c_4352,negated_conjecture,
( index(status,host(sK0)) != index(status,host(sK0))
| ~ elem(m_Halt(sK0),queue(host(A)))
| leq(nbr_proc,host(sK3)) ),
inference(paramod,[status(thm)],[c_336,c_4351]) ).
cnf(c_3018,negated_conjecture,
( ~ elem(m_Halt(sK0),queue(host(A)))
| leq(nbr_proc,host(sK3)) ),
inference(copy,[status(thm)],[c_4352]) ).
cnf(c_4353,plain,
( ~ elem(m_Halt(sK0),queue(nbr_proc))
| leq(nbr_proc,host(sK3)) ),
inference(paramod,[status(thm)],[c_2614,c_3018]) ).
cnf(c_4354,plain,
( ~ elem(m_Halt(sK0),cons(m_Halt(sK0),sK1))
| leq(nbr_proc,host(sK3)) ),
inference(paramod,[status(thm)],[c_2801,c_4353]) ).
cnf(c_4281,plain,
leq(nbr_proc,host(sK3)),
inference(resolve,[status(thm)],[c_233,c_4354]) ).
cnf(c_4355,plain,
host(sK3) = nbr_proc,
inference(resolve,[status(thm)],[c_4281,c_270]) ).
cnf(c_4321,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2800,c_4355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV457+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 13:52:39 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3896001 was started by sandbox2 on n007,
% 0.19/0.45 % Sat Sep 26 13:52:39 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 17.74/2.78
% 17.74/2.78 % given #500 (T,wt=10): 921 leq(zero,A) | -leq(B,s(A)) | leq(B,nbr_proc). [resolve(904,a,154,b)].
% 17.74/2.78
% 17.74/2.78 % SZS status Theorem for theBenchmark
% 17.74/2.78
% 17.74/2.78 % Proof 1 at 1.68 (+ 0.57) seconds.
% 17.74/2.78 % Length of proof is 59.
% 17.74/2.78 % Level of proof is 12.
% 17.74/2.78 % Maximum clause weight is 51.000.
% 17.74/2.78 % Given clauses 643.
% 17.74/2.78
% 17.74/2.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------