%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV469+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 : n019.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 10.18s 1.72s
% Output : CNFRefutation 10.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 25 unt; 0 def)
% Number of atoms : 708 ( 316 equ)
% Maximal formula atoms : 128 ( 10 avg)
% Number of connectives : 1059 ( 419 ~; 329 |; 253 &)
% ( 3 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 17 con; 0-3 aty)
% Number of variables : 297 ( 9 sgn 234 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_01,axiom,
! [P,Q] :
( s(host(P)) = host(Q)
=> host(P) != host(Q) ),
file('theBenchmark.p',axiom_01) ).
fof(axiom_02,axiom,
! [P] : leq(s(zero),host(P)),
file('theBenchmark.p',axiom_02) ).
fof(axiom_38,axiom,
! [Y,Q] : init(snoc(Q,Y)) = Q,
file('theBenchmark.p',axiom_38) ).
fof(axiom_46,axiom,
! [X,Y,Q] :
( elem(X,cons(Y,Q))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_46) ).
fof(axiom_58,axiom,
! [X] : ~ leq(s(X),X),
file('theBenchmark.p',axiom_58) ).
fof(axiom_60,axiom,
! [X,Y] :
( leq(Y,X)
| leq(X,Y) ),
file('theBenchmark.p',axiom_60) ).
fof(axiom_61,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
<=> X = Y ),
file('theBenchmark.p',axiom_61) ).
fof(axiom_64,axiom,
! [X,Y] :
( leq(X,s(Y))
<=> ( leq(X,Y)
| X = s(Y) ) ),
file('theBenchmark.p',axiom_64) ).
fof(conj,conjecture,
! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Down(Y),V)
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& elem(m_Down(Pid20),queue(host(Pid0)))
& ~ leq(host(Pid0),host(Z))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& 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,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,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& 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,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Pid0)
& setIn(Pid0,alive) )
=> ~ ( elem(m_Down(Pid20),queue(host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& elem(m_Down(Pid20),queue(host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,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,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Ack(Pid0,Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( 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(Pid0)),host(Z)) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Pid0),host(Z)) )
=> ~ elem(m_Down(Pid20),queue(host(Z))) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& setIn(Pid0,alive) )
=> ~ ( setIn(host(Pid0),index(down,host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(host(Pid0),index(down,host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(Pid0,alive) )
=> ~ elem(m_Ack(Z,Pid0),queue(host(Z))) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( ~ leq(host(X),host(Y))
=> ( ~ ( ( host(Y) = host(index(elid,host(X)))
& index(status,host(X)) = wait )
| ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(Y) ) )
=> ( ( index(status,host(X)) = elec_1
& ! [Z] :
( ( leq(s(zero),Z)
& ~ leq(host(X),Z) )
=> ( Z = host(Y)
| setIn(Z,index(down,host(X))) ) ) )
=> ( ~ leq(nbr_proc,host(X))
=> ! [Z] :
( host(X) != host(Z)
=> ! [W0] :
( host(X) = host(W0)
=> ( ( setIn(W0,alive)
& ~ leq(s(host(X)),host(Z)) )
=> ~ ( 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_Down(Y),V)
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& elem(m_Down(Pid20),queue(host(Pid0)))
& ~ leq(host(Pid0),host(Z))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& 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,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,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& 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,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Pid0)
& setIn(Pid0,alive) )
=> ~ ( elem(m_Down(Pid20),queue(host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& elem(m_Down(Pid20),queue(host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,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,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Ack(Pid0,Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( 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(Pid0)),host(Z)) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Pid0),host(Z)) )
=> ~ elem(m_Down(Pid20),queue(host(Z))) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& setIn(Pid0,alive) )
=> ~ ( setIn(host(Pid0),index(down,host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(host(Pid0),index(down,host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(Pid0,alive) )
=> ~ elem(m_Ack(Z,Pid0),queue(host(Z))) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( ~ leq(host(X),host(Y))
=> ( ~ ( ( host(Y) = host(index(elid,host(X)))
& index(status,host(X)) = wait )
| ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(Y) ) )
=> ( ( index(status,host(X)) = elec_1
& ! [Z] :
( ( leq(s(zero),Z)
& ~ leq(host(X),Z) )
=> ( Z = host(Y)
| setIn(Z,index(down,host(X))) ) ) )
=> ( ~ leq(nbr_proc,host(X))
=> ! [Z] :
( host(X) != host(Z)
=> ! [W0] :
( host(X) = host(W0)
=> ( ( setIn(W0,alive)
& ~ leq(s(host(X)),host(Z)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_61,plain,
( host(B) != host(A)
| s(host(A)) != host(B) ),
inference(clausify,[status(thm)],[axiom_01]) ).
cnf(c_62,plain,
leq(s(zero),host(A)),
inference(clausify,[status(thm)],[axiom_02]) ).
cnf(c_108,plain,
init(snoc(A,B)) = A,
inference(clausify,[status(thm)],[axiom_38]) ).
cnf(c_117,plain,
( B != A
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
cnf(c_147,plain,
~ leq(s(A),A),
inference(clausify,[status(thm)],[axiom_58]) ).
cnf(c_149,plain,
( leq(B,A)
| leq(A,B) ),
inference(clausify,[status(thm)],[axiom_60]) ).
cnf(c_150,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[axiom_61]) ).
cnf(c_156,plain,
( leq(A,B)
| s(B) = A
| ~ leq(A,s(B)) ),
inference(clausify,[status(thm)],[axiom_64]) ).
fof(nnf_58,plain,
? [V,W,X,Y] :
( ? [Z] :
( ? [W0] :
( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive)
& setIn(W0,alive)
& ~ leq(s(host(X)),host(Z))
& host(W0) = host(X) )
& host(Z) != host(X) )
& ~ leq(nbr_proc,host(X))
& index(status,host(X)) = elec_1
& ! [X38] :
( host(Y) = X38
| setIn(X38,index(down,host(X)))
| ~ leq(s(zero),X38)
| leq(host(X),X38) )
& ( host(index(elid,host(X))) != host(Y)
| index(status,host(X)) != wait )
& ( index(status,host(X)) != norm
| index(ldr,host(X)) != host(Y) )
& ~ leq(host(X),host(Y))
& setIn(X,alive)
& cons(m_Down(Y),V) = queue(host(X))
& ! [X37,Pid20,Pid0] :
( index(status,host(X37)) != norm
| index(ldr,host(X37)) != host(X37)
| ~ setIn(X37,alive)
| index(status,host(Pid0)) != elec_1
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| leq(host(Pid0),host(X37))
| ? [V0] :
( host(Pid20) != V0
& ~ setIn(V0,index(down,host(Pid0)))
& leq(s(zero),V0)
& ~ leq(host(Pid0),V0) ) )
& ! [X34,X35,X36] :
( index(status,host(X34)) != norm
| index(ldr,host(X34)) != host(X34)
| ~ setIn(X34,alive)
| index(status,host(X36)) != elec_2
| host(X35) != host(X34)
| ~ elem(m_Down(X35),queue(host(X36)))
| ~ setIn(X36,alive) )
& ! [X32,X33] :
( ~ leq(index(pendack,host(X32)),index(pendack,host(X33)))
| index(status,host(X33)) != elec_2
| index(status,host(X32)) != elec_2
| ~ setIn(X33,alive)
| ~ setIn(X32,alive)
| leq(host(X32),host(X33)) )
& ! [X30,X31] :
( index(status,host(X30)) != norm
| index(ldr,host(X30)) != host(X30)
| ~ setIn(X30,alive)
| index(status,host(X31)) != elec_2
| ~ setIn(X31,alive)
| leq(index(pendack,host(X31)),host(X30)) )
& ! [X27,X28,X29] :
( ~ elem(m_Down(X28),queue(host(X27)))
| ~ setIn(X27,alive)
| index(ldr,host(X29)) != host(X29)
| index(status,host(X29)) != norm
| host(X28) != host(X29)
| ~ setIn(X29,alive) )
& ! [X24,X25,X26] :
( leq(index(pendack,host(X26)),host(X24))
| index(status,host(X26)) != elec_2
| host(X25) != host(X26)
| ~ elem(m_Down(X25),queue(host(X24)))
| ~ setIn(X26,alive)
| ~ setIn(X24,alive) )
& ! [X21,X22,X23] :
( ~ elem(m_Ack(X21,X22),queue(host(X21)))
| index(status,host(X23)) != elec_2
| index(status,host(X21)) != elec_2
| host(X22) != host(X23)
| ~ setIn(X23,alive)
| ~ setIn(X21,alive) )
& ! [X18,X19,X20] :
( index(status,host(X18)) != norm
| index(ldr,host(X18)) != host(X18)
| ~ setIn(X18,alive)
| host(X19) != host(X18)
| ~ elem(m_Ack(X20,X19),queue(host(X20)))
| ~ setIn(X20,alive) )
& ! [X16,X17] :
( leq(index(pendack,host(X17)),host(X16))
| index(status,host(X17)) != elec_2
| index(status,host(X16)) != elec_2
| ~ setIn(X17,alive)
| ~ setIn(X16,alive)
| leq(host(X16),host(X17)) )
& ! [X13,X14,X15] :
( ~ elem(m_Down(X14),queue(host(X13)))
| index(status,host(X15)) != elec_2
| host(X14) != host(X15)
| ~ setIn(X15,alive)
| ~ setIn(X13,alive)
| leq(host(X15),host(X13)) )
& ! [X11,X12] :
( ~ setIn(host(X12),index(down,host(X11)))
| ~ setIn(X11,alive)
| index(ldr,host(X12)) != host(X12)
| index(status,host(X12)) != norm
| ~ setIn(X12,alive) )
& ! [X9,X10] :
( leq(index(pendack,host(X10)),host(X9))
| index(status,host(X10)) != elec_2
| ~ setIn(host(X10),index(down,host(X9)))
| ~ setIn(X10,alive)
| ~ setIn(X9,alive) )
& ! [X8] :
( index(elid,host(X8)) = X8
| ~ setIn(X8,alive)
| ( index(status,host(X8)) != elec_2
& index(status,host(X8)) != elec_1 ) )
& ! [X6,X7] :
( ~ elem(m_Ack(X6,X7),queue(host(X6)))
| index(status,host(X7)) != elec_2
| ~ setIn(X7,alive) )
& ! [X4,X5] :
( ~ setIn(X5,alive)
| ~ setIn(X4,alive)
| host(X5) != host(X4)
| X5 = X4 )
& ! [X0,X3] :
( ~ leq(host(X0),host(X3))
| ~ elem(m_Ldr(X3),queue(host(X0))) ) ),
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)
& setIn(sK5,alive)
& ~ leq(s(host(sK2)),host(sK3))
& host(sK5) = host(sK2)
& host(sK3) != host(sK2)
& ~ leq(nbr_proc,host(sK2))
& index(status,host(sK2)) = elec_1
& ! [X38] :
( host(sK0) = X38
| setIn(X38,index(down,host(sK2)))
| ~ leq(s(zero),X38)
| leq(host(sK2),X38) )
& ( host(index(elid,host(sK2))) != host(sK0)
| index(status,host(sK2)) != wait )
& ( index(status,host(sK2)) != norm
| index(ldr,host(sK2)) != host(sK0) )
& ~ leq(host(sK2),host(sK0))
& setIn(sK2,alive)
& cons(m_Down(sK0),sK1) = queue(host(sK2))
& ! [X37,Pid20,Pid0] :
( index(status,host(X37)) != norm
| index(ldr,host(X37)) != host(X37)
| ~ setIn(X37,alive)
| index(status,host(Pid0)) != elec_1
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| leq(host(Pid0),host(X37))
| ( host(Pid20) != sK4(X37,Pid20,Pid0)
& ~ setIn(sK4(X37,Pid20,Pid0),index(down,host(Pid0)))
& leq(s(zero),sK4(X37,Pid20,Pid0))
& ~ leq(host(Pid0),sK4(X37,Pid20,Pid0)) ) )
& ! [X34,X35,X36] :
( index(status,host(X34)) != norm
| index(ldr,host(X34)) != host(X34)
| ~ setIn(X34,alive)
| index(status,host(X36)) != elec_2
| host(X35) != host(X34)
| ~ elem(m_Down(X35),queue(host(X36)))
| ~ setIn(X36,alive) )
& ! [X32,X33] :
( ~ leq(index(pendack,host(X32)),index(pendack,host(X33)))
| index(status,host(X33)) != elec_2
| index(status,host(X32)) != elec_2
| ~ setIn(X33,alive)
| ~ setIn(X32,alive)
| leq(host(X32),host(X33)) )
& ! [X30,X31] :
( index(status,host(X30)) != norm
| index(ldr,host(X30)) != host(X30)
| ~ setIn(X30,alive)
| index(status,host(X31)) != elec_2
| ~ setIn(X31,alive)
| leq(index(pendack,host(X31)),host(X30)) )
& ! [X27,X28,X29] :
( ~ elem(m_Down(X28),queue(host(X27)))
| ~ setIn(X27,alive)
| index(ldr,host(X29)) != host(X29)
| index(status,host(X29)) != norm
| host(X28) != host(X29)
| ~ setIn(X29,alive) )
& ! [X24,X25,X26] :
( leq(index(pendack,host(X26)),host(X24))
| index(status,host(X26)) != elec_2
| host(X25) != host(X26)
| ~ elem(m_Down(X25),queue(host(X24)))
| ~ setIn(X26,alive)
| ~ setIn(X24,alive) )
& ! [X21,X22,X23] :
( ~ elem(m_Ack(X21,X22),queue(host(X21)))
| index(status,host(X23)) != elec_2
| index(status,host(X21)) != elec_2
| host(X22) != host(X23)
| ~ setIn(X23,alive)
| ~ setIn(X21,alive) )
& ! [X18,X19,X20] :
( index(status,host(X18)) != norm
| index(ldr,host(X18)) != host(X18)
| ~ setIn(X18,alive)
| host(X19) != host(X18)
| ~ elem(m_Ack(X20,X19),queue(host(X20)))
| ~ setIn(X20,alive) )
& ! [X16,X17] :
( leq(index(pendack,host(X17)),host(X16))
| index(status,host(X17)) != elec_2
| index(status,host(X16)) != elec_2
| ~ setIn(X17,alive)
| ~ setIn(X16,alive)
| leq(host(X16),host(X17)) )
& ! [X13,X14,X15] :
( ~ elem(m_Down(X14),queue(host(X13)))
| index(status,host(X15)) != elec_2
| host(X14) != host(X15)
| ~ setIn(X15,alive)
| ~ setIn(X13,alive)
| leq(host(X15),host(X13)) )
& ! [X11,X12] :
( ~ setIn(host(X12),index(down,host(X11)))
| ~ setIn(X11,alive)
| index(ldr,host(X12)) != host(X12)
| index(status,host(X12)) != norm
| ~ setIn(X12,alive) )
& ! [X9,X10] :
( leq(index(pendack,host(X10)),host(X9))
| index(status,host(X10)) != elec_2
| ~ setIn(host(X10),index(down,host(X9)))
| ~ setIn(X10,alive)
| ~ setIn(X9,alive) )
& ! [X8] :
( index(elid,host(X8)) = X8
| ~ setIn(X8,alive)
| ( index(status,host(X8)) != elec_2
& index(status,host(X8)) != elec_1 ) )
& ! [X6,X7] :
( ~ elem(m_Ack(X6,X7),queue(host(X6)))
| index(status,host(X7)) != elec_2
| ~ setIn(X7,alive) )
& ! [X4,X5] :
( ~ setIn(X5,alive)
| ~ setIn(X4,alive)
| host(X5) != host(X4)
| X5 = X4 )
& ! [X0,X3] :
( ~ leq(host(X0),host(X3))
| ~ elem(m_Ldr(X3),queue(host(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK0,sK1,sK2,sK3,sK5]),skolemize(V,sK1),skolemize(W,sK6),skolemize(X,sK2),skolemize(Y,sK0),skolemize(V0,sK4(X37,Pid20,Pid0)),skolemize(Z,sK3),skolemize(W0,sK5)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( index(status,host(sK3)) = norm
& index(ldr,host(sK3)) = host(sK3)
& setIn(sK3,alive)
& setIn(sK5,alive)
& ~ leq(s(host(sK2)),host(sK3))
& host(sK5) = host(sK2)
& host(sK3) != host(sK2)
& ~ leq(nbr_proc,host(sK2))
& index(status,host(sK2)) = elec_1
& ! [VAR_0] :
( host(sK0) = VAR_0
| setIn(VAR_0,index(down,host(sK2)))
| ~ leq(s(zero),VAR_0)
| leq(host(sK2),VAR_0) )
& ( host(index(elid,host(sK2))) != host(sK0)
| index(status,host(sK2)) != wait )
& ( index(status,host(sK2)) != norm
| index(ldr,host(sK2)) != host(sK0) )
& ~ leq(host(sK2),host(sK0))
& setIn(sK2,alive)
& cons(m_Down(sK0),sK1) = queue(host(sK2))
& ! [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_2)) != elec_1
| ~ elem(m_Down(VAR_0),queue(host(VAR_2)))
| leq(host(VAR_2),host(VAR_1))
| host(VAR_0) != sK4(VAR_1,VAR_0,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(status,host(VAR_0)) != norm
| index(ldr,host(VAR_0)) != host(VAR_0)
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_2)) != elec_1
| ~ elem(m_Down(VAR_1),queue(host(VAR_2)))
| leq(host(VAR_2),host(VAR_0))
| ~ setIn(sK4(VAR_0,VAR_1,VAR_2),index(down,host(VAR_2))) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(status,host(VAR_0)) != norm
| index(ldr,host(VAR_0)) != host(VAR_0)
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_2)) != elec_1
| ~ elem(m_Down(VAR_1),queue(host(VAR_2)))
| leq(host(VAR_2),host(VAR_0))
| leq(s(zero),sK4(VAR_0,VAR_1,VAR_2)) )
& ! [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_1
| ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| leq(host(VAR_0),host(VAR_1))
| ~ leq(host(VAR_0),sK4(VAR_1,VAR_2,VAR_0)) )
& ! [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(status,host(VAR_0)) != elec_2
| host(VAR_1) != host(VAR_2)
| ~ elem(m_Down(VAR_1),queue(host(VAR_0)))
| ~ setIn(VAR_0,alive) )
& ! [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] :
( 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
| ~ setIn(VAR_0,alive)
| leq(index(pendack,host(VAR_0)),host(VAR_1)) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ elem(m_Down(VAR_1),queue(host(VAR_2)))
| ~ setIn(VAR_2,alive)
| index(ldr,host(VAR_0)) != host(VAR_0)
| index(status,host(VAR_0)) != norm
| host(VAR_1) != host(VAR_0)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1,VAR_2] :
( leq(index(pendack,host(VAR_1)),host(VAR_0))
| index(status,host(VAR_1)) != elec_2
| host(VAR_2) != host(VAR_1)
| ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1,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,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_Ack(VAR_0,VAR_1),queue(host(VAR_0)))
| ~ 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] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| index(status,host(VAR_0)) != elec_2
| host(VAR_2) != host(VAR_0)
| ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| leq(host(VAR_0),host(VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ setIn(host(VAR_0),index(down,host(VAR_1)))
| ~ setIn(VAR_1,alive)
| index(ldr,host(VAR_0)) != host(VAR_0)
| index(status,host(VAR_0)) != norm
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1] :
( leq(index(pendack,host(VAR_1)),host(VAR_0))
| index(status,host(VAR_1)) != elec_2
| ~ setIn(host(VAR_1),index(down,host(VAR_0)))
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_2 )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_1 )
& ! [VAR_0,VAR_1] :
( ~ elem(m_Ack(VAR_1,VAR_0),queue(host(VAR_1)))
| index(status,host(VAR_0)) != elec_2
| ~ 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] :
( ~ 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_165,negated_conjecture,
( ~ setIn(host(A),index(down,host(B)))
| ~ setIn(B,alive)
| index(ldr,host(A)) != host(A)
| index(status,host(A)) != norm
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_171,negated_conjecture,
( ~ elem(m_Down(B),queue(host(C)))
| ~ setIn(C,alive)
| index(ldr,host(A)) != host(A)
| index(status,host(A)) != norm
| host(B) != host(A)
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_179,negated_conjecture,
cons(m_Down(sK0),sK1) = queue(host(sK2)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_180,negated_conjecture,
queue(host(sK2)) = cons(m_Down(sK0),sK1),
inference(copy,[status(thm)],[c_179]) ).
cnf(c_181,negated_conjecture,
setIn(sK2,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_186,negated_conjecture,
( host(sK0) = A
| setIn(A,index(down,host(sK2)))
| ~ leq(s(zero),A)
| leq(host(sK2),A) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_190,negated_conjecture,
host(sK3) != host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_192,negated_conjecture,
~ leq(s(host(sK2)),host(sK3)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_194,negated_conjecture,
setIn(sK3,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_195,negated_conjecture,
index(ldr,host(sK3)) = host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_196,negated_conjecture,
index(status,host(sK3)) = norm,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_197,negated_conjecture,
norm = index(status,host(sK3)),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_3595,negated_conjecture,
( ~ elem(m_Down(B),queue(host(C)))
| ~ setIn(C,alive)
| index(ldr,host(A)) != host(A)
| index(status,host(A)) != index(status,host(sK3))
| host(B) != host(A)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_197,c_171]) ).
cnf(c_214,negated_conjecture,
( ~ elem(m_Down(B),queue(host(C)))
| ~ setIn(C,alive)
| index(ldr,host(A)) != host(A)
| index(status,host(sK3)) != index(status,host(A))
| host(B) != host(A)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_3595]) ).
cnf(c_3596,negated_conjecture,
( ~ setIn(host(A),index(down,host(B)))
| ~ setIn(B,alive)
| index(ldr,host(A)) != host(A)
| index(status,host(A)) != index(status,host(sK3))
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_197,c_165]) ).
cnf(c_216,negated_conjecture,
( ~ setIn(host(A),index(down,host(B)))
| ~ setIn(B,alive)
| index(ldr,host(A)) != host(A)
| index(status,host(sK3)) != index(status,host(A))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_3596]) ).
cnf(c_219,plain,
s(host(A)) != host(A),
inference(xxres,[status(thm)],[c_61]) ).
cnf(c_3597,plain,
elem(A,cons(init(snoc(A,B)),C)),
inference(resolve,[status(thm)],[c_117,c_108]) ).
cnf(c_243,plain,
elem(A,cons(A,B)),
inference(paramod,[status(thm)],[c_108,c_3597]) ).
cnf(c_313,plain,
( leq(s(A),B)
| leq(B,A)
| s(A) = B ),
inference(resolve,[status(thm)],[c_156,c_149]) ).
cnf(c_335,plain,
( host(sK0) = host(A)
| setIn(host(A),index(down,host(sK2)))
| leq(host(sK2),host(A)) ),
inference(resolve,[status(thm)],[c_186,c_62]) ).
cnf(c_3598,negated_conjecture,
( ~ elem(m_Down(A),queue(host(B)))
| ~ setIn(B,alive)
| index(ldr,host(sK3)) != host(sK3)
| index(status,host(sK3)) != index(status,host(sK3))
| host(A) != host(sK3) ),
inference(resolve,[status(thm)],[c_214,c_194]) ).
cnf(c_3599,negated_conjecture,
( ~ elem(m_Down(A),queue(host(B)))
| ~ setIn(B,alive)
| host(sK3) != host(sK3)
| index(status,host(sK3)) != index(status,host(sK3))
| host(A) != host(sK3) ),
inference(paramod,[status(thm)],[c_195,c_3598]) ).
cnf(c_3600,negated_conjecture,
( ~ elem(m_Down(A),queue(host(B)))
| ~ setIn(B,alive)
| host(sK3) != host(sK3)
| index(status,host(sK3)) != index(status,host(sK3))
| host(sK3) != host(A) ),
inference(copy,[status(thm)],[c_3599]) ).
cnf(c_3601,negated_conjecture,
( ~ elem(m_Down(A),queue(host(B)))
| ~ setIn(B,alive)
| host(sK3) != host(sK3)
| host(sK3) != host(A) ),
inference(copy,[status(thm)],[c_3600]) ).
cnf(c_360,negated_conjecture,
( ~ elem(m_Down(A),queue(host(B)))
| ~ setIn(B,alive)
| host(sK3) != host(A) ),
inference(copy,[status(thm)],[c_3601]) ).
cnf(c_3602,negated_conjecture,
( ~ setIn(host(sK3),index(down,host(A)))
| ~ setIn(A,alive)
| index(ldr,host(sK3)) != host(sK3)
| index(status,host(sK3)) != index(status,host(sK3)) ),
inference(resolve,[status(thm)],[c_216,c_194]) ).
cnf(c_3603,negated_conjecture,
( ~ setIn(host(sK3),index(down,host(A)))
| ~ setIn(A,alive)
| host(sK3) != host(sK3)
| index(status,host(sK3)) != index(status,host(sK3)) ),
inference(paramod,[status(thm)],[c_195,c_3602]) ).
cnf(c_3604,negated_conjecture,
( ~ setIn(host(sK3),index(down,host(A)))
| ~ setIn(A,alive)
| host(sK3) != host(sK3) ),
inference(copy,[status(thm)],[c_3603]) ).
cnf(c_368,negated_conjecture,
( ~ setIn(host(sK3),index(down,host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_3604]) ).
cnf(c_546,plain,
~ setIn(host(sK3),index(down,host(sK2))),
inference(resolve,[status(thm)],[c_368,c_181]) ).
cnf(c_3605,negated_conjecture,
( ~ elem(m_Down(A),queue(host(sK2)))
| host(sK3) != host(A) ),
inference(resolve,[status(thm)],[c_360,c_181]) ).
cnf(c_871,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| host(sK3) != host(A) ),
inference(paramod,[status(thm)],[c_180,c_3605]) ).
cnf(c_956,plain,
host(sK3) != host(sK0),
inference(resolve,[status(thm)],[c_871,c_243]) ).
cnf(c_2743,plain,
( leq(s(host(sK3)),s(host(sK2)))
| s(host(sK3)) = s(host(sK2)) ),
inference(resolve,[status(thm)],[c_313,c_192]) ).
cnf(c_2760,plain,
( leq(host(sK3),host(sK2))
| s(host(sK2)) = host(sK3) ),
inference(resolve,[status(thm)],[c_313,c_192]) ).
cnf(c_3606,plain,
( host(sK0) = host(sK3)
| leq(host(sK2),host(sK3)) ),
inference(resolve,[status(thm)],[c_335,c_546]) ).
cnf(c_3607,plain,
( host(sK3) = host(sK0)
| leq(host(sK2),host(sK3)) ),
inference(copy,[status(thm)],[c_3606]) ).
cnf(c_3545,plain,
leq(host(sK2),host(sK3)),
inference(resolve,[status(thm)],[c_956,c_3607]) ).
cnf(c_3608,plain,
( host(sK2) = host(sK3)
| ~ leq(host(sK3),host(sK2)) ),
inference(resolve,[status(thm)],[c_3545,c_150]) ).
cnf(c_3609,plain,
( host(sK3) = host(sK2)
| ~ leq(host(sK3),host(sK2)) ),
inference(copy,[status(thm)],[c_3608]) ).
cnf(c_3575,negated_conjecture,
~ leq(host(sK3),host(sK2)),
inference(resolve,[status(thm)],[c_190,c_3609]) ).
cnf(c_3576,plain,
s(host(sK2)) = host(sK3),
inference(resolve,[status(thm)],[c_3575,c_2760]) ).
cnf(c_3610,plain,
( leq(s(host(sK3)),s(host(sK2)))
| s(host(sK3)) = host(sK3) ),
inference(paramod,[status(thm)],[c_3576,c_2743]) ).
cnf(c_3611,plain,
( leq(s(host(sK3)),host(sK3))
| s(host(sK3)) = host(sK3) ),
inference(paramod,[status(thm)],[c_3576,c_3610]) ).
cnf(c_3612,plain,
leq(s(host(sK3)),host(sK3)),
inference(resolve,[status(thm)],[c_219,c_3611]) ).
cnf(c_3594,plain,
$false,
inference(resolve,[status(thm)],[c_147,c_3612]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV469+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 13:56:05 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.39 % Process 1482297 was started by sandbox2 on n019,
% 0.12/0.39 % Sat Sep 26 13:56:05 2026
% 0.12/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.41
% 0.12/0.41 % From the command line: assign(max_seconds, 300).
% 10.18/1.72
% 10.18/1.72 % SZS status Theorem for theBenchmark
% 10.18/1.72
% 10.18/1.72 % Proof 1 at 1.05 (+ 0.23) seconds.
% 10.18/1.72 % Length of proof is 46.
% 10.18/1.72 % Level of proof is 10.
% 10.18/1.72 % Maximum clause weight is 48.000.
% 10.18/1.72 % Given clauses 420.
% 10.18/1.72
% 10.18/1.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------