%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV475+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 : n013.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 09:08:02 AM UTC 2026
% Result : Theorem 37.76s 6.11s
% Output : CNFRefutation 37.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 115 ( 46 unt; 0 def)
% Number of atoms : 927 ( 411 equ)
% Maximal formula atoms : 176 ( 8 avg)
% Number of connectives : 1300 ( 488 ~; 444 |; 308 &)
% ( 3 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 22 con; 0-4 aty)
% Number of variables : 376 ( 9 sgn 289 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_02,axiom,
! [P] : leq(s(zero),host(P)),
file('theBenchmark.p',axiom_02) ).
fof(axiom_04,axiom,
! [P] : leq(host(P),nbr_proc),
file('theBenchmark.p',axiom_04) ).
fof(axiom_18,axiom,
! [X,Y] : m_Down(X) != m_Ldr(Y),
file('theBenchmark.p',axiom_18) ).
fof(axiom_47,axiom,
! [X,Y,Q] :
( elem(X,snoc(Q,Y))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_47) ).
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_62,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('theBenchmark.p',axiom_62) ).
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_Ack(W,Y),V)
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid30) = s(host(Pid0))
& elem(m_Down(Pid30),queue(host(Pid0)))
& elem(m_Down(Pid20),queue(host(Pid0)))
& leq(nbr_proc,s(host(Pid0)))
& setIn(Pid0,alive)
& ! [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,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& index(status,host(Z)) = elec_2
& host(Pid30) = host(Pid0)
& elem(m_Down(Pid20),queue(host(Pid0)))
& leq(host(Z),host(Pid0))
& setIn(Z,alive)
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ elem(m_Ack(Z,Pid30),queue(host(Z))) )
& ! [Z,Pid20,Pid0] :
( ( host(index(elid,host(Pid0))) = host(Pid20)
& index(status,host(Pid0)) = wait
& host(Pid20) = host(Z)
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ ( index(ldr,host(Pid20)) = host(Pid20)
& index(status,host(Pid20)) = norm
& setIn(Pid20,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid20)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Z)
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ ( index(ldr,host(Pid20)) = host(Pid20)
& index(status,host(Pid20)) = norm
& setIn(Pid20,alive) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Pid30) = host(Z)
& setIn(Pid20,alive)
& setIn(Z,alive)
& host(Pid20) != host(Z) )
=> ~ ( setIn(host(Pid30),index(down,host(Pid20)))
& elem(m_Down(Pid0),queue(host(Z))) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Pid30) = host(Z)
& setIn(Pid20,alive)
& setIn(Z,alive)
& host(Pid20) != host(Z) )
=> ~ ( elem(m_Down(Pid30),queue(host(Pid20)))
& elem(m_Down(Pid0),queue(host(Z))) ) )
& ! [Z,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive)
& ~ leq(host(Pid20),host(Pid0)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> Pid0 = Z )
& ! [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,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] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> host(Pid0) != host(Z) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W )
=> ( leq(nbr_proc,index(pendack,host(X)))
=> ! [Z] :
( ( host(Z) = host(Y)
| setIn(host(Z),index(acks,host(X))) )
=> ! [V0] :
( host(X) = host(V0)
=> ! [W0,X0,Y0] :
( host(Z) = host(Y0)
=> ( host(X) != host(Y0)
=> ( ( index(status,host(Y0)) = elec_1
& host(W0) = s(host(Y0))
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X)))
& elem(m_Down(W0),snoc(queue(host(Y0)),m_Ldr(X)))
& leq(nbr_proc,s(host(Y0)))
& setIn(Y0,alive)
& ! [V1] :
( ( leq(s(zero),V1)
& ~ leq(host(Y0),V1) )
=> ( V1 = host(X0)
| setIn(V1,index(down,host(Y0))) ) ) )
=> ~ ( host(X) = host(V0)
& setIn(V0,alive) ) ) ) ) ) ) ) ) ) ),
file('theBenchmark.p',conj) ).
fof(conj_neg,negated_conjecture,
~ ! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Ack(W,Y),V)
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid30) = s(host(Pid0))
& elem(m_Down(Pid30),queue(host(Pid0)))
& elem(m_Down(Pid20),queue(host(Pid0)))
& leq(nbr_proc,s(host(Pid0)))
& setIn(Pid0,alive)
& ! [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,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& index(status,host(Z)) = elec_2
& host(Pid30) = host(Pid0)
& elem(m_Down(Pid20),queue(host(Pid0)))
& leq(host(Z),host(Pid0))
& setIn(Z,alive)
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ elem(m_Ack(Z,Pid30),queue(host(Z))) )
& ! [Z,Pid20,Pid0] :
( ( host(index(elid,host(Pid0))) = host(Pid20)
& index(status,host(Pid0)) = wait
& host(Pid20) = host(Z)
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ ( index(ldr,host(Pid20)) = host(Pid20)
& index(status,host(Pid20)) = norm
& setIn(Pid20,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid20)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Z)
& elem(m_Down(Z),queue(host(Pid0)))
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ ( index(ldr,host(Pid20)) = host(Pid20)
& index(status,host(Pid20)) = norm
& setIn(Pid20,alive) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Pid30) = host(Z)
& setIn(Pid20,alive)
& setIn(Z,alive)
& host(Pid20) != host(Z) )
=> ~ ( setIn(host(Pid30),index(down,host(Pid20)))
& elem(m_Down(Pid0),queue(host(Z))) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Pid30) = host(Z)
& setIn(Pid20,alive)
& setIn(Z,alive)
& host(Pid20) != host(Z) )
=> ~ ( elem(m_Down(Pid30),queue(host(Pid20)))
& elem(m_Down(Pid0),queue(host(Z))) ) )
& ! [Z,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive)
& ~ leq(host(Pid20),host(Pid0)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> Pid0 = Z )
& ! [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,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] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> host(Pid0) != host(Z) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W )
=> ( leq(nbr_proc,index(pendack,host(X)))
=> ! [Z] :
( ( host(Z) = host(Y)
| setIn(host(Z),index(acks,host(X))) )
=> ! [V0] :
( host(X) = host(V0)
=> ! [W0,X0,Y0] :
( host(Z) = host(Y0)
=> ( host(X) != host(Y0)
=> ( ( index(status,host(Y0)) = elec_1
& host(W0) = s(host(Y0))
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X)))
& elem(m_Down(W0),snoc(queue(host(Y0)),m_Ldr(X)))
& leq(nbr_proc,s(host(Y0)))
& setIn(Y0,alive)
& ! [V1] :
( ( leq(s(zero),V1)
& ~ leq(host(Y0),V1) )
=> ( V1 = host(X0)
| setIn(V1,index(down,host(Y0))) ) ) )
=> ~ ( host(X) = host(V0)
& setIn(V0,alive) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_62,plain,
leq(s(zero),host(A)),
inference(clausify,[status(thm)],[axiom_02]) ).
cnf(c_64,plain,
leq(host(A),nbr_proc),
inference(clausify,[status(thm)],[axiom_04]) ).
cnf(c_81,plain,
m_Ldr(A) != m_Down(B),
inference(clausify,[status(thm)],[axiom_18]) ).
cnf(c_119,plain,
( elem(A,B)
| C = A
| ~ elem(A,snoc(B,C)) ),
inference(clausify,[status(thm)],[axiom_47]) ).
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_152,plain,
( A != B
| leq(A,B) ),
inference(clausify,[status(thm)],[axiom_61]) ).
cnf(c_153,plain,
( leq(A,C)
| ~ leq(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[axiom_62]) ).
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] :
( ? [V0] :
( ? [W0,X0,Y0] :
( host(V0) = host(X)
& setIn(V0,alive)
& index(status,host(Y0)) = elec_1
& s(host(Y0)) = host(W0)
& elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X)))
& elem(m_Down(W0),snoc(queue(host(Y0)),m_Ldr(X)))
& leq(nbr_proc,s(host(Y0)))
& setIn(Y0,alive)
& ! [V1] :
( host(X0) = V1
| setIn(V1,index(down,host(Y0)))
| ~ leq(s(zero),V1)
| leq(host(Y0),V1) )
& host(Y0) != host(X)
& host(Y0) = host(Z) )
& host(V0) = host(X) )
& ( host(Z) = host(Y)
| setIn(host(Z),index(acks,host(X))) ) )
& leq(nbr_proc,index(pendack,host(X)))
& index(pendack,host(X)) = host(Y)
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W
& setIn(X,alive)
& cons(m_Ack(W,Y),V) = queue(host(X))
& ! [X44,Pid30,Pid20,Pid0] :
( index(status,host(X44)) != norm
| index(ldr,host(X44)) != host(X44)
| ~ setIn(X44,alive)
| index(status,host(Pid0)) != elec_1
| s(host(Pid0)) != host(Pid30)
| ~ elem(m_Down(Pid30),queue(host(Pid0)))
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ leq(nbr_proc,s(host(Pid0)))
| ~ setIn(Pid0,alive)
| ? [X45] :
( host(Pid20) != X45
& ~ setIn(X45,index(down,host(Pid0)))
& leq(s(zero),X45)
& ~ leq(host(Pid0),X45) ) )
& ! [X39,X40,X41,X42] :
( ~ elem(m_Ack(X39,X40),queue(host(X39)))
| index(status,host(X42)) != elec_1
| index(status,host(X39)) != elec_2
| host(X40) != host(X42)
| ~ elem(m_Down(X41),queue(host(X42)))
| ~ leq(host(X39),host(X42))
| ~ setIn(X39,alive)
| ? [X43] :
( host(X41) != X43
& ~ setIn(X43,index(down,host(X42)))
& leq(s(zero),X43)
& ~ leq(host(X42),X43) ) )
& ! [X36,X37,X38] :
( index(ldr,host(X37)) != host(X37)
| index(status,host(X37)) != norm
| ~ setIn(X37,alive)
| host(index(elid,host(X38))) != host(X37)
| index(status,host(X38)) != wait
| host(X37) != host(X36)
| ~ elem(m_Down(X36),queue(host(X38)))
| ~ setIn(X38,alive)
| host(X37) = host(X38) )
& ! [X33,X34,X35] :
( index(ldr,host(X34)) != host(X34)
| index(status,host(X34)) != norm
| ~ setIn(X34,alive)
| index(ldr,host(X35)) != host(X34)
| index(status,host(X35)) != norm
| host(X34) != host(X33)
| ~ elem(m_Down(X33),queue(host(X35)))
| ~ setIn(X35,alive)
| host(X34) = host(X35) )
& ! [X29,X30,X31,X32] :
( ~ setIn(host(X30),index(down,host(X31)))
| ~ elem(m_Down(X32),queue(host(X29)))
| host(X31) != host(X32)
| host(X30) != host(X29)
| ~ setIn(X31,alive)
| ~ setIn(X29,alive)
| host(X31) = host(X29) )
& ! [X25,X26,X27,X28] :
( ~ elem(m_Down(X26),queue(host(X27)))
| ~ elem(m_Down(X28),queue(host(X25)))
| host(X27) != host(X28)
| host(X26) != host(X25)
| ~ setIn(X27,alive)
| ~ setIn(X25,alive)
| host(X27) = host(X25) )
& ! [X22,X23,X24] :
( index(status,host(X22)) != norm
| index(ldr,host(X22)) != host(X22)
| ~ setIn(X22,alive)
| host(X23) != host(X22)
| ~ elem(m_Down(X23),queue(host(X24)))
| ~ setIn(X24,alive)
| leq(host(X23),host(X24)) )
& ! [X20,X21] :
( X21 = X20
| index(ldr,host(X21)) != host(X21)
| index(status,host(X21)) != norm
| index(status,host(X20)) != norm
| index(ldr,host(X20)) != host(X20)
| ~ setIn(X21,alive)
| ~ setIn(X20,alive) )
& ! [X17,X18,X19] :
( ~ elem(m_Down(X18),queue(host(X17)))
| ~ setIn(X17,alive)
| index(ldr,host(X19)) != host(X19)
| index(status,host(X19)) != norm
| host(X18) != host(X19)
| ~ setIn(X19,alive) )
& ! [X14,X15,X16] :
( leq(index(pendack,host(X16)),host(X14))
| index(status,host(X16)) != elec_2
| host(X15) != host(X16)
| ~ elem(m_Down(X15),queue(host(X14)))
| ~ setIn(X16,alive)
| ~ setIn(X14,alive) )
& ! [X12,X13] :
( ~ setIn(host(X13),index(down,host(X12)))
| ~ setIn(X12,alive)
| index(ldr,host(X13)) != host(X13)
| index(status,host(X13)) != norm
| ~ setIn(X13,alive) )
& ! [X10,X11] :
( leq(index(pendack,host(X11)),host(X10))
| index(status,host(X11)) != elec_2
| ~ setIn(host(X11),index(down,host(X10)))
| ~ setIn(X11,alive)
| ~ setIn(X10,alive) )
& ! [X9] :
( index(elid,host(X9)) = X9
| ~ setIn(X9,alive)
| ( index(status,host(X9)) != elec_2
& index(status,host(X9)) != elec_1 ) )
& ! [X7,X8] :
( ~ setIn(X8,alive)
| ~ setIn(X7,alive)
| host(X8) != host(X7)
| X8 = X7 )
& ! [X5,X6] :
( host(X6) != host(X5)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( ~ leq(host(X3),host(X4))
| ~ elem(m_Ldr(X4),queue(host(X3))) ) ),
inference(fof_nnf,[status(thm)],[conj_neg]) ).
fof(sk_conj_neg_sk,plain,
( host(sK10) = host(sK0)
& setIn(sK10,alive)
& index(status,host(sK3)) = elec_1
& s(host(sK3)) = host(sK6)
& elem(m_Down(sK5),snoc(queue(host(sK3)),m_Ldr(sK0)))
& elem(m_Down(sK6),snoc(queue(host(sK3)),m_Ldr(sK0)))
& leq(nbr_proc,s(host(sK3)))
& setIn(sK3,alive)
& ! [V1] :
( host(sK5) = V1
| setIn(V1,index(down,host(sK3)))
| ~ leq(s(zero),V1)
| leq(host(sK3),V1) )
& host(sK3) != host(sK0)
& host(sK3) = host(sK4)
& host(sK10) = host(sK0)
& ( host(sK4) = host(sK2)
| setIn(host(sK4),index(acks,host(sK0))) )
& leq(nbr_proc,index(pendack,host(sK0)))
& index(pendack,host(sK0)) = host(sK2)
& index(status,host(sK0)) = elec_2
& index(elid,host(sK0)) = sK1
& setIn(sK0,alive)
& cons(m_Ack(sK1,sK2),sK9) = queue(host(sK0))
& ! [X44,Pid30,Pid20,Pid0] :
( index(status,host(X44)) != norm
| index(ldr,host(X44)) != host(X44)
| ~ setIn(X44,alive)
| index(status,host(Pid0)) != elec_1
| s(host(Pid0)) != host(Pid30)
| ~ elem(m_Down(Pid30),queue(host(Pid0)))
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ leq(nbr_proc,s(host(Pid0)))
| ~ setIn(Pid0,alive)
| ( host(Pid20) != sK8(X44,Pid30,Pid20,Pid0)
& ~ setIn(sK8(X44,Pid30,Pid20,Pid0),index(down,host(Pid0)))
& leq(s(zero),sK8(X44,Pid30,Pid20,Pid0))
& ~ leq(host(Pid0),sK8(X44,Pid30,Pid20,Pid0)) ) )
& ! [X39,X40,X41,X42] :
( ~ elem(m_Ack(X39,X40),queue(host(X39)))
| index(status,host(X42)) != elec_1
| index(status,host(X39)) != elec_2
| host(X40) != host(X42)
| ~ elem(m_Down(X41),queue(host(X42)))
| ~ leq(host(X39),host(X42))
| ~ setIn(X39,alive)
| ( host(X41) != sK7(X39,X40,X41,X42)
& ~ setIn(sK7(X39,X40,X41,X42),index(down,host(X42)))
& leq(s(zero),sK7(X39,X40,X41,X42))
& ~ leq(host(X42),sK7(X39,X40,X41,X42)) ) )
& ! [X36,X37,X38] :
( index(ldr,host(X37)) != host(X37)
| index(status,host(X37)) != norm
| ~ setIn(X37,alive)
| host(index(elid,host(X38))) != host(X37)
| index(status,host(X38)) != wait
| host(X37) != host(X36)
| ~ elem(m_Down(X36),queue(host(X38)))
| ~ setIn(X38,alive)
| host(X37) = host(X38) )
& ! [X33,X34,X35] :
( index(ldr,host(X34)) != host(X34)
| index(status,host(X34)) != norm
| ~ setIn(X34,alive)
| index(ldr,host(X35)) != host(X34)
| index(status,host(X35)) != norm
| host(X34) != host(X33)
| ~ elem(m_Down(X33),queue(host(X35)))
| ~ setIn(X35,alive)
| host(X34) = host(X35) )
& ! [X29,X30,X31,X32] :
( ~ setIn(host(X30),index(down,host(X31)))
| ~ elem(m_Down(X32),queue(host(X29)))
| host(X31) != host(X32)
| host(X30) != host(X29)
| ~ setIn(X31,alive)
| ~ setIn(X29,alive)
| host(X31) = host(X29) )
& ! [X25,X26,X27,X28] :
( ~ elem(m_Down(X26),queue(host(X27)))
| ~ elem(m_Down(X28),queue(host(X25)))
| host(X27) != host(X28)
| host(X26) != host(X25)
| ~ setIn(X27,alive)
| ~ setIn(X25,alive)
| host(X27) = host(X25) )
& ! [X22,X23,X24] :
( index(status,host(X22)) != norm
| index(ldr,host(X22)) != host(X22)
| ~ setIn(X22,alive)
| host(X23) != host(X22)
| ~ elem(m_Down(X23),queue(host(X24)))
| ~ setIn(X24,alive)
| leq(host(X23),host(X24)) )
& ! [X20,X21] :
( X21 = X20
| index(ldr,host(X21)) != host(X21)
| index(status,host(X21)) != norm
| index(status,host(X20)) != norm
| index(ldr,host(X20)) != host(X20)
| ~ setIn(X21,alive)
| ~ setIn(X20,alive) )
& ! [X17,X18,X19] :
( ~ elem(m_Down(X18),queue(host(X17)))
| ~ setIn(X17,alive)
| index(ldr,host(X19)) != host(X19)
| index(status,host(X19)) != norm
| host(X18) != host(X19)
| ~ setIn(X19,alive) )
& ! [X14,X15,X16] :
( leq(index(pendack,host(X16)),host(X14))
| index(status,host(X16)) != elec_2
| host(X15) != host(X16)
| ~ elem(m_Down(X15),queue(host(X14)))
| ~ setIn(X16,alive)
| ~ setIn(X14,alive) )
& ! [X12,X13] :
( ~ setIn(host(X13),index(down,host(X12)))
| ~ setIn(X12,alive)
| index(ldr,host(X13)) != host(X13)
| index(status,host(X13)) != norm
| ~ setIn(X13,alive) )
& ! [X10,X11] :
( leq(index(pendack,host(X11)),host(X10))
| index(status,host(X11)) != elec_2
| ~ setIn(host(X11),index(down,host(X10)))
| ~ setIn(X11,alive)
| ~ setIn(X10,alive) )
& ! [X9] :
( index(elid,host(X9)) = X9
| ~ setIn(X9,alive)
| ( index(status,host(X9)) != elec_2
& index(status,host(X9)) != elec_1 ) )
& ! [X7,X8] :
( ~ setIn(X8,alive)
| ~ setIn(X7,alive)
| host(X8) != host(X7)
| X8 = X7 )
& ! [X5,X6] :
( host(X6) != host(X5)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( ~ leq(host(X3),host(X4))
| ~ elem(m_Ldr(X4),queue(host(X3))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK1,sK2,sK9,sK0,sK4,sK10,sK3,sK5,sK6]),skolemize(V,sK9),skolemize(W,sK1),skolemize(X,sK0),skolemize(Y,sK2),skolemize(X43,sK7(X39,X40,X41,X42)),skolemize(X45,sK8(X44,Pid30,Pid20,Pid0)),skolemize(Z,sK4),skolemize(V0,sK10),skolemize(W0,sK6),skolemize(X0,sK5),skolemize(Y0,sK3)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( setIn(sK10,alive)
& index(status,host(sK3)) = elec_1
& s(host(sK3)) = host(sK6)
& elem(m_Down(sK5),snoc(queue(host(sK3)),m_Ldr(sK0)))
& elem(m_Down(sK6),snoc(queue(host(sK3)),m_Ldr(sK0)))
& leq(nbr_proc,s(host(sK3)))
& setIn(sK3,alive)
& ! [VAR_0] :
( host(sK5) = VAR_0
| setIn(VAR_0,index(down,host(sK3)))
| ~ leq(s(zero),VAR_0)
| leq(host(sK3),VAR_0) )
& host(sK3) != host(sK0)
& host(sK3) = host(sK4)
& host(sK10) = host(sK0)
& ( host(sK4) = host(sK2)
| setIn(host(sK4),index(acks,host(sK0))) )
& leq(nbr_proc,index(pendack,host(sK0)))
& index(pendack,host(sK0)) = host(sK2)
& index(status,host(sK0)) = elec_2
& index(elid,host(sK0)) = sK1
& setIn(sK0,alive)
& cons(m_Ack(sK1,sK2),sK9) = queue(host(sK0))
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( index(status,host(VAR_1)) != norm
| index(ldr,host(VAR_1)) != host(VAR_1)
| ~ setIn(VAR_1,alive)
| index(status,host(VAR_3)) != elec_1
| s(host(VAR_3)) != host(VAR_2)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ elem(m_Down(VAR_0),queue(host(VAR_3)))
| ~ leq(nbr_proc,s(host(VAR_3)))
| ~ setIn(VAR_3,alive)
| host(VAR_0) != sK8(VAR_1,VAR_2,VAR_0,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( index(status,host(VAR_0)) != norm
| index(ldr,host(VAR_0)) != host(VAR_0)
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_3)) != elec_1
| s(host(VAR_3)) != host(VAR_1)
| ~ elem(m_Down(VAR_1),queue(host(VAR_3)))
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ leq(nbr_proc,s(host(VAR_3)))
| ~ setIn(VAR_3,alive)
| ~ setIn(sK8(VAR_0,VAR_1,VAR_2,VAR_3),index(down,host(VAR_3))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( index(status,host(VAR_0)) != norm
| index(ldr,host(VAR_0)) != host(VAR_0)
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_3)) != elec_1
| s(host(VAR_3)) != host(VAR_1)
| ~ elem(m_Down(VAR_1),queue(host(VAR_3)))
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ leq(nbr_proc,s(host(VAR_3)))
| ~ setIn(VAR_3,alive)
| leq(s(zero),sK8(VAR_0,VAR_1,VAR_2,VAR_3)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( 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
| s(host(VAR_0)) != host(VAR_2)
| ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| ~ elem(m_Down(VAR_3),queue(host(VAR_0)))
| ~ leq(nbr_proc,s(host(VAR_0)))
| ~ setIn(VAR_0,alive)
| ~ leq(host(VAR_0),sK8(VAR_1,VAR_2,VAR_3,VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Ack(VAR_1,VAR_2),queue(host(VAR_1)))
| index(status,host(VAR_3)) != elec_1
| index(status,host(VAR_1)) != elec_2
| host(VAR_2) != host(VAR_3)
| ~ elem(m_Down(VAR_0),queue(host(VAR_3)))
| ~ leq(host(VAR_1),host(VAR_3))
| ~ setIn(VAR_1,alive)
| host(VAR_0) != sK7(VAR_1,VAR_2,VAR_0,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_0)))
| index(status,host(VAR_3)) != elec_1
| index(status,host(VAR_0)) != elec_2
| host(VAR_1) != host(VAR_3)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ leq(host(VAR_0),host(VAR_3))
| ~ setIn(VAR_0,alive)
| ~ setIn(sK7(VAR_0,VAR_1,VAR_2,VAR_3),index(down,host(VAR_3))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_0)))
| index(status,host(VAR_3)) != elec_1
| index(status,host(VAR_0)) != elec_2
| host(VAR_1) != host(VAR_3)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ leq(host(VAR_0),host(VAR_3))
| ~ setIn(VAR_0,alive)
| leq(s(zero),sK7(VAR_0,VAR_1,VAR_2,VAR_3)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Ack(VAR_1,VAR_2),queue(host(VAR_1)))
| index(status,host(VAR_0)) != elec_1
| index(status,host(VAR_1)) != elec_2
| host(VAR_2) != host(VAR_0)
| ~ elem(m_Down(VAR_3),queue(host(VAR_0)))
| ~ leq(host(VAR_1),host(VAR_0))
| ~ setIn(VAR_1,alive)
| ~ leq(host(VAR_0),sK7(VAR_1,VAR_2,VAR_3,VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(ldr,host(VAR_0)) != host(VAR_0)
| index(status,host(VAR_0)) != norm
| ~ setIn(VAR_0,alive)
| host(index(elid,host(VAR_1))) != host(VAR_0)
| index(status,host(VAR_1)) != wait
| host(VAR_0) != host(VAR_2)
| ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(ldr,host(VAR_0)) != host(VAR_0)
| index(status,host(VAR_0)) != norm
| ~ setIn(VAR_0,alive)
| index(ldr,host(VAR_1)) != host(VAR_0)
| index(status,host(VAR_1)) != norm
| host(VAR_0) != host(VAR_2)
| ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ setIn(host(VAR_2),index(down,host(VAR_0)))
| ~ elem(m_Down(VAR_3),queue(host(VAR_1)))
| host(VAR_0) != host(VAR_3)
| host(VAR_2) != host(VAR_1)
| ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| ~ elem(m_Down(VAR_3),queue(host(VAR_1)))
| host(VAR_0) != host(VAR_3)
| host(VAR_2) != host(VAR_1)
| ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(status,host(VAR_2)) != norm
| index(ldr,host(VAR_2)) != host(VAR_2)
| ~ setIn(VAR_2,alive)
| host(VAR_0) != host(VAR_2)
| ~ elem(m_Down(VAR_0),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| leq(host(VAR_0),host(VAR_1)) )
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| index(ldr,host(VAR_1)) != host(VAR_1)
| index(status,host(VAR_1)) != norm
| index(status,host(VAR_0)) != norm
| index(ldr,host(VAR_0)) != host(VAR_0)
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [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] :
( ~ 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] :
( ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) != host(VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( host(VAR_0) != host(VAR_1)
| ~ elem(m_Down(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Ldr(VAR_0),queue(host(VAR_1))) ) ),
inference(cnf_transformation,[status(thm)],[sk_conj_neg_sk]) ).
cnf(c_163,negated_conjecture,
( index(elid,host(A)) = A
| ~ setIn(A,alive)
| index(status,host(A)) != elec_2 ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_164,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != elec_2
| ~ setIn(host(B),index(down,host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_166,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != elec_2
| host(C) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_184,negated_conjecture,
setIn(sK0,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_185,negated_conjecture,
index(elid,host(sK0)) = sK1,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_186,negated_conjecture,
index(status,host(sK0)) = elec_2,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_187,negated_conjecture,
elec_2 = index(status,host(sK0)),
inference(copy,[status(thm)],[c_186]) ).
cnf(c_188,negated_conjecture,
index(pendack,host(sK0)) = host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_189,negated_conjecture,
leq(nbr_proc,index(pendack,host(sK0))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_190,negated_conjecture,
leq(nbr_proc,host(sK2)),
inference(paramod,[status(thm)],[c_188,c_189]) ).
cnf(c_193,negated_conjecture,
host(sK3) = host(sK4),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_194,negated_conjecture,
host(sK3) != host(sK0),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_195,negated_conjecture,
host(sK4) != host(sK0),
inference(paramod,[status(thm)],[c_193,c_194]) ).
cnf(c_196,negated_conjecture,
( host(sK5) = A
| setIn(A,index(down,host(sK3)))
| ~ leq(s(zero),A)
| leq(host(sK3),A) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_6901,negated_conjecture,
( host(sK5) = A
| setIn(A,index(down,host(sK3)))
| ~ leq(s(zero),A)
| leq(host(sK4),A) ),
inference(paramod,[status(thm)],[c_193,c_196]) ).
cnf(c_197,negated_conjecture,
( host(sK5) = A
| setIn(A,index(down,host(sK4)))
| ~ leq(s(zero),A)
| leq(host(sK4),A) ),
inference(paramod,[status(thm)],[c_193,c_6901]) ).
cnf(c_198,negated_conjecture,
setIn(sK3,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_199,negated_conjecture,
leq(nbr_proc,s(host(sK3))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_200,negated_conjecture,
leq(nbr_proc,s(host(sK4))),
inference(paramod,[status(thm)],[c_193,c_199]) ).
cnf(c_201,negated_conjecture,
elem(m_Down(sK6),snoc(queue(host(sK3)),m_Ldr(sK0))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_202,negated_conjecture,
elem(m_Down(sK6),snoc(queue(host(sK4)),m_Ldr(sK0))),
inference(paramod,[status(thm)],[c_193,c_201]) ).
cnf(c_203,negated_conjecture,
elem(m_Down(sK5),snoc(queue(host(sK3)),m_Ldr(sK0))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_204,negated_conjecture,
elem(m_Down(sK5),snoc(queue(host(sK4)),m_Ldr(sK0))),
inference(paramod,[status(thm)],[c_193,c_203]) ).
cnf(c_205,negated_conjecture,
s(host(sK3)) = host(sK6),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_206,negated_conjecture,
s(host(sK4)) = host(sK6),
inference(paramod,[status(thm)],[c_193,c_205]) ).
cnf(c_6902,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != index(status,host(sK0))
| host(C) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_187,c_166]) ).
cnf(c_225,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(sK0)) != index(status,host(B))
| host(C) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_6902]) ).
cnf(c_6903,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != index(status,host(sK0))
| ~ setIn(host(B),index(down,host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_187,c_164]) ).
cnf(c_226,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(sK0)) != index(status,host(B))
| ~ setIn(host(B),index(down,host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_6903]) ).
cnf(c_6904,negated_conjecture,
( index(elid,host(A)) = A
| ~ setIn(A,alive)
| index(status,host(A)) != index(status,host(sK0)) ),
inference(paramod,[status(thm)],[c_187,c_163]) ).
cnf(c_227,negated_conjecture,
( index(elid,host(A)) = A
| ~ setIn(A,alive)
| index(status,host(sK0)) != index(status,host(A)) ),
inference(copy,[status(thm)],[c_6904]) ).
cnf(c_231,negated_conjecture,
leq(nbr_proc,host(sK6)),
inference(paramod,[status(thm)],[c_206,c_200]) ).
cnf(c_333,plain,
( leq(host(B),A)
| ~ leq(nbr_proc,A) ),
inference(resolve,[status(thm)],[c_153,c_64]) ).
cnf(c_343,plain,
( leq(s(A),B)
| leq(B,A)
| s(A) = B ),
inference(resolve,[status(thm)],[c_156,c_149]) ).
cnf(c_6905,negated_conjecture,
( nbr_proc = host(sK2)
| ~ leq(host(sK2),nbr_proc) ),
inference(resolve,[status(thm)],[c_190,c_150]) ).
cnf(c_6906,negated_conjecture,
( host(sK2) = nbr_proc
| ~ leq(host(sK2),nbr_proc) ),
inference(copy,[status(thm)],[c_6905]) ).
cnf(c_371,negated_conjecture,
host(sK2) = nbr_proc,
inference(resolve,[status(thm)],[c_64,c_6906]) ).
cnf(c_373,negated_conjecture,
index(pendack,host(sK0)) = nbr_proc,
inference(paramod,[status(thm)],[c_371,c_188]) ).
cnf(c_395,plain,
( host(sK5) = host(A)
| setIn(host(A),index(down,host(sK4)))
| leq(host(sK4),host(A)) ),
inference(resolve,[status(thm)],[c_197,c_62]) ).
cnf(c_6907,negated_conjecture,
( elem(m_Down(sK6),queue(host(sK4)))
| m_Ldr(sK0) = m_Down(sK6) ),
inference(resolve,[status(thm)],[c_202,c_119]) ).
cnf(c_407,negated_conjecture,
elem(m_Down(sK6),queue(host(sK4))),
inference(resolve,[status(thm)],[c_81,c_6907]) ).
cnf(c_6908,negated_conjecture,
( elem(m_Down(sK5),queue(host(sK4)))
| m_Ldr(sK0) = m_Down(sK5) ),
inference(resolve,[status(thm)],[c_204,c_119]) ).
cnf(c_413,negated_conjecture,
elem(m_Down(sK5),queue(host(sK4))),
inference(resolve,[status(thm)],[c_81,c_6908]) ).
cnf(c_415,plain,
~ leq(host(sK6),host(sK4)),
inference(paramod,[status(thm)],[c_206,c_147]) ).
cnf(c_6909,negated_conjecture,
( leq(index(pendack,host(sK0)),host(A))
| index(status,host(sK0)) != index(status,host(sK0))
| host(B) != host(sK0)
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(resolve,[status(thm)],[c_225,c_184]) ).
cnf(c_6910,negated_conjecture,
( leq(nbr_proc,host(A))
| index(status,host(sK0)) != index(status,host(sK0))
| host(B) != host(sK0)
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_373,c_6909]) ).
cnf(c_6911,negated_conjecture,
( leq(nbr_proc,host(A))
| index(status,host(sK0)) != index(status,host(sK0))
| host(sK0) != host(B)
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_6910]) ).
cnf(c_475,negated_conjecture,
( leq(nbr_proc,host(A))
| host(sK0) != host(B)
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_6911]) ).
cnf(c_6912,negated_conjecture,
( leq(index(pendack,host(sK0)),host(A))
| index(status,host(sK0)) != index(status,host(sK0))
| ~ setIn(host(sK0),index(down,host(A)))
| ~ setIn(A,alive) ),
inference(resolve,[status(thm)],[c_226,c_184]) ).
cnf(c_6913,negated_conjecture,
( leq(nbr_proc,host(A))
| index(status,host(sK0)) != index(status,host(sK0))
| ~ setIn(host(sK0),index(down,host(A)))
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_373,c_6912]) ).
cnf(c_479,negated_conjecture,
( leq(nbr_proc,host(A))
| ~ setIn(host(sK0),index(down,host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_6913]) ).
cnf(c_6914,plain,
( index(elid,host(sK0)) = sK0
| ~ setIn(sK0,alive) ),
inference(xxres,[status(thm)],[c_227]) ).
cnf(c_6915,plain,
( sK1 = sK0
| ~ setIn(sK0,alive) ),
inference(paramod,[status(thm)],[c_185,c_6914]) ).
cnf(c_6916,plain,
( sK0 = sK1
| ~ setIn(sK0,alive) ),
inference(copy,[status(thm)],[c_6915]) ).
cnf(c_480,negated_conjecture,
sK0 = sK1,
inference(resolve,[status(thm)],[c_184,c_6916]) ).
cnf(c_483,negated_conjecture,
( leq(nbr_proc,host(A))
| ~ setIn(host(sK1),index(down,host(A)))
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_480,c_479]) ).
cnf(c_487,negated_conjecture,
( leq(nbr_proc,host(A))
| host(sK1) != host(B)
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_480,c_475]) ).
cnf(c_560,negated_conjecture,
host(sK4) != host(sK1),
inference(paramod,[status(thm)],[c_480,c_195]) ).
cnf(c_6917,negated_conjecture,
( nbr_proc = host(sK6)
| ~ leq(host(sK6),nbr_proc) ),
inference(resolve,[status(thm)],[c_231,c_150]) ).
cnf(c_6918,negated_conjecture,
( host(sK6) = nbr_proc
| ~ leq(host(sK6),nbr_proc) ),
inference(copy,[status(thm)],[c_6917]) ).
cnf(c_568,negated_conjecture,
host(sK6) = nbr_proc,
inference(resolve,[status(thm)],[c_64,c_6918]) ).
cnf(c_581,plain,
~ leq(nbr_proc,host(sK4)),
inference(paramod,[status(thm)],[c_568,c_415]) ).
cnf(c_583,negated_conjecture,
s(host(sK4)) = nbr_proc,
inference(paramod,[status(thm)],[c_568,c_206]) ).
cnf(c_6919,plain,
( leq(s(B),A)
| leq(s(B),A)
| leq(A,B) ),
inference(resolve,[status(thm)],[c_343,c_152]) ).
cnf(c_3070,plain,
( leq(s(B),A)
| leq(A,B) ),
inference(copy,[status(thm)],[c_6919]) ).
cnf(c_3244,plain,
( leq(host(B),A)
| leq(s(A),nbr_proc) ),
inference(resolve,[status(thm)],[c_3070,c_333]) ).
cnf(c_3278,plain,
( A = B
| ~ leq(A,B)
| leq(s(A),B) ),
inference(resolve,[status(thm)],[c_3070,c_150]) ).
cnf(c_3323,plain,
( leq(B,A)
| ~ leq(B,host(C))
| leq(s(A),nbr_proc) ),
inference(resolve,[status(thm)],[c_3244,c_153]) ).
cnf(c_6920,plain,
( ~ leq(s(nbr_proc),host(A))
| leq(s(nbr_proc),nbr_proc) ),
inference(factor,[status(thm)],[c_3323]) ).
cnf(c_3326,plain,
~ leq(s(nbr_proc),host(A)),
inference(resolve,[status(thm)],[c_147,c_6920]) ).
cnf(c_6921,negated_conjecture,
( leq(nbr_proc,host(sK3))
| ~ setIn(host(sK1),index(down,host(sK3))) ),
inference(resolve,[status(thm)],[c_483,c_198]) ).
cnf(c_6922,negated_conjecture,
( leq(nbr_proc,host(sK3))
| ~ setIn(host(sK1),index(down,host(sK4))) ),
inference(paramod,[status(thm)],[c_193,c_6921]) ).
cnf(c_6923,negated_conjecture,
( leq(nbr_proc,host(sK4))
| ~ setIn(host(sK1),index(down,host(sK4))) ),
inference(paramod,[status(thm)],[c_193,c_6922]) ).
cnf(c_6607,negated_conjecture,
~ setIn(host(sK1),index(down,host(sK4))),
inference(resolve,[status(thm)],[c_581,c_6923]) ).
cnf(c_6615,plain,
( host(sK5) = host(sK1)
| leq(host(sK4),host(sK1)) ),
inference(resolve,[status(thm)],[c_6607,c_395]) ).
cnf(c_6924,plain,
( host(sK4) = host(sK1)
| leq(s(host(sK4)),host(sK1))
| host(sK5) = host(sK1) ),
inference(resolve,[status(thm)],[c_6615,c_3278]) ).
cnf(c_6925,plain,
( host(sK4) = host(sK1)
| leq(nbr_proc,host(sK1))
| host(sK5) = host(sK1) ),
inference(paramod,[status(thm)],[c_583,c_6924]) ).
cnf(c_6637,negated_conjecture,
( leq(nbr_proc,host(sK1))
| host(sK5) = host(sK1) ),
inference(resolve,[status(thm)],[c_560,c_6925]) ).
cnf(c_6926,plain,
( nbr_proc = host(sK1)
| leq(s(nbr_proc),host(sK1))
| host(sK5) = host(sK1) ),
inference(resolve,[status(thm)],[c_6637,c_3278]) ).
cnf(c_6927,plain,
( host(sK1) = nbr_proc
| leq(s(nbr_proc),host(sK1))
| host(sK5) = host(sK1) ),
inference(copy,[status(thm)],[c_6926]) ).
cnf(c_6739,plain,
( host(sK1) = nbr_proc
| host(sK5) = host(sK1) ),
inference(resolve,[status(thm)],[c_3326,c_6927]) ).
cnf(c_6928,negated_conjecture,
( leq(nbr_proc,host(sK3))
| host(sK1) != host(A)
| ~ elem(m_Down(A),queue(host(sK3))) ),
inference(resolve,[status(thm)],[c_487,c_198]) ).
cnf(c_6929,negated_conjecture,
( leq(nbr_proc,host(sK3))
| host(sK1) != host(A)
| ~ elem(m_Down(A),queue(host(sK4))) ),
inference(paramod,[status(thm)],[c_193,c_6928]) ).
cnf(c_6930,negated_conjecture,
( leq(nbr_proc,host(sK4))
| host(sK1) != host(A)
| ~ elem(m_Down(A),queue(host(sK4))) ),
inference(paramod,[status(thm)],[c_193,c_6929]) ).
cnf(c_6850,negated_conjecture,
( host(sK1) != host(A)
| ~ elem(m_Down(A),queue(host(sK4))) ),
inference(resolve,[status(thm)],[c_581,c_6930]) ).
cnf(c_6931,plain,
host(sK1) != host(sK5),
inference(resolve,[status(thm)],[c_6850,c_413]) ).
cnf(c_6875,plain,
host(sK5) != host(sK1),
inference(copy,[status(thm)],[c_6931]) ).
cnf(c_6932,plain,
host(sK1) != host(sK6),
inference(resolve,[status(thm)],[c_6850,c_407]) ).
cnf(c_6876,plain,
host(sK1) != nbr_proc,
inference(paramod,[status(thm)],[c_568,c_6932]) ).
cnf(c_6933,plain,
host(sK1) = nbr_proc,
inference(resolve,[status(thm)],[c_6875,c_6739]) ).
cnf(c_6900,plain,
$false,
inference(resolve,[status(thm)],[c_6876,c_6933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV475+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.62 % Computer : n013.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Sat Sep 26 13:56:07 UTC 2026
% 0.15/0.63 % CPUTime :
% 0.15/0.63 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.63 % Process 2876052 was started by sandbox on n013,
% 0.15/0.63 % Sat Sep 26 13:56:07 2026
% 0.15/0.63 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.66
% 0.20/0.66 % From the command line: assign(max_seconds, 300).
% 37.76/6.11
% 37.76/6.11 % given #500 (F,wt=27): 4880 -setIn(c5,alive) | -setIn(c7,alive) | host(c5) != host(A) | -setIn(host(A),index(down,nbr_proc)). [resolve(355,e,407,a),rewrite([568(2),568(18)]),flip(a),flip(d),unit_del(a,582)].
% 37.76/6.11
% 37.76/6.11 % SZS status Theorem for theBenchmark
% 37.76/6.11
% 37.76/6.11 % Proof 1 at 4.40 (+ 0.97) seconds.
% 37.76/6.11 % Length of proof is 78.
% 37.76/6.11 % Level of proof is 11.
% 37.76/6.11 % Maximum clause weight is 48.000.
% 37.76/6.11 % Given clauses 657.
% 37.76/6.11
% 37.76/6.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------