%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV458+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 : n026.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 24.41s 13.90s
% Output : CNFRefutation 24.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 102 ( 28 unt; 0 def)
% Number of atoms : 852 ( 372 equ)
% Maximal formula atoms : 118 ( 8 avg)
% Number of connectives : 1259 ( 509 ~; 449 |; 241 &)
% ( 3 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 18 con; 0-3 aty)
% Number of variables : 360 ( 8 sgn 221 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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_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_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
& elem(m_Halt(Pid0),queue(host(Pid20)))
& setIn(Pid0,alive)
& ~ leq(index(pendack,host(Pid0)),host(Z)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0))) )
& ! [Z,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,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] :
( ( 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] :
( ( host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& leq(Pid0,Z)
& ~ setIn(Z,alive) )
=> ~ setIn(Pid0,alive) )
& ! [Z,Pid20,Pid0] :
( elem(m_Ack(Pid0,Z),queue(host(Pid20)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Halt(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> ~ setIn(Pid0,alive) )
& ! [Z] : leq(index(pendack,host(Z)),nbr_proc) )
=> ( 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] :
( s(host(X)) = host(W0)
=> ( host(X) != host(W0)
=> ! [X0] :
( host(X) = host(X0)
=> ( ( elem(m_Halt(X0),snoc(queue(host(W0)),m_Halt(X)))
& setIn(X0,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
& elem(m_Halt(Pid0),queue(host(Pid20)))
& setIn(Pid0,alive)
& ~ leq(index(pendack,host(Pid0)),host(Z)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0))) )
& ! [Z,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,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] :
( ( 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] :
( ( host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& leq(Pid0,Z)
& ~ setIn(Z,alive) )
=> ~ setIn(Pid0,alive) )
& ! [Z,Pid20,Pid0] :
( elem(m_Ack(Pid0,Z),queue(host(Pid20)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Halt(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> ~ setIn(Pid0,alive) )
& ! [Z] : leq(index(pendack,host(Z)),nbr_proc) )
=> ( 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] :
( s(host(X)) = host(W0)
=> ( host(X) != host(W0)
=> ! [X0] :
( host(X) = host(X0)
=> ( ( elem(m_Halt(X0),snoc(queue(host(W0)),m_Halt(X)))
& setIn(X0,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_106,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_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] :
( ? [W0] :
( ? [X0] :
( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive)
& elem(m_Halt(X0),snoc(queue(host(W0)),m_Halt(X)))
& setIn(X0,alive)
& ~ leq(s(host(X)),host(Z))
& host(X0) = host(X) )
& host(W0) != host(X)
& s(host(X)) = host(W0) )
& host(Z) != host(X) )
& ~ leq(nbr_proc,host(X))
& index(status,host(X)) = elec_1
& ! [X36] :
( host(Y) = X36
| setIn(X36,index(down,host(X)))
| ~ leq(s(zero),X36)
| leq(host(X),X36) )
& ( 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))
& ! [X35,Pid20,Pid0] :
( index(status,host(X35)) != norm
| index(ldr,host(X35)) != host(X35)
| ~ setIn(X35,alive)
| index(status,host(Pid0)) != elec_1
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| leq(host(Pid0),host(X35))
| ? [V0] :
( host(Pid20) != V0
& ~ setIn(V0,index(down,host(Pid0)))
& leq(s(zero),V0)
& ~ leq(host(Pid0),V0) ) )
& ! [X32,X33,X34] :
( index(status,host(X32)) != norm
| index(ldr,host(X32)) != host(X32)
| ~ setIn(X32,alive)
| index(status,host(X34)) != elec_2
| ~ elem(m_Halt(X34),queue(host(X33)))
| ~ setIn(X34,alive)
| leq(index(pendack,host(X34)),host(X32)) )
& ! [X30,X31] :
( ~ leq(index(pendack,host(X30)),index(pendack,host(X31)))
| index(status,host(X31)) != elec_2
| index(status,host(X30)) != elec_2
| ~ setIn(X31,alive)
| ~ setIn(X30,alive)
| leq(host(X30),host(X31)) )
& ! [X28,X29] :
( X29 = X28
| index(ldr,host(X29)) != host(X29)
| index(status,host(X29)) != norm
| index(status,host(X28)) != norm
| index(ldr,host(X28)) != host(X28)
| ~ setIn(X29,alive)
| ~ setIn(X28,alive) )
& ! [X26,X27] :
( index(status,host(X26)) != norm
| index(ldr,host(X26)) != host(X26)
| ~ setIn(X26,alive)
| index(status,host(X27)) != elec_2
| ~ setIn(X27,alive)
| leq(index(pendack,host(X27)),host(X26)) )
& ! [X23,X24,X25] :
( index(status,host(X23)) != norm
| index(ldr,host(X23)) != host(X23)
| ~ setIn(X23,alive)
| host(X24) != host(X23)
| ~ elem(m_Ack(X25,X24),queue(host(X25)))
| ~ setIn(X25,alive) )
& ! [X21,X22] :
( leq(index(pendack,host(X22)),host(X21))
| index(status,host(X22)) != elec_2
| index(status,host(X21)) != elec_2
| ~ setIn(X22,alive)
| ~ setIn(X21,alive)
| leq(host(X21),host(X22)) )
& ! [X18,X19,X20] :
( index(status,host(X18)) != norm
| index(ldr,host(X18)) != host(X18)
| ~ setIn(X18,alive)
| host(X19) != host(X18)
| ~ elem(m_Down(X19),queue(host(X20)))
| ~ setIn(X20,alive) )
& ! [X17] :
( index(elid,host(X17)) = X17
| ~ setIn(X17,alive)
| ( index(status,host(X17)) != elec_2
& index(status,host(X17)) != elec_1 ) )
& ! [X15,X16] :
( ~ setIn(X16,alive)
| ~ setIn(X15,alive)
| host(X16) != host(X15)
| X16 = X15 )
& ! [X13,X14] :
( ~ setIn(X14,alive)
| host(X14) != host(X13)
| ~ leq(X14,X13)
| setIn(X13,alive) )
& ! [X10,X11,X12] :
( ~ leq(host(X10),host(X12))
| ~ elem(m_Ack(X12,X10),queue(host(X11))) )
& ! [X8,X9] :
( ~ leq(host(X8),host(X9))
| ~ elem(m_Halt(X9),queue(host(X8))) )
& ! [X6,X7] :
( ~ leq(host(X6),host(X7))
| ~ elem(m_Ldr(X7),queue(host(X6))) )
& ! [X4,X5] :
( ~ setIn(X5,alive)
| ~ elem(m_Down(X5),queue(host(X4))) )
& ! [X3] : leq(index(pendack,host(X3)),nbr_proc) ),
inference(fof_nnf,[status(thm)],[conj_neg]) ).
fof(sk_conj_neg_sk,plain,
( index(status,host(sK4)) = norm
& index(ldr,host(sK4)) = host(sK4)
& setIn(sK4,alive)
& elem(m_Halt(sK6),snoc(queue(host(sK5)),m_Halt(sK3)))
& setIn(sK6,alive)
& ~ leq(s(host(sK3)),host(sK4))
& host(sK6) = host(sK3)
& host(sK5) != host(sK3)
& s(host(sK3)) = host(sK5)
& host(sK4) != host(sK3)
& ~ leq(nbr_proc,host(sK3))
& index(status,host(sK3)) = elec_1
& ! [X36] :
( host(sK1) = X36
| setIn(X36,index(down,host(sK3)))
| ~ leq(s(zero),X36)
| leq(host(sK3),X36) )
& ( host(index(elid,host(sK3))) != host(sK1)
| index(status,host(sK3)) != wait )
& ( index(status,host(sK3)) != norm
| index(ldr,host(sK3)) != host(sK1) )
& ~ leq(host(sK3),host(sK1))
& setIn(sK3,alive)
& cons(m_Down(sK1),sK2) = queue(host(sK3))
& ! [X35,Pid20,Pid0] :
( index(status,host(X35)) != norm
| index(ldr,host(X35)) != host(X35)
| ~ setIn(X35,alive)
| index(status,host(Pid0)) != elec_1
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| leq(host(Pid0),host(X35))
| ( host(Pid20) != sK0(X35,Pid20,Pid0)
& ~ setIn(sK0(X35,Pid20,Pid0),index(down,host(Pid0)))
& leq(s(zero),sK0(X35,Pid20,Pid0))
& ~ leq(host(Pid0),sK0(X35,Pid20,Pid0)) ) )
& ! [X32,X33,X34] :
( index(status,host(X32)) != norm
| index(ldr,host(X32)) != host(X32)
| ~ setIn(X32,alive)
| index(status,host(X34)) != elec_2
| ~ elem(m_Halt(X34),queue(host(X33)))
| ~ setIn(X34,alive)
| leq(index(pendack,host(X34)),host(X32)) )
& ! [X30,X31] :
( ~ leq(index(pendack,host(X30)),index(pendack,host(X31)))
| index(status,host(X31)) != elec_2
| index(status,host(X30)) != elec_2
| ~ setIn(X31,alive)
| ~ setIn(X30,alive)
| leq(host(X30),host(X31)) )
& ! [X28,X29] :
( X29 = X28
| index(ldr,host(X29)) != host(X29)
| index(status,host(X29)) != norm
| index(status,host(X28)) != norm
| index(ldr,host(X28)) != host(X28)
| ~ setIn(X29,alive)
| ~ setIn(X28,alive) )
& ! [X26,X27] :
( index(status,host(X26)) != norm
| index(ldr,host(X26)) != host(X26)
| ~ setIn(X26,alive)
| index(status,host(X27)) != elec_2
| ~ setIn(X27,alive)
| leq(index(pendack,host(X27)),host(X26)) )
& ! [X23,X24,X25] :
( index(status,host(X23)) != norm
| index(ldr,host(X23)) != host(X23)
| ~ setIn(X23,alive)
| host(X24) != host(X23)
| ~ elem(m_Ack(X25,X24),queue(host(X25)))
| ~ setIn(X25,alive) )
& ! [X21,X22] :
( leq(index(pendack,host(X22)),host(X21))
| index(status,host(X22)) != elec_2
| index(status,host(X21)) != elec_2
| ~ setIn(X22,alive)
| ~ setIn(X21,alive)
| leq(host(X21),host(X22)) )
& ! [X18,X19,X20] :
( index(status,host(X18)) != norm
| index(ldr,host(X18)) != host(X18)
| ~ setIn(X18,alive)
| host(X19) != host(X18)
| ~ elem(m_Down(X19),queue(host(X20)))
| ~ setIn(X20,alive) )
& ! [X17] :
( index(elid,host(X17)) = X17
| ~ setIn(X17,alive)
| ( index(status,host(X17)) != elec_2
& index(status,host(X17)) != elec_1 ) )
& ! [X15,X16] :
( ~ setIn(X16,alive)
| ~ setIn(X15,alive)
| host(X16) != host(X15)
| X16 = X15 )
& ! [X13,X14] :
( ~ setIn(X14,alive)
| host(X14) != host(X13)
| ~ leq(X14,X13)
| setIn(X13,alive) )
& ! [X10,X11,X12] :
( ~ leq(host(X10),host(X12))
| ~ elem(m_Ack(X12,X10),queue(host(X11))) )
& ! [X8,X9] :
( ~ leq(host(X8),host(X9))
| ~ elem(m_Halt(X9),queue(host(X8))) )
& ! [X6,X7] :
( ~ leq(host(X6),host(X7))
| ~ elem(m_Ldr(X7),queue(host(X6))) )
& ! [X4,X5] :
( ~ setIn(X5,alive)
| ~ elem(m_Down(X5),queue(host(X4))) )
& ! [X3] : leq(index(pendack,host(X3)),nbr_proc) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(V,sK2),skolemize(W,sK7),skolemize(X,sK3),skolemize(Y,sK1),skolemize(V0,sK0(X35,Pid20,Pid0)),skolemize(Z,sK4),skolemize(W0,sK5),skolemize(X0,sK6)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( index(status,host(sK4)) = norm
& index(ldr,host(sK4)) = host(sK4)
& setIn(sK4,alive)
& elem(m_Halt(sK6),snoc(queue(host(sK5)),m_Halt(sK3)))
& setIn(sK6,alive)
& ~ leq(s(host(sK3)),host(sK4))
& host(sK6) = host(sK3)
& host(sK5) != host(sK3)
& s(host(sK3)) = host(sK5)
& host(sK4) != host(sK3)
& ~ leq(nbr_proc,host(sK3))
& index(status,host(sK3)) = elec_1
& ! [VAR_0] :
( host(sK1) = VAR_0
| setIn(VAR_0,index(down,host(sK3)))
| ~ leq(s(zero),VAR_0)
| leq(host(sK3),VAR_0) )
& ( host(index(elid,host(sK3))) != host(sK1)
| index(status,host(sK3)) != wait )
& ( index(status,host(sK3)) != norm
| index(ldr,host(sK3)) != host(sK1) )
& ~ leq(host(sK3),host(sK1))
& setIn(sK3,alive)
& cons(m_Down(sK1),sK2) = queue(host(sK3))
& ! [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) != sK0(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(sK0(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),sK0(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),sK0(VAR_1,VAR_2,VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2] :
( index(status,host(VAR_1)) != norm
| index(ldr,host(VAR_1)) != host(VAR_1)
| ~ setIn(VAR_1,alive)
| index(status,host(VAR_0)) != elec_2
| ~ elem(m_Halt(VAR_0),queue(host(VAR_2)))
| ~ setIn(VAR_0,alive)
| leq(index(pendack,host(VAR_0)),host(VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ leq(index(pendack,host(VAR_0)),index(pendack,host(VAR_1)))
| index(status,host(VAR_1)) != elec_2
| index(status,host(VAR_0)) != elec_2
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive)
| leq(host(VAR_0),host(VAR_1)) )
& ! [VAR_0,VAR_1] :
( VAR_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] :
( 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] :
( 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] :
( index(status,host(VAR_2)) != norm
| index(ldr,host(VAR_2)) != host(VAR_2)
| ~ setIn(VAR_2,alive)
| host(VAR_1) != host(VAR_2)
| ~ elem(m_Down(VAR_1),queue(host(VAR_0)))
| ~ setIn(VAR_0,alive) )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_2 )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_1 )
& ! [VAR_0,VAR_1] :
( ~ 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_Halt(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Ldr(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( ~ setIn(VAR_0,alive)
| ~ elem(m_Down(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0] : leq(index(pendack,host(VAR_0)),nbr_proc) ),
inference(cnf_transformation,[status(thm)],[sk_conj_neg_sk]) ).
cnf(c_174,negated_conjecture,
( index(status,host(B)) != norm
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(A)) != elec_1
| ~ elem(m_Down(C),queue(host(A)))
| leq(host(A),host(B))
| ~ leq(host(A),sK0(B,C,A)) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_175,negated_conjecture,
( index(status,host(A)) != norm
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(C)) != elec_1
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| leq(s(zero),sK0(A,B,C)) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_176,negated_conjecture,
( index(status,host(A)) != norm
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(C)) != elec_1
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| ~ setIn(sK0(A,B,C),index(down,host(C))) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_177,negated_conjecture,
( index(status,host(B)) != norm
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(C)) != elec_1
| ~ elem(m_Down(A),queue(host(C)))
| leq(host(C),host(B))
| host(A) != sK0(B,A,C) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_178,negated_conjecture,
( index(status,host(A)) != norm
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(C)) != elec_1
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| sK0(A,B,C) != host(B) ),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_179,negated_conjecture,
cons(m_Down(sK1),sK2) = queue(host(sK3)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_184,negated_conjecture,
( host(sK1) = 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_185,negated_conjecture,
index(status,host(sK3)) = elec_1,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_186,negated_conjecture,
elec_1 = index(status,host(sK3)),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_188,negated_conjecture,
host(sK4) != host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_189,negated_conjecture,
s(host(sK3)) = host(sK5),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_192,negated_conjecture,
~ leq(s(host(sK3)),host(sK4)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_193,negated_conjecture,
~ leq(host(sK5),host(sK4)),
inference(paramod,[status(thm)],[c_189,c_192]) ).
cnf(c_196,negated_conjecture,
setIn(sK4,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_197,negated_conjecture,
index(ldr,host(sK4)) = host(sK4),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_198,negated_conjecture,
index(status,host(sK4)) = norm,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_199,negated_conjecture,
norm = index(status,host(sK4)),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_7183,negated_conjecture,
( index(status,host(A)) != norm
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(C)) != index(status,host(sK3))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| sK0(A,B,C) != host(B) ),
inference(paramod,[status(thm)],[c_186,c_178]) ).
cnf(c_7184,negated_conjecture,
( index(status,host(A)) != index(status,host(sK4))
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(C)) != index(status,host(sK3))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| sK0(A,B,C) != host(B) ),
inference(paramod,[status(thm)],[c_199,c_7183]) ).
cnf(c_7185,negated_conjecture,
( index(status,host(A)) != index(status,host(sK4))
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(sK3)) != index(status,host(C))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| sK0(A,B,C) != host(B) ),
inference(copy,[status(thm)],[c_7184]) ).
cnf(c_203,negated_conjecture,
( index(status,host(sK4)) != index(status,host(A))
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(sK3)) != index(status,host(C))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| sK0(A,B,C) != host(B) ),
inference(copy,[status(thm)],[c_7185]) ).
cnf(c_7186,negated_conjecture,
( index(status,host(A)) != norm
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(C)) != index(status,host(sK3))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| ~ setIn(sK0(A,B,C),index(down,host(C))) ),
inference(paramod,[status(thm)],[c_186,c_176]) ).
cnf(c_7187,negated_conjecture,
( index(status,host(A)) != index(status,host(sK4))
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(C)) != index(status,host(sK3))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| ~ setIn(sK0(A,B,C),index(down,host(C))) ),
inference(paramod,[status(thm)],[c_199,c_7186]) ).
cnf(c_7188,negated_conjecture,
( index(status,host(A)) != index(status,host(sK4))
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(sK3)) != index(status,host(C))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| ~ setIn(sK0(A,B,C),index(down,host(C))) ),
inference(copy,[status(thm)],[c_7187]) ).
cnf(c_204,negated_conjecture,
( index(status,host(sK4)) != index(status,host(A))
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(sK3)) != index(status,host(C))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| ~ setIn(sK0(A,B,C),index(down,host(C))) ),
inference(copy,[status(thm)],[c_7188]) ).
cnf(c_7189,negated_conjecture,
( index(status,host(A)) != norm
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(C)) != index(status,host(sK3))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| leq(s(zero),sK0(A,B,C)) ),
inference(paramod,[status(thm)],[c_186,c_175]) ).
cnf(c_7190,negated_conjecture,
( index(status,host(A)) != index(status,host(sK4))
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(C)) != index(status,host(sK3))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| leq(s(zero),sK0(A,B,C)) ),
inference(paramod,[status(thm)],[c_199,c_7189]) ).
cnf(c_7191,negated_conjecture,
( index(status,host(A)) != index(status,host(sK4))
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(sK3)) != index(status,host(C))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| leq(s(zero),sK0(A,B,C)) ),
inference(copy,[status(thm)],[c_7190]) ).
cnf(c_205,negated_conjecture,
( index(status,host(sK4)) != index(status,host(A))
| index(ldr,host(A)) != host(A)
| ~ setIn(A,alive)
| index(status,host(sK3)) != index(status,host(C))
| ~ elem(m_Down(B),queue(host(C)))
| leq(host(C),host(A))
| leq(s(zero),sK0(A,B,C)) ),
inference(copy,[status(thm)],[c_7191]) ).
cnf(c_7192,negated_conjecture,
( index(status,host(B)) != norm
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(A)) != index(status,host(sK3))
| ~ elem(m_Down(C),queue(host(A)))
| leq(host(A),host(B))
| ~ leq(host(A),sK0(B,C,A)) ),
inference(paramod,[status(thm)],[c_186,c_174]) ).
cnf(c_7193,negated_conjecture,
( index(status,host(B)) != index(status,host(sK4))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(A)) != index(status,host(sK3))
| ~ elem(m_Down(C),queue(host(A)))
| leq(host(A),host(B))
| ~ leq(host(A),sK0(B,C,A)) ),
inference(paramod,[status(thm)],[c_199,c_7192]) ).
cnf(c_7194,negated_conjecture,
( index(status,host(B)) != index(status,host(sK4))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(sK3)) != index(status,host(A))
| ~ elem(m_Down(C),queue(host(A)))
| leq(host(A),host(B))
| ~ leq(host(A),sK0(B,C,A)) ),
inference(copy,[status(thm)],[c_7193]) ).
cnf(c_206,negated_conjecture,
( index(status,host(sK4)) != index(status,host(B))
| index(ldr,host(B)) != host(B)
| ~ setIn(B,alive)
| index(status,host(sK3)) != index(status,host(A))
| ~ elem(m_Down(C),queue(host(A)))
| leq(host(A),host(B))
| ~ leq(host(A),sK0(B,C,A)) ),
inference(copy,[status(thm)],[c_7194]) ).
cnf(c_7195,plain,
elem(A,cons(init(snoc(A,B)),C)),
inference(resolve,[status(thm)],[c_117,c_106]) ).
cnf(c_254,plain,
elem(A,cons(A,B)),
inference(paramod,[status(thm)],[c_106,c_7195]) ).
cnf(c_292,plain,
leq(A,s(A)),
inference(resolve,[status(thm)],[c_149,c_147]) ).
cnf(c_317,plain,
( leq(s(A),B)
| leq(B,A)
| s(A) = B ),
inference(resolve,[status(thm)],[c_156,c_149]) ).
cnf(c_7196,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| index(ldr,host(sK4)) != host(sK4)
| index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| sK0(sK4,A,B) != host(A) ),
inference(resolve,[status(thm)],[c_203,c_196]) ).
cnf(c_7197,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| host(sK4) != host(sK4)
| index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| sK0(sK4,A,B) != host(A) ),
inference(paramod,[status(thm)],[c_197,c_7196]) ).
cnf(c_7198,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| sK0(sK4,A,B) != host(A) ),
inference(copy,[status(thm)],[c_7197]) ).
cnf(c_358,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| sK0(sK4,A,B) != host(A) ),
inference(copy,[status(thm)],[c_7198]) ).
cnf(c_7199,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| index(ldr,host(sK4)) != host(sK4)
| index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| ~ setIn(sK0(sK4,A,B),index(down,host(B))) ),
inference(resolve,[status(thm)],[c_204,c_196]) ).
cnf(c_7200,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| host(sK4) != host(sK4)
| index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| ~ setIn(sK0(sK4,A,B),index(down,host(B))) ),
inference(paramod,[status(thm)],[c_197,c_7199]) ).
cnf(c_7201,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| ~ setIn(sK0(sK4,A,B),index(down,host(B))) ),
inference(copy,[status(thm)],[c_7200]) ).
cnf(c_360,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| ~ setIn(sK0(sK4,A,B),index(down,host(B))) ),
inference(copy,[status(thm)],[c_7201]) ).
cnf(c_7202,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| index(ldr,host(sK4)) != host(sK4)
| index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| leq(s(zero),sK0(sK4,A,B)) ),
inference(resolve,[status(thm)],[c_205,c_196]) ).
cnf(c_7203,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| host(sK4) != host(sK4)
| index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| leq(s(zero),sK0(sK4,A,B)) ),
inference(paramod,[status(thm)],[c_197,c_7202]) ).
cnf(c_7204,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| leq(s(zero),sK0(sK4,A,B)) ),
inference(copy,[status(thm)],[c_7203]) ).
cnf(c_362,negated_conjecture,
( index(status,host(sK3)) != index(status,host(B))
| ~ elem(m_Down(A),queue(host(B)))
| leq(host(B),host(sK4))
| leq(s(zero),sK0(sK4,A,B)) ),
inference(copy,[status(thm)],[c_7204]) ).
cnf(c_7205,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| index(ldr,host(sK4)) != host(sK4)
| index(status,host(sK3)) != index(status,host(A))
| ~ elem(m_Down(B),queue(host(A)))
| leq(host(A),host(sK4))
| ~ leq(host(A),sK0(sK4,B,A)) ),
inference(resolve,[status(thm)],[c_206,c_196]) ).
cnf(c_7206,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| host(sK4) != host(sK4)
| index(status,host(sK3)) != index(status,host(A))
| ~ elem(m_Down(B),queue(host(A)))
| leq(host(A),host(sK4))
| ~ leq(host(A),sK0(sK4,B,A)) ),
inference(paramod,[status(thm)],[c_197,c_7205]) ).
cnf(c_7207,negated_conjecture,
( index(status,host(sK4)) != index(status,host(sK4))
| index(status,host(sK3)) != index(status,host(A))
| ~ elem(m_Down(B),queue(host(A)))
| leq(host(A),host(sK4))
| ~ leq(host(A),sK0(sK4,B,A)) ),
inference(copy,[status(thm)],[c_7206]) ).
cnf(c_365,negated_conjecture,
( index(status,host(sK3)) != index(status,host(A))
| ~ elem(m_Down(B),queue(host(A)))
| leq(host(A),host(sK4))
| ~ leq(host(A),sK0(sK4,B,A)) ),
inference(copy,[status(thm)],[c_7207]) ).
cnf(c_455,plain,
( leq(A,B)
| ~ leq(s(A),B) ),
inference(resolve,[status(thm)],[c_292,c_153]) ).
cnf(c_563,plain,
elem(m_Down(sK1),queue(host(sK3))),
inference(paramod,[status(thm)],[c_179,c_254]) ).
cnf(c_7208,plain,
( leq(s(B),A)
| leq(s(B),A)
| leq(A,B) ),
inference(resolve,[status(thm)],[c_317,c_152]) ).
cnf(c_2992,plain,
( leq(s(B),A)
| leq(A,B) ),
inference(copy,[status(thm)],[c_7208]) ).
cnf(c_3081,plain,
( B = A
| ~ leq(A,B)
| leq(s(A),B) ),
inference(resolve,[status(thm)],[c_2992,c_150]) ).
cnf(c_3483,plain,
( leq(s(B),A)
| B = A
| leq(s(A),B) ),
inference(resolve,[status(thm)],[c_3081,c_2992]) ).
cnf(c_7209,plain,
( index(status,host(sK3)) != index(status,host(sK3))
| leq(host(sK3),host(sK4))
| sK0(sK4,sK1,sK3) != host(sK1) ),
inference(resolve,[status(thm)],[c_358,c_563]) ).
cnf(c_4561,plain,
( leq(host(sK3),host(sK4))
| sK0(sK4,sK1,sK3) != host(sK1) ),
inference(copy,[status(thm)],[c_7209]) ).
cnf(c_7210,plain,
( index(status,host(sK3)) != index(status,host(sK3))
| leq(host(sK3),host(sK4))
| ~ setIn(sK0(sK4,sK1,sK3),index(down,host(sK3))) ),
inference(resolve,[status(thm)],[c_360,c_563]) ).
cnf(c_4605,plain,
( leq(host(sK3),host(sK4))
| ~ setIn(sK0(sK4,sK1,sK3),index(down,host(sK3))) ),
inference(copy,[status(thm)],[c_7210]) ).
cnf(c_7211,plain,
( index(status,host(sK3)) != index(status,host(sK3))
| leq(host(sK3),host(sK4))
| leq(s(zero),sK0(sK4,sK1,sK3)) ),
inference(resolve,[status(thm)],[c_362,c_563]) ).
cnf(c_4607,plain,
( leq(host(sK3),host(sK4))
| leq(s(zero),sK0(sK4,sK1,sK3)) ),
inference(copy,[status(thm)],[c_7211]) ).
cnf(c_7212,plain,
( index(status,host(sK3)) != index(status,host(sK3))
| leq(host(sK3),host(sK4))
| ~ leq(host(sK3),sK0(sK4,sK1,sK3)) ),
inference(resolve,[status(thm)],[c_365,c_563]) ).
cnf(c_4707,plain,
( leq(host(sK3),host(sK4))
| ~ leq(host(sK3),sK0(sK4,sK1,sK3)) ),
inference(copy,[status(thm)],[c_7212]) ).
cnf(c_7213,negated_conjecture,
( leq(s(host(sK4)),host(sK3))
| leq(s(host(sK3)),host(sK4)) ),
inference(resolve,[status(thm)],[c_3483,c_188]) ).
cnf(c_7214,negated_conjecture,
( leq(s(host(sK4)),host(sK3))
| leq(host(sK5),host(sK4)) ),
inference(paramod,[status(thm)],[c_189,c_7213]) ).
cnf(c_6995,negated_conjecture,
leq(s(host(sK4)),host(sK3)),
inference(resolve,[status(thm)],[c_193,c_7214]) ).
cnf(c_7135,plain,
leq(host(sK4),host(sK3)),
inference(resolve,[status(thm)],[c_6995,c_455]) ).
cnf(c_7215,plain,
( host(sK4) = host(sK3)
| ~ leq(host(sK3),host(sK4)) ),
inference(resolve,[status(thm)],[c_7135,c_150]) ).
cnf(c_7150,negated_conjecture,
~ leq(host(sK3),host(sK4)),
inference(resolve,[status(thm)],[c_188,c_7215]) ).
cnf(c_7151,plain,
~ leq(host(sK3),sK0(sK4,sK1,sK3)),
inference(resolve,[status(thm)],[c_7150,c_4707]) ).
cnf(c_7157,plain,
leq(s(zero),sK0(sK4,sK1,sK3)),
inference(resolve,[status(thm)],[c_7150,c_4607]) ).
cnf(c_7159,plain,
~ setIn(sK0(sK4,sK1,sK3),index(down,host(sK3))),
inference(resolve,[status(thm)],[c_7150,c_4605]) ).
cnf(c_7162,plain,
sK0(sK4,sK1,sK3) != host(sK1),
inference(resolve,[status(thm)],[c_7150,c_4561]) ).
cnf(c_7216,negated_conjecture,
( host(sK1) = sK0(sK4,sK1,sK3)
| setIn(sK0(sK4,sK1,sK3),index(down,host(sK3)))
| leq(host(sK3),sK0(sK4,sK1,sK3)) ),
inference(resolve,[status(thm)],[c_7157,c_184]) ).
cnf(c_7217,negated_conjecture,
( sK0(sK4,sK1,sK3) = host(sK1)
| setIn(sK0(sK4,sK1,sK3),index(down,host(sK3)))
| leq(host(sK3),sK0(sK4,sK1,sK3)) ),
inference(copy,[status(thm)],[c_7216]) ).
cnf(c_7218,negated_conjecture,
( sK0(sK4,sK1,sK3) = host(sK1)
| setIn(sK0(sK4,sK1,sK3),index(down,host(sK3))) ),
inference(resolve,[status(thm)],[c_7151,c_7217]) ).
cnf(c_7219,negated_conjecture,
sK0(sK4,sK1,sK3) = host(sK1),
inference(resolve,[status(thm)],[c_7159,c_7218]) ).
cnf(c_7182,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_7162,c_7219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV458+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n026.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Sat Sep 26 13:58:35 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.38 % Process 1169006 was started by sandbox on n026,
% 0.10/10.38 % Sat Sep 26 13:58:35 2026
% 0.10/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/10.39
% 0.10/10.39 % From the command line: assign(max_seconds, 300).
% 24.41/13.90
% 24.41/13.90 % given #500 (T,wt=21): 1473 leq(A,s(nbr_proc)) | -leq(B,s(zero)) | leq(B,A). [resolve(575,b,153,b)].
% 24.41/13.90
% 24.41/13.90 % SZS status Theorem for theBenchmark
% 24.41/13.90
% 24.41/13.90 % Proof 1 at 2.76 (+ 0.71) seconds.
% 24.41/13.90 % Length of proof is 61.
% 24.41/13.90 % Level of proof is 10.
% 24.41/13.90 % Maximum clause weight is 63.000.
% 24.41/13.90 % Given clauses 617.
% 24.41/13.90
% 24.41/13.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------