%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV476+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:48:00 PM UTC 2026
% Result : Theorem 9.38s 1.66s
% Output : CNFRefutation 9.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 128 ( 26 unt; 19 def)
% Number of atoms : 967 ( 370 equ)
% Maximal formula atoms : 127 ( 7 avg)
% Number of connectives : 1337 ( 498 ~; 446 |; 316 &)
% ( 21 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 20 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 22 con; 0-4 aty)
% Number of variables : 322 ( 300 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [P] : leq(s(zero),host(P)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [P] : leq(host(P),nbr_proc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [X] : ~ leq(s(X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
<=> X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [X,Y] :
( leq(X,s(Y))
<=> ( leq(X,Y)
| X = s(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,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),queue(host(Y0)))
& elem(m_Down(W0),queue(host(Y0)))
& 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('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,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),queue(host(Y0)))
& elem(m_Down(W0),queue(host(Y0)))
& 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(negated_conjecture,[status(cth)],[f67]) ).
fof(f74,plain,
! [X0] : leq(s(zero),host(X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f76,plain,
! [X0] : leq(host(X0),nbr_proc),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f191,plain,
! [X0] : ~ leq(s(X0),X0),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f194,plain,
! [X,Y] :
( ( X != Y
| ( leq(Y,X)
& leq(X,Y) ) )
& ( X = Y
| ~ leq(Y,X)
| ~ leq(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f195,plain,
( ! [X,Y] :
( X != Y
| ( leq(Y,X)
& leq(X,Y) ) )
& ! [X,Y] :
( X = Y
| ~ leq(Y,X)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f194]) ).
fof(f196,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f206,plain,
! [X,Y] :
( ( ( ~ leq(X,Y)
& X != s(Y) )
| leq(X,s(Y)) )
& ( leq(X,Y)
| X = s(Y)
| ~ leq(X,s(Y)) ) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f207,plain,
( ! [X,Y] :
( ( ~ leq(X,Y)
& X != s(Y) )
| leq(X,s(Y)) )
& ! [X,Y] :
( leq(X,Y)
| X = s(Y)
| ~ leq(X,s(Y)) ) ),
inference(miniscoping,[status(thm)],[f206]) ).
fof(f208,plain,
! [X0,X1] :
( leq(X0,X1)
| X0 = s(X1)
| ~ leq(X0,s(X1)) ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f212,plain,
? [V,W,X,Y] :
( ? [Z] :
( ? [V0] :
( ? [W0,X0,Y0] :
( host(X) = host(V0)
& setIn(V0,alive)
& index(status,host(Y0)) = elec_1
& host(W0) = s(host(Y0))
& elem(m_Down(X0),queue(host(Y0)))
& elem(m_Down(W0),queue(host(Y0)))
& leq(nbr_proc,s(host(Y0)))
& setIn(Y0,alive)
& ! [V1] :
( V1 = host(X0)
| setIn(V1,index(down,host(Y0)))
| ~ leq(s(zero),V1)
| leq(host(Y0),V1) )
& host(X) != host(Y0)
& host(Z) != host(Y0) )
& host(X) = host(V0) )
& ( host(Z) = host(Y)
| setIn(host(Z),index(acks,host(X))) ) )
& leq(nbr_proc,index(pendack,host(X)))
& host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W
& setIn(X,alive)
& queue(host(X)) = cons(m_Ack(W,Y),V)
& ! [Z,Pid30,Pid20,Pid0] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| 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] :
( V0 != host(Pid20)
& ~ setIn(V0,index(down,host(Pid0)))
& leq(s(zero),V0)
& ~ leq(host(Pid0),V0) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ~ elem(m_Ack(Z,Pid30),queue(host(Z)))
| 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] :
( V0 != host(Pid20)
& ~ setIn(V0,index(down,host(Pid0)))
& leq(s(zero),V0)
& ~ leq(host(Pid0),V0) ) )
& ! [Z,Pid20,Pid0] :
( index(ldr,host(Pid20)) != host(Pid20)
| index(status,host(Pid20)) != norm
| ~ setIn(Pid20,alive)
| 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) )
& ! [Z,Pid20,Pid0] :
( index(ldr,host(Pid20)) != host(Pid20)
| index(status,host(Pid20)) != norm
| ~ setIn(Pid20,alive)
| 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) )
& ! [Z,Pid30,Pid20,Pid0] :
( ~ setIn(host(Pid30),index(down,host(Pid20)))
| ~ elem(m_Down(Pid0),queue(host(Z)))
| host(Pid0) != host(Pid20)
| host(Pid30) != host(Z)
| ~ setIn(Pid20,alive)
| ~ setIn(Z,alive)
| host(Pid20) = host(Z) )
& ! [Z,Pid30,Pid20,Pid0] :
( ~ elem(m_Down(Pid30),queue(host(Pid20)))
| ~ elem(m_Down(Pid0),queue(host(Z)))
| host(Pid0) != host(Pid20)
| host(Pid30) != host(Z)
| ~ setIn(Pid20,alive)
| ~ setIn(Z,alive)
| host(Pid20) = host(Z) )
& ! [Z,Pid20,Pid0] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| host(Pid20) != host(Z)
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive)
| leq(host(Pid20),host(Pid0)) )
& ! [Z,Pid0] :
( Pid0 = Z
| 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) )
& ! [Z,Pid20,Pid0] :
( ~ elem(m_Down(Pid20),queue(host(Z)))
| ~ setIn(Z,alive)
| index(ldr,host(Pid0)) != host(Pid0)
| index(status,host(Pid0)) != norm
| host(Pid20) != host(Pid0)
| ~ setIn(Pid0,alive) )
& ! [Z,Pid20,Pid0] :
( leq(index(pendack,host(Pid0)),host(Z))
| index(status,host(Pid0)) != elec_2
| host(Pid0) != host(Pid20)
| ~ elem(m_Down(Pid20),queue(host(Z)))
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) )
& ! [Z,Pid0] :
( ~ setIn(host(Pid0),index(down,host(Z)))
| ~ setIn(Z,alive)
| index(ldr,host(Pid0)) != host(Pid0)
| index(status,host(Pid0)) != norm
| ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( leq(index(pendack,host(Pid0)),host(Z))
| index(status,host(Pid0)) != elec_2
| ~ setIn(host(Pid0),index(down,host(Z)))
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) )
& ! [Z] :
( index(elid,host(Z)) = Z
| ~ setIn(Z,alive)
| ( index(status,host(Z)) != elec_2
& index(status,host(Z)) != elec_1 ) )
& ! [Z,Pid0] :
( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| host(Pid0) != host(Z)
| Pid0 = Z )
& ! [Z,Pid0] :
( host(Pid0) != host(Z)
| ~ elem(m_Down(Pid0),queue(host(Z))) )
& ! [Z,Pid0] :
( ~ leq(host(Z),host(Pid0))
| ~ elem(m_Ldr(Pid0),queue(host(Z))) ) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f213,plain,
? [W,X,Y] :
( ? [Z] :
( ? [V0] :
( ? [Y0] :
( host(X) = host(V0)
& setIn(V0,alive)
& index(status,host(Y0)) = elec_1
& ? [W0] :
( host(W0) = s(host(Y0))
& ? [X0] :
( elem(m_Down(X0),queue(host(Y0)))
& elem(m_Down(W0),queue(host(Y0)))
& leq(nbr_proc,s(host(Y0)))
& setIn(Y0,alive)
& ! [V1] :
( V1 = host(X0)
| setIn(V1,index(down,host(Y0)))
| ~ leq(s(zero),V1)
| leq(host(Y0),V1) ) ) )
& host(X) != host(Y0)
& host(Z) != host(Y0) )
& host(X) = host(V0) )
& ( host(Z) = host(Y)
| setIn(host(Z),index(acks,host(X))) ) )
& leq(nbr_proc,index(pendack,host(X)))
& host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W
& setIn(X,alive)
& ? [V] : queue(host(X)) = cons(m_Ack(W,Y),V)
& ( ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive) )
| ! [Pid0] :
( index(status,host(Pid0)) != elec_1
| ! [Pid30] :
( host(Pid30) != s(host(Pid0))
| ~ elem(m_Down(Pid30),queue(host(Pid0)))
| ! [Pid20] :
( ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ leq(nbr_proc,s(host(Pid0)))
| ~ setIn(Pid0,alive)
| ? [V0] :
( V0 != host(Pid20)
& ~ setIn(V0,index(down,host(Pid0)))
& leq(s(zero),V0)
& ~ leq(host(Pid0),V0) ) ) ) ) )
& ! [Z,Pid30] :
( ~ elem(m_Ack(Z,Pid30),queue(host(Z)))
| ! [Pid0] :
( index(status,host(Pid0)) != elec_1
| index(status,host(Z)) != elec_2
| host(Pid30) != host(Pid0)
| ! [Pid20] :
( ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ leq(host(Z),host(Pid0))
| ~ setIn(Z,alive)
| ? [V0] :
( V0 != host(Pid20)
& ~ setIn(V0,index(down,host(Pid0)))
& leq(s(zero),V0)
& ~ leq(host(Pid0),V0) ) ) ) )
& ! [Pid20] :
( index(ldr,host(Pid20)) != host(Pid20)
| index(status,host(Pid20)) != norm
| ~ setIn(Pid20,alive)
| ! [Pid0] :
( host(index(elid,host(Pid0))) != host(Pid20)
| index(status,host(Pid0)) != wait
| ! [Z] :
( host(Pid20) != host(Z)
| ~ elem(m_Down(Z),queue(host(Pid0)))
| ~ setIn(Pid0,alive)
| host(Pid0) = host(Pid20) ) ) )
& ! [Pid20] :
( index(ldr,host(Pid20)) != host(Pid20)
| index(status,host(Pid20)) != norm
| ~ setIn(Pid20,alive)
| ! [Pid0] :
( index(ldr,host(Pid0)) != host(Pid20)
| index(status,host(Pid0)) != norm
| ! [Z] :
( host(Pid20) != host(Z)
| ~ elem(m_Down(Z),queue(host(Pid0)))
| ~ setIn(Pid0,alive)
| host(Pid0) = host(Pid20) ) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ~ setIn(host(Pid30),index(down,host(Pid20)))
| ~ elem(m_Down(Pid0),queue(host(Z)))
| host(Pid0) != host(Pid20)
| host(Pid30) != host(Z)
| ~ setIn(Pid20,alive)
| ~ setIn(Z,alive)
| host(Pid20) = host(Z) )
& ! [Z,Pid30,Pid20,Pid0] :
( ~ elem(m_Down(Pid30),queue(host(Pid20)))
| ~ elem(m_Down(Pid0),queue(host(Z)))
| host(Pid0) != host(Pid20)
| host(Pid30) != host(Z)
| ~ setIn(Pid20,alive)
| ~ setIn(Z,alive)
| host(Pid20) = host(Z) )
& ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| ! [Pid20] :
( host(Pid20) != host(Z)
| ! [Pid0] :
( ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive)
| leq(host(Pid20),host(Pid0)) ) ) )
& ! [Z,Pid0] :
( Pid0 = Z
| 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) )
& ! [Pid20] :
( ! [Z] :
( ~ elem(m_Down(Pid20),queue(host(Z)))
| ~ setIn(Z,alive) )
| ! [Pid0] :
( index(ldr,host(Pid0)) != host(Pid0)
| index(status,host(Pid0)) != norm
| host(Pid20) != host(Pid0)
| ~ setIn(Pid0,alive) ) )
& ! [Z,Pid0] :
( leq(index(pendack,host(Pid0)),host(Z))
| index(status,host(Pid0)) != elec_2
| ! [Pid20] :
( host(Pid0) != host(Pid20)
| ~ elem(m_Down(Pid20),queue(host(Z)))
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Pid0] :
( ! [Z] :
( ~ setIn(host(Pid0),index(down,host(Z)))
| ~ setIn(Z,alive) )
| index(ldr,host(Pid0)) != host(Pid0)
| index(status,host(Pid0)) != norm
| ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( leq(index(pendack,host(Pid0)),host(Z))
| index(status,host(Pid0)) != elec_2
| ~ setIn(host(Pid0),index(down,host(Z)))
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) )
& ! [Z] :
( index(elid,host(Z)) = Z
| ~ setIn(Z,alive)
| ( index(status,host(Z)) != elec_2
& index(status,host(Z)) != elec_1 ) )
& ! [Z,Pid0] :
( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| host(Pid0) != host(Z)
| Pid0 = Z )
& ! [Z,Pid0] :
( host(Pid0) != host(Z)
| ~ elem(m_Down(Pid0),queue(host(Z))) )
& ! [Z,Pid0] :
( ~ leq(host(Z),host(Pid0))
| ~ elem(m_Ldr(Pid0),queue(host(Z))) ) ),
inference(miniscoping,[status(thm)],[f212]) ).
fof(f214,plain,
( host(sK5_skl) = host(sK11_skl)
& setIn(sK11_skl,alive)
& index(status,host(sK12_skl)) = elec_1
& host(sK13_skl) = s(host(sK12_skl))
& elem(m_Down(sK14_skl),queue(host(sK12_skl)))
& elem(m_Down(sK13_skl),queue(host(sK12_skl)))
& leq(nbr_proc,s(host(sK12_skl)))
& setIn(sK12_skl,alive)
& ! [V1] :
( V1 = host(sK14_skl)
| setIn(V1,index(down,host(sK12_skl)))
| ~ leq(s(zero),V1)
| leq(host(sK12_skl),V1) )
& host(sK5_skl) != host(sK12_skl)
& host(sK10_skl) != host(sK12_skl)
& host(sK5_skl) = host(sK11_skl)
& ( host(sK10_skl) = host(sK6_skl)
| setIn(host(sK10_skl),index(acks,host(sK5_skl))) )
& leq(nbr_proc,index(pendack,host(sK5_skl)))
& host(sK6_skl) = index(pendack,host(sK5_skl))
& index(status,host(sK5_skl)) = elec_2
& index(elid,host(sK5_skl)) = sK4_skl
& setIn(sK5_skl,alive)
& queue(host(sK5_skl)) = cons(m_Ack(sK4_skl,sK6_skl),sK9_skl)
& ( ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive) )
| ! [Pid0] :
( index(status,host(Pid0)) != elec_1
| ! [Pid30] :
( host(Pid30) != s(host(Pid0))
| ~ elem(m_Down(Pid30),queue(host(Pid0)))
| ! [Pid20] :
( ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ leq(nbr_proc,s(host(Pid0)))
| ~ setIn(Pid0,alive)
| ( sK8_skl(Pid20,Pid30,Pid0) != host(Pid20)
& ~ setIn(sK8_skl(Pid20,Pid30,Pid0),index(down,host(Pid0)))
& leq(s(zero),sK8_skl(Pid20,Pid30,Pid0))
& ~ leq(host(Pid0),sK8_skl(Pid20,Pid30,Pid0)) ) ) ) ) )
& ! [Z,Pid30] :
( ~ elem(m_Ack(Z,Pid30),queue(host(Z)))
| ! [Pid0] :
( index(status,host(Pid0)) != elec_1
| index(status,host(Z)) != elec_2
| host(Pid30) != host(Pid0)
| ! [Pid20] :
( ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ leq(host(Z),host(Pid0))
| ~ setIn(Z,alive)
| ( sK7_skl(Pid20,Pid0,Pid30,Z) != host(Pid20)
& ~ setIn(sK7_skl(Pid20,Pid0,Pid30,Z),index(down,host(Pid0)))
& leq(s(zero),sK7_skl(Pid20,Pid0,Pid30,Z))
& ~ leq(host(Pid0),sK7_skl(Pid20,Pid0,Pid30,Z)) ) ) ) )
& ! [Pid20] :
( index(ldr,host(Pid20)) != host(Pid20)
| index(status,host(Pid20)) != norm
| ~ setIn(Pid20,alive)
| ! [Pid0] :
( host(index(elid,host(Pid0))) != host(Pid20)
| index(status,host(Pid0)) != wait
| ! [Z] :
( host(Pid20) != host(Z)
| ~ elem(m_Down(Z),queue(host(Pid0)))
| ~ setIn(Pid0,alive)
| host(Pid0) = host(Pid20) ) ) )
& ! [Pid20] :
( index(ldr,host(Pid20)) != host(Pid20)
| index(status,host(Pid20)) != norm
| ~ setIn(Pid20,alive)
| ! [Pid0] :
( index(ldr,host(Pid0)) != host(Pid20)
| index(status,host(Pid0)) != norm
| ! [Z] :
( host(Pid20) != host(Z)
| ~ elem(m_Down(Z),queue(host(Pid0)))
| ~ setIn(Pid0,alive)
| host(Pid0) = host(Pid20) ) ) )
& ! [Z,Pid30,Pid20,Pid0] :
( ~ setIn(host(Pid30),index(down,host(Pid20)))
| ~ elem(m_Down(Pid0),queue(host(Z)))
| host(Pid0) != host(Pid20)
| host(Pid30) != host(Z)
| ~ setIn(Pid20,alive)
| ~ setIn(Z,alive)
| host(Pid20) = host(Z) )
& ! [Z,Pid30,Pid20,Pid0] :
( ~ elem(m_Down(Pid30),queue(host(Pid20)))
| ~ elem(m_Down(Pid0),queue(host(Z)))
| host(Pid0) != host(Pid20)
| host(Pid30) != host(Z)
| ~ setIn(Pid20,alive)
| ~ setIn(Z,alive)
| host(Pid20) = host(Z) )
& ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| ! [Pid20] :
( host(Pid20) != host(Z)
| ! [Pid0] :
( ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive)
| leq(host(Pid20),host(Pid0)) ) ) )
& ! [Z,Pid0] :
( Pid0 = Z
| 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) )
& ! [Pid20] :
( ! [Z] :
( ~ elem(m_Down(Pid20),queue(host(Z)))
| ~ setIn(Z,alive) )
| ! [Pid0] :
( index(ldr,host(Pid0)) != host(Pid0)
| index(status,host(Pid0)) != norm
| host(Pid20) != host(Pid0)
| ~ setIn(Pid0,alive) ) )
& ! [Z,Pid0] :
( leq(index(pendack,host(Pid0)),host(Z))
| index(status,host(Pid0)) != elec_2
| ! [Pid20] :
( host(Pid0) != host(Pid20)
| ~ elem(m_Down(Pid20),queue(host(Z)))
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Pid0] :
( ! [Z] :
( ~ setIn(host(Pid0),index(down,host(Z)))
| ~ setIn(Z,alive) )
| index(ldr,host(Pid0)) != host(Pid0)
| index(status,host(Pid0)) != norm
| ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( leq(index(pendack,host(Pid0)),host(Z))
| index(status,host(Pid0)) != elec_2
| ~ setIn(host(Pid0),index(down,host(Z)))
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) )
& ! [Z] :
( index(elid,host(Z)) = Z
| ~ setIn(Z,alive)
| ( index(status,host(Z)) != elec_2
& index(status,host(Z)) != elec_1 ) )
& ! [Z,Pid0] :
( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| host(Pid0) != host(Z)
| Pid0 = Z )
& ! [Z,Pid0] :
( host(Pid0) != host(Z)
| ~ elem(m_Down(Pid0),queue(host(Z))) )
& ! [Z,Pid0] :
( ~ leq(host(Z),host(Pid0))
| ~ elem(m_Ldr(Pid0),queue(host(Z))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(W,sK4_skl),skolemize(X,sK5_skl),skolemize(Y,sK6_skl),skolemize(V0,sK7_skl(Pid20,Pid0,Pid30,Z)),skolemize(V0,sK8_skl(Pid20,Pid30,Pid0)),skolemize(V,sK9_skl),skolemize(Z,sK10_skl),skolemize(V0,sK11_skl),skolemize(Y0,sK12_skl),skolemize(W0,sK13_skl),skolemize(X0,sK14_skl)],[f213]) ).
fof(f219,plain,
! [X0] :
( index(elid,host(X0)) = X0
| ~ setIn(X0,alive)
| index(status,host(X0)) != elec_2 ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f220,plain,
! [X0,X1] :
( leq(index(pendack,host(X1)),host(X0))
| index(status,host(X1)) != elec_2
| ~ setIn(host(X1),index(down,host(X0)))
| ~ setIn(X1,alive)
| ~ setIn(X0,alive) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f222,plain,
! [X0,X1,X2] :
( leq(index(pendack,host(X1)),host(X0))
| index(status,host(X1)) != elec_2
| host(X1) != host(X2)
| ~ elem(m_Down(X2),queue(host(X0)))
| ~ setIn(X1,alive)
| ~ setIn(X0,alive) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f239,plain,
setIn(sK5_skl,alive),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f240,plain,
index(elid,host(sK5_skl)) = sK4_skl,
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f241,plain,
index(status,host(sK5_skl)) = elec_2,
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f242,plain,
host(sK6_skl) = index(pendack,host(sK5_skl)),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f243,plain,
leq(nbr_proc,index(pendack,host(sK5_skl))),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f247,plain,
host(sK5_skl) != host(sK12_skl),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f248,plain,
! [X0] :
( X0 = host(sK14_skl)
| setIn(X0,index(down,host(sK12_skl)))
| ~ leq(s(zero),X0)
| leq(host(sK12_skl),X0) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f249,plain,
setIn(sK12_skl,alive),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f250,plain,
leq(nbr_proc,s(host(sK12_skl))),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f251,plain,
elem(m_Down(sK13_skl),queue(host(sK12_skl))),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f252,plain,
elem(m_Down(sK14_skl),queue(host(sK12_skl))),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f253,plain,
host(sK13_skl) = s(host(sK12_skl)),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f307,definition,
( sQ9_spl
<=> setIn(sK5_skl,alive) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ9_spl
| ~ setIn(sK5_skl,alive) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f362,plain,
( sK4_skl = sK5_skl
| ~ setIn(sK5_skl,alive)
| index(status,host(sK5_skl)) != elec_2 ),
inference(paramodulation,[status(thm)],[f240,f219]) ).
fof(f364,definition,
( sQ15_spl
<=> index(status,host(sK5_skl)) = elec_2 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( sQ15_spl
| index(status,host(sK5_skl)) != elec_2 ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f367,definition,
( sQ16_spl
<=> sK4_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( ~ sQ16_spl
| sK4_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f362,f364,f307,f367]) ).
fof(f375,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f309,f239]) ).
fof(f376,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f378,plain,
( ~ sQ16_spl
| host(sK4_skl) != host(sK12_skl) ),
inference(backward_demodulation,[status(thm)],[f368,f247]) ).
fof(f419,plain,
! [X0] :
( nbr_proc = host(X0)
| ~ leq(nbr_proc,host(X0)) ),
inference(resolution,[status(thm)],[f196,f76]) ).
fof(f529,definition,
( sQ24_spl
<=> s(host(sK12_skl)) = nbr_proc ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( ~ sQ24_spl
| s(host(sK12_skl)) = nbr_proc ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f540,plain,
( leq(nbr_proc,host(sK12_skl))
| nbr_proc = s(host(sK12_skl)) ),
inference(resolution,[status(thm)],[f208,f250]) ).
fof(f546,definition,
( sQ25_spl
<=> leq(nbr_proc,host(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( ~ sQ25_spl
| leq(nbr_proc,host(sK12_skl)) ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f549,plain,
( sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f540,f529,f546]) ).
fof(f750,plain,
! [X0,X1] :
( leq(host(sK6_skl),host(X0))
| index(status,host(sK5_skl)) != elec_2
| host(sK5_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(sK5_skl,alive)
| ~ setIn(X0,alive) ),
inference(paramodulation,[status(thm)],[f242,f222]) ).
fof(f751,plain,
! [X0] :
( leq(host(sK6_skl),host(X0))
| index(status,host(sK5_skl)) != elec_2
| ~ setIn(host(sK5_skl),index(down,host(X0)))
| ~ setIn(sK5_skl,alive)
| ~ setIn(X0,alive) ),
inference(paramodulation,[status(thm)],[f242,f220]) ).
fof(f752,definition,
! [X0,X1] :
( sQ39_spl
<=> ( leq(host(sK6_skl),host(X0))
| host(sK5_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(X0,alive) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f753,plain,
! [X0,X1] :
( ~ sQ39_spl
| leq(host(sK6_skl),host(X0))
| host(sK5_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(X0,alive) ),
inference(component_clause,[status(thm)],[f752]) ).
fof(f755,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f750,f752,f307,f364]) ).
fof(f756,definition,
! [X0] :
( sQ40_spl
<=> ( leq(host(sK6_skl),host(X0))
| ~ setIn(host(sK5_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f757,plain,
! [X0] :
( ~ sQ40_spl
| leq(host(sK6_skl),host(X0))
| ~ setIn(host(sK5_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ),
inference(component_clause,[status(thm)],[f756]) ).
fof(f759,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f751,f756,f307,f364]) ).
fof(f771,plain,
leq(nbr_proc,host(sK6_skl)),
inference(forward_demodulation,[status(thm)],[f242,f243]) ).
fof(f773,plain,
( host(sK6_skl) = nbr_proc
| ~ leq(host(sK6_skl),nbr_proc) ),
inference(resolution,[status(thm)],[f771,f196]) ).
fof(f774,definition,
( sQ41_spl
<=> leq(host(sK6_skl),nbr_proc) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f776,plain,
( sQ41_spl
| ~ leq(host(sK6_skl),nbr_proc) ),
inference(component_clause,[status(thm)],[f774]) ).
fof(f777,definition,
( sQ42_spl
<=> host(sK6_skl) = nbr_proc ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f778,plain,
( ~ sQ42_spl
| host(sK6_skl) = nbr_proc ),
inference(component_clause,[status(thm)],[f777]) ).
fof(f780,plain,
( sQ42_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f773,f774,f777]) ).
fof(f794,definition,
( sQ46_spl
<=> setIn(sK12_skl,alive) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f796,plain,
( sQ46_spl
| ~ setIn(sK12_skl,alive) ),
inference(component_clause,[status(thm)],[f794]) ).
fof(f802,plain,
( sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f796,f249]) ).
fof(f803,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f802]) ).
fof(f832,plain,
! [X0] :
( leq(X0,host(sK12_skl))
| X0 = s(host(sK12_skl))
| ~ leq(X0,host(sK13_skl)) ),
inference(paramodulation,[status(thm)],[f253,f208]) ).
fof(f841,plain,
! [X0] :
( leq(X0,host(sK12_skl))
| X0 = host(sK13_skl)
| ~ leq(X0,host(sK13_skl)) ),
inference(forward_demodulation,[status(thm)],[f253,f832]) ).
fof(f1398,plain,
( ~ sQ24_spl
| host(sK13_skl) = nbr_proc ),
inference(backward_demodulation,[status(thm)],[f530,f253]) ).
fof(f1784,plain,
( sQ15_spl
| elec_2 != elec_2 ),
inference(forward_demodulation,[status(thm)],[f241,f366]) ).
fof(f1785,plain,
( sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1784]) ).
fof(f1786,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1785]) ).
fof(f1787,plain,
( sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f776,f76]) ).
fof(f1788,plain,
sQ41_spl,
inference(contradiction_clause,[status(thm)],[f1787]) ).
fof(f2196,plain,
( ~ sQ25_spl
| nbr_proc = host(sK12_skl) ),
inference(resolution,[status(thm)],[f547,f419]) ).
fof(f4107,plain,
! [X0] :
( ~ sQ24_spl
| leq(X0,host(sK12_skl))
| X0 = host(sK13_skl)
| ~ leq(X0,nbr_proc) ),
inference(forward_demodulation,[status(thm)],[f1398,f841]) ).
fof(f4108,plain,
! [X0] :
( ~ sQ24_spl
| leq(X0,host(sK12_skl))
| X0 = nbr_proc
| ~ leq(X0,nbr_proc) ),
inference(forward_demodulation,[status(thm)],[f1398,f4107]) ).
fof(f4470,definition,
( sQ259_spl
<=> host(sK4_skl) = host(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f4471,plain,
( ~ sQ259_spl
| host(sK4_skl) = host(sK12_skl) ),
inference(component_clause,[status(thm)],[f4470]) ).
fof(f4473,definition,
( sQ260_spl
<=> host(sK14_skl) = host(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f4499,plain,
( ~ sQ259_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4471,f378]) ).
fof(f4500,plain,
( ~ sQ259_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f4499]) ).
fof(f4675,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ sQ16_spl
| leq(host(sK6_skl),host(X0))
| host(sK4_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(X0,alive) ),
inference(forward_demodulation,[status(thm)],[f368,f753]) ).
fof(f4676,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ sQ16_spl
| ~ sQ42_spl
| leq(nbr_proc,host(X0))
| host(sK4_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(X0,alive) ),
inference(forward_demodulation,[status(thm)],[f778,f4675]) ).
fof(f4677,plain,
( ~ sQ39_spl
| ~ sQ16_spl
| ~ sQ42_spl
| leq(nbr_proc,host(sK12_skl))
| host(sK4_skl) != host(sK13_skl)
| ~ setIn(sK12_skl,alive) ),
inference(resolution,[status(thm)],[f4676,f251]) ).
fof(f4678,plain,
( ~ sQ39_spl
| ~ sQ16_spl
| ~ sQ42_spl
| leq(nbr_proc,host(sK12_skl))
| host(sK4_skl) != host(sK14_skl)
| ~ setIn(sK12_skl,alive) ),
inference(resolution,[status(thm)],[f4676,f252]) ).
fof(f4682,definition,
( sQ287_spl
<=> host(sK4_skl) = host(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f4684,plain,
( sQ287_spl
| host(sK4_skl) != host(sK13_skl) ),
inference(component_clause,[status(thm)],[f4682]) ).
fof(f4685,plain,
( ~ sQ39_spl
| ~ sQ16_spl
| ~ sQ42_spl
| sQ25_spl
| ~ sQ287_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f4677,f794,f4682,f546,f777,f367,f752]) ).
fof(f4686,plain,
( ~ sQ39_spl
| ~ sQ16_spl
| ~ sQ42_spl
| sQ25_spl
| ~ sQ260_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f4678,f794,f4473,f546,f777,f367,f752]) ).
fof(f4705,plain,
( sQ287_spl
| ~ sQ24_spl
| host(sK4_skl) != nbr_proc ),
inference(forward_demodulation,[status(thm)],[f1398,f4684]) ).
fof(f4706,plain,
! [X0] :
( ~ sQ40_spl
| ~ sQ16_spl
| leq(host(sK6_skl),host(X0))
| ~ setIn(host(sK4_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ),
inference(forward_demodulation,[status(thm)],[f368,f757]) ).
fof(f4707,plain,
! [X0] :
( ~ sQ40_spl
| ~ sQ16_spl
| ~ sQ42_spl
| leq(nbr_proc,host(X0))
| ~ setIn(host(sK4_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ),
inference(forward_demodulation,[status(thm)],[f778,f4706]) ).
fof(f4708,plain,
( ~ sQ40_spl
| ~ sQ16_spl
| ~ sQ42_spl
| host(sK4_skl) = host(sK14_skl)
| ~ leq(s(zero),host(sK4_skl))
| leq(host(sK12_skl),host(sK4_skl))
| leq(nbr_proc,host(sK12_skl))
| ~ setIn(sK12_skl,alive) ),
inference(resolution,[status(thm)],[f4707,f248]) ).
fof(f4711,definition,
( sQ293_spl
<=> leq(host(sK12_skl),host(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f4712,plain,
( ~ sQ293_spl
| leq(host(sK12_skl),host(sK4_skl)) ),
inference(component_clause,[status(thm)],[f4711]) ).
fof(f4714,definition,
( sQ294_spl
<=> leq(s(zero),host(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f4716,plain,
( sQ294_spl
| ~ leq(s(zero),host(sK4_skl)) ),
inference(component_clause,[status(thm)],[f4714]) ).
fof(f4717,plain,
( ~ sQ40_spl
| ~ sQ16_spl
| ~ sQ42_spl
| sQ260_spl
| ~ sQ294_spl
| sQ293_spl
| sQ25_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f4708,f794,f546,f4711,f4714,f4473,f777,f367,f756]) ).
fof(f4788,plain,
( ~ sQ293_spl
| host(sK4_skl) = host(sK12_skl)
| ~ leq(host(sK4_skl),host(sK12_skl)) ),
inference(resolution,[status(thm)],[f4712,f196]) ).
fof(f4793,definition,
( sQ304_spl
<=> leq(host(sK4_skl),host(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f4795,plain,
( sQ304_spl
| ~ leq(host(sK4_skl),host(sK12_skl)) ),
inference(component_clause,[status(thm)],[f4793]) ).
fof(f4796,plain,
( ~ sQ293_spl
| sQ259_spl
| ~ sQ304_spl ),
inference(split_clause,[status(thm)],[f4788,f4793,f4470,f4711]) ).
fof(f4797,plain,
( ~ sQ24_spl
| sQ304_spl
| host(sK4_skl) = nbr_proc
| ~ leq(host(sK4_skl),nbr_proc) ),
inference(resolution,[status(thm)],[f4795,f4108]) ).
fof(f4803,definition,
( sQ305_spl
<=> leq(host(sK4_skl),nbr_proc) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f4805,plain,
( sQ305_spl
| ~ leq(host(sK4_skl),nbr_proc) ),
inference(component_clause,[status(thm)],[f4803]) ).
fof(f4806,definition,
( sQ306_spl
<=> host(sK4_skl) = nbr_proc ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f4807,plain,
( ~ sQ306_spl
| host(sK4_skl) = nbr_proc ),
inference(component_clause,[status(thm)],[f4806]) ).
fof(f4809,plain,
( ~ sQ24_spl
| sQ304_spl
| sQ306_spl
| ~ sQ305_spl ),
inference(split_clause,[status(thm)],[f4797,f4803,f4806,f4793,f529]) ).
fof(f4810,plain,
( sQ305_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4805,f76]) ).
fof(f4811,plain,
sQ305_spl,
inference(contradiction_clause,[status(thm)],[f4810]) ).
fof(f4812,plain,
( ~ sQ306_spl
| sQ287_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4807,f4705]) ).
fof(f4813,plain,
( ~ sQ306_spl
| sQ287_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f4812]) ).
fof(f4814,plain,
( sQ294_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4716,f74]) ).
fof(f4815,plain,
sQ294_spl,
inference(contradiction_clause,[status(thm)],[f4814]) ).
fof(f5054,definition,
( sQ338_spl
<=> leq(host(sK13_skl),nbr_proc) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f5056,plain,
( sQ338_spl
| ~ leq(host(sK13_skl),nbr_proc) ),
inference(component_clause,[status(thm)],[f5054]) ).
fof(f5058,plain,
( sQ338_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5056,f76]) ).
fof(f5059,plain,
sQ338_spl,
inference(contradiction_clause,[status(thm)],[f5058]) ).
fof(f5069,plain,
( ~ sQ25_spl
| host(sK13_skl) = s(nbr_proc) ),
inference(forward_demodulation,[status(thm)],[f2196,f253]) ).
fof(f5100,plain,
( ~ sQ25_spl
| ~ leq(host(sK13_skl),nbr_proc) ),
inference(paramodulation,[status(thm)],[f5069,f191]) ).
fof(f5110,plain,
( ~ sQ25_spl
| ~ sQ338_spl ),
inference(split_clause,[status(thm)],[f5100,f5054,f546]) ).
fof(f5111,plain,
$false,
inference(sat_refutation,[status(thm)],[f370,f376,f549,f755,f759,f780,f803,f1786,f1788,f4500,f4685,f4686,f4717,f4796,f4809,f4811,f4813,f4815,f5059,f5110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV476+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 08:50:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 9.38/1.66 % Refutation found
% 9.38/1.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.38/1.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.38/1.68 % Elapsed time: 1.292991 seconds
% 9.38/1.68 % CPU time: 9.949596 seconds
% 9.38/1.68 % Total memory used: 192.371 MB
% 9.38/1.68 % Net memory used: 176.222 MB
%------------------------------------------------------------------------------