%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV478+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:48:01 PM UTC 2026
% Result : Theorem 86.01s 11.27s
% Output : CNFRefutation 86.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 36
% Syntax : Number of formulae : 169 ( 35 unt; 24 def)
% Number of atoms : 1044 ( 383 equ)
% Maximal formula atoms : 126 ( 6 avg)
% Number of connectives : 1398 ( 523 ~; 464 |; 323 &)
% ( 28 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 29 ( 27 usr; 25 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 21 con; 0-4 aty)
% Number of variables : 384 ( 363 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [P,Q] :
( s(host(P)) = host(Q)
=> host(P) != host(Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [P] : leq(s(zero),host(P)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [P] : leq(host(P),nbr_proc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] : m_Down(X) != m_Ldr(Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X,Y,Q] :
( elem(X,cons(Y,Q))
<=> ( elem(X,Q)
| X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [X,Y,Q] :
( elem(X,snoc(Q,Y))
<=> ( elem(X,Q)
| X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [X] : leq(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [X,Y] :
( leq(Y,X)
| leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
<=> X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [X,Y] :
( leq(X,s(Y))
<=> ( leq(X,Y)
| X = s(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,conjecture,
! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Down(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)
=> ( leq(host(X),host(Y))
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2 )
=> ( leq(nbr_proc,index(pendack,host(X)))
=> ! [Z] :
( 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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,negated_conjecture,
~ ! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Down(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)
=> ( leq(host(X),host(Y))
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2 )
=> ( leq(nbr_proc,index(pendack,host(X)))
=> ! [Z] :
( 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(negated_conjecture,[status(cth)],[f67]) ).
fof(f72,plain,
! [P,Q] :
( host(P) != host(Q)
| s(host(P)) != host(Q) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f73,plain,
! [X0,X1] :
( host(X0) != host(X1)
| s(host(X0)) != host(X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
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(f90,plain,
! [X0,X1] : m_Down(X0) != m_Ldr(X1),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f138,plain,
! [X,Y,Q] :
( ( ( ~ elem(X,Q)
& X != Y )
| elem(X,cons(Y,Q)) )
& ( elem(X,Q)
| X = Y
| ~ elem(X,cons(Y,Q)) ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f139,plain,
( ! [X,Y,Q] :
( ( ~ elem(X,Q)
& X != Y )
| elem(X,cons(Y,Q)) )
& ! [X,Y,Q] :
( elem(X,Q)
| X = Y
| ~ elem(X,cons(Y,Q)) ) ),
inference(miniscoping,[status(thm)],[f138]) ).
fof(f141,plain,
! [X0,X1,X2] :
( X0 != X1
| elem(X0,cons(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
! [X,Y,Q] :
( ( ( ~ elem(X,Q)
& X != Y )
| elem(X,snoc(Q,Y)) )
& ( elem(X,Q)
| X = Y
| ~ elem(X,snoc(Q,Y)) ) ),
inference(NNF_transformation,[status(thm)],[f48]) ).
fof(f144,plain,
( ! [X,Y,Q] :
( ( ~ elem(X,Q)
& X != Y )
| elem(X,snoc(Q,Y)) )
& ! [X,Y,Q] :
( elem(X,Q)
| X = Y
| ~ elem(X,snoc(Q,Y)) ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f145,plain,
! [X0,X1,X2] :
( elem(X0,X1)
| X0 = X2
| ~ elem(X0,snoc(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f192,plain,
! [X0] : leq(X0,X0),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f193,plain,
! [X0,X1] :
( leq(X1,X0)
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
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(f199,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f200,plain,
! [X,Z] :
( leq(X,Z)
| ! [Y] :
( ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f199]) ).
fof(f201,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
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),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] :
( 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) )
& 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
& leq(host(X),host(Y))
& setIn(X,alive)
& queue(host(X)) = cons(m_Down(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,
? [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),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] :
( 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) )
& 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
& leq(host(X),host(Y))
& setIn(X,alive)
& ? [V] : queue(host(X)) = cons(m_Down(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(sK4_skl) = host(sK10_skl)
& setIn(sK10_skl,alive)
& index(status,host(sK11_skl)) = elec_1
& host(sK12_skl) = s(host(sK11_skl))
& elem(m_Down(sK13_skl),snoc(queue(host(sK11_skl)),m_Ldr(sK4_skl)))
& elem(m_Down(sK12_skl),snoc(queue(host(sK11_skl)),m_Ldr(sK4_skl)))
& leq(nbr_proc,s(host(sK11_skl)))
& setIn(sK11_skl,alive)
& ! [V1] :
( V1 = host(sK13_skl)
| setIn(V1,index(down,host(sK11_skl)))
| ~ leq(s(zero),V1)
| leq(host(sK11_skl),V1) )
& host(sK4_skl) != host(sK11_skl)
& host(sK9_skl) = host(sK11_skl)
& host(sK4_skl) = host(sK10_skl)
& setIn(host(sK9_skl),index(acks,host(sK4_skl)))
& leq(nbr_proc,index(pendack,host(sK4_skl)))
& host(sK5_skl) = index(pendack,host(sK4_skl))
& index(status,host(sK4_skl)) = elec_2
& leq(host(sK4_skl),host(sK5_skl))
& setIn(sK4_skl,alive)
& queue(host(sK4_skl)) = cons(m_Down(sK5_skl),sK8_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)
| ( sK7_skl(Pid20,Pid30,Pid0) != host(Pid20)
& ~ setIn(sK7_skl(Pid20,Pid30,Pid0),index(down,host(Pid0)))
& leq(s(zero),sK7_skl(Pid20,Pid30,Pid0))
& ~ leq(host(Pid0),sK7_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)
| ( sK6_skl(Pid20,Pid0,Pid30,Z) != host(Pid20)
& ~ setIn(sK6_skl(Pid20,Pid0,Pid30,Z),index(down,host(Pid0)))
& leq(s(zero),sK6_skl(Pid20,Pid0,Pid30,Z))
& ~ leq(host(Pid0),sK6_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]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl),skolemize(V0,sK6_skl(Pid20,Pid0,Pid30,Z)),skolemize(V0,sK7_skl(Pid20,Pid30,Pid0)),skolemize(V,sK8_skl),skolemize(Z,sK9_skl),skolemize(V0,sK10_skl),skolemize(Y0,sK11_skl),skolemize(W0,sK12_skl),skolemize(X0,sK13_skl)],[f213]) ).
fof(f216,plain,
! [X0,X1] :
( host(X0) != host(X1)
| ~ elem(m_Down(X0),queue(host(X1))) ),
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(f238,plain,
queue(host(sK4_skl)) = cons(m_Down(sK5_skl),sK8_skl),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f239,plain,
setIn(sK4_skl,alive),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f240,plain,
leq(host(sK4_skl),host(sK5_skl)),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f241,plain,
index(status,host(sK4_skl)) = elec_2,
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f242,plain,
host(sK5_skl) = index(pendack,host(sK4_skl)),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f243,plain,
leq(nbr_proc,index(pendack,host(sK4_skl))),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f246,plain,
host(sK9_skl) = host(sK11_skl),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f247,plain,
host(sK4_skl) != host(sK11_skl),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f248,plain,
! [X0] :
( X0 = host(sK13_skl)
| setIn(X0,index(down,host(sK11_skl)))
| ~ leq(s(zero),X0)
| leq(host(sK11_skl),X0) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f249,plain,
setIn(sK11_skl,alive),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f250,plain,
leq(nbr_proc,s(host(sK11_skl))),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f252,plain,
elem(m_Down(sK13_skl),snoc(queue(host(sK11_skl)),m_Ldr(sK4_skl))),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f253,plain,
host(sK12_skl) = s(host(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f276,plain,
! [X0,X1] : elem(X0,cons(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f141]) ).
fof(f329,definition,
( sQ10_spl
<=> setIn(sK11_skl,alive) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ10_spl
| ~ setIn(sK11_skl,alive) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f342,definition,
( sQ14_spl
<=> setIn(sK4_skl,alive) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( sQ14_spl
| ~ setIn(sK4_skl,alive) ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f386,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f344,f239]) ).
fof(f387,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f427,plain,
( host(sK5_skl) = host(sK4_skl)
| ~ leq(host(sK5_skl),host(sK4_skl)) ),
inference(resolution,[status(thm)],[f196,f240]) ).
fof(f428,plain,
! [X0] :
( nbr_proc = host(X0)
| ~ leq(nbr_proc,host(X0)) ),
inference(resolution,[status(thm)],[f196,f76]) ).
fof(f434,definition,
( sQ25_spl
<=> leq(host(sK5_skl),host(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( sQ25_spl
| ~ leq(host(sK5_skl),host(sK4_skl)) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ26_spl
<=> host(sK5_skl) = host(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ26_spl
| host(sK5_skl) = host(sK4_skl) ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f427,f434,f437]) ).
fof(f482,plain,
leq(nbr_proc,host(sK12_skl)),
inference(backward_demodulation,[status(thm)],[f253,f250]) ).
fof(f502,plain,
( host(sK12_skl) = nbr_proc
| ~ leq(host(sK12_skl),nbr_proc) ),
inference(resolution,[status(thm)],[f482,f196]) ).
fof(f503,definition,
( sQ34_spl
<=> leq(host(sK12_skl),nbr_proc) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ34_spl
| ~ leq(host(sK12_skl),nbr_proc) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
( sQ35_spl
<=> host(sK12_skl) = nbr_proc ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( ~ sQ35_spl
| host(sK12_skl) = nbr_proc ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,plain,
( sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f502,f503,f506]) ).
fof(f510,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f76]) ).
fof(f511,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f513,plain,
( ~ sQ35_spl
| nbr_proc = s(host(sK11_skl)) ),
inference(backward_demodulation,[status(thm)],[f507,f253]) ).
fof(f572,plain,
! [X0] :
( ~ sQ35_spl
| host(sK11_skl) != host(X0)
| nbr_proc != host(X0) ),
inference(paramodulation,[status(thm)],[f513,f73]) ).
fof(f640,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f331,f249]) ).
fof(f641,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f640]) ).
fof(f753,plain,
! [X0,X1] :
( leq(X0,nbr_proc)
| ~ leq(X0,host(X1)) ),
inference(resolution,[status(thm)],[f201,f76]) ).
fof(f870,plain,
! [X0] :
( ~ sQ35_spl
| leq(X0,host(sK11_skl))
| X0 = s(host(sK11_skl))
| ~ leq(X0,nbr_proc) ),
inference(paramodulation,[status(thm)],[f513,f208]) ).
fof(f871,plain,
! [X0] :
( ~ sQ35_spl
| leq(X0,host(sK11_skl))
| X0 = nbr_proc
| ~ leq(X0,nbr_proc) ),
inference(forward_demodulation,[status(thm)],[f513,f870]) ).
fof(f1142,plain,
elem(m_Down(sK5_skl),queue(host(sK4_skl))),
inference(paramodulation,[status(thm)],[f238,f276]) ).
fof(f1180,plain,
! [X0,X1] :
( leq(host(sK5_skl),host(X0))
| index(status,host(sK4_skl)) != elec_2
| host(sK4_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(sK4_skl,alive)
| ~ setIn(X0,alive) ),
inference(paramodulation,[status(thm)],[f242,f222]) ).
fof(f1181,plain,
! [X0] :
( leq(host(sK5_skl),host(X0))
| index(status,host(sK4_skl)) != elec_2
| ~ setIn(host(sK4_skl),index(down,host(X0)))
| ~ setIn(sK4_skl,alive)
| ~ setIn(X0,alive) ),
inference(paramodulation,[status(thm)],[f242,f220]) ).
fof(f1182,definition,
! [X0,X1] :
( sQ97_spl
<=> ( leq(host(sK5_skl),host(X0))
| host(sK4_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(X0,alive) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1183,plain,
! [X0,X1] :
( ~ sQ97_spl
| leq(host(sK5_skl),host(X0))
| host(sK4_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(X0,alive) ),
inference(component_clause,[status(thm)],[f1182]) ).
fof(f1185,definition,
( sQ98_spl
<=> index(status,host(sK4_skl)) = elec_2 ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1187,plain,
( sQ98_spl
| index(status,host(sK4_skl)) != elec_2 ),
inference(component_clause,[status(thm)],[f1185]) ).
fof(f1188,plain,
( ~ sQ98_spl
| ~ sQ14_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1180,f1182,f342,f1185]) ).
fof(f1189,definition,
! [X0] :
( sQ99_spl
<=> ( leq(host(sK5_skl),host(X0))
| ~ setIn(host(sK4_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1190,plain,
! [X0] :
( ~ sQ99_spl
| leq(host(sK5_skl),host(X0))
| ~ setIn(host(sK4_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ),
inference(component_clause,[status(thm)],[f1189]) ).
fof(f1192,plain,
( ~ sQ98_spl
| ~ sQ14_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1181,f1189,f342,f1185]) ).
fof(f1193,plain,
( sQ98_spl
| elec_2 != elec_2 ),
inference(forward_demodulation,[status(thm)],[f241,f1187]) ).
fof(f1194,plain,
( sQ98_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1193]) ).
fof(f1195,plain,
sQ98_spl,
inference(contradiction_clause,[status(thm)],[f1194]) ).
fof(f1196,plain,
leq(nbr_proc,host(sK5_skl)),
inference(forward_demodulation,[status(thm)],[f242,f243]) ).
fof(f1199,plain,
( host(sK5_skl) = nbr_proc
| ~ leq(host(sK5_skl),nbr_proc) ),
inference(resolution,[status(thm)],[f1196,f196]) ).
fof(f1200,definition,
( sQ100_spl
<=> leq(host(sK5_skl),nbr_proc) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1202,plain,
( sQ100_spl
| ~ leq(host(sK5_skl),nbr_proc) ),
inference(component_clause,[status(thm)],[f1200]) ).
fof(f1203,definition,
( sQ101_spl
<=> host(sK5_skl) = nbr_proc ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1204,plain,
( ~ sQ101_spl
| host(sK5_skl) = nbr_proc ),
inference(component_clause,[status(thm)],[f1203]) ).
fof(f1206,plain,
( sQ101_spl
| ~ sQ100_spl ),
inference(split_clause,[status(thm)],[f1199,f1200,f1203]) ).
fof(f1207,plain,
( sQ100_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1202,f76]) ).
fof(f1208,plain,
sQ100_spl,
inference(contradiction_clause,[status(thm)],[f1207]) ).
fof(f1211,plain,
( sQ25_spl
| ~ sQ101_spl
| ~ leq(nbr_proc,host(sK4_skl)) ),
inference(backward_demodulation,[status(thm)],[f1204,f436]) ).
fof(f1346,plain,
! [X0] :
( sQ25_spl
| ~ sQ101_spl
| ~ leq(X0,host(sK4_skl))
| ~ leq(nbr_proc,X0) ),
inference(resolution,[status(thm)],[f1211,f201]) ).
fof(f1399,plain,
( elem(m_Down(sK13_skl),queue(host(sK11_skl)))
| m_Down(sK13_skl) = m_Ldr(sK4_skl) ),
inference(resolution,[status(thm)],[f252,f145]) ).
fof(f1400,definition,
( sQ131_spl
<=> m_Down(sK13_skl) = m_Ldr(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1401,plain,
( ~ sQ131_spl
| m_Down(sK13_skl) = m_Ldr(sK4_skl) ),
inference(component_clause,[status(thm)],[f1400]) ).
fof(f1403,definition,
( sQ132_spl
<=> elem(m_Down(sK13_skl),queue(host(sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1404,plain,
( ~ sQ132_spl
| elem(m_Down(sK13_skl),queue(host(sK11_skl))) ),
inference(component_clause,[status(thm)],[f1403]) ).
fof(f1406,plain,
( sQ132_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1399,f1400,f1403]) ).
fof(f1407,plain,
( ~ sQ131_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1401,f90]) ).
fof(f1408,plain,
~ sQ131_spl,
inference(contradiction_clause,[status(thm)],[f1407]) ).
fof(f1463,plain,
! [X0,X1] :
( leq(host(X1),X0)
| leq(X0,nbr_proc) ),
inference(resolution,[status(thm)],[f753,f193]) ).
fof(f1530,plain,
( ~ sQ35_spl
| host(sK11_skl) != host(sK11_skl)
| nbr_proc != host(sK9_skl) ),
inference(paramodulation,[status(thm)],[f246,f572]) ).
fof(f1538,definition,
( sQ147_spl
<=> nbr_proc = host(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1541,definition,
( sQ148_spl
<=> host(sK11_skl) = host(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1543,plain,
( sQ148_spl
| host(sK11_skl) != host(sK11_skl) ),
inference(component_clause,[status(thm)],[f1541]) ).
fof(f1544,plain,
( ~ sQ35_spl
| ~ sQ148_spl
| ~ sQ147_spl ),
inference(split_clause,[status(thm)],[f1530,f1538,f1541,f506]) ).
fof(f1641,plain,
( nbr_proc = host(sK9_skl)
| ~ leq(nbr_proc,host(sK11_skl)) ),
inference(paramodulation,[status(thm)],[f246,f428]) ).
fof(f1651,definition,
( sQ152_spl
<=> leq(nbr_proc,host(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1654,plain,
( sQ147_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f1641,f1651,f1538]) ).
fof(f1655,plain,
( sQ148_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1543]) ).
fof(f1656,plain,
sQ148_spl,
inference(contradiction_clause,[status(thm)],[f1655]) ).
fof(f1678,definition,
! [X0] :
( sQ155_spl
<=> ~ leq(nbr_proc,host(X0)) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1679,plain,
! [X0] :
( ~ sQ155_spl
| ~ leq(nbr_proc,host(X0)) ),
inference(component_clause,[status(thm)],[f1678]) ).
fof(f1821,definition,
( sQ160_spl
<=> host(sK4_skl) = nbr_proc ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1822,plain,
( ~ sQ160_spl
| host(sK4_skl) = nbr_proc ),
inference(component_clause,[status(thm)],[f1821]) ).
fof(f1832,definition,
( sQ163_spl
<=> host(sK4_skl) = host(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1833,plain,
( ~ sQ163_spl
| host(sK4_skl) = host(sK11_skl) ),
inference(component_clause,[status(thm)],[f1832]) ).
fof(f2008,plain,
( ~ sQ101_spl
| ~ sQ155_spl
| ~ leq(nbr_proc,nbr_proc) ),
inference(paramodulation,[status(thm)],[f1204,f1679]) ).
fof(f2011,plain,
( ~ sQ101_spl
| ~ sQ155_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2008,f192]) ).
fof(f2012,plain,
( ~ sQ101_spl
| ~ sQ155_spl ),
inference(contradiction_clause,[status(thm)],[f2011]) ).
fof(f2407,plain,
host(sK5_skl) != host(sK4_skl),
inference(resolution,[status(thm)],[f1142,f216]) ).
fof(f2412,plain,
( ~ sQ101_spl
| nbr_proc != host(sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1204,f2407]) ).
fof(f2609,plain,
! [X0] :
( sQ25_spl
| ~ sQ101_spl
| leq(host(sK4_skl),nbr_proc)
| ~ leq(nbr_proc,host(X0)) ),
inference(resolution,[status(thm)],[f1346,f1463]) ).
fof(f2623,definition,
( sQ208_spl
<=> leq(host(sK4_skl),nbr_proc) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2636,plain,
( sQ25_spl
| ~ sQ101_spl
| sQ208_spl
| sQ155_spl ),
inference(split_clause,[status(thm)],[f2609,f1678,f2623,f1203,f434]) ).
fof(f2642,plain,
( ~ sQ26_spl
| ~ sQ101_spl
| nbr_proc = host(sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1204,f438]) ).
fof(f2643,plain,
( ~ sQ26_spl
| ~ sQ101_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2642,f2412]) ).
fof(f2644,plain,
( ~ sQ26_spl
| ~ sQ101_spl ),
inference(contradiction_clause,[status(thm)],[f2643]) ).
fof(f5258,plain,
! [X0,X1] :
( ~ sQ97_spl
| ~ sQ101_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)],[f1204,f1183]) ).
fof(f5260,plain,
( ~ sQ132_spl
| ~ sQ97_spl
| ~ sQ101_spl
| leq(nbr_proc,host(sK11_skl))
| host(sK4_skl) != host(sK13_skl)
| ~ setIn(sK11_skl,alive) ),
inference(resolution,[status(thm)],[f5258,f1404]) ).
fof(f5266,definition,
( sQ322_spl
<=> host(sK4_skl) = host(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f5269,plain,
( ~ sQ132_spl
| ~ sQ97_spl
| ~ sQ101_spl
| sQ152_spl
| ~ sQ322_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5260,f329,f5266,f1651,f1203,f1182,f1403]) ).
fof(f5293,plain,
! [X0] :
( ~ sQ99_spl
| ~ sQ101_spl
| leq(nbr_proc,host(X0))
| ~ setIn(host(sK4_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ),
inference(forward_demodulation,[status(thm)],[f1204,f1190]) ).
fof(f5294,plain,
( ~ sQ99_spl
| ~ sQ101_spl
| host(sK4_skl) = host(sK13_skl)
| ~ leq(s(zero),host(sK4_skl))
| leq(host(sK11_skl),host(sK4_skl))
| leq(nbr_proc,host(sK11_skl))
| ~ setIn(sK11_skl,alive) ),
inference(resolution,[status(thm)],[f5293,f248]) ).
fof(f5298,definition,
( sQ329_spl
<=> leq(host(sK11_skl),host(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f5299,plain,
( ~ sQ329_spl
| leq(host(sK11_skl),host(sK4_skl)) ),
inference(component_clause,[status(thm)],[f5298]) ).
fof(f5301,definition,
( sQ330_spl
<=> leq(s(zero),host(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f5303,plain,
( sQ330_spl
| ~ leq(s(zero),host(sK4_skl)) ),
inference(component_clause,[status(thm)],[f5301]) ).
fof(f5304,plain,
( ~ sQ99_spl
| ~ sQ101_spl
| sQ322_spl
| ~ sQ330_spl
| sQ329_spl
| sQ152_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5294,f329,f1651,f5298,f5301,f5266,f1203,f1189]) ).
fof(f5926,plain,
( ~ sQ329_spl
| host(sK4_skl) = host(sK11_skl)
| ~ leq(host(sK4_skl),host(sK11_skl)) ),
inference(resolution,[status(thm)],[f5299,f196]) ).
fof(f5931,definition,
( sQ346_spl
<=> leq(host(sK4_skl),host(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f5933,plain,
( sQ346_spl
| ~ leq(host(sK4_skl),host(sK11_skl)) ),
inference(component_clause,[status(thm)],[f5931]) ).
fof(f5934,plain,
( ~ sQ329_spl
| sQ163_spl
| ~ sQ346_spl ),
inference(split_clause,[status(thm)],[f5926,f5931,f1832,f5298]) ).
fof(f5935,plain,
( ~ sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1833,f247]) ).
fof(f5936,plain,
~ sQ163_spl,
inference(contradiction_clause,[status(thm)],[f5935]) ).
fof(f6411,plain,
( sQ330_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5303,f74]) ).
fof(f6412,plain,
sQ330_spl,
inference(contradiction_clause,[status(thm)],[f6411]) ).
fof(f6926,plain,
( sQ346_spl
| ~ sQ35_spl
| host(sK4_skl) = nbr_proc
| ~ leq(host(sK4_skl),nbr_proc) ),
inference(resolution,[status(thm)],[f871,f5933]) ).
fof(f6962,plain,
( sQ346_spl
| ~ sQ35_spl
| sQ160_spl
| ~ sQ208_spl ),
inference(split_clause,[status(thm)],[f6926,f2623,f1821,f506,f5931]) ).
fof(f6982,plain,
( ~ sQ160_spl
| ~ sQ101_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1822,f2412]) ).
fof(f6983,plain,
( ~ sQ160_spl
| ~ sQ101_spl ),
inference(contradiction_clause,[status(thm)],[f6982]) ).
fof(f6984,plain,
$false,
inference(sat_refutation,[status(thm)],[f387,f440,f509,f511,f641,f1188,f1192,f1195,f1206,f1208,f1406,f1408,f1544,f1654,f1656,f2012,f2636,f2644,f5269,f5304,f5934,f5936,f6412,f6962,f6983]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV478+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 08:53:48 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 86.01/11.27 % Refutation found
% 86.01/11.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 86.01/11.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 86.01/11.33 % Elapsed time: 10.961573 seconds
% 86.01/11.33 % CPU time: 86.687571 seconds
% 86.01/11.33 % Total memory used: 406.836 MB
% 86.01/11.33 % Net memory used: 346.799 MB
%------------------------------------------------------------------------------