%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV468+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 : n015.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 13.35s 2.15s
% Output : CNFRefutation 13.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 26 unt; 0 def)
% Number of atoms : 682 ( 287 equ)
% Maximal formula atoms : 109 ( 11 avg)
% Number of connectives : 1001 ( 381 ~; 298 |; 264 &)
% ( 2 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 19 con; 0-3 aty)
% Number of variables : 279 ( 264 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
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(f47,axiom,
! [X,Y,Q] :
( elem(X,cons(Y,Q))
<=> ( elem(X,Q)
| 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(f67,conjecture,
! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Down(Y),V)
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& elem(m_Down(Pid20),queue(host(Pid0)))
& ~ leq(host(Pid0),host(Z))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0))) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(Pid0,alive)
& ~ leq(index(pendack,host(Pid0)),host(Z)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Pid0)
& setIn(Pid0,alive) )
=> ~ ( elem(m_Down(Pid20),queue(host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& elem(m_Down(Pid20),queue(host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& host(Pid0) = host(Pid20)
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> ~ elem(m_Ack(Z,Pid20),queue(host(Z))) )
& ! [Z,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Ack(Pid0,Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Pid0),host(Z)) )
=> ~ elem(m_Down(Pid20),queue(host(Z))) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& setIn(Pid0,alive) )
=> ~ ( setIn(host(Pid0),index(down,host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(host(Pid0),index(down,host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(Pid0,alive) )
=> ~ elem(m_Ack(Z,Pid0),queue(host(Z))) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( ~ leq(host(X),host(Y))
=> ( ~ ( ( host(Y) = host(index(elid,host(X)))
& index(status,host(X)) = wait )
| ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(Y) ) )
=> ( ( index(status,host(X)) = elec_1
& ! [Z] :
( ( leq(s(zero),Z)
& ~ leq(host(X),Z) )
=> ( Z = host(Y)
| setIn(Z,index(down,host(X))) ) ) )
=> ( leq(nbr_proc,host(X))
=> ! [Z] :
( ~ setIn(host(Z),setEmpty)
=> ! [V0] :
( host(X) = host(V0)
=> ! [W0] :
( host(X) != host(W0)
=> ( ( index(status,host(W0)) = elec_2
& setIn(W0,alive)
& ~ leq(index(pendack,host(W0)),host(V0)) )
=> ~ ( 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,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& elem(m_Down(Pid20),queue(host(Pid0)))
& ~ leq(host(Pid0),host(Z))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid20) = host(Z)
& elem(m_Down(Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0))) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(Pid0,alive)
& ~ leq(index(pendack,host(Pid0)),host(Z)) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& host(Pid20) = host(Pid0)
& setIn(Pid0,alive) )
=> ~ ( elem(m_Down(Pid20),queue(host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& elem(m_Down(Pid20),queue(host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& host(Pid0) = host(Pid20)
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> ~ elem(m_Ack(Z,Pid20),queue(host(Z))) )
& ! [Z,Pid20,Pid0] :
( ( host(Pid20) = host(Z)
& elem(m_Ack(Pid0,Pid20),queue(host(Pid0)))
& setIn(Pid0,alive) )
=> ~ ( index(status,host(Z)) = norm
& index(ldr,host(Z)) = host(Z)
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& index(status,host(Z)) = elec_2
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(Pid0)) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& host(Pid0) = host(Pid20)
& setIn(Pid0,alive)
& setIn(Z,alive)
& ~ leq(host(Pid0),host(Z)) )
=> ~ elem(m_Down(Pid20),queue(host(Z))) )
& ! [Z,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid0)
& index(status,host(Pid0)) = norm
& setIn(Pid0,alive) )
=> ~ ( setIn(host(Pid0),index(down,host(Z)))
& setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(host(Pid0),index(down,host(Z)))
& setIn(Pid0,alive)
& setIn(Z,alive) )
=> leq(index(pendack,host(Pid0)),host(Z)) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( index(status,host(Pid0)) = elec_2
& setIn(Pid0,alive) )
=> ~ elem(m_Ack(Z,Pid0),queue(host(Z))) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( ~ leq(host(X),host(Y))
=> ( ~ ( ( host(Y) = host(index(elid,host(X)))
& index(status,host(X)) = wait )
| ( index(status,host(X)) = norm
& index(ldr,host(X)) = host(Y) ) )
=> ( ( index(status,host(X)) = elec_1
& ! [Z] :
( ( leq(s(zero),Z)
& ~ leq(host(X),Z) )
=> ( Z = host(Y)
| setIn(Z,index(down,host(X))) ) ) )
=> ( leq(nbr_proc,host(X))
=> ! [Z] :
( ~ setIn(host(Z),setEmpty)
=> ! [V0] :
( host(X) = host(V0)
=> ! [W0] :
( host(X) != host(W0)
=> ( ( index(status,host(W0)) = elec_2
& setIn(W0,alive)
& ~ leq(index(pendack,host(W0)),host(V0)) )
=> ~ ( 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(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(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(f212,plain,
? [V,W,X,Y] :
( ? [Z] :
( ? [V0] :
( ? [W0] :
( host(X) = host(V0)
& setIn(V0,alive)
& index(status,host(W0)) = elec_2
& setIn(W0,alive)
& ~ leq(index(pendack,host(W0)),host(V0))
& host(X) != host(W0) )
& host(X) = host(V0) )
& ~ setIn(host(Z),setEmpty) )
& leq(nbr_proc,host(X))
& index(status,host(X)) = elec_1
& ! [Z] :
( Z = host(Y)
| setIn(Z,index(down,host(X)))
| ~ leq(s(zero),Z)
| leq(host(X),Z) )
& ( host(Y) != host(index(elid,host(X)))
| index(status,host(X)) != wait )
& ( index(status,host(X)) != norm
| index(ldr,host(X)) != host(Y) )
& ~ leq(host(X),host(Y))
& setIn(X,alive)
& queue(host(X)) = cons(m_Down(Y),V)
& ! [Z,Pid20,Pid0] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| index(status,host(Pid0)) != elec_1
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| leq(host(Pid0),host(Z))
| ? [V0] :
( V0 != host(Pid20)
& ~ setIn(V0,index(down,host(Pid0)))
& leq(s(zero),V0)
& ~ leq(host(Pid0),V0) ) )
& ! [Z,Pid20,Pid0] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| index(status,host(Pid0)) != elec_2
| host(Pid20) != host(Z)
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0)))
| index(status,host(Pid0)) != elec_2
| index(status,host(Z)) != elec_2
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| index(status,host(Pid0)) != elec_2
| ~ setIn(Pid0,alive)
| leq(index(pendack,host(Pid0)),host(Z)) )
& ! [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,Pid20,Pid0] :
( ~ elem(m_Ack(Z,Pid20),queue(host(Z)))
| index(status,host(Pid0)) != elec_2
| index(status,host(Z)) != elec_2
| host(Pid0) != host(Pid20)
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) )
& ! [Z,Pid20,Pid0] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| host(Pid20) != host(Z)
| ~ elem(m_Ack(Pid0,Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( leq(index(pendack,host(Pid0)),host(Z))
| index(status,host(Pid0)) != elec_2
| index(status,host(Z)) != elec_2
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| leq(host(Z),host(Pid0)) )
& ! [Z,Pid20,Pid0] :
( ~ elem(m_Down(Pid20),queue(host(Z)))
| index(status,host(Pid0)) != elec_2
| host(Pid0) != host(Pid20)
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| leq(host(Pid0),host(Z)) )
& ! [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] :
( ~ elem(m_Ack(Z,Pid0),queue(host(Z)))
| index(status,host(Pid0)) != elec_2
| ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| host(Pid0) != host(Z)
| Pid0 = 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] :
( ? [V0] :
( ? [W0] :
( host(X) = host(V0)
& setIn(V0,alive)
& index(status,host(W0)) = elec_2
& setIn(W0,alive)
& ~ leq(index(pendack,host(W0)),host(V0))
& host(X) != host(W0) )
& host(X) = host(V0) )
& ? [Z] : ~ setIn(host(Z),setEmpty)
& leq(nbr_proc,host(X))
& index(status,host(X)) = elec_1
& ! [Z] :
( Z = host(Y)
| setIn(Z,index(down,host(X)))
| ~ leq(s(zero),Z)
| leq(host(X),Z) )
& ( host(Y) != host(index(elid,host(X)))
| index(status,host(X)) != wait )
& ( index(status,host(X)) != norm
| index(ldr,host(X)) != host(Y) )
& ~ 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
| ! [Pid20] :
( ~ elem(m_Down(Pid20),queue(host(Pid0)))
| leq(host(Pid0),host(Z))
| ? [V0] :
( V0 != host(Pid20)
& ~ setIn(V0,index(down,host(Pid0)))
& leq(s(zero),V0)
& ~ leq(host(Pid0),V0) ) ) ) )
& ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| ! [Pid0] :
( index(status,host(Pid0)) != elec_2
| ! [Pid20] :
( host(Pid20) != host(Z)
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive) ) ) )
& ! [Z,Pid0] :
( ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0)))
| index(status,host(Pid0)) != elec_2
| index(status,host(Z)) != elec_2
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| leq(host(Z),host(Pid0)) )
& ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| ! [Pid0] :
( index(status,host(Pid0)) != elec_2
| ~ setIn(Pid0,alive)
| leq(index(pendack,host(Pid0)),host(Z)) ) )
& ! [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) ) )
& ! [Z,Pid20] :
( ~ elem(m_Ack(Z,Pid20),queue(host(Z)))
| ! [Pid0] :
( index(status,host(Pid0)) != elec_2
| index(status,host(Z)) != elec_2
| host(Pid0) != host(Pid20)
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| ! [Pid20] :
( host(Pid20) != host(Z)
| ! [Pid0] :
( ~ elem(m_Ack(Pid0,Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive) ) ) )
& ! [Z,Pid0] :
( leq(index(pendack,host(Pid0)),host(Z))
| index(status,host(Pid0)) != elec_2
| index(status,host(Z)) != elec_2
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| leq(host(Z),host(Pid0)) )
& ! [Z,Pid20] :
( ~ elem(m_Down(Pid20),queue(host(Z)))
| ! [Pid0] :
( index(status,host(Pid0)) != elec_2
| host(Pid0) != host(Pid20)
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| leq(host(Pid0),host(Z)) ) )
& ! [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 ) )
& ! [Pid0] :
( ! [Z] : ~ elem(m_Ack(Z,Pid0),queue(host(Z)))
| index(status,host(Pid0)) != elec_2
| ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| host(Pid0) != host(Z)
| Pid0 = 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(sK9_skl)
& setIn(sK9_skl,alive)
& index(status,host(sK10_skl)) = elec_2
& setIn(sK10_skl,alive)
& ~ leq(index(pendack,host(sK10_skl)),host(sK9_skl))
& host(sK4_skl) != host(sK10_skl)
& host(sK4_skl) = host(sK9_skl)
& ~ setIn(host(sK8_skl),setEmpty)
& leq(nbr_proc,host(sK4_skl))
& index(status,host(sK4_skl)) = elec_1
& ! [Z] :
( Z = host(sK5_skl)
| setIn(Z,index(down,host(sK4_skl)))
| ~ leq(s(zero),Z)
| leq(host(sK4_skl),Z) )
& ( host(sK5_skl) != host(index(elid,host(sK4_skl)))
| index(status,host(sK4_skl)) != wait )
& ( index(status,host(sK4_skl)) != norm
| index(ldr,host(sK4_skl)) != host(sK5_skl) )
& ~ leq(host(sK4_skl),host(sK5_skl))
& setIn(sK4_skl,alive)
& queue(host(sK4_skl)) = cons(m_Down(sK5_skl),sK7_skl)
& ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| ! [Pid0] :
( index(status,host(Pid0)) != elec_1
| ! [Pid20] :
( ~ elem(m_Down(Pid20),queue(host(Pid0)))
| leq(host(Pid0),host(Z))
| ( sK6_skl(Pid20,Pid0,Z) != host(Pid20)
& ~ setIn(sK6_skl(Pid20,Pid0,Z),index(down,host(Pid0)))
& leq(s(zero),sK6_skl(Pid20,Pid0,Z))
& ~ leq(host(Pid0),sK6_skl(Pid20,Pid0,Z)) ) ) ) )
& ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| ! [Pid0] :
( index(status,host(Pid0)) != elec_2
| ! [Pid20] :
( host(Pid20) != host(Z)
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive) ) ) )
& ! [Z,Pid0] :
( ~ leq(index(pendack,host(Z)),index(pendack,host(Pid0)))
| index(status,host(Pid0)) != elec_2
| index(status,host(Z)) != elec_2
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| leq(host(Z),host(Pid0)) )
& ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| ! [Pid0] :
( index(status,host(Pid0)) != elec_2
| ~ setIn(Pid0,alive)
| leq(index(pendack,host(Pid0)),host(Z)) ) )
& ! [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) ) )
& ! [Z,Pid20] :
( ~ elem(m_Ack(Z,Pid20),queue(host(Z)))
| ! [Pid0] :
( index(status,host(Pid0)) != elec_2
| index(status,host(Z)) != elec_2
| host(Pid0) != host(Pid20)
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z] :
( index(status,host(Z)) != norm
| index(ldr,host(Z)) != host(Z)
| ~ setIn(Z,alive)
| ! [Pid20] :
( host(Pid20) != host(Z)
| ! [Pid0] :
( ~ elem(m_Ack(Pid0,Pid20),queue(host(Pid0)))
| ~ setIn(Pid0,alive) ) ) )
& ! [Z,Pid0] :
( leq(index(pendack,host(Pid0)),host(Z))
| index(status,host(Pid0)) != elec_2
| index(status,host(Z)) != elec_2
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| leq(host(Z),host(Pid0)) )
& ! [Z,Pid20] :
( ~ elem(m_Down(Pid20),queue(host(Z)))
| ! [Pid0] :
( index(status,host(Pid0)) != elec_2
| host(Pid0) != host(Pid20)
| ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| leq(host(Pid0),host(Z)) ) )
& ! [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 ) )
& ! [Pid0] :
( ! [Z] : ~ elem(m_Ack(Z,Pid0),queue(host(Z)))
| index(status,host(Pid0)) != elec_2
| ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive)
| host(Pid0) != host(Z)
| Pid0 = 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]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl),skolemize(V0,sK6_skl(Pid20,Pid0,Z)),skolemize(V,sK7_skl),skolemize(Z,sK8_skl),skolemize(V0,sK9_skl),skolemize(W0,sK10_skl)],[f213]) ).
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(f226,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(f235,plain,
queue(host(sK4_skl)) = cons(m_Down(sK5_skl),sK7_skl),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f240,plain,
! [X0] :
( X0 = host(sK5_skl)
| setIn(X0,index(down,host(sK4_skl)))
| ~ leq(s(zero),X0)
| leq(host(sK4_skl),X0) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f242,plain,
leq(nbr_proc,host(sK4_skl)),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f244,plain,
host(sK4_skl) = host(sK9_skl),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f245,plain,
host(sK4_skl) != host(sK10_skl),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f246,plain,
~ leq(index(pendack,host(sK10_skl)),host(sK9_skl)),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f247,plain,
setIn(sK10_skl,alive),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f248,plain,
index(status,host(sK10_skl)) = elec_2,
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f249,plain,
setIn(sK9_skl,alive),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f251,plain,
! [X0,X1] : elem(X0,cons(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f141]) ).
fof(f262,plain,
leq(nbr_proc,host(sK9_skl)),
inference(backward_demodulation,[status(thm)],[f244,f242]) ).
fof(f281,plain,
host(sK9_skl) != host(sK10_skl),
inference(forward_demodulation,[status(thm)],[f244,f245]) ).
fof(f305,plain,
( host(sK9_skl) = nbr_proc
| ~ leq(host(sK9_skl),nbr_proc) ),
inference(resolution,[status(thm)],[f196,f262]) ).
fof(f306,plain,
! [X0] :
( nbr_proc = host(X0)
| ~ leq(nbr_proc,host(X0)) ),
inference(resolution,[status(thm)],[f196,f76]) ).
fof(f312,plain,
host(sK9_skl) = nbr_proc,
inference(forward_subsumption_resolution,[status(thm)],[f305,f76]) ).
fof(f316,plain,
nbr_proc != host(sK10_skl),
inference(backward_demodulation,[status(thm)],[f312,f281]) ).
fof(f317,plain,
host(sK4_skl) = nbr_proc,
inference(backward_demodulation,[status(thm)],[f312,f244]) ).
fof(f412,plain,
! [X0] :
( leq(index(pendack,host(sK10_skl)),host(X0))
| index(status,host(sK10_skl)) != elec_2
| ~ setIn(host(sK10_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ),
inference(resolution,[status(thm)],[f220,f247]) ).
fof(f420,plain,
! [X0] :
( leq(index(pendack,host(sK10_skl)),host(X0))
| elec_2 != elec_2
| ~ setIn(host(sK10_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ),
inference(forward_demodulation,[status(thm)],[f248,f412]) ).
fof(f421,plain,
! [X0] :
( leq(index(pendack,host(sK10_skl)),host(X0))
| ~ setIn(host(sK10_skl),index(down,host(X0)))
| ~ setIn(X0,alive) ),
inference(trivial_equality_resolution,[status(thm)],[f420]) ).
fof(f863,plain,
! [X0,X1] :
( leq(index(pendack,host(sK10_skl)),host(X0))
| index(status,host(sK10_skl)) != elec_2
| host(sK10_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(X0,alive) ),
inference(resolution,[status(thm)],[f226,f247]) ).
fof(f871,plain,
! [X0,X1] :
( leq(index(pendack,host(sK10_skl)),host(X0))
| elec_2 != elec_2
| host(sK10_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(X0,alive) ),
inference(forward_demodulation,[status(thm)],[f248,f863]) ).
fof(f872,plain,
! [X0,X1] :
( leq(index(pendack,host(sK10_skl)),host(X0))
| host(sK10_skl) != host(X1)
| ~ elem(m_Down(X1),queue(host(X0)))
| ~ setIn(X0,alive) ),
inference(trivial_equality_resolution,[status(thm)],[f871]) ).
fof(f1249,plain,
queue(nbr_proc) = cons(m_Down(sK5_skl),sK7_skl),
inference(forward_demodulation,[status(thm)],[f317,f235]) ).
fof(f1265,plain,
elem(m_Down(sK5_skl),queue(nbr_proc)),
inference(paramodulation,[status(thm)],[f1249,f251]) ).
fof(f1372,plain,
! [X0] :
( X0 = host(sK5_skl)
| setIn(X0,index(down,host(sK4_skl)))
| ~ leq(s(zero),X0)
| leq(nbr_proc,X0) ),
inference(forward_demodulation,[status(thm)],[f317,f240]) ).
fof(f1373,plain,
! [X0] :
( X0 = host(sK5_skl)
| setIn(X0,index(down,nbr_proc))
| ~ leq(s(zero),X0)
| leq(nbr_proc,X0) ),
inference(forward_demodulation,[status(thm)],[f317,f1372]) ).
fof(f1376,plain,
~ leq(index(pendack,host(sK10_skl)),nbr_proc),
inference(forward_demodulation,[status(thm)],[f312,f246]) ).
fof(f2084,plain,
( leq(index(pendack,host(sK10_skl)),host(sK9_skl))
| ~ setIn(host(sK10_skl),index(down,host(sK9_skl))) ),
inference(resolution,[status(thm)],[f421,f249]) ).
fof(f2088,plain,
( leq(index(pendack,host(sK10_skl)),host(sK9_skl))
| ~ setIn(host(sK10_skl),index(down,nbr_proc)) ),
inference(forward_demodulation,[status(thm)],[f312,f2084]) ).
fof(f2089,plain,
( leq(index(pendack,host(sK10_skl)),nbr_proc)
| ~ setIn(host(sK10_skl),index(down,nbr_proc)) ),
inference(forward_demodulation,[status(thm)],[f312,f2088]) ).
fof(f2090,plain,
~ setIn(host(sK10_skl),index(down,nbr_proc)),
inference(forward_subsumption_resolution,[status(thm)],[f2089,f1376]) ).
fof(f2098,plain,
( host(sK10_skl) = host(sK5_skl)
| ~ leq(s(zero),host(sK10_skl))
| leq(nbr_proc,host(sK10_skl)) ),
inference(resolution,[status(thm)],[f2090,f1373]) ).
fof(f2103,plain,
( host(sK10_skl) = host(sK5_skl)
| leq(nbr_proc,host(sK10_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2098,f74]) ).
fof(f4076,plain,
! [X0] :
( leq(index(pendack,host(sK10_skl)),host(sK9_skl))
| host(sK10_skl) != host(X0)
| ~ elem(m_Down(X0),queue(host(sK9_skl))) ),
inference(resolution,[status(thm)],[f872,f249]) ).
fof(f4080,plain,
! [X0] :
( leq(index(pendack,host(sK10_skl)),host(sK9_skl))
| host(sK10_skl) != host(X0)
| ~ elem(m_Down(X0),queue(nbr_proc)) ),
inference(forward_demodulation,[status(thm)],[f312,f4076]) ).
fof(f4081,plain,
! [X0] :
( leq(index(pendack,host(sK10_skl)),nbr_proc)
| host(sK10_skl) != host(X0)
| ~ elem(m_Down(X0),queue(nbr_proc)) ),
inference(forward_demodulation,[status(thm)],[f312,f4080]) ).
fof(f4082,plain,
! [X0] :
( host(sK10_skl) != host(X0)
| ~ elem(m_Down(X0),queue(nbr_proc)) ),
inference(forward_subsumption_resolution,[status(thm)],[f4081,f1376]) ).
fof(f6572,plain,
( nbr_proc = host(sK10_skl)
| host(sK10_skl) = host(sK5_skl) ),
inference(resolution,[status(thm)],[f2103,f306]) ).
fof(f6586,plain,
host(sK10_skl) = host(sK5_skl),
inference(forward_subsumption_resolution,[status(thm)],[f6572,f316]) ).
fof(f8689,plain,
host(sK10_skl) != host(sK5_skl),
inference(resolution,[status(thm)],[f4082,f1265]) ).
fof(f8702,plain,
host(sK10_skl) != host(sK10_skl),
inference(forward_demodulation,[status(thm)],[f6586,f8689]) ).
fof(f8703,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f8702]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV468+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:56:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 13.35/2.15 % Refutation found
% 13.35/2.15 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.35/2.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.35/2.19 % Elapsed time: 1.808502 seconds
% 13.35/2.19 % CPU time: 13.924100 seconds
% 13.35/2.19 % Total memory used: 207.040 MB
% 13.35/2.19 % Net memory used: 188.145 MB
%------------------------------------------------------------------------------