%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV460+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:08:00 AM UTC 2026
% Result : Theorem 215.11s 29.69s
% Output : CNFRefutation 215.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 76 ( 26 unt; 0 def)
% Number of atoms : 524 ( 201 equ)
% Maximal formula atoms : 74 ( 6 avg)
% Number of connectives : 726 ( 278 ~; 227 |; 173 &)
% ( 2 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 17 con; 0-2 aty)
% Number of variables : 221 ( 9 sgn 164 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_01,axiom,
! [P,Q] :
( s(host(P)) = host(Q)
=> host(P) != host(Q) ),
file('theBenchmark.p',axiom_01) ).
fof(axiom_02,axiom,
! [P] : leq(s(zero),host(P)),
file('theBenchmark.p',axiom_02) ).
fof(axiom_38,axiom,
! [Y,Q] : init(snoc(Q,Y)) = Q,
file('theBenchmark.p',axiom_38) ).
fof(axiom_46,axiom,
! [X,Y,Q] :
( elem(X,cons(Y,Q))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_46) ).
fof(axiom_58,axiom,
! [X] : ~ leq(s(X),X),
file('theBenchmark.p',axiom_58) ).
fof(axiom_60,axiom,
! [X,Y] :
( leq(Y,X)
| leq(X,Y) ),
file('theBenchmark.p',axiom_60) ).
fof(axiom_61,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
<=> X = Y ),
file('theBenchmark.p',axiom_61) ).
fof(axiom_62,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('theBenchmark.p',axiom_62) ).
fof(conj,conjecture,
! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Down(Y),V)
& ! [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,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,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(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,Pid20,Pid0] :
( elem(m_Ack(Pid0,Z),queue(host(Pid20)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z] :
( index(status,host(Z)) = elec_2
=> ~ leq(index(pendack,host(Z)),host(Z)) )
& ! [Z,Pid0] :
( elem(m_Halt(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] :
( host(X) = host(Z)
=> ! [W0] :
( host(X) != host(W0)
=> ( ( index(status,host(W0)) = elec_2
& setIn(W0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(W0)) )
=> ~ leq(s(host(X)),index(pendack,host(W0))) ) ) ) ) ) ) ) ) ),
file('theBenchmark.p',conj) ).
fof(conj_neg,negated_conjecture,
~ ! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Down(Y),V)
& ! [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,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,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(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,Pid20,Pid0] :
( elem(m_Ack(Pid0,Z),queue(host(Pid20)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z] :
( index(status,host(Z)) = elec_2
=> ~ leq(index(pendack,host(Z)),host(Z)) )
& ! [Z,Pid0] :
( elem(m_Halt(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] :
( host(X) = host(Z)
=> ! [W0] :
( host(X) != host(W0)
=> ( ( index(status,host(W0)) = elec_2
& setIn(W0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(W0)) )
=> ~ leq(s(host(X)),index(pendack,host(W0))) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_61,plain,
( host(B) != host(A)
| s(host(A)) != host(B) ),
inference(clausify,[status(thm)],[axiom_01]) ).
cnf(c_62,plain,
leq(s(zero),host(A)),
inference(clausify,[status(thm)],[axiom_02]) ).
cnf(c_108,plain,
init(snoc(A,B)) = A,
inference(clausify,[status(thm)],[axiom_38]) ).
cnf(c_117,plain,
( B != A
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
cnf(c_147,plain,
~ leq(s(A),A),
inference(clausify,[status(thm)],[axiom_58]) ).
cnf(c_149,plain,
( leq(B,A)
| leq(A,B) ),
inference(clausify,[status(thm)],[axiom_60]) ).
cnf(c_150,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[axiom_61]) ).
cnf(c_153,plain,
( leq(A,C)
| ~ leq(B,C)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[axiom_62]) ).
fof(nnf_58,plain,
? [V,W,X,Y] :
( ? [Z] :
( ? [W0] :
( leq(s(host(X)),index(pendack,host(W0)))
& index(status,host(W0)) = elec_2
& setIn(W0,alive)
& setIn(Z,alive)
& ~ leq(host(Z),host(W0))
& host(W0) != host(X) )
& host(Z) = host(X) )
& ~ leq(nbr_proc,host(X))
& index(status,host(X)) = elec_1
& ! [X26] :
( host(Y) = X26
| setIn(X26,index(down,host(X)))
| ~ leq(s(zero),X26)
| leq(host(X),X26) )
& ( host(index(elid,host(X))) != host(Y)
| index(status,host(X)) != wait )
& ( index(status,host(X)) != norm
| index(ldr,host(X)) != host(Y) )
& ~ leq(host(X),host(Y))
& setIn(X,alive)
& cons(m_Down(Y),V) = queue(host(X))
& ! [X25,Pid0] :
( ~ leq(index(pendack,host(X25)),index(pendack,host(Pid0)))
| index(status,host(Pid0)) != elec_2
| index(status,host(X25)) != elec_2
| ~ setIn(Pid0,alive)
| ~ setIn(X25,alive)
| leq(host(X25),host(Pid0)) )
& ! [X23,Pid20,X24] :
( leq(index(pendack,host(X24)),host(X23))
| index(status,host(X24)) != elec_2
| host(Pid20) != host(X24)
| ~ elem(m_Down(Pid20),queue(host(X23)))
| ~ setIn(X24,alive)
| ~ setIn(X23,alive) )
& ! [X20,X21,X22] :
( ~ elem(m_Ack(X20,X21),queue(host(X20)))
| index(status,host(X22)) != elec_2
| index(status,host(X20)) != elec_2
| host(X21) != host(X22)
| ~ setIn(X22,alive)
| ~ setIn(X20,alive) )
& ! [X18,X19] :
( leq(index(pendack,host(X19)),host(X18))
| index(status,host(X19)) != elec_2
| index(status,host(X18)) != elec_2
| ~ setIn(X19,alive)
| ~ setIn(X18,alive)
| leq(host(X18),host(X19)) )
& ! [X15,X16,X17] :
( ~ elem(m_Down(X16),queue(host(X15)))
| index(status,host(X17)) != elec_2
| host(X16) != host(X17)
| ~ setIn(X17,alive)
| ~ setIn(X15,alive)
| leq(host(X17),host(X15)) )
& ! [X13,X14] :
( leq(index(pendack,host(X14)),host(X13))
| index(status,host(X14)) != elec_2
| ~ setIn(host(X14),index(down,host(X13)))
| ~ setIn(X14,alive)
| ~ setIn(X13,alive) )
& ! [X12] :
( index(elid,host(X12)) = X12
| ~ setIn(X12,alive)
| ( index(status,host(X12)) != elec_2
& index(status,host(X12)) != elec_1 ) )
& ! [X10,X11] :
( ~ elem(m_Ack(X10,X11),queue(host(X10)))
| index(status,host(X11)) != elec_2
| ~ setIn(X11,alive) )
& ! [X8,X9] :
( ~ setIn(X9,alive)
| ~ setIn(X8,alive)
| host(X9) != host(X8)
| X9 = X8 )
& ! [X5,X6,X7] :
( ~ leq(host(X5),host(X7))
| ~ elem(m_Ack(X7,X5),queue(host(X6))) )
& ! [X4] :
( ~ leq(index(pendack,host(X4)),host(X4))
| index(status,host(X4)) != elec_2 )
& ! [X0,X3] :
( ~ leq(host(X0),host(X3))
| ~ elem(m_Halt(X3),queue(host(X0))) ) ),
inference(fof_nnf,[status(thm)],[conj_neg]) ).
fof(sk_conj_neg_sk,plain,
( leq(s(host(sK2)),index(pendack,host(sK4)))
& index(status,host(sK4)) = elec_2
& setIn(sK4,alive)
& setIn(sK3,alive)
& ~ leq(host(sK3),host(sK4))
& host(sK4) != host(sK2)
& host(sK3) = host(sK2)
& ~ leq(nbr_proc,host(sK2))
& index(status,host(sK2)) = elec_1
& ! [X26] :
( host(sK0) = X26
| setIn(X26,index(down,host(sK2)))
| ~ leq(s(zero),X26)
| leq(host(sK2),X26) )
& ( host(index(elid,host(sK2))) != host(sK0)
| index(status,host(sK2)) != wait )
& ( index(status,host(sK2)) != norm
| index(ldr,host(sK2)) != host(sK0) )
& ~ leq(host(sK2),host(sK0))
& setIn(sK2,alive)
& cons(m_Down(sK0),sK1) = queue(host(sK2))
& ! [X25,Pid0] :
( ~ leq(index(pendack,host(X25)),index(pendack,host(Pid0)))
| index(status,host(Pid0)) != elec_2
| index(status,host(X25)) != elec_2
| ~ setIn(Pid0,alive)
| ~ setIn(X25,alive)
| leq(host(X25),host(Pid0)) )
& ! [X23,Pid20,X24] :
( leq(index(pendack,host(X24)),host(X23))
| index(status,host(X24)) != elec_2
| host(Pid20) != host(X24)
| ~ elem(m_Down(Pid20),queue(host(X23)))
| ~ setIn(X24,alive)
| ~ setIn(X23,alive) )
& ! [X20,X21,X22] :
( ~ elem(m_Ack(X20,X21),queue(host(X20)))
| index(status,host(X22)) != elec_2
| index(status,host(X20)) != elec_2
| host(X21) != host(X22)
| ~ setIn(X22,alive)
| ~ setIn(X20,alive) )
& ! [X18,X19] :
( leq(index(pendack,host(X19)),host(X18))
| index(status,host(X19)) != elec_2
| index(status,host(X18)) != elec_2
| ~ setIn(X19,alive)
| ~ setIn(X18,alive)
| leq(host(X18),host(X19)) )
& ! [X15,X16,X17] :
( ~ elem(m_Down(X16),queue(host(X15)))
| index(status,host(X17)) != elec_2
| host(X16) != host(X17)
| ~ setIn(X17,alive)
| ~ setIn(X15,alive)
| leq(host(X17),host(X15)) )
& ! [X13,X14] :
( leq(index(pendack,host(X14)),host(X13))
| index(status,host(X14)) != elec_2
| ~ setIn(host(X14),index(down,host(X13)))
| ~ setIn(X14,alive)
| ~ setIn(X13,alive) )
& ! [X12] :
( index(elid,host(X12)) = X12
| ~ setIn(X12,alive)
| ( index(status,host(X12)) != elec_2
& index(status,host(X12)) != elec_1 ) )
& ! [X10,X11] :
( ~ elem(m_Ack(X10,X11),queue(host(X10)))
| index(status,host(X11)) != elec_2
| ~ setIn(X11,alive) )
& ! [X8,X9] :
( ~ setIn(X9,alive)
| ~ setIn(X8,alive)
| host(X9) != host(X8)
| X9 = X8 )
& ! [X5,X6,X7] :
( ~ leq(host(X5),host(X7))
| ~ elem(m_Ack(X7,X5),queue(host(X6))) )
& ! [X4] :
( ~ leq(index(pendack,host(X4)),host(X4))
| index(status,host(X4)) != elec_2 )
& ! [X0,X3] :
( ~ leq(host(X0),host(X3))
| ~ elem(m_Halt(X3),queue(host(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(V,sK1),skolemize(W,sK5),skolemize(X,sK2),skolemize(Y,sK0),skolemize(Z,sK3),skolemize(W0,sK4)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( leq(s(host(sK2)),index(pendack,host(sK4)))
& index(status,host(sK4)) = elec_2
& setIn(sK4,alive)
& setIn(sK3,alive)
& ~ leq(host(sK3),host(sK4))
& host(sK4) != host(sK2)
& host(sK3) = host(sK2)
& ~ leq(nbr_proc,host(sK2))
& index(status,host(sK2)) = elec_1
& ! [VAR_0] :
( host(sK0) = VAR_0
| setIn(VAR_0,index(down,host(sK2)))
| ~ leq(s(zero),VAR_0)
| leq(host(sK2),VAR_0) )
& ( host(index(elid,host(sK2))) != host(sK0)
| index(status,host(sK2)) != wait )
& ( index(status,host(sK2)) != norm
| index(ldr,host(sK2)) != host(sK0) )
& ~ leq(host(sK2),host(sK0))
& setIn(sK2,alive)
& cons(m_Down(sK0),sK1) = queue(host(sK2))
& ! [VAR_0,VAR_1] :
( ~ leq(index(pendack,host(VAR_0)),index(pendack,host(VAR_1)))
| index(status,host(VAR_1)) != elec_2
| index(status,host(VAR_0)) != elec_2
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive)
| leq(host(VAR_0),host(VAR_1)) )
& ! [VAR_0,VAR_1,VAR_2] :
( leq(index(pendack,host(VAR_1)),host(VAR_0))
| index(status,host(VAR_1)) != elec_2
| host(VAR_2) != host(VAR_1)
| ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ elem(m_Ack(VAR_0,VAR_2),queue(host(VAR_0)))
| index(status,host(VAR_1)) != elec_2
| index(status,host(VAR_0)) != elec_2
| host(VAR_2) != host(VAR_1)
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1] :
( leq(index(pendack,host(VAR_1)),host(VAR_0))
| index(status,host(VAR_1)) != elec_2
| index(status,host(VAR_0)) != elec_2
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive)
| leq(host(VAR_0),host(VAR_1)) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| index(status,host(VAR_0)) != elec_2
| host(VAR_2) != host(VAR_0)
| ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| leq(host(VAR_0),host(VAR_1)) )
& ! [VAR_0,VAR_1] :
( leq(index(pendack,host(VAR_1)),host(VAR_0))
| index(status,host(VAR_1)) != elec_2
| ~ setIn(host(VAR_1),index(down,host(VAR_0)))
| ~ setIn(VAR_1,alive)
| ~ setIn(VAR_0,alive) )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_2 )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_1 )
& ! [VAR_0,VAR_1] :
( ~ elem(m_Ack(VAR_1,VAR_0),queue(host(VAR_1)))
| index(status,host(VAR_0)) != elec_2
| ~ setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1] :
( ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) != host(VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_2))) )
& ! [VAR_0] :
( ~ leq(index(pendack,host(VAR_0)),host(VAR_0))
| index(status,host(VAR_0)) != elec_2 )
& ! [VAR_0,VAR_1] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Halt(VAR_0),queue(host(VAR_1))) ) ),
inference(cnf_transformation,[status(thm)],[sk_conj_neg_sk]) ).
cnf(c_166,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != elec_2
| ~ setIn(host(B),index(down,host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_170,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != elec_2
| host(C) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_172,negated_conjecture,
cons(m_Down(sK0),sK1) = queue(host(sK2)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_173,negated_conjecture,
setIn(sK2,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_177,negated_conjecture,
( host(sK0) = A
| setIn(A,index(down,host(sK2)))
| ~ leq(s(zero),A)
| leq(host(sK2),A) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_181,negated_conjecture,
host(sK3) = host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_183,negated_conjecture,
~ leq(host(sK3),host(sK4)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_184,negated_conjecture,
~ leq(host(sK2),host(sK4)),
inference(paramod,[status(thm)],[c_181,c_183]) ).
cnf(c_186,negated_conjecture,
setIn(sK4,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_187,negated_conjecture,
index(status,host(sK4)) = elec_2,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_188,negated_conjecture,
elec_2 = index(status,host(sK4)),
inference(copy,[status(thm)],[c_187]) ).
cnf(c_189,negated_conjecture,
leq(s(host(sK2)),index(pendack,host(sK4))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_14200,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != index(status,host(sK4))
| host(C) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_188,c_170]) ).
cnf(c_198,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(sK4)) != index(status,host(B))
| host(C) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_14200]) ).
cnf(c_14201,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(B)) != index(status,host(sK4))
| ~ setIn(host(B),index(down,host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(paramod,[status(thm)],[c_188,c_166]) ).
cnf(c_202,negated_conjecture,
( leq(index(pendack,host(B)),host(A))
| index(status,host(sK4)) != index(status,host(B))
| ~ setIn(host(B),index(down,host(A)))
| ~ setIn(B,alive)
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_14201]) ).
cnf(c_208,plain,
s(host(A)) != host(A),
inference(xxres,[status(thm)],[c_61]) ).
cnf(c_14202,plain,
elem(A,cons(init(snoc(A,B)),C)),
inference(resolve,[status(thm)],[c_117,c_108]) ).
cnf(c_229,plain,
elem(A,cons(A,B)),
inference(paramod,[status(thm)],[c_108,c_14202]) ).
cnf(c_257,plain,
leq(A,s(A)),
inference(resolve,[status(thm)],[c_149,c_147]) ).
cnf(c_295,plain,
( host(sK0) = host(A)
| setIn(host(A),index(down,host(sK2)))
| leq(host(sK2),host(A)) ),
inference(resolve,[status(thm)],[c_177,c_62]) ).
cnf(c_302,plain,
( leq(s(host(sK2)),A)
| ~ leq(index(pendack,host(sK4)),A) ),
inference(resolve,[status(thm)],[c_189,c_153]) ).
cnf(c_14203,negated_conjecture,
( s(host(sK2)) = index(pendack,host(sK4))
| ~ leq(index(pendack,host(sK4)),s(host(sK2))) ),
inference(resolve,[status(thm)],[c_189,c_150]) ).
cnf(c_303,negated_conjecture,
( index(pendack,host(sK4)) = s(host(sK2))
| ~ leq(index(pendack,host(sK4)),s(host(sK2))) ),
inference(copy,[status(thm)],[c_14203]) ).
cnf(c_14204,negated_conjecture,
( leq(index(pendack,host(sK4)),host(A))
| index(status,host(sK4)) != index(status,host(sK4))
| host(B) != host(sK4)
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(resolve,[status(thm)],[c_198,c_186]) ).
cnf(c_14205,negated_conjecture,
( leq(index(pendack,host(sK4)),host(A))
| index(status,host(sK4)) != index(status,host(sK4))
| host(sK4) != host(B)
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_14204]) ).
cnf(c_314,negated_conjecture,
( leq(index(pendack,host(sK4)),host(A))
| host(sK4) != host(B)
| ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_14205]) ).
cnf(c_14206,negated_conjecture,
( leq(index(pendack,host(sK4)),host(A))
| index(status,host(sK4)) != index(status,host(sK4))
| ~ setIn(host(sK4),index(down,host(A)))
| ~ setIn(A,alive) ),
inference(resolve,[status(thm)],[c_202,c_186]) ).
cnf(c_326,negated_conjecture,
( leq(index(pendack,host(sK4)),host(A))
| ~ setIn(host(sK4),index(down,host(A)))
| ~ setIn(A,alive) ),
inference(copy,[status(thm)],[c_14206]) ).
cnf(c_369,plain,
( leq(A,B)
| ~ leq(s(A),B) ),
inference(resolve,[status(thm)],[c_257,c_153]) ).
cnf(c_374,plain,
elem(m_Down(sK0),queue(host(sK2))),
inference(paramod,[status(thm)],[c_172,c_229]) ).
cnf(c_697,plain,
leq(host(sK2),index(pendack,host(sK4))),
inference(resolve,[status(thm)],[c_369,c_189]) ).
cnf(c_14207,plain,
( host(sK2) = index(pendack,host(sK4))
| ~ leq(index(pendack,host(sK4)),host(sK2)) ),
inference(resolve,[status(thm)],[c_697,c_150]) ).
cnf(c_838,plain,
( index(pendack,host(sK4)) = host(sK2)
| ~ leq(index(pendack,host(sK4)),host(sK2)) ),
inference(copy,[status(thm)],[c_14207]) ).
cnf(c_14208,plain,
( leq(index(pendack,host(sK4)),host(sK2))
| host(sK4) != host(sK0)
| ~ setIn(sK2,alive) ),
inference(resolve,[status(thm)],[c_314,c_374]) ).
cnf(c_1626,negated_conjecture,
( leq(index(pendack,host(sK4)),host(sK2))
| host(sK4) != host(sK0) ),
inference(resolve,[status(thm)],[c_173,c_14208]) ).
cnf(c_14209,plain,
( host(sK0) = host(sK4)
| leq(host(sK2),host(sK4))
| leq(index(pendack,host(sK4)),host(sK2))
| ~ setIn(sK2,alive) ),
inference(resolve,[status(thm)],[c_326,c_295]) ).
cnf(c_14210,plain,
( host(sK4) = host(sK0)
| leq(host(sK2),host(sK4))
| leq(index(pendack,host(sK4)),host(sK2))
| ~ setIn(sK2,alive) ),
inference(copy,[status(thm)],[c_14209]) ).
cnf(c_14211,negated_conjecture,
( host(sK4) = host(sK0)
| leq(host(sK2),host(sK4))
| leq(index(pendack,host(sK4)),host(sK2)) ),
inference(resolve,[status(thm)],[c_173,c_14210]) ).
cnf(c_1819,negated_conjecture,
( host(sK4) = host(sK0)
| leq(index(pendack,host(sK4)),host(sK2)) ),
inference(resolve,[status(thm)],[c_184,c_14211]) ).
cnf(c_14212,plain,
( leq(s(host(sK2)),host(sK2))
| host(sK4) = host(sK0) ),
inference(resolve,[status(thm)],[c_1819,c_302]) ).
cnf(c_12684,plain,
host(sK4) = host(sK0),
inference(resolve,[status(thm)],[c_147,c_14212]) ).
cnf(c_14213,negated_conjecture,
( leq(index(pendack,host(sK4)),host(sK2))
| host(sK0) != host(sK0) ),
inference(paramod,[status(thm)],[c_12684,c_1626]) ).
cnf(c_14214,negated_conjecture,
( leq(index(pendack,host(sK0)),host(sK2))
| host(sK0) != host(sK0) ),
inference(paramod,[status(thm)],[c_12684,c_14213]) ).
cnf(c_14033,negated_conjecture,
leq(index(pendack,host(sK0)),host(sK2)),
inference(copy,[status(thm)],[c_14214]) ).
cnf(c_14215,plain,
( index(pendack,host(sK4)) = host(sK2)
| ~ leq(index(pendack,host(sK0)),host(sK2)) ),
inference(paramod,[status(thm)],[c_12684,c_838]) ).
cnf(c_14216,plain,
( index(pendack,host(sK0)) = host(sK2)
| ~ leq(index(pendack,host(sK0)),host(sK2)) ),
inference(paramod,[status(thm)],[c_12684,c_14215]) ).
cnf(c_14145,plain,
index(pendack,host(sK0)) = host(sK2),
inference(resolve,[status(thm)],[c_14033,c_14216]) ).
cnf(c_14217,negated_conjecture,
( index(pendack,host(sK4)) = s(host(sK2))
| ~ leq(index(pendack,host(sK0)),s(host(sK2))) ),
inference(paramod,[status(thm)],[c_12684,c_303]) ).
cnf(c_14218,negated_conjecture,
( index(pendack,host(sK4)) = s(host(sK2))
| ~ leq(host(sK2),s(host(sK2))) ),
inference(paramod,[status(thm)],[c_14145,c_14217]) ).
cnf(c_14219,negated_conjecture,
( index(pendack,host(sK0)) = s(host(sK2))
| ~ leq(host(sK2),s(host(sK2))) ),
inference(paramod,[status(thm)],[c_12684,c_14218]) ).
cnf(c_14220,negated_conjecture,
( host(sK2) = s(host(sK2))
| ~ leq(host(sK2),s(host(sK2))) ),
inference(paramod,[status(thm)],[c_14145,c_14219]) ).
cnf(c_14221,negated_conjecture,
( s(host(sK2)) = host(sK2)
| ~ leq(host(sK2),s(host(sK2))) ),
inference(copy,[status(thm)],[c_14220]) ).
cnf(c_14222,negated_conjecture,
s(host(sK2)) = host(sK2),
inference(resolve,[status(thm)],[c_257,c_14221]) ).
cnf(c_14199,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_208,c_14222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV460+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 13:55:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2875238 was started by sandbox2 on n013,
% 0.09/0.37 % Sat Sep 26 13:55:06 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 215.11/29.69
% 215.11/29.69 % given #500 (A,wt=42): 350 q_nil = A | -setIn(B,alive) | -setIn(cons(head(A),tail(A)),alive) | index(status,host(c6)) != index(status,host(B)) | index(status,host(cons(head(A),tail(A)))) != index(status,host(c6)) | -elem(m_Ack(B,A),queue(host(B))). [resolve(209,b,199,c(flip)),flip(e)].
% 215.11/29.69
% 215.11/29.69 % given #1000 (T,wt=11): 1576 leq(s(s(s(host(A)))),s(s(s(s(nbr_proc))))). [resolve(715,a,154,a)].
% 215.11/29.69
% 215.11/29.69 % SZS status Theorem for theBenchmark
% 215.11/29.69
% 215.11/29.69 % Proof 1 at 4.18 (+ 0.95) seconds.
% 215.11/29.69 % Length of proof is 49.
% 215.11/29.69 % Level of proof is 9.
% 215.11/29.69 % Maximum clause weight is 33.000.
% 215.11/29.69 % Given clauses 1369.
% 215.11/29.69
% 215.11/29.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------