%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV473+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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:08:02 AM UTC 2026
% Result : Theorem 33.53s 4.64s
% Output : CNFRefutation 33.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 26 unt; 0 def)
% Number of atoms : 513 ( 258 equ)
% Maximal formula atoms : 87 ( 8 avg)
% Number of connectives : 751 ( 300 ~; 249 |; 164 &)
% ( 2 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 20 con; 0-4 aty)
% Number of variables : 238 ( 5 sgn 178 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_02,axiom,
! [P] : leq(s(zero),host(P)),
file('theBenchmark.p',axiom_02) ).
fof(axiom_04,axiom,
! [P] : leq(host(P),nbr_proc),
file('theBenchmark.p',axiom_04) ).
fof(axiom_46,axiom,
! [X,Y,Q] :
( elem(X,cons(Y,Q))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_46) ).
fof(axiom_61,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
<=> X = Y ),
file('theBenchmark.p',axiom_61) ).
fof(conj,conjecture,
! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Ack(W,Y),V)
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid0) = host(Pid30)
& host(Pid0) = nbr_proc
& elem(m_Down(Pid20),queue(host(Pid0)))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( elem(m_Down(Pid30),queue(host(Z)))
& setIn(Z,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(index(elid,host(Pid0))) = host(Pid20)
& index(status,host(Pid0)) = wait
& host(Pid0) = host(Z)
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ elem(m_Down(Z),queue(host(Pid20))) )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid20)
& index(status,host(Pid0)) = norm
& host(Pid0) = host(Z)
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ elem(m_Down(Z),queue(host(Pid20))) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( host(Pid0) = nbr_proc
=> ~ elem(m_NotNorm(Z),queue(host(Pid0))) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> host(Pid0) != host(Z) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( ~ ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W )
=> ! [Z] :
( host(X) != host(Z)
=> ! [W0,X0,Y0] :
( host(X) = host(Y0)
=> ( ( index(status,host(Y0)) = elec_1
& host(Y0) = nbr_proc
& host(Y0) = host(W0)
& elem(m_Down(X0),V)
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Y0),V0) )
=> ( V0 = host(X0)
| setIn(V0,index(down,host(Y0))) ) ) )
=> ~ ( elem(m_Down(W0),queue(host(Z)))
& setIn(Z,alive) ) ) ) ) ) ) ),
file('theBenchmark.p',conj) ).
fof(conj_neg,negated_conjecture,
~ ! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Ack(W,Y),V)
& ! [Z,Pid30,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid0) = host(Pid30)
& host(Pid0) = nbr_proc
& elem(m_Down(Pid20),queue(host(Pid0)))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Pid0),V0) )
=> ( V0 = host(Pid20)
| setIn(V0,index(down,host(Pid0))) ) ) )
=> ~ ( elem(m_Down(Pid30),queue(host(Z)))
& setIn(Z,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(index(elid,host(Pid0))) = host(Pid20)
& index(status,host(Pid0)) = wait
& host(Pid0) = host(Z)
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ elem(m_Down(Z),queue(host(Pid20))) )
& ! [Z,Pid20,Pid0] :
( ( index(ldr,host(Pid0)) = host(Pid20)
& index(status,host(Pid0)) = norm
& host(Pid0) = host(Z)
& setIn(Pid0,alive)
& host(Pid0) != host(Pid20) )
=> ~ elem(m_Down(Z),queue(host(Pid20))) )
& ! [Z] :
( ( setIn(Z,alive)
& ( index(status,host(Z)) = elec_2
| index(status,host(Z)) = elec_1 ) )
=> index(elid,host(Z)) = Z )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( host(Pid0) = nbr_proc
=> ~ elem(m_NotNorm(Z),queue(host(Pid0))) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> host(Pid0) != host(Z) )
& ! [Z,Pid0] :
( elem(m_Ldr(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) ) )
=> ( setIn(X,alive)
=> ( ~ ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W )
=> ! [Z] :
( host(X) != host(Z)
=> ! [W0,X0,Y0] :
( host(X) = host(Y0)
=> ( ( index(status,host(Y0)) = elec_1
& host(Y0) = nbr_proc
& host(Y0) = host(W0)
& elem(m_Down(X0),V)
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Y0),V0) )
=> ( V0 = host(X0)
| setIn(V0,index(down,host(Y0))) ) ) )
=> ~ ( elem(m_Down(W0),queue(host(Z)))
& setIn(Z,alive) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_62,plain,
leq(s(zero),host(A)),
inference(clausify,[status(thm)],[axiom_02]) ).
cnf(c_64,plain,
leq(host(A),nbr_proc),
inference(clausify,[status(thm)],[axiom_04]) ).
cnf(c_119,plain,
( ~ elem(A,C)
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
cnf(c_151,plain,
( B = A
| ~ leq(B,A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[axiom_61]) ).
fof(nnf_58,plain,
? [V,W,X,Y] :
( ? [Z] :
( ? [W0,X0,Y0] :
( elem(m_Down(W0),queue(host(Z)))
& setIn(Z,alive)
& index(status,host(Y0)) = elec_1
& host(Y0) = nbr_proc
& host(W0) = host(Y0)
& elem(m_Down(X0),V)
& ! [V0] :
( host(X0) = V0
| setIn(V0,index(down,host(Y0)))
| ~ leq(s(zero),V0)
| leq(host(Y0),V0) )
& host(Y0) = host(X) )
& host(Z) != host(X) )
& ( index(pendack,host(X)) != host(Y)
| index(status,host(X)) != elec_2
| index(elid,host(X)) != W )
& setIn(X,alive)
& cons(m_Ack(W,Y),V) = queue(host(X))
& ! [X26,Pid30,Pid20,Pid0] :
( ~ elem(m_Down(Pid30),queue(host(X26)))
| ~ setIn(X26,alive)
| index(status,host(Pid0)) != elec_1
| host(Pid30) != host(Pid0)
| host(Pid0) != nbr_proc
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ? [X27] :
( host(Pid20) != X27
& ~ setIn(X27,index(down,host(Pid0)))
& leq(s(zero),X27)
& ~ leq(host(Pid0),X27) ) )
& ! [X22,X23,X24,X25] :
( ~ setIn(host(X23),index(down,host(X24)))
| ~ elem(m_Down(X25),queue(host(X22)))
| host(X24) != host(X25)
| host(X23) != host(X22)
| ~ setIn(X24,alive)
| ~ setIn(X22,alive)
| host(X24) = host(X22) )
& ! [X18,X19,X20,X21] :
( ~ elem(m_Down(X19),queue(host(X20)))
| ~ elem(m_Down(X21),queue(host(X18)))
| host(X20) != host(X21)
| host(X19) != host(X18)
| ~ setIn(X20,alive)
| ~ setIn(X18,alive)
| host(X20) = host(X18) )
& ! [X15,X16,X17] :
( ~ elem(m_Down(X15),queue(host(X16)))
| host(index(elid,host(X17))) != host(X16)
| index(status,host(X17)) != wait
| host(X17) != host(X15)
| ~ setIn(X17,alive)
| host(X16) = host(X17) )
& ! [X12,X13,X14] :
( ~ elem(m_Down(X12),queue(host(X13)))
| index(ldr,host(X14)) != host(X13)
| index(status,host(X14)) != norm
| host(X14) != host(X12)
| ~ setIn(X14,alive)
| host(X13) = host(X14) )
& ! [X11] :
( index(elid,host(X11)) = X11
| ~ setIn(X11,alive)
| ( index(status,host(X11)) != elec_2
& index(status,host(X11)) != elec_1 ) )
& ! [X9,X10] :
( ~ setIn(X10,alive)
| ~ setIn(X9,alive)
| host(X10) != host(X9)
| X10 = X9 )
& ! [X7,X8] :
( ~ elem(m_NotNorm(X7),queue(host(X8)))
| host(X8) != nbr_proc )
& ! [X5,X6] :
( host(X6) != host(X5)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( ~ leq(host(X3),host(X4))
| ~ elem(m_Ldr(X4),queue(host(X3))) ) ),
inference(fof_nnf,[status(thm)],[conj_neg]) ).
fof(sk_conj_neg_sk,plain,
( elem(m_Down(sK7),queue(host(sK4)))
& setIn(sK4,alive)
& index(status,host(sK5)) = elec_1
& host(sK5) = nbr_proc
& host(sK7) = host(sK5)
& elem(m_Down(sK6),sK2)
& ! [V0] :
( host(sK6) = V0
| setIn(V0,index(down,host(sK5)))
| ~ leq(s(zero),V0)
| leq(host(sK5),V0) )
& host(sK5) = host(sK3)
& host(sK4) != host(sK3)
& ( index(pendack,host(sK3)) != host(sK1)
| index(status,host(sK3)) != elec_2
| index(elid,host(sK3)) != sK0 )
& setIn(sK3,alive)
& cons(m_Ack(sK0,sK1),sK2) = queue(host(sK3))
& ! [X26,Pid30,Pid20,Pid0] :
( ~ elem(m_Down(Pid30),queue(host(X26)))
| ~ setIn(X26,alive)
| index(status,host(Pid0)) != elec_1
| host(Pid30) != host(Pid0)
| host(Pid0) != nbr_proc
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ( host(Pid20) != sK8(X26,Pid30,Pid20,Pid0)
& ~ setIn(sK8(X26,Pid30,Pid20,Pid0),index(down,host(Pid0)))
& leq(s(zero),sK8(X26,Pid30,Pid20,Pid0))
& ~ leq(host(Pid0),sK8(X26,Pid30,Pid20,Pid0)) ) )
& ! [X22,X23,X24,X25] :
( ~ setIn(host(X23),index(down,host(X24)))
| ~ elem(m_Down(X25),queue(host(X22)))
| host(X24) != host(X25)
| host(X23) != host(X22)
| ~ setIn(X24,alive)
| ~ setIn(X22,alive)
| host(X24) = host(X22) )
& ! [X18,X19,X20,X21] :
( ~ elem(m_Down(X19),queue(host(X20)))
| ~ elem(m_Down(X21),queue(host(X18)))
| host(X20) != host(X21)
| host(X19) != host(X18)
| ~ setIn(X20,alive)
| ~ setIn(X18,alive)
| host(X20) = host(X18) )
& ! [X15,X16,X17] :
( ~ elem(m_Down(X15),queue(host(X16)))
| host(index(elid,host(X17))) != host(X16)
| index(status,host(X17)) != wait
| host(X17) != host(X15)
| ~ setIn(X17,alive)
| host(X16) = host(X17) )
& ! [X12,X13,X14] :
( ~ elem(m_Down(X12),queue(host(X13)))
| index(ldr,host(X14)) != host(X13)
| index(status,host(X14)) != norm
| host(X14) != host(X12)
| ~ setIn(X14,alive)
| host(X13) = host(X14) )
& ! [X11] :
( index(elid,host(X11)) = X11
| ~ setIn(X11,alive)
| ( index(status,host(X11)) != elec_2
& index(status,host(X11)) != elec_1 ) )
& ! [X9,X10] :
( ~ setIn(X10,alive)
| ~ setIn(X9,alive)
| host(X10) != host(X9)
| X10 = X9 )
& ! [X7,X8] :
( ~ elem(m_NotNorm(X7),queue(host(X8)))
| host(X8) != nbr_proc )
& ! [X5,X6] :
( host(X6) != host(X5)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( ~ leq(host(X3),host(X4))
| ~ elem(m_Ldr(X4),queue(host(X3))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(V,sK2),skolemize(W,sK0),skolemize(X,sK3),skolemize(Y,sK1),skolemize(X27,sK8(X26,Pid30,Pid20,Pid0)),skolemize(Z,sK4),skolemize(W0,sK7),skolemize(X0,sK6),skolemize(Y0,sK5)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( elem(m_Down(sK7),queue(host(sK4)))
& setIn(sK4,alive)
& index(status,host(sK5)) = elec_1
& host(sK5) = nbr_proc
& host(sK7) = host(sK5)
& elem(m_Down(sK6),sK2)
& ! [VAR_0] :
( host(sK6) = VAR_0
| setIn(VAR_0,index(down,host(sK5)))
| ~ leq(s(zero),VAR_0)
| leq(host(sK5),VAR_0) )
& host(sK5) = host(sK3)
& host(sK4) != host(sK3)
& ( index(pendack,host(sK3)) != host(sK1)
| index(status,host(sK3)) != elec_2
| index(elid,host(sK3)) != sK0 )
& setIn(sK3,alive)
& cons(m_Ack(sK0,sK1),sK2) = queue(host(sK3))
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| index(status,host(VAR_3)) != elec_1
| host(VAR_2) != host(VAR_3)
| host(VAR_3) != nbr_proc
| ~ elem(m_Down(VAR_0),queue(host(VAR_3)))
| host(VAR_0) != sK8(VAR_1,VAR_2,VAR_0,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_1),queue(host(VAR_0)))
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_3)) != elec_1
| host(VAR_1) != host(VAR_3)
| host(VAR_3) != nbr_proc
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ setIn(sK8(VAR_0,VAR_1,VAR_2,VAR_3),index(down,host(VAR_3))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_1),queue(host(VAR_0)))
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_3)) != elec_1
| host(VAR_1) != host(VAR_3)
| host(VAR_3) != nbr_proc
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| leq(s(zero),sK8(VAR_0,VAR_1,VAR_2,VAR_3)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_1)))
| ~ setIn(VAR_1,alive)
| index(status,host(VAR_0)) != elec_1
| host(VAR_2) != host(VAR_0)
| host(VAR_0) != nbr_proc
| ~ elem(m_Down(VAR_3),queue(host(VAR_0)))
| ~ leq(host(VAR_0),sK8(VAR_1,VAR_2,VAR_3,VAR_0)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ setIn(host(VAR_2),index(down,host(VAR_0)))
| ~ elem(m_Down(VAR_3),queue(host(VAR_1)))
| host(VAR_0) != host(VAR_3)
| host(VAR_2) != host(VAR_1)
| ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| ~ elem(m_Down(VAR_3),queue(host(VAR_1)))
| host(VAR_0) != host(VAR_3)
| host(VAR_2) != host(VAR_1)
| ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| host(index(elid,host(VAR_1))) != host(VAR_0)
| index(status,host(VAR_1)) != wait
| host(VAR_1) != host(VAR_2)
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ elem(m_Down(VAR_2),queue(host(VAR_0)))
| index(ldr,host(VAR_1)) != host(VAR_0)
| index(status,host(VAR_1)) != norm
| host(VAR_1) != host(VAR_2)
| ~ setIn(VAR_1,alive)
| host(VAR_0) = host(VAR_1) )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_2 )
& ! [VAR_0] :
( index(elid,host(VAR_0)) = VAR_0
| ~ setIn(VAR_0,alive)
| index(status,host(VAR_0)) != elec_1 )
& ! [VAR_0,VAR_1] :
( ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) != host(VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( ~ elem(m_NotNorm(VAR_1),queue(host(VAR_0)))
| host(VAR_0) != nbr_proc )
& ! [VAR_0,VAR_1] :
( host(VAR_0) != host(VAR_1)
| ~ elem(m_Down(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Ldr(VAR_0),queue(host(VAR_1))) ) ),
inference(cnf_transformation,[status(thm)],[sk_conj_neg_sk]) ).
cnf(c_168,negated_conjecture,
( ~ elem(m_Down(C),queue(host(A)))
| ~ elem(m_Down(D),queue(host(B)))
| host(A) != host(D)
| host(C) != host(B)
| ~ setIn(A,alive)
| ~ setIn(B,alive)
| host(A) = host(B) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_169,negated_conjecture,
( ~ setIn(host(C),index(down,host(A)))
| ~ elem(m_Down(D),queue(host(B)))
| host(A) != host(D)
| host(C) != host(B)
| ~ setIn(A,alive)
| ~ setIn(B,alive)
| host(A) = host(B) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_175,negated_conjecture,
cons(m_Ack(sK0,sK1),sK2) = queue(host(sK3)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_176,negated_conjecture,
queue(host(sK3)) = cons(m_Ack(sK0,sK1),sK2),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_177,negated_conjecture,
setIn(sK3,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_180,negated_conjecture,
host(sK4) != host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_181,negated_conjecture,
host(sK5) = host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_182,negated_conjecture,
( host(sK6) = A
| setIn(A,index(down,host(sK5)))
| ~ leq(s(zero),A)
| leq(host(sK5),A) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_7529,negated_conjecture,
( host(sK6) = A
| setIn(A,index(down,host(sK5)))
| ~ leq(s(zero),A)
| leq(host(sK3),A) ),
inference(paramod,[status(thm)],[c_181,c_182]) ).
cnf(c_183,negated_conjecture,
( host(sK6) = A
| setIn(A,index(down,host(sK3)))
| ~ leq(s(zero),A)
| leq(host(sK3),A) ),
inference(paramod,[status(thm)],[c_181,c_7529]) ).
cnf(c_184,negated_conjecture,
elem(m_Down(sK6),sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_185,negated_conjecture,
host(sK7) = host(sK5),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_186,negated_conjecture,
host(sK7) = host(sK3),
inference(paramod,[status(thm)],[c_181,c_185]) ).
cnf(c_187,negated_conjecture,
host(sK5) = nbr_proc,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_7530,negated_conjecture,
host(sK3) = nbr_proc,
inference(paramod,[status(thm)],[c_181,c_187]) ).
cnf(c_188,negated_conjecture,
nbr_proc = host(sK3),
inference(copy,[status(thm)],[c_7530]) ).
cnf(c_191,negated_conjecture,
setIn(sK4,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_192,negated_conjecture,
elem(m_Down(sK7),queue(host(sK4))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_198,plain,
leq(host(A),host(sK3)),
inference(paramod,[status(thm)],[c_188,c_64]) ).
cnf(c_7531,plain,
( ~ elem(m_Down(B),queue(host(A)))
| ~ elem(m_Down(C),cons(m_Ack(sK0,sK1),sK2))
| host(A) != host(C)
| host(B) != host(sK3)
| ~ setIn(A,alive)
| ~ setIn(sK3,alive)
| host(A) = host(sK3) ),
inference(paramod,[status(thm)],[c_176,c_168]) ).
cnf(c_7532,plain,
( ~ elem(m_Down(B),queue(host(A)))
| ~ elem(m_Down(C),cons(m_Ack(sK0,sK1),sK2))
| host(A) != host(C)
| host(B) != host(sK3)
| ~ setIn(A,alive)
| ~ setIn(sK3,alive)
| host(sK3) = host(A) ),
inference(copy,[status(thm)],[c_7531]) ).
cnf(c_7533,plain,
( ~ elem(m_Down(B),queue(host(A)))
| ~ elem(m_Down(C),cons(m_Ack(sK0,sK1),sK2))
| host(A) != host(C)
| host(sK3) != host(B)
| ~ setIn(A,alive)
| ~ setIn(sK3,alive)
| host(sK3) = host(A) ),
inference(copy,[status(thm)],[c_7532]) ).
cnf(c_312,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ elem(m_Down(C),cons(m_Ack(sK0,sK1),sK2))
| host(A) != host(C)
| host(sK3) != host(B)
| ~ setIn(A,alive)
| host(sK3) = host(A) ),
inference(resolve,[status(thm)],[c_177,c_7533]) ).
cnf(c_315,plain,
( ~ setIn(host(B),index(down,host(sK3)))
| ~ elem(m_Down(C),queue(host(A)))
| host(sK3) != host(C)
| host(B) != host(A)
| ~ setIn(A,alive)
| host(sK3) = host(A) ),
inference(resolve,[status(thm)],[c_177,c_169]) ).
cnf(c_344,plain,
( host(sK6) = host(A)
| setIn(host(A),index(down,host(sK3)))
| leq(host(sK3),host(A)) ),
inference(resolve,[status(thm)],[c_183,c_62]) ).
cnf(c_349,plain,
elem(m_Down(sK6),cons(A,sK2)),
inference(resolve,[status(thm)],[c_184,c_119]) ).
cnf(c_7534,plain,
( host(A) = host(sK3)
| ~ leq(host(sK3),host(A)) ),
inference(resolve,[status(thm)],[c_198,c_151]) ).
cnf(c_461,plain,
( host(sK3) = host(A)
| ~ leq(host(sK3),host(A)) ),
inference(copy,[status(thm)],[c_7534]) ).
cnf(c_7535,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| host(sK4) != host(A)
| host(sK3) != host(sK7)
| ~ setIn(sK4,alive)
| host(sK3) = host(sK4) ),
inference(resolve,[status(thm)],[c_312,c_192]) ).
cnf(c_7536,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| host(sK4) != host(A)
| host(sK3) != host(sK3)
| ~ setIn(sK4,alive)
| host(sK3) = host(sK4) ),
inference(paramod,[status(thm)],[c_186,c_7535]) ).
cnf(c_7537,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| host(sK4) != host(A)
| host(sK3) != host(sK3)
| ~ setIn(sK4,alive)
| host(sK4) = host(sK3) ),
inference(copy,[status(thm)],[c_7536]) ).
cnf(c_7538,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| host(sK4) != host(A)
| ~ setIn(sK4,alive)
| host(sK4) = host(sK3) ),
inference(copy,[status(thm)],[c_7537]) ).
cnf(c_7539,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| host(sK4) != host(A)
| ~ setIn(sK4,alive) ),
inference(resolve,[status(thm)],[c_180,c_7538]) ).
cnf(c_5029,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| host(sK4) != host(A) ),
inference(resolve,[status(thm)],[c_191,c_7539]) ).
cnf(c_7540,plain,
host(sK4) != host(sK6),
inference(resolve,[status(thm)],[c_5029,c_349]) ).
cnf(c_5074,plain,
host(sK6) != host(sK4),
inference(copy,[status(thm)],[c_7540]) ).
cnf(c_7541,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK3)))
| host(sK3) != host(sK7)
| host(A) != host(sK4)
| ~ setIn(sK4,alive)
| host(sK3) = host(sK4) ),
inference(resolve,[status(thm)],[c_315,c_192]) ).
cnf(c_7542,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK3)))
| host(sK3) != host(sK3)
| host(A) != host(sK4)
| ~ setIn(sK4,alive)
| host(sK3) = host(sK4) ),
inference(paramod,[status(thm)],[c_186,c_7541]) ).
cnf(c_7543,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK3)))
| host(sK3) != host(sK3)
| host(A) != host(sK4)
| ~ setIn(sK4,alive)
| host(sK4) = host(sK3) ),
inference(copy,[status(thm)],[c_7542]) ).
cnf(c_7544,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK3)))
| host(sK3) != host(sK3)
| host(sK4) != host(A)
| ~ setIn(sK4,alive)
| host(sK4) = host(sK3) ),
inference(copy,[status(thm)],[c_7543]) ).
cnf(c_7545,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK3)))
| host(sK4) != host(A)
| ~ setIn(sK4,alive)
| host(sK4) = host(sK3) ),
inference(copy,[status(thm)],[c_7544]) ).
cnf(c_7546,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK3)))
| host(sK4) != host(A)
| ~ setIn(sK4,alive) ),
inference(resolve,[status(thm)],[c_180,c_7545]) ).
cnf(c_5636,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK3)))
| host(sK4) != host(A) ),
inference(resolve,[status(thm)],[c_191,c_7546]) ).
cnf(c_5677,plain,
~ setIn(host(sK4),index(down,host(sK3))),
inference(xxres,[status(thm)],[c_5636]) ).
cnf(c_7547,plain,
( host(sK6) = host(sK4)
| leq(host(sK3),host(sK4)) ),
inference(resolve,[status(thm)],[c_344,c_5677]) ).
cnf(c_7328,plain,
leq(host(sK3),host(sK4)),
inference(resolve,[status(thm)],[c_5074,c_7547]) ).
cnf(c_7548,plain,
host(sK3) = host(sK4),
inference(resolve,[status(thm)],[c_7328,c_461]) ).
cnf(c_7549,plain,
host(sK4) = host(sK3),
inference(copy,[status(thm)],[c_7548]) ).
cnf(c_7528,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_180,c_7549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV473+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:58:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1169401 was started by sandbox2 on n026,
% 0.09/0.36 % Sat Sep 26 13:58:43 2026
% 0.09/0.36 % 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).
% 33.53/4.64
% 33.53/4.64 % given #500 (A,wt=27): 323 -ordered(cons(m_Halt(c3),A)) | -elem(m_Down(c8),A) | leq(c3,c8). [resolve(181,a,147,b)].
% 33.53/4.64
% 33.53/4.64 % SZS status Theorem for theBenchmark
% 33.53/4.64
% 33.53/4.64 % Proof 1 at 3.64 (+ 0.58) seconds.
% 33.53/4.64 % Length of proof is 37.
% 33.53/4.64 % Level of proof is 7.
% 33.53/4.64 % Maximum clause weight is 49.000.
% 33.53/4.64 % Given clauses 572.
% 33.53/4.64
% 33.53/4.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------