%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV470+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 : n004.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 09:08:01 AM UTC 2026
% Result : Theorem 108.64s 15.25s
% Output : CNFRefutation 108.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 81 ( 23 unt; 0 def)
% Number of atoms : 635 ( 297 equ)
% Maximal formula atoms : 86 ( 7 avg)
% Number of connectives : 979 ( 425 ~; 352 |; 162 &)
% ( 2 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 18 con; 0-4 aty)
% Number of variables : 308 ( 5 sgn 178 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_12,axiom,
! [X,Y,Z] : m_Ack(X,Y) != m_Down(Z),
file('theBenchmark.p',axiom_12) ).
fof(axiom_46,axiom,
! [X,Y,Q] :
( elem(X,cons(Y,Q))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_46) ).
fof(axiom_47,axiom,
! [X,Y,Q] :
( elem(X,snoc(Q,Y))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_47) ).
fof(conj,conjecture,
! [V,W,X] :
( ( queue(host(W)) = cons(m_Halt(X),V)
& ! [Y,Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid0) = nbr_proc
& host(Pid0) = host(Z)
& 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(Z),queue(host(Y)))
& setIn(Y,alive) ) )
& ! [Y,Z,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Z) = host(Y)
& setIn(Pid20,alive)
& setIn(Y,alive)
& host(Pid20) != host(Y) )
=> ~ ( setIn(host(Z),index(down,host(Pid20)))
& elem(m_Down(Pid0),queue(host(Y))) ) )
& ! [Y,Z,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Z) = host(Y)
& setIn(Pid20,alive)
& setIn(Y,alive)
& host(Pid20) != host(Y) )
=> ~ ( elem(m_Down(Z),queue(host(Pid20)))
& elem(m_Down(Pid0),queue(host(Y))) ) )
& ! [Y,Z,Pid0] :
( ( host(index(elid,host(Pid0))) = host(Z)
& index(status,host(Pid0)) = wait
& host(Pid0) = host(Y)
& setIn(Pid0,alive)
& host(Pid0) != host(Z) )
=> ~ elem(m_Down(Y),queue(host(Z))) )
& ! [Y,Z,Pid0] :
( ( index(status,host(Pid0)) = norm
& index(ldr,host(Pid0)) = host(Z)
& host(Pid0) = host(Y)
& setIn(Pid0,alive)
& host(Pid0) != host(Z) )
=> ~ elem(m_Down(Y),queue(host(Z))) )
& ! [Y] :
( ( setIn(Y,alive)
& ( index(status,host(Y)) = elec_2
| index(status,host(Y)) = elec_1 ) )
=> index(elid,host(Y)) = Y )
& ! [Y,Z] :
( ( host(Z) = host(Y)
& Z != Y )
=> ( ~ setIn(Z,alive)
| ~ setIn(Y,alive) ) )
& ! [Y,Z] :
( host(Z) = nbr_proc
=> ~ elem(m_NotNorm(Y),queue(host(Z))) )
& ! [Y,Z] :
( elem(m_Down(Z),queue(host(Y)))
=> host(Z) != host(Y) )
& ! [Y,Z] :
( elem(m_Ldr(Z),queue(host(Y)))
=> ~ leq(host(Y),host(Z)) ) )
=> ( setIn(W,alive)
=> ! [Y] :
( host(X) = host(Y)
=> ( host(W) = host(Y)
=> ! [Z,X0,Y0] :
( host(X) != host(Y0)
=> ( host(W) != host(Y0)
=> ( ( index(status,host(Y0)) = elec_1
& host(Y0) = nbr_proc
& host(Y0) = host(Z)
& elem(m_Down(X0),queue(host(Y0)))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Y0),V0) )
=> ( V0 = host(X0)
| setIn(V0,index(down,host(Y0))) ) ) )
=> ~ ( elem(m_Down(Z),snoc(V,m_Ack(X,W)))
& setIn(Y,alive) ) ) ) ) ) ) ) ),
file('theBenchmark.p',conj) ).
fof(conj_neg,negated_conjecture,
~ ! [V,W,X] :
( ( queue(host(W)) = cons(m_Halt(X),V)
& ! [Y,Z,Pid20,Pid0] :
( ( index(status,host(Pid0)) = elec_1
& host(Pid0) = nbr_proc
& host(Pid0) = host(Z)
& 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(Z),queue(host(Y)))
& setIn(Y,alive) ) )
& ! [Y,Z,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Z) = host(Y)
& setIn(Pid20,alive)
& setIn(Y,alive)
& host(Pid20) != host(Y) )
=> ~ ( setIn(host(Z),index(down,host(Pid20)))
& elem(m_Down(Pid0),queue(host(Y))) ) )
& ! [Y,Z,Pid20,Pid0] :
( ( host(Pid0) = host(Pid20)
& host(Z) = host(Y)
& setIn(Pid20,alive)
& setIn(Y,alive)
& host(Pid20) != host(Y) )
=> ~ ( elem(m_Down(Z),queue(host(Pid20)))
& elem(m_Down(Pid0),queue(host(Y))) ) )
& ! [Y,Z,Pid0] :
( ( host(index(elid,host(Pid0))) = host(Z)
& index(status,host(Pid0)) = wait
& host(Pid0) = host(Y)
& setIn(Pid0,alive)
& host(Pid0) != host(Z) )
=> ~ elem(m_Down(Y),queue(host(Z))) )
& ! [Y,Z,Pid0] :
( ( index(status,host(Pid0)) = norm
& index(ldr,host(Pid0)) = host(Z)
& host(Pid0) = host(Y)
& setIn(Pid0,alive)
& host(Pid0) != host(Z) )
=> ~ elem(m_Down(Y),queue(host(Z))) )
& ! [Y] :
( ( setIn(Y,alive)
& ( index(status,host(Y)) = elec_2
| index(status,host(Y)) = elec_1 ) )
=> index(elid,host(Y)) = Y )
& ! [Y,Z] :
( ( host(Z) = host(Y)
& Z != Y )
=> ( ~ setIn(Z,alive)
| ~ setIn(Y,alive) ) )
& ! [Y,Z] :
( host(Z) = nbr_proc
=> ~ elem(m_NotNorm(Y),queue(host(Z))) )
& ! [Y,Z] :
( elem(m_Down(Z),queue(host(Y)))
=> host(Z) != host(Y) )
& ! [Y,Z] :
( elem(m_Ldr(Z),queue(host(Y)))
=> ~ leq(host(Y),host(Z)) ) )
=> ( setIn(W,alive)
=> ! [Y] :
( host(X) = host(Y)
=> ( host(W) = host(Y)
=> ! [Z,X0,Y0] :
( host(X) != host(Y0)
=> ( host(W) != host(Y0)
=> ( ( index(status,host(Y0)) = elec_1
& host(Y0) = nbr_proc
& host(Y0) = host(Z)
& elem(m_Down(X0),queue(host(Y0)))
& ! [V0] :
( ( leq(s(zero),V0)
& ~ leq(host(Y0),V0) )
=> ( V0 = host(X0)
| setIn(V0,index(down,host(Y0))) ) ) )
=> ~ ( elem(m_Down(Z),snoc(V,m_Ack(X,W)))
& setIn(Y,alive) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_78,plain,
m_Down(A) != m_Ack(B,C),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_121,plain,
( ~ elem(A,C)
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
cnf(c_122,plain,
( elem(A,B)
| C = A
| ~ elem(A,snoc(B,C)) ),
inference(clausify,[status(thm)],[axiom_47]) ).
fof(nnf_58,plain,
? [V,W,X] :
( ? [Y] :
( ? [Z,X0,Y0] :
( elem(m_Down(Z),snoc(V,m_Ack(X,W)))
& setIn(Y,alive)
& index(status,host(Y0)) = elec_1
& host(Y0) = nbr_proc
& host(Y0) = host(Z)
& elem(m_Down(X0),queue(host(Y0)))
& ! [V0] :
( host(X0) = V0
| setIn(V0,index(down,host(Y0)))
| ~ leq(s(zero),V0)
| leq(host(Y0),V0) )
& host(Y0) != host(W)
& host(Y0) != host(X) )
& host(W) = host(Y)
& host(Y) = host(X) )
& setIn(W,alive)
& cons(m_Halt(X),V) = queue(host(W))
& ! [X26,X27,Pid20,Pid0] :
( ~ elem(m_Down(X27),queue(host(X26)))
| ~ setIn(X26,alive)
| index(status,host(Pid0)) != elec_1
| host(Pid0) != nbr_proc
| host(Pid0) != host(X27)
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ? [X28] :
( host(Pid20) != X28
& ~ setIn(X28,index(down,host(Pid0)))
& leq(s(zero),X28)
& ~ leq(host(Pid0),X28) ) )
& ! [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(X17) = host(X16) )
& ! [X12,X13,X14] :
( ~ elem(m_Down(X12),queue(host(X13)))
| index(status,host(X14)) != norm
| index(ldr,host(X14)) != host(X13)
| host(X14) != host(X12)
| ~ setIn(X14,alive)
| host(X14) = host(X13) )
& ! [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(sK6),snoc(sK2,m_Ack(sK1,sK3)))
& setIn(sK7,alive)
& index(status,host(sK4)) = elec_1
& host(sK4) = nbr_proc
& host(sK4) = host(sK6)
& elem(m_Down(sK5),queue(host(sK4)))
& ! [V0] :
( host(sK5) = V0
| setIn(V0,index(down,host(sK4)))
| ~ leq(s(zero),V0)
| leq(host(sK4),V0) )
& host(sK4) != host(sK3)
& host(sK4) != host(sK1)
& host(sK3) = host(sK7)
& host(sK7) = host(sK1)
& setIn(sK3,alive)
& cons(m_Halt(sK1),sK2) = queue(host(sK3))
& ! [X26,X27,Pid20,Pid0] :
( ~ elem(m_Down(X27),queue(host(X26)))
| ~ setIn(X26,alive)
| index(status,host(Pid0)) != elec_1
| host(Pid0) != nbr_proc
| host(Pid0) != host(X27)
| ~ elem(m_Down(Pid20),queue(host(Pid0)))
| ( host(Pid20) != sK0(X26,X27,Pid20,Pid0)
& ~ setIn(sK0(X26,X27,Pid20,Pid0),index(down,host(Pid0)))
& leq(s(zero),sK0(X26,X27,Pid20,Pid0))
& ~ leq(host(Pid0),sK0(X26,X27,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(X17) = host(X16) )
& ! [X12,X13,X14] :
( ~ elem(m_Down(X12),queue(host(X13)))
| index(status,host(X14)) != norm
| index(ldr,host(X14)) != host(X13)
| host(X14) != host(X12)
| ~ setIn(X14,alive)
| host(X14) = host(X13) )
& ! [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,[sK0,sK1,sK2,sK3,sK7,sK4,sK5,sK6]),skolemize(V,sK2),skolemize(W,sK3),skolemize(X,sK1),skolemize(X28,sK0(X26,X27,Pid20,Pid0)),skolemize(Y,sK7),skolemize(Z,sK6),skolemize(X0,sK5),skolemize(Y0,sK4)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( elem(m_Down(sK6),snoc(sK2,m_Ack(sK1,sK3)))
& setIn(sK7,alive)
& index(status,host(sK4)) = elec_1
& host(sK4) = nbr_proc
& host(sK4) = host(sK6)
& elem(m_Down(sK5),queue(host(sK4)))
& ! [VAR_0] :
( host(sK5) = VAR_0
| setIn(VAR_0,index(down,host(sK4)))
| ~ leq(s(zero),VAR_0)
| leq(host(sK4),VAR_0) )
& host(sK4) != host(sK3)
& host(sK4) != host(sK1)
& host(sK3) = host(sK7)
& host(sK7) = host(sK1)
& setIn(sK3,alive)
& cons(m_Halt(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_3) != nbr_proc
| host(VAR_3) != host(VAR_2)
| ~ elem(m_Down(VAR_0),queue(host(VAR_3)))
| host(VAR_0) != sK0(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_3) != nbr_proc
| host(VAR_3) != host(VAR_1)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| ~ setIn(sK0(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_3) != nbr_proc
| host(VAR_3) != host(VAR_1)
| ~ elem(m_Down(VAR_2),queue(host(VAR_3)))
| leq(s(zero),sK0(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_0) != nbr_proc
| host(VAR_0) != host(VAR_2)
| ~ elem(m_Down(VAR_3),queue(host(VAR_0)))
| ~ leq(host(VAR_0),sK0(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_1)))
| host(index(elid,host(VAR_0))) != host(VAR_1)
| index(status,host(VAR_0)) != wait
| host(VAR_0) != host(VAR_2)
| ~ setIn(VAR_0,alive)
| 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)) != norm
| index(ldr,host(VAR_0)) != host(VAR_1)
| host(VAR_0) != host(VAR_2)
| ~ setIn(VAR_0,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_172,negated_conjecture,
( ~ elem(m_Down(C),queue(host(B)))
| ~ setIn(B,alive)
| index(status,host(A)) != elec_1
| host(A) != nbr_proc
| host(A) != host(C)
| ~ elem(m_Down(D),queue(host(A)))
| ~ leq(host(A),sK0(B,C,D,A)) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_173,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != elec_1
| host(D) != nbr_proc
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| leq(s(zero),sK0(A,B,C,D)) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_174,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != elec_1
| host(D) != nbr_proc
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| ~ setIn(sK0(A,B,C,D),index(down,host(D))) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_175,negated_conjecture,
( ~ elem(m_Down(C),queue(host(B)))
| ~ setIn(B,alive)
| index(status,host(D)) != elec_1
| host(D) != nbr_proc
| host(D) != host(C)
| ~ elem(m_Down(A),queue(host(D)))
| host(A) != sK0(B,C,A,D) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_176,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != elec_1
| host(D) != nbr_proc
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| sK0(A,B,C,D) != host(C) ),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_177,negated_conjecture,
cons(m_Halt(sK1),sK2) = queue(host(sK3)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_178,negated_conjecture,
setIn(sK3,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_184,negated_conjecture,
( host(sK5) = A
| setIn(A,index(down,host(sK4)))
| ~ leq(s(zero),A)
| leq(host(sK4),A) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_185,negated_conjecture,
elem(m_Down(sK5),queue(host(sK4))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_186,negated_conjecture,
host(sK4) = host(sK6),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_187,negated_conjecture,
host(sK4) = nbr_proc,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_13775,negated_conjecture,
host(sK6) = nbr_proc,
inference(paramod,[status(thm)],[c_186,c_187]) ).
cnf(c_188,negated_conjecture,
nbr_proc = host(sK6),
inference(copy,[status(thm)],[c_13775]) ).
cnf(c_189,negated_conjecture,
index(status,host(sK4)) = elec_1,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_13776,negated_conjecture,
index(status,host(sK6)) = elec_1,
inference(paramod,[status(thm)],[c_186,c_189]) ).
cnf(c_190,negated_conjecture,
elec_1 = index(status,host(sK6)),
inference(copy,[status(thm)],[c_13776]) ).
cnf(c_192,negated_conjecture,
elem(m_Down(sK6),snoc(sK2,m_Ack(sK1,sK3))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_198,negated_conjecture,
elem(m_Down(sK5),queue(host(sK6))),
inference(paramod,[status(thm)],[c_186,c_185]) ).
cnf(c_13777,negated_conjecture,
( host(sK5) = A
| setIn(A,index(down,host(sK4)))
| ~ leq(s(zero),A)
| leq(host(sK6),A) ),
inference(paramod,[status(thm)],[c_186,c_184]) ).
cnf(c_199,negated_conjecture,
( host(sK5) = A
| setIn(A,index(down,host(sK6)))
| ~ leq(s(zero),A)
| leq(host(sK6),A) ),
inference(paramod,[status(thm)],[c_186,c_13777]) ).
cnf(c_13778,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != elec_1
| host(D) != host(sK6)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| sK0(A,B,C,D) != host(C) ),
inference(paramod,[status(thm)],[c_188,c_176]) ).
cnf(c_13779,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != index(status,host(sK6))
| host(D) != host(sK6)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| sK0(A,B,C,D) != host(C) ),
inference(paramod,[status(thm)],[c_190,c_13778]) ).
cnf(c_13780,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != index(status,host(sK6))
| host(sK6) != host(D)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| sK0(A,B,C,D) != host(C) ),
inference(copy,[status(thm)],[c_13779]) ).
cnf(c_201,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(sK6)) != index(status,host(D))
| host(sK6) != host(D)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| sK0(A,B,C,D) != host(C) ),
inference(copy,[status(thm)],[c_13780]) ).
cnf(c_13781,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != elec_1
| host(D) != host(sK6)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| ~ setIn(sK0(A,B,C,D),index(down,host(D))) ),
inference(paramod,[status(thm)],[c_188,c_174]) ).
cnf(c_13782,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != index(status,host(sK6))
| host(D) != host(sK6)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| ~ setIn(sK0(A,B,C,D),index(down,host(D))) ),
inference(paramod,[status(thm)],[c_190,c_13781]) ).
cnf(c_13783,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != index(status,host(sK6))
| host(sK6) != host(D)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| ~ setIn(sK0(A,B,C,D),index(down,host(D))) ),
inference(copy,[status(thm)],[c_13782]) ).
cnf(c_202,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(sK6)) != index(status,host(D))
| host(sK6) != host(D)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| ~ setIn(sK0(A,B,C,D),index(down,host(D))) ),
inference(copy,[status(thm)],[c_13783]) ).
cnf(c_13784,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != elec_1
| host(D) != host(sK6)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| leq(s(zero),sK0(A,B,C,D)) ),
inference(paramod,[status(thm)],[c_188,c_173]) ).
cnf(c_13785,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != index(status,host(sK6))
| host(D) != host(sK6)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| leq(s(zero),sK0(A,B,C,D)) ),
inference(paramod,[status(thm)],[c_190,c_13784]) ).
cnf(c_13786,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(D)) != index(status,host(sK6))
| host(sK6) != host(D)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| leq(s(zero),sK0(A,B,C,D)) ),
inference(copy,[status(thm)],[c_13785]) ).
cnf(c_203,negated_conjecture,
( ~ elem(m_Down(B),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(sK6)) != index(status,host(D))
| host(sK6) != host(D)
| host(D) != host(B)
| ~ elem(m_Down(C),queue(host(D)))
| leq(s(zero),sK0(A,B,C,D)) ),
inference(copy,[status(thm)],[c_13786]) ).
cnf(c_13787,negated_conjecture,
( ~ elem(m_Down(C),queue(host(B)))
| ~ setIn(B,alive)
| index(status,host(A)) != elec_1
| host(A) != host(sK6)
| host(A) != host(C)
| ~ elem(m_Down(D),queue(host(A)))
| ~ leq(host(A),sK0(B,C,D,A)) ),
inference(paramod,[status(thm)],[c_188,c_172]) ).
cnf(c_13788,negated_conjecture,
( ~ elem(m_Down(C),queue(host(B)))
| ~ setIn(B,alive)
| index(status,host(A)) != index(status,host(sK6))
| host(A) != host(sK6)
| host(A) != host(C)
| ~ elem(m_Down(D),queue(host(A)))
| ~ leq(host(A),sK0(B,C,D,A)) ),
inference(paramod,[status(thm)],[c_190,c_13787]) ).
cnf(c_13789,negated_conjecture,
( ~ elem(m_Down(C),queue(host(B)))
| ~ setIn(B,alive)
| index(status,host(A)) != index(status,host(sK6))
| host(sK6) != host(A)
| host(A) != host(C)
| ~ elem(m_Down(D),queue(host(A)))
| ~ leq(host(A),sK0(B,C,D,A)) ),
inference(copy,[status(thm)],[c_13788]) ).
cnf(c_204,negated_conjecture,
( ~ elem(m_Down(C),queue(host(B)))
| ~ setIn(B,alive)
| index(status,host(sK6)) != index(status,host(A))
| host(sK6) != host(A)
| host(A) != host(C)
| ~ elem(m_Down(D),queue(host(A)))
| ~ leq(host(A),sK0(B,C,D,A)) ),
inference(copy,[status(thm)],[c_13789]) ).
cnf(c_13790,plain,
( ~ elem(m_Down(sK6),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(sK6)) != index(status,host(sK6))
| host(sK6) != host(sK6)
| ~ elem(m_Down(B),queue(host(sK6)))
| ~ setIn(sK0(A,sK6,B,sK6),index(down,host(sK6))) ),
inference(factor,[status(thm)],[c_202]) ).
cnf(c_13791,plain,
( ~ elem(m_Down(sK6),queue(host(A)))
| ~ setIn(A,alive)
| index(status,host(sK6)) != index(status,host(sK6))
| ~ elem(m_Down(B),queue(host(sK6)))
| ~ setIn(sK0(A,sK6,B,sK6),index(down,host(sK6))) ),
inference(copy,[status(thm)],[c_13790]) ).
cnf(c_216,plain,
( ~ elem(m_Down(sK6),queue(host(A)))
| ~ setIn(A,alive)
| ~ elem(m_Down(B),queue(host(sK6)))
| ~ setIn(sK0(A,sK6,B,sK6),index(down,host(sK6))) ),
inference(copy,[status(thm)],[c_13791]) ).
cnf(c_13792,negated_conjecture,
( elem(m_Down(sK6),sK2)
| m_Ack(sK1,sK3) = m_Down(sK6) ),
inference(resolve,[status(thm)],[c_192,c_122]) ).
cnf(c_13793,negated_conjecture,
( elem(m_Down(sK6),sK2)
| m_Down(sK6) = m_Ack(sK1,sK3) ),
inference(copy,[status(thm)],[c_13792]) ).
cnf(c_322,negated_conjecture,
elem(m_Down(sK6),sK2),
inference(resolve,[status(thm)],[c_78,c_13793]) ).
cnf(c_336,plain,
( ~ elem(m_Down(A),queue(host(sK3)))
| index(status,host(sK6)) != index(status,host(C))
| host(sK6) != host(C)
| host(C) != host(A)
| ~ elem(m_Down(B),queue(host(C)))
| sK0(sK3,A,B,C) != host(B) ),
inference(resolve,[status(thm)],[c_201,c_178]) ).
cnf(c_13794,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| index(status,host(sK6)) != index(status,host(sK6))
| host(sK6) != host(sK6)
| ~ elem(m_Down(A),queue(host(sK6)))
| sK0(sK3,sK6,A,sK6) != host(A) ),
inference(factor,[status(thm)],[c_336]) ).
cnf(c_13795,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| index(status,host(sK6)) != index(status,host(sK6))
| ~ elem(m_Down(A),queue(host(sK6)))
| sK0(sK3,sK6,A,sK6) != host(A) ),
inference(copy,[status(thm)],[c_13794]) ).
cnf(c_338,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| ~ elem(m_Down(A),queue(host(sK6)))
| sK0(sK3,sK6,A,sK6) != host(A) ),
inference(copy,[status(thm)],[c_13795]) ).
cnf(c_341,plain,
( ~ elem(m_Down(A),queue(host(sK3)))
| index(status,host(sK6)) != index(status,host(C))
| host(sK6) != host(C)
| host(C) != host(A)
| ~ elem(m_Down(B),queue(host(C)))
| leq(s(zero),sK0(sK3,A,B,C)) ),
inference(resolve,[status(thm)],[c_203,c_178]) ).
cnf(c_13796,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| index(status,host(sK6)) != index(status,host(sK6))
| host(sK6) != host(sK6)
| ~ elem(m_Down(A),queue(host(sK6)))
| leq(s(zero),sK0(sK3,sK6,A,sK6)) ),
inference(factor,[status(thm)],[c_341]) ).
cnf(c_13797,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| index(status,host(sK6)) != index(status,host(sK6))
| ~ elem(m_Down(A),queue(host(sK6)))
| leq(s(zero),sK0(sK3,sK6,A,sK6)) ),
inference(copy,[status(thm)],[c_13796]) ).
cnf(c_343,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| ~ elem(m_Down(A),queue(host(sK6)))
| leq(s(zero),sK0(sK3,sK6,A,sK6)) ),
inference(copy,[status(thm)],[c_13797]) ).
cnf(c_345,plain,
( ~ elem(m_Down(B),queue(host(sK3)))
| index(status,host(sK6)) != index(status,host(A))
| host(sK6) != host(A)
| host(A) != host(B)
| ~ elem(m_Down(C),queue(host(A)))
| ~ leq(host(A),sK0(sK3,B,C,A)) ),
inference(resolve,[status(thm)],[c_204,c_178]) ).
cnf(c_13798,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| index(status,host(sK6)) != index(status,host(sK6))
| host(sK6) != host(sK6)
| ~ elem(m_Down(A),queue(host(sK6)))
| ~ leq(host(sK6),sK0(sK3,sK6,A,sK6)) ),
inference(factor,[status(thm)],[c_345]) ).
cnf(c_13799,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| index(status,host(sK6)) != index(status,host(sK6))
| ~ elem(m_Down(A),queue(host(sK6)))
| ~ leq(host(sK6),sK0(sK3,sK6,A,sK6)) ),
inference(copy,[status(thm)],[c_13798]) ).
cnf(c_347,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| ~ elem(m_Down(A),queue(host(sK6)))
| ~ leq(host(sK6),sK0(sK3,sK6,A,sK6)) ),
inference(copy,[status(thm)],[c_13799]) ).
cnf(c_394,plain,
elem(m_Down(sK6),cons(A,sK2)),
inference(resolve,[status(thm)],[c_322,c_121]) ).
cnf(c_446,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| sK0(sK3,sK6,sK5,sK6) != host(sK5) ),
inference(resolve,[status(thm)],[c_338,c_198]) ).
cnf(c_479,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| ~ leq(host(sK6),sK0(sK3,sK6,sK5,sK6)) ),
inference(resolve,[status(thm)],[c_347,c_198]) ).
cnf(c_518,plain,
elem(m_Down(sK6),queue(host(sK3))),
inference(paramod,[status(thm)],[c_177,c_394]) ).
cnf(c_522,plain,
~ leq(host(sK6),sK0(sK3,sK6,sK5,sK6)),
inference(resolve,[status(thm)],[c_518,c_479]) ).
cnf(c_526,plain,
sK0(sK3,sK6,sK5,sK6) != host(sK5),
inference(resolve,[status(thm)],[c_518,c_446]) ).
cnf(c_531,plain,
( ~ elem(m_Down(A),queue(host(sK6)))
| leq(s(zero),sK0(sK3,sK6,A,sK6)) ),
inference(resolve,[status(thm)],[c_518,c_343]) ).
cnf(c_13632,plain,
leq(s(zero),sK0(sK3,sK6,sK5,sK6)),
inference(resolve,[status(thm)],[c_531,c_198]) ).
cnf(c_13800,negated_conjecture,
( host(sK5) = sK0(sK3,sK6,sK5,sK6)
| setIn(sK0(sK3,sK6,sK5,sK6),index(down,host(sK6)))
| leq(host(sK6),sK0(sK3,sK6,sK5,sK6)) ),
inference(resolve,[status(thm)],[c_13632,c_199]) ).
cnf(c_13801,negated_conjecture,
( sK0(sK3,sK6,sK5,sK6) = host(sK5)
| setIn(sK0(sK3,sK6,sK5,sK6),index(down,host(sK6)))
| leq(host(sK6),sK0(sK3,sK6,sK5,sK6)) ),
inference(copy,[status(thm)],[c_13800]) ).
cnf(c_13802,negated_conjecture,
( sK0(sK3,sK6,sK5,sK6) = host(sK5)
| setIn(sK0(sK3,sK6,sK5,sK6),index(down,host(sK6))) ),
inference(resolve,[status(thm)],[c_522,c_13801]) ).
cnf(c_13662,negated_conjecture,
setIn(sK0(sK3,sK6,sK5,sK6),index(down,host(sK6))),
inference(resolve,[status(thm)],[c_526,c_13802]) ).
cnf(c_13803,plain,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| ~ setIn(sK3,alive)
| ~ elem(m_Down(sK5),queue(host(sK6))) ),
inference(resolve,[status(thm)],[c_13662,c_216]) ).
cnf(c_13804,negated_conjecture,
( ~ elem(m_Down(sK6),queue(host(sK3)))
| ~ setIn(sK3,alive) ),
inference(resolve,[status(thm)],[c_198,c_13803]) ).
cnf(c_13805,negated_conjecture,
~ elem(m_Down(sK6),queue(host(sK3))),
inference(resolve,[status(thm)],[c_178,c_13804]) ).
cnf(c_13774,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_518,c_13805]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV470+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.65 % Computer : n004.cluster.edu
% 0.17/0.65 % Model : x86_64 x86_64
% 0.17/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.65 % Memory : 8046.5625MB
% 0.17/0.65 % OS : Linux 6.8.0-71-generic
% 0.17/0.65 % CPULimit : 300
% 0.21/0.65 % WCLimit : 300
% 0.21/0.65 % DateTime : Sat Sep 26 13:55:38 UTC 2026
% 0.21/0.65 % CPUTime :
% 0.21/0.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/0.66 % Process 1890368 was started by sandbox2 on n004,
% 0.21/0.66 % Sat Sep 26 13:55:38 2026
% 0.21/0.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.68
% 0.21/0.68 % From the command line: assign(max_seconds, 300).
% 108.64/15.25
% 108.64/15.25 % given #500 (T,wt=11): 942 leq(s(A),s(B)) | -leq(C,B) | leq(C,A). [resolve(289,b,156,b)].
% 108.64/15.25
% 108.64/15.25 % given #1000 (T,wt=12): 1487 leq(A,s(host(B))) | -leq(s(A),C) | leq(zero,C). [resolve(1003,b,156,a)].
% 108.64/15.25
% 108.64/15.25 % SZS status Theorem for theBenchmark
% 108.64/15.25
% 108.64/15.25 % Proof 1 at 12.47 (+ 1.97) seconds.
% 108.64/15.25 % Length of proof is 46.
% 108.64/15.25 % Level of proof is 9.
% 108.64/15.25 % Maximum clause weight is 44.000.
% 108.64/15.25 % Given clauses 1140.
% 108.64/15.25
% 108.64/15.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
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