%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV474+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 82.72s 21.58s
% Output : CNFRefutation 82.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 89 ( 40 unt; 0 def)
% Number of atoms : 593 ( 310 equ)
% Maximal formula atoms : 98 ( 6 avg)
% Number of connectives : 837 ( 333 ~; 274 |; 186 &)
% ( 2 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 19 con; 0-4 aty)
% Number of variables : 255 ( 13 sgn 182 !; 10 ?)
% 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_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_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_Down(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)
=> ( ~ 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))) ) ) )
=> ! [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)
| V0 = host(Y)
| setIn(V0,index(down,host(X))) ) ) )
=> ~ ( 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_Down(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)
=> ( ~ 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))) ) ) )
=> ! [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)
| V0 = host(Y)
| setIn(V0,index(down,host(X))) ) ) )
=> ~ ( 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_109,plain,
init(snoc(A,B)) = A,
inference(clausify,[status(thm)],[axiom_38]) ).
cnf(c_118,plain,
( B != A
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
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
| host(Y) = V0
| setIn(V0,index(down,host(X)))
| ~ leq(s(zero),V0)
| leq(host(Y0),V0) )
& host(Y0) = host(X) )
& host(Z) != host(X) )
& ( index(status,host(X)) != elec_1
| ? [X28] :
( host(Y) != X28
& ~ setIn(X28,index(down,host(X)))
& leq(s(zero),X28)
& ~ leq(host(X),X28) ) )
& ( 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))
& ! [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),sK1)
& ! [V0] :
( host(sK6) = V0
| host(sK0) = V0
| setIn(V0,index(down,host(sK2)))
| ~ leq(s(zero),V0)
| leq(host(sK5),V0) )
& host(sK5) = host(sK2)
& host(sK4) != host(sK2)
& ( index(status,host(sK2)) != elec_1
| ( host(sK0) != sK3
& ~ setIn(sK3,index(down,host(sK2)))
& leq(s(zero),sK3)
& ~ leq(host(sK2),sK3) ) )
& ( 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))
& ! [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,sK1),skolemize(W,sK9),skolemize(X,sK2),skolemize(Y,sK0),skolemize(X27,sK8(X26,Pid30,Pid20,Pid0)),skolemize(X28,sK3),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),sK1)
& ! [VAR_0] :
( host(sK6) = VAR_0
| host(sK0) = VAR_0
| setIn(VAR_0,index(down,host(sK2)))
| ~ leq(s(zero),VAR_0)
| leq(host(sK5),VAR_0) )
& host(sK5) = host(sK2)
& host(sK4) != host(sK2)
& ( index(status,host(sK2)) != elec_1
| host(sK0) != sK3 )
& ( index(status,host(sK2)) != elec_1
| ~ setIn(sK3,index(down,host(sK2))) )
& ( index(status,host(sK2)) != elec_1
| leq(s(zero),sK3) )
& ( index(status,host(sK2)) != elec_1
| ~ leq(host(sK2),sK3) )
& ( 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,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_Down(sK0),sK1) = queue(host(sK2)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_176,negated_conjecture,
queue(host(sK2)) = cons(m_Down(sK0),sK1),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_177,negated_conjecture,
setIn(sK2,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_182,negated_conjecture,
( index(status,host(sK2)) != elec_1
| ~ leq(host(sK2),sK3) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_183,negated_conjecture,
( index(status,host(sK2)) != elec_1
| leq(s(zero),sK3) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_184,negated_conjecture,
( index(status,host(sK2)) != elec_1
| ~ setIn(sK3,index(down,host(sK2))) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_185,negated_conjecture,
( index(status,host(sK2)) != elec_1
| host(sK0) != sK3 ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_186,negated_conjecture,
host(sK4) != host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_187,negated_conjecture,
host(sK5) = host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_188,negated_conjecture,
( host(sK6) = A
| host(sK0) = A
| setIn(A,index(down,host(sK2)))
| ~ leq(s(zero),A)
| leq(host(sK5),A) ),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_189,negated_conjecture,
( host(sK6) = A
| host(sK0) = A
| setIn(A,index(down,host(sK2)))
| ~ leq(s(zero),A)
| leq(host(sK2),A) ),
inference(paramod,[status(thm)],[c_187,c_188]) ).
cnf(c_190,negated_conjecture,
elem(m_Down(sK6),sK1),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_191,negated_conjecture,
host(sK7) = host(sK5),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_192,negated_conjecture,
host(sK7) = host(sK2),
inference(paramod,[status(thm)],[c_187,c_191]) ).
cnf(c_193,negated_conjecture,
host(sK5) = nbr_proc,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_2515,negated_conjecture,
host(sK2) = nbr_proc,
inference(paramod,[status(thm)],[c_187,c_193]) ).
cnf(c_194,negated_conjecture,
nbr_proc = host(sK2),
inference(copy,[status(thm)],[c_2515]) ).
cnf(c_195,negated_conjecture,
index(status,host(sK5)) = elec_1,
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_2516,negated_conjecture,
index(status,host(sK2)) = elec_1,
inference(paramod,[status(thm)],[c_187,c_195]) ).
cnf(c_196,negated_conjecture,
elec_1 = index(status,host(sK2)),
inference(copy,[status(thm)],[c_2516]) ).
cnf(c_197,negated_conjecture,
setIn(sK4,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_198,negated_conjecture,
elem(m_Down(sK7),queue(host(sK4))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_204,plain,
leq(host(A),host(sK2)),
inference(paramod,[status(thm)],[c_194,c_64]) ).
cnf(c_2517,negated_conjecture,
( index(status,host(sK2)) != index(status,host(sK2))
| host(sK0) != sK3 ),
inference(paramod,[status(thm)],[c_196,c_185]) ).
cnf(c_205,negated_conjecture,
host(sK0) != sK3,
inference(copy,[status(thm)],[c_2517]) ).
cnf(c_2518,negated_conjecture,
( index(status,host(sK2)) != index(status,host(sK2))
| ~ setIn(sK3,index(down,host(sK2))) ),
inference(paramod,[status(thm)],[c_196,c_184]) ).
cnf(c_206,negated_conjecture,
~ setIn(sK3,index(down,host(sK2))),
inference(copy,[status(thm)],[c_2518]) ).
cnf(c_2519,negated_conjecture,
( index(status,host(sK2)) != index(status,host(sK2))
| leq(s(zero),sK3) ),
inference(paramod,[status(thm)],[c_196,c_183]) ).
cnf(c_207,negated_conjecture,
leq(s(zero),sK3),
inference(copy,[status(thm)],[c_2519]) ).
cnf(c_2520,negated_conjecture,
( index(status,host(sK2)) != index(status,host(sK2))
| ~ leq(host(sK2),sK3) ),
inference(paramod,[status(thm)],[c_196,c_182]) ).
cnf(c_208,negated_conjecture,
~ leq(host(sK2),sK3),
inference(copy,[status(thm)],[c_2520]) ).
cnf(c_2521,plain,
elem(A,cons(init(snoc(A,B)),C)),
inference(resolve,[status(thm)],[c_118,c_109]) ).
cnf(c_237,plain,
elem(A,cons(A,B)),
inference(paramod,[status(thm)],[c_109,c_2521]) ).
cnf(c_283,plain,
( ~ setIn(host(B),index(down,host(sK2)))
| ~ elem(m_Down(C),queue(host(A)))
| host(sK2) != host(C)
| host(B) != host(A)
| ~ setIn(A,alive)
| host(sK2) = host(A) ),
inference(resolve,[status(thm)],[c_177,c_169]) ).
cnf(c_2522,negated_conjecture,
( ~ elem(m_Down(B),queue(host(sK2)))
| ~ elem(m_Down(C),queue(host(A)))
| host(sK2) != host(C)
| host(B) != host(A)
| ~ setIn(A,alive)
| host(sK2) = host(A) ),
inference(resolve,[status(thm)],[c_177,c_168]) ).
cnf(c_285,negated_conjecture,
( ~ elem(m_Down(B),cons(m_Down(sK0),sK1))
| ~ elem(m_Down(C),queue(host(A)))
| host(sK2) != host(C)
| host(B) != host(A)
| ~ setIn(A,alive)
| host(sK2) = host(A) ),
inference(paramod,[status(thm)],[c_176,c_2522]) ).
cnf(c_290,plain,
( host(sK6) = host(A)
| host(sK0) = host(A)
| setIn(host(A),index(down,host(sK2)))
| leq(host(sK2),host(A)) ),
inference(resolve,[status(thm)],[c_189,c_62]) ).
cnf(c_295,plain,
elem(m_Down(sK6),cons(A,sK1)),
inference(resolve,[status(thm)],[c_190,c_119]) ).
cnf(c_2523,plain,
( host(A) = host(sK2)
| ~ leq(host(sK2),host(A)) ),
inference(resolve,[status(thm)],[c_204,c_151]) ).
cnf(c_325,plain,
( host(sK2) = host(A)
| ~ leq(host(sK2),host(A)) ),
inference(copy,[status(thm)],[c_2523]) ).
cnf(c_2524,negated_conjecture,
( host(sK6) = sK3
| host(sK0) = sK3
| setIn(sK3,index(down,host(sK2)))
| leq(host(sK2),sK3) ),
inference(resolve,[status(thm)],[c_207,c_189]) ).
cnf(c_2525,negated_conjecture,
( host(sK6) = sK3
| host(sK0) = sK3
| setIn(sK3,index(down,host(sK2))) ),
inference(resolve,[status(thm)],[c_208,c_2524]) ).
cnf(c_2526,negated_conjecture,
( host(sK6) = sK3
| host(sK0) = sK3 ),
inference(resolve,[status(thm)],[c_206,c_2525]) ).
cnf(c_327,negated_conjecture,
host(sK6) = sK3,
inference(resolve,[status(thm)],[c_205,c_2526]) ).
cnf(c_2527,plain,
( sK3 = host(A)
| host(sK0) = host(A)
| setIn(host(A),index(down,host(sK2)))
| leq(host(sK2),host(A)) ),
inference(paramod,[status(thm)],[c_327,c_290]) ).
cnf(c_337,plain,
( host(A) = sK3
| host(sK0) = host(A)
| setIn(host(A),index(down,host(sK2)))
| leq(host(sK2),host(A)) ),
inference(copy,[status(thm)],[c_2527]) ).
cnf(c_2528,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK2)))
| ~ elem(m_Down(B),queue(host(sK4)))
| host(sK2) != host(B)
| host(A) != host(sK4)
| host(sK2) = host(sK4) ),
inference(resolve,[status(thm)],[c_283,c_197]) ).
cnf(c_2529,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK2)))
| ~ elem(m_Down(B),queue(host(sK4)))
| host(sK2) != host(B)
| host(A) != host(sK4)
| host(sK4) = host(sK2) ),
inference(copy,[status(thm)],[c_2528]) ).
cnf(c_2530,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK2)))
| ~ elem(m_Down(B),queue(host(sK4)))
| host(sK2) != host(B)
| host(sK4) != host(A)
| host(sK4) = host(sK2) ),
inference(copy,[status(thm)],[c_2529]) ).
cnf(c_1860,negated_conjecture,
( ~ setIn(host(A),index(down,host(sK2)))
| ~ elem(m_Down(B),queue(host(sK4)))
| host(sK2) != host(B)
| host(sK4) != host(A) ),
inference(resolve,[status(thm)],[c_186,c_2530]) ).
cnf(c_2531,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| ~ elem(m_Down(B),queue(host(sK4)))
| host(sK2) != host(B)
| host(A) != host(sK4)
| host(sK2) = host(sK4) ),
inference(resolve,[status(thm)],[c_285,c_197]) ).
cnf(c_2532,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| ~ elem(m_Down(B),queue(host(sK4)))
| host(sK2) != host(B)
| host(A) != host(sK4)
| host(sK4) = host(sK2) ),
inference(copy,[status(thm)],[c_2531]) ).
cnf(c_2533,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| ~ elem(m_Down(B),queue(host(sK4)))
| host(sK2) != host(B)
| host(sK4) != host(A)
| host(sK4) = host(sK2) ),
inference(copy,[status(thm)],[c_2532]) ).
cnf(c_2186,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| ~ elem(m_Down(B),queue(host(sK4)))
| host(sK2) != host(B)
| host(sK4) != host(A) ),
inference(resolve,[status(thm)],[c_186,c_2533]) ).
cnf(c_2534,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| host(sK2) != host(sK7)
| host(sK4) != host(A) ),
inference(resolve,[status(thm)],[c_2186,c_198]) ).
cnf(c_2535,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| host(sK2) != host(sK2)
| host(sK4) != host(A) ),
inference(paramod,[status(thm)],[c_192,c_2534]) ).
cnf(c_2187,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| host(sK4) != host(A) ),
inference(copy,[status(thm)],[c_2535]) ).
cnf(c_2536,plain,
host(sK4) != host(sK6),
inference(resolve,[status(thm)],[c_2187,c_295]) ).
cnf(c_2190,plain,
host(sK4) != sK3,
inference(paramod,[status(thm)],[c_327,c_2536]) ).
cnf(c_2191,plain,
host(sK4) != host(sK0),
inference(resolve,[status(thm)],[c_2187,c_237]) ).
cnf(c_2537,plain,
( ~ setIn(host(sK4),index(down,host(sK2)))
| ~ elem(m_Down(A),queue(host(sK4)))
| host(sK2) != host(A) ),
inference(xxres,[status(thm)],[c_1860]) ).
cnf(c_2538,negated_conjecture,
host(sK2) = host(sK7),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_2539,negated_conjecture,
( ~ setIn(host(sK4),index(down,host(sK2)))
| ~ elem(m_Down(sK7),queue(host(sK4))) ),
inference(resolve,[status(thm)],[c_2537,c_2538]) ).
cnf(c_2540,negated_conjecture,
~ setIn(host(sK4),index(down,host(sK2))),
inference(resolve,[status(thm)],[c_2539,c_198]) ).
cnf(c_2541,negated_conjecture,
( host(sK4) = sK3
| host(sK0) = host(sK4)
| leq(host(sK2),host(sK4)) ),
inference(resolve,[status(thm)],[c_2540,c_337]) ).
cnf(c_2542,negated_conjecture,
( host(sK4) = sK3
| host(sK4) = host(sK0)
| leq(host(sK2),host(sK4)) ),
inference(copy,[status(thm)],[c_2541]) ).
cnf(c_2543,negated_conjecture,
( host(sK4) = sK3
| leq(host(sK2),host(sK4)) ),
inference(resolve,[status(thm)],[c_2191,c_2542]) ).
cnf(c_2508,negated_conjecture,
leq(host(sK2),host(sK4)),
inference(resolve,[status(thm)],[c_2190,c_2543]) ).
cnf(c_2544,plain,
host(sK2) = host(sK4),
inference(resolve,[status(thm)],[c_2508,c_325]) ).
cnf(c_2545,plain,
host(sK4) = host(sK2),
inference(copy,[status(thm)],[c_2544]) ).
cnf(c_2514,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_186,c_2545]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV474+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.58 % Computer : n006.cluster.edu
% 0.09/10.58 % Model : x86_64 x86_64
% 0.09/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.58 % Memory : 8046.5625MB
% 0.09/10.58 % OS : Linux 6.8.0-71-generic
% 0.09/10.58 % CPULimit : 300
% 0.09/10.58 % WCLimit : 300
% 0.09/10.58 % DateTime : Sat Sep 26 13:56:41 UTC 2026
% 0.09/10.58 % CPUTime :
% 0.09/10.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.58 % Process 1412653 was started by sandbox on n006,
% 0.09/10.58 % Sat Sep 26 13:56:41 2026
% 0.09/10.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.59
% 0.09/10.59 % From the command line: assign(max_seconds, 300).
% 82.72/21.58
% 82.72/21.58 % SZS status Theorem for theBenchmark
% 82.72/21.58
% 82.72/21.58 % Proof 1 at 1.97 (+ 0.55) seconds.
% 82.72/21.58 % Length of proof is 54.
% 82.72/21.58 % Level of proof is 8.
% 82.72/21.58 % Maximum clause weight is 40.000.
% 82.72/21.58 % Given clauses 345.
% 82.72/21.58
% 82.72/21.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------