%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV450+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 : n005.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 09:07:59 AM UTC 2026
% Result : Theorem 3.90s 0.96s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 22 unt; 0 def)
% Number of atoms : 272 ( 128 equ)
% Maximal formula atoms : 44 ( 6 avg)
% Number of connectives : 371 ( 143 ~; 94 |; 96 &)
% ( 2 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 16 con; 0-2 aty)
% Number of variables : 147 ( 4 sgn 102 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_18,axiom,
! [X,Y] : m_Down(X) != m_Ldr(Y),
file('theBenchmark.p',axiom_18) ).
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,Y] :
( ( queue(host(X)) = cons(m_Ack(W,Y),V)
& ! [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,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& leq(Pid0,Z)
& ~ setIn(Z,alive) )
=> ~ setIn(Pid0,alive) )
& ! [Z,Pid20,Pid0] :
( elem(m_Ack(Pid0,Z),queue(host(Pid20)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Halt(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> host(Pid0) != host(Z) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( setIn(Pid0,alive)
=> ~ elem(m_Down(Pid0),queue(host(Z))) ) )
=> ( setIn(X,alive)
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W )
=> ( leq(nbr_proc,index(pendack,host(X)))
=> ! [Z] :
( ( host(Z) = host(Y)
| setIn(host(Z),index(acks,host(X))) )
=> ! [V0] :
( host(Z) != host(V0)
=> ( host(X) = host(V0)
=> ! [W0,X0] :
( host(Z) = host(X0)
=> ( host(X) != host(X0)
=> ! [Y0] :
( ( host(Y0) = host(X0)
& host(W0) = host(V0)
& setIn(X0,alive)
& setIn(V0,alive)
& host(X0) != host(V0) )
=> ~ ( elem(m_Down(W0),snoc(queue(host(X0)),m_Ldr(X)))
& elem(m_Down(Y0),V) ) ) ) ) ) ) ) ) ) ) ),
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] :
( ( 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,Pid0] :
( ( host(Pid0) = host(Z)
& Pid0 != Z )
=> ( ~ setIn(Pid0,alive)
| ~ setIn(Z,alive) ) )
& ! [Z,Pid0] :
( ( host(Pid0) = host(Z)
& leq(Pid0,Z)
& ~ setIn(Z,alive) )
=> ~ setIn(Pid0,alive) )
& ! [Z,Pid20,Pid0] :
( elem(m_Ack(Pid0,Z),queue(host(Pid20)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Halt(Pid0),queue(host(Z)))
=> ~ leq(host(Z),host(Pid0)) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> host(Pid0) != host(Z) )
& ! [Z,Pid0] :
( elem(m_Down(Pid0),queue(host(Z)))
=> ~ setIn(Pid0,alive) )
& ! [Z,Pid0] :
( setIn(Pid0,alive)
=> ~ elem(m_Down(Pid0),queue(host(Z))) ) )
=> ( setIn(X,alive)
=> ( ( host(Y) = index(pendack,host(X))
& index(status,host(X)) = elec_2
& index(elid,host(X)) = W )
=> ( leq(nbr_proc,index(pendack,host(X)))
=> ! [Z] :
( ( host(Z) = host(Y)
| setIn(host(Z),index(acks,host(X))) )
=> ! [V0] :
( host(Z) != host(V0)
=> ( host(X) = host(V0)
=> ! [W0,X0] :
( host(Z) = host(X0)
=> ( host(X) != host(X0)
=> ! [Y0] :
( ( host(Y0) = host(X0)
& host(W0) = host(V0)
& setIn(X0,alive)
& setIn(V0,alive)
& host(X0) != host(V0) )
=> ~ ( elem(m_Down(W0),snoc(queue(host(X0)),m_Ldr(X)))
& elem(m_Down(Y0),V) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_83,plain,
m_Ldr(A) != m_Down(B),
inference(clausify,[status(thm)],[axiom_18]) ).
cnf(c_120,plain,
( ~ elem(A,C)
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
cnf(c_121,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] :
( ? [V0] :
( ? [W0,X0] :
( ? [Y0] :
( elem(m_Down(W0),snoc(queue(host(X0)),m_Ldr(X)))
& elem(m_Down(Y0),V)
& host(Y0) = host(X0)
& host(W0) = host(V0)
& setIn(X0,alive)
& setIn(V0,alive)
& host(X0) != host(V0) )
& host(X0) != host(X)
& host(X0) = host(Z) )
& host(V0) = host(X)
& host(V0) != host(Z) )
& ( host(Z) = host(Y)
| setIn(host(Z),index(acks,host(X))) ) )
& leq(nbr_proc,index(pendack,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))
& ! [X18,Pid30,Pid20,Pid0] :
( ~ elem(m_Down(Pid30),queue(host(Pid20)))
| ~ elem(m_Down(Pid0),queue(host(X18)))
| host(Pid20) != host(Pid0)
| host(Pid30) != host(X18)
| ~ setIn(Pid20,alive)
| ~ setIn(X18,alive)
| host(Pid20) = host(X18) )
& ! [X16,X17] :
( ~ setIn(X17,alive)
| ~ setIn(X16,alive)
| host(X17) != host(X16)
| X17 = X16 )
& ! [X14,X15] :
( ~ setIn(X15,alive)
| host(X15) != host(X14)
| ~ leq(X15,X14)
| setIn(X14,alive) )
& ! [X11,X12,X13] :
( ~ leq(host(X11),host(X13))
| ~ elem(m_Ack(X13,X11),queue(host(X12))) )
& ! [X9,X10] :
( ~ leq(host(X9),host(X10))
| ~ elem(m_Halt(X10),queue(host(X9))) )
& ! [X7,X8] :
( host(X8) != host(X7)
| ~ elem(m_Down(X8),queue(host(X7))) )
& ! [X5,X6] :
( ~ setIn(X6,alive)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( ~ elem(m_Down(X4),queue(host(X3)))
| ~ setIn(X4,alive) ) ),
inference(fof_nnf,[status(thm)],[conj_neg]) ).
fof(sk_conj_neg,plain,
( elem(m_Down(sK7),snoc(queue(host(sK5)),m_Ldr(sK3)))
& elem(m_Down(sK8),sK2)
& host(sK8) = host(sK5)
& host(sK7) = host(sK4)
& setIn(sK5,alive)
& setIn(sK4,alive)
& host(sK5) != host(sK4)
& host(sK5) != host(sK3)
& host(sK5) = host(sK6)
& host(sK4) = host(sK3)
& host(sK4) != host(sK6)
& ( host(sK6) = host(sK1)
| setIn(host(sK6),index(acks,host(sK3))) )
& leq(nbr_proc,index(pendack,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))
& ! [X18,Pid30,Pid20,Pid0] :
( ~ elem(m_Down(Pid30),queue(host(Pid20)))
| ~ elem(m_Down(Pid0),queue(host(X18)))
| host(Pid20) != host(Pid0)
| host(Pid30) != host(X18)
| ~ setIn(Pid20,alive)
| ~ setIn(X18,alive)
| host(Pid20) = host(X18) )
& ! [X16,X17] :
( ~ setIn(X17,alive)
| ~ setIn(X16,alive)
| host(X17) != host(X16)
| X17 = X16 )
& ! [X14,X15] :
( ~ setIn(X15,alive)
| host(X15) != host(X14)
| ~ leq(X15,X14)
| setIn(X14,alive) )
& ! [X11,X12,X13] :
( ~ leq(host(X11),host(X13))
| ~ elem(m_Ack(X13,X11),queue(host(X12))) )
& ! [X9,X10] :
( ~ leq(host(X9),host(X10))
| ~ elem(m_Halt(X10),queue(host(X9))) )
& ! [X7,X8] :
( host(X8) != host(X7)
| ~ elem(m_Down(X8),queue(host(X7))) )
& ! [X5,X6] :
( ~ setIn(X6,alive)
| ~ elem(m_Down(X6),queue(host(X5))) )
& ! [X3,X4] :
( ~ elem(m_Down(X4),queue(host(X3)))
| ~ setIn(X4,alive) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK6,sK4,sK5,sK7,sK8]),skolemize(V,sK2),skolemize(W,sK0),skolemize(X,sK3),skolemize(Y,sK1),skolemize(Z,sK6),skolemize(V0,sK4),skolemize(W0,sK7),skolemize(X0,sK5),skolemize(Y0,sK8)],[nnf_58]) ).
cnf(c_167,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_168,negated_conjecture,
cons(m_Ack(sK0,sK1),sK2) = queue(host(sK3)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_169,negated_conjecture,
queue(host(sK3)) = cons(m_Ack(sK0,sK1),sK2),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_170,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(sK6),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_182,negated_conjecture,
host(sK5) != host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_183,negated_conjecture,
host(sK6) != host(sK3),
inference(paramod,[status(thm)],[c_181,c_182]) ).
cnf(c_186,negated_conjecture,
setIn(sK5,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_187,negated_conjecture,
host(sK7) = host(sK4),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_188,negated_conjecture,
host(sK7) = host(sK3),
inference(paramod,[status(thm)],[c_180,c_187]) ).
cnf(c_189,negated_conjecture,
host(sK8) = host(sK5),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_190,negated_conjecture,
host(sK8) = host(sK6),
inference(paramod,[status(thm)],[c_181,c_189]) ).
cnf(c_191,negated_conjecture,
elem(m_Down(sK8),sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_192,negated_conjecture,
elem(m_Down(sK7),snoc(queue(host(sK5)),m_Ldr(sK3))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_193,negated_conjecture,
elem(m_Down(sK7),snoc(queue(host(sK6)),m_Ldr(sK3))),
inference(paramod,[status(thm)],[c_181,c_192]) ).
cnf(c_2193,negated_conjecture,
( ~ elem(m_Down(B),queue(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_170,c_167]) ).
cnf(c_287,negated_conjecture,
( ~ elem(m_Down(B),cons(m_Ack(sK0,sK1),sK2))
| ~ elem(m_Down(C),queue(host(A)))
| host(sK3) != host(C)
| host(B) != host(A)
| ~ setIn(A,alive)
| host(sK3) = host(A) ),
inference(paramod,[status(thm)],[c_169,c_2193]) ).
cnf(c_338,plain,
elem(m_Down(sK8),cons(A,sK2)),
inference(resolve,[status(thm)],[c_191,c_120]) ).
cnf(c_2194,negated_conjecture,
( elem(m_Down(sK7),queue(host(sK6)))
| m_Ldr(sK3) = m_Down(sK7) ),
inference(resolve,[status(thm)],[c_193,c_121]) ).
cnf(c_343,negated_conjecture,
elem(m_Down(sK7),queue(host(sK6))),
inference(resolve,[status(thm)],[c_83,c_2194]) ).
cnf(c_2195,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| ~ elem(m_Down(B),queue(host(sK5)))
| host(sK3) != host(B)
| host(A) != host(sK5)
| host(sK3) = host(sK5) ),
inference(resolve,[status(thm)],[c_287,c_186]) ).
cnf(c_2196,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| ~ elem(m_Down(B),queue(host(sK5)))
| host(sK3) != host(B)
| host(A) != host(sK5)
| host(sK3) = host(sK6) ),
inference(paramod,[status(thm)],[c_181,c_2195]) ).
cnf(c_2197,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| ~ elem(m_Down(B),queue(host(sK5)))
| host(sK3) != host(B)
| host(A) != host(sK6)
| host(sK3) = host(sK6) ),
inference(paramod,[status(thm)],[c_181,c_2196]) ).
cnf(c_2198,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| ~ elem(m_Down(B),queue(host(sK6)))
| host(sK3) != host(B)
| host(A) != host(sK6)
| host(sK3) = host(sK6) ),
inference(paramod,[status(thm)],[c_181,c_2197]) ).
cnf(c_2199,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| ~ elem(m_Down(B),queue(host(sK6)))
| host(sK3) != host(B)
| host(A) != host(sK6)
| host(sK6) = host(sK3) ),
inference(copy,[status(thm)],[c_2198]) ).
cnf(c_2200,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| ~ elem(m_Down(B),queue(host(sK6)))
| host(sK3) != host(B)
| host(sK6) != host(A)
| host(sK6) = host(sK3) ),
inference(copy,[status(thm)],[c_2199]) ).
cnf(c_2189,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Ack(sK0,sK1),sK2))
| ~ elem(m_Down(B),queue(host(sK6)))
| host(sK3) != host(B)
| host(sK6) != host(A) ),
inference(resolve,[status(thm)],[c_183,c_2200]) ).
cnf(c_2201,plain,
( ~ elem(m_Down(A),queue(host(sK6)))
| host(sK3) != host(A)
| host(sK6) != host(sK8) ),
inference(resolve,[status(thm)],[c_2189,c_338]) ).
cnf(c_2202,plain,
( ~ elem(m_Down(A),queue(host(sK6)))
| host(sK3) != host(A)
| host(sK6) != host(sK6) ),
inference(paramod,[status(thm)],[c_190,c_2201]) ).
cnf(c_2191,plain,
( ~ elem(m_Down(A),queue(host(sK6)))
| host(sK3) != host(A) ),
inference(copy,[status(thm)],[c_2202]) ).
cnf(c_2203,plain,
host(sK3) != host(sK7),
inference(resolve,[status(thm)],[c_2191,c_343]) ).
cnf(c_2204,plain,
host(sK3) != host(sK3),
inference(paramod,[status(thm)],[c_188,c_2203]) ).
cnf(c_2192,plain,
$false,
inference(copy,[status(thm)],[c_2204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV450+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 : n005.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 13:54:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2307586 was started by sandbox2 on n005,
% 0.09/0.37 % Sat Sep 26 13:54:01 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).
% 3.90/0.96
% 3.90/0.96 % SZS status Theorem for theBenchmark
% 3.90/0.96
% 3.90/0.96 % Proof 1 at 0.42 (+ 0.13) seconds.
% 3.90/0.96 % Length of proof is 29.
% 3.90/0.96 % Level of proof is 6.
% 3.90/0.96 % Maximum clause weight is 33.000.
% 3.90/0.96 % Given clauses 408.
% 3.90/0.96
% 3.90/0.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------