%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV455+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 : n012.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 1.93s 11.24s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 299 ( 133 equ)
% Maximal formula atoms : 49 ( 9 avg)
% Number of connectives : 452 ( 185 ~; 107 |; 125 &)
% ( 1 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 150 ( 5 sgn 116 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_46,axiom,
! [X,Y,Q] :
( elem(X,cons(Y,Q))
<=> ( elem(X,Q)
| X = Y ) ),
file('theBenchmark.p',axiom_46) ).
fof(conj,conjecture,
! [V,W,X,Y] :
( ( queue(host(X)) = cons(m_Down(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)
=> ( ~ 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] :
( host(X) = host(X0)
=> ! [Y0] :
( ( host(Y0) = host(X0)
& host(W0) = host(Z)
& setIn(X0,alive)
& setIn(Z,alive)
& host(X0) != host(Z) )
=> ~ ( elem(m_Down(Y0),queue(host(Z)))
& elem(m_Down(W0),V) ) ) ) ) ) ) ) ) ),
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] :
( ( 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)
=> ( ~ 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] :
( host(X) = host(X0)
=> ! [Y0] :
( ( host(Y0) = host(X0)
& host(W0) = host(Z)
& setIn(X0,alive)
& setIn(Z,alive)
& host(X0) != host(Z) )
=> ~ ( elem(m_Down(Y0),queue(host(Z)))
& elem(m_Down(W0),V) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
cnf(c_119,plain,
( ~ elem(A,C)
| elem(A,cons(B,C)) ),
inference(clausify,[status(thm)],[axiom_46]) ).
fof(nnf_58,plain,
? [V,W,X,Y] :
( ? [Z] :
( ? [W0,X0] :
( ? [Y0] :
( elem(m_Down(Y0),queue(host(Z)))
& elem(m_Down(W0),V)
& host(Y0) = host(X0)
& host(W0) = host(Z)
& setIn(X0,alive)
& setIn(Z,alive)
& host(X0) != host(Z) )
& host(X0) = host(X) )
& host(Z) != host(X) )
& ( index(status,host(X)) != elec_1
| ? [X19] :
( host(Y) != X19
& ~ setIn(X19,index(down,host(X)))
& leq(s(zero),X19)
& ~ leq(host(X),X19) ) )
& ( 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))
& ! [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_sk,plain,
( elem(m_Down(sK6),queue(host(sK3)))
& elem(m_Down(sK5),sK1)
& host(sK6) = host(sK4)
& host(sK5) = host(sK3)
& setIn(sK4,alive)
& setIn(sK3,alive)
& host(sK4) != host(sK3)
& host(sK4) = host(sK2)
& host(sK3) != host(sK2)
& ( index(status,host(sK2)) != elec_1
| ( host(sK0) != sK7
& ~ setIn(sK7,index(down,host(sK2)))
& leq(s(zero),sK7)
& ~ leq(host(sK2),sK7) ) )
& ( 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))
& ! [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,sK7,sK3,sK4,sK5,sK6]),skolemize(V,sK1),skolemize(W,sK8),skolemize(X,sK2),skolemize(Y,sK0),skolemize(X19,sK7),skolemize(Z,sK3),skolemize(W0,sK5),skolemize(X0,sK4),skolemize(Y0,sK6)],[nnf_58]) ).
fof(sk_conj_neg,plain,
( elem(m_Down(sK6),queue(host(sK3)))
& elem(m_Down(sK5),sK1)
& host(sK6) = host(sK4)
& host(sK5) = host(sK3)
& setIn(sK4,alive)
& setIn(sK3,alive)
& host(sK4) != host(sK3)
& host(sK4) = host(sK2)
& host(sK3) != host(sK2)
& ( index(status,host(sK2)) != elec_1
| host(sK0) != sK7 )
& ( index(status,host(sK2)) != elec_1
| ~ setIn(sK7,index(down,host(sK2))) )
& ( index(status,host(sK2)) != elec_1
| leq(s(zero),sK7) )
& ( index(status,host(sK2)) != elec_1
| ~ leq(host(sK2),sK7) )
& ( 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_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] :
( ~ setIn(VAR_0,alive)
| ~ setIn(VAR_1,alive)
| host(VAR_0) != host(VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( ~ setIn(VAR_1,alive)
| host(VAR_1) != host(VAR_0)
| ~ leq(VAR_1,VAR_0)
| setIn(VAR_0,alive) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Ack(VAR_0,VAR_1),queue(host(VAR_2))) )
& ! [VAR_0,VAR_1] :
( ~ leq(host(VAR_1),host(VAR_0))
| ~ elem(m_Halt(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( host(VAR_0) != host(VAR_1)
| ~ elem(m_Down(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( ~ setIn(VAR_0,alive)
| ~ elem(m_Down(VAR_0),queue(host(VAR_1))) )
& ! [VAR_0,VAR_1] :
( ~ elem(m_Down(VAR_0),queue(host(VAR_1)))
| ~ setIn(VAR_0,alive) ) ),
inference(cnf_transformation,[status(thm)],[sk_conj_neg_sk]) ).
cnf(c_166,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_167,negated_conjecture,
cons(m_Down(sK0),sK1) = queue(host(sK2)),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_168,negated_conjecture,
queue(host(sK2)) = cons(m_Down(sK0),sK1),
inference(copy,[status(thm)],[c_167]) ).
cnf(c_169,negated_conjecture,
setIn(sK2,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_178,negated_conjecture,
host(sK3) != host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_179,negated_conjecture,
host(sK4) = host(sK2),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_181,negated_conjecture,
setIn(sK3,alive),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_183,negated_conjecture,
host(sK5) = host(sK3),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_184,negated_conjecture,
host(sK6) = host(sK4),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_185,negated_conjecture,
host(sK6) = host(sK2),
inference(paramod,[status(thm)],[c_179,c_184]) ).
cnf(c_186,negated_conjecture,
elem(m_Down(sK5),sK1),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_187,negated_conjecture,
elem(m_Down(sK6),queue(host(sK3))),
inference(split_conjunct,[status(thm)],[sk_conj_neg]) ).
cnf(c_2060,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_169,c_166]) ).
cnf(c_278,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_168,c_2060]) ).
cnf(c_306,plain,
elem(m_Down(sK5),cons(A,sK1)),
inference(resolve,[status(thm)],[c_186,c_119]) ).
cnf(c_2061,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| ~ elem(m_Down(B),queue(host(sK3)))
| host(sK2) != host(B)
| host(A) != host(sK3)
| host(sK2) = host(sK3) ),
inference(resolve,[status(thm)],[c_278,c_181]) ).
cnf(c_2062,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| ~ elem(m_Down(B),queue(host(sK3)))
| host(sK2) != host(B)
| host(A) != host(sK3)
| host(sK3) = host(sK2) ),
inference(copy,[status(thm)],[c_2061]) ).
cnf(c_2063,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| ~ elem(m_Down(B),queue(host(sK3)))
| host(sK2) != host(B)
| host(sK3) != host(A)
| host(sK3) = host(sK2) ),
inference(copy,[status(thm)],[c_2062]) ).
cnf(c_2056,negated_conjecture,
( ~ elem(m_Down(A),cons(m_Down(sK0),sK1))
| ~ elem(m_Down(B),queue(host(sK3)))
| host(sK2) != host(B)
| host(sK3) != host(A) ),
inference(resolve,[status(thm)],[c_178,c_2063]) ).
cnf(c_2064,plain,
( ~ elem(m_Down(A),queue(host(sK3)))
| host(sK2) != host(A)
| host(sK3) != host(sK5) ),
inference(resolve,[status(thm)],[c_2056,c_306]) ).
cnf(c_2065,plain,
( ~ elem(m_Down(A),queue(host(sK3)))
| host(sK2) != host(A)
| host(sK3) != host(sK3) ),
inference(paramod,[status(thm)],[c_183,c_2064]) ).
cnf(c_2058,plain,
( ~ elem(m_Down(A),queue(host(sK3)))
| host(sK2) != host(A) ),
inference(copy,[status(thm)],[c_2065]) ).
cnf(c_2066,negated_conjecture,
host(sK2) != host(sK6),
inference(resolve,[status(thm)],[c_2058,c_187]) ).
cnf(c_2067,negated_conjecture,
host(sK2) != host(sK2),
inference(paramod,[status(thm)],[c_185,c_2066]) ).
cnf(c_2059,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_2067]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV455+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/10.94 % Computer : n012.cluster.edu
% 0.04/10.94 % Model : x86_64 x86_64
% 0.04/10.94 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/10.94 % Memory : 8046.5625MB
% 0.04/10.94 % OS : Linux 6.8.0-71-generic
% 0.04/10.94 % CPULimit : 300
% 0.04/10.94 % WCLimit : 300
% 0.04/10.94 % DateTime : Sat Sep 26 13:54:29 UTC 2026
% 0.04/10.94 % CPUTime :
% 0.04/10.94 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/10.94 % Process 775660 was started by sandbox2 on n012,
% 0.04/10.94 % Sat Sep 26 13:54:29 2026
% 0.04/10.94 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/10.95
% 0.04/10.95 % From the command line: assign(max_seconds, 300).
% 1.93/11.24
% 1.93/11.24 % SZS status Theorem for theBenchmark
% 1.93/11.24
% 1.93/11.24 % Proof 1 at 0.20 (+ 0.08) seconds.
% 1.93/11.24 % Length of proof is 20.
% 1.93/11.24 % Level of proof is 6.
% 1.93/11.24 % Maximum clause weight is 33.000.
% 1.93/11.24 % Given clauses 401.
% 1.93/11.24
% 1.93/11.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------