0.00/0.02 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.03 % Command : prover9 -casc 180 -f /export/starexec/sandbox2/benchmark/theBenchmark.p 0.08/0.34 % Computer : n017.cluster.edu 0.08/0.34 % Model : x86_64 x86_64 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.34 % Memory : 8046.5625MB 0.08/0.34 % OS : Linux 6.8.0-71-generic 0.08/0.35 % CPULimit : 1440 0.08/0.35 % WCLimit : 180 0.08/0.35 % DateTime : Mon Jul 27 10:09:38 UTC 2026 0.08/0.35 % CPUTime : 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13. 0.08/0.35 % Process 1240248 was started by sandbox2 on n017, 0.08/0.35 % Mon Jul 27 10:09:38 2026 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 180 -f /export/starexec/sandbox2/benchmark/theBenchmark.p". 0.12/0.37 0.12/0.37 % From the command line: assign(max_seconds, 180). 42.75/6.70 42.75/6.70 % given #500 (T,wt=19): 2899 q_nil = A | elem(head(A),cons(B,A)). [resolve(1387,b,127,a)]. 42.75/6.70 42.75/6.70 % SZS status Theorem for theBenchmark 42.75/6.70 42.75/6.70 % Proof 1 at 5.20 (+ 1.09) seconds. 42.75/6.70 % Length of proof is 30. 42.75/6.70 % Level of proof is 9. 42.75/6.70 % Maximum clause weight is 48.000. 42.75/6.70 % Given clauses 795. 42.75/6.70 42.75/6.70 % SZS output start CNFRefutation for theBenchmark 42.75/6.70 fof(axiom_46, axiom, ! [X,Y,Q] : ((elem(X,Q) | X = Y) <=> elem(X,cons(Y,Q))), file('theBenchmark.p',axiom_46)). 42.75/6.70 fof(conj, conjecture, ! [V,W,X,Y] : ((! [Z,Pid20,Pid0] : (elem(m_Ack(Pid0,Z),queue(host(Pid20))) => ~ (leq(host(Z),host(Pid0)))) & ! [Z,Pid0] : ((leq(Pid0,Z) & host(Z) = host(Pid0) & ~ (setIn(Z,alive))) => ~ (setIn(Pid0,alive))) & cons(m_Down(Y),V) = queue(host(X)) & ! [Z,Pid30,Pid20,Pid0] : ((setIn(Pid20,alive) & host(Z) = host(Pid30) & host(Pid20) = host(Pid0) & setIn(Z,alive) & ~ (host(Z) = host(Pid20))) => ~ ((elem(m_Down(Pid0),queue(host(Z))) & elem(m_Down(Pid30),queue(host(Pid20)))))) & ! [Z,Pid0] : ((~ (Pid0 = Z) & host(Pid0) = host(Z)) => (~ (setIn(Pid0,alive)) | ~ (setIn(Z,alive)))) & ! [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))) => (((norm = index(status,host(X)) & host(Y) = index(ldr,host(X))) | (host(Y) = host(index(elid,host(X))) & wait = index(status,host(X)))) => ((~ (setIn(W,pids)) & host(X) = host(W) & ! [Z] : (host(X) = host(Z) => leq(Z,W))) => (~ (s(zero) = host(W)) => ! [Z] : (~ (host(Z) = host(X)) => ! [X0,Y0] : (host(X) = host(Y0) => ! [Z0] : ((~ (host(Y0) = host(Z)) & host(Z) = host(X0) & host(Z0) = host(Y0) & ((setIn(Y0,alive) & ~ (Y0 = X)) | Y0 = W) & (W = Z | (setIn(Z,alive) & ~ (Z = X)))) => ~ ((elem(m_Down(Z0),queue(host(Z))) & elem(m_Down(X0),V)))))))))))), file('theBenchmark.p',conj)). 42.75/6.70 fof(conj_neg, negated_conjecture, ~(! [V,W,X,Y] : ((! [Z,Pid20,Pid0] : (elem(m_Ack(Pid0,Z),queue(host(Pid20))) => ~ (leq(host(Z),host(Pid0)))) & ! [Z,Pid0] : ((leq(Pid0,Z) & host(Z) = host(Pid0) & ~ (setIn(Z,alive))) => ~ (setIn(Pid0,alive))) & cons(m_Down(Y),V) = queue(host(X)) & ! [Z,Pid30,Pid20,Pid0] : ((setIn(Pid20,alive) & host(Z) = host(Pid30) & host(Pid20) = host(Pid0) & setIn(Z,alive) & ~ (host(Z) = host(Pid20))) => ~ ((elem(m_Down(Pid0),queue(host(Z))) & elem(m_Down(Pid30),queue(host(Pid20)))))) & ! [Z,Pid0] : ((~ (Pid0 = Z) & host(Pid0) = host(Z)) => (~ (setIn(Pid0,alive)) | ~ (setIn(Z,alive)))) & ! [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))) => (((norm = index(status,host(X)) & host(Y) = index(ldr,host(X))) | (host(Y) = host(index(elid,host(X))) & wait = index(status,host(X)))) => ((~ (setIn(W,pids)) & host(X) = host(W) & ! [Z] : (host(X) = host(Z) => leq(Z,W))) => (~ (s(zero) = host(W)) => ! [Z] : (~ (host(Z) = host(X)) => ! [X0,Y0] : (host(X) = host(Y0) => ! [Z0] : ((~ (host(Y0) = host(Z)) & host(Z) = host(X0) & host(Z0) = host(Y0) & ((setIn(Y0,alive) & ~ (Y0 = X)) | Y0 = W) & (W = Z | (setIn(Z,alive) & ~ (Z = X)))) => ~ ((elem(m_Down(Z0),queue(host(Z))) & elem(m_Down(X0),V))))))))))))), inference(assume_negation, [status(cth)], [conj])). 42.75/6.70 cnf(c_127, plain, ~elem(A,B) | elem(A,cons(C,B)), inference(clausify, [status(thm)], [axiom_46])). 42.75/6.70 fof(nnf_58, plain, ? [V,W,X,Y] : (setIn(X,alive) & ~ (leq(host(X),host(Y))) & ~ (setIn(W,pids)) & host(W) = host(X) & ! [X3] : (leq(X3,W) | ~ (host(X3) = host(X))) & ~ (s(zero) = host(W)) & ? [X4] : (~ (host(X4) = host(X)) & ? [X0,Y0] : (host(Y0) = host(X) & ? [Z0] : (elem(m_Down(Z0),queue(host(X4))) & elem(m_Down(X0),V) & ~ (host(Y0) = host(X4)) & host(X0) = host(X4) & host(Z0) = host(Y0) & ((setIn(Y0,alive) & ~ (Y0 = X)) | Y0 = W) & (W = X4 | (setIn(X4,alive) & ~ (X4 = X)))))) & ((index(status,host(X)) = norm & index(ldr,host(X)) = host(Y)) | (host(index(elid,host(X))) = host(Y) & index(status,host(X)) = wait)) & ! [X5,X6,X7] : (~ (leq(host(X5),host(X7))) | ~ (elem(m_Ack(X7,X5),queue(host(X6))))) & ! [X8,X9] : (~ (leq(X9,X8)) | ~ (host(X9) = host(X8)) | setIn(X8,alive) | ~ (setIn(X9,alive))) & queue(host(X)) = cons(m_Down(Y),V) & ! [X10,Pid30,Pid20,X11] : (~ (setIn(Pid20,alive)) | ~ (host(Pid30) = host(X10)) | ~ (host(Pid20) = host(X11)) | ~ (setIn(X10,alive)) | host(Pid20) = host(X10) | ~ (elem(m_Down(X11),queue(host(X10)))) | ~ (elem(m_Down(Pid30),queue(host(Pid20))))) & ! [X12,X13] : (X13 = X12 | ~ (host(X13) = host(X12)) | ~ (setIn(X13,alive)) | ~ (setIn(X12,alive))) & ! [X14,X15] : (~ (elem(m_Halt(X15),queue(host(X14)))) | ~ (leq(host(X14),host(X15)))) & ! [X16,X17] : (~ (host(X17) = host(X16)) | ~ (elem(m_Down(X17),queue(host(X16))))) & ! [X18,X19] : (~ (elem(m_Down(X19),queue(host(X18)))) | ~ (setIn(X19,alive))) & ! [Z,Pid0] : (~ (elem(m_Down(Pid0),queue(host(Z)))) | ~ (setIn(Pid0,alive)))), inference(fof_nnf, [status(thm)], [conj_neg])). 42.75/6.70 fof(sk_conj_neg_sk, plain, (setIn(sK0,alive) & ~ (leq(host(sK0),host(sK7))) & ~ (setIn(sK1,pids)) & host(sK1) = host(sK0) & ! [X3] : (leq(X3,sK1) | ~ (host(X3) = host(sK0))) & ~ (s(zero) = host(sK1)) & ~ (host(sK2) = host(sK0)) & host(sK3) = host(sK0) & elem(m_Down(sK4),queue(host(sK2))) & elem(m_Down(sK5),sK6) & ~ (host(sK3) = host(sK2)) & host(sK5) = host(sK2) & host(sK4) = host(sK3) & ((setIn(sK3,alive) & ~ (sK3 = sK0)) | sK3 = sK1) & (sK1 = sK2 | (setIn(sK2,alive) & ~ (sK2 = sK0))) & ((index(status,host(sK0)) = norm & index(ldr,host(sK0)) = host(sK7)) | (host(index(elid,host(sK0))) = host(sK7) & index(status,host(sK0)) = wait)) & ! [X5,X6,X7] : (~ (leq(host(X5),host(X7))) | ~ (elem(m_Ack(X7,X5),queue(host(X6))))) & ! [X8,X9] : (~ (leq(X9,X8)) | ~ (host(X9) = host(X8)) | setIn(X8,alive) | ~ (setIn(X9,alive))) & queue(host(sK0)) = cons(m_Down(sK7),sK6) & ! [X10,Pid30,Pid20,X11] : (~ (setIn(Pid20,alive)) | ~ (host(Pid30) = host(X10)) | ~ (host(Pid20) = host(X11)) | ~ (setIn(X10,alive)) | host(Pid20) = host(X10) | ~ (elem(m_Down(X11),queue(host(X10)))) | ~ (elem(m_Down(Pid30),queue(host(Pid20))))) & ! [X12,X13] : (X13 = X12 | ~ (host(X13) = host(X12)) | ~ (setIn(X13,alive)) | ~ (setIn(X12,alive))) & ! [X14,X15] : (~ (elem(m_Halt(X15),queue(host(X14)))) | ~ (leq(host(X14),host(X15)))) & ! [X16,X17] : (~ (host(X17) = host(X16)) | ~ (elem(m_Down(X17),queue(host(X16))))) & ! [X18,X19] : (~ (elem(m_Down(X19),queue(host(X18)))) | ~ (setIn(X19,alive))) & ! [Z,Pid0] : (~ (elem(m_Down(Pid0),queue(host(Z)))) | ~ (setIn(Pid0,alive)))), inference(skolemize, [status(esa), new_symbols(skolem, [sK0,sK7,sK1,sK2,sK3,sK4,sK5,sK6]), skolemize(V,sK6), skolemize(W,sK1), skolemize(X,sK0), skolemize(Y,sK7), skolemize(X4,sK2), skolemize(X0,sK5), skolemize(Y0,sK3), skolemize(Z0,sK4)], [nnf_58])). 42.75/6.70 fof(sk_conj_neg, plain, ((setIn(sK0,alive)) & (~ (leq(host(sK0),host(sK7)))) & (~ (setIn(sK1,pids))) & (host(sK1) = host(sK0)) & ! [VAR_0] : (leq(VAR_0,sK1) | ~ (host(VAR_0) = host(sK0))) & (~ (s(zero) = host(sK1))) & (~ (host(sK2) = host(sK0))) & (host(sK3) = host(sK0)) & (elem(m_Down(sK4),queue(host(sK2)))) & (elem(m_Down(sK5),sK6)) & (~ (host(sK3) = host(sK2))) & (host(sK5) = host(sK2)) & (host(sK4) = host(sK3)) & (setIn(sK3,alive) | sK3 = sK1) & (~ (sK3 = sK0) | sK3 = sK1) & (sK1 = sK2 | setIn(sK2,alive)) & (sK1 = sK2 | ~ (sK2 = sK0)) & (index(status,host(sK0)) = norm | host(index(elid,host(sK0))) = host(sK7)) & (index(status,host(sK0)) = norm | index(status,host(sK0)) = wait) & (index(ldr,host(sK0)) = host(sK7) | host(index(elid,host(sK0))) = host(sK7)) & (index(ldr,host(sK0)) = host(sK7) | index(status,host(sK0)) = wait) & ! [VAR_0,VAR_1,VAR_2] : (~ (leq(host(VAR_0),host(VAR_1))) | ~ (elem(m_Ack(VAR_1,VAR_0),queue(host(VAR_2))))) & ! [VAR_0,VAR_1] : (~ (leq(VAR_0,VAR_1)) | ~ (host(VAR_0) = host(VAR_1)) | setIn(VAR_1,alive) | ~ (setIn(VAR_0,alive))) & (queue(host(sK0)) = cons(m_Down(sK7),sK6)) & ! [VAR_0,VAR_1,VAR_2,VAR_3] : (~ (setIn(VAR_0,alive)) | ~ (host(VAR_1) = host(VAR_2)) | ~ (host(VAR_0) = host(VAR_3)) | ~ (setIn(VAR_2,alive)) | host(VAR_0) = host(VAR_2) | ~ (elem(m_Down(VAR_3),queue(host(VAR_2)))) | ~ (elem(m_Down(VAR_1),queue(host(VAR_0))))) & ! [VAR_0,VAR_1] : (VAR_0 = VAR_1 | ~ (host(VAR_0) = host(VAR_1)) | ~ (setIn(VAR_0,alive)) | ~ (setIn(VAR_1,alive))) & ! [VAR_0,VAR_1] : (~ (elem(m_Halt(VAR_0),queue(host(VAR_1)))) | ~ (leq(host(VAR_1),host(VAR_0)))) & ! [VAR_0,VAR_1] : (~ (host(VAR_0) = host(VAR_1)) | ~ (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))) & ! [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])). 42.75/6.70 cnf(c_161, negated_conjecture, setIn(sK0,alive), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_164, negated_conjecture, host(sK1) = host(sK0), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_165, negated_conjecture, host(sK0) = host(sK1), 42.75/6.70 inference(copy, [status(thm)], [c_164])). 42.75/6.70 cnf(c_166, negated_conjecture, leq(A,sK1) | host(A) != host(sK0), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_9593, negated_conjecture, leq(A,sK1) | host(A) != host(sK1), 42.75/6.70 inference(paramod, [status(thm)], [c_165, c_166])). 42.75/6.70 cnf(c_167, negated_conjecture, leq(A,sK1) | host(sK1) != host(A), 42.75/6.70 inference(copy, [status(thm)], [c_9593])). 42.75/6.70 cnf(c_169, negated_conjecture, host(sK2) != host(sK0), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_170, negated_conjecture, host(sK2) != host(sK1), 42.75/6.70 inference(paramod, [status(thm)], [c_165, c_169])). 42.75/6.70 cnf(c_171, negated_conjecture, host(sK3) = host(sK0), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_172, negated_conjecture, host(sK3) = host(sK1), 42.75/6.70 inference(paramod, [status(thm)], [c_165, c_171])). 42.75/6.70 cnf(c_173, negated_conjecture, elem(m_Down(sK4),queue(host(sK2))), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_174, negated_conjecture, elem(m_Down(sK5),sK6), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_176, negated_conjecture, host(sK5) = host(sK2), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_177, negated_conjecture, host(sK4) = host(sK3), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_178, negated_conjecture, host(sK4) = host(sK1), 42.75/6.70 inference(paramod, [status(thm)], [c_172, c_177])). 42.75/6.70 cnf(c_181, negated_conjecture, sK1 = sK2 | setIn(sK2,alive), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_182, negated_conjecture, sK2 = sK1 | setIn(sK2,alive), 42.75/6.70 inference(copy, [status(thm)], [c_181])). 42.75/6.70 cnf(c_194, negated_conjecture, ~leq(A,B) | host(A) != host(B) | setIn(B,alive) | ~setIn(A,alive), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_195, negated_conjecture, queue(host(sK0)) = cons(m_Down(sK7),sK6), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_196, negated_conjecture, queue(host(sK1)) = cons(m_Down(sK7),sK6), 42.75/6.70 inference(paramod, [status(thm)], [c_165, c_195])). 42.75/6.70 cnf(c_197, negated_conjecture, ~setIn(A,alive) | host(B) != host(C) | host(A) != host(D) | ~setIn(C,alive) | host(A) = host(C) | ~elem(m_Down(D),queue(host(C))) | ~elem(m_Down(B),queue(host(A))), inference(split_conjunct, [status(thm)], [sk_conj_neg])). 42.75/6.70 cnf(c_9594, negated_conjecture, host(sK1) = host(sK0), 42.75/6.70 inference(copy, [status(thm)], [c_165])). 42.75/6.70 cnf(c_307, negated_conjecture, leq(sK0,sK1), 42.75/6.70 inference(resolve, [status(thm)], [c_167, c_9594])). 42.75/6.70 cnf(c_319, plain, elem(m_Down(sK5),cons(A,sK6)), 42.75/6.70 inference(resolve, [status(thm)], [c_174, c_127])). 42.75/6.70 cnf(c_9595, negated_conjecture, ~leq(sK0,sK1) | setIn(sK1,alive) | ~setIn(sK0,alive), 42.75/6.70 inference(resolve, [status(thm)], [c_194, c_165])). 42.75/6.70 cnf(c_9596, negated_conjecture, setIn(sK1,alive) | ~setIn(sK0,alive), 42.75/6.70 inference(resolve, [status(thm)], [c_307, c_9595])). 42.75/6.70 cnf(c_449, negated_conjecture, setIn(sK1,alive), 42.75/6.70 inference(resolve, [status(thm)], [c_161, c_9596])). 42.75/6.70 cnf(c_9597, negated_conjecture, ~setIn(A,alive) | host(A) != host(B) | ~setIn(sK1,alive) | host(A) = host(sK1) | ~elem(m_Down(B),queue(host(sK1))) | ~elem(m_Down(sK4),queue(host(A))), 42.75/6.70 inference(resolve, [status(thm)], [c_197, c_178])). 42.75/6.70 cnf(c_9598, negated_conjecture, ~setIn(A,alive) | host(A) != host(B) | ~setIn(sK1,alive) | host(A) = host(sK1) | ~elem(m_Down(B),cons(m_Down(sK7),sK6)) | ~elem(m_Down(sK4),queue(host(A))), 42.75/6.70 inference(paramod, [status(thm)], [c_196, c_9597])). 42.75/6.70 cnf(c_9599, negated_conjecture, ~setIn(A,alive) | host(A) != host(B) | ~setIn(sK1,alive) | host(sK1) = host(A) | ~elem(m_Down(B),cons(m_Down(sK7),sK6)) | ~elem(m_Down(sK4),queue(host(A))), 42.75/6.70 inference(copy, [status(thm)], [c_9598])). 42.75/6.70 cnf(c_476, negated_conjecture, ~setIn(A,alive) | host(A) != host(B) | host(sK1) = host(A) | ~elem(m_Down(B),cons(m_Down(sK7),sK6)) | ~elem(m_Down(sK4),queue(host(A))), 42.75/6.70 inference(resolve, [status(thm)], [c_449, c_9599])). 42.75/6.70 cnf(c_9600, negated_conjecture, host(sK2) = host(sK5), 42.75/6.70 inference(copy, [status(thm)], [c_176])). 42.75/6.70 cnf(c_9601, negated_conjecture, ~setIn(sK2,alive) | host(sK1) = host(sK2) | ~elem(m_Down(sK5),cons(m_Down(sK7),sK6)) | ~elem(m_Down(sK4),queue(host(sK2))), 42.75/6.70 inference(resolve, [status(thm)], [c_476, c_9600])). 42.75/6.70 cnf(c_9602, negated_conjecture, ~setIn(sK2,alive) | host(sK2) = host(sK1) | ~elem(m_Down(sK5),cons(m_Down(sK7),sK6)) | ~elem(m_Down(sK4),queue(host(sK2))), 42.75/6.70 inference(copy, [status(thm)], [c_9601])). 42.75/6.70 cnf(c_9603, negated_conjecture, ~setIn(sK2,alive) | ~elem(m_Down(sK5),cons(m_Down(sK7),sK6)) | ~elem(m_Down(sK4),queue(host(sK2))), 42.75/6.70 inference(resolve, [status(thm)], [c_170, c_9602])). 42.75/6.70 cnf(c_9604, negated_conjecture, ~setIn(sK2,alive) | ~elem(m_Down(sK4),queue(host(sK2))), 42.75/6.70 inference(resolve, [status(thm)], [c_319, c_9603])). 42.75/6.70 cnf(c_9587, negated_conjecture, ~setIn(sK2,alive), 42.75/6.70 inference(resolve, [status(thm)], [c_173, c_9604])). 42.75/6.70 cnf(c_9591, negated_conjecture, sK2 = sK1, 42.75/6.70 inference(resolve, [status(thm)], [c_9587, c_182])). 42.75/6.70 cnf(c_9605, negated_conjecture, ~setIn(sK1,alive), 42.75/6.70 inference(paramod, [status(thm)], [c_9591, c_9587])). 42.75/6.70 cnf(c_9592, negated_conjecture, $false, 42.75/6.70 inference(resolve, [status(thm)], [c_449, c_9605])). 42.75/6.70 % SZS output end CNFRefutation for theBenchmark 42.75/6.70 EOF