0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.23 % Computer : n115.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 05:19:40 CDT 2018 0.03/0.23 % CPUTime : 0.06/0.49 ============================== Prover9 =============================== 0.06/0.49 Prover9 (32) version 2009-11A, November 2009. 0.06/0.49 Process 2646 was started by sandbox2 on n115.star.cs.uiowa.edu, 0.06/0.49 Sat Jul 14 05:19:40 2018 0.06/0.49 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2614_n115.star.cs.uiowa.edu". 0.06/0.49 ============================== end of head =========================== 0.06/0.49 0.06/0.49 ============================== INPUT ================================= 0.06/0.49 0.06/0.49 % Reading from file /tmp/Prover9_2614_n115.star.cs.uiowa.edu 0.06/0.49 0.06/0.49 set(prolog_style_variables). 0.06/0.49 set(auto2). 0.06/0.49 % set(auto2) -> set(auto). 0.06/0.49 % set(auto) -> set(auto_inference). 0.06/0.49 % set(auto) -> set(auto_setup). 0.06/0.49 % set(auto_setup) -> set(predicate_elim). 0.06/0.49 % set(auto_setup) -> assign(eq_defs, unfold). 0.06/0.49 % set(auto) -> set(auto_limits). 0.06/0.49 % set(auto_limits) -> assign(max_weight, "100.000"). 0.06/0.49 % set(auto_limits) -> assign(sos_limit, 20000). 0.06/0.49 % set(auto) -> set(auto_denials). 0.06/0.49 % set(auto) -> set(auto_process). 0.06/0.49 % set(auto2) -> assign(new_constants, 1). 0.06/0.49 % set(auto2) -> assign(fold_denial_max, 3). 0.06/0.49 % set(auto2) -> assign(max_weight, "200.000"). 0.06/0.49 % set(auto2) -> assign(max_hours, 1). 0.06/0.49 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.06/0.49 % set(auto2) -> assign(max_seconds, 0). 0.06/0.49 % set(auto2) -> assign(max_minutes, 5). 0.06/0.49 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.06/0.49 % set(auto2) -> set(sort_initial_sos). 0.06/0.49 % set(auto2) -> assign(sos_limit, -1). 0.06/0.49 % set(auto2) -> assign(lrs_ticks, 3000). 0.06/0.49 % set(auto2) -> assign(max_megs, 400). 0.06/0.49 % set(auto2) -> assign(stats, some). 0.06/0.49 % set(auto2) -> clear(echo_input). 0.06/0.49 % set(auto2) -> set(quiet). 0.06/0.49 % set(auto2) -> clear(print_initial_clauses). 0.06/0.49 % set(auto2) -> clear(print_given). 0.06/0.49 assign(lrs_ticks,-1). 0.06/0.49 assign(sos_limit,10000). 0.06/0.49 assign(order,kbo). 0.06/0.49 set(lex_order_vars). 0.06/0.49 clear(print_given). 0.06/0.49 0.06/0.49 % formulas(sos). % not echoed (67 formulas) 0.06/0.49 0.06/0.49 ============================== end of input ========================== 0.06/0.49 0.06/0.49 % From the command line: assign(max_seconds, 300). 0.06/0.49 0.06/0.49 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.06/0.49 0.06/0.49 % Formulas that are not ordinary clauses: 0.06/0.49 1 (all X all Y (s(Y) = X | leq(X,Y) <-> leq(X,s(Y)))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 2 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 3 (all Q all X all Y (ordered(Q) -> ordered(snoc(Q,m_Ack(X,Y))))) # label(axiom_55) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 4 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 5 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 6 (all Q all X all Y (host(X) = host(Y) & elem(m_Down(Y),Q) & ordered(cons(m_Halt(X),Q)) -> leq(X,Y))) # label(axiom_57) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 7 (all X all Y all Q (elem(X,snoc(Q,Y)) <-> elem(X,Q) | Y = X)) # label(axiom_47) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 8 (all X ((exists Y (m_Down(Y) = X | X = m_Halt(Y))) <-> pidElem(X))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 9 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 10 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 11 (all X all Y m_Halt(Y) != m_Ldr(X)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 12 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 13 (all Pid all Pid2 (elem(m_Ack(Pid,Pid2),queue(host(Pid))) -> setIn(Pid,pids) & setIn(Pid2,pids))) # label(axiom) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 14 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 15 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 16 (all X all Y m_Halt(Y) != m_NotNorm(X)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 17 (all X all Q (ordered(snoc(Q,X)) <-> (all Y (elem(Y,Q) & host(pidMsg(Y)) = host(pidMsg(X)) & pidElem(Y) & pidElem(X) -> leq(pidMsg(Y),pidMsg(X)))) & ordered(Q))) # label(axiom_54) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 18 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 19 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 20 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 21 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 22 (all X1 all X2 all Y1 all Y2 (X1 != X2 -> m_Ack(X1,Y1) != m_Ack(X2,Y2))) # label(axiom_31) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 23 (all X (ordered(snoc(q_nil,X)) & ordered(cons(X,q_nil)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 24 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 25 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 26 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 27 (all X1 all X2 all Y1 all Y2 (Y1 != Y2 -> m_Ack(X2,Y2) != m_Ack(X1,Y1))) # label(axiom_32) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 28 (all Y all Q Y = last(snoc(Q,Y))) # label(axiom_37) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 29 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 30 (all X all Q X = head(cons(X,Q))) # label(axiom_35) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 31 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 32 (all X all Y (leq(Y,X) & leq(X,Y) <-> Y = X)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 33 (all Q (q_nil = Q | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 34 (all Q (snoc(init(Q),last(Q)) = Q | q_nil = Q)) # label(axiom_40) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 35 (all X all Y all Z (leq(Y,Z) & leq(X,Y) -> leq(X,Z))) # label(axiom_62) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 36 (all X all Y (Y != X <-> m_Ldr(Y) != m_Ldr(X))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 37 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 38 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 39 (all X all Q (ordered(cons(X,Q)) <-> (all Y (elem(Y,Q) & pidElem(Y) & host(pidMsg(Y)) = host(pidMsg(X)) & pidElem(X) -> leq(pidMsg(X),pidMsg(Y)))) & ordered(Q))) # label(axiom_53) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 40 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 41 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 42 (all P all Q (host(Q) = s(host(P)) -> host(Q) != host(P))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 43 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 44 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 45 (all X all Y all Q (elem(X,cons(Y,Q)) <-> elem(X,Q) | X = Y)) # label(axiom_46) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 46 (all X all Y (m_Halt(X) != m_Halt(Y) <-> X != Y)) # label(axiom_26) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 47 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 48 (all Pid all Pid2 (host(Pid2) != host(Pid) -> Pid2 != Pid)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 49 (all X X = pidMsg(m_Down(X))) # label(axiom_50) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 50 (all X all Y m_NotNorm(Y) != m_Ldr(X)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 51 (all X all Y (m_NotNorm(Y) != m_NotNorm(X) <-> Y != X)) # label(axiom_28) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 52 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 53 (all X snoc(q_nil,X) = cons(X,q_nil)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 54 (all X all Y m_NormQ(Y) != m_Down(X)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 55 (all X all Y all Q cons(X,snoc(Q,Y)) = snoc(cons(X,Q),Y)) # label(axiom_44) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 56 (all X all Y (leq(s(X),s(Y)) <-> leq(X,Y))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 57 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Down(Pid0),queue(host(Z))) -> host(Z) != host(Pid0))) & (all Z all Pid0 (Pid0 != Z & host(Pid0) = host(Z) -> -setIn(Pid0,alive) | -setIn(Z,alive))) & (all Z ((index(status,host(Z)) = elec_1 | index(status,host(Z)) = elec_2) & setIn(Z,alive) -> Z = index(elid,host(Z)))) & (all Z all Pid20 all Pid0 (elem(m_Down(Pid20),queue(host(Pid0))) & host(Z) = host(Pid20) & setIn(Pid0,alive) -> -(host(Z) = index(ldr,host(Z)) & norm = index(status,host(Z)) & setIn(Z,alive)))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & host(Pid0) = host(Pid20) & index(status,host(Pid0)) = elec_2 & index(status,host(Z)) = elec_2 & setIn(Pid0,alive) -> -elem(m_Ack(Z,Pid20),queue(host(Z))))) & (all Z all Pid0 (setIn(Z,alive) & elec_2 = index(status,host(Pid0)) & elec_2 = index(status,host(Z)) & setIn(Pid0,alive) & -leq(host(Z),host(Pid0)) -> -leq(index(pendack,host(Z)),index(pendack,host(Pid0))))) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid0) = nbr_proc & host(Pid0) = host(Pid30) & elec_1 = index(status,host(Pid0)) & elem(m_Down(Pid20),queue(host(Pid0))) & (all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(Pid0))) | V0 = host(Pid20))) -> -(setIn(Z,alive) & elem(m_Down(Pid30),queue(host(Z)))))) & (all Z all Pid30 all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & leq(nbr_proc,s(index(pendack,host(Pid0)))) & index(status,host(Pid0)) = elec_2 & host(Pid20) = s(index(pendack,host(Pid0))) & index(pendack,host(Pid0)) = host(Pid30) & elem(m_Ack(Pid0,Pid30),queue(host(Pid0))) -> -(setIn(Z,alive) & index(status,host(Z)) = norm & host(Z) = index(ldr,host(Z))))) & queue(host(X)) = cons(m_Down(Y),V) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Halt(Pid0),queue(host(Pid20))) & index(status,host(Pid0)) = elec_2 & -leq(index(pendack,host(Pid0)),host(Z)) -> -(norm = index(status,host(Z)) & index(ldr,host(Z)) = host(Z) & setIn(Z,alive)))) & (all Z all Pid0 (setIn(Pid0,alive) & index(status,host(Z)) = elec_2 & elec_2 = index(status,host(Pid0)) & setIn(Z,alive) & -leq(host(Z),host(Pid0)) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (setIn(Pid0,alive) & elec_1 = index(status,host(Pid0)) -> -elem(m_Ack(Pid0,Z),queue(host(Pid0))))) & (all Z all Pid0 (elem(m_Ack(Pid0,Z),queue(host(Pid0))) & setIn(Pid0,alive) -> leq(host(Z),index(pendack,host(Pid0))))) & (all Z all Pid20 all Pid0 (elem(m_Ack(Pid0,Z),queue(host(Pid20))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (elem(m_Halt(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (elem(m_Ldr(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) -> (setIn(X,alive) -> (leq(host(X),host(Y)) -> (index(status,host(X)) = elec_2 & host(Y) = index(pendack,host(X)) -> (leq(nbr_proc,index(pendack,host(X))) -> (all Z (setIn(host(Z),index(acks,host(X))) -> (all V0 (host(X) = host(V0) -> (all W0 all X0 all Y0 (host(Y0) = host(Z) -> (host(Y0) != host(X) -> (setIn(Y0,alive) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X))) & index(status,host(Y0)) = elec_2 & s(index(pendack,host(Y0))) = host(X0) & index(pendack,host(Y0)) = host(W0) & elem(m_Ack(Y0,W0),snoc(queue(host(Y0)),m_Ldr(X))) & leq(nbr_proc,s(index(pendack,host(Y0)))) -> -(host(X) = host(V0) & setIn(V0,alive)))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption]. 0.77/0.99 0.77/0.99 ============================== end of process non-clausal formulas === 0.77/0.99 0.77/0.99 ============================== PROCESS INITIAL CLAUSES =============== 0.77/0.99 0.77/0.99 ============================== PREDICATE ELIMINATION ================= 0.77/0.99 0.77/0.99 ============================== end predicate elimination ============= 0.77/0.99 0.77/0.99 Auto_denials: (non-Horn, no changes). 0.77/0.99 0.77/0.99 Term ordering decisions: 0.77/0.99 Function symbol KB weights: alive=1. status=1. pendack=1. elec_2=1. q_nil=1. nbr_proc=1. zero=1. elec_1=1. elid=1. pids=1. acks=1. ldr=1. norm=1. down=1. nil=1. setEmpty=1. wait=1. c1=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. index=1. snoc=1. cons=1. m_Ack=1. f2=1. f3=1. host=1. pidMsg=1. s=1. m_Down=1. m_Halt=1. queue=1. m_Ldr=1. m_NormQ=1. m_NotNorm=1. head=1. init=1. last=1. tail=1. f1=1. f4=1. 0.77/0.99 0.77/0.99 ============================== end of process initial clauses ======== 0.77/0.99 0.77/0.99 ============================== CLAUSES FOR SEARCH ==================== 0.77/0.99 0.77/0.99 ============================== end of clauses for search ============= 0.77/0.99 0.77/0.99 ============================== SEARCH ================================ 0.77/0.99 0.77/0.99 % Starting search at 0.02 seconds. 0.77/0.99 0.77/0.99 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 63 (0.00 of 0.24 sec). 0.77/0.99 0.77/0.99 ============================== PROOF ================================= 0.77/0.99 % SZS status Theorem 0.77/0.99 % SZS output start Refutation 0.77/0.99 0.77/0.99 % Proof 1 at 0.50 (+ 0.01) seconds. 0.77/0.99 % Length of proof is 87. 0.77/0.99 % Level of proof is 13. 0.77/0.99 % Maximum clause weight is 38.000. 0.77/0.99 % Given clauses 724. 0.77/0.99 0.77/0.99 1 (all X all Y (s(Y) = X | leq(X,Y) <-> leq(X,s(Y)))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption]. 0.77/0.99 5 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption]. 0.77/0.99 7 (all X all Y all Q (elem(X,snoc(Q,Y)) <-> elem(X,Q) | Y = X)) # label(axiom_47) # label(axiom) # label(non_clause). [assumption]. 0.77/0.99 32 (all X all Y (leq(Y,X) & leq(X,Y) <-> Y = X)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption]. 0.77/1.00 38 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption]. 0.77/1.00 41 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption]. 0.77/1.00 43 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption]. 0.77/1.00 45 (all X all Y all Q (elem(X,cons(Y,Q)) <-> elem(X,Q) | X = Y)) # label(axiom_46) # label(axiom) # label(non_clause). [assumption]. 0.77/1.00 56 (all X all Y (leq(s(X),s(Y)) <-> leq(X,Y))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption]. 0.77/1.00 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Down(Pid0),queue(host(Z))) -> host(Z) != host(Pid0))) & (all Z all Pid0 (Pid0 != Z & host(Pid0) = host(Z) -> -setIn(Pid0,alive) | -setIn(Z,alive))) & (all Z ((index(status,host(Z)) = elec_1 | index(status,host(Z)) = elec_2) & setIn(Z,alive) -> Z = index(elid,host(Z)))) & (all Z all Pid20 all Pid0 (elem(m_Down(Pid20),queue(host(Pid0))) & host(Z) = host(Pid20) & setIn(Pid0,alive) -> -(host(Z) = index(ldr,host(Z)) & norm = index(status,host(Z)) & setIn(Z,alive)))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & host(Pid0) = host(Pid20) & index(status,host(Pid0)) = elec_2 & index(status,host(Z)) = elec_2 & setIn(Pid0,alive) -> -elem(m_Ack(Z,Pid20),queue(host(Z))))) & (all Z all Pid0 (setIn(Z,alive) & elec_2 = index(status,host(Pid0)) & elec_2 = index(status,host(Z)) & setIn(Pid0,alive) & -leq(host(Z),host(Pid0)) -> -leq(index(pendack,host(Z)),index(pendack,host(Pid0))))) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid0) = nbr_proc & host(Pid0) = host(Pid30) & elec_1 = index(status,host(Pid0)) & elem(m_Down(Pid20),queue(host(Pid0))) & (all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(Pid0))) | V0 = host(Pid20))) -> -(setIn(Z,alive) & elem(m_Down(Pid30),queue(host(Z)))))) & (all Z all Pid30 all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & leq(nbr_proc,s(index(pendack,host(Pid0)))) & index(status,host(Pid0)) = elec_2 & host(Pid20) = s(index(pendack,host(Pid0))) & index(pendack,host(Pid0)) = host(Pid30) & elem(m_Ack(Pid0,Pid30),queue(host(Pid0))) -> -(setIn(Z,alive) & index(status,host(Z)) = norm & host(Z) = index(ldr,host(Z))))) & queue(host(X)) = cons(m_Down(Y),V) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Halt(Pid0),queue(host(Pid20))) & index(status,host(Pid0)) = elec_2 & -leq(index(pendack,host(Pid0)),host(Z)) -> -(norm = index(status,host(Z)) & index(ldr,host(Z)) = host(Z) & setIn(Z,alive)))) & (all Z all Pid0 (setIn(Pid0,alive) & index(status,host(Z)) = elec_2 & elec_2 = index(status,host(Pid0)) & setIn(Z,alive) & -leq(host(Z),host(Pid0)) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (setIn(Pid0,alive) & elec_1 = index(status,host(Pid0)) -> -elem(m_Ack(Pid0,Z),queue(host(Pid0))))) & (all Z all Pid0 (elem(m_Ack(Pid0,Z),queue(host(Pid0))) & setIn(Pid0,alive) -> leq(host(Z),index(pendack,host(Pid0))))) & (all Z all Pid20 all Pid0 (elem(m_Ack(Pid0,Z),queue(host(Pid20))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (elem(m_Halt(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (elem(m_Ldr(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) -> (setIn(X,alive) -> (leq(host(X),host(Y)) -> (index(status,host(X)) = elec_2 & host(Y) = index(pendack,host(X)) -> (leq(nbr_proc,index(pendack,host(X))) -> (all Z (setIn(host(Z),index(acks,host(X))) -> (all V0 (host(X) = host(V0) -> (all W0 all X0 all Y0 (host(Y0) = host(Z) -> (host(Y0) != host(X) -> (setIn(Y0,alive) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X))) & index(status,host(Y0)) = elec_2 & s(index(pendack,host(Y0))) = host(X0) & index(pendack,host(Y0)) = host(W0) & elem(m_Ack(Y0,W0),snoc(queue(host(Y0)),m_Ldr(X))) & leq(nbr_proc,s(index(pendack,host(Y0)))) -> -(host(X) = host(V0) & setIn(V0,alive)))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption]. 0.77/1.00 61 s(A) = B | leq(B,A) | -leq(B,s(A)) # label(axiom_64) # label(axiom). [clausify(1)]. 0.77/1.00 67 m_Ldr(A) != m_Ack(B,C) # label(axiom_14) # label(axiom). [clausify(5)]. 0.77/1.00 69 -elem(A,snoc(B,C)) | elem(A,B) | C = A # label(axiom_47) # label(axiom). [clausify(7)]. 0.77/1.00 110 -leq(A,B) | -leq(B,A) | A = B # label(axiom_61) # label(axiom). [clausify(32)]. 0.77/1.00 122 leq(A,A) # label(axiom_59) # label(axiom). [clausify(38)]. 0.77/1.00 134 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(41)]. 0.77/1.00 136 init(snoc(A,B)) = A # label(axiom_38) # label(axiom). [clausify(43)]. 0.77/1.00 141 elem(A,cons(B,C)) | B != A # label(axiom_46) # label(axiom). [clausify(45)]. 0.77/1.00 156 -leq(s(A),s(B)) | leq(A,B) # label(axiom_63) # label(axiom). [clausify(56)]. 0.77/1.00 157 leq(s(A),s(B)) | -leq(A,B) # label(axiom_63) # label(axiom). [clausify(56)]. 0.77/1.00 159 -elem(m_Down(A),queue(host(B))) | host(A) != host(B) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 164 -setIn(A,alive) | host(B) != host(C) | index(status,host(C)) != elec_2 | index(status,host(A)) != elec_2 | -setIn(C,alive) | -elem(m_Ack(A,B),queue(host(A))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 165 -setIn(A,alive) | index(status,host(B)) != elec_2 | index(status,host(A)) != elec_2 | -setIn(B,alive) | leq(host(A),host(B)) | -leq(index(pendack,host(A)),index(pendack,host(B))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 172 queue(host(c3)) = cons(m_Down(c4),c1) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 173 cons(m_Down(c4),c1) = queue(host(c3)). [copy(172),flip(a)]. 0.77/1.00 175 -setIn(A,alive) | index(status,host(B)) != elec_2 | index(status,host(A)) != elec_2 | -setIn(B,alive) | leq(host(B),host(A)) | leq(index(pendack,host(A)),host(B)) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 181 setIn(c3,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 183 index(status,host(c3)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 184 elec_2 = index(status,host(c3)). [copy(183),flip(a)]. 0.77/1.00 185 index(pendack,host(c3)) = host(c4) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 186 leq(nbr_proc,index(pendack,host(c3))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 187 leq(nbr_proc,host(c4)). [copy(186),rewrite([185(5)])]. 0.77/1.00 189 host(c6) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 190 host(c9) = host(c5) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 191 host(c9) != host(c3) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 192 host(c5) != host(c3). [copy(191),rewrite([190(2)])]. 0.77/1.00 193 setIn(c9,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 196 index(status,host(c9)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 197 index(status,host(c5)) = index(status,host(c3)). [copy(196),rewrite([190(3),184(5)])]. 0.77/1.00 198 host(c8) = s(index(pendack,host(c9))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 199 s(index(pendack,host(c5))) = host(c8). [copy(198),rewrite([190(5)]),flip(a)]. 0.77/1.00 200 index(pendack,host(c9)) = host(c7) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 201 index(pendack,host(c5)) = host(c7). [copy(200),rewrite([190(3)])]. 0.77/1.00 202 elem(m_Ack(c9,c7),snoc(queue(host(c9)),m_Ldr(c3))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 203 elem(m_Ack(c9,c7),snoc(queue(host(c5)),m_Ldr(c3))). [copy(202),rewrite([190(5)])]. 0.77/1.00 204 leq(nbr_proc,s(index(pendack,host(c9)))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.77/1.00 205 leq(nbr_proc,s(host(c7))). [copy(204),rewrite([190(4),201(5)])]. 0.77/1.00 210 -setIn(A,alive) | index(status,host(c3)) != index(status,host(B)) | index(status,host(c3)) != index(status,host(A)) | -setIn(B,alive) | leq(host(B),host(A)) | leq(index(pendack,host(A)),host(B)). [back_rewrite(175),rewrite([184(6),184(14)]),flip(b),flip(c)]. 0.77/1.00 213 -setIn(A,alive) | index(status,host(c3)) != index(status,host(B)) | index(status,host(c3)) != index(status,host(A)) | -setIn(B,alive) | leq(host(A),host(B)) | -leq(index(pendack,host(A)),index(pendack,host(B))). [back_rewrite(165),rewrite([184(6),184(14)]),flip(b),flip(c)]. 0.77/1.00 214 -setIn(A,alive) | host(B) != host(C) | index(status,host(c3)) != index(status,host(C)) | index(status,host(c3)) != index(status,host(A)) | -setIn(C,alive) | -elem(m_Ack(A,B),queue(host(A))). [back_rewrite(164),rewrite([184(9),184(17)]),flip(c),flip(d)]. 0.77/1.00 219 host(c5) = c_0. [new_symbol(192)]. 0.77/1.00 220 s(index(pendack,c_0)) = host(c8). [back_rewrite(199),rewrite([219(3)])]. 0.77/1.00 221 elem(m_Ack(c9,c7),snoc(queue(c_0),m_Ldr(c3))). [back_rewrite(203),rewrite([219(5)])]. 0.77/1.00 222 index(pendack,c_0) = host(c7). [back_rewrite(201),rewrite([219(3)])]. 0.77/1.00 223 index(status,host(c3)) = index(status,c_0). [back_rewrite(197),rewrite([219(3)]),flip(a)]. 0.77/1.00 225 host(c3) != c_0. [back_rewrite(192),rewrite([219(2)]),flip(a)]. 0.77/1.00 226 host(c9) = c_0. [back_rewrite(190),rewrite([219(4)])]. 0.77/1.00 228 s(host(c7)) = host(c8). [back_rewrite(220),rewrite([222(3)])]. 0.77/1.00 233 -setIn(A,alive) | host(B) != host(C) | index(status,host(C)) != index(status,c_0) | index(status,host(A)) != index(status,c_0) | -setIn(C,alive) | -elem(m_Ack(A,B),queue(host(A))). [back_rewrite(214),rewrite([223(9),223(16)]),flip(c),flip(d)]. 0.77/1.00 234 -setIn(A,alive) | index(status,host(B)) != index(status,c_0) | index(status,host(A)) != index(status,c_0) | -setIn(B,alive) | leq(host(A),host(B)) | -leq(index(pendack,host(A)),index(pendack,host(B))). [back_rewrite(213),rewrite([223(6),223(13)]),flip(b),flip(c)]. 0.77/1.00 237 -setIn(A,alive) | index(status,host(B)) != index(status,c_0) | index(status,host(A)) != index(status,c_0) | -setIn(B,alive) | leq(host(B),host(A)) | leq(index(pendack,host(A)),host(B)). [back_rewrite(210),rewrite([223(6),223(13)]),flip(b),flip(c)]. 0.77/1.00 242 leq(nbr_proc,host(c8)). [back_rewrite(205),rewrite([228(4)])]. 0.77/1.00 289 -leq(nbr_proc,host(A)) | host(A) = nbr_proc. [resolve(134,a,110,b),flip(b)]. 0.77/1.00 294 elem(A,cons(A,B)). [resolve(141,b,136,a),rewrite([136(2)])]. 0.77/1.00 343 host(c4) = nbr_proc. [resolve(187,a,110,b),unit_del(a,134)]. 0.77/1.00 344 index(pendack,host(c3)) = nbr_proc. [back_rewrite(185),rewrite([343(6)])]. 0.77/1.00 348 -elem(m_Down(A),queue(host(c3))) | host(c3) != host(A). [para(189(a,1),159(a,2,1)),rewrite([189(8)]),flip(b)]. 0.77/1.00 373 elem(m_Ack(c9,c7),queue(c_0)). [resolve(221,a,69,a),flip(b),unit_del(b(flip),67)]. 0.77/1.00 387 -leq(s(A),host(c8)) | leq(A,host(c7)). [para(228(a,1),156(a,2))]. 0.77/1.00 392 host(A) != host(B) | index(status,host(B)) != index(status,c_0) | -setIn(B,alive) | -elem(m_Ack(c9,A),queue(c_0)). [resolve(233,a,193,a),rewrite([226(13),226(23)]),xx(c)]. 0.77/1.00 396 index(status,host(A)) != index(status,c_0) | -setIn(A,alive) | leq(c_0,host(A)) | -leq(host(c7),index(pendack,host(A))). [resolve(234,a,193,a),rewrite([226(10),226(18),226(22),222(22)]),xx(b)]. 0.77/1.00 404 index(status,host(A)) != index(status,c_0) | -setIn(A,alive) | leq(host(A),c_0) | leq(host(c7),host(A)). [resolve(237,a,193,a),rewrite([226(10),226(19),226(22),222(22)]),xx(b)]. 0.77/1.00 413 host(c8) = nbr_proc. [resolve(242,a,110,b),unit_del(a,134)]. 0.77/1.00 415 -leq(s(A),nbr_proc) | leq(A,host(c7)). [back_rewrite(387),rewrite([413(3)])]. 0.77/1.00 424 s(host(c7)) = nbr_proc. [back_rewrite(228),rewrite([413(5)])]. 0.77/1.00 478 elem(m_Down(c4),queue(host(c3))). [para(173(a,1),294(a,2))]. 0.77/1.00 583 host(c3) != host(A) | -elem(m_Ack(c9,A),queue(c_0)). [resolve(392,c,181,a),rewrite([223(8)]),flip(a),xx(b)]. 0.77/1.00 601 host(c7) != host(c3). [resolve(373,a,583,b),flip(a)]. 0.77/1.00 652 host(c3) != nbr_proc. [resolve(478,a,348,a),rewrite([343(4)])]. 0.77/1.00 2246 leq(c_0,host(c3)). [resolve(396,b,181,a),rewrite([223(4),344(17)]),xx(a),unit_del(b,134)]. 0.77/1.00 2253 -leq(host(c3),c_0). [resolve(2246,a,110,b),unit_del(b,225)]. 0.77/1.00 2382 leq(host(c7),host(c3)). [resolve(404,b,181,a),rewrite([223(4)]),xx(a),unit_del(a,2253)]. 0.77/1.00 2386 leq(nbr_proc,s(host(c3))). [resolve(2382,a,157,b),rewrite([424(3)])]. 0.77/1.00 2389 -leq(host(c3),host(c7)). [resolve(2382,a,110,b),flip(b),unit_del(b,601)]. 0.77/1.00 2399 s(host(c3)) = nbr_proc | leq(nbr_proc,host(c3)). [resolve(2386,a,61,c)]. 0.77/1.00 3537 s(host(c3)) = nbr_proc. [resolve(2399,b,289,a),unit_del(b,652)]. 0.77/1.00 3561 $F. [para(3537(a,1),415(a,1)),unit_del(a,122),unit_del(b,2389)]. 0.77/1.00 0.77/1.00 % SZS output end Refutation 0.77/1.00 ============================== end of proof ========================== 0.77/1.00 0.77/1.00 ============================== STATISTICS ============================ 0.77/1.00 0.77/1.00 Given=724. Generated=16635. Kept=3487. proofs=1. 0.77/1.00 Usable=668. Sos=2466. Demods=36. Limbo=6, Disabled=480. Hints=0. 0.77/1.00 Megabytes=6.27. 0.77/1.00 User_CPU=0.50, System_CPU=0.01, Wall_clock=0. 0.77/1.00 0.77/1.00 ============================== end of statistics ===================== 0.77/1.00 0.77/1.00 ============================== end of search ========================= 0.77/1.00 0.77/1.00 THEOREM PROVED 0.77/1.00 % SZS status Theorem 0.77/1.00 0.77/1.00 Exiting with 1 proof. 0.77/1.00 0.77/1.00 Process 2646 exit (max_proofs) Sat Jul 14 05:19:40 2018 0.77/1.00 Prover9 interrupted 0.77/1.00 EOF