0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.02/0.24 % Computer : n024.star.cs.uiowa.edu 0.02/0.24 % Model : x86_64 x86_64 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.24 % Memory : 32218.625MB 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.24 % CPULimit : 300 0.02/0.24 % DateTime : Sat Jul 14 05:23:10 CDT 2018 0.02/0.24 % CPUTime : 0.07/0.53 ============================== Prover9 =============================== 0.07/0.53 Prover9 (32) version 2009-11A, November 2009. 0.07/0.53 Process 7397 was started by sandbox on n024.star.cs.uiowa.edu, 0.07/0.53 Sat Jul 14 05:23:10 2018 0.07/0.53 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7356_n024.star.cs.uiowa.edu". 0.07/0.53 ============================== end of head =========================== 0.07/0.53 0.07/0.53 ============================== INPUT ================================= 0.07/0.53 0.07/0.53 % Reading from file /tmp/Prover9_7356_n024.star.cs.uiowa.edu 0.07/0.53 0.07/0.53 set(prolog_style_variables). 0.07/0.53 set(auto2). 0.07/0.53 % set(auto2) -> set(auto). 0.07/0.53 % set(auto) -> set(auto_inference). 0.07/0.53 % set(auto) -> set(auto_setup). 0.07/0.53 % set(auto_setup) -> set(predicate_elim). 0.07/0.53 % set(auto_setup) -> assign(eq_defs, unfold). 0.07/0.53 % set(auto) -> set(auto_limits). 0.07/0.53 % set(auto_limits) -> assign(max_weight, "100.000"). 0.07/0.53 % set(auto_limits) -> assign(sos_limit, 20000). 0.07/0.53 % set(auto) -> set(auto_denials). 0.07/0.53 % set(auto) -> set(auto_process). 0.07/0.53 % set(auto2) -> assign(new_constants, 1). 0.07/0.53 % set(auto2) -> assign(fold_denial_max, 3). 0.07/0.53 % set(auto2) -> assign(max_weight, "200.000"). 0.07/0.53 % set(auto2) -> assign(max_hours, 1). 0.07/0.53 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.07/0.53 % set(auto2) -> assign(max_seconds, 0). 0.07/0.53 % set(auto2) -> assign(max_minutes, 5). 0.07/0.53 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.07/0.53 % set(auto2) -> set(sort_initial_sos). 0.07/0.53 % set(auto2) -> assign(sos_limit, -1). 0.07/0.53 % set(auto2) -> assign(lrs_ticks, 3000). 0.07/0.53 % set(auto2) -> assign(max_megs, 400). 0.07/0.53 % set(auto2) -> assign(stats, some). 0.07/0.53 % set(auto2) -> clear(echo_input). 0.07/0.53 % set(auto2) -> set(quiet). 0.07/0.53 % set(auto2) -> clear(print_initial_clauses). 0.07/0.53 % set(auto2) -> clear(print_given). 0.07/0.53 assign(lrs_ticks,-1). 0.07/0.53 assign(sos_limit,10000). 0.07/0.53 assign(order,kbo). 0.07/0.53 set(lex_order_vars). 0.07/0.53 clear(print_given). 0.07/0.53 0.07/0.53 % formulas(sos). % not echoed (67 formulas) 0.07/0.53 0.07/0.53 ============================== end of input ========================== 0.07/0.53 0.07/0.53 % From the command line: assign(max_seconds, 300). 0.07/0.53 0.07/0.53 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.07/0.53 0.07/0.53 % Formulas that are not ordinary clauses: 0.07/0.53 1 (all X all Y (s(Y) = X | leq(X,Y) <-> leq(X,s(Y)))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 2 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 4 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 5 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 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]. 0.07/0.53 8 (all X ((exists Y (m_Down(Y) = X | X = m_Halt(Y))) <-> pidElem(X))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 9 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 10 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 11 (all X all Y m_Halt(Y) != m_Ldr(X)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 12 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 14 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 15 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 16 (all X all Y m_Halt(Y) != m_NotNorm(X)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 18 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 19 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 20 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 21 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 23 (all X (ordered(snoc(q_nil,X)) & ordered(cons(X,q_nil)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 24 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 25 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 26 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 28 (all Y all Q Y = last(snoc(Q,Y))) # label(axiom_37) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 29 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 30 (all X all Q X = head(cons(X,Q))) # label(axiom_35) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 31 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 32 (all X all Y (leq(Y,X) & leq(X,Y) <-> Y = X)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 33 (all Q (q_nil = Q | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 34 (all Q (snoc(init(Q),last(Q)) = Q | q_nil = Q)) # label(axiom_40) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 36 (all X all Y (Y != X <-> m_Ldr(Y) != m_Ldr(X))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 37 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 38 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 40 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 41 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 42 (all P all Q (host(Q) = s(host(P)) -> host(Q) != host(P))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 43 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 44 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 46 (all X all Y (m_Halt(X) != m_Halt(Y) <-> X != Y)) # label(axiom_26) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 47 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 48 (all Pid all Pid2 (host(Pid2) != host(Pid) -> Pid2 != Pid)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 49 (all X X = pidMsg(m_Down(X))) # label(axiom_50) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 50 (all X all Y m_NotNorm(Y) != m_Ldr(X)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 51 (all X all Y (m_NotNorm(Y) != m_NotNorm(X) <-> Y != X)) # label(axiom_28) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 52 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 53 (all X snoc(q_nil,X) = cons(X,q_nil)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 54 (all X all Y m_NormQ(Y) != m_Down(X)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 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]. 0.07/0.53 56 (all X all Y (leq(s(X),s(Y)) <-> leq(X,Y))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 57 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption]. 0.07/0.53 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Ldr(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (elem(m_Down(Pid0),queue(host(Z))) -> host(Pid0) != host(Z))) & (all Z all Pid0 (Z != Pid0 & host(Pid0) = host(Z) -> -setIn(Z,alive) | -setIn(Pid0,alive))) & (all Z all Pid20 all Pid0 (index(status,host(Pid0)) = norm & host(Pid0) = index(ldr,host(Pid0)) & host(Pid20) = host(Pid0) & setIn(Pid0,alive) -> -(elem(m_Down(Pid20),queue(host(Z))) & setIn(Z,alive)))) & (all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & norm = index(status,host(Z)) & norm = index(status,host(Pid0)) & host(Pid0) = index(ldr,host(Pid0)) & host(Z) = index(ldr,host(Z)) -> Pid0 = Z)) & (all Z all Pid20 all Pid0 (elem(m_Down(Pid20),queue(host(Pid0))) & host(Z) = host(Pid20) & setIn(Pid0,alive) & -leq(host(Pid20),host(Pid0)) -> -(index(status,host(Z)) = norm & index(ldr,host(Z)) = host(Z) & setIn(Z,alive)))) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid0) = host(Pid20) & host(Z) = host(Pid30) & setIn(Pid20,alive) & setIn(Z,alive) & host(Z) != host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Z))) & elem(m_Down(Pid30),queue(host(Pid20)))))) & (all Z all Pid30 all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid20,alive) & host(Pid20) = host(Pid0) & host(Pid30) = host(Z) & host(Pid20) != host(Z) -> -(elem(m_Down(Pid0),queue(host(Z))) & setIn(host(Pid30),index(down,host(Pid20)))))) & (all Z all Pid30 all Pid20 all Pid0 (elem(m_Down(Pid30),queue(host(Pid0))) & host(Pid30) = s(host(Pid0)) & index(status,host(Pid0)) = elec_1 & elem(m_Down(Pid20),queue(host(Pid0))) & leq(nbr_proc,s(host(Pid0))) & setIn(Pid0,alive) & (all V0 (leq(s(zero),V0) & -leq(host(Pid0),V0) -> host(Pid20) = V0 | setIn(V0,index(down,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 Pid30 all Pid20 all Pid0 ((all V0 (leq(s(zero),V0) & -leq(host(Pid0),V0) -> setIn(V0,index(down,host(Pid0))) | host(Pid20) = V0)) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid0) = host(Pid30) & index(status,host(Z)) = elec_2 & elec_1 = index(status,host(Pid0)) & leq(host(Z),host(Pid0)) & setIn(Z,alive) -> -elem(m_Ack(Z,Pid30),queue(host(Z))))) & (all Z all Pid20 all Pid0 (host(Pid20) != host(Pid0) & host(Z) = host(Pid20) & wait = index(status,host(Pid0)) & host(index(elid,host(Pid0))) = host(Pid20) & elem(m_Down(Z),queue(host(Pid0))) & setIn(Pid0,alive) -> -(index(ldr,host(Pid20)) = host(Pid20) & norm = index(status,host(Pid20)) & setIn(Pid20,alive)))) & (all Z all Pid20 all Pid0 (host(Pid0) != host(Pid20) & setIn(Pid0,alive) & host(Pid20) = host(Z) & index(ldr,host(Pid0)) = host(Pid20) & index(status,host(Pid0)) = norm & elem(m_Down(Z),queue(host(Pid0))) -> -(setIn(Pid20,alive) & index(status,host(Pid20)) = norm & host(Pid20) = index(ldr,host(Pid20))))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Z))) & elec_2 = index(status,host(Pid0)) & host(Pid20) = host(Pid0) & setIn(Z,alive) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (host(Pid0) = index(ldr,host(Pid0)) & norm = index(status,host(Pid0)) & setIn(Pid0,alive) -> -(setIn(Z,alive) & setIn(host(Pid0),index(down,host(Z)))))) & (all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & setIn(host(Pid0),index(down,host(Z))) & index(status,host(Pid0)) = elec_2 -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z (setIn(Z,alive) & (elec_1 = index(status,host(Z)) | index(status,host(Z)) = elec_2) -> index(elid,host(Z)) = Z)) -> (setIn(X,alive) -> (-leq(host(X),host(Y)) -> (-(index(status,host(X)) = norm & index(ldr,host(X)) = host(Y) | wait = index(status,host(X)) & host(Y) = host(index(elid,host(X)))) -> (-((all Z (-leq(host(X),Z) & leq(s(zero),Z) -> host(Y) = Z | setIn(Z,index(down,host(X))))) & index(status,host(X)) = elec_1) -> (all Z all W0 all X0 all Y0 (host(Y0) = host(X) -> ((all V0 (-leq(host(Y0),V0) & leq(s(zero),V0) -> V0 = host(X0) | V0 = host(Y) | setIn(V0,index(down,host(X))))) & elem(m_Down(W0),V) & elem(m_Down(X0),V) & leq(nbr_proc,s(host(Y0))) & elec_1 = index(status,host(Y0)) & s(host(Y0)) = host(W0) & setIn(Y0,alive) -> -(host(Z) = index(ldr,host(Z)) & norm = index(status,host(Z)) & setIn(Z,alive))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption]. 60.15/60.37 60.15/60.37 ============================== end of process non-clausal formulas === 60.15/60.37 60.15/60.37 ============================== PROCESS INITIAL CLAUSES =============== 60.15/60.37 60.15/60.37 ============================== PREDICATE ELIMINATION ================= 60.15/60.37 60.15/60.37 ============================== end predicate elimination ============= 60.15/60.37 60.15/60.37 Auto_denials: (non-Horn, no changes). 60.15/60.37 60.15/60.37 Term ordering decisions: 60.15/60.37 Function symbol KB weights: alive=1. status=1. ldr=1. norm=1. q_nil=1. zero=1. elec_1=1. elec_2=1. nbr_proc=1. down=1. elid=1. pendack=1. pids=1. wait=1. nil=1. setEmpty=1. c1=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. index=1. cons=1. snoc=1. m_Ack=1. f2=1. f3=1. host=1. m_Down=1. s=1. pidMsg=1. queue=1. m_Halt=1. m_Ldr=1. m_NormQ=1. m_NotNorm=1. head=1. init=1. last=1. tail=1. f1=1. f4=1. f5=1. 60.15/60.37 60.15/60.37 ============================== end of process initial clauses ======== 60.15/60.37 60.15/60.37 ============================== CLAUSES FOR SEARCH ==================== 60.15/60.37 60.15/60.37 ============================== end of clauses for search ============= 60.15/60.37 60.15/60.37 ============================== SEARCH ================================ 60.15/60.37 60.15/60.37 % Starting search at 0.03 seconds. 60.15/60.37 60.15/60.37 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 103 (0.00 of 0.20 sec). 60.15/60.37 60.15/60.37 Low Water (keep): wt=57.000, iters=4594 60.15/60.37 60.15/60.37 Low Water (keep): wt=44.000, iters=4327 60.15/60.37 60.15/60.37 Low Water (keep): wt=34.000, iters=4091 60.15/60.37 60.15/60.37 Low Water (keep): wt=18.000, iters=4268 60.15/60.37 60.15/60.37 Low Water (keep): wt=16.000, iters=3663 60.15/60.37 60.15/60.37 Low Water (keep): wt=15.000, iters=3391 60.15/60.37 60.15/60.37 Low Water (keep): wt=14.000, iters=3358 60.15/60.37 60.15/60.37 ============================== PROOF ================================= 60.15/60.37 % SZS status Theorem 60.15/60.37 % SZS output start Refutation 60.15/60.37 60.15/60.37 % Proof 1 at 57.99 (+ 1.86) seconds. 60.15/60.37 % Length of proof is 75. 60.15/60.37 % Level of proof is 10. 60.15/60.37 % Maximum clause weight is 33.000. 60.15/60.37 % Given clauses 9117. 60.15/60.37 60.15/60.37 1 (all X all Y (s(Y) = X | leq(X,Y) <-> leq(X,s(Y)))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption]. 60.15/60.37 26 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption]. 60.15/60.37 32 (all X all Y (leq(Y,X) & leq(X,Y) <-> Y = X)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption]. 60.15/60.38 41 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption]. 60.15/60.38 43 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption]. 60.15/60.38 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]. 60.15/60.38 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Ldr(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (elem(m_Down(Pid0),queue(host(Z))) -> host(Pid0) != host(Z))) & (all Z all Pid0 (Z != Pid0 & host(Pid0) = host(Z) -> -setIn(Z,alive) | -setIn(Pid0,alive))) & (all Z all Pid20 all Pid0 (index(status,host(Pid0)) = norm & host(Pid0) = index(ldr,host(Pid0)) & host(Pid20) = host(Pid0) & setIn(Pid0,alive) -> -(elem(m_Down(Pid20),queue(host(Z))) & setIn(Z,alive)))) & (all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & norm = index(status,host(Z)) & norm = index(status,host(Pid0)) & host(Pid0) = index(ldr,host(Pid0)) & host(Z) = index(ldr,host(Z)) -> Pid0 = Z)) & (all Z all Pid20 all Pid0 (elem(m_Down(Pid20),queue(host(Pid0))) & host(Z) = host(Pid20) & setIn(Pid0,alive) & -leq(host(Pid20),host(Pid0)) -> -(index(status,host(Z)) = norm & index(ldr,host(Z)) = host(Z) & setIn(Z,alive)))) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid0) = host(Pid20) & host(Z) = host(Pid30) & setIn(Pid20,alive) & setIn(Z,alive) & host(Z) != host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Z))) & elem(m_Down(Pid30),queue(host(Pid20)))))) & (all Z all Pid30 all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid20,alive) & host(Pid20) = host(Pid0) & host(Pid30) = host(Z) & host(Pid20) != host(Z) -> -(elem(m_Down(Pid0),queue(host(Z))) & setIn(host(Pid30),index(down,host(Pid20)))))) & (all Z all Pid30 all Pid20 all Pid0 (elem(m_Down(Pid30),queue(host(Pid0))) & host(Pid30) = s(host(Pid0)) & index(status,host(Pid0)) = elec_1 & elem(m_Down(Pid20),queue(host(Pid0))) & leq(nbr_proc,s(host(Pid0))) & setIn(Pid0,alive) & (all V0 (leq(s(zero),V0) & -leq(host(Pid0),V0) -> host(Pid20) = V0 | setIn(V0,index(down,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 Pid30 all Pid20 all Pid0 ((all V0 (leq(s(zero),V0) & -leq(host(Pid0),V0) -> setIn(V0,index(down,host(Pid0))) | host(Pid20) = V0)) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid0) = host(Pid30) & index(status,host(Z)) = elec_2 & elec_1 = index(status,host(Pid0)) & leq(host(Z),host(Pid0)) & setIn(Z,alive) -> -elem(m_Ack(Z,Pid30),queue(host(Z))))) & (all Z all Pid20 all Pid0 (host(Pid20) != host(Pid0) & host(Z) = host(Pid20) & wait = index(status,host(Pid0)) & host(index(elid,host(Pid0))) = host(Pid20) & elem(m_Down(Z),queue(host(Pid0))) & setIn(Pid0,alive) -> -(index(ldr,host(Pid20)) = host(Pid20) & norm = index(status,host(Pid20)) & setIn(Pid20,alive)))) & (all Z all Pid20 all Pid0 (host(Pid0) != host(Pid20) & setIn(Pid0,alive) & host(Pid20) = host(Z) & index(ldr,host(Pid0)) = host(Pid20) & index(status,host(Pid0)) = norm & elem(m_Down(Z),queue(host(Pid0))) -> -(setIn(Pid20,alive) & index(status,host(Pid20)) = norm & host(Pid20) = index(ldr,host(Pid20))))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Z))) & elec_2 = index(status,host(Pid0)) & host(Pid20) = host(Pid0) & setIn(Z,alive) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (host(Pid0) = index(ldr,host(Pid0)) & norm = index(status,host(Pid0)) & setIn(Pid0,alive) -> -(setIn(Z,alive) & setIn(host(Pid0),index(down,host(Z)))))) & (all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & setIn(host(Pid0),index(down,host(Z))) & index(status,host(Pid0)) = elec_2 -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z (setIn(Z,alive) & (elec_1 = index(status,host(Z)) | index(status,host(Z)) = elec_2) -> index(elid,host(Z)) = Z)) -> (setIn(X,alive) -> (-leq(host(X),host(Y)) -> (-(index(status,host(X)) = norm & index(ldr,host(X)) = host(Y) | wait = index(status,host(X)) & host(Y) = host(index(elid,host(X)))) -> (-((all Z (-leq(host(X),Z) & leq(s(zero),Z) -> host(Y) = Z | setIn(Z,index(down,host(X))))) & index(status,host(X)) = elec_1) -> (all Z all W0 all X0 all Y0 (host(Y0) = host(X) -> ((all V0 (-leq(host(Y0),V0) & leq(s(zero),V0) -> V0 = host(X0) | V0 = host(Y) | setIn(V0,index(down,host(X))))) & elem(m_Down(W0),V) & elem(m_Down(X0),V) & leq(nbr_proc,s(host(Y0))) & elec_1 = index(status,host(Y0)) & s(host(Y0)) = host(W0) & setIn(Y0,alive) -> -(host(Z) = index(ldr,host(Z)) & norm = index(status,host(Z)) & setIn(Z,alive))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption]. 60.15/60.38 61 s(A) = B | leq(B,A) | -leq(B,s(A)) # label(axiom_64) # label(axiom). [clausify(1)]. 60.15/60.38 103 leq(s(zero),host(A)) # label(axiom_02) # label(axiom). [clausify(26)]. 60.15/60.38 109 -leq(A,B) | -leq(B,A) | A = B # label(axiom_61) # label(axiom). [clausify(32)]. 60.15/60.38 131 elec_1 != norm # label(axiom_07) # label(axiom). [assumption]. 60.15/60.38 133 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(41)]. 60.15/60.38 135 init(snoc(A,B)) = A # label(axiom_38) # label(axiom). [clausify(43)]. 60.15/60.38 139 elem(A,cons(B,C)) | -elem(A,C) # label(axiom_46) # label(axiom). [clausify(45)]. 60.15/60.38 140 elem(A,cons(B,C)) | B != A # label(axiom_46) # label(axiom). [clausify(45)]. 60.15/60.38 162 A = B | host(A) != host(B) | -setIn(B,alive) | -setIn(A,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 163 index(status,host(A)) != norm | index(ldr,host(A)) != host(A) | host(B) != host(A) | -setIn(A,alive) | -elem(m_Down(B),queue(host(C))) | -setIn(C,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 172 queue(host(c3)) = cons(m_Down(c4),c1) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 173 cons(m_Down(c4),c1) = queue(host(c3)). [copy(172),flip(a)]. 60.15/60.38 182 index(ldr,host(A)) != host(A) | index(status,host(A)) != norm | -setIn(A,alive) | -setIn(B,alive) | -setIn(host(A),index(down,host(B))) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 186 setIn(c3,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 190 -leq(host(c3),c5) | index(status,host(c3)) != elec_1 # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 191 leq(s(zero),c5) | index(status,host(c3)) != elec_1 # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 192 host(c4) != c5 | index(status,host(c3)) != elec_1 # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 193 -setIn(c5,index(down,host(c3))) | index(status,host(c3)) != elec_1 # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 194 host(c9) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 195 leq(host(c9),A) | -leq(s(zero),A) | host(c8) = A | host(c4) = A | setIn(A,index(down,host(c3))) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 196 leq(host(c3),A) | -leq(s(zero),A) | host(c8) = A | host(c4) = A | setIn(A,index(down,host(c3))). [copy(195),rewrite([194(2)])]. 60.15/60.38 197 elem(m_Down(c7),c1) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 198 elem(m_Down(c8),c1) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 199 leq(nbr_proc,s(host(c9))) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 200 leq(nbr_proc,s(host(c3))). [copy(199),rewrite([194(3)])]. 60.15/60.38 201 index(status,host(c9)) = elec_1 # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 202 elec_1 = index(status,host(c3)). [copy(201),rewrite([194(3)]),flip(a)]. 60.15/60.38 203 host(c7) = s(host(c9)) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 204 s(host(c3)) = host(c7). [copy(203),rewrite([194(4)]),flip(a)]. 60.15/60.38 206 index(ldr,host(c6)) = host(c6) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 207 index(status,host(c6)) = norm # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 208 norm = index(status,host(c6)). [copy(207),flip(a)]. 60.15/60.38 209 setIn(c6,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 60.15/60.38 221 -setIn(c5,index(down,host(c3))). [back_rewrite(193),rewrite([202(11)]),xx(b)]. 60.15/60.38 222 host(c4) != c5. [back_rewrite(192),rewrite([202(9)]),xx(b)]. 60.15/60.38 223 leq(s(zero),c5). [back_rewrite(191),rewrite([202(9)]),xx(b)]. 60.15/60.38 224 -leq(host(c3),c5). [back_rewrite(190),rewrite([202(9)]),xx(b)]. 60.15/60.38 234 index(status,host(c6)) != index(status,host(c3)). [back_rewrite(131),rewrite([202(1),208(5)]),flip(a)]. 60.15/60.38 237 leq(nbr_proc,host(c7)). [back_rewrite(200),rewrite([204(4)])]. 60.15/60.38 238 index(ldr,host(A)) != host(A) | index(status,host(c6)) != index(status,host(A)) | -setIn(A,alive) | -setIn(B,alive) | -setIn(host(A),index(down,host(B))). [back_rewrite(182),rewrite([208(9)]),flip(b)]. 60.15/60.38 242 index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A) | host(B) != host(A) | -setIn(A,alive) | -elem(m_Down(B),queue(host(C))) | -setIn(C,alive). [back_rewrite(163),rewrite([208(4)]),flip(a)]. 60.15/60.38 300 elem(A,cons(A,B)). [resolve(140,b,135,a),rewrite([135(2)])]. 60.15/60.38 336 c3 = A | host(c3) != host(A) | -setIn(A,alive). [resolve(186,a,162,d)]. 60.15/60.38 349 leq(host(c3),host(A)) | host(c8) = host(A) | host(c4) = host(A) | setIn(host(A),index(down,host(c3))). [resolve(196,b,103,a)]. 60.15/60.38 351 elem(m_Down(c7),cons(A,c1)). [resolve(197,a,139,b)]. 60.15/60.38 356 elem(m_Down(c8),cons(A,c1)). [resolve(198,a,139,b)]. 60.15/60.38 362 host(c7) = A | leq(A,host(c3)) | -leq(A,host(c7)). [para(204(a,1),61(c,2)),rewrite([204(3)])]. 60.15/60.38 372 host(c8) = c5. [resolve(223,a,196,b),unit_del(a,224),unit_del(c,222),unit_del(d,221)]. 60.15/60.38 382 leq(host(c3),host(A)) | host(A) = c5 | host(c4) = host(A) | setIn(host(A),index(down,host(c3))). [back_rewrite(349),rewrite([372(6)]),flip(b)]. 60.15/60.38 396 host(c7) = nbr_proc. [resolve(237,a,109,b),unit_del(a,133)]. 60.15/60.38 404 nbr_proc = A | leq(A,host(c3)) | -leq(A,nbr_proc). [back_rewrite(362),rewrite([396(2),396(7)])]. 60.15/60.38 544 elem(m_Down(c4),queue(host(c3))). [para(173(a,1),300(a,2))]. 60.15/60.38 673 elem(m_Down(c7),queue(host(c3))). [para(173(a,1),351(a,2))]. 60.15/60.38 691 elem(m_Down(c8),queue(host(c3))). [para(173(a,1),356(a,2))]. 60.15/60.38 731 index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A) | host(c4) != host(A) | -setIn(A,alive). [resolve(544,a,242,e),unit_del(e,186)]. 60.15/60.38 759 host(c6) != host(c4). [resolve(731,d,209,a),rewrite([206(13)]),flip(c),xx(a),xx(b)]. 60.15/60.38 833 index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A) | host(A) != nbr_proc | -setIn(A,alive). [resolve(673,a,242,e),rewrite([396(15)]),flip(c),unit_del(e,186)]. 60.15/60.38 861 index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A) | host(A) != c5 | -setIn(A,alive). [resolve(691,a,242,e),rewrite([372(15)]),flip(c),unit_del(e,186)]. 60.15/60.38 891 host(c6) != nbr_proc. [resolve(833,d,209,a),rewrite([206(13)]),xx(a),xx(b)]. 60.15/60.38 892 host(c6) != c5. [resolve(861,d,209,a),rewrite([206(13)]),xx(a),xx(b)]. 60.15/60.38 2756 c6 = c3 | host(c6) != host(c3). [resolve(336,c,209,a),flip(a),flip(b)]. 60.15/60.38 3067 leq(host(c3),host(A)) | host(A) = c5 | host(c4) = host(A) | index(ldr,host(A)) != host(A) | index(status,host(c6)) != index(status,host(A)) | -setIn(A,alive). [resolve(382,d,238,e),unit_del(g,186)]. 60.15/60.38 3200 host(A) = nbr_proc | leq(host(A),host(c3)). [resolve(404,c,133,a),flip(a)]. 60.15/60.38 3983 host(A) = nbr_proc | -leq(host(c3),host(A)) | host(c3) = host(A). [resolve(3200,b,109,b)]. 60.15/60.38 18875 leq(host(c3),host(c6)). [resolve(3067,f,209,a),rewrite([206(18)]),flip(c),xx(d),xx(e),unit_del(b,892),unit_del(c,759)]. 60.15/60.38 18927 host(c6) = host(c3). [resolve(18875,a,3983,b),flip(b),unit_del(a,891)]. 60.15/60.38 19162 c6 = c3. [back_rewrite(2756),rewrite([18927(5)]),xx(b)]. 60.15/60.38 19253 $F. [back_rewrite(234),rewrite([19162(2)]),xx(a)]. 60.15/60.38 60.15/60.38 % SZS output end Refutation 60.15/60.38 ============================== end of proof ========================== 60.15/60.38 60.15/60.38 ============================== STATISTICS ============================ 60.15/60.38 60.15/60.38 Given=9117. Generated=3839109. Kept=19181. proofs=1. 60.15/60.38 Usable=8593. Sos=9151. Demods=48. Limbo=326, Disabled=1250. Hints=0. 60.15/60.38 Megabytes=35.28. 60.15/60.38 User_CPU=57.99, System_CPU=1.86, Wall_clock=60. 60.15/60.38 60.15/60.38 ============================== end of statistics ===================== 60.15/60.38 60.15/60.38 ============================== end of search ========================= 60.15/60.38 60.15/60.38 THEOREM PROVED 60.15/60.38 % SZS status Theorem 60.15/60.38 60.15/60.38 Exiting with 1 proof. 60.15/60.38 60.15/60.38 Process 7397 exit (max_proofs) Sat Jul 14 05:24:10 2018 60.15/60.38 Prover9 interrupted 60.15/60.38 EOF