0.01/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.01/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.24 % Computer : n066.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 05:13:09 CDT 2018 0.03/0.24 % CPUTime : 0.07/0.52 ============================== Prover9 =============================== 0.07/0.52 Prover9 (32) version 2009-11A, November 2009. 0.07/0.52 Process 50230 was started by sandbox on n066.star.cs.uiowa.edu, 0.07/0.52 Sat Jul 14 05:13:10 2018 0.07/0.52 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_50198_n066.star.cs.uiowa.edu". 0.07/0.52 ============================== end of head =========================== 0.07/0.52 0.07/0.52 ============================== INPUT ================================= 0.07/0.52 0.07/0.52 % Reading from file /tmp/Prover9_50198_n066.star.cs.uiowa.edu 0.07/0.52 0.07/0.52 set(prolog_style_variables). 0.07/0.52 set(auto2). 0.07/0.52 % set(auto2) -> set(auto). 0.07/0.52 % set(auto) -> set(auto_inference). 0.07/0.52 % set(auto) -> set(auto_setup). 0.07/0.52 % set(auto_setup) -> set(predicate_elim). 0.07/0.52 % set(auto_setup) -> assign(eq_defs, unfold). 0.07/0.52 % set(auto) -> set(auto_limits). 0.07/0.52 % set(auto_limits) -> assign(max_weight, "100.000"). 0.07/0.52 % set(auto_limits) -> assign(sos_limit, 20000). 0.07/0.52 % set(auto) -> set(auto_denials). 0.07/0.52 % set(auto) -> set(auto_process). 0.07/0.52 % set(auto2) -> assign(new_constants, 1). 0.07/0.52 % set(auto2) -> assign(fold_denial_max, 3). 0.07/0.52 % set(auto2) -> assign(max_weight, "200.000"). 0.07/0.52 % set(auto2) -> assign(max_hours, 1). 0.07/0.52 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.07/0.52 % set(auto2) -> assign(max_seconds, 0). 0.07/0.52 % set(auto2) -> assign(max_minutes, 5). 0.07/0.52 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.07/0.52 % set(auto2) -> set(sort_initial_sos). 0.07/0.52 % set(auto2) -> assign(sos_limit, -1). 0.07/0.52 % set(auto2) -> assign(lrs_ticks, 3000). 0.07/0.52 % set(auto2) -> assign(max_megs, 400). 0.07/0.52 % set(auto2) -> assign(stats, some). 0.07/0.52 % set(auto2) -> clear(echo_input). 0.07/0.52 % set(auto2) -> set(quiet). 0.07/0.52 % set(auto2) -> clear(print_initial_clauses). 0.07/0.52 % set(auto2) -> clear(print_given). 0.07/0.52 assign(lrs_ticks,-1). 0.07/0.52 assign(sos_limit,10000). 0.07/0.52 assign(order,kbo). 0.07/0.52 set(lex_order_vars). 0.07/0.52 clear(print_given). 0.07/0.52 0.07/0.52 % formulas(sos). % not echoed (67 formulas) 0.07/0.52 0.07/0.52 ============================== end of input ========================== 0.07/0.52 0.07/0.52 % From the command line: assign(max_seconds, 300). 0.07/0.52 0.07/0.52 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.07/0.52 0.07/0.52 % Formulas that are not ordinary clauses: 0.07/0.52 1 (all X all Y (s(Y) = X | leq(X,Y) <-> leq(X,s(Y)))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 2 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 4 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 5 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 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]. 0.07/0.52 8 (all X ((exists Y (m_Down(Y) = X | X = m_Halt(Y))) <-> pidElem(X))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 9 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 10 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 11 (all X all Y m_Halt(Y) != m_Ldr(X)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 12 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 14 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 15 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 16 (all X all Y m_Halt(Y) != m_NotNorm(X)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 18 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 19 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 20 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 21 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 23 (all X (ordered(snoc(q_nil,X)) & ordered(cons(X,q_nil)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 24 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 25 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 26 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 28 (all Y all Q Y = last(snoc(Q,Y))) # label(axiom_37) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 29 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 30 (all X all Q X = head(cons(X,Q))) # label(axiom_35) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 31 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 32 (all X all Y (leq(Y,X) & leq(X,Y) <-> Y = X)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 33 (all Q (q_nil = Q | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 34 (all Q (snoc(init(Q),last(Q)) = Q | q_nil = Q)) # label(axiom_40) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 36 (all X all Y (Y != X <-> m_Ldr(Y) != m_Ldr(X))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 37 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 38 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 40 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 41 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 42 (all P all Q (host(Q) = s(host(P)) -> host(Q) != host(P))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 43 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 44 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 46 (all X all Y (m_Halt(X) != m_Halt(Y) <-> X != Y)) # label(axiom_26) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 47 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 48 (all Pid all Pid2 (host(Pid2) != host(Pid) -> Pid2 != Pid)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 49 (all X X = pidMsg(m_Down(X))) # label(axiom_50) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 50 (all X all Y m_NotNorm(Y) != m_Ldr(X)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 51 (all X all Y (m_NotNorm(Y) != m_NotNorm(X) <-> Y != X)) # label(axiom_28) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 52 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 53 (all X snoc(q_nil,X) = cons(X,q_nil)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 54 (all X all Y m_NormQ(Y) != m_Down(X)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 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]. 0.07/0.52 56 (all X all Y (leq(s(X),s(Y)) <-> leq(X,Y))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 57 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption]. 0.07/0.52 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Down(Pid0),queue(host(Z))) -> host(Pid0) != host(Z))) & (all Z all Pid0 (host(Pid0) = host(Z) & Z != Pid0 -> -setIn(Pid0,alive) | -setIn(Z,alive))) & (all Z (setIn(Z,alive) & (index(status,host(Z)) = elec_1 | elec_2 = index(status,host(Z))) -> index(elid,host(Z)) = Z)) & (all Z all Pid0 (index(status,host(Pid0)) = elec_2 & setIn(host(Pid0),index(down,host(Z))) & setIn(Pid0,alive) & setIn(Z,alive) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & index(status,host(Pid0)) = elec_2 & host(Pid0) = host(Pid20) & elem(m_Down(Pid20),queue(host(Z))) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (setIn(Z,alive) & host(Z) = index(ldr,host(Z)) & norm = index(status,host(Pid0)) & host(Pid0) = index(ldr,host(Pid0)) & norm = index(status,host(Z)) & setIn(Pid0,alive) -> Pid0 = Z)) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid20) != host(Z) & setIn(Z,alive) & host(Z) = host(Pid30) & host(Pid20) = host(Pid0) & setIn(Pid20,alive) -> -(elem(m_Down(Pid0),queue(host(Z))) & elem(m_Down(Pid30),queue(host(Pid20)))))) & (all Z all Pid30 all Pid20 all Pid0 ((all V0 (leq(s(zero),V0) & -leq(host(Pid0),V0) -> host(Pid20) = V0 | setIn(V0,index(down,host(Pid0))))) & elec_1 = index(status,host(Pid0)) & s(host(Pid0)) = host(Pid30) & elem(m_Down(Pid30),queue(host(Pid0))) & elem(m_Down(Pid20),queue(host(Pid0))) & leq(nbr_proc,s(host(Pid0))) & setIn(Pid0,alive) -> -(host(Z) = index(ldr,host(Z)) & norm = index(status,host(Z)) & setIn(Z,alive)))) & queue(host(X)) = cons(m_Ack(W,Y),V) & (all Z all Pid30 all Pid20 all Pid0 (index(status,host(Pid0)) = elec_1 & index(status,host(Z)) = elec_2 & host(Pid0) = host(Pid30) & elem(m_Down(Pid20),queue(host(Pid0))) & leq(host(Z),host(Pid0)) & setIn(Z,alive) & (all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> V0 = host(Pid20) | setIn(V0,index(down,host(Pid0))))) -> -elem(m_Ack(Z,Pid30),queue(host(Z))))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & host(Z) = host(Pid20) & index(status,host(Pid0)) = wait & host(Pid20) = host(index(elid,host(Pid0))) & host(Pid0) != host(Pid20) -> -(setIn(Pid20,alive) & index(ldr,host(Pid20)) = host(Pid20) & index(status,host(Pid20)) = norm))) & (all Z all Pid20 all Pid0 (host(Pid20) != host(Pid0) & setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & norm = index(status,host(Pid0)) & host(Pid20) = index(ldr,host(Pid0)) & host(Z) = host(Pid20) -> -(setIn(Pid20,alive) & index(ldr,host(Pid20)) = host(Pid20) & index(status,host(Pid20)) = norm))) & (all Z all Pid30 all Pid20 all Pid0 (host(Z) != host(Pid20) & setIn(Z,alive) & host(Pid30) = host(Z) & host(Pid20) = host(Pid0) & setIn(Pid20,alive) -> -(elem(m_Down(Pid0),queue(host(Z))) & setIn(host(Pid30),index(down,host(Pid20)))))) & (all Z all Pid20 all Pid0 (-leq(host(Pid20),host(Pid0)) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Z) = host(Pid20) & setIn(Pid0,alive) -> -(host(Z) = index(ldr,host(Z)) & index(status,host(Z)) = norm & setIn(Z,alive)))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & index(status,host(Pid0)) = norm & host(Pid0) = index(ldr,host(Pid0)) & host(Pid20) = host(Pid0) -> -(elem(m_Down(Pid20),queue(host(Z))) & setIn(Z,alive)))) & (all Z all Pid0 (setIn(Pid0,alive) & index(ldr,host(Pid0)) = host(Pid0) & index(status,host(Pid0)) = norm -> -(setIn(host(Pid0),index(down,host(Z))) & setIn(Z,alive)))) & (all Z all Pid0 (elem(m_Ldr(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) -> (setIn(X,alive) -> (index(elid,host(X)) = W & index(pendack,host(X)) = host(Y) & elec_2 = index(status,host(X)) -> (leq(nbr_proc,index(pendack,host(X))) -> (all Z (setIn(host(Z),index(acks,host(X))) | host(Z) = host(Y) -> (all V0 (host(V0) = host(X) -> (all W0 all X0 all Y0 (host(Y0) != host(Z) -> (host(Y0) != host(X) -> (setIn(Y0,alive) & elem(m_Down(W0),queue(host(Y0))) & elem(m_Down(X0),queue(host(Y0))) & s(host(Y0)) = host(W0) & elec_1 = index(status,host(Y0)) & leq(nbr_proc,s(host(Y0))) & (all V1 (leq(s(zero),V1) & -leq(host(Y0),V1) -> host(X0) = V1 | setIn(V1,index(down,host(Y0))))) -> -(host(V0) = host(X) & setIn(V0,alive))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption]. 0.88/1.15 0.88/1.15 ============================== end of process non-clausal formulas === 0.88/1.15 0.88/1.15 ============================== PROCESS INITIAL CLAUSES =============== 0.88/1.15 0.88/1.15 ============================== PREDICATE ELIMINATION ================= 0.88/1.15 0.88/1.15 ============================== end predicate elimination ============= 0.88/1.15 0.88/1.15 Auto_denials: (non-Horn, no changes). 0.88/1.15 0.88/1.15 Term ordering decisions: 0.88/1.15 Function symbol KB weights: alive=1. status=1. ldr=1. norm=1. q_nil=1. elec_2=1. nbr_proc=1. zero=1. elec_1=1. elid=1. pendack=1. down=1. pids=1. acks=1. wait=1. nil=1. setEmpty=1. c1=1. c2=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. pidMsg=1. s=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. 0.88/1.15 0.88/1.15 ============================== end of process initial clauses ======== 0.88/1.15 0.88/1.15 ============================== CLAUSES FOR SEARCH ==================== 0.88/1.15 0.88/1.15 ============================== end of clauses for search ============= 0.88/1.15 0.88/1.15 ============================== SEARCH ================================ 0.88/1.15 0.88/1.15 % Starting search at 0.03 seconds. 0.88/1.15 0.88/1.15 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 95 (0.00 of 0.28 sec). 0.88/1.15 0.88/1.15 ============================== PROOF ================================= 0.88/1.15 % SZS status Theorem 0.88/1.15 % SZS output start Refutation 0.88/1.15 0.88/1.15 % Proof 1 at 0.62 (+ 0.02) seconds. 0.88/1.15 % Length of proof is 61. 0.88/1.15 % Level of proof is 10. 0.88/1.15 % Maximum clause weight is 33.000. 0.88/1.15 % Given clauses 688. 0.88/1.15 0.88/1.15 1 (all X all Y (s(Y) = X | leq(X,Y) <-> leq(X,s(Y)))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption]. 0.88/1.15 15 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption]. 0.88/1.15 26 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption]. 0.88/1.15 32 (all X all Y (leq(Y,X) & leq(X,Y) <-> Y = X)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption]. 0.88/1.15 41 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption]. 0.88/1.15 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Down(Pid0),queue(host(Z))) -> host(Pid0) != host(Z))) & (all Z all Pid0 (host(Pid0) = host(Z) & Z != Pid0 -> -setIn(Pid0,alive) | -setIn(Z,alive))) & (all Z (setIn(Z,alive) & (index(status,host(Z)) = elec_1 | elec_2 = index(status,host(Z))) -> index(elid,host(Z)) = Z)) & (all Z all Pid0 (index(status,host(Pid0)) = elec_2 & setIn(host(Pid0),index(down,host(Z))) & setIn(Pid0,alive) & setIn(Z,alive) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & index(status,host(Pid0)) = elec_2 & host(Pid0) = host(Pid20) & elem(m_Down(Pid20),queue(host(Z))) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (setIn(Z,alive) & host(Z) = index(ldr,host(Z)) & norm = index(status,host(Pid0)) & host(Pid0) = index(ldr,host(Pid0)) & norm = index(status,host(Z)) & setIn(Pid0,alive) -> Pid0 = Z)) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid20) != host(Z) & setIn(Z,alive) & host(Z) = host(Pid30) & host(Pid20) = host(Pid0) & setIn(Pid20,alive) -> -(elem(m_Down(Pid0),queue(host(Z))) & elem(m_Down(Pid30),queue(host(Pid20)))))) & (all Z all Pid30 all Pid20 all Pid0 ((all V0 (leq(s(zero),V0) & -leq(host(Pid0),V0) -> host(Pid20) = V0 | setIn(V0,index(down,host(Pid0))))) & elec_1 = index(status,host(Pid0)) & s(host(Pid0)) = host(Pid30) & elem(m_Down(Pid30),queue(host(Pid0))) & elem(m_Down(Pid20),queue(host(Pid0))) & leq(nbr_proc,s(host(Pid0))) & setIn(Pid0,alive) -> -(host(Z) = index(ldr,host(Z)) & norm = index(status,host(Z)) & setIn(Z,alive)))) & queue(host(X)) = cons(m_Ack(W,Y),V) & (all Z all Pid30 all Pid20 all Pid0 (index(status,host(Pid0)) = elec_1 & index(status,host(Z)) = elec_2 & host(Pid0) = host(Pid30) & elem(m_Down(Pid20),queue(host(Pid0))) & leq(host(Z),host(Pid0)) & setIn(Z,alive) & (all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> V0 = host(Pid20) | setIn(V0,index(down,host(Pid0))))) -> -elem(m_Ack(Z,Pid30),queue(host(Z))))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & host(Z) = host(Pid20) & index(status,host(Pid0)) = wait & host(Pid20) = host(index(elid,host(Pid0))) & host(Pid0) != host(Pid20) -> -(setIn(Pid20,alive) & index(ldr,host(Pid20)) = host(Pid20) & index(status,host(Pid20)) = norm))) & (all Z all Pid20 all Pid0 (host(Pid20) != host(Pid0) & setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & norm = index(status,host(Pid0)) & host(Pid20) = index(ldr,host(Pid0)) & host(Z) = host(Pid20) -> -(setIn(Pid20,alive) & index(ldr,host(Pid20)) = host(Pid20) & index(status,host(Pid20)) = norm))) & (all Z all Pid30 all Pid20 all Pid0 (host(Z) != host(Pid20) & setIn(Z,alive) & host(Pid30) = host(Z) & host(Pid20) = host(Pid0) & setIn(Pid20,alive) -> -(elem(m_Down(Pid0),queue(host(Z))) & setIn(host(Pid30),index(down,host(Pid20)))))) & (all Z all Pid20 all Pid0 (-leq(host(Pid20),host(Pid0)) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Z) = host(Pid20) & setIn(Pid0,alive) -> -(host(Z) = index(ldr,host(Z)) & index(status,host(Z)) = norm & setIn(Z,alive)))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & index(status,host(Pid0)) = norm & host(Pid0) = index(ldr,host(Pid0)) & host(Pid20) = host(Pid0) -> -(elem(m_Down(Pid20),queue(host(Z))) & setIn(Z,alive)))) & (all Z all Pid0 (setIn(Pid0,alive) & index(ldr,host(Pid0)) = host(Pid0) & index(status,host(Pid0)) = norm -> -(setIn(host(Pid0),index(down,host(Z))) & setIn(Z,alive)))) & (all Z all Pid0 (elem(m_Ldr(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) -> (setIn(X,alive) -> (index(elid,host(X)) = W & index(pendack,host(X)) = host(Y) & elec_2 = index(status,host(X)) -> (leq(nbr_proc,index(pendack,host(X))) -> (all Z (setIn(host(Z),index(acks,host(X))) | host(Z) = host(Y) -> (all V0 (host(V0) = host(X) -> (all W0 all X0 all Y0 (host(Y0) != host(Z) -> (host(Y0) != host(X) -> (setIn(Y0,alive) & elem(m_Down(W0),queue(host(Y0))) & elem(m_Down(X0),queue(host(Y0))) & s(host(Y0)) = host(W0) & elec_1 = index(status,host(Y0)) & leq(nbr_proc,s(host(Y0))) & (all V1 (leq(s(zero),V1) & -leq(host(Y0),V1) -> host(X0) = V1 | setIn(V1,index(down,host(Y0))))) -> -(host(V0) = host(X) & setIn(V0,alive))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption]. 0.88/1.15 61 s(A) = B | leq(B,A) | -leq(B,s(A)) # label(axiom_64) # label(axiom). [clausify(1)]. 0.88/1.15 83 -leq(s(A),A) # label(axiom_58) # label(axiom). [clausify(15)]. 0.88/1.15 104 leq(s(zero),host(A)) # label(axiom_02) # label(axiom). [clausify(26)]. 0.88/1.15 110 -leq(A,B) | -leq(B,A) | A = B # label(axiom_61) # label(axiom). [clausify(32)]. 0.88/1.15 134 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(41)]. 0.88/1.15 164 -setIn(A,alive) | index(status,host(A)) != elec_2 | index(elid,host(A)) = A # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 165 index(status,host(A)) != elec_2 | -setIn(host(A),index(down,host(B))) | -setIn(A,alive) | -setIn(B,alive) | leq(index(pendack,host(A)),host(B)) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 166 -setIn(A,alive) | -setIn(B,alive) | index(status,host(B)) != elec_2 | host(C) != host(B) | -elem(m_Down(C),queue(host(A))) | leq(index(pendack,host(B)),host(A)) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 188 setIn(c3,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 189 index(elid,host(c3)) = c2 # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 190 index(pendack,host(c3)) = host(c4) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 191 index(status,host(c3)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 192 elec_2 = index(status,host(c3)). [copy(191),flip(a)]. 0.88/1.15 193 leq(nbr_proc,index(pendack,host(c3))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 194 leq(nbr_proc,host(c4)). [copy(193),rewrite([190(5)])]. 0.88/1.15 196 host(c6) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 198 host(c9) != host(c3) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 199 setIn(c9,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 200 elem(m_Down(c7),queue(host(c9))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 201 elem(m_Down(c8),queue(host(c9))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 202 host(c7) = s(host(c9)) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 203 s(host(c9)) = host(c7). [copy(202),flip(a)]. 0.88/1.15 206 leq(nbr_proc,s(host(c9))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 207 leq(nbr_proc,host(c7)). [copy(206),rewrite([203(4)])]. 0.88/1.15 208 -leq(s(zero),A) | leq(host(c9),A) | host(c8) = A | setIn(A,index(down,host(c9))) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 209 setIn(c6,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 0.88/1.15 225 -setIn(A,alive) | -setIn(B,alive) | index(status,host(c3)) != index(status,host(B)) | host(C) != host(B) | -elem(m_Down(C),queue(host(A))) | leq(index(pendack,host(B)),host(A)). [back_rewrite(166),rewrite([192(8)]),flip(c)]. 0.88/1.15 226 index(status,host(c3)) != index(status,host(A)) | -setIn(host(A),index(down,host(B))) | -setIn(A,alive) | -setIn(B,alive) | leq(index(pendack,host(A)),host(B)). [back_rewrite(165),rewrite([192(4)]),flip(a)]. 0.88/1.15 227 -setIn(A,alive) | index(status,host(c3)) != index(status,host(A)) | index(elid,host(A)) = A. [back_rewrite(164),rewrite([192(6)]),flip(b)]. 0.88/1.15 333 host(c4) = nbr_proc. [resolve(194,a,110,b),unit_del(a,134)]. 0.88/1.15 335 index(pendack,host(c3)) = nbr_proc. [back_rewrite(190),rewrite([333(6)])]. 0.88/1.15 364 host(c7) = A | leq(A,host(c9)) | -leq(A,host(c7)). [para(203(a,1),61(c,2)),rewrite([203(3)])]. 0.88/1.15 365 -leq(host(c7),host(c9)). [para(203(a,1),83(a,1))]. 0.88/1.15 372 host(c7) = nbr_proc. [resolve(207,a,110,b),unit_del(a,134)]. 0.88/1.15 376 -leq(nbr_proc,host(c9)). [back_rewrite(365),rewrite([372(2)])]. 0.88/1.15 377 nbr_proc = A | leq(A,host(c9)) | -leq(A,nbr_proc). [back_rewrite(364),rewrite([372(2),372(7)])]. 0.88/1.15 387 leq(host(c9),host(A)) | host(c8) = host(A) | setIn(host(A),index(down,host(c9))). [resolve(208,a,104,a)]. 0.88/1.15 411 -setIn(A,alive) | index(status,host(c3)) != index(status,host(A)) | host(c8) != host(A) | leq(index(pendack,host(A)),host(c9)). [resolve(225,e,201,a),unit_del(a,199)]. 0.88/1.15 412 -setIn(A,alive) | index(status,host(c3)) != index(status,host(A)) | host(A) != nbr_proc | leq(index(pendack,host(A)),host(c9)). [resolve(225,e,200,a),rewrite([372(15)]),flip(d),unit_del(a,199)]. 0.88/1.15 414 -setIn(host(c3),index(down,host(A))) | -setIn(A,alive) | leq(nbr_proc,host(A)). [para(196(a,1),226(b,1)),rewrite([196(7),196(23),335(24)]),xx(a),unit_del(b,209)]. 0.88/1.15 416 c6 = c2. [resolve(227,a,209,a),rewrite([196(7),196(12),189(13)]),flip(b),xx(a)]. 0.88/1.15 417 c3 = c2. [resolve(227,a,188,a),rewrite([189(13)]),flip(b),xx(a)]. 0.88/1.15 423 setIn(c2,alive). [back_rewrite(209),rewrite([416(1)])]. 0.88/1.15 425 -setIn(host(c2),index(down,host(A))) | -setIn(A,alive) | leq(nbr_proc,host(A)). [back_rewrite(414),rewrite([417(1)])]. 0.88/1.15 427 -setIn(A,alive) | index(status,host(c2)) != index(status,host(A)) | host(A) != nbr_proc | leq(index(pendack,host(A)),host(c9)). [back_rewrite(412),rewrite([417(4)])]. 0.88/1.15 428 -setIn(A,alive) | index(status,host(c2)) != index(status,host(A)) | host(c8) != host(A) | leq(index(pendack,host(A)),host(c9)). [back_rewrite(411),rewrite([417(4)])]. 0.88/1.15 445 index(pendack,host(c2)) = nbr_proc. [back_rewrite(335),rewrite([417(2)])]. 0.88/1.15 464 host(c9) != host(c2). [back_rewrite(198),rewrite([417(3)])]. 0.88/1.15 2679 host(A) = nbr_proc | leq(host(A),host(c9)). [resolve(377,c,134,a),flip(a)]. 0.88/1.15 3413 leq(host(c9),host(c2)) | host(c8) = host(c2). [resolve(425,a,387,c),unit_del(a,199),unit_del(b,376)]. 0.88/1.15 3524 host(c2) != nbr_proc. [resolve(427,a,423,a),rewrite([445(17)]),xx(a),unit_del(b,376)]. 0.88/1.15 3553 host(c8) != host(c2). [resolve(428,a,423,a),rewrite([445(18)]),xx(a),unit_del(b,376)]. 0.88/1.15 3554 leq(host(c9),host(c2)). [back_unit_del(3413),unit_del(b,3553)]. 0.88/1.15 3563 -leq(host(c2),host(c9)). [resolve(3554,a,110,b),flip(b),unit_del(b,464)]. 0.88/1.15 3596 $F. [resolve(3563,a,2679,b),unit_del(a,3524)]. 0.88/1.15 0.88/1.15 % SZS output end Refutation 0.88/1.15 ============================== end of proof ========================== 0.88/1.15 0.88/1.15 ============================== STATISTICS ============================ 0.88/1.15 0.88/1.15 Given=688. Generated=15035. Kept=3523. proofs=1. 0.88/1.15 Usable=664. Sos=2706. Demods=34. Limbo=0, Disabled=290. Hints=0. 0.88/1.15 Megabytes=7.90. 0.88/1.15 User_CPU=0.63, System_CPU=0.02, Wall_clock=0. 0.88/1.15 0.88/1.15 ============================== end of statistics ===================== 0.88/1.15 0.88/1.15 ============================== end of search ========================= 0.88/1.15 0.88/1.15 THEOREM PROVED 0.88/1.15 % SZS status Theorem 0.88/1.15 0.88/1.15 Exiting with 1 proof. 0.88/1.15 0.88/1.15 Process 50230 exit (max_proofs) Sat Jul 14 05:13:10 2018 0.88/1.15 Prover9 interrupted 0.88/1.16 EOF