0.08/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n004.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 04:01:20 EDT 2022 0.13/0.34 % CPUTime : 0.64/0.96 ============================== Prover9 =============================== 0.64/0.96 Prover9 (32) version 2009-11A, November 2009. 0.64/0.96 Process 3812 was started by sandbox on n004.cluster.edu, 0.64/0.96 Tue Aug 9 04:01:21 2022 0.64/0.96 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_3659_n004.cluster.edu". 0.64/0.96 ============================== end of head =========================== 0.64/0.96 0.64/0.96 ============================== INPUT ================================= 0.64/0.96 0.64/0.96 % Reading from file /tmp/Prover9_3659_n004.cluster.edu 0.64/0.96 0.64/0.96 set(prolog_style_variables). 0.64/0.96 set(auto2). 0.64/0.96 % set(auto2) -> set(auto). 0.64/0.96 % set(auto) -> set(auto_inference). 0.64/0.96 % set(auto) -> set(auto_setup). 0.64/0.96 % set(auto_setup) -> set(predicate_elim). 0.64/0.96 % set(auto_setup) -> assign(eq_defs, unfold). 0.64/0.96 % set(auto) -> set(auto_limits). 0.64/0.96 % set(auto_limits) -> assign(max_weight, "100.000"). 0.64/0.96 % set(auto_limits) -> assign(sos_limit, 20000). 0.64/0.96 % set(auto) -> set(auto_denials). 0.64/0.96 % set(auto) -> set(auto_process). 0.64/0.96 % set(auto2) -> assign(new_constants, 1). 0.64/0.96 % set(auto2) -> assign(fold_denial_max, 3). 0.64/0.96 % set(auto2) -> assign(max_weight, "200.000"). 0.64/0.96 % set(auto2) -> assign(max_hours, 1). 0.64/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.64/0.96 % set(auto2) -> assign(max_seconds, 0). 0.64/0.96 % set(auto2) -> assign(max_minutes, 5). 0.64/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.64/0.96 % set(auto2) -> set(sort_initial_sos). 0.64/0.96 % set(auto2) -> assign(sos_limit, -1). 0.64/0.96 % set(auto2) -> assign(lrs_ticks, 3000). 0.64/0.96 % set(auto2) -> assign(max_megs, 400). 0.64/0.96 % set(auto2) -> assign(stats, some). 0.64/0.96 % set(auto2) -> clear(echo_input). 0.64/0.96 % set(auto2) -> set(quiet). 0.64/0.96 % set(auto2) -> clear(print_initial_clauses). 0.64/0.96 % set(auto2) -> clear(print_given). 0.64/0.96 assign(lrs_ticks,-1). 0.64/0.96 assign(sos_limit,10000). 0.64/0.96 assign(order,kbo). 0.64/0.96 set(lex_order_vars). 0.64/0.96 clear(print_given). 0.64/0.96 0.64/0.96 % formulas(sos). % not echoed (67 formulas) 0.64/0.96 0.64/0.96 ============================== end of input ========================== 0.64/0.96 0.64/0.96 % From the command line: assign(max_seconds, 960). 0.64/0.96 0.64/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.64/0.96 0.64/0.96 % Formulas that are not ordinary clauses: 0.64/0.96 1 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 2 (all X X = pidMsg(m_Halt(X))) # label(axiom_49) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 3 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 4 (all X1 all X2 all Y1 all Y2 (Y1 != Y2 -> m_Ack(X1,Y1) != m_Ack(X2,Y2))) # label(axiom_32) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 5 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 6 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 7 (all X all Y all Q (elem(X,Q) | Y = X <-> elem(X,cons(Y,Q)))) # label(axiom_46) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 8 (all X all Y all Q snoc(cons(X,Q),Y) = cons(X,snoc(Q,Y))) # label(axiom_44) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 9 (all Pid all Pid2 (elem(m_Ack(Pid,Pid2),queue(host(Pid))) -> setIn(Pid2,pids) & setIn(Pid,pids))) # label(axiom) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 10 (all X all Y (leq(X,s(Y)) <-> s(Y) = X | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 11 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 12 (all X ((exists Y (m_Halt(Y) = X | m_Down(Y) = X)) <-> pidElem(X))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 13 (all X all Y all Z (leq(Y,Z) & leq(X,Y) -> leq(X,Z))) # label(axiom_62) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 14 (all X all Y m_NotNorm(Y) != m_NormQ(X)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 15 (all X all Y all Z m_NotNorm(Z) != m_Ack(X,Y)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 16 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 17 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid2 != Pid)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 18 (all P all Q (host(Q) = s(host(P)) -> host(Q) != host(P))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 19 (all X all Y all Q (elem(X,Q) | X = Y <-> elem(X,snoc(Q,Y)))) # label(axiom_47) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 20 (all Q all X all Y (ordered(cons(m_Halt(X),Q)) & host(X) = host(Y) & elem(m_Down(Y),Q) -> leq(X,Y))) # label(axiom_57) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 21 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 22 (all X all Y m_Halt(Y) != m_NotNorm(X)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 23 (all X all Y (Y != X <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 24 (all X snoc(q_nil,X) = cons(X,q_nil)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 25 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 26 (all X all Y all Z m_Down(Z) != m_Ack(X,Y)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 27 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 28 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 29 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 30 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 31 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 32 (all X all Y m_Ldr(Y) != m_Down(X)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 33 (all X all Y (leq(Y,X) & leq(X,Y) <-> Y = X)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 34 (all X all Y m_NormQ(Y) != m_Down(X)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 35 (all X all Q (ordered(cons(X,Q)) <-> (all Y (pidElem(X) & pidElem(Y) & host(pidMsg(Y)) = host(pidMsg(X)) & elem(Y,Q) -> leq(pidMsg(X),pidMsg(Y)))) & ordered(Q))) # label(axiom_53) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 36 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 37 (all X all Q (ordered(snoc(Q,X)) <-> (all Y (elem(Y,Q) & pidElem(Y) & host(pidMsg(X)) = host(pidMsg(Y)) & pidElem(X) -> leq(pidMsg(Y),pidMsg(X)))) & ordered(Q))) # label(axiom_54) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 38 (all X all Y m_Halt(Y) != m_NormQ(X)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 39 (all X all Y (X != Y <-> m_NormQ(Y) != m_NormQ(X))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 40 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 41 (all X all Y m_Halt(Y) != m_Ldr(X)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 42 (all Q (cons(head(Q),tail(Q)) = Q | Q = q_nil)) # label(axiom_39) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 43 (all X all Q X = head(cons(X,Q))) # label(axiom_35) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 44 (all Q (Q = q_nil | snoc(init(Q),last(Q)) = Q)) # label(axiom_40) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 45 (all Y all Q Y = last(snoc(Q,Y))) # label(axiom_37) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 46 (all X all Y (m_NotNorm(Y) != m_NotNorm(X) <-> Y != X)) # label(axiom_28) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 47 (all X (ordered(snoc(q_nil,X)) & ordered(cons(X,q_nil)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 48 (all X1 all X2 all Y1 all Y2 (X2 != X1 -> m_Ack(X2,Y2) != m_Ack(X1,Y1))) # label(axiom_31) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 49 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption]. 0.64/0.96 50 (all X all Y m_NotNorm(Y) != m_Ldr(X)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption]. 0.64/0.97 51 (all Q all X all Y (ordered(Q) -> ordered(snoc(Q,m_Ack(X,Y))))) # label(axiom_55) # label(axiom) # label(non_clause). [assumption]. 0.64/0.97 52 (all X all Y (X != Y <-> m_Down(Y) != m_Down(X))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption]. 0.64/0.97 53 (all X all Y m_Halt(Y) != m_Down(X)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption]. 0.64/0.97 54 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption]. 0.64/0.97 55 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption]. 0.64/0.97 56 (all X all Y m_NotNorm(Y) != m_Down(X)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption]. 0.64/0.97 57 (all X all Y (m_Ldr(X) != m_Ldr(Y) <-> Y != X)) # label(axiom_29) # label(axiom) # label(non_clause). [assumption]. 0.64/0.97 58 -(all V all W all X ((all Y all Z (elec_1 = index(status,host(Z)) & setIn(Z,alive) -> -elem(m_Ack(Y,Z),queue(host(Y))))) & (all Y (setIn(Y,alive) & (elec_1 = index(status,host(Y)) | elec_2 = index(status,host(Y))) -> Y = index(elid,host(Y)))) & (all Y all Z all Pid0 (-leq(index(pendack,host(Pid0)),host(Y)) & setIn(Pid0,alive) & index(status,host(Pid0)) = elec_2 & elem(m_Halt(Pid0),queue(host(Z))) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & (all Y all Z all Pid0 (index(status,host(Pid0)) = elec_2 & host(Z) = index(pendack,host(Pid0)) & leq(nbr_proc,index(pendack,host(Pid0))) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & setIn(Pid0,alive) -> -(setIn(Y,alive) & norm = index(status,host(Y)) & index(ldr,host(Y)) = host(Y)))) & cons(m_Halt(X),V) = queue(host(W)) & (all Y all Z (setIn(Z,alive) & elec_2 = index(status,host(Y)) & elec_2 = index(status,host(Z)) & setIn(Y,alive) & -leq(host(Y),host(Z)) -> -leq(index(pendack,host(Y)),index(pendack,host(Z))))) & (all Y all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & host(Y) = host(Z) & elem(m_Ack(Pid0,Y),queue(host(Pid0))) -> -setIn(host(Pid0),index(down,host(Z))))) & (all Y all Z all Pid0 (elem(m_Down(Y),queue(host(Z))) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & host(Pid0) = host(Y) -> -setIn(Pid0,alive))) & (all Y all Z (setIn(Z,alive) & index(status,host(Z)) = elec_1 -> -elem(m_Ack(Z,Y),queue(host(Z))))) & (all Y all Z (setIn(Z,alive) & elem(m_Ack(Z,Y),queue(host(Z))) -> leq(host(Y),index(pendack,host(Z))))) & (all Y all Z (host(Z) = host(Y) & Y != Z -> -setIn(Z,alive) | -setIn(Y,alive))) & (all Y all Z (host(Y) = host(Z) & leq(Z,Y) & -setIn(Y,alive) -> -setIn(Z,alive))) & (all Y all Z all Pid0 (elem(m_Ack(Pid0,Y),queue(host(Z))) -> -leq(host(Y),host(Pid0)))) & (all Y all Z (elem(m_Ldr(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) & (all Y all Z (elem(m_Down(Z),queue(host(Y))) -> -setIn(Z,alive))) & (all Y all Z (elem(m_Ack(Z,Y),queue(host(Z))) -> setIn(Z,pids))) -> (setIn(W,alive) -> (all Y (host(Y) != host(W) -> (all Z all X0 (host(X0) = host(X) -> (host(W) != host(X0) -> (elec_2 = index(status,host(X0)) & index(pendack,host(X0)) = host(Z) & elem(m_Ack(X0,Z),snoc(queue(host(X0)),m_Ack(X,W))) & leq(nbr_proc,index(pendack,host(X0))) & setIn(X0,alive) -> -(index(ldr,host(Y)) = host(Y) & norm = index(status,host(Y)) & setIn(Y,alive))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption]. 0.64/0.97 0.64/0.97 ============================== end of process non-clausal formulas === 0.64/0.97 0.64/0.97 ============================== PROCESS INITIAL CLAUSES =============== 0.64/0.97 0.64/0.97 ============================== PREDICATE ELIMINATION ================= 0.64/0.97 0.64/0.97 ============================== end predicate elimination ============= 0.64/0.97 0.64/0.97 Auto_denials: (non-Horn, no changes). 0.64/0.97 0.64/0.97 Term ordering decisions: 0.64/0.97 Function symbol KB weights: alive=1. status=1. q_nil=1. pendack=1. elec_2=1. nbr_proc=1. pids=1. elid=1. ldr=1. norm=1. zero=1. elec_1=1. down=1. nil=1. setEmpty=1. wait=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. snoc=1. cons=1. index=1. m_Ack=1. f2=1. f3=1. host=1. pidMsg=1. s=1. m_Halt=1. m_Down=1. queue=1. m_Ldr=1. m_NormQ=1. m_NotNorm=1. head=1. init=1. last=1. tail=1. f1=1. 0.64/0.97 0.64/0.97 ============================== end of process initial clauses ======== 1.03/1.33 1.03/1.33 ============================== CLAUSES FOR SEARCH ==================== 1.03/1.33 1.03/1.33 ============================== end of clauses for search ============= 1.03/1.33 1.03/1.33 ============================== SEARCH ================================ 1.03/1.33 1.03/1.33 % Starting search at 0.02 seconds. 1.03/1.33 1.03/1.33 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 161 (0.00 of 0.27 sec). 1.03/1.33 1.03/1.33 ============================== PROOF ================================= 1.03/1.33 % SZS status Theorem 1.03/1.33 % SZS output start Refutation 1.03/1.33 1.03/1.33 % Proof 1 at 0.35 (+ 0.02) seconds. 1.03/1.33 % Length of proof is 62. 1.03/1.33 % Level of proof is 14. 1.03/1.33 % Maximum clause weight is 50.000. 1.03/1.33 % Given clauses 611. 1.03/1.33 1.03/1.33 2 (all X X = pidMsg(m_Halt(X))) # label(axiom_49) # label(axiom) # label(non_clause). [assumption]. 1.03/1.33 4 (all X1 all X2 all Y1 all Y2 (Y1 != Y2 -> m_Ack(X1,Y1) != m_Ack(X2,Y2))) # label(axiom_32) # label(axiom) # label(non_clause). [assumption]. 1.03/1.33 5 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption]. 1.03/1.33 7 (all X all Y all Q (elem(X,Q) | Y = X <-> elem(X,cons(Y,Q)))) # label(axiom_46) # label(axiom) # label(non_clause). [assumption]. 1.03/1.33 19 (all X all Y all Q (elem(X,Q) | X = Y <-> elem(X,snoc(Q,Y)))) # label(axiom_47) # label(axiom) # label(non_clause). [assumption]. 1.03/1.33 27 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption]. 1.03/1.33 33 (all X all Y (leq(Y,X) & leq(X,Y) <-> Y = X)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption]. 1.03/1.33 48 (all X1 all X2 all Y1 all Y2 (X2 != X1 -> m_Ack(X2,Y2) != m_Ack(X1,Y1))) # label(axiom_31) # label(axiom) # label(non_clause). [assumption]. 1.03/1.33 58 -(all V all W all X ((all Y all Z (elec_1 = index(status,host(Z)) & setIn(Z,alive) -> -elem(m_Ack(Y,Z),queue(host(Y))))) & (all Y (setIn(Y,alive) & (elec_1 = index(status,host(Y)) | elec_2 = index(status,host(Y))) -> Y = index(elid,host(Y)))) & (all Y all Z all Pid0 (-leq(index(pendack,host(Pid0)),host(Y)) & setIn(Pid0,alive) & index(status,host(Pid0)) = elec_2 & elem(m_Halt(Pid0),queue(host(Z))) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & (all Y all Z all Pid0 (index(status,host(Pid0)) = elec_2 & host(Z) = index(pendack,host(Pid0)) & leq(nbr_proc,index(pendack,host(Pid0))) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & setIn(Pid0,alive) -> -(setIn(Y,alive) & norm = index(status,host(Y)) & index(ldr,host(Y)) = host(Y)))) & cons(m_Halt(X),V) = queue(host(W)) & (all Y all Z (setIn(Z,alive) & elec_2 = index(status,host(Y)) & elec_2 = index(status,host(Z)) & setIn(Y,alive) & -leq(host(Y),host(Z)) -> -leq(index(pendack,host(Y)),index(pendack,host(Z))))) & (all Y all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & host(Y) = host(Z) & elem(m_Ack(Pid0,Y),queue(host(Pid0))) -> -setIn(host(Pid0),index(down,host(Z))))) & (all Y all Z all Pid0 (elem(m_Down(Y),queue(host(Z))) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & host(Pid0) = host(Y) -> -setIn(Pid0,alive))) & (all Y all Z (setIn(Z,alive) & index(status,host(Z)) = elec_1 -> -elem(m_Ack(Z,Y),queue(host(Z))))) & (all Y all Z (setIn(Z,alive) & elem(m_Ack(Z,Y),queue(host(Z))) -> leq(host(Y),index(pendack,host(Z))))) & (all Y all Z (host(Z) = host(Y) & Y != Z -> -setIn(Z,alive) | -setIn(Y,alive))) & (all Y all Z (host(Y) = host(Z) & leq(Z,Y) & -setIn(Y,alive) -> -setIn(Z,alive))) & (all Y all Z all Pid0 (elem(m_Ack(Pid0,Y),queue(host(Z))) -> -leq(host(Y),host(Pid0)))) & (all Y all Z (elem(m_Ldr(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) & (all Y all Z (elem(m_Down(Z),queue(host(Y))) -> -setIn(Z,alive))) & (all Y all Z (elem(m_Ack(Z,Y),queue(host(Z))) -> setIn(Z,pids))) -> (setIn(W,alive) -> (all Y (host(Y) != host(W) -> (all Z all X0 (host(X0) = host(X) -> (host(W) != host(X0) -> (elec_2 = index(status,host(X0)) & index(pendack,host(X0)) = host(Z) & elem(m_Ack(X0,Z),snoc(queue(host(X0)),m_Ack(X,W))) & leq(nbr_proc,index(pendack,host(X0))) & setIn(X0,alive) -> -(index(ldr,host(Y)) = host(Y) & norm = index(status,host(Y)) & setIn(Y,alive))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption]. 1.03/1.33 61 pidMsg(m_Halt(A)) = A # label(axiom_49) # label(axiom). [clausify(2)]. 1.03/1.33 63 A = B | m_Ack(C,A) != m_Ack(D,B) # label(axiom_32) # label(axiom). [clausify(4)]. 1.03/1.33 65 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(5)]. 1.03/1.33 68 A != B | elem(B,cons(A,C)) # label(axiom_46) # label(axiom). [clausify(7)]. 1.03/1.33 95 elem(A,B) | C = A | -elem(A,snoc(B,C)) # label(axiom_47) # label(axiom). [clausify(19)]. 1.03/1.33 105 leq(A,A) # label(axiom_59) # label(axiom). [clausify(27)]. 1.03/1.33 111 -leq(A,B) | -leq(B,A) | A = B # label(axiom_61) # label(axiom). [clausify(33)]. 1.03/1.33 146 A = B | m_Ack(A,C) != m_Ack(B,D) # label(axiom_31) # label(axiom). [clausify(48)]. 1.03/1.33 161 leq(index(pendack,host(A)),host(B)) | -setIn(A,alive) | index(status,host(A)) != elec_2 | -elem(m_Halt(A),queue(host(C))) | -setIn(B,alive) | index(ldr,host(B)) != host(B) | index(status,host(B)) != norm # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 162 index(status,host(A)) != elec_2 | index(pendack,host(A)) != host(B) | -leq(nbr_proc,index(pendack,host(A))) | -elem(m_Ack(A,B),queue(host(A))) | -setIn(A,alive) | -setIn(C,alive) | index(status,host(C)) != norm | index(ldr,host(C)) != host(C) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 163 queue(host(c2)) = cons(m_Halt(c3),c1) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 164 cons(m_Halt(c3),c1) = queue(host(c2)). [copy(163),flip(a)]. 1.03/1.33 176 host(c2) != host(c4) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 177 host(c4) != host(c2). [copy(176),flip(a)]. 1.03/1.33 178 host(c6) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 181 index(status,host(c6)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 182 elec_2 = index(status,host(c3)). [copy(181),rewrite([178(3)]),flip(a)]. 1.03/1.33 183 index(pendack,host(c6)) = host(c5) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 184 index(pendack,host(c3)) = host(c5). [copy(183),rewrite([178(3)])]. 1.03/1.33 185 elem(m_Ack(c6,c5),snoc(queue(host(c6)),m_Ack(c3,c2))) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 186 elem(m_Ack(c6,c5),snoc(queue(host(c3)),m_Ack(c3,c2))). [copy(185),rewrite([178(5)])]. 1.03/1.33 187 leq(nbr_proc,index(pendack,host(c6))) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 188 leq(nbr_proc,host(c5)). [copy(187),rewrite([178(4),184(5)])]. 1.03/1.33 189 setIn(c6,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 190 index(ldr,host(c4)) = host(c4) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 191 index(status,host(c4)) = norm # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 192 norm = index(status,host(c4)). [copy(191),flip(a)]. 1.03/1.33 193 setIn(c4,alive) # label(conj) # label(negated_conjecture). [clausify(58)]. 1.03/1.33 197 host(c4) = c_0. [new_symbol(177)]. 1.03/1.33 199 index(status,host(c3)) != index(status,host(A)) | index(pendack,host(A)) != host(B) | -leq(nbr_proc,index(pendack,host(A))) | -elem(m_Ack(A,B),queue(host(A))) | -setIn(A,alive) | -setIn(C,alive) | index(status,host(C)) != index(status,c_0) | index(ldr,host(C)) != host(C). [back_rewrite(162),rewrite([182(4),192(30),197(32)]),flip(a)]. 1.03/1.33 200 leq(index(pendack,host(A)),host(B)) | -setIn(A,alive) | index(status,host(c3)) != index(status,host(A)) | -elem(m_Halt(A),queue(host(C))) | -setIn(B,alive) | index(ldr,host(B)) != host(B) | index(status,host(B)) != index(status,c_0). [back_rewrite(161),rewrite([182(11),192(30),197(32)]),flip(c)]. 1.03/1.33 210 index(ldr,c_0) = c_0. [back_rewrite(190),rewrite([197(3),197(5)])]. 1.03/1.33 211 host(c2) != c_0. [back_rewrite(177),rewrite([197(2)]),flip(a)]. 1.03/1.33 213 elem(A,cons(A,B)). [resolve(68,a,61,a),rewrite([61(2)])]. 1.03/1.33 314 elem(m_Ack(c6,c5),queue(host(c3))) | m_Ack(c6,c5) = m_Ack(c3,c2). [resolve(186,a,95,c),flip(b)]. 1.03/1.33 317 host(c5) = nbr_proc. [resolve(188,a,111,b),unit_del(a,65)]. 1.03/1.33 318 index(pendack,host(c3)) = nbr_proc. [back_rewrite(184),rewrite([317(6)])]. 1.03/1.33 329 leq(c_0,nbr_proc). [para(197(a,1),65(a,1))]. 1.03/1.33 344 host(A) != nbr_proc | -elem(m_Ack(c6,A),queue(host(c3))) | -setIn(B,alive) | index(status,host(B)) != index(status,c_0) | index(ldr,host(B)) != host(B). [resolve(199,e,189,a),rewrite([178(7),178(12),318(13),178(16),318(17),178(19)]),flip(b),xx(a),unit_del(b,105)]. 1.03/1.33 349 leq(index(pendack,host(A)),c_0) | -setIn(A,alive) | index(status,host(c3)) != index(status,host(A)) | -elem(m_Halt(A),queue(host(B))). [resolve(200,e,193,a),rewrite([197(5),197(22),210(22),197(22),197(25)]),xx(e),xx(f)]. 1.03/1.33 360 -leq(nbr_proc,c_0) | c_0 = nbr_proc. [resolve(329,a,111,b),flip(b)]. 1.03/1.33 382 elem(m_Halt(c3),queue(host(c2))). [para(164(a,1),213(a,2))]. 1.03/1.33 663 host(A) != nbr_proc | -elem(m_Ack(c6,A),queue(host(c3))). [resolve(344,c,193,a),rewrite([197(12),197(19),210(19),197(19)]),xx(c),xx(d)]. 1.03/1.33 2541 m_Ack(c6,c5) = m_Ack(c3,c2). [resolve(314,a,663,b),rewrite([317(9)]),xx(b)]. 1.03/1.33 2567 c6 = c3. [resolve(2541,a,146,b)]. 1.03/1.33 2576 c5 = c2. [resolve(2541,a,63,b)]. 1.03/1.33 2605 setIn(c3,alive). [back_rewrite(189),rewrite([2567(1)])]. 1.03/1.33 2627 host(c2) = nbr_proc. [back_rewrite(317),rewrite([2576(1)])]. 1.03/1.33 2721 elem(m_Halt(c3),queue(nbr_proc)). [back_rewrite(382),rewrite([2627(4)])]. 1.03/1.33 2739 c_0 != nbr_proc. [back_rewrite(211),rewrite([2627(2)]),flip(a)]. 1.03/1.33 2742 -leq(nbr_proc,c_0). [back_unit_del(360),unit_del(b,2739)]. 1.03/1.33 2861 -elem(m_Halt(c3),queue(host(A))). [resolve(349,b,2605,a),rewrite([318(4)]),xx(b),unit_del(a,2742)]. 1.03/1.33 2865 $F. [para(2627(a,1),2861(a,2,1)),unit_del(a,2721)]. 1.03/1.33 1.03/1.33 % SZS output end Refutation 1.03/1.33 ============================== end of proof ========================== 1.03/1.33 1.03/1.33 ============================== STATISTICS ============================ 1.03/1.33 1.03/1.33 Given=611. Generated=11940. Kept=2794. proofs=1. 1.03/1.33 Usable=545. Sos=2000. Demods=32. Limbo=1, Disabled=373. Hints=0. 1.03/1.33 Megabytes=5.08. 1.03/1.33 User_CPU=0.35, System_CPU=0.02, Wall_clock=0. 1.03/1.33 1.03/1.33 ============================== end of statistics ===================== 1.03/1.33 1.03/1.33 ============================== end of search ========================= 1.03/1.33 1.03/1.33 THEOREM PROVED 1.03/1.33 % SZS status Theorem 1.03/1.33 1.03/1.33 Exiting with 1 proof. 1.03/1.33 1.03/1.33 Process 3812 exit (max_proofs) Tue Aug 9 04:01:21 2022 1.03/1.33 Prover9 interrupted 1.03/1.33 EOF