0.06/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command  : tptp2X_and_run_prover9 %d %s
0.11/0.33	% Computer : n029.cluster.edu
0.11/0.33	% Model    : x86_64 x86_64
0.11/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory   : 8042.1875MB
0.11/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit : 1440
0.11/0.33	% WCLimit  : 180
0.11/0.33	% DateTime : Mon Jul  3 08:26:42 EDT 2023
0.11/0.33	% CPUTime  : 
0.78/1.05	============================== Prover9 ===============================
0.78/1.05	Prover9 (32) version 2009-11A, November 2009.
0.78/1.05	Process 20606 was started by sandbox2 on n029.cluster.edu,
0.78/1.05	Mon Jul  3 08:26:43 2023
0.78/1.05	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_20453_n029.cluster.edu".
0.78/1.05	============================== end of head ===========================
0.78/1.05	
0.78/1.05	============================== INPUT =================================
0.78/1.05	
0.78/1.05	% Reading from file /tmp/Prover9_20453_n029.cluster.edu
0.78/1.05	
0.78/1.05	set(prolog_style_variables).
0.78/1.05	set(auto2).
0.78/1.05	    % set(auto2) -> set(auto).
0.78/1.05	    % set(auto) -> set(auto_inference).
0.78/1.05	    % set(auto) -> set(auto_setup).
0.78/1.05	    % set(auto_setup) -> set(predicate_elim).
0.78/1.05	    % set(auto_setup) -> assign(eq_defs, unfold).
0.78/1.05	    % set(auto) -> set(auto_limits).
0.78/1.05	    % set(auto_limits) -> assign(max_weight, "100.000").
0.78/1.05	    % set(auto_limits) -> assign(sos_limit, 20000).
0.78/1.05	    % set(auto) -> set(auto_denials).
0.78/1.05	    % set(auto) -> set(auto_process).
0.78/1.05	    % set(auto2) -> assign(new_constants, 1).
0.78/1.05	    % set(auto2) -> assign(fold_denial_max, 3).
0.78/1.05	    % set(auto2) -> assign(max_weight, "200.000").
0.78/1.05	    % set(auto2) -> assign(max_hours, 1).
0.78/1.05	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.78/1.05	    % set(auto2) -> assign(max_seconds, 0).
0.78/1.05	    % set(auto2) -> assign(max_minutes, 5).
0.78/1.05	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.78/1.05	    % set(auto2) -> set(sort_initial_sos).
0.78/1.05	    % set(auto2) -> assign(sos_limit, -1).
0.78/1.05	    % set(auto2) -> assign(lrs_ticks, 3000).
0.78/1.05	    % set(auto2) -> assign(max_megs, 400).
0.78/1.05	    % set(auto2) -> assign(stats, some).
0.78/1.05	    % set(auto2) -> clear(echo_input).
0.78/1.05	    % set(auto2) -> set(quiet).
0.78/1.05	    % set(auto2) -> clear(print_initial_clauses).
0.78/1.05	    % set(auto2) -> clear(print_given).
0.78/1.05	assign(lrs_ticks,-1).
0.78/1.05	assign(sos_limit,10000).
0.78/1.05	assign(order,kbo).
0.78/1.05	set(lex_order_vars).
0.78/1.05	clear(print_given).
0.78/1.05	
0.78/1.05	% formulas(sos).  % not echoed (67 formulas)
0.78/1.05	
0.78/1.05	============================== end of input ==========================
0.78/1.05	
0.78/1.05	% From the command line: assign(max_seconds, 1440).
0.78/1.05	
0.78/1.05	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.78/1.05	
0.78/1.05	% Formulas that are not ordinary clauses:
0.78/1.05	1 (all X1 all X2 all Y1 all Y2 (Y2 != Y1 -> m_Ack(X2,Y2) != m_Ack(X1,Y1))) # label(axiom_32) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	2 (all X all Y (m_Ldr(X) != m_Ldr(Y) <-> X != Y)) # label(axiom_29) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	3 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	4 (all X snoc(q_nil,X) = cons(X,q_nil)) # label(axiom_43) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	5 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	6 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	7 (all X all Q (ordered(cons(X,Q)) <-> ordered(Q) & (all Y (pidElem(Y) & host(pidMsg(X)) = host(pidMsg(Y)) & pidElem(X) & elem(Y,Q) -> leq(pidMsg(X),pidMsg(Y)))))) # label(axiom_53) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	8 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	9 (all X all Y all Z (leq(Y,Z) & leq(X,Y) -> leq(X,Z))) # label(axiom_62) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	10 (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].
0.78/1.05	11 (all X all Y all Z m_Halt(Z) != m_Ack(X,Y)) # label(axiom_11) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	12 (all X all Y all Z m_NotNorm(Z) != m_Ack(X,Y)) # label(axiom_13) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	13 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	14 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	15 (all X all Y (Y = X <-> leq(Y,X) & leq(X,Y))) # label(axiom_61) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	16 (all X all Q X = head(cons(X,Q))) # label(axiom_35) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	17 (all X all Q (ordered(snoc(Q,X)) <-> ordered(Q) & (all Y (elem(Y,Q) & pidElem(Y) & host(pidMsg(X)) = host(pidMsg(Y)) & pidElem(X) -> leq(pidMsg(Y),pidMsg(X)))))) # label(axiom_54) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	18 (all X1 all X2 all Y1 all Y2 (X1 != X2 -> m_Ack(X2,Y2) != m_Ack(X1,Y1))) # label(axiom_31) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	19 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	20 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	21 (all X all Y m_NormQ(Y) != m_Ldr(X)) # label(axiom_23) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	22 (all X X = pidMsg(m_Halt(X))) # label(axiom_49) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	23 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	24 (all Q (cons(head(Q),tail(Q)) = Q | Q = q_nil)) # label(axiom_39) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	25 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	26 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	27 (all P all Q (host(Q) = s(host(P)) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	28 (all Q all X all Y (elem(m_Down(Y),Q) & host(X) = host(Y) & ordered(cons(m_Halt(X),Q)) -> leq(X,Y))) # label(axiom_57) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	29 (all X all Y m_Halt(Y) != m_NotNorm(X)) # label(axiom_16) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	30 (all X all Y all Q (X = Y | elem(X,Q) <-> elem(X,cons(Y,Q)))) # label(axiom_46) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	31 (all X (pidElem(X) <-> (exists Y (m_Down(Y) = X | m_Halt(Y) = X)))) # label(axiom_48) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	32 (all X all Y (m_Halt(Y) != m_Halt(X) <-> Y != X)) # label(axiom_26) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	33 (all Q all X all Y (ordered(Q) -> ordered(snoc(Q,m_Ack(X,Y))))) # label(axiom_55) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	34 (all Y all Q Q = init(snoc(Q,Y))) # label(axiom_38) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	35 (all Q (Q = q_nil | snoc(init(Q),last(Q)) = Q)) # label(axiom_40) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	36 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	37 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	38 (all X all Y m_Halt(Y) != m_NormQ(X)) # label(axiom_21) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	39 (all X all Y (leq(s(X),s(Y)) <-> leq(X,Y))) # label(axiom_63) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	40 (all X all Y (m_Down(X) != m_Down(Y) <-> X != Y)) # label(axiom_30) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	41 (all X all Y m_NotNorm(Y) != m_Down(X)) # label(axiom_19) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	42 (all Y all Q Y = last(snoc(Q,Y))) # label(axiom_37) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	43 (all X all Y m_Ldr(X) != m_NotNorm(Y)) # label(axiom_24) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	44 (all X all Y (Y != X <-> m_NotNorm(X) != m_NotNorm(Y))) # label(axiom_28) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	45 (all X all Y m_NotNorm(Y) != m_NormQ(X)) # label(axiom_25) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	46 (all X all Y m_Ldr(Y) != m_Down(X)) # label(axiom_18) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	47 (all X all Y all Q (Y = X | elem(X,Q) <-> elem(X,snoc(Q,Y)))) # label(axiom_47) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	48 (all X all Y (leq(X,Y) | s(Y) = X <-> leq(X,s(Y)))) # label(axiom_64) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	49 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause).  [assumption].
0.78/1.05	50 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	51 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	52 (all X all Y all Z m_Ldr(Z) != m_Ack(X,Y)) # label(axiom_14) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	53 (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].
0.78/1.06	54 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	55 (all X all Y m_NormQ(Y) != m_Down(X)) # label(axiom_20) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	56 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	57 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	58 -(all V all W all X ((all Y all Z (elem(m_Down(Z),queue(host(Y))) -> host(Y) != host(Z))) & (all Y all Z (elem(m_Halt(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) & (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_Ack(Z,Y),queue(host(Z))) & setIn(Z,alive) -> leq(host(Y),index(pendack,host(Z))))) & (all Y all Z (setIn(Z,alive) & index(status,host(Z)) = elec_1 -> -elem(m_Ack(Z,Y),queue(host(Z))))) & (all Y (setIn(Y,alive) & (elec_2 = index(status,host(Y)) | elec_1 = index(status,host(Y))) -> Y = index(elid,host(Y)))) & (all Y all Z all Pid0 (setIn(Pid0,alive) & host(Pid0) = host(Z) & elec_2 = index(status,host(Y)) & index(status,host(Pid0)) = elec_2 & setIn(Y,alive) -> -elem(m_Ack(Y,Z),queue(host(Y))))) & cons(m_Halt(X),V) = queue(host(W)) & (all Y all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & index(pendack,host(Pid0)) = host(Z) & s(index(pendack,host(Pid0))) = host(Pid20) & index(status,host(Pid0)) = elec_2 & leq(nbr_proc,s(index(pendack,host(Pid0)))) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) -> -(setIn(Y,alive) & index(status,host(Y)) = norm & host(Y) = index(ldr,host(Y))))) & (all Y all Z all Pid20 all Pid0 (host(Pid0) = host(Z) & nbr_proc = host(Pid0) & elec_1 = index(status,host(Pid0)) & elem(m_Down(Pid20),queue(host(Pid0))) & (all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> host(Pid20) = V0 | setIn(V0,index(down,host(Pid0))))) -> -(elem(m_Down(Z),queue(host(Y))) & setIn(Y,alive)))) & (all Y all Z all Pid0 (index(status,host(Pid0)) = elec_2 & elem(m_Halt(Pid0),queue(host(Z))) & setIn(Pid0,alive) & -leq(index(pendack,host(Pid0)),host(Y)) -> -(norm = index(status,host(Y)) & host(Y) = index(ldr,host(Y)) & setIn(Y,alive)))) & (all Y all Z (-leq(host(Y),host(Z)) & setIn(Y,alive) & elec_2 = index(status,host(Z)) & index(status,host(Y)) = elec_2 & setIn(Z,alive) -> -leq(index(pendack,host(Y)),index(pendack,host(Z))))) & (all Y all Z all Pid0 (setIn(Pid0,alive) & host(Y) = host(Z) & elem(m_Down(Z),queue(host(Pid0))) -> -(host(Y) = index(ldr,host(Y)) & index(status,host(Y)) = norm & setIn(Y,alive)))) & (all Y all Z (setIn(Y,alive) & setIn(Z,alive) & index(status,host(Z)) = elec_2 & index(status,host(Y)) = elec_2 & -leq(host(Y),host(Z)) -> leq(index(pendack,host(Z)),host(Y)))) & (all Y all Z (host(Z) = host(Y) & Z != Y -> -setIn(Y,alive) | -setIn(Z,alive))) & (all Y all Z (elem(m_Ldr(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) -> (setIn(W,alive) -> (all Y (host(Y) != host(W) -> (all Z all X0 all Y0 (host(X) = host(Y0) -> (host(Y0) != host(W) -> (setIn(Y0,alive) & leq(nbr_proc,s(index(pendack,host(Y0)))) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ack(X,W))) & host(Z) = index(pendack,host(Y0)) & host(X0) = s(index(pendack,host(Y0))) & elec_2 = index(status,host(Y0)) & elem(m_Ack(Y0,Z),snoc(queue(host(Y0)),m_Ack(X,W))) -> -(setIn(Y,alive) & host(Y) = index(ldr,host(Y)) & index(status,host(Y)) = norm)))))))))) # label(conj) # label(negated_conjecture) # label(non_clause).  [assumption].
0.78/1.06	
0.78/1.06	============================== end of process non-clausal formulas ===
0.78/1.06	
0.78/1.06	============================== PROCESS INITIAL CLAUSES ===============
0.78/1.06	
0.78/1.06	============================== PREDICATE ELIMINATION =================
1.71/2.01	
1.71/2.01	============================== end predicate elimination =============
1.71/2.01	
1.71/2.01	Auto_denials:  (non-Horn, no changes).
1.71/2.01	
1.71/2.01	Term ordering decisions:
1.71/2.01	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. ldr=1. norm=1. pids=1. down=1. nil=1. setEmpty=1. wait=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. index=1. snoc=1. cons=1. m_Ack=1. f1=1. f2=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. f3=1. f4=1.
1.71/2.01	
1.71/2.01	============================== end of process initial clauses ========
1.71/2.01	
1.71/2.01	============================== CLAUSES FOR SEARCH ====================
1.71/2.01	
1.71/2.01	============================== end of clauses for search =============
1.71/2.01	
1.71/2.01	============================== SEARCH ================================
1.71/2.01	
1.71/2.01	% Starting search at 0.04 seconds.
1.71/2.01	
1.71/2.01	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 83 (0.00 of 0.30 sec).
1.71/2.01	
1.71/2.01	Low Water (keep): wt=20.000, iters=3402
1.71/2.01	
1.71/2.01	Low Water (keep): wt=19.000, iters=3397
1.71/2.01	
1.71/2.01	============================== PROOF =================================
1.71/2.01	% SZS status Theorem
1.71/2.01	% SZS output start Refutation
1.71/2.01	
1.71/2.01	% Proof 1 at 0.94 (+ 0.03) seconds.
1.71/2.01	% Length of proof is 80.
1.71/2.01	% Level of proof is 16.
1.71/2.01	% Maximum clause weight is 65.000.
1.71/2.01	% Given clauses 963.
1.71/2.01	
1.71/2.01	1 (all X1 all X2 all Y1 all Y2 (Y2 != Y1 -> m_Ack(X2,Y2) != m_Ack(X1,Y1))) # label(axiom_32) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	13 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	15 (all X all Y (Y = X <-> leq(Y,X) & leq(X,Y))) # label(axiom_61) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	18 (all X1 all X2 all Y1 all Y2 (X1 != X2 -> m_Ack(X2,Y2) != m_Ack(X1,Y1))) # label(axiom_31) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	22 (all X X = pidMsg(m_Halt(X))) # label(axiom_49) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	30 (all X all Y all Q (X = Y | elem(X,Q) <-> elem(X,cons(Y,Q)))) # label(axiom_46) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	36 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	37 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	47 (all X all Y all Q (Y = X | elem(X,Q) <-> elem(X,snoc(Q,Y)))) # label(axiom_47) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	48 (all X all Y (leq(X,Y) | s(Y) = X <-> leq(X,s(Y)))) # label(axiom_64) # label(axiom) # label(non_clause).  [assumption].
1.71/2.01	58 -(all V all W all X ((all Y all Z (elem(m_Down(Z),queue(host(Y))) -> host(Y) != host(Z))) & (all Y all Z (elem(m_Halt(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) & (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_Ack(Z,Y),queue(host(Z))) & setIn(Z,alive) -> leq(host(Y),index(pendack,host(Z))))) & (all Y all Z (setIn(Z,alive) & index(status,host(Z)) = elec_1 -> -elem(m_Ack(Z,Y),queue(host(Z))))) & (all Y (setIn(Y,alive) & (elec_2 = index(status,host(Y)) | elec_1 = index(status,host(Y))) -> Y = index(elid,host(Y)))) & (all Y all Z all Pid0 (setIn(Pid0,alive) & host(Pid0) = host(Z) & elec_2 = index(status,host(Y)) & index(status,host(Pid0)) = elec_2 & setIn(Y,alive) -> -elem(m_Ack(Y,Z),queue(host(Y))))) & cons(m_Halt(X),V) = queue(host(W)) & (all Y all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & index(pendack,host(Pid0)) = host(Z) & s(index(pendack,host(Pid0))) = host(Pid20) & index(status,host(Pid0)) = elec_2 & leq(nbr_proc,s(index(pendack,host(Pid0)))) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) -> -(setIn(Y,alive) & index(status,host(Y)) = norm & host(Y) = index(ldr,host(Y))))) & (all Y all Z all Pid20 all Pid0 (host(Pid0) = host(Z) & nbr_proc = host(Pid0) & elec_1 = index(status,host(Pid0)) & elem(m_Down(Pid20),queue(host(Pid0))) & (all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> host(Pid20) = V0 | setIn(V0,index(down,host(Pid0))))) -> -(elem(m_Down(Z),queue(host(Y))) & setIn(Y,alive)))) & (all Y all Z all Pid0 (index(status,host(Pid0)) = elec_2 & elem(m_Halt(Pid0),queue(host(Z))) & setIn(Pid0,alive) & -leq(index(pendack,host(Pid0)),host(Y)) -> -(norm = index(status,host(Y)) & host(Y) = index(ldr,host(Y)) & setIn(Y,alive)))) & (all Y all Z (-leq(host(Y),host(Z)) & setIn(Y,alive) & elec_2 = index(status,host(Z)) & index(status,host(Y)) = elec_2 & setIn(Z,alive) -> -leq(index(pendack,host(Y)),index(pendack,host(Z))))) & (all Y all Z all Pid0 (setIn(Pid0,alive) & host(Y) = host(Z) & elem(m_Down(Z),queue(host(Pid0))) -> -(host(Y) = index(ldr,host(Y)) & index(status,host(Y)) = norm & setIn(Y,alive)))) & (all Y all Z (setIn(Y,alive) & setIn(Z,alive) & index(status,host(Z)) = elec_2 & index(status,host(Y)) = elec_2 & -leq(host(Y),host(Z)) -> leq(index(pendack,host(Z)),host(Y)))) & (all Y all Z (host(Z) = host(Y) & Z != Y -> -setIn(Y,alive) | -setIn(Z,alive))) & (all Y all Z (elem(m_Ldr(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) -> (setIn(W,alive) -> (all Y (host(Y) != host(W) -> (all Z all X0 all Y0 (host(X) = host(Y0) -> (host(Y0) != host(W) -> (setIn(Y0,alive) & leq(nbr_proc,s(index(pendack,host(Y0)))) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ack(X,W))) & host(Z) = index(pendack,host(Y0)) & host(X0) = s(index(pendack,host(Y0))) & elec_2 = index(status,host(Y0)) & elem(m_Ack(Y0,Z),snoc(queue(host(Y0)),m_Ack(X,W))) -> -(setIn(Y,alive) & host(Y) = index(ldr,host(Y)) & index(status,host(Y)) = norm)))))))))) # label(conj) # label(negated_conjecture) # label(non_clause).  [assumption].
1.71/2.01	59 A = B | m_Ack(C,A) != m_Ack(D,B) # label(axiom_32) # label(axiom).  [clausify(1)].
1.71/2.01	82 m_Down(A) != m_Ack(B,C) # label(axiom_12) # label(axiom).  [clausify(13)].
1.71/2.01	88 A = B | -leq(A,B) | -leq(B,A) # label(axiom_61) # label(axiom).  [clausify(15)].
1.71/2.01	97 A = B | m_Ack(A,C) != m_Ack(B,D) # label(axiom_31) # label(axiom).  [clausify(18)].
1.71/2.01	102 pidMsg(m_Halt(A)) = A # label(axiom_49) # label(axiom).  [clausify(22)].
1.71/2.01	110 A != B | elem(B,cons(A,C)) # label(axiom_46) # label(axiom).  [clausify(30)].
1.71/2.01	121 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom).  [clausify(36)].
1.71/2.01	123 leq(A,A) # label(axiom_59) # label(axiom).  [clausify(37)].
1.71/2.01	138 A = B | elem(B,C) | -elem(B,snoc(C,A)) # label(axiom_47) # label(axiom).  [clausify(47)].
1.71/2.01	140 leq(A,B) | s(B) = A | -leq(A,s(B)) # label(axiom_64) # label(axiom).  [clausify(48)].
1.71/2.01	163 queue(host(c2)) = cons(m_Halt(c3),c1) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	164 cons(m_Halt(c3),c1) = queue(host(c2)).  [copy(163),flip(a)].
1.71/2.01	165 -setIn(A,alive) | -elem(m_Down(B),queue(host(A))) | index(pendack,host(A)) != host(C) | s(index(pendack,host(A))) != host(B) | index(status,host(A)) != elec_2 | -leq(nbr_proc,s(index(pendack,host(A)))) | -elem(m_Ack(A,C),queue(host(A))) | -setIn(D,alive) | index(status,host(D)) != norm | index(ldr,host(D)) != host(D) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	171 index(status,host(A)) != elec_2 | -elem(m_Halt(A),queue(host(B))) | -setIn(A,alive) | leq(index(pendack,host(A)),host(C)) | index(status,host(C)) != norm | index(ldr,host(C)) != host(C) | -setIn(C,alive) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	173 -setIn(A,alive) | host(B) != host(C) | -elem(m_Down(B),queue(host(A))) | index(ldr,host(C)) != host(C) | index(status,host(C)) != norm | -setIn(C,alive) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	178 host(c2) != host(c4) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	179 host(c4) != host(c2).  [copy(178),flip(a)].
1.71/2.01	180 host(c7) = host(c3) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	183 setIn(c7,alive) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	184 leq(nbr_proc,s(index(pendack,host(c7)))) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	185 leq(nbr_proc,s(index(pendack,host(c3)))).  [copy(184),rewrite([180(4)])].
1.71/2.01	186 elem(m_Down(c6),snoc(queue(host(c7)),m_Ack(c3,c2))) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	187 elem(m_Down(c6),snoc(queue(host(c3)),m_Ack(c3,c2))).  [copy(186),rewrite([180(4)])].
1.71/2.01	188 index(pendack,host(c7)) = host(c5) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	189 index(pendack,host(c3)) = host(c5).  [copy(188),rewrite([180(3)])].
1.71/2.01	190 s(index(pendack,host(c7))) = host(c6) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	191 s(host(c5)) = host(c6).  [copy(190),rewrite([180(3),189(4)])].
1.71/2.01	192 index(status,host(c7)) = elec_2 # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	193 elec_2 = index(status,host(c3)).  [copy(192),rewrite([180(3)]),flip(a)].
1.71/2.01	194 elem(m_Ack(c7,c5),snoc(queue(host(c7)),m_Ack(c3,c2))) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	195 elem(m_Ack(c7,c5),snoc(queue(host(c3)),m_Ack(c3,c2))).  [copy(194),rewrite([180(5)])].
1.71/2.01	196 setIn(c4,alive) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	197 index(ldr,host(c4)) = host(c4) # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	198 index(status,host(c4)) = norm # label(conj) # label(negated_conjecture).  [clausify(58)].
1.71/2.01	199 norm = index(status,host(c4)).  [copy(198),flip(a)].
1.71/2.01	207 host(c4) = c_0.  [new_symbol(179)].
1.71/2.01	208 leq(nbr_proc,host(c6)).  [back_rewrite(185),rewrite([189(5),191(4)])].
1.71/2.01	211 index(status,host(c3)) != index(status,host(A)) | -elem(m_Halt(A),queue(host(B))) | -setIn(A,alive) | leq(index(pendack,host(A)),host(C)) | index(status,host(C)) != index(status,c_0) | index(ldr,host(C)) != host(C) | -setIn(C,alive).  [back_rewrite(171),rewrite([193(4),199(23),207(25)]),flip(a)].
1.71/2.01	212 -setIn(A,alive) | -elem(m_Down(B),queue(host(A))) | index(pendack,host(A)) != host(C) | s(index(pendack,host(A))) != host(B) | index(status,host(c3)) != index(status,host(A)) | -leq(nbr_proc,s(index(pendack,host(A)))) | -elem(m_Ack(A,C),queue(host(A))) | -setIn(D,alive) | index(status,host(D)) != index(status,c_0) | index(ldr,host(D)) != host(D).  [back_rewrite(165),rewrite([193(21),199(41),207(43)]),flip(e)].
1.71/2.01	218 -setIn(A,alive) | host(B) != host(C) | -elem(m_Down(B),queue(host(A))) | index(ldr,host(C)) != host(C) | index(status,host(C)) != index(status,c_0) | -setIn(C,alive).  [back_rewrite(173),rewrite([199(18),207(20)])].
1.71/2.01	224 index(ldr,c_0) = c_0.  [back_rewrite(197),rewrite([207(3),207(5)])].
1.71/2.01	225 host(c2) != c_0.  [back_rewrite(179),rewrite([207(2)]),flip(a)].
1.71/2.01	250 elem(A,cons(A,B)).  [resolve(110,a,102,a),rewrite([102(2)])].
1.71/2.01	331 elem(m_Down(c6),queue(host(c3))).  [resolve(187,a,138,c),unit_del(a(flip),82)].
1.71/2.01	342 leq(A,host(c5)) | host(c6) = A | -leq(A,host(c6)).  [para(191(a,1),140(c,2)),rewrite([191(6)])].
1.71/2.01	343 m_Ack(c7,c5) = m_Ack(c3,c2) | elem(m_Ack(c7,c5),queue(host(c3))).  [resolve(195,a,138,c),flip(a)].
1.71/2.01	359 leq(c_0,nbr_proc).  [para(207(a,1),121(a,1))].
1.71/2.01	367 host(c6) = nbr_proc.  [resolve(208,a,88,c),unit_del(b,121)].
1.71/2.01	368 leq(A,host(c5)) | nbr_proc = A | -leq(A,nbr_proc).  [back_rewrite(342),rewrite([367(5),367(7)])].
1.71/2.01	377 s(host(c5)) = nbr_proc.  [back_rewrite(191),rewrite([367(5)])].
1.71/2.01	388 index(status,host(c3)) != index(status,host(A)) | -elem(m_Halt(A),queue(host(B))) | -setIn(A,alive) | leq(index(pendack,host(A)),c_0).  [resolve(211,g,196,a),rewrite([207(19),207(22),207(29),224(29),207(29)]),xx(e),xx(f)].
1.71/2.01	390 -elem(m_Down(A),queue(host(c3))) | host(c5) != host(B) | host(A) != nbr_proc | -elem(m_Ack(c7,B),queue(host(c3))) | -setIn(C,alive) | index(status,host(C)) != index(status,c_0) | index(ldr,host(C)) != host(C).  [resolve(212,a,183,a),rewrite([180(3),180(8),189(9),180(12),189(13),377(12),180(19),180(25),189(26),377(25),180(28)]),flip(c),xx(d),unit_del(d,123)].
1.71/2.01	402 -setIn(A,alive) | host(B) != c_0 | -elem(m_Down(B),queue(host(A))).  [resolve(218,f,196,a),rewrite([207(5),207(12),224(12),207(12),207(15)]),xx(d),xx(e)].
1.71/2.01	453 elem(m_Halt(c3),queue(host(c2))).  [para(164(a,1),250(a,2))].
1.71/2.01	546 host(A) != c_0 | -elem(m_Down(A),queue(host(c3))).  [resolve(402,a,183,a),rewrite([180(6)])].
1.71/2.01	569 c_0 != nbr_proc.  [resolve(331,a,546,b),rewrite([367(2)]),flip(a)].
1.71/2.01	776 -elem(m_Down(A),queue(host(c3))) | host(c5) != host(B) | host(A) != nbr_proc | -elem(m_Ack(c7,B),queue(host(c3))).  [resolve(390,e,196,a),rewrite([207(21),207(28),224(28),207(28)]),xx(e),xx(f)].
1.71/2.01	790 host(c5) != host(A) | -elem(m_Ack(c7,A),queue(host(c3))).  [resolve(776,a,331,a),rewrite([367(6)]),xx(b)].
1.71/2.01	2454 m_Ack(c7,c5) = m_Ack(c3,c2).  [resolve(343,b,790,b),xx(b)].
1.71/2.01	2455 c7 = c3.  [resolve(2454,a,97,b)].
1.71/2.01	2460 c5 = c2.  [resolve(2454,a,59,b)].
1.71/2.01	2528 setIn(c3,alive).  [back_rewrite(183),rewrite([2455(1)])].
1.71/2.01	2591 leq(A,host(c2)) | nbr_proc = A | -leq(A,nbr_proc).  [back_rewrite(368),rewrite([2460(1)])].
1.71/2.01	2592 index(pendack,host(c3)) = host(c2).  [back_rewrite(189),rewrite([2460(5)])].
1.71/2.01	2774 -elem(m_Halt(c3),queue(host(A))) | leq(host(c2),c_0).  [resolve(388,c,2528,a),rewrite([2592(18)]),xx(a)].
1.71/2.01	5721 leq(c_0,host(c2)).  [resolve(2591,c,359,a),flip(b),unit_del(b,569)].
1.71/2.01	5728 -leq(host(c2),c_0).  [resolve(5721,a,88,c),unit_del(a,225)].
1.71/2.01	5731 -elem(m_Halt(c3),queue(host(A))).  [back_unit_del(2774),unit_del(b,5728)].
1.71/2.01	5732 $F.  [resolve(5731,a,453,a)].
1.71/2.01	
1.71/2.01	% SZS output end Refutation
1.71/2.01	============================== end of proof ==========================
1.71/2.01	
1.71/2.01	============================== STATISTICS ============================
1.71/2.01	
1.71/2.01	Given=963. Generated=37734. Kept=5660. proofs=1.
1.71/2.01	Usable=907. Sos=4465. Demods=36. Limbo=3, Disabled=414. Hints=0.
1.71/2.01	Megabytes=8.88.
1.71/2.01	User_CPU=0.95, System_CPU=0.03, Wall_clock=1.
1.71/2.01	
1.71/2.01	============================== end of statistics =====================
1.71/2.01	
1.71/2.01	============================== end of search =========================
1.71/2.01	
1.71/2.01	THEOREM PROVED
1.71/2.01	% SZS status Theorem
1.71/2.01	
1.71/2.01	Exiting with 1 proof.
1.71/2.01	
1.71/2.01	Process 20606 exit (max_proofs) Mon Jul  3 08:26:44 2023
1.71/2.01	Prover9 interrupted
1.71/2.01	EOF