0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.34	% Computer   : n011.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 1200
0.12/0.34	% DateTime   : Wed Jul 14 14:48:25 EDT 2021
0.12/0.34	% CPUTime    : 
0.45/1.06	============================== Prover9 ===============================
0.45/1.06	Prover9 (32) version 2009-11A, November 2009.
0.45/1.06	Process 6142 was started by sandbox on n011.cluster.edu,
0.45/1.06	Wed Jul 14 14:48:25 2021
0.45/1.06	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_5981_n011.cluster.edu".
0.45/1.06	============================== end of head ===========================
0.45/1.06	
0.45/1.06	============================== INPUT =================================
0.45/1.06	
0.45/1.06	% Reading from file /tmp/Prover9_5981_n011.cluster.edu
0.45/1.06	
0.45/1.06	set(prolog_style_variables).
0.45/1.06	set(auto2).
0.45/1.06	    % set(auto2) -> set(auto).
0.45/1.06	    % set(auto) -> set(auto_inference).
0.45/1.06	    % set(auto) -> set(auto_setup).
0.45/1.06	    % set(auto_setup) -> set(predicate_elim).
0.45/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.45/1.06	    % set(auto) -> set(auto_limits).
0.45/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.45/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.45/1.06	    % set(auto) -> set(auto_denials).
0.45/1.06	    % set(auto) -> set(auto_process).
0.45/1.06	    % set(auto2) -> assign(new_constants, 1).
0.45/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.45/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.45/1.06	    % set(auto2) -> assign(max_hours, 1).
0.45/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.45/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.45/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.45/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.45/1.06	    % set(auto2) -> set(sort_initial_sos).
0.45/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.45/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.45/1.06	    % set(auto2) -> assign(max_megs, 400).
0.45/1.06	    % set(auto2) -> assign(stats, some).
0.45/1.06	    % set(auto2) -> clear(echo_input).
0.45/1.06	    % set(auto2) -> set(quiet).
0.45/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.45/1.06	    % set(auto2) -> clear(print_given).
0.45/1.06	assign(lrs_ticks,-1).
0.45/1.06	assign(sos_limit,10000).
0.45/1.06	assign(order,kbo).
0.45/1.06	set(lex_order_vars).
0.45/1.06	clear(print_given).
0.45/1.06	
0.45/1.06	% formulas(sos).  % not echoed (67 formulas)
0.45/1.06	
0.45/1.06	============================== end of input ==========================
0.45/1.06	
0.45/1.06	% From the command line: assign(max_seconds, 1200).
0.45/1.06	
0.45/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.45/1.06	
0.45/1.06	% Formulas that are not ordinary clauses:
0.45/1.06	1 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	2 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	4 (all X all Y all Z m_Down(Z) != m_Ack(X,Y)) # label(axiom_12) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	5 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	6 (all X all Q X = head(cons(X,Q))) # label(axiom_35) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	7 (all X all Y all Z (leq(X,Y) & leq(Y,Z) -> leq(X,Z))) # label(axiom_62) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	8 (all Q (cons(head(Q),tail(Q)) = Q | q_nil = Q)) # label(axiom_39) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	9 (all X all Y (X != Y <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	10 (all Pid all Pid2 (host(Pid2) != host(Pid) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	11 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	12 (all X all Y (leq(Y,X) | leq(X,Y))) # label(axiom_60) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	13 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	14 (all X all Y (m_NormQ(Y) != m_NormQ(X) <-> X != Y)) # label(axiom_27) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	15 (all X all Y all Z m_Halt(Z) != m_Ack(X,Y)) # label(axiom_11) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	16 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	17 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	18 (all X1 all X2 all Y1 all Y2 (Y2 != Y1 -> m_Ack(X1,Y1) != m_Ack(X2,Y2))) # label(axiom_32) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	19 (all X (pidElem(X) <-> (exists Y (X = m_Down(Y) | m_Halt(Y) = X)))) # label(axiom_48) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	20 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	21 (all X all Y (X = s(Y) | leq(X,Y) <-> leq(X,s(Y)))) # label(axiom_64) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	22 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	23 (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].
0.45/1.06	24 (all X all Y (m_NotNorm(X) != m_NotNorm(Y) <-> X != Y)) # label(axiom_28) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	25 (all Y all Q last(snoc(Q,Y)) = Y) # label(axiom_37) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	26 (all X all Y (X != Y <-> m_Ldr(Y) != m_Ldr(X))) # label(axiom_29) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	27 (all X all Y all Q (elem(X,Q) | Y = X <-> elem(X,snoc(Q,Y)))) # label(axiom_47) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	28 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	29 (all Q (Q = snoc(init(Q),last(Q)) | q_nil = Q)) # label(axiom_40) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	30 (all X cons(X,q_nil) = snoc(q_nil,X)) # label(axiom_43) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	31 (all X all Y (X = Y <-> leq(X,Y) & leq(Y,X))) # label(axiom_61) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	32 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	33 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	34 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	35 (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].
0.45/1.06	36 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	37 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	38 (all X all Y m_NotNorm(X) != m_Halt(Y)) # label(axiom_16) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	39 (all X all Y all Q (elem(X,cons(Y,Q)) <-> X = Y | elem(X,Q))) # label(axiom_46) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	40 (all X all Y m_NormQ(Y) != m_Down(X)) # label(axiom_20) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	41 (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].
0.45/1.06	42 (all X all Y all Z m_NormQ(Z) != m_Ack(X,Y)) # label(axiom_15) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	43 (all X all Y (m_Down(Y) != m_Down(X) <-> Y != X)) # label(axiom_30) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	44 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	45 (all Y all Q Q = init(snoc(Q,Y))) # label(axiom_38) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	46 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	47 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	48 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	49 (all Q all X all Y (ordered(Q) -> ordered(snoc(Q,m_Ack(X,Y))))) # label(axiom_55) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	50 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause).  [assumption].
0.45/1.06	52 (all X all Y m_NotNorm(Y) != m_Ldr(X)) # label(axiom_24) # label(axiom) # label(non_clause).  [assumption].
0.45/1.08	53 (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].
0.45/1.08	54 (all X all Y (leq(s(X),s(Y)) <-> leq(X,Y))) # label(axiom_63) # label(axiom) # label(non_clause).  [assumption].
0.45/1.08	55 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause).  [assumption].
0.45/1.08	56 (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].
0.45/1.08	57 (all X all Q ((all Y (elem(Y,Q) & pidElem(X) & host(pidMsg(Y)) = host(pidMsg(X)) & pidElem(Y) -> leq(pidMsg(Y),pidMsg(X)))) & ordered(Q) <-> ordered(snoc(Q,X)))) # label(axiom_54) # label(axiom) # label(non_clause).  [assumption].
0.45/1.08	58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Halt(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid20 all Pid0 (elem(m_Ack(Pid0,Z),queue(host(Pid20))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (setIn(Pid0,alive) & elec_2 = index(status,host(Pid0)) -> -elem(m_Ack(Z,Pid0),queue(host(Z))))) & (all Z all Pid0 (setIn(Pid0,alive) & setIn(host(Pid0),index(down,host(Z))) & elec_2 = index(status,host(Pid0)) & setIn(Z,alive) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (setIn(Pid0,alive) & elec_2 = index(status,host(Z)) & elec_2 = index(status,host(Pid0)) & setIn(Z,alive) & -leq(host(Z),host(Pid0)) -> -leq(index(pendack,host(Z)),index(pendack,host(Pid0))))) & cons(m_Down(Y),V) = queue(host(X)) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Z))) & index(status,host(Pid0)) = elec_2 & host(Pid0) = host(Pid20) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & elec_2 = index(status,host(Z)) & elec_2 = index(status,host(Pid0)) & host(Pid20) = host(Pid0) -> -elem(m_Ack(Z,Pid20),queue(host(Z))))) & (all Z all Pid0 (-leq(host(Z),host(Pid0)) & setIn(Pid0,alive) & elec_2 = index(status,host(Pid0)) & elec_2 = index(status,host(Z)) & setIn(Z,alive) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (-leq(host(Pid0),host(Z)) & setIn(Z,alive) & host(Pid20) = host(Pid0) & elec_2 = index(status,host(Pid0)) & setIn(Pid0,alive) -> -elem(m_Down(Pid20),queue(host(Z))))) & (all Z ((elec_2 = index(status,host(Z)) | index(status,host(Z)) = elec_1) & setIn(Z,alive) -> Z = index(elid,host(Z)))) & (all Z all Pid0 (Z != Pid0 & host(Pid0) = host(Z) -> -setIn(Pid0,alive) | -setIn(Z,alive))) & (all Z (index(status,host(Z)) = elec_2 -> -leq(index(pendack,host(Z)),host(Z)))) -> (setIn(X,alive) -> (-leq(host(X),host(Y)) -> (-(index(ldr,host(X)) = host(Y) & index(status,host(X)) = norm | host(Y) = host(index(elid,host(X))) & index(status,host(X)) = wait) -> (index(status,host(X)) = elec_1 & (all Z (-leq(host(X),Z) & leq(s(zero),Z) -> setIn(Z,index(down,host(X))) | host(Y) = Z)) -> (-leq(nbr_proc,host(X)) -> (all Z (host(X) = host(Z) -> (all W0 (host(W0) != host(X) -> (-leq(host(Z),host(W0)) & elec_2 = index(status,host(W0)) & setIn(W0,alive) & setIn(Z,alive) -> -leq(s(host(X)),index(pendack,host(W0))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause).  [assumption].
0.45/1.08	
0.45/1.08	============================== end of process non-clausal formulas ===
0.45/1.08	
0.45/1.08	============================== PROCESS INITIAL CLAUSES ===============
0.45/1.08	
0.45/1.08	============================== PREDICATE ELIMINATION =================
0.45/1.08	
0.45/1.08	============================== end predicate elimination =============
0.45/1.08	
0.45/1.08	Auto_denials:  (non-Horn, no changes).
0.45/1.08	
0.45/1.08	Term ordering decisions:
0.45/1.08	Function symbol KB weights:  alive=1. status=1. elec_2=1. q_nil=1. pendack=1. zero=1. down=1. elec_1=1. elid=1. nbr_proc=1. pids=1. ldr=1. nil=1. norm=1. setEmpty=1. wait=1. c1=1. c3=1. c4=1. c5=1. c6=1. index=1. cons=1. snoc=1. m_Ack=1. f2=1. f3=1. host=1. pidMsg=1. s=1. m_Down=1. m_Halt=1. m_Ldr=1. queue=1. m_NormQ=1. m_NotNorm=1. head=1. init=1. last=1. tail=1. f1=1.
0.45/1.08	
0.45/1.08	============================== end of process initial clauses ========
17.70/17.99	
17.70/17.99	============================== CLAUSES FOR SEARCH ====================
17.70/17.99	
17.70/17.99	============================== end of clauses for search =============
17.70/17.99	
17.70/17.99	============================== SEARCH ================================
17.70/17.99	
17.70/17.99	% Starting search at 0.03 seconds.
17.70/17.99	
17.70/17.99	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 151 (0.00 of 0.46 sec).
17.70/17.99	
17.70/17.99	Low Water (keep): wt=22.000, iters=3918
17.70/17.99	
17.70/17.99	Low Water (keep): wt=18.000, iters=3522
17.70/17.99	
17.70/17.99	Low Water (keep): wt=16.000, iters=5254
17.70/17.99	
17.70/17.99	Low Water (keep): wt=15.000, iters=4033
17.70/17.99	
17.70/17.99	Low Water (keep): wt=14.000, iters=3368
17.70/17.99	
17.70/17.99	Low Water (displace): id=5263, wt=112.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=5181, wt=108.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=5317, wt=92.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=5951, wt=90.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=6083, wt=83.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=6022, wt=73.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=5869, wt=71.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=6125, wt=69.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=5262, wt=62.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=6025, wt=60.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=6124, wt=59.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=16108, wt=57.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=15926, wt=56.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=15899, wt=55.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=16164, wt=54.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=16147, wt=53.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=17016, wt=52.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=15901, wt=51.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=16122, wt=50.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=17269, wt=49.000
17.70/17.99	
17.70/17.99	Low Water (displace): id=17486, wt=48.000
17.70/17.99	
17.70/17.99	============================== PROOF =================================
17.70/17.99	% SZS status Theorem
17.70/17.99	% SZS output start Refutation
17.70/17.99	
17.70/17.99	% Proof 1 at 16.29 (+ 0.65) seconds.
17.70/17.99	% Length of proof is 86.
17.70/17.99	% Level of proof is 14.
17.70/17.99	% Maximum clause weight is 33.000.
17.70/17.99	% Given clauses 6330.
17.70/17.99	
17.70/17.99	2 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	6 (all X all Q X = head(cons(X,Q))) # label(axiom_35) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	7 (all X all Y all Z (leq(X,Y) & leq(Y,Z) -> leq(X,Z))) # label(axiom_62) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	8 (all Q (cons(head(Q),tail(Q)) = Q | q_nil = Q)) # label(axiom_39) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	10 (all Pid all Pid2 (host(Pid2) != host(Pid) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	12 (all X all Y (leq(Y,X) | leq(X,Y))) # label(axiom_60) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	13 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	20 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	29 (all Q (Q = snoc(init(Q),last(Q)) | q_nil = Q)) # label(axiom_40) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	31 (all X all Y (X = Y <-> leq(X,Y) & leq(Y,X))) # label(axiom_61) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	35 (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].
17.70/17.99	37 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	39 (all X all Y all Q (elem(X,cons(Y,Q)) <-> X = Y | elem(X,Q))) # label(axiom_46) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	45 (all Y all Q Q = init(snoc(Q,Y))) # label(axiom_38) # label(axiom) # label(non_clause).  [assumption].
17.70/17.99	58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Halt(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid20 all Pid0 (elem(m_Ack(Pid0,Z),queue(host(Pid20))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (setIn(Pid0,alive) & elec_2 = index(status,host(Pid0)) -> -elem(m_Ack(Z,Pid0),queue(host(Z))))) & (all Z all Pid0 (setIn(Pid0,alive) & setIn(host(Pid0),index(down,host(Z))) & elec_2 = index(status,host(Pid0)) & setIn(Z,alive) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (setIn(Pid0,alive) & elec_2 = index(status,host(Z)) & elec_2 = index(status,host(Pid0)) & setIn(Z,alive) & -leq(host(Z),host(Pid0)) -> -leq(index(pendack,host(Z)),index(pendack,host(Pid0))))) & cons(m_Down(Y),V) = queue(host(X)) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Z))) & index(status,host(Pid0)) = elec_2 & host(Pid0) = host(Pid20) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & elec_2 = index(status,host(Z)) & elec_2 = index(status,host(Pid0)) & host(Pid20) = host(Pid0) -> -elem(m_Ack(Z,Pid20),queue(host(Z))))) & (all Z all Pid0 (-leq(host(Z),host(Pid0)) & setIn(Pid0,alive) & elec_2 = index(status,host(Pid0)) & elec_2 = index(status,host(Z)) & setIn(Z,alive) -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (-leq(host(Pid0),host(Z)) & setIn(Z,alive) & host(Pid20) = host(Pid0) & elec_2 = index(status,host(Pid0)) & setIn(Pid0,alive) -> -elem(m_Down(Pid20),queue(host(Z))))) & (all Z ((elec_2 = index(status,host(Z)) | index(status,host(Z)) = elec_1) & setIn(Z,alive) -> Z = index(elid,host(Z)))) & (all Z all Pid0 (Z != Pid0 & host(Pid0) = host(Z) -> -setIn(Pid0,alive) | -setIn(Z,alive))) & (all Z (index(status,host(Z)) = elec_2 -> -leq(index(pendack,host(Z)),host(Z)))) -> (setIn(X,alive) -> (-leq(host(X),host(Y)) -> (-(index(ldr,host(X)) = host(Y) & index(status,host(X)) = norm | host(Y) = host(index(elid,host(X))) & index(status,host(X)) = wait) -> (index(status,host(X)) = elec_1 & (all Z (-leq(host(X),Z) & leq(s(zero),Z) -> setIn(Z,index(down,host(X))) | host(Y) = Z)) -> (-leq(nbr_proc,host(X)) -> (all Z (host(X) = host(Z) -> (all W0 (host(W0) != host(X) -> (-leq(host(Z),host(W0)) & elec_2 = index(status,host(W0)) & setIn(W0,alive) & setIn(Z,alive) -> -leq(s(host(X)),index(pendack,host(W0))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause).  [assumption].
17.70/17.99	61 -leq(s(A),A) # label(axiom_58) # label(axiom).  [clausify(2)].
17.70/17.99	63 leq(s(zero),host(A)) # label(axiom_02) # label(axiom).  [clausify(3)].
17.70/17.99	66 head(cons(A,B)) = A # label(axiom_35) # label(axiom).  [clausify(6)].
17.70/17.99	67 -leq(A,B) | -leq(B,C) | leq(A,C) # label(axiom_62) # label(axiom).  [clausify(7)].
17.70/17.99	68 cons(head(A),tail(A)) = A | A = q_nil # label(axiom_39) # label(axiom).  [clausify(8)].
17.70/17.99	69 cons(head(A),tail(A)) = A | q_nil = A.  [copy(68),flip(b)].
17.70/17.99	73 host(A) = host(B) | A != B # label(axiom_33) # label(axiom).  [clausify(10)].
17.70/17.99	77 leq(A,B) | leq(B,A) # label(axiom_60) # label(axiom).  [clausify(12)].
17.70/17.99	78 host(A) != s(host(B)) | host(A) != host(B) # label(axiom_01) # label(axiom).  [clausify(13)].
17.70/17.99	89 cons(A,B) != q_nil # label(axiom_41) # label(axiom).  [clausify(20)].
17.70/17.99	105 snoc(init(A),last(A)) = A | A = q_nil # label(axiom_40) # label(axiom).  [clausify(29)].
17.70/17.99	106 snoc(init(A),last(A)) = A | q_nil = A.  [copy(105),flip(b)].
17.70/17.99	110 A = B | -leq(B,A) | -leq(A,B) # label(axiom_61) # label(axiom).  [clausify(31)].
17.70/17.99	116 snoc(cons(A,B),C) = cons(A,snoc(B,C)) # label(axiom_44) # label(axiom).  [clausify(35)].
17.70/17.99	118 pidMsg(m_Down(A)) = A # label(axiom_50) # label(axiom).  [clausify(37)].
17.70/17.99	121 elem(A,cons(B,C)) | B != A # label(axiom_46) # label(axiom).  [clausify(39)].
17.70/17.99	130 init(snoc(A,B)) = A # label(axiom_38) # label(axiom).  [clausify(45)].
17.70/17.99	161 -setIn(A,alive) | -setIn(host(A),index(down,host(B))) | index(status,host(A)) != elec_2 | -setIn(B,alive) | leq(index(pendack,host(A)),host(B)) # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	163 queue(host(c3)) = cons(m_Down(c4),c1) # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	164 cons(m_Down(c4),c1) = queue(host(c3)).  [copy(163),flip(a)].
17.70/17.99	165 -setIn(A,alive) | -setIn(B,alive) | -elem(m_Down(C),queue(host(A))) | index(status,host(B)) != elec_2 | host(C) != host(B) | leq(index(pendack,host(B)),host(A)) # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	173 setIn(c3,alive) # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	179 leq(host(c3),A) | -leq(s(zero),A) | setIn(A,index(down,host(c3))) | host(c4) = A # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	181 host(c5) = host(c3) # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	183 -leq(host(c5),host(c6)) # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	184 -leq(host(c3),host(c6)).  [copy(183),rewrite([181(2)])].
17.70/17.99	185 index(status,host(c6)) = elec_2 # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	186 elec_2 = index(status,host(c6)).  [copy(185),flip(a)].
17.70/17.99	187 setIn(c6,alive) # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	189 leq(s(host(c3)),index(pendack,host(c6))) # label(conj) # label(negated_conjecture).  [clausify(58)].
17.70/17.99	202 -setIn(A,alive) | -setIn(B,alive) | -elem(m_Down(C),queue(host(A))) | index(status,host(c6)) != index(status,host(B)) | host(C) != host(B) | leq(index(pendack,host(B)),host(A)).  [back_rewrite(165),rewrite([186(12)]),flip(d)].
17.70/17.99	204 -setIn(A,alive) | -setIn(host(A),index(down,host(B))) | index(status,host(c6)) != index(status,host(A)) | -setIn(B,alive) | leq(index(pendack,host(A)),host(B)).  [back_rewrite(161),rewrite([186(11)]),flip(c)].
17.70/17.99	213 host(cons(head(A),tail(A))) = host(A) | q_nil = A.  [resolve(73,b,69,a)].
17.70/17.99	215 leq(A,s(A)).  [resolve(77,a,61,a)].
17.70/17.99	249 q_nil = A | cons(head(A),snoc(tail(A),B)) = snoc(A,B).  [para(69(a,1),116(a,1,1)),flip(b)].
17.70/17.99	252 q_nil = A | cons(B,snoc(init(A),last(A))) = cons(B,A).  [para(106(a,1),116(a,2,2)),rewrite([116(6)])].
17.70/17.99	254 elem(A,cons(A,B)).  [resolve(121,b,118,a),rewrite([118(2)])].
17.70/17.99	262 init(cons(A,snoc(B,C))) = cons(A,B).  [para(116(a,1),130(a,1,1))].
17.70/17.99	290 queue(host(c3)) != q_nil.  [para(164(a,1),89(a,1))].
17.70/17.99	299 leq(host(c3),host(A)) | setIn(host(A),index(down,host(c3))) | host(c4) = host(A).  [resolve(179,b,63,a)].
17.70/17.99	300 s(host(A)) != host(c3) | host(c3) != host(A).  [para(181(a,1),78(a,1)),rewrite([181(7)]),flip(a)].
17.70/17.99	301 host(A) != s(host(c3)) | host(c3) != host(A).  [para(181(a,1),78(a,2,1)),rewrite([181(8)]),flip(b)].
17.70/17.99	308 index(pendack,host(c6)) = s(host(c3)) | -leq(index(pendack,host(c6)),s(host(c3))).  [resolve(189,a,110,c),flip(a)].
17.70/17.99	311 -leq(index(pendack,host(c6)),A) | leq(s(host(c3)),A).  [resolve(189,a,67,a)].
17.70/17.99	326 -leq(s(A),B) | leq(A,B).  [resolve(215,a,67,a)].
17.70/17.99	372 elem(m_Down(c4),queue(host(c3))).  [para(164(a,1),254(a,2))].
17.70/17.99	441 q_nil = A | s(host(A)) != host(c3) | host(cons(head(A),tail(A))) != host(c3).  [para(213(a,1),300(a,1,1)),flip(c)].
17.70/17.99	482 -setIn(A,alive) | index(status,host(c6)) != index(status,host(A)) | host(c4) != host(A) | leq(index(pendack,host(A)),host(c3)).  [resolve(372,a,202,c),unit_del(a,173)].
17.70/17.99	573 leq(host(c3),index(pendack,host(c6))).  [resolve(326,a,189,a)].
17.70/17.99	771 index(pendack,host(c6)) = host(c3) | -leq(index(pendack,host(c6)),host(c3)).  [resolve(573,a,110,c),flip(a)].
17.70/17.99	1152 q_nil = A | head(snoc(A,B)) = head(A).  [para(249(b,1),66(a,1,1))].
17.70/17.99	2123 leq(host(c3),host(A)) | host(c4) = host(A) | -setIn(A,alive) | index(status,host(c6)) != index(status,host(A)) | leq(index(pendack,host(A)),host(c3)).  [resolve(299,b,204,b),unit_del(e,173)].
17.70/17.99	3736 q_nil = A | init(A) = q_nil | head(init(A)) = head(A).  [para(106(a,1),1152(b,1,1)),flip(b),flip(c)].
17.70/17.99	6198 c3 = q_nil | s(host(c3)) != host(c3).  [resolve(441,c,213,a),flip(a),flip(c),merge(c)].
17.70/17.99	7293 host(c6) != host(c4) | leq(index(pendack,host(c6)),host(c3)).  [resolve(482,a,187,a),flip(b),xx(a)].
17.70/17.99	12095 init(cons(A,B)) = q_nil | head(init(cons(A,B))) = A.  [para(66(a,1),3736(c,2)),flip(a),unit_del(a,89)].
17.70/17.99	12994 q_nil = A | head(init(cons(B,A))) = B.  [para(252(b,1),12095(b,1,1,1)),rewrite([262(7)]),unit_del(b,89)].
17.70/17.99	13004 q_nil = A | host(head(init(cons(B,A)))) = host(B).  [resolve(12994,b,73,b)].
17.70/17.99	17781 host(c6) = host(c4) | leq(index(pendack,host(c6)),host(c3)).  [resolve(2123,c,187,a),flip(b),xx(c),unit_del(a,184)].
17.70/17.99	17788 host(c6) = host(c4).  [resolve(17781,b,311,a),unit_del(b,61)].
17.70/17.99	18006 leq(index(pendack,host(c4)),host(c3)).  [back_rewrite(7293),rewrite([17788(2),17788(8)]),xx(a)].
17.70/17.99	18328 index(pendack,host(c4)) = host(c3).  [back_rewrite(771),rewrite([17788(3),17788(10)]),unit_del(b,18006)].
17.70/17.99	18333 s(host(c3)) = host(c3).  [back_rewrite(308),rewrite([17788(3),18328(4),17788(9),18328(10)]),flip(a),unit_del(b,215)].
17.70/17.99	18478 c3 = q_nil.  [back_rewrite(6198),rewrite([18333(6)]),xx(b)].
17.70/17.99	18631 host(A) != s(host(q_nil)) | host(q_nil) != host(A).  [back_rewrite(301),rewrite([18478(2),18478(6)])].
17.70/17.99	18769 s(host(q_nil)) = host(q_nil).  [back_rewrite(18333),rewrite([18478(1),18478(4)])].
17.70/17.99	19776 queue(host(q_nil)) != q_nil.  [back_rewrite(290),rewrite([18478(1)])].
17.70/17.99	19785 host(q_nil) != host(A).  [back_rewrite(18631),rewrite([18769(4)]),flip(a),merge(b)].
17.70/17.99	19871 q_nil = A.  [resolve(19785,a,13004,b(flip))].
17.70/17.99	19872 $F.  [resolve(19871,a,19776,a(flip))].
17.70/17.99	
17.70/17.99	% SZS output end Refutation
17.70/17.99	============================== end of proof ==========================
17.70/17.99	
17.70/17.99	============================== STATISTICS ============================
17.70/17.99	
17.70/17.99	Given=6330. Generated=1263473. Kept=19806. proofs=1.
17.70/17.99	Usable=3337. Sos=8651. Demods=67. Limbo=0, Disabled=7941. Hints=0.
17.70/17.99	Megabytes=32.80.
17.70/17.99	User_CPU=16.29, System_CPU=0.65, Wall_clock=17.
17.70/17.99	
17.70/17.99	============================== end of statistics =====================
17.70/17.99	
17.70/17.99	============================== end of search =========================
17.70/17.99	
17.70/17.99	THEOREM PROVED
17.70/17.99	% SZS status Theorem
17.70/17.99	
17.70/17.99	Exiting with 1 proof.
17.70/17.99	
17.70/17.99	Process 6142 exit (max_proofs) Wed Jul 14 14:48:42 2021
17.70/17.99	Prover9 interrupted
17.70/17.99	EOF