TSTP Solution File: SWV478+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV478+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:13:11 EDT 2022
% Result : Theorem 51.35s 51.64s
% Output : Refutation 51.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV478+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n015.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 : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 03:32:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/1.20 ============================== Prover9 ===============================
% 0.46/1.20 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.20 Process 13378 was started by sandbox on n015.cluster.edu,
% 0.46/1.20 Thu Jun 16 03:32:41 2022
% 0.46/1.20 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13225_n015.cluster.edu".
% 0.46/1.20 ============================== end of head ===========================
% 0.46/1.20
% 0.46/1.20 ============================== INPUT =================================
% 0.46/1.20
% 0.46/1.20 % Reading from file /tmp/Prover9_13225_n015.cluster.edu
% 0.46/1.20
% 0.46/1.20 set(prolog_style_variables).
% 0.46/1.20 set(auto2).
% 0.46/1.20 % set(auto2) -> set(auto).
% 0.46/1.20 % set(auto) -> set(auto_inference).
% 0.46/1.20 % set(auto) -> set(auto_setup).
% 0.46/1.20 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.20 % set(auto) -> set(auto_limits).
% 0.46/1.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.20 % set(auto) -> set(auto_denials).
% 0.46/1.20 % set(auto) -> set(auto_process).
% 0.46/1.20 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.20 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.20 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.20 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.20 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.20 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.20 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.20 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.20 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.20 % set(auto2) -> assign(stats, some).
% 0.46/1.20 % set(auto2) -> clear(echo_input).
% 0.46/1.20 % set(auto2) -> set(quiet).
% 0.46/1.20 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.20 % set(auto2) -> clear(print_given).
% 0.46/1.20 assign(lrs_ticks,-1).
% 0.46/1.20 assign(sos_limit,10000).
% 0.46/1.20 assign(order,kbo).
% 0.46/1.20 set(lex_order_vars).
% 0.46/1.20 clear(print_given).
% 0.46/1.20
% 0.46/1.20 % formulas(sos). % not echoed (67 formulas)
% 0.46/1.20
% 0.46/1.20 ============================== end of input ==========================
% 0.46/1.20
% 0.46/1.20 % From the command line: assign(max_seconds, 300).
% 0.46/1.20
% 0.46/1.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.20
% 0.46/1.20 % Formulas that are not ordinary clauses:
% 0.46/1.20 1 (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].
% 0.46/1.20 2 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 5 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 6 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 7 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 9 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 10 (all X all Y m_NotNorm(X) != m_Halt(Y)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 11 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 13 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 14 (all X all Y m_Down(X) != m_NormQ(Y)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 15 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 16 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 17 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 18 (all X all Y m_Ldr(X) != m_NotNorm(Y)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 19 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 20 (all X all Y (X != Y <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 21 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 22 (all X all Y (X != Y <-> m_NotNorm(X) != m_NotNorm(Y))) # label(axiom_28) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 23 (all X all Y (X != Y <-> m_Ldr(X) != m_Ldr(Y))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 24 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 25 (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].
% 0.46/1.20 26 (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].
% 0.46/1.20 27 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 28 (all X all Q head(cons(X,Q)) = X) # label(axiom_35) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 29 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 30 (all Y all Q last(snoc(Q,Y)) = Y) # label(axiom_37) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 32 (all Q (Q = q_nil | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 33 (all Q (Q = q_nil | Q = snoc(init(Q),last(Q)))) # label(axiom_40) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 34 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 35 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 36 (all X cons(X,q_nil) = snoc(q_nil,X)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 37 (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].
% 0.46/1.20 38 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 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].
% 0.46/1.20 40 (all X all Y all Q (elem(X,snoc(Q,Y)) <-> X = Y | elem(X,Q))) # label(axiom_47) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 41 (all X (pidElem(X) <-> (exists Y (X = m_Halt(Y) | X = m_Down(Y))))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 42 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 43 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 44 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 45 (all X all Q (ordered(cons(X,Q)) <-> ordered(Q) & (all Y (elem(Y,Q) & pidElem(X) & pidElem(Y) & host(pidMsg(Y)) = host(pidMsg(X)) -> leq(pidMsg(X),pidMsg(Y)))))) # label(axiom_53) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 46 (all X all Q (ordered(snoc(Q,X)) <-> ordered(Q) & (all Y (elem(Y,Q) & pidElem(X) & pidElem(Y) & host(pidMsg(Y)) = host(pidMsg(X)) -> leq(pidMsg(Y),pidMsg(X)))))) # label(axiom_54) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 47 (all Q all X all Y (ordered(Q) -> ordered(snoc(Q,m_Ack(X,Y))))) # label(axiom_55) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 48 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.20 49 (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].
% 0.46/1.21 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.21 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.21 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.21 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.21 54 (all X all Y all Z (leq(X,Y) & leq(Y,Z) -> leq(X,Z))) # label(axiom_62) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.21 55 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.21 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.21 57 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.21 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Ldr(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (elem(m_Down(Pid0),queue(host(Z))) -> host(Pid0) != host(Z))) & (all Z all Pid0 (Pid0 != Z & host(Pid0) = host(Z) -> -setIn(Z,alive) | -setIn(Pid0,alive))) & (all Z ((index(status,host(Z)) = elec_1 | index(status,host(Z)) = elec_2) & setIn(Z,alive) -> index(elid,host(Z)) = Z)) & (all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & setIn(host(Pid0),index(down,host(Z))) & index(status,host(Pid0)) = elec_2 -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (setIn(Pid0,alive) & index(status,host(Pid0)) = norm & index(ldr,host(Pid0)) = host(Pid0) -> -(setIn(Z,alive) & setIn(host(Pid0),index(down,host(Z)))))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Z))) & host(Pid0) = host(Pid20) & index(status,host(Pid0)) = elec_2 -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & host(Pid20) = host(Pid0) & index(status,host(Pid0)) = norm & index(ldr,host(Pid0)) = host(Pid0) -> -(setIn(Z,alive) & elem(m_Down(Pid20),queue(host(Z)))))) & (all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm & index(status,host(Pid0)) = norm & index(ldr,host(Pid0)) = host(Pid0) -> Pid0 = Z)) & (all Z all Pid20 all Pid0 (-leq(host(Pid20),host(Pid0)) & setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid20) = host(Z) -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid20) != host(Z) & setIn(Z,alive) & setIn(Pid20,alive) & host(Pid30) = host(Z) & host(Pid0) = host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Z))) & elem(m_Down(Pid30),queue(host(Pid20)))))) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid20) != host(Z) & setIn(Z,alive) & setIn(Pid20,alive) & host(Pid30) = host(Z) & host(Pid0) = host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Z))) & setIn(host(Pid30),index(down,host(Pid20)))))) & (all Z all Pid20 all Pid0 (host(Pid0) != host(Pid20) & setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & host(Pid20) = host(Z) & index(status,host(Pid0)) = norm & index(ldr,host(Pid0)) = host(Pid20) -> -(setIn(Pid20,alive) & index(status,host(Pid20)) = norm & index(ldr,host(Pid20)) = host(Pid20)))) & (all Z all Pid20 all Pid0 (host(Pid0) != host(Pid20) & setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & host(Pid20) = host(Z) & index(status,host(Pid0)) = wait & host(index(elid,host(Pid0))) = host(Pid20) -> -(setIn(Pid20,alive) & index(status,host(Pid20)) = norm & index(ldr,host(Pid20)) = host(Pid20)))) & (all Z all Pid30 all Pid20 all Pid0 ((all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(Pid0))) | V0 = host(Pid20))) & setIn(Z,alive) & leq(host(Z),host(Pid0)) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid30) = host(Pid0) & index(status,host(Z)) = elec_2 & index(status,host(Pid0)) = elec_1 -> -elem(m_Ack(Z,Pid30),queue(host(Z))))) & (all Z all Pid30 all Pid20 all Pid0 ((all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(Pid0))) | V0 = host(Pid20))) & setIn(Pid0,alive) & leq(nbr_proc,s(host(Pid0))) & elem(m_Down(Pid20),queue(host(Pid0))) & elem(m_Down(Pid30),queue(host(Pid0))) & host(Pid30) = s(host(Pid0)) & index(status,host(Pid0)) = elec_1 -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))) & queue(host(X)) = cons(m_Down(Y),V) -> (setIn(X,alive) -> (leq(host(X),host(Y)) -> (index(status,host(X)) = elec_2 & host(Y) = index(pendack,host(X)) -> (leq(nbr_proc,index(pendack,host(X))) -> (all Z (setIn(host(Z),index(acks,host(X))) -> (all V0 (host(X) = host(V0) -> (all W0 all X0 all Y0 (host(Z) = host(Y0) -> (host(X) != host(Y0) -> ((all V1 (-leq(host(Y0),V1) & leq(s(zero),V1) -> setIn(V1,index(down,host(Y0))) | V1 = host(X0))) & setIn(Y0,alive) & leq(nbr_proc,s(host(Y0))) & elem(m_Down(W0),snoc(queue(host(Y0)),m_Ldr(X))) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X))) & host(W0) = s(host(Y0)) & index(status,host(Y0)) = elec_1 -> -(setIn(V0,alive) & host(X) = host(V0)))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 51.35/51.64
% 51.35/51.64 ============================== end of process non-clausal formulas ===
% 51.35/51.64
% 51.35/51.64 ============================== PROCESS INITIAL CLAUSES ===============
% 51.35/51.64
% 51.35/51.64 ============================== PREDICATE ELIMINATION =================
% 51.35/51.64
% 51.35/51.64 ============================== end predicate elimination =============
% 51.35/51.64
% 51.35/51.64 Auto_denials: (non-Horn, no changes).
% 51.35/51.64
% 51.35/51.64 Term ordering decisions:
% 51.35/51.64 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. pendack=1. down=1. elid=1. pids=1. acks=1. wait=1. nil=1. setEmpty=1. c1=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. index=1. snoc=1. cons=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.
% 51.35/51.64
% 51.35/51.64 ============================== end of process initial clauses ========
% 51.35/51.64
% 51.35/51.64 ============================== CLAUSES FOR SEARCH ====================
% 51.35/51.64
% 51.35/51.64 ============================== end of clauses for search =============
% 51.35/51.64
% 51.35/51.64 ============================== SEARCH ================================
% 51.35/51.64
% 51.35/51.64 % Starting search at 0.05 seconds.
% 51.35/51.64
% 51.35/51.64 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 68 (0.00 of 0.33 sec).
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=52.000, iters=3503
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=48.000, iters=3353
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=47.000, iters=3389
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=45.000, iters=3345
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=42.000, iters=3465
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=37.000, iters=3496
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=35.000, iters=3486
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=34.000, iters=3466
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=28.000, iters=3334
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=21.000, iters=3360
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=20.000, iters=3352
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=18.000, iters=3339
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=17.000, iters=3340
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=16.000, iters=3354
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=15.000, iters=3333
% 51.35/51.64
% 51.35/51.64 Low Water (keep): wt=14.000, iters=3333
% 51.35/51.64
% 51.35/51.64 ============================== PROOF =================================
% 51.35/51.64 % SZS status Theorem
% 51.35/51.64 % SZS output start Refutation
% 51.35/51.64
% 51.35/51.64 % Proof 1 at 48.62 (+ 1.84) seconds.
% 51.35/51.64 % Length of proof is 76.
% 51.35/51.64 % Level of proof is 13.
% 51.35/51.64 % Maximum clause weight is 33.000.
% 51.35/51.64 % Given clauses 12000.
% 51.35/51.64
% 51.35/51.64 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 51.35/51.64 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 51.35/51.64 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 51.35/51.64 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 51.35/51.64 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].
% 51.35/51.64 40 (all X all Y all Q (elem(X,snoc(Q,Y)) <-> X = Y | elem(X,Q))) # label(axiom_47) # label(axiom) # label(non_clause). [assumption].
% 51.35/51.64 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 51.35/51.64 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 51.35/51.64 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 51.35/51.64 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Ldr(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z all Pid0 (elem(m_Down(Pid0),queue(host(Z))) -> host(Pid0) != host(Z))) & (all Z all Pid0 (Pid0 != Z & host(Pid0) = host(Z) -> -setIn(Z,alive) | -setIn(Pid0,alive))) & (all Z ((index(status,host(Z)) = elec_1 | index(status,host(Z)) = elec_2) & setIn(Z,alive) -> index(elid,host(Z)) = Z)) & (all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & setIn(host(Pid0),index(down,host(Z))) & index(status,host(Pid0)) = elec_2 -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid0 (setIn(Pid0,alive) & index(status,host(Pid0)) = norm & index(ldr,host(Pid0)) = host(Pid0) -> -(setIn(Z,alive) & setIn(host(Pid0),index(down,host(Z)))))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Z))) & host(Pid0) = host(Pid20) & index(status,host(Pid0)) = elec_2 -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & host(Pid20) = host(Pid0) & index(status,host(Pid0)) = norm & index(ldr,host(Pid0)) = host(Pid0) -> -(setIn(Z,alive) & elem(m_Down(Pid20),queue(host(Z)))))) & (all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm & index(status,host(Pid0)) = norm & index(ldr,host(Pid0)) = host(Pid0) -> Pid0 = Z)) & (all Z all Pid20 all Pid0 (-leq(host(Pid20),host(Pid0)) & setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid20) = host(Z) -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid20) != host(Z) & setIn(Z,alive) & setIn(Pid20,alive) & host(Pid30) = host(Z) & host(Pid0) = host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Z))) & elem(m_Down(Pid30),queue(host(Pid20)))))) & (all Z all Pid30 all Pid20 all Pid0 (host(Pid20) != host(Z) & setIn(Z,alive) & setIn(Pid20,alive) & host(Pid30) = host(Z) & host(Pid0) = host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Z))) & setIn(host(Pid30),index(down,host(Pid20)))))) & (all Z all Pid20 all Pid0 (host(Pid0) != host(Pid20) & setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & host(Pid20) = host(Z) & index(status,host(Pid0)) = norm & index(ldr,host(Pid0)) = host(Pid20) -> -(setIn(Pid20,alive) & index(status,host(Pid20)) = norm & index(ldr,host(Pid20)) = host(Pid20)))) & (all Z all Pid20 all Pid0 (host(Pid0) != host(Pid20) & setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & host(Pid20) = host(Z) & index(status,host(Pid0)) = wait & host(index(elid,host(Pid0))) = host(Pid20) -> -(setIn(Pid20,alive) & index(status,host(Pid20)) = norm & index(ldr,host(Pid20)) = host(Pid20)))) & (all Z all Pid30 all Pid20 all Pid0 ((all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(Pid0))) | V0 = host(Pid20))) & setIn(Z,alive) & leq(host(Z),host(Pid0)) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid30) = host(Pid0) & index(status,host(Z)) = elec_2 & index(status,host(Pid0)) = elec_1 -> -elem(m_Ack(Z,Pid30),queue(host(Z))))) & (all Z all Pid30 all Pid20 all Pid0 ((all V0 (-leq(host(Pid0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(Pid0))) | V0 = host(Pid20))) & setIn(Pid0,alive) & leq(nbr_proc,s(host(Pid0))) & elem(m_Down(Pid20),queue(host(Pid0))) & elem(m_Down(Pid30),queue(host(Pid0))) & host(Pid30) = s(host(Pid0)) & index(status,host(Pid0)) = elec_1 -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))) & queue(host(X)) = cons(m_Down(Y),V) -> (setIn(X,alive) -> (leq(host(X),host(Y)) -> (index(status,host(X)) = elec_2 & host(Y) = index(pendack,host(X)) -> (leq(nbr_proc,index(pendack,host(X))) -> (all Z (setIn(host(Z),index(acks,host(X))) -> (all V0 (host(X) = host(V0) -> (all W0 all X0 all Y0 (host(Z) = host(Y0) -> (host(X) != host(Y0) -> ((all V1 (-leq(host(Y0),V1) & leq(s(zero),V1) -> setIn(V1,index(down,host(Y0))) | V1 = host(X0))) & setIn(Y0,alive) & leq(nbr_proc,s(host(Y0))) & elem(m_Down(W0),snoc(queue(host(Y0)),m_Ldr(X))) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X))) & host(W0) = s(host(Y0)) & index(status,host(Y0)) = elec_1 -> -(setIn(V0,alive) & host(X) = host(V0)))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 51.35/51.64 62 leq(s(zero),host(A)) # label(axiom_02) # label(axiom). [clausify(3)].
% 51.35/51.64 64 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(4)].
% 51.35/51.64 81 m_Ldr(A) != m_Down(B) # label(axiom_18) # label(axiom). [clausify(12)].
% 51.35/51.64 106 init(snoc(A,B)) = A # label(axiom_38) # label(axiom). [clausify(31)].
% 51.35/51.64 117 elem(A,cons(B,C)) | B != A # label(axiom_46) # label(axiom). [clausify(39)].
% 51.35/51.64 119 -elem(A,snoc(B,C)) | C = A | elem(A,B) # label(axiom_47) # label(axiom). [clausify(40)].
% 51.35/51.64 147 -leq(s(A),A) # label(axiom_58) # label(axiom). [clausify(50)].
% 51.35/51.64 150 -leq(A,B) | -leq(B,A) | B = A # label(axiom_61) # label(axiom). [clausify(53)].
% 51.35/51.64 156 -leq(A,s(B)) | s(B) = A | leq(A,B) # label(axiom_64) # label(axiom). [clausify(56)].
% 51.35/51.64 160 -elem(m_Down(A),queue(host(B))) | host(A) != host(B) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 164 -setIn(A,alive) | -setIn(B,alive) | -setIn(host(B),index(down,host(A))) | index(status,host(B)) != elec_2 | leq(index(pendack,host(B)),host(A)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 166 -setIn(A,alive) | -setIn(B,alive) | -elem(m_Down(C),queue(host(A))) | host(C) != host(B) | index(status,host(B)) != elec_2 | leq(index(pendack,host(B)),host(A)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 183 cons(m_Down(c4),c1) = queue(host(c3)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 184 setIn(c3,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 186 index(status,host(c3)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 187 elec_2 = index(status,host(c3)). [copy(186),flip(a)].
% 51.35/51.64 188 index(pendack,host(c3)) = host(c4) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 189 leq(nbr_proc,index(pendack,host(c3))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 190 leq(nbr_proc,host(c4)). [copy(189),rewrite([188(5)])].
% 51.35/51.64 192 host(c6) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 193 host(c9) = host(c5) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 194 host(c9) != host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 195 host(c5) != host(c3). [copy(194),rewrite([193(2)])].
% 51.35/51.64 196 leq(host(c9),A) | -leq(s(zero),A) | setIn(A,index(down,host(c9))) | host(c8) = A # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 197 leq(host(c5),A) | -leq(s(zero),A) | setIn(A,index(down,host(c5))) | host(c8) = A. [copy(196),rewrite([193(2),193(9)])].
% 51.35/51.64 198 setIn(c9,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 199 leq(nbr_proc,s(host(c9))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 200 leq(nbr_proc,s(host(c5))). [copy(199),rewrite([193(3)])].
% 51.35/51.64 203 elem(m_Down(c8),snoc(queue(host(c9)),m_Ldr(c3))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 204 elem(m_Down(c8),snoc(queue(host(c5)),m_Ldr(c3))). [copy(203),rewrite([193(4)])].
% 51.35/51.64 205 s(host(c9)) = host(c7) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 206 s(host(c5)) = host(c7). [copy(205),rewrite([193(2)])].
% 51.35/51.64 209 setIn(c6,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 51.35/51.64 225 -setIn(A,alive) | -setIn(B,alive) | -elem(m_Down(C),queue(host(A))) | host(C) != host(B) | index(status,host(c3)) != index(status,host(B)) | leq(index(pendack,host(B)),host(A)). [back_rewrite(166),rewrite([187(15)]),flip(e)].
% 51.35/51.64 226 -setIn(A,alive) | -setIn(B,alive) | -setIn(host(B),index(down,host(A))) | index(status,host(c3)) != index(status,host(B)) | leq(index(pendack,host(B)),host(A)). [back_rewrite(164),rewrite([187(13)]),flip(d)].
% 51.35/51.64 231 host(c5) = c_0. [new_symbol(195)].
% 51.35/51.64 232 leq(nbr_proc,s(c_0)). [back_rewrite(200),rewrite([231(3)])].
% 51.35/51.64 258 s(c_0) = host(c7). [back_rewrite(206),rewrite([231(2)])].
% 51.35/51.64 259 elem(m_Down(c8),snoc(queue(c_0),m_Ldr(c3))). [back_rewrite(204),rewrite([231(4)])].
% 51.35/51.64 261 leq(c_0,A) | -leq(s(zero),A) | setIn(A,index(down,c_0)) | host(c8) = A. [back_rewrite(197),rewrite([231(2),231(8)])].
% 51.35/51.64 262 host(c3) != c_0. [back_rewrite(195),rewrite([231(2)]),flip(a)].
% 51.35/51.64 263 host(c9) = c_0. [back_rewrite(193),rewrite([231(4)])].
% 51.35/51.64 265 leq(nbr_proc,host(c7)). [back_rewrite(232),rewrite([258(3)])].
% 51.35/51.64 291 elem(A,cons(A,B)). [resolve(117,b,106,a),rewrite([106(2)])].
% 51.35/51.64 366 host(c4) = nbr_proc. [resolve(190,a,150,b),flip(b),unit_del(a,64)].
% 51.35/51.64 367 index(pendack,host(c3)) = nbr_proc. [back_rewrite(188),rewrite([366(6)])].
% 51.35/51.64 371 -elem(m_Down(A),queue(host(c3))) | host(c3) != host(A). [para(192(a,1),160(a,2,1)),rewrite([192(8)]),flip(b)].
% 51.35/51.64 381 -setIn(A,alive) | -setIn(host(c3),index(down,host(A))) | leq(nbr_proc,host(A)). [para(192(a,1),226(c,1)),rewrite([192(18),192(23),367(24)]),xx(d),unit_del(b,209)].
% 51.35/51.64 414 -leq(host(c7),c_0). [para(258(a,1),147(a,1))].
% 51.35/51.64 417 -leq(A,host(c7)) | host(c7) = A | leq(A,c_0). [para(258(a,1),156(a,2)),rewrite([258(5)])].
% 51.35/51.64 422 elem(m_Down(c8),queue(c_0)). [resolve(259,a,119,a),unit_del(a,81)].
% 51.35/51.64 432 leq(c_0,host(A)) | setIn(host(A),index(down,c_0)) | host(c8) = host(A). [resolve(261,b,62,a)].
% 51.35/51.64 440 -setIn(A,alive) | -elem(m_Down(B),queue(c_0)) | host(B) != host(A) | index(status,host(c3)) != index(status,host(A)) | leq(index(pendack,host(A)),c_0). [para(263(a,1),225(c,2,1)),rewrite([263(25)]),unit_del(a,198)].
% 51.35/51.64 458 host(c7) = nbr_proc. [resolve(265,a,150,b),flip(b),unit_del(a,64)].
% 51.35/51.64 470 -leq(A,nbr_proc) | nbr_proc = A | leq(A,c_0). [back_rewrite(417),rewrite([458(2),458(4)])].
% 51.35/51.64 473 -leq(nbr_proc,c_0). [back_rewrite(414),rewrite([458(2)])].
% 51.35/51.64 750 elem(m_Down(c4),queue(host(c3))). [para(183(a,1),291(a,2))].
% 51.35/51.64 1095 host(c3) != nbr_proc. [resolve(750,a,371,a),rewrite([366(4)])].
% 51.35/51.64 2364 host(A) = nbr_proc | leq(host(A),c_0). [resolve(470,a,64,a),flip(a)].
% 51.35/51.64 2778 -setIn(host(c3),index(down,c_0)). [para(263(a,1),381(b,2,2)),rewrite([263(12)]),unit_del(a,198),unit_del(c,473)].
% 51.35/51.64 2931 leq(c_0,host(c3)) | host(c8) = host(c3). [resolve(432,b,2778,a)].
% 51.35/51.64 3080 -setIn(A,alive) | host(c8) != host(A) | index(status,host(c3)) != index(status,host(A)) | leq(index(pendack,host(A)),c_0). [resolve(440,b,422,a)].
% 51.35/51.64 3283 host(c8) = host(c3) | -leq(host(c3),c_0). [resolve(2931,a,150,b),flip(c),unit_del(c,262)].
% 51.35/51.64 3284 host(c8) = host(c3). [resolve(3283,b,2364,b),unit_del(b,1095)].
% 51.35/51.64 3287 -setIn(A,alive) | host(c3) != host(A) | index(status,host(c3)) != index(status,host(A)) | leq(index(pendack,host(A)),c_0). [back_rewrite(3080),rewrite([3284(4)])].
% 51.35/51.64 22949 $F. [resolve(3287,a,184,a),rewrite([367(18)]),xx(a),xx(b),unit_del(a,473)].
% 51.35/51.64
% 51.35/51.64 % SZS output end Refutation
% 51.35/51.64 ============================== end of proof ==========================
% 51.35/51.64
% 51.35/51.64 ============================== STATISTICS ============================
% 51.35/51.64
% 51.35/51.64 Given=12000. Generated=3567651. Kept=22873. proofs=1.
% 51.35/51.64 Usable=8325. Sos=9597. Demods=36. Limbo=0, Disabled=5088. Hints=0.
% 51.35/51.64 Megabytes=44.34.
% 51.35/51.64 User_CPU=48.62, System_CPU=1.84, Wall_clock=51.
% 51.35/51.64
% 51.35/51.64 ============================== end of statistics =====================
% 51.35/51.64
% 51.35/51.64 ============================== end of search =========================
% 51.35/51.64
% 51.35/51.64 THEOREM PROVED
% 51.35/51.64 % SZS status Theorem
% 51.35/51.64
% 51.35/51.64 Exiting with 1 proof.
% 51.35/51.64
% 51.35/51.64 Process 13378 exit (max_proofs) Thu Jun 16 03:33:32 2022
% 51.35/51.64 Prover9 interrupted
%------------------------------------------------------------------------------