TSTP Solution File: SWV481+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV481+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 21:13:12 EDT 2022
% Result : Theorem 61.11s 61.47s
% Output : Refutation 61.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV481+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 15 23:11:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.82/1.15 ============================== Prover9 ===============================
% 0.82/1.15 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.15 Process 23084 was started by sandbox2 on n024.cluster.edu,
% 0.82/1.15 Wed Jun 15 23:11:19 2022
% 0.82/1.15 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22931_n024.cluster.edu".
% 0.82/1.15 ============================== end of head ===========================
% 0.82/1.15
% 0.82/1.15 ============================== INPUT =================================
% 0.82/1.15
% 0.82/1.15 % Reading from file /tmp/Prover9_22931_n024.cluster.edu
% 0.82/1.15
% 0.82/1.15 set(prolog_style_variables).
% 0.82/1.15 set(auto2).
% 0.82/1.15 % set(auto2) -> set(auto).
% 0.82/1.15 % set(auto) -> set(auto_inference).
% 0.82/1.15 % set(auto) -> set(auto_setup).
% 0.82/1.15 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.15 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.15 % set(auto) -> set(auto_limits).
% 0.82/1.15 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.15 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.15 % set(auto) -> set(auto_denials).
% 0.82/1.15 % set(auto) -> set(auto_process).
% 0.82/1.15 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.15 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.15 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.15 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.15 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.15 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.15 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.15 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.15 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.15 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.15 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.15 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.15 % set(auto2) -> assign(stats, some).
% 0.82/1.15 % set(auto2) -> clear(echo_input).
% 0.82/1.15 % set(auto2) -> set(quiet).
% 0.82/1.15 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.15 % set(auto2) -> clear(print_given).
% 0.82/1.15 assign(lrs_ticks,-1).
% 0.82/1.15 assign(sos_limit,10000).
% 0.82/1.15 assign(order,kbo).
% 0.82/1.15 set(lex_order_vars).
% 0.82/1.15 clear(print_given).
% 0.82/1.15
% 0.82/1.15 % formulas(sos). % not echoed (67 formulas)
% 0.82/1.15
% 0.82/1.15 ============================== end of input ==========================
% 0.82/1.15
% 0.82/1.15 % From the command line: assign(max_seconds, 300).
% 0.82/1.15
% 0.82/1.15 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.15
% 0.82/1.15 % Formulas that are not ordinary clauses:
% 0.82/1.15 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].
% 0.82/1.15 2 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 5 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 6 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 7 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 9 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 10 (all X all Y m_NotNorm(X) != m_Halt(Y)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 11 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 13 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 14 (all X all Y m_Down(X) != m_NormQ(Y)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 15 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 16 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 17 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 18 (all X all Y m_Ldr(X) != m_NotNorm(Y)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 19 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 20 (all X all Y (X != Y <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 21 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 22 (all X all Y (X != Y <-> m_NotNorm(X) != m_NotNorm(Y))) # label(axiom_28) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 23 (all X all Y (X != Y <-> m_Ldr(X) != m_Ldr(Y))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 24 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 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].
% 0.82/1.15 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].
% 0.82/1.15 27 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 28 (all X all Q head(cons(X,Q)) = X) # label(axiom_35) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 29 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 30 (all Y all Q last(snoc(Q,Y)) = Y) # label(axiom_37) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 32 (all Q (Q = q_nil | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 33 (all Q (Q = q_nil | Q = snoc(init(Q),last(Q)))) # label(axiom_40) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 34 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 35 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 36 (all X cons(X,q_nil) = snoc(q_nil,X)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 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].
% 0.82/1.15 38 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 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].
% 0.82/1.15 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].
% 0.82/1.15 41 (all X (pidElem(X) <-> (exists Y (X = m_Halt(Y) | X = m_Down(Y))))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 42 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 43 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 44 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 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].
% 0.82/1.15 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].
% 0.82/1.15 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].
% 0.82/1.15 48 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 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].
% 0.82/1.15 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 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].
% 0.82/1.15 55 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 57 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.15 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(ldr,host(X)) = host(Y) & index(status,host(X)) = norm | index(status,host(X)) = wait & host(Y) = host(index(elid,host(X)))) -> (-((all Z (-leq(host(X),Z) & leq(s(zero),Z) -> setIn(Z,index(down,host(X))) | Z = host(Y))) & index(status,host(X)) = elec_1) -> (all Z all W0 all X0 all Y0 (host(X) = host(Y0) -> ((all V0 (-leq(host(Y0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(X))) | V0 = host(Y) | V0 = host(X0))) & setIn(Y0,alive) & elem(m_Down(W0),V) & elem(m_Down(X0),V) & leq(nbr_proc,s(host(Y0))) & host(W0) = s(host(Y0)) & index(status,host(Y0)) = elec_1 -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm)))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 61.11/61.47
% 61.11/61.47 ============================== end of process non-clausal formulas ===
% 61.11/61.47
% 61.11/61.47 ============================== PROCESS INITIAL CLAUSES ===============
% 61.11/61.47
% 61.11/61.47 ============================== PREDICATE ELIMINATION =================
% 61.11/61.47
% 61.11/61.47 ============================== end predicate elimination =============
% 61.11/61.47
% 61.11/61.47 Auto_denials: (non-Horn, no changes).
% 61.11/61.47
% 61.11/61.47 Term ordering decisions:
% 61.11/61.47 Function symbol KB weights: alive=1. status=1. ldr=1. norm=1. q_nil=1. zero=1. elec_1=1. elec_2=1. nbr_proc=1. down=1. elid=1. pendack=1. pids=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. cons=1. snoc=1. m_Ack=1. f2=1. f3=1. host=1. m_Down=1. s=1. pidMsg=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.
% 61.11/61.47
% 61.11/61.47 ============================== end of process initial clauses ========
% 61.11/61.47
% 61.11/61.47 ============================== CLAUSES FOR SEARCH ====================
% 61.11/61.47
% 61.11/61.47 ============================== end of clauses for search =============
% 61.11/61.47
% 61.11/61.47 ============================== SEARCH ================================
% 61.11/61.47
% 61.11/61.47 % Starting search at 0.03 seconds.
% 61.11/61.47
% 61.11/61.47 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 108 (0.00 of 0.36 sec).
% 61.11/61.47
% 61.11/61.47 Low Water (keep): wt=63.000, iters=3579
% 61.11/61.47
% 61.11/61.47 Low Water (keep): wt=55.000, iters=3373
% 61.11/61.47
% 61.11/61.47 Low Water (keep): wt=22.000, iters=3341
% 61.11/61.47
% 61.11/61.47 Low Water (keep): wt=20.000, iters=3400
% 61.11/61.47
% 61.11/61.47 Low Water (keep): wt=19.000, iters=3564
% 61.11/61.47
% 61.11/61.47 Low Water (keep): wt=18.000, iters=3484
% 61.11/61.47
% 61.11/61.47 Low Water (keep): wt=16.000, iters=3350
% 61.11/61.47
% 61.11/61.47 Low Water (keep): wt=14.000, iters=3447
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5256, wt=196.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=4922, wt=195.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=4951, wt=194.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5433, wt=191.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5366, wt=182.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5333, wt=178.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5028, wt=176.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5566, wt=174.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5748, wt=172.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=4921, wt=168.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5431, wt=164.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5636, wt=158.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5325, wt=154.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5263, wt=152.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5562, wt=151.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=4958, wt=150.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5744, wt=149.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5373, wt=142.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5423, wt=138.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5632, wt=137.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5945, wt=133.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=4923, wt=132.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=6121, wt=131.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5570, wt=123.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=6183, wt=122.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=5752, wt=121.000
% 61.11/61.47
% 61.11/61.47 Low Water (displace): id=6153, wt=120.000
% 61.11/61.47
% 61.11/61.47 ============================== PROOF =================================
% 61.11/61.47 % SZS status Theorem
% 61.11/61.47 % SZS output start Refutation
% 61.11/61.47
% 61.11/61.47 % Proof 1 at 57.93 (+ 2.32) seconds.
% 61.11/61.47 % Length of proof is 74.
% 61.11/61.47 % Level of proof is 10.
% 61.11/61.47 % Maximum clause weight is 33.000.
% 61.11/61.47 % Given clauses 11086.
% 61.11/61.47
% 61.11/61.47 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 61.11/61.47 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 61.11/61.47 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 61.11/61.47 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].
% 61.11/61.47 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 61.11/61.47 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 61.11/61.47 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(ldr,host(X)) = host(Y) & index(status,host(X)) = norm | index(status,host(X)) = wait & host(Y) = host(index(elid,host(X)))) -> (-((all Z (-leq(host(X),Z) & leq(s(zero),Z) -> setIn(Z,index(down,host(X))) | Z = host(Y))) & index(status,host(X)) = elec_1) -> (all Z all W0 all X0 all Y0 (host(X) = host(Y0) -> ((all V0 (-leq(host(Y0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(X))) | V0 = host(Y) | V0 = host(X0))) & setIn(Y0,alive) & elem(m_Down(W0),V) & elem(m_Down(X0),V) & leq(nbr_proc,s(host(Y0))) & host(W0) = s(host(Y0)) & index(status,host(Y0)) = elec_1 -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm)))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 61.11/61.47 62 leq(s(zero),host(A)) # label(axiom_02) # label(axiom). [clausify(3)].
% 61.11/61.47 64 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(4)].
% 61.11/61.47 69 elec_1 != norm # label(axiom_07) # label(axiom). [assumption].
% 61.11/61.47 107 init(snoc(A,B)) = A # label(axiom_38) # label(axiom). [clausify(31)].
% 61.11/61.47 116 elem(A,cons(B,C)) | B != A # label(axiom_46) # label(axiom). [clausify(39)].
% 61.11/61.47 117 elem(A,cons(B,C)) | -elem(A,C) # label(axiom_46) # label(axiom). [clausify(39)].
% 61.11/61.47 149 -leq(A,B) | -leq(B,A) | B = A # label(axiom_61) # label(axiom). [clausify(53)].
% 61.11/61.47 155 -leq(A,s(B)) | s(B) = A | leq(A,B) # label(axiom_64) # label(axiom). [clausify(56)].
% 61.11/61.47 160 A = B | host(A) != host(B) | -setIn(B,alive) | -setIn(A,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 164 -setIn(A,alive) | index(status,host(A)) != norm | index(ldr,host(A)) != host(A) | -setIn(B,alive) | -setIn(host(A),index(down,host(B))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 166 -setIn(A,alive) | host(B) != host(A) | index(status,host(A)) != norm | index(ldr,host(A)) != host(A) | -setIn(C,alive) | -elem(m_Down(B),queue(host(C))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 182 cons(m_Down(c4),c1) = queue(host(c3)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 183 setIn(c3,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 187 -leq(host(c3),c5) | index(status,host(c3)) != elec_1 # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 188 leq(s(zero),c5) | index(status,host(c3)) != elec_1 # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 189 -setIn(c5,index(down,host(c3))) | index(status,host(c3)) != elec_1 # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 190 host(c4) != c5 | index(status,host(c3)) != elec_1 # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 191 host(c9) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 192 leq(host(c9),A) | -leq(s(zero),A) | setIn(A,index(down,host(c3))) | host(c4) = A | host(c8) = A # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 193 leq(host(c3),A) | -leq(s(zero),A) | setIn(A,index(down,host(c3))) | host(c4) = A | host(c8) = A. [copy(192),rewrite([191(2)])].
% 61.11/61.47 195 elem(m_Down(c7),c1) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 196 elem(m_Down(c8),c1) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 197 leq(nbr_proc,s(host(c9))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 198 leq(nbr_proc,s(host(c3))). [copy(197),rewrite([191(3)])].
% 61.11/61.47 199 s(host(c9)) = host(c7) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 200 s(host(c3)) = host(c7). [copy(199),rewrite([191(2)])].
% 61.11/61.47 201 index(status,host(c9)) = elec_1 # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 202 elec_1 = index(status,host(c3)). [copy(201),rewrite([191(3)]),flip(a)].
% 61.11/61.47 203 setIn(c6,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 204 index(ldr,host(c6)) = host(c6) # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 205 index(status,host(c6)) = norm # label(conj) # label(negated_conjecture). [clausify(58)].
% 61.11/61.47 206 norm = index(status,host(c6)). [copy(205),flip(a)].
% 61.11/61.47 218 leq(nbr_proc,host(c7)). [back_rewrite(198),rewrite([200(4)])].
% 61.11/61.47 219 host(c4) != c5. [back_rewrite(190),rewrite([202(9)]),xx(b)].
% 61.11/61.47 220 -setIn(c5,index(down,host(c3))). [back_rewrite(189),rewrite([202(11)]),xx(b)].
% 61.11/61.47 221 leq(s(zero),c5). [back_rewrite(188),rewrite([202(9)]),xx(b)].
% 61.11/61.47 222 -leq(host(c3),c5). [back_rewrite(187),rewrite([202(9)]),xx(b)].
% 61.11/61.47 232 index(status,host(c6)) != index(status,host(c3)). [back_rewrite(69),rewrite([202(1),206(5)]),flip(a)].
% 61.11/61.47 238 -setIn(A,alive) | host(B) != host(A) | index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A) | -setIn(C,alive) | -elem(m_Down(B),queue(host(C))). [back_rewrite(166),rewrite([206(9)]),flip(c)].
% 61.11/61.47 239 -setIn(A,alive) | index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A) | -setIn(B,alive) | -setIn(host(A),index(down,host(B))). [back_rewrite(164),rewrite([206(6)]),flip(b)].
% 61.11/61.47 269 elem(A,cons(A,B)). [resolve(116,b,107,a),rewrite([107(2)])].
% 61.11/61.47 337 c3 = A | host(c3) != host(A) | -setIn(A,alive). [resolve(183,a,160,d)].
% 61.11/61.47 350 leq(host(c3),host(A)) | setIn(host(A),index(down,host(c3))) | host(c4) = host(A) | host(c8) = host(A). [resolve(193,b,62,a)].
% 61.11/61.47 356 elem(m_Down(c7),cons(A,c1)). [resolve(195,a,117,b)].
% 61.11/61.47 361 elem(m_Down(c8),cons(A,c1)). [resolve(196,a,117,b)].
% 61.11/61.47 366 -leq(A,host(c7)) | host(c7) = A | leq(A,host(c3)). [para(200(a,1),155(a,2)),rewrite([200(6)])].
% 61.11/61.47 376 host(c7) = nbr_proc. [resolve(218,a,149,b),flip(b),unit_del(a,64)].
% 61.11/61.47 381 -leq(A,nbr_proc) | nbr_proc = A | leq(A,host(c3)). [back_rewrite(366),rewrite([376(2),376(4)])].
% 61.11/61.47 391 host(c8) = c5. [resolve(221,a,193,b),unit_del(a,222),unit_del(b,220),unit_del(c,219)].
% 61.11/61.47 400 leq(host(c3),host(A)) | setIn(host(A),index(down,host(c3))) | host(c4) = host(A) | host(A) = c5. [back_rewrite(350),rewrite([391(16)]),flip(d)].
% 61.11/61.47 704 elem(m_Down(c4),queue(host(c3))). [para(182(a,1),269(a,2))].
% 61.11/61.47 1090 elem(m_Down(c7),queue(host(c3))). [para(182(a,1),356(a,2))].
% 61.11/61.47 1100 elem(m_Down(c8),queue(host(c3))). [para(182(a,1),361(a,2))].
% 61.11/61.47 1181 -setIn(A,alive) | host(c4) != host(A) | index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A). [resolve(704,a,238,f),unit_del(e,183)].
% 61.11/61.47 1203 host(c6) != host(c4). [resolve(1181,a,203,a),rewrite([204(18)]),flip(a),xx(b),xx(c)].
% 61.11/61.47 1307 -setIn(A,alive) | host(A) != nbr_proc | index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A). [resolve(1090,a,238,f),rewrite([376(4)]),flip(b),unit_del(e,183)].
% 61.11/61.47 1338 -setIn(A,alive) | host(A) != c5 | index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A). [resolve(1100,a,238,f),rewrite([391(4)]),flip(b),unit_del(e,183)].
% 61.11/61.47 1362 host(c6) != nbr_proc. [resolve(1307,a,203,a),rewrite([204(17)]),xx(b),xx(c)].
% 61.11/61.47 1363 host(c6) != c5. [resolve(1338,a,203,a),rewrite([204(17)]),xx(b),xx(c)].
% 61.11/61.47 2625 c6 = c3 | host(c6) != host(c3). [resolve(337,c,203,a),flip(a),flip(b)].
% 61.11/61.47 2888 host(A) = nbr_proc | leq(host(A),host(c3)). [resolve(381,a,64,a),flip(a)].
% 61.11/61.47 3086 leq(host(c3),host(A)) | host(c4) = host(A) | host(A) = c5 | -setIn(A,alive) | index(status,host(c6)) != index(status,host(A)) | index(ldr,host(A)) != host(A). [resolve(400,b,239,e),unit_del(g,183)].
% 61.11/61.47 4473 host(A) = nbr_proc | -leq(host(c3),host(A)) | host(c3) = host(A). [resolve(2888,b,149,b),flip(c)].
% 61.11/61.47 21419 leq(host(c3),host(c6)). [resolve(3086,d,203,a),rewrite([204(27)]),flip(b),xx(d),xx(e),unit_del(b,1203),unit_del(c,1363)].
% 61.11/61.47 21436 host(c6) = host(c3). [resolve(21419,a,4473,b),flip(b),unit_del(a,1362)].
% 61.11/61.47 21786 c6 = c3. [back_rewrite(2625),rewrite([21436(5)]),xx(b)].
% 61.11/61.47 21880 $F. [back_rewrite(232),rewrite([21786(2)]),xx(a)].
% 61.11/61.47
% 61.11/61.47 % SZS output end Refutation
% 61.11/61.47 ============================== end of proof ==========================
% 61.11/61.47
% 61.11/61.47 ============================== STATISTICS ============================
% 61.11/61.47
% 61.11/61.47 Given=11086. Generated=3313987. Kept=21809. proofs=1.
% 61.11/61.47 Usable=10281. Sos=8843. Demods=51. Limbo=444, Disabled=2380. Hints=0.
% 61.11/61.47 Megabytes=47.65.
% 61.11/61.47 User_CPU=57.93, System_CPU=2.32, Wall_clock=60.
% 61.11/61.47
% 61.11/61.47 ============================== end of statistics =====================
% 61.11/61.47
% 61.11/61.47 ============================== end of search =========================
% 61.11/61.47
% 61.11/61.47 THEOREM PROVED
% 61.11/61.47 % SZS status Theorem
% 61.11/61.47
% 61.11/61.47 Exiting with 1 proof.
% 61.11/61.47
% 61.11/61.47 Process 23084 exit (max_proofs) Wed Jun 15 23:12:19 2022
% 61.11/61.47 Prover9 interrupted
%------------------------------------------------------------------------------