TSTP Solution File: SWV466+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV466+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 21:13:09 EDT 2022
% Result : Theorem 0.82s 1.65s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV466+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 20:22:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.82/1.09 ============================== Prover9 ===============================
% 0.82/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.09 Process 17693 was started by sandbox2 on n014.cluster.edu,
% 0.82/1.09 Wed Jun 15 20:22:21 2022
% 0.82/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17539_n014.cluster.edu".
% 0.82/1.09 ============================== end of head ===========================
% 0.82/1.09
% 0.82/1.09 ============================== INPUT =================================
% 0.82/1.09
% 0.82/1.09 % Reading from file /tmp/Prover9_17539_n014.cluster.edu
% 0.82/1.09
% 0.82/1.09 set(prolog_style_variables).
% 0.82/1.09 set(auto2).
% 0.82/1.09 % set(auto2) -> set(auto).
% 0.82/1.09 % set(auto) -> set(auto_inference).
% 0.82/1.09 % set(auto) -> set(auto_setup).
% 0.82/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.09 % set(auto) -> set(auto_limits).
% 0.82/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.09 % set(auto) -> set(auto_denials).
% 0.82/1.09 % set(auto) -> set(auto_process).
% 0.82/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.09 % set(auto2) -> assign(stats, some).
% 0.82/1.09 % set(auto2) -> clear(echo_input).
% 0.82/1.09 % set(auto2) -> set(quiet).
% 0.82/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.09 % set(auto2) -> clear(print_given).
% 0.82/1.09 assign(lrs_ticks,-1).
% 0.82/1.09 assign(sos_limit,10000).
% 0.82/1.09 assign(order,kbo).
% 0.82/1.09 set(lex_order_vars).
% 0.82/1.09 clear(print_given).
% 0.82/1.09
% 0.82/1.09 % formulas(sos). % not echoed (67 formulas)
% 0.82/1.09
% 0.82/1.09 ============================== end of input ==========================
% 0.82/1.09
% 0.82/1.09 % From the command line: assign(max_seconds, 300).
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.09
% 0.82/1.09 % Formulas that are not ordinary clauses:
% 0.82/1.09 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].
% 0.82/1.09 2 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 5 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 6 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 7 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 9 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 10 (all X all Y m_NotNorm(X) != m_Halt(Y)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 11 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 13 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 14 (all X all Y m_Down(X) != m_NormQ(Y)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 15 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 16 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 17 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 18 (all X all Y m_Ldr(X) != m_NotNorm(Y)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 19 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 20 (all X all Y (X != Y <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 21 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 22 (all X all Y (X != Y <-> m_NotNorm(X) != m_NotNorm(Y))) # label(axiom_28) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 23 (all X all Y (X != Y <-> m_Ldr(X) != m_Ldr(Y))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 24 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 27 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 28 (all X all Q head(cons(X,Q)) = X) # label(axiom_35) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 29 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 30 (all Y all Q last(snoc(Q,Y)) = Y) # label(axiom_37) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 32 (all Q (Q = q_nil | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 33 (all Q (Q = q_nil | Q = snoc(init(Q),last(Q)))) # label(axiom_40) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 34 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 35 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 36 (all X cons(X,q_nil) = snoc(q_nil,X)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 38 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 41 (all X (pidElem(X) <-> (exists Y (X = m_Halt(Y) | X = m_Down(Y))))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 42 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 43 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 44 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 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].
% 0.82/1.09 48 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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].
% 0.82/1.09 55 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 57 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 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 (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 (Pid0 != Z & host(Pid0) = host(Z) -> -setIn(Z,alive) | -setIn(Pid0,alive))) & (all Z all Pid0 (setIn(Pid0,alive) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) -> leq(host(Z),index(pendack,host(Pid0))))) & (all Z all Pid0 (setIn(Pid0,alive) & index(status,host(Pid0)) = elec_1 -> -elem(m_Ack(Pid0,Z),queue(host(Pid0))))) & (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 Pid20 all 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 Pid0 (-leq(host(Z),host(Pid0)) & setIn(Z,alive) & setIn(Pid0,alive) & index(status,host(Z)) = elec_2 & index(status,host(Pid0)) = elec_2 -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & host(Pid0) = host(Pid20) & index(status,host(Z)) = elec_2 & index(status,host(Pid0)) = elec_2 -> -elem(m_Ack(Z,Pid20),queue(host(Z))))) & (all Z all Pid0 (-leq(host(Z),host(Pid0)) & setIn(Z,alive) & setIn(Pid0,alive) & index(status,host(Z)) = elec_2 & index(status,host(Pid0)) = elec_2 -> -leq(index(pendack,host(Z)),index(pendack,host(Pid0))))) & (all Z all Pid20 all Pid0 (-leq(index(pendack,host(Pid0)),host(Z)) & setIn(Pid0,alive) & elem(m_Halt(Pid0),queue(host(Pid20))) & index(status,host(Pid0)) = elec_2 -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))) & (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))) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid0) = nbr_proc & host(Pid0) = host(Pid30) & index(status,host(Pid0)) = elec_1 -> -(setIn(Z,alive) & elem(m_Down(Pid30),queue(host(Z)))))) & (all Z all Pid30 all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & elem(m_Ack(Pid0,Pid30),queue(host(Pid0))) & leq(nbr_proc,s(index(pendack,host(Pid0)))) & index(status,host(Pid0)) = elec_2 & host(Pid30) = index(pendack,host(Pid0)) & host(Pid20) = s(index(pendack,host(Pid0))) -> -(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) -> (setIn(Y0,alive) & leq(nbr_proc,s(index(pendack,host(Y0)))) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X))) & elem(m_Ack(Y0,W0),snoc(queue(host(Y0)),m_Ldr(X))) & index(status,host(Y0)) = elec_2 & host(W0) = index(pendack,host(Y0)) & host(X0) = s(index(pendack,host(Y0))) -> -(setIn(V0,alive) & host(X) = host(V0)))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.65
% 0.82/1.65 ============================== end of process non-clausal formulas ===
% 0.82/1.65
% 0.82/1.65 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.65
% 0.82/1.65 ============================== PREDICATE ELIMINATION =================
% 0.82/1.65
% 0.82/1.65 ============================== end predicate elimination =============
% 0.82/1.65
% 0.82/1.65 Auto_denials: (non-Horn, no changes).
% 0.82/1.65
% 0.82/1.65 Term ordering decisions:
% 0.82/1.65 Function symbol KB weights: alive=1. status=1. pendack=1. elec_2=1. q_nil=1. nbr_proc=1. zero=1. elec_1=1. elid=1. pids=1. acks=1. ldr=1. norm=1. down=1. nil=1. setEmpty=1. wait=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. pidMsg=1. s=1. m_Down=1. m_Halt=1. queue=1. m_Ldr=1. m_NormQ=1. m_NotNorm=1. head=1. init=1. last=1. tail=1. f1=1. f4=1.
% 0.82/1.65
% 0.82/1.65 ============================== end of process initial clauses ========
% 0.82/1.65
% 0.82/1.65 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.65
% 0.82/1.65 ============================== end of clauses for search =============
% 0.82/1.65
% 0.82/1.65 ============================== SEARCH ================================
% 0.82/1.65
% 0.82/1.65 % Starting search at 0.04 seconds.
% 0.82/1.65
% 0.82/1.65 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 61 (0.00 of 0.28 sec).
% 0.82/1.65
% 0.82/1.65 ============================== PROOF =================================
% 0.82/1.65 % SZS status Theorem
% 0.82/1.65 % SZS output start Refutation
% 0.82/1.65
% 0.82/1.65 % Proof 1 at 0.57 (+ 0.01) seconds.
% 0.82/1.65 % Length of proof is 84.
% 0.82/1.65 % Level of proof is 13.
% 0.82/1.65 % Maximum clause weight is 36.000.
% 0.82/1.65 % Given clauses 771.
% 0.82/1.65
% 0.82/1.65 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.65 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.65 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.65 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.65 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].
% 0.82/1.65 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].
% 0.82/1.65 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.65 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.65 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 (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 (Pid0 != Z & host(Pid0) = host(Z) -> -setIn(Z,alive) | -setIn(Pid0,alive))) & (all Z all Pid0 (setIn(Pid0,alive) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) -> leq(host(Z),index(pendack,host(Pid0))))) & (all Z all Pid0 (setIn(Pid0,alive) & index(status,host(Pid0)) = elec_1 -> -elem(m_Ack(Pid0,Z),queue(host(Pid0))))) & (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 Pid20 all 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 Pid0 (-leq(host(Z),host(Pid0)) & setIn(Z,alive) & setIn(Pid0,alive) & index(status,host(Z)) = elec_2 & index(status,host(Pid0)) = elec_2 -> leq(index(pendack,host(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & host(Pid0) = host(Pid20) & index(status,host(Z)) = elec_2 & index(status,host(Pid0)) = elec_2 -> -elem(m_Ack(Z,Pid20),queue(host(Z))))) & (all Z all Pid0 (-leq(host(Z),host(Pid0)) & setIn(Z,alive) & setIn(Pid0,alive) & index(status,host(Z)) = elec_2 & index(status,host(Pid0)) = elec_2 -> -leq(index(pendack,host(Z)),index(pendack,host(Pid0))))) & (all Z all Pid20 all Pid0 (-leq(index(pendack,host(Pid0)),host(Z)) & setIn(Pid0,alive) & elem(m_Halt(Pid0),queue(host(Pid20))) & index(status,host(Pid0)) = elec_2 -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))) & (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))) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid0) = nbr_proc & host(Pid0) = host(Pid30) & index(status,host(Pid0)) = elec_1 -> -(setIn(Z,alive) & elem(m_Down(Pid30),queue(host(Z)))))) & (all Z all Pid30 all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & elem(m_Ack(Pid0,Pid30),queue(host(Pid0))) & leq(nbr_proc,s(index(pendack,host(Pid0)))) & index(status,host(Pid0)) = elec_2 & host(Pid30) = index(pendack,host(Pid0)) & host(Pid20) = s(index(pendack,host(Pid0))) -> -(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) -> (setIn(Y0,alive) & leq(nbr_proc,s(index(pendack,host(Y0)))) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ldr(X))) & elem(m_Ack(Y0,W0),snoc(queue(host(Y0)),m_Ldr(X))) & index(status,host(Y0)) = elec_2 & host(W0) = index(pendack,host(Y0)) & host(X0) = s(index(pendack,host(Y0))) -> -(setIn(V0,alive) & host(X) = host(V0)))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.65 64 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(4)].
% 0.82/1.65 79 m_Ldr(A) != m_Ack(B,C) # label(axiom_14) # label(axiom). [clausify(8)].
% 0.82/1.65 83 m_Ldr(A) != m_Down(B) # label(axiom_18) # label(axiom). [clausify(12)].
% 0.82/1.65 108 init(snoc(A,B)) = A # label(axiom_38) # label(axiom). [clausify(31)].
% 0.82/1.65 119 elem(A,cons(B,C)) | B != A # label(axiom_46) # label(axiom). [clausify(39)].
% 0.82/1.65 121 -elem(A,snoc(B,C)) | C = A | elem(A,B) # label(axiom_47) # label(axiom). [clausify(40)].
% 0.82/1.65 152 -leq(A,B) | -leq(B,A) | B = A # label(axiom_61) # label(axiom). [clausify(53)].
% 0.82/1.65 158 -leq(A,s(B)) | s(B) = A | leq(A,B) # label(axiom_64) # label(axiom). [clausify(56)].
% 0.82/1.65 162 -elem(m_Down(A),queue(host(B))) | host(A) != host(B) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 171 leq(host(A),host(B)) | -setIn(A,alive) | -setIn(B,alive) | index(status,host(A)) != elec_2 | index(status,host(B)) != elec_2 | leq(index(pendack,host(B)),host(A)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 172 -setIn(A,alive) | -setIn(B,alive) | host(C) != host(B) | index(status,host(A)) != elec_2 | index(status,host(B)) != elec_2 | -elem(m_Ack(A,C),queue(host(A))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 181 cons(m_Down(c4),c1) = queue(host(c3)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 182 setIn(c3,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 184 index(status,host(c3)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 185 elec_2 = index(status,host(c3)). [copy(184),flip(a)].
% 0.82/1.65 186 index(pendack,host(c3)) = host(c4) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 187 leq(nbr_proc,index(pendack,host(c3))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 188 leq(nbr_proc,host(c4)). [copy(187),rewrite([186(5)])].
% 0.82/1.65 190 host(c6) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 191 host(c9) = host(c5) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 192 host(c9) != host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 193 host(c5) != host(c3). [copy(192),rewrite([191(2)])].
% 0.82/1.65 194 setIn(c9,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 195 leq(nbr_proc,s(index(pendack,host(c9)))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 196 leq(nbr_proc,s(index(pendack,host(c5)))). [copy(195),rewrite([191(4)])].
% 0.82/1.65 197 elem(m_Down(c8),snoc(queue(host(c9)),m_Ldr(c3))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 198 elem(m_Down(c8),snoc(queue(host(c5)),m_Ldr(c3))). [copy(197),rewrite([191(4)])].
% 0.82/1.65 199 elem(m_Ack(c9,c7),snoc(queue(host(c9)),m_Ldr(c3))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 200 elem(m_Ack(c9,c7),snoc(queue(host(c5)),m_Ldr(c3))). [copy(199),rewrite([191(5)])].
% 0.82/1.65 201 index(status,host(c9)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 202 index(status,host(c5)) = index(status,host(c3)). [copy(201),rewrite([191(3),185(5)])].
% 0.82/1.65 203 index(pendack,host(c9)) = host(c7) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 204 index(pendack,host(c5)) = host(c7). [copy(203),rewrite([191(3)])].
% 0.82/1.65 205 s(index(pendack,host(c9))) = host(c8) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.82/1.65 206 s(host(c7)) = host(c8). [copy(205),rewrite([191(3),204(4)])].
% 0.82/1.65 214 -setIn(A,alive) | -setIn(B,alive) | host(C) != host(B) | index(status,host(c3)) != index(status,host(A)) | index(status,host(c3)) != index(status,host(B)) | -elem(m_Ack(A,C),queue(host(A))). [back_rewrite(172),rewrite([185(11),185(19)]),flip(d),flip(e)].
% 0.82/1.65 215 leq(host(A),host(B)) | -setIn(A,alive) | -setIn(B,alive) | index(status,host(c3)) != index(status,host(A)) | index(status,host(c3)) != index(status,host(B)) | leq(index(pendack,host(B)),host(A)). [back_rewrite(171),rewrite([185(11),185(19)]),flip(d),flip(e)].
% 0.82/1.65 220 host(c5) = c_0. [new_symbol(193)].
% 0.82/1.65 221 leq(nbr_proc,s(index(pendack,c_0))). [back_rewrite(196),rewrite([220(4)])].
% 0.82/1.65 222 index(pendack,c_0) = host(c7). [back_rewrite(204),rewrite([220(3)])].
% 0.82/1.65 223 index(status,host(c3)) = index(status,c_0). [back_rewrite(202),rewrite([220(3)]),flip(a)].
% 0.82/1.65 224 elem(m_Ack(c9,c7),snoc(queue(c_0),m_Ldr(c3))). [back_rewrite(200),rewrite([220(5)])].
% 0.82/1.65 225 elem(m_Down(c8),snoc(queue(c_0),m_Ldr(c3))). [back_rewrite(198),rewrite([220(4)])].
% 0.82/1.65 226 host(c3) != c_0. [back_rewrite(193),rewrite([220(2)]),flip(a)].
% 0.82/1.65 227 host(c9) = c_0. [back_rewrite(191),rewrite([220(4)])].
% 0.82/1.65 229 leq(nbr_proc,host(c8)). [back_rewrite(221),rewrite([222(4),206(4)])].
% 0.82/1.65 234 leq(host(A),host(B)) | -setIn(A,alive) | -setIn(B,alive) | index(status,host(A)) != index(status,c_0) | index(status,host(B)) != index(status,c_0) | leq(index(pendack,host(B)),host(A)). [back_rewrite(215),rewrite([223(11),223(18)]),flip(d),flip(e)].
% 0.82/1.65 235 -setIn(A,alive) | -setIn(B,alive) | host(C) != host(B) | index(status,host(A)) != index(status,c_0) | index(status,host(B)) != index(status,c_0) | -elem(m_Ack(A,C),queue(host(A))). [back_rewrite(214),rewrite([223(11),223(18)]),flip(d),flip(e)].
% 0.82/1.65 268 elem(A,cons(A,B)). [resolve(119,b,108,a),rewrite([108(2)])].
% 0.82/1.65 348 host(c4) = nbr_proc. [resolve(188,a,152,b),flip(b),unit_del(a,64)].
% 0.82/1.65 349 index(pendack,host(c3)) = nbr_proc. [back_rewrite(186),rewrite([348(6)])].
% 0.82/1.65 353 -elem(m_Down(A),queue(host(c3))) | host(c3) != host(A). [para(190(a,1),162(a,2,1)),rewrite([190(8)]),flip(b)].
% 0.82/1.65 365 -leq(A,host(c8)) | host(c8) = A | leq(A,host(c7)). [para(206(a,1),158(a,2)),rewrite([206(6)])].
% 0.82/1.65 375 leq(c_0,nbr_proc). [para(220(a,1),64(a,1))].
% 0.82/1.65 377 -elem(m_Down(A),queue(c_0)) | host(A) != c_0. [para(220(a,1),162(a,2,1)),rewrite([220(7)])].
% 0.82/1.65 383 elem(m_Ack(c9,c7),queue(c_0)). [resolve(224,a,121,a),flip(a),unit_del(a(flip),79)].
% 0.82/1.65 389 elem(m_Down(c8),queue(c_0)). [resolve(225,a,121,a),unit_del(a,83)].
% 0.82/1.65 397 host(c8) = nbr_proc. [resolve(229,a,152,b),flip(b),unit_del(a,64)].
% 0.82/1.65 401 -leq(A,nbr_proc) | nbr_proc = A | leq(A,host(c7)). [back_rewrite(365),rewrite([397(2),397(4)])].
% 0.82/1.65 412 leq(c_0,host(A)) | -setIn(A,alive) | index(status,host(A)) != index(status,c_0) | leq(index(pendack,host(A)),c_0). [resolve(234,b,194,a),rewrite([227(2),227(8),227(24)]),xx(c)].
% 0.82/1.65 413 leq(host(c3),host(A)) | -setIn(A,alive) | index(status,host(A)) != index(status,c_0) | leq(index(pendack,host(A)),host(c3)). [resolve(234,b,182,a),rewrite([223(10)]),xx(c)].
% 0.82/1.65 416 -setIn(A,alive) | host(B) != host(A) | index(status,host(A)) != index(status,c_0) | -elem(m_Ack(c9,B),queue(c_0)). [resolve(235,a,194,a),rewrite([227(8),227(23)]),xx(c)].
% 0.82/1.66 461 -leq(nbr_proc,c_0) | c_0 = nbr_proc. [resolve(375,a,152,b)].
% 0.82/1.66 533 elem(m_Down(c4),queue(host(c3))). [para(181(a,1),268(a,2))].
% 0.82/1.66 575 c_0 != nbr_proc. [resolve(389,a,377,a),rewrite([397(2)]),flip(a)].
% 0.82/1.66 581 -leq(nbr_proc,c_0). [back_unit_del(461),unit_del(b,575)].
% 0.82/1.66 676 host(c3) != host(A) | -elem(m_Ack(c9,A),queue(c_0)). [resolve(416,a,182,a),rewrite([223(8)]),flip(a),xx(b)].
% 0.82/1.66 784 host(c7) != host(c3). [resolve(383,a,676,b),flip(a)].
% 0.82/1.66 869 host(c3) != nbr_proc. [resolve(533,a,353,a),rewrite([348(4)])].
% 0.82/1.66 2130 host(A) = nbr_proc | leq(host(A),host(c7)). [resolve(401,a,64,a),flip(a)].
% 0.82/1.66 2150 leq(c_0,host(c3)). [resolve(412,b,182,a),rewrite([223(8),349(15)]),xx(b),unit_del(b,581)].
% 0.82/1.66 2157 -leq(host(c3),c_0). [resolve(2150,a,152,b),flip(b),unit_del(b,226)].
% 0.82/1.66 2176 leq(host(c7),host(c3)). [resolve(413,b,194,a),rewrite([227(4),227(7),227(14),222(14)]),xx(b),unit_del(a,2157)].
% 0.82/1.66 2183 -leq(host(c3),host(c7)). [resolve(2176,a,152,b),unit_del(b,784)].
% 0.82/1.66 4013 $F. [resolve(2130,b,2183,a),unit_del(a,869)].
% 0.82/1.66
% 0.82/1.66 % SZS output end Refutation
% 0.82/1.66 ============================== end of proof ==========================
% 0.82/1.66
% 0.82/1.66 ============================== STATISTICS ============================
% 0.82/1.66
% 0.82/1.66 Given=771. Generated=17197. Kept=3936. proofs=1.
% 0.82/1.66 Usable=755. Sos=3077. Demods=35. Limbo=0, Disabled=237. Hints=0.
% 0.82/1.66 Megabytes=8.47.
% 0.82/1.66 User_CPU=0.57, System_CPU=0.01, Wall_clock=1.
% 0.82/1.66
% 0.82/1.66 ============================== end of statistics =====================
% 0.82/1.66
% 0.82/1.66 ============================== end of search =========================
% 0.82/1.66
% 0.82/1.66 THEOREM PROVED
% 0.82/1.66 % SZS status Theorem
% 0.82/1.66
% 0.82/1.66 Exiting with 1 proof.
% 0.82/1.66
% 0.82/1.66 Process 17693 exit (max_proofs) Wed Jun 15 20:22:22 2022
% 0.82/1.66 Prover9 interrupted
%------------------------------------------------------------------------------