TSTP Solution File: SWV465+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV465+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 0.90s 1.19s
% Output : Refutation 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV465+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n003.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 : Thu Jun 16 06:21:11 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/1.06 ============================== Prover9 ===============================
% 0.45/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.06 Process 2536 was started by sandbox on n003.cluster.edu,
% 0.45/1.06 Thu Jun 16 06:21:12 2022
% 0.45/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2383_n003.cluster.edu".
% 0.45/1.06 ============================== end of head ===========================
% 0.45/1.06
% 0.45/1.06 ============================== INPUT =================================
% 0.45/1.06
% 0.45/1.06 % Reading from file /tmp/Prover9_2383_n003.cluster.edu
% 0.45/1.06
% 0.45/1.06 set(prolog_style_variables).
% 0.45/1.06 set(auto2).
% 0.45/1.06 % set(auto2) -> set(auto).
% 0.45/1.06 % set(auto) -> set(auto_inference).
% 0.45/1.06 % set(auto) -> set(auto_setup).
% 0.45/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.06 % set(auto) -> set(auto_limits).
% 0.45/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.06 % set(auto) -> set(auto_denials).
% 0.45/1.06 % set(auto) -> set(auto_process).
% 0.45/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.06 % set(auto2) -> assign(stats, some).
% 0.45/1.06 % set(auto2) -> clear(echo_input).
% 0.45/1.06 % set(auto2) -> set(quiet).
% 0.45/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.06 % set(auto2) -> clear(print_given).
% 0.45/1.06 assign(lrs_ticks,-1).
% 0.45/1.06 assign(sos_limit,10000).
% 0.45/1.06 assign(order,kbo).
% 0.45/1.06 set(lex_order_vars).
% 0.45/1.06 clear(print_given).
% 0.45/1.06
% 0.45/1.06 % formulas(sos). % not echoed (67 formulas)
% 0.45/1.06
% 0.45/1.06 ============================== end of input ==========================
% 0.45/1.06
% 0.45/1.06 % From the command line: assign(max_seconds, 300).
% 0.45/1.06
% 0.45/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.06
% 0.45/1.06 % Formulas that are not ordinary clauses:
% 0.45/1.06 1 (all Pid all Pid2 (elem(m_Ack(Pid,Pid2),queue(host(Pid))) -> setIn(Pid,pids) & setIn(Pid2,pids))) # label(axiom) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 2 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 5 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 6 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 7 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 9 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 10 (all X all Y m_NotNorm(X) != m_Halt(Y)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 11 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 13 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 14 (all X all Y m_Down(X) != m_NormQ(Y)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 15 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 16 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 17 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 18 (all X all Y m_Ldr(X) != m_NotNorm(Y)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 19 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 20 (all X all Y (X != Y <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 21 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 22 (all X all Y (X != Y <-> m_NotNorm(X) != m_NotNorm(Y))) # label(axiom_28) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 23 (all X all Y (X != Y <-> m_Ldr(X) != m_Ldr(Y))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 24 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 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].
% 0.45/1.06 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].
% 0.45/1.06 27 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 28 (all X all Q head(cons(X,Q)) = X) # label(axiom_35) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 29 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 30 (all Y all Q last(snoc(Q,Y)) = Y) # label(axiom_37) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 32 (all Q (Q = q_nil | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 33 (all Q (Q = q_nil | Q = snoc(init(Q),last(Q)))) # label(axiom_40) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 34 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 35 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 36 (all X cons(X,q_nil) = snoc(q_nil,X)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 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].
% 0.45/1.06 38 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 39 (all X all Y all Q (elem(X,cons(Y,Q)) <-> X = Y | elem(X,Q))) # label(axiom_46) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 40 (all X all Y all Q (elem(X,snoc(Q,Y)) <-> X = Y | elem(X,Q))) # label(axiom_47) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 41 (all X (pidElem(X) <-> (exists Y (X = m_Halt(Y) | X = m_Down(Y))))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 42 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 43 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 44 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 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].
% 0.45/1.06 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].
% 0.45/1.06 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].
% 0.45/1.06 48 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 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].
% 0.45/1.06 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 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].
% 0.45/1.06 55 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 57 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 58 -(all V all W all X ((all Y all Z (elem(m_Ldr(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) & (all Y all Z (elem(m_Down(Z),queue(host(Y))) -> host(Z) != host(Y))) & (all Y all Z (elem(m_Halt(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) & (all Y all Z all Pid0 (elem(m_Ack(Pid0,Y),queue(host(Z))) -> -leq(host(Y),host(Pid0)))) & (all Y all Z (Z != Y & host(Z) = host(Y) -> -setIn(Y,alive) | -setIn(Z,alive))) & (all Y all Z (setIn(Z,alive) & elem(m_Ack(Z,Y),queue(host(Z))) -> leq(host(Y),index(pendack,host(Z))))) & (all Y all Z (setIn(Z,alive) & index(status,host(Z)) = elec_1 -> -elem(m_Ack(Z,Y),queue(host(Z))))) & (all Y ((index(status,host(Y)) = elec_1 | index(status,host(Y)) = elec_2) & setIn(Y,alive) -> index(elid,host(Y)) = Y)) & (all Y all Z (-leq(host(Y),host(Z)) & setIn(Y,alive) & setIn(Z,alive) & index(status,host(Y)) = elec_2 & index(status,host(Z)) = elec_2 -> leq(index(pendack,host(Z)),host(Y)))) & (all Y all Z all Pid0 (setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & host(Z) = host(Y) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & (all Y all Z all Pid0 (setIn(Y,alive) & setIn(Pid0,alive) & host(Pid0) = host(Z) & index(status,host(Y)) = elec_2 & index(status,host(Pid0)) = elec_2 -> -elem(m_Ack(Y,Z),queue(host(Y))))) & (all Y all Z (-leq(host(Y),host(Z)) & setIn(Y,alive) & setIn(Z,alive) & index(status,host(Y)) = elec_2 & index(status,host(Z)) = elec_2 -> -leq(index(pendack,host(Y)),index(pendack,host(Z))))) & (all Y all Z all Pid0 (-leq(index(pendack,host(Pid0)),host(Y)) & setIn(Pid0,alive) & elem(m_Halt(Pid0),queue(host(Z))) & index(status,host(Pid0)) = elec_2 -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & (all Y all Z 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) = host(Z) & host(Pid0) = nbr_proc & index(status,host(Pid0)) = elec_1 -> -(setIn(Y,alive) & elem(m_Down(Z),queue(host(Y)))))) & (all Y all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & elem(m_Down(Pid20),queue(host(Pid0))) & leq(nbr_proc,s(index(pendack,host(Pid0)))) & index(status,host(Pid0)) = elec_2 & host(Z) = index(pendack,host(Pid0)) & host(Pid20) = s(index(pendack,host(Pid0))) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & queue(host(X)) = cons(m_NormQ(W),V) -> (setIn(X,alive) -> (index(status,host(X)) != norm -> (all Y all Z all X0 all Y0 (host(W) = host(Y0) -> (host(X) = host(Y0) -> (setIn(Y0,alive) & elem(m_Down(X0),snoc(V,m_NotNorm(W))) & elem(m_Ack(Y0,Z),snoc(V,m_NotNorm(W))) & leq(nbr_proc,s(index(pendack,host(Y0)))) & index(status,host(Y0)) = elec_2 & host(Z) = index(pendack,host(Y0)) & host(X0) = s(index(pendack,host(Y0))) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.06
% 0.45/1.06 ============================== end of process non-clausal formulas ===
% 0.45/1.06
% 0.45/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.06
% 0.45/1.06 ============================== PREDICATE ELIMINATION =================
% 0.90/1.19
% 0.90/1.19 ============================== end predicate elimination =============
% 0.90/1.19
% 0.90/1.19 Auto_denials: (non-Horn, no changes).
% 0.90/1.19
% 0.90/1.19 Term ordering decisions:
% 0.90/1.19 Function symbol KB weights: alive=1. status=1. pendack=1. elec_2=1. q_nil=1. nbr_proc=1. zero=1. elec_1=1. elid=1. ldr=1. norm=1. pids=1. down=1. nil=1. setEmpty=1. wait=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. index=1. snoc=1. cons=1. m_Ack=1. f2=1. f3=1. host=1. pidMsg=1. s=1. m_Down=1. m_Halt=1. queue=1. m_NotNorm=1. m_Ldr=1. m_NormQ=1. head=1. init=1. last=1. tail=1. f1=1. f4=1.
% 0.90/1.19
% 0.90/1.19 ============================== end of process initial clauses ========
% 0.90/1.19
% 0.90/1.19 ============================== CLAUSES FOR SEARCH ====================
% 0.90/1.19
% 0.90/1.19 ============================== end of clauses for search =============
% 0.90/1.19
% 0.90/1.19 ============================== SEARCH ================================
% 0.90/1.19
% 0.90/1.19 % Starting search at 0.03 seconds.
% 0.90/1.19
% 0.90/1.19 ============================== PROOF =================================
% 0.90/1.19 % SZS status Theorem
% 0.90/1.19 % SZS output start Refutation
% 0.90/1.19
% 0.90/1.19 % Proof 1 at 0.14 (+ 0.01) seconds.
% 0.90/1.19 % Length of proof is 54.
% 0.90/1.19 % Level of proof is 9.
% 0.90/1.19 % Maximum clause weight is 66.000.
% 0.90/1.19 % Given clauses 273.
% 0.90/1.19
% 0.90/1.19 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 7 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 13 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 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].
% 0.90/1.19 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].
% 0.90/1.19 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 58 -(all V all W all X ((all Y all Z (elem(m_Ldr(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) & (all Y all Z (elem(m_Down(Z),queue(host(Y))) -> host(Z) != host(Y))) & (all Y all Z (elem(m_Halt(Z),queue(host(Y))) -> -leq(host(Y),host(Z)))) & (all Y all Z all Pid0 (elem(m_Ack(Pid0,Y),queue(host(Z))) -> -leq(host(Y),host(Pid0)))) & (all Y all Z (Z != Y & host(Z) = host(Y) -> -setIn(Y,alive) | -setIn(Z,alive))) & (all Y all Z (setIn(Z,alive) & elem(m_Ack(Z,Y),queue(host(Z))) -> leq(host(Y),index(pendack,host(Z))))) & (all Y all Z (setIn(Z,alive) & index(status,host(Z)) = elec_1 -> -elem(m_Ack(Z,Y),queue(host(Z))))) & (all Y ((index(status,host(Y)) = elec_1 | index(status,host(Y)) = elec_2) & setIn(Y,alive) -> index(elid,host(Y)) = Y)) & (all Y all Z (-leq(host(Y),host(Z)) & setIn(Y,alive) & setIn(Z,alive) & index(status,host(Y)) = elec_2 & index(status,host(Z)) = elec_2 -> leq(index(pendack,host(Z)),host(Y)))) & (all Y all Z all Pid0 (setIn(Pid0,alive) & elem(m_Down(Z),queue(host(Pid0))) & host(Z) = host(Y) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & (all Y all Z all Pid0 (setIn(Y,alive) & setIn(Pid0,alive) & host(Pid0) = host(Z) & index(status,host(Y)) = elec_2 & index(status,host(Pid0)) = elec_2 -> -elem(m_Ack(Y,Z),queue(host(Y))))) & (all Y all Z (-leq(host(Y),host(Z)) & setIn(Y,alive) & setIn(Z,alive) & index(status,host(Y)) = elec_2 & index(status,host(Z)) = elec_2 -> -leq(index(pendack,host(Y)),index(pendack,host(Z))))) & (all Y all Z all Pid0 (-leq(index(pendack,host(Pid0)),host(Y)) & setIn(Pid0,alive) & elem(m_Halt(Pid0),queue(host(Z))) & index(status,host(Pid0)) = elec_2 -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & (all Y all Z 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) = host(Z) & host(Pid0) = nbr_proc & index(status,host(Pid0)) = elec_1 -> -(setIn(Y,alive) & elem(m_Down(Z),queue(host(Y)))))) & (all Y all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & elem(m_Down(Pid20),queue(host(Pid0))) & leq(nbr_proc,s(index(pendack,host(Pid0)))) & index(status,host(Pid0)) = elec_2 & host(Z) = index(pendack,host(Pid0)) & host(Pid20) = s(index(pendack,host(Pid0))) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & queue(host(X)) = cons(m_NormQ(W),V) -> (setIn(X,alive) -> (index(status,host(X)) != norm -> (all Y all Z all X0 all Y0 (host(W) = host(Y0) -> (host(X) = host(Y0) -> (setIn(Y0,alive) & elem(m_Down(X0),snoc(V,m_NotNorm(W))) & elem(m_Ack(Y0,Z),snoc(V,m_NotNorm(W))) & leq(nbr_proc,s(index(pendack,host(Y0)))) & index(status,host(Y0)) = elec_2 & host(Z) = index(pendack,host(Y0)) & host(X0) = s(index(pendack,host(Y0))) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.90/1.19 64 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(4)].
% 0.90/1.19 78 m_NotNorm(A) != m_Ack(B,C) # label(axiom_13) # label(axiom). [clausify(7)].
% 0.90/1.19 84 m_NotNorm(A) != m_Down(B) # label(axiom_19) # label(axiom). [clausify(13)].
% 0.90/1.19 120 elem(A,cons(B,C)) | -elem(A,C) # label(axiom_46) # label(axiom). [clausify(39)].
% 0.90/1.19 121 -elem(A,snoc(B,C)) | C = A | elem(A,B) # label(axiom_47) # label(axiom). [clausify(40)].
% 0.90/1.19 152 -leq(A,B) | -leq(B,A) | B = A # label(axiom_61) # label(axiom). [clausify(53)].
% 0.90/1.19 169 index(status,host(A)) != elec_2 | -setIn(A,alive) | index(elid,host(A)) = A # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 180 -setIn(A,alive) | -elem(m_Ack(A,B),queue(host(A))) | -elem(m_Down(C),queue(host(A))) | -leq(nbr_proc,s(index(pendack,host(A)))) | index(status,host(A)) != elec_2 | index(pendack,host(A)) != host(B) | s(index(pendack,host(A))) != host(C) | -setIn(D,alive) | index(ldr,host(D)) != host(D) | index(status,host(D)) != norm # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 181 cons(m_NormQ(c2),c1) = queue(host(c3)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 182 setIn(c3,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 184 host(c7) = host(c2) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 185 host(c7) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 186 host(c3) = host(c2). [copy(185),rewrite([184(2)]),flip(a)].
% 0.90/1.19 187 setIn(c7,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 188 elem(m_Down(c6),snoc(c1,m_NotNorm(c2))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 189 elem(m_Ack(c7,c5),snoc(c1,m_NotNorm(c2))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 190 leq(nbr_proc,s(index(pendack,host(c7)))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 191 leq(nbr_proc,s(index(pendack,host(c2)))). [copy(190),rewrite([184(4)])].
% 0.90/1.19 192 index(status,host(c7)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 193 elec_2 = index(status,host(c2)). [copy(192),rewrite([184(3)]),flip(a)].
% 0.90/1.19 194 index(pendack,host(c7)) = host(c5) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 195 index(pendack,host(c2)) = host(c5). [copy(194),rewrite([184(3)])].
% 0.90/1.19 196 s(index(pendack,host(c7))) = host(c6) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 197 s(host(c5)) = host(c6). [copy(196),rewrite([184(3),195(4)])].
% 0.90/1.19 198 setIn(c4,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 199 index(ldr,host(c4)) = host(c4) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 200 index(status,host(c4)) = norm # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.90/1.19 201 norm = index(status,host(c4)). [copy(200),flip(a)].
% 0.90/1.19 210 cons(m_NormQ(c2),c1) = queue(host(c2)). [back_rewrite(181),rewrite([186(6)])].
% 0.90/1.19 211 -setIn(A,alive) | -elem(m_Ack(A,B),queue(host(A))) | -elem(m_Down(C),queue(host(A))) | -leq(nbr_proc,s(index(pendack,host(A)))) | index(status,host(c2)) != index(status,host(A)) | index(pendack,host(A)) != host(B) | s(index(pendack,host(A))) != host(C) | -setIn(D,alive) | index(ldr,host(D)) != host(D) | index(status,host(c4)) != index(status,host(D)). [back_rewrite(180),rewrite([193(20),201(46)]),flip(e),flip(j)].
% 0.90/1.19 216 index(status,host(c2)) != index(status,host(A)) | -setIn(A,alive) | index(elid,host(A)) = A. [back_rewrite(169),rewrite([193(4)]),flip(a)].
% 0.90/1.19 219 leq(nbr_proc,host(c6)). [back_rewrite(191),rewrite([195(5),197(4)])].
% 0.90/1.19 328 elem(m_Down(c6),c1). [resolve(188,a,121,a),unit_del(a,84)].
% 0.90/1.19 333 elem(m_Ack(c7,c5),c1). [resolve(189,a,121,a),flip(a),unit_del(a(flip),78)].
% 0.90/1.19 354 -elem(m_Ack(c3,A),queue(host(c2))) | -elem(m_Down(B),queue(host(c2))) | host(c5) != host(A) | host(c6) != host(B) | -setIn(C,alive) | index(ldr,host(C)) != host(C) | index(status,host(c4)) != index(status,host(C)). [resolve(211,a,182,a),rewrite([186(4),186(9),186(15),195(16),197(15),186(22),186(27),195(28),186(31),195(32),197(31)]),xx(d),unit_del(c,219)].
% 0.90/1.19 366 index(elid,host(c2)) = c7. [resolve(216,b,187,a),rewrite([184(7),184(12)]),xx(a)].
% 0.90/1.19 367 c7 = c3. [resolve(216,b,182,a),rewrite([186(7),186(12),366(13)]),xx(a)].
% 0.90/1.19 370 elem(m_Ack(c3,c5),c1). [back_rewrite(333),rewrite([367(1)])].
% 0.90/1.19 379 host(c6) = nbr_proc. [resolve(219,a,152,b),flip(b),unit_del(a,64)].
% 0.90/1.19 380 -elem(m_Ack(c3,A),queue(host(c2))) | -elem(m_Down(B),queue(host(c2))) | host(c5) != host(A) | host(B) != nbr_proc | -setIn(C,alive) | index(ldr,host(C)) != host(C) | index(status,host(c4)) != index(status,host(C)). [back_rewrite(354),rewrite([379(17)]),flip(d)].
% 0.90/1.19 443 elem(m_Down(c6),cons(A,c1)). [resolve(328,a,120,b)].
% 0.90/1.19 524 elem(m_Ack(c3,c5),cons(A,c1)). [resolve(370,a,120,b)].
% 0.90/1.19 652 elem(m_Down(c6),queue(host(c2))). [para(210(a,1),443(a,2))].
% 0.90/1.19 700 -elem(m_Ack(c3,A),queue(host(c2))) | -elem(m_Down(B),queue(host(c2))) | host(c5) != host(A) | host(B) != nbr_proc. [resolve(380,e,198,a),rewrite([199(22)]),xx(e),xx(f)].
% 0.90/1.19 765 -elem(m_Ack(c3,A),queue(host(c2))) | host(c5) != host(A). [resolve(652,a,700,b),rewrite([379(12)]),xx(c)].
% 0.90/1.19 945 elem(m_Ack(c3,c5),queue(host(c2))). [para(210(a,1),524(a,2))].
% 0.90/1.19 1016 $F. [resolve(945,a,765,a),xx(a)].
% 0.90/1.19
% 0.90/1.19 % SZS output end Refutation
% 0.90/1.19 ============================== end of proof ==========================
% 0.90/1.19
% 0.90/1.19 ============================== STATISTICS ============================
% 0.90/1.19
% 0.90/1.19 Given=273. Generated=2691. Kept=942. proofs=1.
% 0.90/1.19 Usable=261. Sos=605. Demods=32. Limbo=0, Disabled=206. Hints=0.
% 0.90/1.19 Megabytes=2.05.
% 0.90/1.19 User_CPU=0.14, System_CPU=0.01, Wall_clock=0.
% 0.90/1.19
% 0.90/1.19 ============================== end of statistics =====================
% 0.90/1.19
% 0.90/1.19 ============================== end of search =========================
% 0.90/1.19
% 0.90/1.19 THEOREM PROVED
% 0.90/1.19 % SZS status Theorem
% 0.90/1.19
% 0.90/1.19 Exiting with 1 proof.
% 0.90/1.19
% 0.90/1.19 Process 2536 exit (max_proofs) Thu Jun 16 06:21:12 2022
% 0.90/1.19 Prover9 interrupted
%------------------------------------------------------------------------------