TSTP Solution File: SWV457+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV457+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 21:13:07 EDT 2022
% Result : Theorem 1.05s 1.32s
% Output : Refutation 1.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV457+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 09:57:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.76/1.03 ============================== Prover9 ===============================
% 0.76/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.03 Process 29463 was started by sandbox on n019.cluster.edu,
% 0.76/1.03 Wed Jun 15 09:57:25 2022
% 0.76/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29309_n019.cluster.edu".
% 0.76/1.03 ============================== end of head ===========================
% 0.76/1.03
% 0.76/1.03 ============================== INPUT =================================
% 0.76/1.03
% 0.76/1.03 % Reading from file /tmp/Prover9_29309_n019.cluster.edu
% 0.76/1.03
% 0.76/1.03 set(prolog_style_variables).
% 0.76/1.03 set(auto2).
% 0.76/1.03 % set(auto2) -> set(auto).
% 0.76/1.03 % set(auto) -> set(auto_inference).
% 0.76/1.03 % set(auto) -> set(auto_setup).
% 0.76/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.03 % set(auto) -> set(auto_limits).
% 0.76/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.03 % set(auto) -> set(auto_denials).
% 0.76/1.03 % set(auto) -> set(auto_process).
% 0.76/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.03 % set(auto2) -> assign(stats, some).
% 0.76/1.03 % set(auto2) -> clear(echo_input).
% 0.76/1.03 % set(auto2) -> set(quiet).
% 0.76/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.03 % set(auto2) -> clear(print_given).
% 0.76/1.03 assign(lrs_ticks,-1).
% 0.76/1.03 assign(sos_limit,10000).
% 0.76/1.03 assign(order,kbo).
% 0.76/1.03 set(lex_order_vars).
% 0.76/1.03 clear(print_given).
% 0.76/1.03
% 0.76/1.03 % formulas(sos). % not echoed (67 formulas)
% 0.76/1.03
% 0.76/1.03 ============================== end of input ==========================
% 0.76/1.03
% 0.76/1.03 % From the command line: assign(max_seconds, 300).
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.03
% 0.76/1.03 % Formulas that are not ordinary clauses:
% 0.76/1.03 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].
% 0.76/1.03 2 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 5 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 6 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 7 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 9 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 10 (all X all Y m_NotNorm(X) != m_Halt(Y)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 11 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 13 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 14 (all X all Y m_Down(X) != m_NormQ(Y)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 15 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 16 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 17 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 18 (all X all Y m_Ldr(X) != m_NotNorm(Y)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 19 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 20 (all X all Y (X != Y <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 21 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 22 (all X all Y (X != Y <-> m_NotNorm(X) != m_NotNorm(Y))) # label(axiom_28) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 23 (all X all Y (X != Y <-> m_Ldr(X) != m_Ldr(Y))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 24 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 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].
% 0.76/1.03 27 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 28 (all X all Q head(cons(X,Q)) = X) # label(axiom_35) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 29 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 30 (all Y all Q last(snoc(Q,Y)) = Y) # label(axiom_37) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 32 (all Q (Q = q_nil | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 33 (all Q (Q = q_nil | Q = snoc(init(Q),last(Q)))) # label(axiom_40) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 34 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 35 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 36 (all X cons(X,q_nil) = snoc(q_nil,X)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 38 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 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].
% 0.76/1.03 41 (all X (pidElem(X) <-> (exists Y (X = m_Halt(Y) | X = m_Down(Y))))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 42 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 43 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 44 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 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].
% 0.76/1.03 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].
% 0.76/1.03 48 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.04 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 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].
% 0.76/1.04 55 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 57 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 58 -(all V all W all X ((all Y all Z (elem(m_Ack(Z,Y),queue(host(Z))) -> setIn(Z,pids))) & (all Y all Z (elem(m_Down(Z),queue(host(Y))) -> -setIn(Z,alive))) & (all Y all Z (elem(m_Ldr(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 (-setIn(Y,alive) & leq(Z,Y) & host(Z) = host(Y) -> -setIn(Z,alive))) & (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(Y,Z),queue(host(Y))))) & (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 all Pid0 (elem(m_Down(Y),queue(host(Z))) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & host(Pid0) = host(Y) -> -setIn(Pid0,alive))) & (all Y all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & elem(m_Ack(Pid0,Y),queue(host(Pid0))) & host(Z) = host(Y) -> -setIn(host(Pid0),index(down,host(Z))))) & (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 Pid0 (setIn(Pid0,alive) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & leq(nbr_proc,index(pendack,host(Pid0))) & index(status,host(Pid0)) = elec_2 & host(Z) = index(pendack,host(Pid0)) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & queue(host(W)) = cons(m_Halt(X),V) -> (setIn(W,alive) -> (all Y (host(W) != host(Y) -> (all Z all X0 (host(X) = host(X0) -> (host(W) != host(X0) -> (setIn(X0,alive) & leq(nbr_proc,index(pendack,host(X0))) & elem(m_Ack(X0,Z),snoc(queue(host(X0)),m_Ack(X,W))) & index(status,host(X0)) = elec_2 & host(Z) = index(pendack,host(X0)) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm)))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.04
% 0.76/1.04 ============================== end of process non-clausal formulas ===
% 0.76/1.04
% 0.76/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.04
% 0.76/1.04 ============================== PREDICATE ELIMINATION =================
% 0.76/1.04
% 0.76/1.04 ============================== end predicate elimination =============
% 0.76/1.04
% 0.76/1.04 Auto_denials: (non-Horn, no changes).
% 0.76/1.04
% 0.76/1.04 Term ordering decisions:
% 0.76/1.04 Function symbol KB weights: alive=1. status=1. q_nil=1. pendack=1. elec_2=1. nbr_proc=1. pids=1. elid=1. ldr=1. norm=1. zero=1. elec_1=1. down=1. nil=1. setEmpty=1. wait=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. snoc=1. cons=1. index=1. m_Ack=1. f2=1. f3=1. host=1. pidMsg=1. s=1. m_Halt=1. m_Down=1. queue=1. m_Ldr=1. m_NormQ=1. m_NotNorm=1. head=1. init=1. last=1. tail=1. f1=1.
% 0.76/1.04
% 0.76/1.04 ============================== end of process initial clauses ========
% 1.05/1.32
% 1.05/1.32 ============================== CLAUSES FOR SEARCH ====================
% 1.05/1.32
% 1.05/1.32 ============================== end of clauses for search =============
% 1.05/1.32
% 1.05/1.32 ============================== SEARCH ================================
% 1.05/1.32
% 1.05/1.32 % Starting search at 0.03 seconds.
% 1.05/1.32
% 1.05/1.32 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 129 (0.00 of 0.27 sec).
% 1.05/1.32
% 1.05/1.32 ============================== PROOF =================================
% 1.05/1.32 % SZS status Theorem
% 1.05/1.32 % SZS output start Refutation
% 1.05/1.32
% 1.05/1.32 % Proof 1 at 0.30 (+ 0.01) seconds.
% 1.05/1.32 % Length of proof is 61.
% 1.05/1.32 % Level of proof is 14.
% 1.05/1.32 % Maximum clause weight is 50.000.
% 1.05/1.32 % Given clauses 537.
% 1.05/1.32
% 1.05/1.32 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.32 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].
% 1.05/1.32 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].
% 1.05/1.32 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.32 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].
% 1.05/1.32 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].
% 1.05/1.32 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.32 58 -(all V all W all X ((all Y all Z (elem(m_Ack(Z,Y),queue(host(Z))) -> setIn(Z,pids))) & (all Y all Z (elem(m_Down(Z),queue(host(Y))) -> -setIn(Z,alive))) & (all Y all Z (elem(m_Ldr(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 (-setIn(Y,alive) & leq(Z,Y) & host(Z) = host(Y) -> -setIn(Z,alive))) & (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(Y,Z),queue(host(Y))))) & (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 all Pid0 (elem(m_Down(Y),queue(host(Z))) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & host(Pid0) = host(Y) -> -setIn(Pid0,alive))) & (all Y all Z all Pid0 (setIn(Z,alive) & setIn(Pid0,alive) & elem(m_Ack(Pid0,Y),queue(host(Pid0))) & host(Z) = host(Y) -> -setIn(host(Pid0),index(down,host(Z))))) & (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 Pid0 (setIn(Pid0,alive) & elem(m_Ack(Pid0,Z),queue(host(Pid0))) & leq(nbr_proc,index(pendack,host(Pid0))) & index(status,host(Pid0)) = elec_2 & host(Z) = index(pendack,host(Pid0)) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm))) & queue(host(W)) = cons(m_Halt(X),V) -> (setIn(W,alive) -> (all Y (host(W) != host(Y) -> (all Z all X0 (host(X) = host(X0) -> (host(W) != host(X0) -> (setIn(X0,alive) & leq(nbr_proc,index(pendack,host(X0))) & elem(m_Ack(X0,Z),snoc(queue(host(X0)),m_Ack(X,W))) & index(status,host(X0)) = elec_2 & host(Z) = index(pendack,host(X0)) -> -(setIn(Y,alive) & index(ldr,host(Y)) = host(Y) & index(status,host(Y)) = norm)))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.05/1.32 64 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(4)].
% 1.05/1.32 100 A = B | m_Ack(A,C) != m_Ack(B,D) # label(axiom_31) # label(axiom). [clausify(25)].
% 1.05/1.32 101 A = B | m_Ack(C,A) != m_Ack(D,B) # label(axiom_32) # label(axiom). [clausify(26)].
% 1.05/1.32 107 init(snoc(A,B)) = A # label(axiom_38) # label(axiom). [clausify(31)].
% 1.05/1.32 118 elem(A,cons(B,C)) | B != A # label(axiom_46) # label(axiom). [clausify(39)].
% 1.05/1.32 120 -elem(A,snoc(B,C)) | C = A | elem(A,B) # label(axiom_47) # label(axiom). [clausify(40)].
% 1.05/1.32 151 -leq(A,B) | -leq(B,A) | B = A # label(axiom_61) # label(axiom). [clausify(53)].
% 1.05/1.32 173 leq(index(pendack,host(A)),host(B)) | -setIn(A,alive) | -elem(m_Halt(A),queue(host(C))) | index(status,host(A)) != elec_2 | -setIn(B,alive) | index(ldr,host(B)) != host(B) | index(status,host(B)) != norm # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 174 -setIn(A,alive) | -elem(m_Ack(A,B),queue(host(A))) | -leq(nbr_proc,index(pendack,host(A))) | index(status,host(A)) != elec_2 | index(pendack,host(A)) != host(B) | -setIn(C,alive) | index(ldr,host(C)) != host(C) | index(status,host(C)) != norm # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 175 cons(m_Halt(c3),c1) = queue(host(c2)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 177 host(c2) != host(c4) # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 178 host(c4) != host(c2). [copy(177),flip(a)].
% 1.05/1.32 179 host(c6) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 182 setIn(c6,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 183 leq(nbr_proc,index(pendack,host(c6))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 184 leq(nbr_proc,index(pendack,host(c3))). [copy(183),rewrite([179(4)])].
% 1.05/1.32 185 elem(m_Ack(c6,c5),snoc(queue(host(c6)),m_Ack(c3,c2))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 186 elem(m_Ack(c6,c5),snoc(queue(host(c3)),m_Ack(c3,c2))). [copy(185),rewrite([179(5)])].
% 1.05/1.32 187 index(status,host(c6)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 188 elec_2 = index(status,host(c3)). [copy(187),rewrite([179(3)]),flip(a)].
% 1.05/1.32 189 index(pendack,host(c6)) = host(c5) # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 190 index(pendack,host(c3)) = host(c5). [copy(189),rewrite([179(3)])].
% 1.05/1.32 191 setIn(c4,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 192 index(ldr,host(c4)) = host(c4) # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 193 index(status,host(c4)) = norm # label(conj) # label(negated_conjecture). [clausify(58)].
% 1.05/1.32 194 norm = index(status,host(c4)). [copy(193),flip(a)].
% 1.05/1.32 198 host(c4) = c_0. [new_symbol(178)].
% 1.05/1.32 199 -setIn(A,alive) | -elem(m_Ack(A,B),queue(host(A))) | -leq(nbr_proc,index(pendack,host(A))) | index(status,host(c3)) != index(status,host(A)) | index(pendack,host(A)) != host(B) | -setIn(C,alive) | index(ldr,host(C)) != host(C) | index(status,host(C)) != index(status,c_0). [back_rewrite(174),rewrite([188(15),194(35),198(37)]),flip(d)].
% 1.05/1.32 200 leq(index(pendack,host(A)),host(B)) | -setIn(A,alive) | -elem(m_Halt(A),queue(host(C))) | index(status,host(c3)) != index(status,host(A)) | -setIn(B,alive) | index(ldr,host(B)) != host(B) | index(status,host(B)) != index(status,c_0). [back_rewrite(173),rewrite([188(15),194(30),198(32)]),flip(d)].
% 1.05/1.32 206 leq(nbr_proc,host(c5)). [back_rewrite(184),rewrite([190(5)])].
% 1.05/1.32 212 index(ldr,c_0) = c_0. [back_rewrite(192),rewrite([198(3),198(5)])].
% 1.05/1.32 213 host(c2) != c_0. [back_rewrite(178),rewrite([198(2)]),flip(a)].
% 1.05/1.32 239 elem(A,cons(A,B)). [resolve(118,b,107,a),rewrite([107(2)])].
% 1.05/1.32 325 m_Ack(c6,c5) = m_Ack(c3,c2) | elem(m_Ack(c6,c5),queue(host(c3))). [resolve(186,a,120,a),flip(a)].
% 1.05/1.32 338 leq(c_0,nbr_proc). [para(198(a,1),64(a,1))].
% 1.05/1.32 344 -elem(m_Ack(c6,A),queue(host(c3))) | host(c5) != host(A) | -setIn(B,alive) | index(ldr,host(B)) != host(B) | index(status,host(B)) != index(status,c_0). [resolve(199,a,182,a),rewrite([179(4),179(10),190(11),179(17),179(22),190(23)]),xx(c),unit_del(b,206)].
% 1.05/1.32 349 leq(index(pendack,host(A)),c_0) | -setIn(A,alive) | -elem(m_Halt(A),queue(host(B))) | index(status,host(c3)) != index(status,host(A)). [resolve(200,e,191,a),rewrite([198(5),198(22),212(22),198(22),198(25)]),xx(e),xx(f)].
% 1.05/1.32 361 host(c5) = nbr_proc. [resolve(206,a,151,b),flip(b),unit_del(a,64)].
% 1.05/1.32 365 -elem(m_Ack(c6,A),queue(host(c3))) | host(A) != nbr_proc | -setIn(B,alive) | index(ldr,host(B)) != host(B) | index(status,host(B)) != index(status,c_0). [back_rewrite(344),rewrite([361(8)]),flip(b)].
% 1.05/1.32 366 index(pendack,host(c3)) = nbr_proc. [back_rewrite(190),rewrite([361(6)])].
% 1.05/1.32 399 -leq(nbr_proc,c_0) | c_0 = nbr_proc. [resolve(338,a,151,b)].
% 1.05/1.32 450 elem(m_Halt(c3),queue(host(c2))). [para(175(a,1),239(a,2))].
% 1.05/1.32 890 -elem(m_Ack(c6,A),queue(host(c3))) | host(A) != nbr_proc. [resolve(365,c,191,a),rewrite([198(12),212(12),198(12),198(15)]),xx(c),xx(d)].
% 1.05/1.32 2167 m_Ack(c6,c5) = m_Ack(c3,c2). [resolve(325,b,890,a),rewrite([361(9)]),xx(b)].
% 1.05/1.32 2193 c5 = c2. [resolve(2167,a,101,b)].
% 1.05/1.32 2194 c6 = c3. [resolve(2167,a,100,b)].
% 1.05/1.32 2218 host(c2) = nbr_proc. [back_rewrite(361),rewrite([2193(1)])].
% 1.05/1.32 2281 setIn(c3,alive). [back_rewrite(182),rewrite([2194(1)])].
% 1.05/1.32 2352 elem(m_Halt(c3),queue(nbr_proc)). [back_rewrite(450),rewrite([2218(4)])].
% 1.05/1.32 2370 c_0 != nbr_proc. [back_rewrite(213),rewrite([2218(2)]),flip(a)].
% 1.05/1.32 2373 -leq(nbr_proc,c_0). [back_unit_del(399),unit_del(b,2370)].
% 1.05/1.32 2417 -elem(m_Halt(c3),queue(host(A))). [resolve(349,b,2281,a),rewrite([366(4)]),xx(c),unit_del(a,2373)].
% 1.05/1.32 2420 $F. [para(2218(a,1),2417(a,2,1)),unit_del(a,2352)].
% 1.05/1.32
% 1.05/1.32 % SZS output end Refutation
% 1.05/1.32 ============================== end of proof ==========================
% 1.05/1.32
% 1.05/1.32 ============================== STATISTICS ============================
% 1.05/1.32
% 1.05/1.32 Given=537. Generated=8359. Kept=2347. proofs=1.
% 1.05/1.32 Usable=467. Sos=1612. Demods=32. Limbo=1, Disabled=392. Hints=0.
% 1.05/1.32 Megabytes=4.38.
% 1.05/1.32 User_CPU=0.30, System_CPU=0.01, Wall_clock=0.
% 1.05/1.32
% 1.05/1.32 ============================== end of statistics =====================
% 1.05/1.32
% 1.05/1.32 ============================== end of search =========================
% 1.05/1.32
% 1.05/1.32 THEOREM PROVED
% 1.05/1.32 % SZS status Theorem
% 1.05/1.32
% 1.05/1.32 Exiting with 1 proof.
% 1.05/1.32
% 1.05/1.32 Process 29463 exit (max_proofs) Wed Jun 15 09:57:25 2022
% 1.05/1.32 Prover9 interrupted
%------------------------------------------------------------------------------