TSTP Solution File: SWV469+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV469+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 18.28s 18.58s
% Output : Refutation 18.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV469+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 22:00:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/1.06 ============================== Prover9 ===============================
% 0.45/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.06 Process 27451 was started by sandbox on n011.cluster.edu,
% 0.45/1.06 Tue Jun 14 22:00:50 2022
% 0.45/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27298_n011.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_27298_n011.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].
% 0.45/1.07 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 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].
% 0.45/1.07 55 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 57 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 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 (Pid0 != Z & host(Pid0) = host(Z) -> -setIn(Z,alive) | -setIn(Pid0,alive))) & (all Z all Pid0 (setIn(Pid0,alive) & index(status,host(Pid0)) = elec_2 -> -elem(m_Ack(Z,Pid0),queue(host(Z))))) & (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 (-leq(host(Pid0),host(Z)) & setIn(Z,alive) & setIn(Pid0,alive) & host(Pid0) = host(Pid20) & index(status,host(Pid0)) = elec_2 -> -elem(m_Down(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(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Ack(Pid0,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 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 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 (-leq(index(pendack,host(Pid0)),host(Z)) & setIn(Pid0,alive) & index(status,host(Pid0)) = elec_2 -> -(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(Z)),index(pendack,host(Pid0))))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid20) = host(Z) & index(status,host(Pid0)) = elec_2 -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))) & (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))) & -leq(host(Pid0),host(Z)) & elem(m_Down(Pid20),queue(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 -> (-leq(nbr_proc,host(X)) -> (all Z (host(X) != host(Z) -> (all W0 (host(X) = host(W0) -> (-leq(s(host(X)),host(Z)) & setIn(W0,alive) -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 18.28/18.58
% 18.28/18.58 ============================== end of process non-clausal formulas ===
% 18.28/18.58
% 18.28/18.58 ============================== PROCESS INITIAL CLAUSES ===============
% 18.28/18.58
% 18.28/18.58 ============================== PREDICATE ELIMINATION =================
% 18.28/18.58
% 18.28/18.58 ============================== end predicate elimination =============
% 18.28/18.58
% 18.28/18.58 Auto_denials: (non-Horn, no changes).
% 18.28/18.58
% 18.28/18.58 Term ordering decisions:
% 18.28/18.58 Function symbol KB weights: alive=1. status=1. elec_2=1. q_nil=1. elec_1=1. ldr=1. norm=1. pendack=1. zero=1. down=1. elid=1. nbr_proc=1. pids=1. nil=1. setEmpty=1. wait=1. c1=1. c3=1. c4=1. c5=1. c6=1. index=1. cons=1. snoc=1. m_Ack=1. f2=1. f3=1. host=1. pidMsg=1. m_Down=1. s=1. queue=1. m_Halt=1. m_Ldr=1. m_NormQ=1. m_NotNorm=1. head=1. init=1. last=1. tail=1. f1=1. f4=1.
% 18.28/18.58
% 18.28/18.58 ============================== end of process initial clauses ========
% 18.28/18.58
% 18.28/18.58 ============================== CLAUSES FOR SEARCH ====================
% 18.28/18.58
% 18.28/18.58 ============================== end of clauses for search =============
% 18.28/18.58
% 18.28/18.58 ============================== SEARCH ================================
% 18.28/18.58
% 18.28/18.58 % Starting search at 0.04 seconds.
% 18.28/18.58
% 18.28/18.58 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 147 (0.00 of 0.41 sec).
% 18.28/18.58
% 18.28/18.58 Low Water (keep): wt=41.000, iters=3956
% 18.28/18.58
% 18.28/18.58 Low Water (keep): wt=16.000, iters=4201
% 18.28/18.58
% 18.28/18.58 Low Water (keep): wt=15.000, iters=3531
% 18.28/18.58
% 18.28/18.58 ============================== PROOF =================================
% 18.28/18.58 % SZS status Theorem
% 18.28/18.58 % SZS output start Refutation
% 18.28/18.58
% 18.28/18.58 % Proof 1 at 16.80 (+ 0.74) seconds.
% 18.28/18.58 % Length of proof is 40.
% 18.28/18.58 % Level of proof is 8.
% 18.28/18.58 % Maximum clause weight is 33.000.
% 18.28/18.58 % Given clauses 6225.
% 18.28/18.58
% 18.28/18.58 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 18.28/18.58 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 18.28/18.58 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].
% 18.28/18.58 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 18.28/18.58 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 18.28/18.58 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 18.28/18.58 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 18.28/18.58 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 (Pid0 != Z & host(Pid0) = host(Z) -> -setIn(Z,alive) | -setIn(Pid0,alive))) & (all Z all Pid0 (setIn(Pid0,alive) & index(status,host(Pid0)) = elec_2 -> -elem(m_Ack(Z,Pid0),queue(host(Z))))) & (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 (-leq(host(Pid0),host(Z)) & setIn(Z,alive) & setIn(Pid0,alive) & host(Pid0) = host(Pid20) & index(status,host(Pid0)) = elec_2 -> -elem(m_Down(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(Pid0)),host(Z)))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Ack(Pid0,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 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 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 (-leq(index(pendack,host(Pid0)),host(Z)) & setIn(Pid0,alive) & index(status,host(Pid0)) = elec_2 -> -(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(Z)),index(pendack,host(Pid0))))) & (all Z all Pid20 all Pid0 (setIn(Pid0,alive) & elem(m_Down(Pid20),queue(host(Pid0))) & host(Pid20) = host(Z) & index(status,host(Pid0)) = elec_2 -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))) & (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))) & -leq(host(Pid0),host(Z)) & elem(m_Down(Pid20),queue(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 -> (-leq(nbr_proc,host(X)) -> (all Z (host(X) != host(Z) -> (all W0 (host(X) = host(W0) -> (-leq(s(host(X)),host(Z)) & setIn(W0,alive) -> -(setIn(Z,alive) & index(ldr,host(Z)) = host(Z) & index(status,host(Z)) = norm))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 18.28/18.58 62 leq(s(zero),host(A)) # label(axiom_02) # label(axiom). [clausify(3)].
% 18.28/18.58 108 init(snoc(A,B)) = A # label(axiom_38) # label(axiom). [clausify(31)].
% 18.28/18.58 117 elem(A,cons(B,C)) | B != A # label(axiom_46) # label(axiom). [clausify(39)].
% 18.28/18.58 148 leq(A,A) # label(axiom_59) # label(axiom). [clausify(51)].
% 18.28/18.58 149 leq(A,B) | leq(B,A) # label(axiom_60) # label(axiom). [clausify(52)].
% 18.28/18.58 150 -leq(A,B) | -leq(B,A) | B = A # label(axiom_61) # label(axiom). [clausify(53)].
% 18.28/18.58 156 -leq(A,s(B)) | s(B) = A | leq(A,B) # label(axiom_64) # label(axiom). [clausify(56)].
% 18.28/18.58 165 -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)].
% 18.28/18.58 171 -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)].
% 18.28/18.58 179 cons(m_Down(c4),c1) = queue(host(c3)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 18.28/18.58 180 setIn(c3,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 18.28/18.58 184 leq(host(c3),A) | -leq(s(zero),A) | setIn(A,index(down,host(c3))) | host(c4) = A # label(conj) # label(negated_conjecture). [clausify(58)].
% 18.28/18.58 188 host(c5) != host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 18.28/18.58 190 -leq(s(host(c3)),host(c5)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 18.28/18.58 192 setIn(c5,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 18.28/18.58 193 index(ldr,host(c5)) = host(c5) # label(conj) # label(negated_conjecture). [clausify(58)].
% 18.28/18.58 194 index(status,host(c5)) = norm # label(conj) # label(negated_conjecture). [clausify(58)].
% 18.28/18.58 195 norm = index(status,host(c5)). [copy(194),flip(a)].
% 18.28/18.58 212 -setIn(A,alive) | host(B) != host(A) | index(status,host(c5)) != index(status,host(A)) | index(ldr,host(A)) != host(A) | -setIn(C,alive) | -elem(m_Down(B),queue(host(C))). [back_rewrite(171),rewrite([195(9)]),flip(c)].
% 18.28/18.58 214 -setIn(A,alive) | index(status,host(c5)) != index(status,host(A)) | index(ldr,host(A)) != host(A) | -setIn(B,alive) | -setIn(host(A),index(down,host(B))). [back_rewrite(165),rewrite([195(6)]),flip(b)].
% 18.28/18.58 240 elem(A,cons(A,B)). [resolve(117,b,108,a),rewrite([108(2)])].
% 18.28/18.58 312 leq(host(c3),host(A)) | setIn(host(A),index(down,host(c3))) | host(c4) = host(A). [resolve(184,b,62,a)].
% 18.28/18.58 320 leq(host(c5),s(host(c3))). [resolve(190,a,149,b)].
% 18.28/18.58 408 elem(m_Down(c4),queue(host(c3))). [para(179(a,1),240(a,2))].
% 18.28/18.58 531 s(host(c3)) = host(c5) | leq(host(c5),host(c3)). [resolve(320,a,156,a)].
% 18.28/18.58 576 -setIn(A,alive) | host(c4) != host(A) | index(status,host(c5)) != index(status,host(A)) | index(ldr,host(A)) != host(A). [resolve(408,a,212,f),unit_del(e,180)].
% 18.28/18.58 624 host(c5) != host(c4). [resolve(576,a,192,a),rewrite([193(18)]),flip(a),xx(b),xx(c)].
% 18.28/18.58 1987 leq(host(c3),host(A)) | host(c4) = host(A) | -setIn(A,alive) | index(status,host(c5)) != index(status,host(A)) | index(ldr,host(A)) != host(A). [resolve(312,b,214,e),unit_del(f,180)].
% 18.28/18.58 3826 s(host(c3)) = host(c5) | -leq(host(c3),host(c5)). [resolve(531,b,150,b),unit_del(c,188)].
% 18.28/18.58 15356 leq(host(c3),host(c5)). [resolve(1987,c,192,a),rewrite([193(23)]),flip(b),xx(c),xx(d),unit_del(b,624)].
% 18.28/18.58 15359 s(host(c3)) = host(c5). [back_unit_del(3826),unit_del(b,15356)].
% 18.28/18.58 15551 $F. [back_rewrite(190),rewrite([15359(3)]),unit_del(a,148)].
% 18.28/18.58
% 18.28/18.58 % SZS output end Refutation
% 18.28/18.58 ============================== end of proof ==========================
% 18.28/18.58
% 18.28/18.58 ============================== STATISTICS ============================
% 18.28/18.58
% 18.28/18.58 Given=6225. Generated=1334918. Kept=15483. proofs=1.
% 18.28/18.58 Usable=5860. Sos=8436. Demods=49. Limbo=192, Disabled=1126. Hints=0.
% 18.28/18.58 Megabytes=30.88.
% 18.28/18.58 User_CPU=16.80, System_CPU=0.74, Wall_clock=18.
% 18.28/18.58
% 18.28/18.58 ============================== end of statistics =====================
% 18.28/18.58
% 18.28/18.58 ============================== end of search =========================
% 18.28/18.58
% 18.28/18.58 THEOREM PROVED
% 18.28/18.58 % SZS status Theorem
% 18.28/18.58
% 18.28/18.58 Exiting with 1 proof.
% 18.28/18.58
% 18.28/18.58 Process 27451 exit (max_proofs) Tue Jun 14 22:01:08 2022
% 18.28/18.58 Prover9 interrupted
%------------------------------------------------------------------------------