TSTP Solution File: SWV463+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV463+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 21:13:08 EDT 2022
% Result : Theorem 0.95s 1.22s
% Output : Refutation 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV463+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 01:41:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.06 ============================== Prover9 ===============================
% 0.44/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.06 Process 5932 was started by sandbox2 on n012.cluster.edu,
% 0.44/1.06 Thu Jun 16 01:41:25 2022
% 0.44/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5779_n012.cluster.edu".
% 0.44/1.06 ============================== end of head ===========================
% 0.44/1.06
% 0.44/1.06 ============================== INPUT =================================
% 0.44/1.06
% 0.44/1.06 % Reading from file /tmp/Prover9_5779_n012.cluster.edu
% 0.44/1.06
% 0.44/1.06 set(prolog_style_variables).
% 0.44/1.06 set(auto2).
% 0.44/1.06 % set(auto2) -> set(auto).
% 0.44/1.06 % set(auto) -> set(auto_inference).
% 0.44/1.06 % set(auto) -> set(auto_setup).
% 0.44/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.06 % set(auto) -> set(auto_limits).
% 0.44/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.06 % set(auto) -> set(auto_denials).
% 0.44/1.06 % set(auto) -> set(auto_process).
% 0.44/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.06 % set(auto2) -> assign(stats, some).
% 0.44/1.06 % set(auto2) -> clear(echo_input).
% 0.44/1.06 % set(auto2) -> set(quiet).
% 0.44/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.06 % set(auto2) -> clear(print_given).
% 0.44/1.06 assign(lrs_ticks,-1).
% 0.44/1.06 assign(sos_limit,10000).
% 0.44/1.06 assign(order,kbo).
% 0.44/1.06 set(lex_order_vars).
% 0.44/1.06 clear(print_given).
% 0.44/1.06
% 0.44/1.06 % formulas(sos). % not echoed (67 formulas)
% 0.44/1.06
% 0.44/1.06 ============================== end of input ==========================
% 0.44/1.06
% 0.44/1.06 % From the command line: assign(max_seconds, 300).
% 0.44/1.06
% 0.44/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.06
% 0.44/1.06 % Formulas that are not ordinary clauses:
% 0.44/1.06 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].
% 0.44/1.06 2 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 5 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 6 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 7 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 9 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 10 (all X all Y m_NotNorm(X) != m_Halt(Y)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 11 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 13 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 14 (all X all Y m_Down(X) != m_NormQ(Y)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 15 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 16 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 17 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.06 18 (all X all Y m_Ldr(X) != m_NotNorm(Y)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 19 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 20 (all X all Y (X != Y <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 21 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 22 (all X all Y (X != Y <-> m_NotNorm(X) != m_NotNorm(Y))) # label(axiom_28) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 23 (all X all Y (X != Y <-> m_Ldr(X) != m_Ldr(Y))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 24 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 27 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 28 (all X all Q head(cons(X,Q)) = X) # label(axiom_35) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 29 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 30 (all Y all Q last(snoc(Q,Y)) = Y) # label(axiom_37) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 32 (all Q (Q = q_nil | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 33 (all Q (Q = q_nil | Q = snoc(init(Q),last(Q)))) # label(axiom_40) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 34 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 35 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 36 (all X cons(X,q_nil) = snoc(q_nil,X)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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].
% 0.44/1.07 38 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 41 (all X (pidElem(X) <-> (exists Y (X = m_Halt(Y) | X = m_Down(Y))))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 42 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 43 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 44 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 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].
% 0.44/1.07 48 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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].
% 0.44/1.07 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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].
% 0.44/1.07 55 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 57 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.07 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 (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_Ack(W,Y),V) -> (setIn(X,alive) -> (index(elid,host(X)) = W & 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))) | host(Z) = host(Y) -> (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) & index(ldr,host(V0)) = host(V0) & index(status,host(V0)) = norm)))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.95/1.22
% 0.95/1.22 ============================== end of process non-clausal formulas ===
% 0.95/1.22
% 0.95/1.22 ============================== PROCESS INITIAL CLAUSES ===============
% 0.95/1.22
% 0.95/1.22 ============================== PREDICATE ELIMINATION =================
% 0.95/1.22
% 0.95/1.22 ============================== end predicate elimination =============
% 0.95/1.22
% 0.95/1.22 Auto_denials: (non-Horn, no changes).
% 0.95/1.22
% 0.95/1.22 Term ordering decisions:
% 0.95/1.22 Function symbol KB weights: alive=1. status=1. pendack=1. elec_2=1. q_nil=1. nbr_proc=1. elid=1. zero=1. elec_1=1. ldr=1. norm=1. pids=1. acks=1. down=1. nil=1. setEmpty=1. wait=1. c1=1. c2=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.
% 0.95/1.22
% 0.95/1.22 ============================== end of process initial clauses ========
% 0.95/1.22
% 0.95/1.22 ============================== CLAUSES FOR SEARCH ====================
% 0.95/1.22
% 0.95/1.22 ============================== end of clauses for search =============
% 0.95/1.22
% 0.95/1.22 ============================== SEARCH ================================
% 0.95/1.22
% 0.95/1.22 % Starting search at 0.04 seconds.
% 0.95/1.22
% 0.95/1.22 ============================== PROOF =================================
% 0.95/1.22 % SZS status Theorem
% 0.95/1.22 % SZS output start Refutation
% 0.95/1.22
% 0.95/1.22 % Proof 1 at 0.17 (+ 0.01) seconds.
% 0.95/1.22 % Length of proof is 54.
% 0.95/1.22 % Level of proof is 11.
% 0.95/1.22 % Maximum clause weight is 66.000.
% 0.95/1.22 % Given clauses 299.
% 0.95/1.22
% 0.95/1.22 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 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].
% 0.95/1.22 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.22 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_Ack(W,Y),V) -> (setIn(X,alive) -> (index(elid,host(X)) = W & 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))) | host(Z) = host(Y) -> (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) & index(ldr,host(V0)) = host(V0) & index(status,host(V0)) = norm)))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.95/1.22 64 leq(host(A),nbr_proc) # label(axiom_04) # label(axiom). [clausify(4)].
% 0.95/1.22 79 m_Ldr(A) != m_Ack(B,C) # label(axiom_14) # label(axiom). [clausify(8)].
% 0.95/1.22 83 m_Ldr(A) != m_Down(B) # label(axiom_18) # label(axiom). [clausify(12)].
% 0.95/1.22 121 -elem(A,snoc(B,C)) | C = A | elem(A,B) # label(axiom_47) # label(axiom). [clausify(40)].
% 0.95/1.22 150 leq(A,A) # label(axiom_59) # label(axiom). [clausify(51)].
% 0.95/1.22 152 -leq(A,B) | -leq(B,A) | B = A # label(axiom_61) # label(axiom). [clausify(53)].
% 0.95/1.22 180 -setIn(A,alive) | -elem(m_Down(B),queue(host(A))) | -elem(m_Ack(A,C),queue(host(A))) | -leq(nbr_proc,s(index(pendack,host(A)))) | index(status,host(A)) != elec_2 | index(pendack,host(A)) != host(C) | s(index(pendack,host(A))) != host(B) | -setIn(D,alive) | index(ldr,host(D)) != host(D) | index(status,host(D)) != norm # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 184 index(status,host(c3)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 185 elec_2 = index(status,host(c3)). [copy(184),flip(a)].
% 0.95/1.22 191 host(c9) = host(c5) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 192 host(c9) != host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 193 host(c5) != host(c3). [copy(192),rewrite([191(2)])].
% 0.95/1.22 194 setIn(c9,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 195 leq(nbr_proc,s(index(pendack,host(c9)))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 196 leq(nbr_proc,s(index(pendack,host(c5)))). [copy(195),rewrite([191(4)])].
% 0.95/1.22 197 elem(m_Down(c8),snoc(queue(host(c9)),m_Ldr(c3))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 198 elem(m_Down(c8),snoc(queue(host(c5)),m_Ldr(c3))). [copy(197),rewrite([191(4)])].
% 0.95/1.22 199 elem(m_Ack(c9,c7),snoc(queue(host(c9)),m_Ldr(c3))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 200 elem(m_Ack(c9,c7),snoc(queue(host(c5)),m_Ldr(c3))). [copy(199),rewrite([191(5)])].
% 0.95/1.22 201 index(status,host(c9)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 202 index(status,host(c5)) = index(status,host(c3)). [copy(201),rewrite([191(3),185(5)])].
% 0.95/1.22 203 index(pendack,host(c9)) = host(c7) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 204 index(pendack,host(c5)) = host(c7). [copy(203),rewrite([191(3)])].
% 0.95/1.22 205 s(index(pendack,host(c9))) = host(c8) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 206 s(host(c7)) = host(c8). [copy(205),rewrite([191(3),204(4)])].
% 0.95/1.22 207 setIn(c6,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 208 index(ldr,host(c6)) = host(c6) # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 209 index(status,host(c6)) = norm # label(conj) # label(negated_conjecture). [clausify(58)].
% 0.95/1.22 210 norm = index(status,host(c6)). [copy(209),flip(a)].
% 0.95/1.22 214 -setIn(A,alive) | -elem(m_Down(B),queue(host(A))) | -elem(m_Ack(A,C),queue(host(A))) | -leq(nbr_proc,s(index(pendack,host(A)))) | index(status,host(c3)) != index(status,host(A)) | index(pendack,host(A)) != host(C) | s(index(pendack,host(A))) != host(B) | -setIn(D,alive) | index(ldr,host(D)) != host(D) | index(status,host(c6)) != index(status,host(D)). [back_rewrite(180),rewrite([185(20),210(46)]),flip(e),flip(j)].
% 0.95/1.22 223 host(c5) = c_0. [new_symbol(193)].
% 0.95/1.22 224 leq(nbr_proc,s(index(pendack,c_0))). [back_rewrite(196),rewrite([223(4)])].
% 0.95/1.22 228 index(pendack,c_0) = host(c7). [back_rewrite(204),rewrite([223(3)])].
% 0.95/1.22 229 index(status,host(c3)) = index(status,c_0). [back_rewrite(202),rewrite([223(3)]),flip(a)].
% 0.95/1.22 230 elem(m_Ack(c9,c7),snoc(queue(c_0),m_Ldr(c3))). [back_rewrite(200),rewrite([223(5)])].
% 0.95/1.22 231 elem(m_Down(c8),snoc(queue(c_0),m_Ldr(c3))). [back_rewrite(198),rewrite([223(4)])].
% 0.95/1.22 233 host(c9) = c_0. [back_rewrite(191),rewrite([223(4)])].
% 0.95/1.22 235 leq(nbr_proc,host(c8)). [back_rewrite(224),rewrite([228(4),206(4)])].
% 0.95/1.22 244 -setIn(A,alive) | -elem(m_Down(B),queue(host(A))) | -elem(m_Ack(A,C),queue(host(A))) | -leq(nbr_proc,s(index(pendack,host(A)))) | index(status,host(A)) != index(status,c_0) | index(pendack,host(A)) != host(C) | s(index(pendack,host(A))) != host(B) | -setIn(D,alive) | index(ldr,host(D)) != host(D) | index(status,host(c6)) != index(status,host(D)). [back_rewrite(214),rewrite([229(20)]),flip(e)].
% 0.95/1.22 384 elem(m_Ack(c9,c7),queue(c_0)). [resolve(230,a,121,a),flip(a),unit_del(a(flip),79)].
% 0.95/1.22 390 elem(m_Down(c8),queue(c_0)). [resolve(231,a,121,a),unit_del(a,83)].
% 0.95/1.22 398 host(c8) = nbr_proc. [resolve(235,a,152,b),flip(b),unit_del(a,64)].
% 0.95/1.22 408 s(host(c7)) = nbr_proc. [back_rewrite(206),rewrite([398(5)])].
% 0.95/1.22 448 -elem(m_Down(A),queue(c_0)) | -elem(m_Ack(c9,B),queue(c_0)) | host(c7) != host(B) | host(A) != nbr_proc | -setIn(C,alive) | index(ldr,host(C)) != host(C) | index(status,host(c6)) != index(status,host(C)). [resolve(244,a,194,a),rewrite([233(3),233(8),233(13),228(13),408(13),233(15),233(22),228(22),233(26),228(26),408(26)]),flip(f),xx(d),unit_del(c,150)].
% 0.95/1.22 1115 -elem(m_Down(A),queue(c_0)) | -elem(m_Ack(c9,B),queue(c_0)) | host(c7) != host(B) | host(A) != nbr_proc. [resolve(448,e,207,a),rewrite([208(20)]),xx(e),xx(f)].
% 0.95/1.22 1117 -elem(m_Down(A),queue(c_0)) | host(A) != nbr_proc. [resolve(1115,b,384,a),xx(b)].
% 0.95/1.22 1138 $F. [resolve(1117,a,390,a),rewrite([398(2)]),xx(a)].
% 0.95/1.22
% 0.95/1.22 % SZS output end Refutation
% 0.95/1.22 ============================== end of proof ==========================
% 0.95/1.22
% 0.95/1.22 ============================== STATISTICS ============================
% 0.95/1.22
% 0.95/1.22 Given=299. Generated=2672. Kept=1060. proofs=1.
% 0.95/1.22 Usable=277. Sos=668. Demods=35. Limbo=0, Disabled=250. Hints=0.
% 0.95/1.22 Megabytes=2.32.
% 0.95/1.22 User_CPU=0.17, System_CPU=0.01, Wall_clock=0.
% 0.95/1.22
% 0.95/1.22 ============================== end of statistics =====================
% 0.95/1.22
% 0.95/1.22 ============================== end of search =========================
% 0.95/1.22
% 0.95/1.22 THEOREM PROVED
% 0.95/1.22 % SZS status Theorem
% 0.95/1.22
% 0.95/1.22 Exiting with 1 proof.
% 0.95/1.22
% 0.95/1.22 Process 5932 exit (max_proofs) Thu Jun 16 01:41:25 2022
% 0.95/1.22 Prover9 interrupted
%------------------------------------------------------------------------------