TSTP Solution File: SWV471+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV471+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 21:13:10 EDT 2022
% Result : Theorem 25.40s 25.67s
% Output : Refutation 25.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV471+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n005.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 : Wed Jun 15 19:27:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.03 ============================== Prover9 ===============================
% 0.44/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.03 Process 7296 was started by sandbox on n005.cluster.edu,
% 0.44/1.03 Wed Jun 15 19:27:09 2022
% 0.44/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7143_n005.cluster.edu".
% 0.44/1.03 ============================== end of head ===========================
% 0.44/1.03
% 0.44/1.03 ============================== INPUT =================================
% 0.44/1.03
% 0.44/1.03 % Reading from file /tmp/Prover9_7143_n005.cluster.edu
% 0.44/1.03
% 0.44/1.03 set(prolog_style_variables).
% 0.44/1.03 set(auto2).
% 0.44/1.03 % set(auto2) -> set(auto).
% 0.44/1.03 % set(auto) -> set(auto_inference).
% 0.44/1.03 % set(auto) -> set(auto_setup).
% 0.44/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.03 % set(auto) -> set(auto_limits).
% 0.44/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.03 % set(auto) -> set(auto_denials).
% 0.44/1.03 % set(auto) -> set(auto_process).
% 0.44/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.03 % set(auto2) -> assign(stats, some).
% 0.44/1.03 % set(auto2) -> clear(echo_input).
% 0.44/1.03 % set(auto2) -> set(quiet).
% 0.44/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.03 % set(auto2) -> clear(print_given).
% 0.44/1.03 assign(lrs_ticks,-1).
% 0.44/1.03 assign(sos_limit,10000).
% 0.44/1.03 assign(order,kbo).
% 0.44/1.03 set(lex_order_vars).
% 0.44/1.03 clear(print_given).
% 0.44/1.03
% 0.44/1.03 % formulas(sos). % not echoed (67 formulas)
% 0.44/1.03
% 0.44/1.03 ============================== end of input ==========================
% 0.44/1.03
% 0.44/1.03 % From the command line: assign(max_seconds, 300).
% 0.44/1.03
% 0.44/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.03
% 0.44/1.03 % Formulas that are not ordinary clauses:
% 0.44/1.03 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].
% 0.44/1.03 2 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 5 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 6 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 7 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 9 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 10 (all X all Y m_NotNorm(X) != m_Halt(Y)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 11 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 13 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 14 (all X all Y m_Down(X) != m_NormQ(Y)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 15 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 16 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 17 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 18 (all X all Y m_Ldr(X) != m_NotNorm(Y)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 19 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 20 (all X all Y (X != Y <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 21 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 22 (all X all Y (X != Y <-> m_NotNorm(X) != m_NotNorm(Y))) # label(axiom_28) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 23 (all X all Y (X != Y <-> m_Ldr(X) != m_Ldr(Y))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 24 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 27 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 28 (all X all Q head(cons(X,Q)) = X) # label(axiom_35) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 29 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 30 (all Y all Q last(snoc(Q,Y)) = Y) # label(axiom_37) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 32 (all Q (Q = q_nil | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 33 (all Q (Q = q_nil | Q = snoc(init(Q),last(Q)))) # label(axiom_40) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 34 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 35 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 36 (all X cons(X,q_nil) = snoc(q_nil,X)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 38 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 41 (all X (pidElem(X) <-> (exists Y (X = m_Halt(Y) | X = m_Down(Y))))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 42 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 43 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 44 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 48 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 1.01/1.34 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 1.01/1.34 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 1.01/1.34 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 1.01/1.34 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 1.01/1.34 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].
% 1.01/1.34 55 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption].
% 1.01/1.34 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 1.01/1.34 57 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption].
% 1.01/1.34 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 (host(Z) = nbr_proc -> -elem(m_NotNorm(Y),queue(host(Z))))) & (all Y all Z (Z != Y & host(Z) = host(Y) -> -setIn(Y,alive) | -setIn(Z,alive))) & (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 (host(Pid0) != host(Z) & setIn(Pid0,alive) & host(Pid0) = host(Y) & index(ldr,host(Pid0)) = host(Z) & index(status,host(Pid0)) = norm -> -elem(m_Down(Y),queue(host(Z))))) & (all Y all Z all Pid0 (host(Pid0) != host(Z) & setIn(Pid0,alive) & host(Pid0) = host(Y) & index(status,host(Pid0)) = wait & host(index(elid,host(Pid0))) = host(Z) -> -elem(m_Down(Y),queue(host(Z))))) & (all Y all Z all Pid20 all Pid0 (host(Pid20) != host(Y) & setIn(Y,alive) & setIn(Pid20,alive) & host(Z) = host(Y) & host(Pid0) = host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Y))) & elem(m_Down(Z),queue(host(Pid20)))))) & (all Y all Z all Pid20 all Pid0 (host(Pid20) != host(Y) & setIn(Y,alive) & setIn(Pid20,alive) & host(Z) = host(Y) & host(Pid0) = host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Y))) & setIn(host(Z),index(down,host(Pid20)))))) & (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)))))) & queue(host(W)) = cons(m_Halt(X),V) -> (setIn(W,alive) -> (all Y (host(X) != host(Y) -> (host(W) = host(Y) -> (all Z all X0 all Y0 (host(X) = host(Y0) -> (host(W) != host(Y0) -> ((all V0 (-leq(host(Y0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(Y0))) | V0 = host(X0))) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ack(X,W))) & host(Y0) = host(Z) & host(Y0) = nbr_proc & index(status,host(Y0)) = elec_1 -> -(setIn(Y,alive) & elem(m_Down(Z),V)))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.01/1.34
% 1.01/1.34 ============================== end of process non-clausal formulas ===
% 1.01/1.34
% 1.01/1.34 ============================== PROCESS INITIAL CLAUSES ===============
% 1.01/1.34
% 1.01/1.34 ============================== PREDICATE ELIMINATION =================
% 1.01/1.34
% 1.01/1.34 ============================== end predicate elimination =============
% 1.01/1.34
% 1.01/1.34 Auto_denials: (non-Horn, no changes).
% 1.01/1.34
% 1.01/1.34 Term ordering decisions:
% 1.01/1.34 Function symbol KB weights: alive=1. q_nil=1. status=1. nbr_proc=1. zero=1. elec_1=1. elid=1. down=1. pids=1. elec_2=1. ldr=1. norm=1. wait=1. nil=1. setEmpty=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. snoc=1. cons=1. index=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.
% 1.01/1.34
% 1.01/1.34 ============================== end of process initial clauses ========
% 1.01/1.34
% 1.01/1.34 ============================== CLAUSES FOR SEARCH ====================
% 1.01/1.34
% 1.01/1.34 ============================== end of clauses for search =============
% 1.01/1.34
% 1.01/1.34 ============================== SEARCH ================================
% 1.01/1.34
% 1.01/1.34 % Starting search at 0.03 seconds.
% 1.01/1.34
% 1.01/1.34 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 136 (0.00 of 0.32 sec).
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=70.000, iters=3747
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=69.000, iters=3746
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=33.000, iters=3403
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=30.000, iters=3373
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=29.000, iters=3349
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=26.000, iters=3393
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=21.000, iters=3333
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=20.000, iters=3444
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=19.000, iters=3348
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=18.000, iters=3369
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=17.000, iters=3363
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=16.000, iters=3339
% 25.40/25.67
% 25.40/25.67 Low Water (keep): wt=15.000, iters=3339
% 25.40/25.67
% 25.40/25.67 ============================== PROOF =================================
% 25.40/25.67 % SZS status Theorem
% 25.40/25.67 % SZS output start Refutation
% 25.40/25.67
% 25.40/25.67 % Proof 1 at 23.76 (+ 0.90) seconds.
% 25.40/25.67 % Length of proof is 54.
% 25.40/25.67 % Level of proof is 10.
% 25.40/25.67 % Maximum clause weight is 42.000.
% 25.40/25.67 % Given clauses 7698.
% 25.40/25.67
% 25.40/25.67 6 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption].
% 25.40/25.67 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].
% 25.40/25.67 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].
% 25.40/25.67 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 (host(Z) = nbr_proc -> -elem(m_NotNorm(Y),queue(host(Z))))) & (all Y all Z (Z != Y & host(Z) = host(Y) -> -setIn(Y,alive) | -setIn(Z,alive))) & (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 (host(Pid0) != host(Z) & setIn(Pid0,alive) & host(Pid0) = host(Y) & index(ldr,host(Pid0)) = host(Z) & index(status,host(Pid0)) = norm -> -elem(m_Down(Y),queue(host(Z))))) & (all Y all Z all Pid0 (host(Pid0) != host(Z) & setIn(Pid0,alive) & host(Pid0) = host(Y) & index(status,host(Pid0)) = wait & host(index(elid,host(Pid0))) = host(Z) -> -elem(m_Down(Y),queue(host(Z))))) & (all Y all Z all Pid20 all Pid0 (host(Pid20) != host(Y) & setIn(Y,alive) & setIn(Pid20,alive) & host(Z) = host(Y) & host(Pid0) = host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Y))) & elem(m_Down(Z),queue(host(Pid20)))))) & (all Y all Z all Pid20 all Pid0 (host(Pid20) != host(Y) & setIn(Y,alive) & setIn(Pid20,alive) & host(Z) = host(Y) & host(Pid0) = host(Pid20) -> -(elem(m_Down(Pid0),queue(host(Y))) & setIn(host(Z),index(down,host(Pid20)))))) & (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)))))) & queue(host(W)) = cons(m_Halt(X),V) -> (setIn(W,alive) -> (all Y (host(X) != host(Y) -> (host(W) = host(Y) -> (all Z all X0 all Y0 (host(X) = host(Y0) -> (host(W) != host(Y0) -> ((all V0 (-leq(host(Y0),V0) & leq(s(zero),V0) -> setIn(V0,index(down,host(Y0))) | V0 = host(X0))) & elem(m_Down(X0),snoc(queue(host(Y0)),m_Ack(X,W))) & host(Y0) = host(Z) & host(Y0) = nbr_proc & index(status,host(Y0)) = elec_1 -> -(setIn(Y,alive) & elem(m_Down(Z),V)))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 25.40/25.67 78 m_Down(A) != m_Ack(B,C) # label(axiom_12) # label(axiom). [clausify(6)].
% 25.40/25.67 121 elem(A,cons(B,C)) | -elem(A,C) # label(axiom_46) # label(axiom). [clausify(39)].
% 25.40/25.67 122 -elem(A,snoc(B,C)) | C = A | elem(A,B) # label(axiom_47) # label(axiom). [clausify(40)].
% 25.40/25.67 172 -leq(host(A),f4(B,C,D,A)) | -elem(m_Down(D),queue(host(A))) | host(A) != host(C) | host(A) != nbr_proc | index(status,host(A)) != elec_1 | -setIn(B,alive) | -elem(m_Down(C),queue(host(B))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 173 leq(s(zero),f4(A,B,C,D)) | -elem(m_Down(C),queue(host(D))) | host(D) != host(B) | host(D) != nbr_proc | index(status,host(D)) != elec_1 | -setIn(A,alive) | -elem(m_Down(B),queue(host(A))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 174 -setIn(f4(A,B,C,D),index(down,host(D))) | -elem(m_Down(C),queue(host(D))) | host(D) != host(B) | host(D) != nbr_proc | index(status,host(D)) != elec_1 | -setIn(A,alive) | -elem(m_Down(B),queue(host(A))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 175 host(A) != f4(B,C,A,D) | -elem(m_Down(A),queue(host(D))) | host(D) != host(C) | host(D) != nbr_proc | index(status,host(D)) != elec_1 | -setIn(B,alive) | -elem(m_Down(C),queue(host(B))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 176 f4(A,B,C,D) != host(C) | -elem(m_Down(C),queue(host(D))) | host(D) != host(B) | host(D) != nbr_proc | index(status,host(D)) != elec_1 | -setIn(A,alive) | -elem(m_Down(B),queue(host(A))). [copy(175),flip(a)].
% 25.40/25.67 177 cons(m_Halt(c3),c1) = queue(host(c2)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 178 setIn(c2,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 182 host(c7) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 183 host(c7) != host(c2) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 184 host(c3) != host(c2). [copy(183),rewrite([182(2)])].
% 25.40/25.67 185 leq(host(c7),A) | -leq(s(zero),A) | setIn(A,index(down,host(c7))) | host(c6) = A # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 186 leq(host(c3),A) | -leq(s(zero),A) | setIn(A,index(down,host(c3))) | host(c6) = A. [copy(185),rewrite([182(2),182(9)])].
% 25.40/25.67 187 elem(m_Down(c6),snoc(queue(host(c7)),m_Ack(c3,c2))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 188 elem(m_Down(c6),snoc(queue(host(c3)),m_Ack(c3,c2))). [copy(187),rewrite([182(4)])].
% 25.40/25.67 189 host(c7) = host(c5) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 190 host(c5) = host(c3). [copy(189),rewrite([182(2)]),flip(a)].
% 25.40/25.67 191 host(c7) = nbr_proc # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 192 nbr_proc = host(c3). [copy(191),rewrite([182(2)]),flip(a)].
% 25.40/25.67 193 index(status,host(c7)) = elec_1 # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 194 elec_1 = index(status,host(c3)). [copy(193),rewrite([182(3)]),flip(a)].
% 25.40/25.67 196 elem(m_Down(c5),c1) # label(conj) # label(negated_conjecture). [clausify(58)].
% 25.40/25.67 201 host(c3) = c_0. [new_symbol(184)].
% 25.40/25.67 202 f4(A,B,C,D) != host(C) | -elem(m_Down(C),queue(host(D))) | host(D) != host(B) | host(D) != c_0 | index(status,host(D)) != index(status,c_0) | -setIn(A,alive) | -elem(m_Down(B),queue(host(A))). [back_rewrite(176),rewrite([192(12),201(13),194(17),201(19)])].
% 25.40/25.67 203 -setIn(f4(A,B,C,D),index(down,host(D))) | -elem(m_Down(C),queue(host(D))) | host(D) != host(B) | host(D) != c_0 | index(status,host(D)) != index(status,c_0) | -setIn(A,alive) | -elem(m_Down(B),queue(host(A))). [back_rewrite(174),rewrite([192(14),201(15),194(19),201(21)])].
% 25.40/25.67 204 leq(s(zero),f4(A,B,C,D)) | -elem(m_Down(C),queue(host(D))) | host(D) != host(B) | host(D) != c_0 | index(status,host(D)) != index(status,c_0) | -setIn(A,alive) | -elem(m_Down(B),queue(host(A))). [back_rewrite(173),rewrite([192(13),201(14),194(18),201(20)])].
% 25.40/25.67 205 -leq(host(A),f4(B,C,D,A)) | -elem(m_Down(D),queue(host(A))) | host(A) != host(C) | host(A) != c_0 | index(status,host(A)) != index(status,c_0) | -setIn(B,alive) | -elem(m_Down(C),queue(host(B))). [back_rewrite(172),rewrite([192(12),201(13),194(17),201(19)])].
% 25.40/25.67 223 host(c5) = c_0. [back_rewrite(190),rewrite([201(4)])].
% 25.40/25.67 224 elem(m_Down(c6),snoc(queue(c_0),m_Ack(c3,c2))). [back_rewrite(188),rewrite([201(4)])].
% 25.40/25.67 225 leq(c_0,A) | -leq(s(zero),A) | setIn(A,index(down,c_0)) | host(c6) = A. [back_rewrite(186),rewrite([201(2),201(8)])].
% 25.40/25.67 326 elem(m_Down(c5),cons(A,c1)). [resolve(196,a,121,b)].
% 25.40/25.67 336 f4(c2,A,B,C) != host(B) | -elem(m_Down(B),queue(host(C))) | host(C) != host(A) | host(C) != c_0 | index(status,host(C)) != index(status,c_0) | -elem(m_Down(A),queue(host(c2))). [resolve(202,f,178,a)].
% 25.40/25.67 337 -setIn(f4(A,B,C,c3),index(down,c_0)) | -elem(m_Down(C),queue(c_0)) | host(B) != c_0 | -setIn(A,alive) | -elem(m_Down(B),queue(host(A))). [para(201(a,1),203(a,2,2)),rewrite([201(9),201(12),201(15),201(19)]),flip(c),xx(d),xx(e)].
% 25.40/25.67 339 leq(s(zero),f4(c2,A,B,C)) | -elem(m_Down(B),queue(host(C))) | host(C) != host(A) | host(C) != c_0 | index(status,host(C)) != index(status,c_0) | -elem(m_Down(A),queue(host(c2))). [resolve(204,f,178,a)].
% 25.40/25.67 341 -leq(host(A),f4(c2,B,C,A)) | -elem(m_Down(C),queue(host(A))) | host(A) != host(B) | host(A) != c_0 | index(status,host(A)) != index(status,c_0) | -elem(m_Down(B),queue(host(c2))). [resolve(205,f,178,a)].
% 25.40/25.67 363 elem(m_Down(c6),queue(c_0)). [resolve(224,a,122,a),unit_del(a(flip),78)].
% 25.40/25.67 569 f4(c2,A,B,c3) != host(B) | -elem(m_Down(B),queue(c_0)) | host(A) != c_0 | -elem(m_Down(A),queue(host(c2))). [para(201(a,1),336(b,2,1)),rewrite([201(11),201(14),201(18)]),flip(c),xx(d),xx(e)].
% 25.40/25.67 576 f4(c2,A,c6,c3) != host(c6) | host(A) != c_0 | -elem(m_Down(A),queue(host(c2))). [resolve(569,b,363,a)].
% 25.40/25.67 584 elem(m_Down(c5),queue(host(c2))). [para(177(a,1),326(a,2))].
% 25.40/25.67 758 -leq(c_0,f4(c2,A,B,c3)) | -elem(m_Down(B),queue(c_0)) | host(A) != c_0 | -elem(m_Down(A),queue(host(c2))). [para(201(a,1),341(b,2,1)),rewrite([201(2),201(11),201(14),201(18)]),flip(c),xx(d),xx(e)].
% 25.40/25.67 777 f4(c2,c5,c6,c3) != host(c6). [resolve(584,a,576,c),rewrite([223(10)]),xx(b)].
% 25.40/25.67 931 -leq(c_0,f4(c2,c5,A,c3)) | -elem(m_Down(A),queue(c_0)). [resolve(758,d,584,a),rewrite([223(12)]),xx(c)].
% 25.40/25.67 936 -leq(c_0,f4(c2,c5,c6,c3)). [resolve(931,b,363,a)].
% 25.40/25.67 2603 leq(s(zero),f4(c2,c5,A,B)) | -elem(m_Down(A),queue(host(B))) | host(B) != c_0 | index(status,host(B)) != index(status,c_0). [resolve(339,f,584,a),rewrite([223(13)]),merge(d)].
% 25.40/25.67 16428 leq(s(zero),f4(c2,c5,A,c3)) | -elem(m_Down(A),queue(c_0)). [para(201(a,1),2603(b,2,1)),rewrite([201(13),201(17)]),xx(c),xx(d)].
% 25.40/25.67 16431 leq(s(zero),f4(c2,c5,c6,c3)). [resolve(16428,b,363,a)].
% 25.40/25.67 16465 setIn(f4(c2,c5,c6,c3),index(down,c_0)). [resolve(16431,a,225,b),flip(c),unit_del(a,936),unit_del(c,777)].
% 25.40/25.67 16515 $F. [resolve(16465,a,337,a),rewrite([223(7)]),xx(b),unit_del(a,363),unit_del(b,178),unit_del(c,584)].
% 25.40/25.67
% 25.40/25.67 % SZS output end Refutation
% 25.40/25.67 ============================== end of proof ==========================
% 25.40/25.67
% 25.40/25.67 ============================== STATISTICS ============================
% 25.40/25.67
% 25.40/25.67 Given=7698. Generated=1634021. Kept=16439. proofs=1.
% 25.40/25.67 Usable=5266. Sos=8101. Demods=30. Limbo=0, Disabled=3195. Hints=0.
% 25.40/25.67 Megabytes=29.97.
% 25.40/25.67 User_CPU=23.76, System_CPU=0.90, Wall_clock=25.
% 25.40/25.67
% 25.40/25.67 ============================== end of statistics =====================
% 25.40/25.67
% 25.40/25.67 ============================== end of search =========================
% 25.40/25.67
% 25.40/25.67 THEOREM PROVED
% 25.40/25.67 % SZS status Theorem
% 25.40/25.67
% 25.40/25.67 Exiting with 1 proof.
% 25.40/25.67
% 25.40/25.67 Process 7296 exit (max_proofs) Wed Jun 15 19:27:34 2022
% 25.40/25.67 Prover9 interrupted
%------------------------------------------------------------------------------