TSTP Solution File: SWV460+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV460+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 15.79s 16.12s
% Output : Refutation 15.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : SWV460+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 21:16:58 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.81/1.09 ============================== Prover9 ===============================
% 0.81/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.09 Process 4897 was started by sandbox2 on n021.cluster.edu,
% 0.81/1.09 Tue Jun 14 21:16:59 2022
% 0.81/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4743_n021.cluster.edu".
% 0.81/1.09 ============================== end of head ===========================
% 0.81/1.09
% 0.81/1.09 ============================== INPUT =================================
% 0.81/1.09
% 0.81/1.09 % Reading from file /tmp/Prover9_4743_n021.cluster.edu
% 0.81/1.09
% 0.81/1.09 set(prolog_style_variables).
% 0.81/1.09 set(auto2).
% 0.81/1.09 % set(auto2) -> set(auto).
% 0.81/1.09 % set(auto) -> set(auto_inference).
% 0.81/1.09 % set(auto) -> set(auto_setup).
% 0.81/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.09 % set(auto) -> set(auto_limits).
% 0.81/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.09 % set(auto) -> set(auto_denials).
% 0.81/1.09 % set(auto) -> set(auto_process).
% 0.81/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.09 % set(auto2) -> assign(stats, some).
% 0.81/1.09 % set(auto2) -> clear(echo_input).
% 0.81/1.09 % set(auto2) -> set(quiet).
% 0.81/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.09 % set(auto2) -> clear(print_given).
% 0.81/1.09 assign(lrs_ticks,-1).
% 0.81/1.09 assign(sos_limit,10000).
% 0.81/1.09 assign(order,kbo).
% 0.81/1.09 set(lex_order_vars).
% 0.81/1.09 clear(print_given).
% 0.81/1.09
% 0.81/1.09 % formulas(sos). % not echoed (67 formulas)
% 0.81/1.09
% 0.81/1.09 ============================== end of input ==========================
% 0.81/1.09
% 0.81/1.09 % From the command line: assign(max_seconds, 300).
% 0.81/1.09
% 0.81/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.09
% 0.81/1.09 % Formulas that are not ordinary clauses:
% 0.81/1.09 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].
% 0.81/1.09 2 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 4 (all P leq(host(P),nbr_proc)) # label(axiom_04) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 5 (all X all Y all Z m_Ack(X,Y) != m_Halt(Z)) # label(axiom_11) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 6 (all X all Y all Z m_Ack(X,Y) != m_Down(Z)) # label(axiom_12) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 7 (all X all Y all Z m_Ack(X,Y) != m_NotNorm(Z)) # label(axiom_13) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 8 (all X all Y all Z m_Ack(X,Y) != m_Ldr(Z)) # label(axiom_14) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 9 (all X all Y all Z m_Ack(X,Y) != m_NormQ(Z)) # label(axiom_15) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 10 (all X all Y m_NotNorm(X) != m_Halt(Y)) # label(axiom_16) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 11 (all X all Y m_Down(X) != m_Halt(Y)) # label(axiom_17) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 12 (all X all Y m_Down(X) != m_Ldr(Y)) # label(axiom_18) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 13 (all X all Y m_Down(X) != m_NotNorm(Y)) # label(axiom_19) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 14 (all X all Y m_Down(X) != m_NormQ(Y)) # label(axiom_20) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 15 (all X all Y m_NormQ(X) != m_Halt(Y)) # label(axiom_21) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 16 (all X all Y m_Ldr(X) != m_Halt(Y)) # label(axiom_22) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 17 (all X all Y m_Ldr(X) != m_NormQ(Y)) # label(axiom_23) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 18 (all X all Y m_Ldr(X) != m_NotNorm(Y)) # label(axiom_24) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 19 (all X all Y m_NormQ(X) != m_NotNorm(Y)) # label(axiom_25) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 20 (all X all Y (X != Y <-> m_Halt(X) != m_Halt(Y))) # label(axiom_26) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 21 (all X all Y (X != Y <-> m_NormQ(X) != m_NormQ(Y))) # label(axiom_27) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 22 (all X all Y (X != Y <-> m_NotNorm(X) != m_NotNorm(Y))) # label(axiom_28) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 23 (all X all Y (X != Y <-> m_Ldr(X) != m_Ldr(Y))) # label(axiom_29) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 24 (all X all Y (X != Y <-> m_Down(X) != m_Down(Y))) # label(axiom_30) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 27 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 28 (all X all Q head(cons(X,Q)) = X) # label(axiom_35) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 29 (all X all Q tail(cons(X,Q)) = Q) # label(axiom_36) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 30 (all Y all Q last(snoc(Q,Y)) = Y) # label(axiom_37) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 32 (all Q (Q = q_nil | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 33 (all Q (Q = q_nil | Q = snoc(init(Q),last(Q)))) # label(axiom_40) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 34 (all X all Q q_nil != cons(X,Q)) # label(axiom_41) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 35 (all Y all Q q_nil != snoc(Q,Y)) # label(axiom_42) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 36 (all X cons(X,q_nil) = snoc(q_nil,X)) # label(axiom_43) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 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].
% 0.81/1.09 38 (all X -elem(X,q_nil)) # label(axiom_45) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 41 (all X (pidElem(X) <-> (exists Y (X = m_Halt(Y) | X = m_Down(Y))))) # label(axiom_48) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 42 (all X pidMsg(m_Halt(X)) = X) # label(axiom_49) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 43 (all X pidMsg(m_Down(X)) = X) # label(axiom_50) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 44 (all X (ordered(cons(X,q_nil)) & ordered(snoc(q_nil,X)))) # label(axiom_52) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 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].
% 0.81/1.09 48 (all Q all X (ordered(Q) -> ordered(snoc(Q,m_Ldr(X))))) # label(axiom_56) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 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].
% 0.81/1.11 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 51 (all X leq(X,X)) # label(axiom_59) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 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].
% 0.81/1.11 55 (all X all Y (leq(X,Y) <-> leq(s(X),s(Y)))) # label(axiom_63) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 56 (all X all Y (leq(X,s(Y)) <-> X = s(Y) | leq(X,Y))) # label(axiom_64) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 57 (all X -setIn(X,setEmpty)) # label(axiom_65) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.11 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Halt(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z (index(status,host(Z)) = elec_2 -> -leq(index(pendack,host(Z)),host(Z)))) & (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) & 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 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(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 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))))) & 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(host(Z),host(W0)) & setIn(Z,alive) & setIn(W0,alive) & index(status,host(W0)) = elec_2 -> -leq(s(host(X)),index(pendack,host(W0))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.11
% 0.81/1.11 ============================== end of process non-clausal formulas ===
% 0.81/1.11
% 0.81/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.11
% 0.81/1.11 ============================== PREDICATE ELIMINATION =================
% 0.81/1.11
% 0.81/1.11 ============================== end predicate elimination =============
% 0.81/1.11
% 0.81/1.11 Auto_denials: (non-Horn, no changes).
% 0.81/1.11
% 0.81/1.11 Term ordering decisions:
% 0.81/1.11 Function symbol KB weights: alive=1. status=1. elec_2=1. q_nil=1. pendack=1. zero=1. down=1. elec_1=1. elid=1. nbr_proc=1. pids=1. ldr=1. nil=1. norm=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. s=1. m_Down=1. m_Halt=1. m_Ldr=1. queue=1. m_NormQ=1. m_NotNorm=1. head=1. init=1. last=1. tail=1. f1=1.
% 0.81/1.11
% 0.81/1.11 ============================== end of process initial clauses ========
% 15.79/16.12
% 15.79/16.12 ============================== CLAUSES FOR SEARCH ====================
% 15.79/16.12
% 15.79/16.12 ============================== end of clauses for search =============
% 15.79/16.12
% 15.79/16.12 ============================== SEARCH ================================
% 15.79/16.12
% 15.79/16.12 % Starting search at 0.03 seconds.
% 15.79/16.12
% 15.79/16.12 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 135 (0.00 of 0.39 sec).
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=33.000, iters=3361
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=31.000, iters=3346
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=30.000, iters=3335
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=27.000, iters=3354
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=25.000, iters=3350
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=24.000, iters=3338
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=23.000, iters=3345
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=22.000, iters=3354
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=21.000, iters=3345
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=20.000, iters=3366
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=19.000, iters=3346
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=16.000, iters=5271
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=15.000, iters=3926
% 15.79/16.12
% 15.79/16.12 Low Water (keep): wt=14.000, iters=3346
% 15.79/16.12
% 15.79/16.12 ============================== PROOF =================================
% 15.79/16.12 % SZS status Theorem
% 15.79/16.12 % SZS output start Refutation
% 15.79/16.12
% 15.79/16.12 % Proof 1 at 14.47 (+ 0.57) seconds.
% 15.79/16.12 % Length of proof is 58.
% 15.79/16.12 % Level of proof is 11.
% 15.79/16.12 % Maximum clause weight is 33.000.
% 15.79/16.12 % Given clauses 5722.
% 15.79/16.12
% 15.79/16.12 2 (all P all Q (s(host(P)) = host(Q) -> host(P) != host(Q))) # label(axiom_01) # label(axiom) # label(non_clause). [assumption].
% 15.79/16.12 3 (all P leq(s(zero),host(P))) # label(axiom_02) # label(axiom) # label(non_clause). [assumption].
% 15.79/16.12 27 (all Pid all Pid2 (host(Pid) != host(Pid2) -> Pid != Pid2)) # label(axiom_33) # label(axiom) # label(non_clause). [assumption].
% 15.79/16.12 31 (all Y all Q init(snoc(Q,Y)) = Q) # label(axiom_38) # label(axiom) # label(non_clause). [assumption].
% 15.79/16.12 32 (all Q (Q = q_nil | Q = cons(head(Q),tail(Q)))) # label(axiom_39) # label(axiom) # label(non_clause). [assumption].
% 15.79/16.12 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].
% 15.79/16.12 50 (all X -leq(s(X),X)) # label(axiom_58) # label(axiom) # label(non_clause). [assumption].
% 15.79/16.12 52 (all X all Y (leq(X,Y) | leq(Y,X))) # label(axiom_60) # label(axiom) # label(non_clause). [assumption].
% 15.79/16.12 53 (all X all Y (leq(X,Y) & leq(Y,X) <-> X = Y)) # label(axiom_61) # label(axiom) # label(non_clause). [assumption].
% 15.79/16.12 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].
% 15.79/16.12 58 -(all V all W all X all Y ((all Z all Pid0 (elem(m_Halt(Pid0),queue(host(Z))) -> -leq(host(Z),host(Pid0)))) & (all Z (index(status,host(Z)) = elec_2 -> -leq(index(pendack,host(Z)),host(Z)))) & (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) & 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 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(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 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))))) & 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(host(Z),host(W0)) & setIn(Z,alive) & setIn(W0,alive) & index(status,host(W0)) = elec_2 -> -leq(s(host(X)),index(pendack,host(W0))))))))))))))) # label(conj) # label(negated_conjecture) # label(non_clause). [assumption].
% 15.79/16.12 61 s(host(A)) != host(B) | host(B) != host(A) # label(axiom_01) # label(axiom). [clausify(2)].
% 15.79/16.12 62 leq(s(zero),host(A)) # label(axiom_02) # label(axiom). [clausify(3)].
% 15.79/16.12 103 host(A) = host(B) | A != B # label(axiom_33) # label(axiom). [clausify(27)].
% 15.79/16.12 108 init(snoc(A,B)) = A # label(axiom_38) # label(axiom). [clausify(31)].
% 15.79/16.12 109 q_nil = A | cons(head(A),tail(A)) = A # label(axiom_39) # label(axiom). [clausify(32)].
% 15.79/16.12 117 elem(A,cons(B,C)) | B != A # label(axiom_46) # label(axiom). [clausify(39)].
% 15.79/16.12 147 -leq(s(A),A) # label(axiom_58) # label(axiom). [clausify(50)].
% 15.79/16.12 149 leq(A,B) | leq(B,A) # label(axiom_60) # label(axiom). [clausify(52)].
% 15.79/16.12 150 -leq(A,B) | -leq(B,A) | B = A # label(axiom_61) # label(axiom). [clausify(53)].
% 15.79/16.12 152 leq(A,B) | A != B # label(axiom_61) # label(axiom). [clausify(53)].
% 15.79/16.12 153 -leq(A,B) | -leq(B,C) | leq(A,C) # label(axiom_62) # label(axiom). [clausify(54)].
% 15.79/16.12 166 -setIn(A,alive) | -setIn(B,alive) | -setIn(host(B),index(down,host(A))) | index(status,host(B)) != elec_2 | leq(index(pendack,host(B)),host(A)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 170 -setIn(A,alive) | -setIn(B,alive) | -elem(m_Down(C),queue(host(A))) | host(C) != host(B) | index(status,host(B)) != elec_2 | leq(index(pendack,host(B)),host(A)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 172 cons(m_Down(c4),c1) = queue(host(c3)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 173 setIn(c3,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 177 leq(host(c3),A) | -leq(s(zero),A) | setIn(A,index(down,host(c3))) | host(c4) = A # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 181 host(c5) = host(c3) # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 183 -leq(host(c5),host(c6)) # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 184 -leq(host(c3),host(c6)). [copy(183),rewrite([181(2)])].
% 15.79/16.12 186 setIn(c6,alive) # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 187 index(status,host(c6)) = elec_2 # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 188 elec_2 = index(status,host(c6)). [copy(187),flip(a)].
% 15.79/16.12 189 leq(s(host(c3)),index(pendack,host(c6))) # label(conj) # label(negated_conjecture). [clausify(58)].
% 15.79/16.12 198 -setIn(A,alive) | -setIn(B,alive) | -elem(m_Down(C),queue(host(A))) | host(C) != host(B) | index(status,host(c6)) != index(status,host(B)) | leq(index(pendack,host(B)),host(A)). [back_rewrite(170),rewrite([188(15)]),flip(e)].
% 15.79/16.12 202 -setIn(A,alive) | -setIn(B,alive) | -setIn(host(B),index(down,host(A))) | index(status,host(c6)) != index(status,host(B)) | leq(index(pendack,host(B)),host(A)). [back_rewrite(166),rewrite([188(13)]),flip(d)].
% 15.79/16.12 208 q_nil = A | host(cons(head(A),tail(A))) = host(A). [resolve(109,b,103,b)].
% 15.79/16.12 231 elem(A,cons(A,B)). [resolve(117,b,108,a),rewrite([108(2)])].
% 15.79/16.12 267 leq(A,s(A)). [resolve(149,a,147,a)].
% 15.79/16.12 303 leq(host(c3),host(A)) | setIn(host(A),index(down,host(c3))) | host(c4) = host(A). [resolve(177,b,62,a)].
% 15.79/16.12 313 -leq(index(pendack,host(c6)),A) | leq(s(host(c3)),A). [resolve(189,a,153,a)].
% 15.79/16.12 314 -leq(index(pendack,host(c6)),s(host(c3))) | index(pendack,host(c6)) = s(host(c3)). [resolve(189,a,150,b),flip(b)].
% 15.79/16.12 338 q_nil = A | s(host(A)) != host(B) | host(cons(head(A),tail(A))) != host(B). [para(208(b,1),61(a,1,1)),flip(c)].
% 15.79/16.12 357 -leq(s(A),B) | leq(A,B). [resolve(267,a,153,a)].
% 15.88/16.12 381 elem(m_Down(c4),queue(host(c3))). [para(172(a,1),231(a,2))].
% 15.88/16.12 539 -setIn(A,alive) | host(c4) != host(A) | index(status,host(c6)) != index(status,host(A)) | leq(index(pendack,host(A)),host(c3)). [resolve(381,a,198,c),unit_del(a,173)].
% 15.88/16.12 702 leq(host(c3),index(pendack,host(c6))). [resolve(357,a,189,a)].
% 15.88/16.12 859 -leq(index(pendack,host(c6)),host(c3)) | index(pendack,host(c6)) = host(c3). [resolve(702,a,150,b),flip(b)].
% 15.88/16.12 1905 leq(host(c3),host(A)) | host(c4) = host(A) | -setIn(A,alive) | index(status,host(c6)) != index(status,host(A)) | leq(index(pendack,host(A)),host(c3)). [resolve(303,b,202,c),unit_del(c,173)].
% 15.88/16.12 3000 q_nil = A | s(host(A)) != host(B) | host(A) != host(B). [para(109(b,1),338(c,1,1)),merge(b)].
% 15.88/16.12 9390 host(c6) != host(c4) | leq(index(pendack,host(c6)),host(c3)). [resolve(539,a,186,a),flip(a),xx(b)].
% 15.88/16.12 14281 host(c6) = host(c4) | leq(index(pendack,host(c6)),host(c3)). [resolve(1905,c,186,a),flip(b),xx(c),unit_del(a,184)].
% 15.88/16.12 14291 host(c6) = host(c4). [resolve(14281,b,313,a),unit_del(b,147)].
% 15.88/16.12 14534 leq(index(pendack,host(c4)),host(c3)). [back_rewrite(9390),rewrite([14291(2),14291(8)]),xx(a)].
% 15.88/16.12 14947 index(pendack,host(c4)) = host(c3). [back_rewrite(859),rewrite([14291(3),14291(10)]),unit_del(a,14534)].
% 15.88/16.12 14949 s(host(c3)) = host(c3). [back_rewrite(314),rewrite([14291(3),14947(4),14291(9),14947(10)]),flip(b),unit_del(a,267)].
% 15.88/16.12 15310 c3 = q_nil. [resolve(14949,a,3000,b),flip(a),xx(b)].
% 15.88/16.12 15311 $F. [resolve(14949,a,152,b),rewrite([15310(1),15310(4)]),unit_del(a,147)].
% 15.88/16.12
% 15.88/16.12 % SZS output end Refutation
% 15.88/16.12 ============================== end of proof ==========================
% 15.88/16.12
% 15.88/16.12 ============================== STATISTICS ============================
% 15.88/16.12
% 15.88/16.12 Given=5722. Generated=1030146. Kept=15243. proofs=1.
% 15.88/16.12 Usable=4731. Sos=7152. Demods=63. Limbo=1, Disabled=3483. Hints=0.
% 15.88/16.12 Megabytes=27.53.
% 15.88/16.12 User_CPU=14.47, System_CPU=0.57, Wall_clock=15.
% 15.88/16.12
% 15.88/16.12 ============================== end of statistics =====================
% 15.88/16.12
% 15.88/16.12 ============================== end of search =========================
% 15.88/16.12
% 15.88/16.12 THEOREM PROVED
% 15.88/16.12 % SZS status Theorem
% 15.88/16.12
% 15.88/16.12 Exiting with 1 proof.
% 15.88/16.12
% 15.88/16.12 Process 4897 exit (max_proofs) Tue Jun 14 21:17:14 2022
% 15.88/16.12 Prover9 interrupted
%------------------------------------------------------------------------------