TSTP Solution File: SWV450+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV450+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n014.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  : 300s
% DateTime : Thu Aug 31 21:41:19 EDT 2023

% Result   : Theorem 0.18s 0.76s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   56
% Syntax   : Number of formulae    :   85 (  17 unt;  51 typ;   0 def)
%            Number of atoms       :  235 (  90 equ)
%            Maximal formula atoms :   44 (   6 avg)
%            Number of connectives :  312 ( 111   ~;  62   |;  91   &)
%                                         (   3 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   40 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   39 (  27   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :   45 (  45 usr;  24 con; 0-2 aty)
%            Number of variables   :  162 (  23 sgn; 122   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    m_Ack: ( $i * $i ) > $i ).

tff(decl_23,type,
    host: $i > $i ).

tff(decl_24,type,
    queue: $i > $i ).

tff(decl_25,type,
    elem: ( $i * $i ) > $o ).

tff(decl_26,type,
    pids: $i ).

tff(decl_27,type,
    setIn: ( $i * $i ) > $o ).

tff(decl_28,type,
    s: $i > $i ).

tff(decl_29,type,
    zero: $i ).

tff(decl_30,type,
    leq: ( $i * $i ) > $o ).

tff(decl_31,type,
    nbr_proc: $i ).

tff(decl_32,type,
    elec_1: $i ).

tff(decl_33,type,
    elec_2: $i ).

tff(decl_34,type,
    wait: $i ).

tff(decl_35,type,
    norm: $i ).

tff(decl_36,type,
    m_Halt: $i > $i ).

tff(decl_37,type,
    m_Down: $i > $i ).

tff(decl_38,type,
    m_NotNorm: $i > $i ).

tff(decl_39,type,
    m_Ldr: $i > $i ).

tff(decl_40,type,
    m_NormQ: $i > $i ).

tff(decl_41,type,
    nil: $i ).

tff(decl_42,type,
    alive: $i ).

tff(decl_43,type,
    cons: ( $i * $i ) > $i ).

tff(decl_44,type,
    head: $i > $i ).

tff(decl_45,type,
    tail: $i > $i ).

tff(decl_46,type,
    snoc: ( $i * $i ) > $i ).

tff(decl_47,type,
    last: $i > $i ).

tff(decl_48,type,
    init: $i > $i ).

tff(decl_49,type,
    q_nil: $i ).

tff(decl_50,type,
    pidElem: $i > $o ).

tff(decl_51,type,
    pidMsg: $i > $i ).

tff(decl_52,type,
    ordered: $i > $o ).

tff(decl_53,type,
    setEmpty: $i ).

tff(decl_54,type,
    elid: $i ).

tff(decl_55,type,
    index: ( $i * $i ) > $i ).

tff(decl_56,type,
    status: $i ).

tff(decl_57,type,
    pendack: $i ).

tff(decl_58,type,
    acks: $i ).

tff(decl_59,type,
    epred1_4: ( $i * $i * $i * $i ) > $o ).

tff(decl_60,type,
    esk1_1: $i > $i ).

tff(decl_61,type,
    esk2_1: $i > $i ).

tff(decl_62,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_64,type,
    esk5_0: $i ).

tff(decl_65,type,
    esk6_0: $i ).

tff(decl_66,type,
    esk7_0: $i ).

tff(decl_67,type,
    esk8_0: $i ).

tff(decl_68,type,
    esk9_0: $i ).

tff(decl_69,type,
    esk10_0: $i ).

tff(decl_70,type,
    esk11_0: $i ).

tff(decl_71,type,
    esk12_0: $i ).

tff(decl_72,type,
    esk13_0: $i ).

fof(conj,conjecture,
    ! [X12,X13,X5,X6] :
      ( ( ! [X7,X14] :
            ( setIn(X14,alive)
           => ~ elem(m_Down(X14),queue(host(X7))) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => ~ setIn(X14,alive) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => host(X14) != host(X7) )
        & ! [X7,X14] :
            ( elem(m_Halt(X14),queue(host(X7)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X15,X14] :
            ( elem(m_Ack(X14,X7),queue(host(X15)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X14] :
            ( ( ~ setIn(X7,alive)
              & leq(X14,X7)
              & host(X14) = host(X7) )
           => ~ setIn(X14,alive) )
        & ! [X7,X14] :
            ( ( X14 != X7
              & host(X14) = host(X7) )
           => ( ~ setIn(X7,alive)
              | ~ setIn(X14,alive) ) )
        & ! [X7,X16,X15,X14] :
            ( ( host(X15) != host(X7)
              & setIn(X7,alive)
              & setIn(X15,alive)
              & host(X16) = host(X7)
              & host(X14) = host(X15) )
           => ~ ( elem(m_Down(X14),queue(host(X7)))
                & elem(m_Down(X16),queue(host(X15))) ) )
        & queue(host(X5)) = cons(m_Ack(X13,X6),X12) )
     => ( setIn(X5,alive)
       => ( ( index(elid,host(X5)) = X13
            & index(status,host(X5)) = elec_2
            & host(X6) = index(pendack,host(X5)) )
         => ( leq(nbr_proc,index(pendack,host(X5)))
           => ! [X7] :
                ( ( setIn(host(X7),index(acks,host(X5)))
                  | host(X7) = host(X6) )
               => ! [X17] :
                    ( host(X7) != host(X17)
                   => ( host(X5) = host(X17)
                     => ! [X18,X19] :
                          ( host(X7) = host(X19)
                         => ( host(X5) != host(X19)
                           => ! [X20] :
                                ( ( host(X19) != host(X17)
                                  & setIn(X17,alive)
                                  & setIn(X19,alive)
                                  & host(X18) = host(X17)
                                  & host(X20) = host(X19) )
                               => ~ ( elem(m_Down(X20),X12)
                                    & elem(m_Down(X18),snoc(queue(host(X19)),m_Ldr(X5))) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

fof(axiom_47,axiom,
    ! [X5,X6,X4] :
      ( elem(X5,snoc(X4,X6))
    <=> ( X5 = X6
        | elem(X5,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_47) ).

fof(axiom_18,axiom,
    ! [X5,X6] : m_Down(X5) != m_Ldr(X6),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_18) ).

fof(axiom_46,axiom,
    ! [X5,X6,X4] :
      ( elem(X5,cons(X6,X4))
    <=> ( X5 = X6
        | elem(X5,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax',axiom_46) ).

fof(c_0_4,plain,
    ! [X13,X5,X6,X12] :
      ( epred1_4(X12,X6,X5,X13)
    <=> ( ! [X7,X14] :
            ( setIn(X14,alive)
           => ~ elem(m_Down(X14),queue(host(X7))) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => ~ setIn(X14,alive) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => host(X14) != host(X7) )
        & ! [X7,X14] :
            ( elem(m_Halt(X14),queue(host(X7)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X15,X14] :
            ( elem(m_Ack(X14,X7),queue(host(X15)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X14] :
            ( ( ~ setIn(X7,alive)
              & leq(X14,X7)
              & host(X14) = host(X7) )
           => ~ setIn(X14,alive) )
        & ! [X7,X14] :
            ( ( X14 != X7
              & host(X14) = host(X7) )
           => ( ~ setIn(X7,alive)
              | ~ setIn(X14,alive) ) )
        & ! [X7,X16,X15,X14] :
            ( ( host(X15) != host(X7)
              & setIn(X7,alive)
              & setIn(X15,alive)
              & host(X16) = host(X7)
              & host(X14) = host(X15) )
           => ~ ( elem(m_Down(X14),queue(host(X7)))
                & elem(m_Down(X16),queue(host(X15))) ) )
        & queue(host(X5)) = cons(m_Ack(X13,X6),X12) ) ),
    introduced(definition) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X12,X13,X5,X6] :
        ( epred1_4(X12,X6,X5,X13)
       => ( setIn(X5,alive)
         => ( ( index(elid,host(X5)) = X13
              & index(status,host(X5)) = elec_2
              & host(X6) = index(pendack,host(X5)) )
           => ( leq(nbr_proc,index(pendack,host(X5)))
             => ! [X7] :
                  ( ( setIn(host(X7),index(acks,host(X5)))
                    | host(X7) = host(X6) )
                 => ! [X17] :
                      ( host(X7) != host(X17)
                     => ( host(X5) = host(X17)
                       => ! [X18,X19] :
                            ( host(X7) = host(X19)
                           => ( host(X5) != host(X19)
                             => ! [X20] :
                                  ( ( host(X19) != host(X17)
                                    & setIn(X17,alive)
                                    & setIn(X19,alive)
                                    & host(X18) = host(X17)
                                    & host(X20) = host(X19) )
                                 => ~ ( elem(m_Down(X20),X12)
                                      & elem(m_Down(X18),snoc(queue(host(X19)),m_Ldr(X5))) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj])]),c_0_4]) ).

fof(c_0_6,plain,
    ! [X13,X5,X6,X12] :
      ( epred1_4(X12,X6,X5,X13)
     => ( ! [X7,X14] :
            ( setIn(X14,alive)
           => ~ elem(m_Down(X14),queue(host(X7))) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => ~ setIn(X14,alive) )
        & ! [X7,X14] :
            ( elem(m_Down(X14),queue(host(X7)))
           => host(X14) != host(X7) )
        & ! [X7,X14] :
            ( elem(m_Halt(X14),queue(host(X7)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X15,X14] :
            ( elem(m_Ack(X14,X7),queue(host(X15)))
           => ~ leq(host(X7),host(X14)) )
        & ! [X7,X14] :
            ( ( ~ setIn(X7,alive)
              & leq(X14,X7)
              & host(X14) = host(X7) )
           => ~ setIn(X14,alive) )
        & ! [X7,X14] :
            ( ( X14 != X7
              & host(X14) = host(X7) )
           => ( ~ setIn(X7,alive)
              | ~ setIn(X14,alive) ) )
        & ! [X7,X16,X15,X14] :
            ( ( host(X15) != host(X7)
              & setIn(X7,alive)
              & setIn(X15,alive)
              & host(X16) = host(X7)
              & host(X14) = host(X15) )
           => ~ ( elem(m_Down(X14),queue(host(X7)))
                & elem(m_Down(X16),queue(host(X15))) ) )
        & queue(host(X5)) = cons(m_Ack(X13,X6),X12) ) ),
    inference(split_equiv,[status(thm)],[c_0_4]) ).

fof(c_0_7,plain,
    ! [X104,X105,X106] :
      ( ( ~ elem(X104,snoc(X106,X105))
        | X104 = X105
        | elem(X104,X106) )
      & ( X104 != X105
        | elem(X104,snoc(X106,X105)) )
      & ( ~ elem(X104,X106)
        | elem(X104,snoc(X106,X105)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_47])])]) ).

fof(c_0_8,negated_conjecture,
    ( epred1_4(esk5_0,esk8_0,esk7_0,esk6_0)
    & setIn(esk7_0,alive)
    & index(elid,host(esk7_0)) = esk6_0
    & index(status,host(esk7_0)) = elec_2
    & host(esk8_0) = index(pendack,host(esk7_0))
    & leq(nbr_proc,index(pendack,host(esk7_0)))
    & ( setIn(host(esk9_0),index(acks,host(esk7_0)))
      | host(esk9_0) = host(esk8_0) )
    & host(esk9_0) != host(esk10_0)
    & host(esk7_0) = host(esk10_0)
    & host(esk9_0) = host(esk12_0)
    & host(esk7_0) != host(esk12_0)
    & host(esk12_0) != host(esk10_0)
    & setIn(esk10_0,alive)
    & setIn(esk12_0,alive)
    & host(esk11_0) = host(esk10_0)
    & host(esk13_0) = host(esk12_0)
    & elem(m_Down(esk13_0),esk5_0)
    & elem(m_Down(esk11_0),snoc(queue(host(esk12_0)),m_Ldr(esk7_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_9,plain,
    ! [X46,X47] : m_Down(X46) != m_Ldr(X47),
    inference(variable_rename,[status(thm)],[axiom_18]) ).

fof(c_0_10,plain,
    ! [X159,X160,X161,X162,X163,X164,X165,X166,X167,X168,X169,X170,X171,X172,X173,X174,X175,X176,X177,X178,X179,X180,X181] :
      ( ( ~ setIn(X164,alive)
        | ~ elem(m_Down(X164),queue(host(X163)))
        | ~ epred1_4(X162,X161,X160,X159) )
      & ( ~ elem(m_Down(X166),queue(host(X165)))
        | ~ setIn(X166,alive)
        | ~ epred1_4(X162,X161,X160,X159) )
      & ( ~ elem(m_Down(X168),queue(host(X167)))
        | host(X168) != host(X167)
        | ~ epred1_4(X162,X161,X160,X159) )
      & ( ~ elem(m_Halt(X170),queue(host(X169)))
        | ~ leq(host(X169),host(X170))
        | ~ epred1_4(X162,X161,X160,X159) )
      & ( ~ elem(m_Ack(X173,X171),queue(host(X172)))
        | ~ leq(host(X171),host(X173))
        | ~ epred1_4(X162,X161,X160,X159) )
      & ( setIn(X174,alive)
        | ~ leq(X175,X174)
        | host(X175) != host(X174)
        | ~ setIn(X175,alive)
        | ~ epred1_4(X162,X161,X160,X159) )
      & ( X177 = X176
        | host(X177) != host(X176)
        | ~ setIn(X176,alive)
        | ~ setIn(X177,alive)
        | ~ epred1_4(X162,X161,X160,X159) )
      & ( host(X180) = host(X178)
        | ~ setIn(X178,alive)
        | ~ setIn(X180,alive)
        | host(X179) != host(X178)
        | host(X181) != host(X180)
        | ~ elem(m_Down(X181),queue(host(X178)))
        | ~ elem(m_Down(X179),queue(host(X180)))
        | ~ epred1_4(X162,X161,X160,X159) )
      & ( queue(host(X160)) = cons(m_Ack(X159,X161),X162)
        | ~ epred1_4(X162,X161,X160,X159) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

cnf(c_0_11,plain,
    ( X1 = X3
    | elem(X1,X2)
    | ~ elem(X1,snoc(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    elem(m_Down(esk11_0),snoc(queue(host(esk12_0)),m_Ldr(esk7_0))),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    m_Down(X1) != m_Ldr(X2),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    host(esk11_0) = host(esk10_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    host(esk7_0) = host(esk10_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,plain,
    ( host(X1) = host(X2)
    | ~ setIn(X2,alive)
    | ~ setIn(X1,alive)
    | host(X3) != host(X2)
    | host(X4) != host(X1)
    | ~ elem(m_Down(X4),queue(host(X2)))
    | ~ elem(m_Down(X3),queue(host(X1)))
    | ~ epred1_4(X5,X6,X7,X8) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,negated_conjecture,
    elem(m_Down(esk11_0),queue(host(esk12_0))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    host(esk11_0) = host(esk7_0),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    setIn(esk12_0,alive),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,plain,
    ( queue(host(X1)) = cons(m_Ack(X2,X3),X4)
    | ~ epred1_4(X4,X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_21,negated_conjecture,
    epred1_4(esk5_0,esk8_0,esk7_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_22,negated_conjecture,
    ( host(X1) = host(esk12_0)
    | host(esk12_0) != host(X2)
    | host(X1) != host(esk7_0)
    | ~ epred1_4(X3,X4,X5,X6)
    | ~ setIn(X1,alive)
    | ~ elem(m_Down(X2),queue(host(X1))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).

cnf(c_0_23,negated_conjecture,
    queue(host(esk7_0)) = cons(m_Ack(esk6_0,esk8_0),esk5_0),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,negated_conjecture,
    setIn(esk7_0,alive),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_25,negated_conjecture,
    host(esk7_0) != host(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_26,plain,
    ! [X101,X102,X103] :
      ( ( ~ elem(X101,cons(X102,X103))
        | X101 = X102
        | elem(X101,X103) )
      & ( X101 != X102
        | elem(X101,cons(X102,X103)) )
      & ( ~ elem(X101,X103)
        | elem(X101,cons(X102,X103)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_46])])]) ).

cnf(c_0_27,negated_conjecture,
    ( host(esk12_0) != host(X1)
    | ~ epred1_4(X2,X3,X4,X5)
    | ~ elem(m_Down(X1),cons(m_Ack(esk6_0,esk8_0),esk5_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]) ).

cnf(c_0_28,plain,
    ( elem(X1,cons(X3,X2))
    | ~ elem(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_29,negated_conjecture,
    ( host(esk12_0) != host(X1)
    | ~ epred1_4(X2,X3,X4,X5)
    | ~ elem(m_Down(X1),esk5_0) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_30,negated_conjecture,
    elem(m_Down(esk13_0),esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_31,negated_conjecture,
    host(esk13_0) = host(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_32,negated_conjecture,
    ~ epred1_4(X1,X2,X3,X4),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_21,c_0_32]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV450+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 29 08:12:30 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.58  start to proof: theBenchmark
% 0.18/0.76  % Version  : CSE_E---1.5
% 0.18/0.76  % Problem  : theBenchmark.p
% 0.18/0.76  % Proof found
% 0.18/0.76  % SZS status Theorem for theBenchmark.p
% 0.18/0.76  % SZS output start Proof
% See solution above
% 0.18/0.77  % Total time : 0.163000 s
% 0.18/0.77  % SZS output end Proof
% 0.18/0.77  % Total time : 0.167000 s
%------------------------------------------------------------------------------