TSTP Solution File: SWV455+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV455+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 21:41:21 EDT 2023

% Result   : Theorem 0.20s 0.73s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   53
% Syntax   : Number of formulae    :   77 (  13 unt;  50 typ;   0 def)
%            Number of atoms       :  227 (  86 equ)
%            Maximal formula atoms :   46 (   8 avg)
%            Number of connectives :  321 ( 121   ~;  62   |;  93   &)
%                                         (   2 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   8 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  27   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   44 (  44 usr;  23 con; 0-2 aty)
%            Number of variables   :  138 (  18 sgn; 109   !;   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,
    ldr: $i ).

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

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

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

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

tff(decl_59,type,
    epred1_3: ( $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 ).

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_Down(X6),X12) )
     => ( setIn(X5,alive)
       => ( ~ leq(host(X5),host(X6))
         => ( ~ ( ( index(ldr,host(X5)) = host(X6)
                  & index(status,host(X5)) = norm )
                | ( index(status,host(X5)) = wait
                  & host(X6) = host(index(elid,host(X5))) ) )
           => ( ~ ( ! [X7] :
                      ( ( ~ leq(host(X5),X7)
                        & leq(s(zero),X7) )
                     => ( setIn(X7,index(down,host(X5)))
                        | X7 = host(X6) ) )
                  & index(status,host(X5)) = elec_1 )
             => ! [X7] :
                  ( host(X5) != host(X7)
                 => ! [X17,X18] :
                      ( host(X5) = host(X18)
                     => ! [X19] :
                          ( ( host(X18) != host(X7)
                            & setIn(X7,alive)
                            & setIn(X18,alive)
                            & host(X17) = host(X7)
                            & host(X19) = host(X18) )
                         => ~ ( elem(m_Down(X17),X12)
                              & elem(m_Down(X19),queue(host(X7))) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

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

fof(c_0_2,plain,
    ! [X5,X6,X12] :
      ( epred1_3(X12,X6,X5)
    <=> ( ! [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_Down(X6),X12) ) ),
    introduced(definition) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X12,X13,X5,X6] :
        ( epred1_3(X12,X6,X5)
       => ( setIn(X5,alive)
         => ( ~ leq(host(X5),host(X6))
           => ( ~ ( ( index(ldr,host(X5)) = host(X6)
                    & index(status,host(X5)) = norm )
                  | ( index(status,host(X5)) = wait
                    & host(X6) = host(index(elid,host(X5))) ) )
             => ( ~ ( ! [X7] :
                        ( ( ~ leq(host(X5),X7)
                          & leq(s(zero),X7) )
                       => ( setIn(X7,index(down,host(X5)))
                          | X7 = host(X6) ) )
                    & index(status,host(X5)) = elec_1 )
               => ! [X7] :
                    ( host(X5) != host(X7)
                   => ! [X17,X18] :
                        ( host(X5) = host(X18)
                       => ! [X19] :
                            ( ( host(X18) != host(X7)
                              & setIn(X7,alive)
                              & setIn(X18,alive)
                              & host(X17) = host(X7)
                              & host(X19) = host(X18) )
                           => ~ ( elem(m_Down(X17),X12)
                                & elem(m_Down(X19),queue(host(X7))) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj])]),c_0_2]) ).

fof(c_0_4,plain,
    ! [X5,X6,X12] :
      ( epred1_3(X12,X6,X5)
     => ( ! [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_Down(X6),X12) ) ),
    inference(split_equiv,[status(thm)],[c_0_2]) ).

fof(c_0_5,negated_conjecture,
    ( epred1_3(esk5_0,esk7_0,esk6_0)
    & setIn(esk6_0,alive)
    & ~ leq(host(esk6_0),host(esk7_0))
    & ( index(ldr,host(esk6_0)) != host(esk7_0)
      | index(status,host(esk6_0)) != norm )
    & ( index(status,host(esk6_0)) != wait
      | host(esk7_0) != host(index(elid,host(esk6_0))) )
    & ( ~ leq(host(esk6_0),esk8_0)
      | index(status,host(esk6_0)) != elec_1 )
    & ( leq(s(zero),esk8_0)
      | index(status,host(esk6_0)) != elec_1 )
    & ( ~ setIn(esk8_0,index(down,host(esk6_0)))
      | index(status,host(esk6_0)) != elec_1 )
    & ( esk8_0 != host(esk7_0)
      | index(status,host(esk6_0)) != elec_1 )
    & host(esk6_0) != host(esk9_0)
    & host(esk6_0) = host(esk11_0)
    & host(esk11_0) != host(esk9_0)
    & setIn(esk9_0,alive)
    & setIn(esk11_0,alive)
    & host(esk10_0) = host(esk9_0)
    & host(esk12_0) = host(esk11_0)
    & elem(m_Down(esk10_0),esk5_0)
    & elem(m_Down(esk12_0),queue(host(esk9_0))) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3])])])])]) ).

fof(c_0_6,plain,
    ! [X157,X158,X159,X160,X161,X162,X163,X164,X165,X166,X167,X168,X169,X170,X171,X172,X173,X174,X175,X176,X177,X178] :
      ( ( ~ setIn(X161,alive)
        | ~ elem(m_Down(X161),queue(host(X160)))
        | ~ epred1_3(X159,X158,X157) )
      & ( ~ elem(m_Down(X163),queue(host(X162)))
        | ~ setIn(X163,alive)
        | ~ epred1_3(X159,X158,X157) )
      & ( ~ elem(m_Down(X165),queue(host(X164)))
        | host(X165) != host(X164)
        | ~ epred1_3(X159,X158,X157) )
      & ( ~ elem(m_Halt(X167),queue(host(X166)))
        | ~ leq(host(X166),host(X167))
        | ~ epred1_3(X159,X158,X157) )
      & ( ~ elem(m_Ack(X170,X168),queue(host(X169)))
        | ~ leq(host(X168),host(X170))
        | ~ epred1_3(X159,X158,X157) )
      & ( setIn(X171,alive)
        | ~ leq(X172,X171)
        | host(X172) != host(X171)
        | ~ setIn(X172,alive)
        | ~ epred1_3(X159,X158,X157) )
      & ( X174 = X173
        | host(X174) != host(X173)
        | ~ setIn(X173,alive)
        | ~ setIn(X174,alive)
        | ~ epred1_3(X159,X158,X157) )
      & ( host(X177) = host(X175)
        | ~ setIn(X175,alive)
        | ~ setIn(X177,alive)
        | host(X176) != host(X175)
        | host(X178) != host(X177)
        | ~ elem(m_Down(X178),queue(host(X175)))
        | ~ elem(m_Down(X176),queue(host(X177)))
        | ~ epred1_3(X159,X158,X157) )
      & ( queue(host(X157)) = cons(m_Down(X158),X159)
        | ~ epred1_3(X159,X158,X157) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

cnf(c_0_7,negated_conjecture,
    host(esk12_0) = host(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    host(esk6_0) = host(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,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_3(X5,X6,X7) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    elem(m_Down(esk12_0),queue(host(esk9_0))),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,negated_conjecture,
    host(esk12_0) = host(esk6_0),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    setIn(esk9_0,alive),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,plain,
    ( queue(host(X1)) = cons(m_Down(X2),X3)
    | ~ epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,negated_conjecture,
    epred1_3(esk5_0,esk7_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_15,negated_conjecture,
    ( host(X1) = host(esk9_0)
    | host(esk9_0) != host(X2)
    | host(X1) != host(esk6_0)
    | ~ epred1_3(X3,X4,X5)
    | ~ 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_9,c_0_10]),c_0_11]),c_0_12])]) ).

cnf(c_0_16,negated_conjecture,
    queue(host(esk6_0)) = cons(m_Down(esk7_0),esk5_0),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    setIn(esk6_0,alive),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_18,negated_conjecture,
    host(esk6_0) != host(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_19,plain,
    ! [X100,X101,X102] :
      ( ( ~ elem(X100,cons(X101,X102))
        | X100 = X101
        | elem(X100,X102) )
      & ( X100 != X101
        | elem(X100,cons(X101,X102)) )
      & ( ~ elem(X100,X102)
        | elem(X100,cons(X101,X102)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_46])])]) ).

cnf(c_0_20,negated_conjecture,
    ( host(esk9_0) != host(X1)
    | ~ epred1_3(X2,X3,X4)
    | ~ elem(m_Down(X1),cons(m_Down(esk7_0),esk5_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]) ).

cnf(c_0_21,plain,
    ( elem(X1,cons(X3,X2))
    | ~ elem(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    ( host(esk9_0) != host(X1)
    | ~ epred1_3(X2,X3,X4)
    | ~ elem(m_Down(X1),esk5_0) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_23,negated_conjecture,
    elem(m_Down(esk10_0),esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_24,negated_conjecture,
    host(esk10_0) = host(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_25,negated_conjecture,
    ~ epred1_3(X1,X2,X3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_26,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_14,c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV455+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 04:15:52 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.73  % Version  : CSE_E---1.5
% 0.20/0.73  % Problem  : theBenchmark.p
% 0.20/0.73  % Proof found
% 0.20/0.73  % SZS status Theorem for theBenchmark.p
% 0.20/0.73  % SZS output start Proof
% See solution above
% 0.20/0.74  % Total time : 0.148000 s
% 0.20/0.74  % SZS output end Proof
% 0.20/0.74  % Total time : 0.152000 s
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