TSTP Solution File: SWV455+1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWV455+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% 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  : 300s
% DateTime : Mon Jun 24 17:42:59 EDT 2024

% Result   : Theorem 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   39 (  12 unt;   0 def)
%            Number of atoms       :  546 ( 232 equ)
%            Maximal formula atoms :   92 (  14 avg)
%            Number of connectives :  822 ( 315   ~; 172   |; 277   &)
%                                         (   2 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   9 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   25 (  25 usr;  17 con; 0-2 aty)
%            Number of variables   :  279 ( 229   !;  50   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f559,plain,
    $false,
    inference(subsumption_resolution,[],[f555,f199]) ).

fof(f199,plain,
    host(sK3) = host(sK4),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,plain,
    ( elem(m_Down(sK6),queue(host(sK3)))
    & elem(m_Down(sK4),sK0)
    & host(sK5) = host(sK6)
    & host(sK3) = host(sK4)
    & setIn(sK5,alive)
    & setIn(sK3,alive)
    & host(sK3) != host(sK5)
    & host(sK1) = host(sK5)
    & host(sK1) != host(sK3)
    & ( elec_1 != index(status,host(sK1))
      | ( host(sK2) != sK7
        & ~ setIn(sK7,index(down,host(sK1)))
        & leq(s(zero),sK7)
        & ~ leq(host(sK1),sK7) ) )
    & ( host(sK2) != host(index(elid,host(sK1)))
      | wait != index(status,host(sK1)) )
    & ( norm != index(status,host(sK1))
      | host(sK2) != index(ldr,host(sK1)) )
    & ~ leq(host(sK1),host(sK2))
    & setIn(sK1,alive)
    & queue(host(sK1)) = cons(m_Down(sK2),sK0)
    & ! [X8,X9,X10,X11] :
        ( ~ elem(m_Down(X9),queue(host(X10)))
        | ~ elem(m_Down(X11),queue(host(X8)))
        | host(X10) != host(X11)
        | host(X8) != host(X9)
        | ~ setIn(X10,alive)
        | ~ setIn(X8,alive)
        | host(X8) = host(X10) )
    & ! [X12,X13] :
        ( ~ setIn(X13,alive)
        | ~ setIn(X12,alive)
        | host(X13) != host(X12)
        | X12 = X13 )
    & ! [X14,X15] :
        ( ~ setIn(X15,alive)
        | host(X14) != host(X15)
        | ~ leq(X15,X14)
        | setIn(X14,alive) )
    & ! [X16,X17,X18] :
        ( ~ leq(host(X16),host(X18))
        | ~ elem(m_Ack(X18,X16),queue(host(X17))) )
    & ! [X19,X20] :
        ( ~ leq(host(X19),host(X20))
        | ~ elem(m_Halt(X20),queue(host(X19))) )
    & ! [X21,X22] :
        ( host(X21) != host(X22)
        | ~ elem(m_Down(X22),queue(host(X21))) )
    & ! [X23,X24] :
        ( ~ setIn(X24,alive)
        | ~ elem(m_Down(X24),queue(host(X23))) )
    & ! [X25,X26] :
        ( ~ elem(m_Down(X26),queue(host(X25)))
        | ~ setIn(X26,alive) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f142,f147,f146,f145,f144,f143]) ).

fof(f143,plain,
    ( ? [X0,X1,X2] :
        ( ? [X3] :
            ( ? [X4,X5] :
                ( ? [X6] :
                    ( elem(m_Down(X6),queue(host(X3)))
                    & elem(m_Down(X4),X0)
                    & host(X5) = host(X6)
                    & host(X3) = host(X4)
                    & setIn(X5,alive)
                    & setIn(X3,alive)
                    & host(X3) != host(X5) )
                & host(X1) = host(X5) )
            & host(X3) != host(X1) )
        & ( elec_1 != index(status,host(X1))
          | ? [X7] :
              ( host(X2) != X7
              & ~ setIn(X7,index(down,host(X1)))
              & leq(s(zero),X7)
              & ~ leq(host(X1),X7) ) )
        & ( host(X2) != host(index(elid,host(X1)))
          | wait != index(status,host(X1)) )
        & ( norm != index(status,host(X1))
          | host(X2) != index(ldr,host(X1)) )
        & ~ leq(host(X1),host(X2))
        & setIn(X1,alive)
        & queue(host(X1)) = cons(m_Down(X2),X0)
        & ! [X8,X9,X10,X11] :
            ( ~ elem(m_Down(X9),queue(host(X10)))
            | ~ elem(m_Down(X11),queue(host(X8)))
            | host(X10) != host(X11)
            | host(X8) != host(X9)
            | ~ setIn(X10,alive)
            | ~ setIn(X8,alive)
            | host(X8) = host(X10) )
        & ! [X12,X13] :
            ( ~ setIn(X13,alive)
            | ~ setIn(X12,alive)
            | host(X13) != host(X12)
            | X12 = X13 )
        & ! [X14,X15] :
            ( ~ setIn(X15,alive)
            | host(X14) != host(X15)
            | ~ leq(X15,X14)
            | setIn(X14,alive) )
        & ! [X16,X17,X18] :
            ( ~ leq(host(X16),host(X18))
            | ~ elem(m_Ack(X18,X16),queue(host(X17))) )
        & ! [X19,X20] :
            ( ~ leq(host(X19),host(X20))
            | ~ elem(m_Halt(X20),queue(host(X19))) )
        & ! [X21,X22] :
            ( host(X21) != host(X22)
            | ~ elem(m_Down(X22),queue(host(X21))) )
        & ! [X23,X24] :
            ( ~ setIn(X24,alive)
            | ~ elem(m_Down(X24),queue(host(X23))) )
        & ! [X25,X26] :
            ( ~ elem(m_Down(X26),queue(host(X25)))
            | ~ setIn(X26,alive) ) )
   => ( ? [X3] :
          ( ? [X5,X4] :
              ( ? [X6] :
                  ( elem(m_Down(X6),queue(host(X3)))
                  & elem(m_Down(X4),sK0)
                  & host(X5) = host(X6)
                  & host(X3) = host(X4)
                  & setIn(X5,alive)
                  & setIn(X3,alive)
                  & host(X3) != host(X5) )
              & host(X5) = host(sK1) )
          & host(X3) != host(sK1) )
      & ( elec_1 != index(status,host(sK1))
        | ? [X7] :
            ( host(sK2) != X7
            & ~ setIn(X7,index(down,host(sK1)))
            & leq(s(zero),X7)
            & ~ leq(host(sK1),X7) ) )
      & ( host(sK2) != host(index(elid,host(sK1)))
        | wait != index(status,host(sK1)) )
      & ( norm != index(status,host(sK1))
        | host(sK2) != index(ldr,host(sK1)) )
      & ~ leq(host(sK1),host(sK2))
      & setIn(sK1,alive)
      & queue(host(sK1)) = cons(m_Down(sK2),sK0)
      & ! [X8,X9,X10,X11] :
          ( ~ elem(m_Down(X9),queue(host(X10)))
          | ~ elem(m_Down(X11),queue(host(X8)))
          | host(X10) != host(X11)
          | host(X8) != host(X9)
          | ~ setIn(X10,alive)
          | ~ setIn(X8,alive)
          | host(X8) = host(X10) )
      & ! [X12,X13] :
          ( ~ setIn(X13,alive)
          | ~ setIn(X12,alive)
          | host(X13) != host(X12)
          | X12 = X13 )
      & ! [X14,X15] :
          ( ~ setIn(X15,alive)
          | host(X14) != host(X15)
          | ~ leq(X15,X14)
          | setIn(X14,alive) )
      & ! [X16,X17,X18] :
          ( ~ leq(host(X16),host(X18))
          | ~ elem(m_Ack(X18,X16),queue(host(X17))) )
      & ! [X19,X20] :
          ( ~ leq(host(X19),host(X20))
          | ~ elem(m_Halt(X20),queue(host(X19))) )
      & ! [X21,X22] :
          ( host(X21) != host(X22)
          | ~ elem(m_Down(X22),queue(host(X21))) )
      & ! [X23,X24] :
          ( ~ setIn(X24,alive)
          | ~ elem(m_Down(X24),queue(host(X23))) )
      & ! [X25,X26] :
          ( ~ elem(m_Down(X26),queue(host(X25)))
          | ~ setIn(X26,alive) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f144,plain,
    ( ? [X3] :
        ( ? [X5,X4] :
            ( ? [X6] :
                ( elem(m_Down(X6),queue(host(X3)))
                & elem(m_Down(X4),sK0)
                & host(X5) = host(X6)
                & host(X3) = host(X4)
                & setIn(X5,alive)
                & setIn(X3,alive)
                & host(X3) != host(X5) )
            & host(X5) = host(sK1) )
        & host(X3) != host(sK1) )
   => ( ? [X5,X4] :
          ( ? [X6] :
              ( elem(m_Down(X6),queue(host(sK3)))
              & elem(m_Down(X4),sK0)
              & host(X5) = host(X6)
              & host(X4) = host(sK3)
              & setIn(X5,alive)
              & setIn(sK3,alive)
              & host(X5) != host(sK3) )
          & host(X5) = host(sK1) )
      & host(sK1) != host(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f145,plain,
    ( ? [X5,X4] :
        ( ? [X6] :
            ( elem(m_Down(X6),queue(host(sK3)))
            & elem(m_Down(X4),sK0)
            & host(X5) = host(X6)
            & host(X4) = host(sK3)
            & setIn(X5,alive)
            & setIn(sK3,alive)
            & host(X5) != host(sK3) )
        & host(X5) = host(sK1) )
   => ( ? [X6] :
          ( elem(m_Down(X6),queue(host(sK3)))
          & elem(m_Down(sK4),sK0)
          & host(X6) = host(sK5)
          & host(sK3) = host(sK4)
          & setIn(sK5,alive)
          & setIn(sK3,alive)
          & host(sK3) != host(sK5) )
      & host(sK1) = host(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ( ? [X6] :
        ( elem(m_Down(X6),queue(host(sK3)))
        & elem(m_Down(sK4),sK0)
        & host(X6) = host(sK5)
        & host(sK3) = host(sK4)
        & setIn(sK5,alive)
        & setIn(sK3,alive)
        & host(sK3) != host(sK5) )
   => ( elem(m_Down(sK6),queue(host(sK3)))
      & elem(m_Down(sK4),sK0)
      & host(sK5) = host(sK6)
      & host(sK3) = host(sK4)
      & setIn(sK5,alive)
      & setIn(sK3,alive)
      & host(sK3) != host(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ( ? [X7] :
        ( host(sK2) != X7
        & ~ setIn(X7,index(down,host(sK1)))
        & leq(s(zero),X7)
        & ~ leq(host(sK1),X7) )
   => ( host(sK2) != sK7
      & ~ setIn(sK7,index(down,host(sK1)))
      & leq(s(zero),sK7)
      & ~ leq(host(sK1),sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f142,plain,
    ? [X0,X1,X2] :
      ( ? [X3] :
          ( ? [X4,X5] :
              ( ? [X6] :
                  ( elem(m_Down(X6),queue(host(X3)))
                  & elem(m_Down(X4),X0)
                  & host(X5) = host(X6)
                  & host(X3) = host(X4)
                  & setIn(X5,alive)
                  & setIn(X3,alive)
                  & host(X3) != host(X5) )
              & host(X1) = host(X5) )
          & host(X3) != host(X1) )
      & ( elec_1 != index(status,host(X1))
        | ? [X7] :
            ( host(X2) != X7
            & ~ setIn(X7,index(down,host(X1)))
            & leq(s(zero),X7)
            & ~ leq(host(X1),X7) ) )
      & ( host(X2) != host(index(elid,host(X1)))
        | wait != index(status,host(X1)) )
      & ( norm != index(status,host(X1))
        | host(X2) != index(ldr,host(X1)) )
      & ~ leq(host(X1),host(X2))
      & setIn(X1,alive)
      & queue(host(X1)) = cons(m_Down(X2),X0)
      & ! [X8,X9,X10,X11] :
          ( ~ elem(m_Down(X9),queue(host(X10)))
          | ~ elem(m_Down(X11),queue(host(X8)))
          | host(X10) != host(X11)
          | host(X8) != host(X9)
          | ~ setIn(X10,alive)
          | ~ setIn(X8,alive)
          | host(X8) = host(X10) )
      & ! [X12,X13] :
          ( ~ setIn(X13,alive)
          | ~ setIn(X12,alive)
          | host(X13) != host(X12)
          | X12 = X13 )
      & ! [X14,X15] :
          ( ~ setIn(X15,alive)
          | host(X14) != host(X15)
          | ~ leq(X15,X14)
          | setIn(X14,alive) )
      & ! [X16,X17,X18] :
          ( ~ leq(host(X16),host(X18))
          | ~ elem(m_Ack(X18,X16),queue(host(X17))) )
      & ! [X19,X20] :
          ( ~ leq(host(X19),host(X20))
          | ~ elem(m_Halt(X20),queue(host(X19))) )
      & ! [X21,X22] :
          ( host(X21) != host(X22)
          | ~ elem(m_Down(X22),queue(host(X21))) )
      & ! [X23,X24] :
          ( ~ setIn(X24,alive)
          | ~ elem(m_Down(X24),queue(host(X23))) )
      & ! [X25,X26] :
          ( ~ elem(m_Down(X26),queue(host(X25)))
          | ~ setIn(X26,alive) ) ),
    inference(rectify,[],[f126]) ).

fof(f126,plain,
    ? [X0,X2,X3] :
      ( ? [X24] :
          ( ? [X25,X26] :
              ( ? [X27] :
                  ( elem(m_Down(X27),queue(host(X24)))
                  & elem(m_Down(X25),X0)
                  & host(X26) = host(X27)
                  & host(X24) = host(X25)
                  & setIn(X26,alive)
                  & setIn(X24,alive)
                  & host(X24) != host(X26) )
              & host(X2) = host(X26) )
          & host(X2) != host(X24) )
      & ( elec_1 != index(status,host(X2))
        | ? [X23] :
            ( host(X3) != X23
            & ~ setIn(X23,index(down,host(X2)))
            & leq(s(zero),X23)
            & ~ leq(host(X2),X23) ) )
      & ( host(X3) != host(index(elid,host(X2)))
        | wait != index(status,host(X2)) )
      & ( norm != index(status,host(X2))
        | host(X3) != index(ldr,host(X2)) )
      & ~ leq(host(X2),host(X3))
      & setIn(X2,alive)
      & queue(host(X2)) = cons(m_Down(X3),X0)
      & ! [X4,X5,X6,X7] :
          ( ~ elem(m_Down(X5),queue(host(X6)))
          | ~ elem(m_Down(X7),queue(host(X4)))
          | host(X6) != host(X7)
          | host(X4) != host(X5)
          | ~ setIn(X6,alive)
          | ~ setIn(X4,alive)
          | host(X4) = host(X6) )
      & ! [X8,X9] :
          ( ~ setIn(X9,alive)
          | ~ setIn(X8,alive)
          | host(X8) != host(X9)
          | X8 = X9 )
      & ! [X10,X11] :
          ( ~ setIn(X11,alive)
          | host(X10) != host(X11)
          | ~ leq(X11,X10)
          | setIn(X10,alive) )
      & ! [X12,X13,X14] :
          ( ~ leq(host(X12),host(X14))
          | ~ elem(m_Ack(X14,X12),queue(host(X13))) )
      & ! [X15,X16] :
          ( ~ leq(host(X15),host(X16))
          | ~ elem(m_Halt(X16),queue(host(X15))) )
      & ! [X17,X18] :
          ( host(X17) != host(X18)
          | ~ elem(m_Down(X18),queue(host(X17))) )
      & ! [X19,X20] :
          ( ~ setIn(X20,alive)
          | ~ elem(m_Down(X20),queue(host(X19))) )
      & ! [X21,X22] :
          ( ~ elem(m_Down(X22),queue(host(X21)))
          | ~ setIn(X22,alive) ) ),
    inference(flattening,[],[f125]) ).

fof(f125,plain,
    ? [X0,X2,X3] :
      ( ? [X24] :
          ( ? [X25,X26] :
              ( ? [X27] :
                  ( elem(m_Down(X27),queue(host(X24)))
                  & elem(m_Down(X25),X0)
                  & host(X26) = host(X27)
                  & host(X24) = host(X25)
                  & setIn(X26,alive)
                  & setIn(X24,alive)
                  & host(X24) != host(X26) )
              & host(X2) = host(X26) )
          & host(X2) != host(X24) )
      & ( elec_1 != index(status,host(X2))
        | ? [X23] :
            ( host(X3) != X23
            & ~ setIn(X23,index(down,host(X2)))
            & leq(s(zero),X23)
            & ~ leq(host(X2),X23) ) )
      & ( host(X3) != host(index(elid,host(X2)))
        | wait != index(status,host(X2)) )
      & ( norm != index(status,host(X2))
        | host(X3) != index(ldr,host(X2)) )
      & ~ leq(host(X2),host(X3))
      & setIn(X2,alive)
      & queue(host(X2)) = cons(m_Down(X3),X0)
      & ! [X4,X5,X6,X7] :
          ( ~ elem(m_Down(X5),queue(host(X6)))
          | ~ elem(m_Down(X7),queue(host(X4)))
          | host(X6) != host(X7)
          | host(X4) != host(X5)
          | ~ setIn(X6,alive)
          | ~ setIn(X4,alive)
          | host(X4) = host(X6) )
      & ! [X8,X9] :
          ( ~ setIn(X9,alive)
          | ~ setIn(X8,alive)
          | host(X8) != host(X9)
          | X8 = X9 )
      & ! [X10,X11] :
          ( ~ setIn(X11,alive)
          | host(X10) != host(X11)
          | ~ leq(X11,X10)
          | setIn(X10,alive) )
      & ! [X12,X13,X14] :
          ( ~ leq(host(X12),host(X14))
          | ~ elem(m_Ack(X14,X12),queue(host(X13))) )
      & ! [X15,X16] :
          ( ~ leq(host(X15),host(X16))
          | ~ elem(m_Halt(X16),queue(host(X15))) )
      & ! [X17,X18] :
          ( host(X17) != host(X18)
          | ~ elem(m_Down(X18),queue(host(X17))) )
      & ! [X19,X20] :
          ( ~ setIn(X20,alive)
          | ~ elem(m_Down(X20),queue(host(X19))) )
      & ! [X21,X22] :
          ( ~ elem(m_Down(X22),queue(host(X21)))
          | ~ setIn(X22,alive) ) ),
    inference(ennf_transformation,[],[f69]) ).

fof(f69,plain,
    ~ ! [X0,X2,X3] :
        ( ( queue(host(X2)) = cons(m_Down(X3),X0)
          & ! [X4,X5,X6,X7] :
              ( ( host(X6) = host(X7)
                & host(X4) = host(X5)
                & setIn(X6,alive)
                & setIn(X4,alive)
                & host(X4) != host(X6) )
             => ~ ( elem(m_Down(X5),queue(host(X6)))
                  & elem(m_Down(X7),queue(host(X4))) ) )
          & ! [X8,X9] :
              ( ( host(X8) = host(X9)
                & X8 != X9 )
             => ( ~ setIn(X9,alive)
                | ~ setIn(X8,alive) ) )
          & ! [X10,X11] :
              ( ( host(X10) = host(X11)
                & leq(X11,X10)
                & ~ setIn(X10,alive) )
             => ~ setIn(X11,alive) )
          & ! [X12,X13,X14] :
              ( elem(m_Ack(X14,X12),queue(host(X13)))
             => ~ leq(host(X12),host(X14)) )
          & ! [X15,X16] :
              ( elem(m_Halt(X16),queue(host(X15)))
             => ~ leq(host(X15),host(X16)) )
          & ! [X17,X18] :
              ( elem(m_Down(X18),queue(host(X17)))
             => host(X17) != host(X18) )
          & ! [X19,X20] :
              ( elem(m_Down(X20),queue(host(X19)))
             => ~ setIn(X20,alive) )
          & ! [X21,X22] :
              ( setIn(X22,alive)
             => ~ elem(m_Down(X22),queue(host(X21))) ) )
       => ( setIn(X2,alive)
         => ( ~ leq(host(X2),host(X3))
           => ( ~ ( ( host(X3) = host(index(elid,host(X2)))
                    & wait = index(status,host(X2)) )
                  | ( norm = index(status,host(X2))
                    & host(X3) = index(ldr,host(X2)) ) )
             => ( ~ ( elec_1 = index(status,host(X2))
                    & ! [X23] :
                        ( ( leq(s(zero),X23)
                          & ~ leq(host(X2),X23) )
                       => ( host(X3) = X23
                          | setIn(X23,index(down,host(X2))) ) ) )
               => ! [X24] :
                    ( host(X2) != host(X24)
                   => ! [X25,X26] :
                        ( host(X2) = host(X26)
                       => ! [X27] :
                            ( ( host(X26) = host(X27)
                              & host(X24) = host(X25)
                              & setIn(X26,alive)
                              & setIn(X24,alive)
                              & host(X24) != host(X26) )
                           => ~ ( elem(m_Down(X27),queue(host(X24)))
                                & elem(m_Down(X25),X0) ) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f68]) ).

fof(f68,negated_conjecture,
    ~ ! [X11,X12,X4,X5] :
        ( ( queue(host(X4)) = cons(m_Down(X5),X11)
          & ! [X6,X15,X14,X13] :
              ( ( host(X13) = host(X14)
                & host(X6) = host(X15)
                & setIn(X14,alive)
                & setIn(X6,alive)
                & host(X6) != host(X14) )
             => ~ ( elem(m_Down(X15),queue(host(X14)))
                  & elem(m_Down(X13),queue(host(X6))) ) )
          & ! [X6,X13] :
              ( ( host(X6) = host(X13)
                & X6 != X13 )
             => ( ~ setIn(X13,alive)
                | ~ setIn(X6,alive) ) )
          & ! [X6,X13] :
              ( ( host(X6) = host(X13)
                & leq(X13,X6)
                & ~ setIn(X6,alive) )
             => ~ setIn(X13,alive) )
          & ! [X6,X14,X13] :
              ( elem(m_Ack(X13,X6),queue(host(X14)))
             => ~ leq(host(X6),host(X13)) )
          & ! [X6,X13] :
              ( elem(m_Halt(X13),queue(host(X6)))
             => ~ leq(host(X6),host(X13)) )
          & ! [X6,X13] :
              ( elem(m_Down(X13),queue(host(X6)))
             => host(X6) != host(X13) )
          & ! [X6,X13] :
              ( elem(m_Down(X13),queue(host(X6)))
             => ~ setIn(X13,alive) )
          & ! [X6,X13] :
              ( setIn(X13,alive)
             => ~ elem(m_Down(X13),queue(host(X6))) ) )
       => ( setIn(X4,alive)
         => ( ~ leq(host(X4),host(X5))
           => ( ~ ( ( host(X5) = host(index(elid,host(X4)))
                    & wait = index(status,host(X4)) )
                  | ( norm = index(status,host(X4))
                    & host(X5) = index(ldr,host(X4)) ) )
             => ( ~ ( elec_1 = index(status,host(X4))
                    & ! [X6] :
                        ( ( leq(s(zero),X6)
                          & ~ leq(host(X4),X6) )
                       => ( host(X5) = X6
                          | setIn(X6,index(down,host(X4))) ) ) )
               => ! [X6] :
                    ( host(X4) != host(X6)
                   => ! [X16,X17] :
                        ( host(X4) = host(X17)
                       => ! [X18] :
                            ( ( host(X17) = host(X18)
                              & host(X6) = host(X16)
                              & setIn(X17,alive)
                              & setIn(X6,alive)
                              & host(X6) != host(X17) )
                           => ~ ( elem(m_Down(X18),queue(host(X6)))
                                & elem(m_Down(X16),X11) ) ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f67]) ).

fof(f67,conjecture,
    ! [X11,X12,X4,X5] :
      ( ( queue(host(X4)) = cons(m_Down(X5),X11)
        & ! [X6,X15,X14,X13] :
            ( ( host(X13) = host(X14)
              & host(X6) = host(X15)
              & setIn(X14,alive)
              & setIn(X6,alive)
              & host(X6) != host(X14) )
           => ~ ( elem(m_Down(X15),queue(host(X14)))
                & elem(m_Down(X13),queue(host(X6))) ) )
        & ! [X6,X13] :
            ( ( host(X6) = host(X13)
              & X6 != X13 )
           => ( ~ setIn(X13,alive)
              | ~ setIn(X6,alive) ) )
        & ! [X6,X13] :
            ( ( host(X6) = host(X13)
              & leq(X13,X6)
              & ~ setIn(X6,alive) )
           => ~ setIn(X13,alive) )
        & ! [X6,X14,X13] :
            ( elem(m_Ack(X13,X6),queue(host(X14)))
           => ~ leq(host(X6),host(X13)) )
        & ! [X6,X13] :
            ( elem(m_Halt(X13),queue(host(X6)))
           => ~ leq(host(X6),host(X13)) )
        & ! [X6,X13] :
            ( elem(m_Down(X13),queue(host(X6)))
           => host(X6) != host(X13) )
        & ! [X6,X13] :
            ( elem(m_Down(X13),queue(host(X6)))
           => ~ setIn(X13,alive) )
        & ! [X6,X13] :
            ( setIn(X13,alive)
           => ~ elem(m_Down(X13),queue(host(X6))) ) )
     => ( setIn(X4,alive)
       => ( ~ leq(host(X4),host(X5))
         => ( ~ ( ( host(X5) = host(index(elid,host(X4)))
                  & wait = index(status,host(X4)) )
                | ( norm = index(status,host(X4))
                  & host(X5) = index(ldr,host(X4)) ) )
           => ( ~ ( elec_1 = index(status,host(X4))
                  & ! [X6] :
                      ( ( leq(s(zero),X6)
                        & ~ leq(host(X4),X6) )
                     => ( host(X5) = X6
                        | setIn(X6,index(down,host(X4))) ) ) )
             => ! [X6] :
                  ( host(X4) != host(X6)
                 => ! [X16,X17] :
                      ( host(X4) = host(X17)
                     => ! [X18] :
                          ( ( host(X17) = host(X18)
                            & host(X6) = host(X16)
                            & setIn(X17,alive)
                            & setIn(X6,alive)
                            & host(X6) != host(X17) )
                         => ~ ( elem(m_Down(X18),queue(host(X6)))
                              & elem(m_Down(X16),X11) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

fof(f555,plain,
    host(sK3) != host(sK4),
    inference(resolution,[],[f536,f408]) ).

fof(f408,plain,
    ! [X0] :
      ( ~ elem(m_Down(X0),queue(host(sK1)))
      | host(X0) != host(sK3) ),
    inference(subsumption_resolution,[],[f407,f194]) ).

fof(f194,plain,
    host(sK1) != host(sK3),
    inference(cnf_transformation,[],[f148]) ).

fof(f407,plain,
    ! [X0] :
      ( ~ elem(m_Down(X0),queue(host(sK1)))
      | host(X0) != host(sK3)
      | host(sK1) = host(sK3) ),
    inference(subsumption_resolution,[],[f406,f198]) ).

fof(f198,plain,
    setIn(sK5,alive),
    inference(cnf_transformation,[],[f148]) ).

fof(f406,plain,
    ! [X0] :
      ( ~ elem(m_Down(X0),queue(host(sK1)))
      | host(X0) != host(sK3)
      | ~ setIn(sK5,alive)
      | host(sK1) = host(sK3) ),
    inference(trivial_inequality_removal,[],[f403]) ).

fof(f403,plain,
    ! [X0] :
      ( host(sK1) != host(sK1)
      | ~ elem(m_Down(X0),queue(host(sK1)))
      | host(X0) != host(sK3)
      | ~ setIn(sK5,alive)
      | host(sK1) = host(sK3) ),
    inference(superposition,[],[f385,f195]) ).

fof(f195,plain,
    host(sK1) = host(sK5),
    inference(cnf_transformation,[],[f148]) ).

fof(f385,plain,
    ! [X0,X1] :
      ( host(X1) != host(sK1)
      | ~ elem(m_Down(X0),queue(host(X1)))
      | host(X0) != host(sK3)
      | ~ setIn(X1,alive)
      | host(X1) = host(sK3) ),
    inference(forward_demodulation,[],[f384,f195]) ).

fof(f384,plain,
    ! [X0,X1] :
      ( host(X1) != host(sK5)
      | ~ elem(m_Down(X0),queue(host(X1)))
      | host(X0) != host(sK3)
      | ~ setIn(X1,alive)
      | host(X1) = host(sK3) ),
    inference(forward_demodulation,[],[f383,f200]) ).

fof(f200,plain,
    host(sK5) = host(sK6),
    inference(cnf_transformation,[],[f148]) ).

fof(f383,plain,
    ! [X0,X1] :
      ( ~ elem(m_Down(X0),queue(host(X1)))
      | host(X0) != host(sK3)
      | host(X1) != host(sK6)
      | ~ setIn(X1,alive)
      | host(X1) = host(sK3) ),
    inference(subsumption_resolution,[],[f379,f197]) ).

fof(f197,plain,
    setIn(sK3,alive),
    inference(cnf_transformation,[],[f148]) ).

fof(f379,plain,
    ! [X0,X1] :
      ( ~ elem(m_Down(X0),queue(host(X1)))
      | host(X0) != host(sK3)
      | host(X1) != host(sK6)
      | ~ setIn(sK3,alive)
      | ~ setIn(X1,alive)
      | host(X1) = host(sK3) ),
    inference(resolution,[],[f184,f202]) ).

fof(f202,plain,
    elem(m_Down(sK6),queue(host(sK3))),
    inference(cnf_transformation,[],[f148]) ).

fof(f184,plain,
    ! [X10,X11,X8,X9] :
      ( ~ elem(m_Down(X9),queue(host(X10)))
      | ~ elem(m_Down(X11),queue(host(X8)))
      | host(X10) != host(X11)
      | host(X8) != host(X9)
      | ~ setIn(X10,alive)
      | ~ setIn(X8,alive)
      | host(X8) = host(X10) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f536,plain,
    elem(m_Down(sK4),queue(host(sK1))),
    inference(resolution,[],[f535,f201]) ).

fof(f201,plain,
    elem(m_Down(sK4),sK0),
    inference(cnf_transformation,[],[f148]) ).

fof(f535,plain,
    ! [X0] :
      ( ~ elem(X0,sK0)
      | elem(X0,queue(host(sK1))) ),
    inference(superposition,[],[f296,f185]) ).

fof(f185,plain,
    queue(host(sK1)) = cons(m_Down(sK2),sK0),
    inference(cnf_transformation,[],[f148]) ).

fof(f296,plain,
    ! [X2,X0,X1] :
      ( elem(X0,cons(X1,X2))
      | ~ elem(X0,X2) ),
    inference(cnf_transformation,[],[f176]) ).

fof(f176,plain,
    ! [X0,X1,X2] :
      ( ( elem(X0,cons(X1,X2))
        | ( ~ elem(X0,X2)
          & X0 != X1 ) )
      & ( elem(X0,X2)
        | X0 = X1
        | ~ elem(X0,cons(X1,X2)) ) ),
    inference(flattening,[],[f175]) ).

fof(f175,plain,
    ! [X0,X1,X2] :
      ( ( elem(X0,cons(X1,X2))
        | ( ~ elem(X0,X2)
          & X0 != X1 ) )
      & ( elem(X0,X2)
        | X0 = X1
        | ~ elem(X0,cons(X1,X2)) ) ),
    inference(nnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( elem(X0,cons(X1,X2))
    <=> ( elem(X0,X2)
        | X0 = X1 ) ),
    inference(rectify,[],[f47]) ).

fof(f47,axiom,
    ! [X4,X5,X3] :
      ( elem(X4,cons(X5,X3))
    <=> ( elem(X4,X3)
        | X4 = X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWV455+1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n021.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   : Thu Jun 20 14:43:24 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.35  Running first-order theorem proving
% 0.12/0.35  Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42  % (20284)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (20288)lrs+1011_1:1_sil=2000:i=103:ep=RS:nm=32:ss=axioms:sos=on_0 on theBenchmark for (2999ds/103Mi)
% 0.20/0.42  % (20284)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (20289)lrs+1011_1:1_sil=32000:rnwc=on:nwc=10.0:lwlo=on:i=121:bd=off:av=off_0 on theBenchmark for (2999ds/121Mi)
% 0.20/0.43  % (20284)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (20286)lrs+1002_74:59_drc=off:tgt=full:sos=all:cond=fast:i=124987:kws=inv_frequency:afp=300:afq=2.0744697298148953:rawr=on:urr=full:sil=128000:si=on:rtra=on:random_seed=3250543_0 on theBenchmark for (2999ds/124987Mi)
% 0.20/0.43  % (20284)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (20290)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=113:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2999ds/113Mi)
% 0.20/0.43  % (20284)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (20287)lrs+11_1:16_to=lpo:drc=off:bsd=on:sp=frequency:i=172350:bs=on:av=off:fsd=on:sil=256000:fdi=50_0 on theBenchmark for (2999ds/172350Mi)
% 0.20/0.43  % (20284)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (20291)lrs+1010_1:1_to=lpo:sil=2000:plsq=on:plsqr=32,1:sp=reverse_arity:sos=on:spb=goal_then_units:i=128:ss=axioms:sgt=50:bd=off:sd=3_0 on theBenchmark for (2999ds/128Mi)
% 0.20/0.44  % (20289)First to succeed.
% 0.20/0.44  % (20289)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20284"
% 0.20/0.45  % (20284)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.45  % (20289)Refutation found. Thanks to Tanya!
% 0.20/0.45  % SZS status Theorem for theBenchmark
% 0.20/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.45  % (20289)------------------------------
% 0.20/0.45  % (20289)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.45  % (20289)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.45  % (20289)Termination reason: Refutation
% 0.20/0.45  
% 0.20/0.45  % (20289)Memory used [KB]: 1429
% 0.20/0.45  % (20289)Time elapsed: 0.024 s
% 0.20/0.45  % (20289)Instructions burned: 36 (million)
% 0.20/0.45  % (20289)------------------------------
% 0.20/0.45  % (20289)------------------------------
% 0.20/0.45  % (20284)Success in time 0.066 s
%------------------------------------------------------------------------------