TSTP Solution File: COM021+4 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : COM021+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 : Fri Jul 15 01:32:35 EDT 2022

% Result   : Theorem 0.19s 0.46s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   31 (  13 unt;   0 def)
%            Number of atoms       :  126 (  28 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  126 (  31   ~;  33   |;  60   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   21 (   1 sgn   4   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__818,hypothesis,
    ( aElement0(xd)
    & ( xw = xd
      | ( ( aReductOfIn0(xd,xw,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xw,xR)
              & sdtmndtplgtdt0(W0,xR,xd) ) )
        & sdtmndtplgtdt0(xw,xR,xd) ) )
    & sdtmndtasgtdt0(xw,xR,xd)
    & ~ ? [W0] : aReductOfIn0(W0,xd,xR)
    & aNormalFormOfIn0(xd,xw,xR) ) ).

fof(m__850,hypothesis,
    ( aElement0(xx)
    & ( xb = xx
      | ( ( aReductOfIn0(xx,xb,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xb,xR)
              & sdtmndtplgtdt0(W0,xR,xx) ) )
        & sdtmndtplgtdt0(xb,xR,xx) ) )
    & sdtmndtasgtdt0(xb,xR,xx)
    & ( xd = xx
      | ( ( aReductOfIn0(xx,xd,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xd,xR)
              & sdtmndtplgtdt0(W0,xR,xx) ) )
        & sdtmndtplgtdt0(xd,xR,xx) ) )
    & sdtmndtasgtdt0(xd,xR,xx) ) ).

fof(m__,conjecture,
    ( xb = xd
    | aReductOfIn0(xd,xb,xR)
    | ? [W0] :
        ( aElement0(W0)
        & aReductOfIn0(W0,xb,xR)
        & sdtmndtplgtdt0(W0,xR,xd) )
    | sdtmndtplgtdt0(xb,xR,xd)
    | sdtmndtasgtdt0(xb,xR,xd) ) ).

fof(subgoal_0,plain,
    ( ( xb != xd
      & ~ aReductOfIn0(xd,xb,xR)
      & ~ ? [W0] :
            ( aElement0(W0)
            & aReductOfIn0(W0,xb,xR)
            & sdtmndtplgtdt0(W0,xR,xd) )
      & ~ sdtmndtplgtdt0(xb,xR,xd) )
   => sdtmndtasgtdt0(xb,xR,xd) ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ( ( xb != xd
        & ~ aReductOfIn0(xd,xb,xR)
        & ~ ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xb,xR)
              & sdtmndtplgtdt0(W0,xR,xd) )
        & ~ sdtmndtplgtdt0(xb,xR,xd) )
     => sdtmndtasgtdt0(xb,xR,xd) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( aElement0(xx)
    & sdtmndtasgtdt0(xb,xR,xx)
    & sdtmndtasgtdt0(xd,xR,xx)
    & ( xb = xx
      | ( sdtmndtplgtdt0(xb,xR,xx)
        & ( aReductOfIn0(xx,xb,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xb,xR)
              & sdtmndtplgtdt0(W0,xR,xx) ) ) ) )
    & ( xd = xx
      | ( sdtmndtplgtdt0(xd,xR,xx)
        & ( aReductOfIn0(xx,xd,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xd,xR)
              & sdtmndtplgtdt0(W0,xR,xx) ) ) ) ) ),
    inference(canonicalize,[],[m__850]) ).

fof(normalize_0_1,plain,
    ( aElement0(xd)
    & aNormalFormOfIn0(xd,xw,xR)
    & sdtmndtasgtdt0(xw,xR,xd)
    & ( xw = xd
      | ( sdtmndtplgtdt0(xw,xR,xd)
        & ( aReductOfIn0(xd,xw,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xw,xR)
              & sdtmndtplgtdt0(W0,xR,xd) ) ) ) )
    & ! [W0] : ~ aReductOfIn0(W0,xd,xR) ),
    inference(canonicalize,[],[m__818]) ).

fof(normalize_0_2,plain,
    ! [W0] : ~ aReductOfIn0(W0,xd,xR),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [W0] : ~ aReductOfIn0(W0,xd,xR),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ( aElement0(xx)
    & sdtmndtasgtdt0(xb,xR,xx)
    & sdtmndtasgtdt0(xd,xR,xx)
    & ( xb = xx
      | ( sdtmndtplgtdt0(xb,xR,xx)
        & ( aReductOfIn0(xx,xb,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xb,xR)
              & sdtmndtplgtdt0(W0,xR,xx) ) ) ) )
    & ( xd = xx
      | ( aReductOfIn0(xx,xd,xR)
        & sdtmndtplgtdt0(xd,xR,xx) ) ) ),
    inference(simplify,[],[normalize_0_0,normalize_0_3]) ).

fof(normalize_0_5,plain,
    sdtmndtasgtdt0(xb,xR,xx),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ( xd = xx
    | ( aReductOfIn0(xx,xd,xR)
      & sdtmndtplgtdt0(xd,xR,xx) ) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_7,plain,
    ( ( xd = xx
      | aReductOfIn0(xx,xd,xR) )
    & ( xd = xx
      | sdtmndtplgtdt0(xd,xR,xx) ) ),
    inference(clausify,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ( xd = xx
    | aReductOfIn0(xx,xd,xR) ),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ( xb != xd
    & ~ aReductOfIn0(xd,xb,xR)
    & ~ sdtmndtasgtdt0(xb,xR,xd)
    & ~ sdtmndtplgtdt0(xb,xR,xd)
    & ! [W0] :
        ( ~ aElement0(W0)
        | ~ aReductOfIn0(W0,xb,xR)
        | ~ sdtmndtplgtdt0(W0,xR,xd) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_10,plain,
    ~ sdtmndtasgtdt0(xb,xR,xd),
    inference(conjunct,[],[normalize_0_9]) ).

cnf(refute_0_0,plain,
    sdtmndtasgtdt0(xb,xR,xx),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_1,plain,
    ( xd = xx
    | aReductOfIn0(xx,xd,xR) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_2,plain,
    ~ aReductOfIn0(W0,xd,xR),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    ~ aReductOfIn0(xx,xd,xR),
    inference(subst,[],[refute_0_2:[bind(W0,$fot(xx))]]) ).

cnf(refute_0_4,plain,
    xd = xx,
    inference(resolve,[$cnf( aReductOfIn0(xx,xd,xR) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_6,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_7,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( xd != xx
    | xx = xd ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(xd)),bind(Y,$fot(xx))]]) ).

cnf(refute_0_9,plain,
    xx = xd,
    inference(resolve,[$cnf( $equal(xd,xx) )],[refute_0_4,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( xx != xd
    | ~ sdtmndtasgtdt0(xb,xR,xx)
    | sdtmndtasgtdt0(xb,xR,xd) ),
    introduced(tautology,[equality,[$cnf( sdtmndtasgtdt0(xb,xR,xx) ),[2],$fot(xd)]]) ).

cnf(refute_0_11,plain,
    ( ~ sdtmndtasgtdt0(xb,xR,xx)
    | sdtmndtasgtdt0(xb,xR,xd) ),
    inference(resolve,[$cnf( $equal(xx,xd) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    sdtmndtasgtdt0(xb,xR,xd),
    inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,xx) )],[refute_0_0,refute_0_11]) ).

cnf(refute_0_13,plain,
    ~ sdtmndtasgtdt0(xb,xR,xd),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,xd) )],[refute_0_12,refute_0_13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : COM021+4 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n018.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  : 600
% 0.12/0.33  % DateTime : Thu Jun 16 16:58:31 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.46  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46  
% 0.19/0.46  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.47  
%------------------------------------------------------------------------------