TSTP Solution File: NUM547+3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM547+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 : Wed May 31 12:29:38 EDT 2023

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (   6 unt;   1 def)
%            Number of atoms       :  251 (  46 equ)
%            Maximal formula atoms :   43 (   8 avg)
%            Number of connectives :  320 (  98   ~;  79   |; 123   &)
%                                         (   4 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :   73 (;  57   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,definition,
    ! [W0] :
      ( W0 = slcrc0
    <=> ( aSet0(W0)
        & ~ ? [W1] : aElementOf0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f63,hypothesis,
    ( aSet0(slbdtsldtrb0(xS,xk))
    & ! [W0] :
        ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
         => ( aSet0(W0)
            & ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xS) )
            & aSubsetOf0(W0,xS)
            & sbrdtbr0(W0) = xk ) )
        & ( ( ( ( aSet0(W0)
                & ! [W1] :
                    ( aElementOf0(W1,W0)
                   => aElementOf0(W1,xS) ) )
              | aSubsetOf0(W0,xS) )
            & sbrdtbr0(W0) = xk )
         => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [W0] :
        ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
         => ( aSet0(W0)
            & ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xT) )
            & aSubsetOf0(W0,xT)
            & sbrdtbr0(W0) = xk ) )
        & ( ( ( ( aSet0(W0)
                & ! [W1] :
                    ( aElementOf0(W1,W0)
                   => aElementOf0(W1,xT) ) )
              | aSubsetOf0(W0,xT) )
            & sbrdtbr0(W0) = xk )
         => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
    & ! [W0] :
        ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
       => aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ~ ( ! [W0] :
            ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
             => ( aSet0(W0)
                & ! [W1] :
                    ( aElementOf0(W1,W0)
                   => aElementOf0(W1,xS) )
                & aSubsetOf0(W0,xS)
                & sbrdtbr0(W0) = xk ) )
            & ( ( ( ( aSet0(W0)
                    & ! [W1] :
                        ( aElementOf0(W1,W0)
                       => aElementOf0(W1,xS) ) )
                  | aSubsetOf0(W0,xS) )
                & sbrdtbr0(W0) = xk )
             => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
       => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
          | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f65,conjecture,
    ? [W0] :
      ( ( ( ( aSet0(W0)
            & ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xS) ) )
          | aSubsetOf0(W0,xS) )
        & sbrdtbr0(W0) = xk )
      | aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f66,negated_conjecture,
    ~ ? [W0] :
        ( ( ( ( aSet0(W0)
              & ! [W1] :
                  ( aElementOf0(W1,W0)
                 => aElementOf0(W1,xS) ) )
            | aSubsetOf0(W0,xS) )
          & sbrdtbr0(W0) = xk )
        | aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
    inference(negated_conjecture,[status(cth)],[f65]) ).

fof(f77,plain,
    ! [W0] :
      ( W0 = slcrc0
    <=> ( aSet0(W0)
        & ! [W1] : ~ aElementOf0(W1,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f78,plain,
    ! [W0] :
      ( ( W0 != slcrc0
        | ( aSet0(W0)
          & ! [W1] : ~ aElementOf0(W1,W0) ) )
      & ( W0 = slcrc0
        | ~ aSet0(W0)
        | ? [W1] : aElementOf0(W1,W0) ) ),
    inference(NNF_transformation,[status(esa)],[f77]) ).

fof(f79,plain,
    ( ! [W0] :
        ( W0 != slcrc0
        | ( aSet0(W0)
          & ! [W1] : ~ aElementOf0(W1,W0) ) )
    & ! [W0] :
        ( W0 = slcrc0
        | ~ aSet0(W0)
        | ? [W1] : aElementOf0(W1,W0) ) ),
    inference(miniscoping,[status(esa)],[f78]) ).

fof(f80,plain,
    ( ! [W0] :
        ( W0 != slcrc0
        | ( aSet0(W0)
          & ! [W1] : ~ aElementOf0(W1,W0) ) )
    & ! [W0] :
        ( W0 = slcrc0
        | ~ aSet0(W0)
        | aElementOf0(sk0_0(W0),W0) ) ),
    inference(skolemization,[status(esa)],[f79]) ).

fof(f83,plain,
    ! [X0] :
      ( X0 = slcrc0
      | ~ aSet0(X0)
      | aElementOf0(sk0_0(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f80]) ).

fof(f269,plain,
    ( aSet0(slbdtsldtrb0(xS,xk))
    & ! [W0] :
        ( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
          | ( aSet0(W0)
            & ! [W1] :
                ( ~ aElementOf0(W1,W0)
                | aElementOf0(W1,xS) )
            & aSubsetOf0(W0,xS)
            & sbrdtbr0(W0) = xk ) )
        & ( ( ( ~ aSet0(W0)
              | ? [W1] :
                  ( aElementOf0(W1,W0)
                  & ~ aElementOf0(W1,xS) ) )
            & ~ aSubsetOf0(W0,xS) )
          | sbrdtbr0(W0) != xk
          | aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [W0] :
        ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
          | ( aSet0(W0)
            & ! [W1] :
                ( ~ aElementOf0(W1,W0)
                | aElementOf0(W1,xT) )
            & aSubsetOf0(W0,xT)
            & sbrdtbr0(W0) = xk ) )
        & ( ( ( ~ aSet0(W0)
              | ? [W1] :
                  ( aElementOf0(W1,W0)
                  & ~ aElementOf0(W1,xT) ) )
            & ~ aSubsetOf0(W0,xT) )
          | sbrdtbr0(W0) != xk
          | aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [W0] :
        ( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
          | ( aSet0(W0)
            & ! [W1] :
                ( ~ aElementOf0(W1,W0)
                | aElementOf0(W1,xS) )
            & aSubsetOf0(W0,xS)
            & sbrdtbr0(W0) = xk ) )
        & ( ( ( ~ aSet0(W0)
              | ? [W1] :
                  ( aElementOf0(W1,W0)
                  & ~ aElementOf0(W1,xS) ) )
            & ~ aSubsetOf0(W0,xS) )
          | sbrdtbr0(W0) != xk
          | aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
    & ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
    & slbdtsldtrb0(xS,xk) != slcrc0 ),
    inference(pre_NNF_transformation,[status(esa)],[f63]) ).

fof(f270,plain,
    ( aSet0(slbdtsldtrb0(xS,xk))
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,xS) )
          & aSubsetOf0(W0,xS)
          & sbrdtbr0(W0) = xk ) )
    & ! [W0] :
        ( ( ( ~ aSet0(W0)
            | ? [W1] :
                ( aElementOf0(W1,W0)
                & ~ aElementOf0(W1,xS) ) )
          & ~ aSubsetOf0(W0,xS) )
        | sbrdtbr0(W0) != xk
        | aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,xT) )
          & aSubsetOf0(W0,xT)
          & sbrdtbr0(W0) = xk ) )
    & ! [W0] :
        ( ( ( ~ aSet0(W0)
            | ? [W1] :
                ( aElementOf0(W1,W0)
                & ~ aElementOf0(W1,xT) ) )
          & ~ aSubsetOf0(W0,xT) )
        | sbrdtbr0(W0) != xk
        | aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,xS) )
          & aSubsetOf0(W0,xS)
          & sbrdtbr0(W0) = xk ) )
    & ! [W0] :
        ( ( ( ~ aSet0(W0)
            | ? [W1] :
                ( aElementOf0(W1,W0)
                & ~ aElementOf0(W1,xS) ) )
          & ~ aSubsetOf0(W0,xS) )
        | sbrdtbr0(W0) != xk
        | aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
    & ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
    & slbdtsldtrb0(xS,xk) != slcrc0 ),
    inference(miniscoping,[status(esa)],[f269]) ).

fof(f271,plain,
    ( aSet0(slbdtsldtrb0(xS,xk))
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,xS) )
          & aSubsetOf0(W0,xS)
          & sbrdtbr0(W0) = xk ) )
    & ! [W0] :
        ( ( ( ~ aSet0(W0)
            | ( aElementOf0(sk0_11(W0),W0)
              & ~ aElementOf0(sk0_11(W0),xS) ) )
          & ~ aSubsetOf0(W0,xS) )
        | sbrdtbr0(W0) != xk
        | aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,xT) )
          & aSubsetOf0(W0,xT)
          & sbrdtbr0(W0) = xk ) )
    & ! [W0] :
        ( ( ( ~ aSet0(W0)
            | ( aElementOf0(sk0_12(W0),W0)
              & ~ aElementOf0(sk0_12(W0),xT) ) )
          & ~ aSubsetOf0(W0,xT) )
        | sbrdtbr0(W0) != xk
        | aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,xS) )
          & aSubsetOf0(W0,xS)
          & sbrdtbr0(W0) = xk ) )
    & ! [W0] :
        ( ( ( ~ aSet0(W0)
            | ( aElementOf0(sk0_13(W0),W0)
              & ~ aElementOf0(sk0_13(W0),xS) ) )
          & ~ aSubsetOf0(W0,xS) )
        | sbrdtbr0(W0) != xk
        | aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
    & aElementOf0(sk0_14,slbdtsldtrb0(xS,xk))
    & slbdtsldtrb0(xS,xk) != slcrc0 ),
    inference(skolemization,[status(esa)],[f270]) ).

fof(f272,plain,
    aSet0(slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[status(esa)],[f271]) ).

fof(f298,plain,
    slbdtsldtrb0(xS,xk) != slcrc0,
    inference(cnf_transformation,[status(esa)],[f271]) ).

fof(f300,plain,
    ! [W0] :
      ( ( ( ( ~ aSet0(W0)
            | ? [W1] :
                ( aElementOf0(W1,W0)
                & ~ aElementOf0(W1,xS) ) )
          & ~ aSubsetOf0(W0,xS) )
        | sbrdtbr0(W0) != xk )
      & ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
    inference(pre_NNF_transformation,[status(esa)],[f66]) ).

fof(f301,plain,
    ( ! [W0] :
        ( ( ( ~ aSet0(W0)
            | ? [W1] :
                ( aElementOf0(W1,W0)
                & ~ aElementOf0(W1,xS) ) )
          & ~ aSubsetOf0(W0,xS) )
        | sbrdtbr0(W0) != xk )
    & ! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
    inference(miniscoping,[status(esa)],[f300]) ).

fof(f302,plain,
    ( ! [W0] :
        ( ( ( ~ aSet0(W0)
            | ( aElementOf0(sk0_15(W0),W0)
              & ~ aElementOf0(sk0_15(W0),xS) ) )
          & ~ aSubsetOf0(W0,xS) )
        | sbrdtbr0(W0) != xk )
    & ! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
    inference(skolemization,[status(esa)],[f301]) ).

fof(f306,plain,
    ! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[status(esa)],[f302]) ).

fof(f376,plain,
    ( spl0_7
  <=> slbdtsldtrb0(xS,xk) = slcrc0 ),
    introduced(split_symbol_definition) ).

fof(f377,plain,
    ( slbdtsldtrb0(xS,xk) = slcrc0
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f376]) ).

fof(f379,plain,
    ( spl0_8
  <=> aSet0(slbdtsldtrb0(xS,xk)) ),
    introduced(split_symbol_definition) ).

fof(f381,plain,
    ( ~ aSet0(slbdtsldtrb0(xS,xk))
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f379]) ).

fof(f382,plain,
    ( slbdtsldtrb0(xS,xk) = slcrc0
    | ~ aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(resolution,[status(thm)],[f83,f306]) ).

fof(f383,plain,
    ( spl0_7
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f382,f376,f379]) ).

fof(f386,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f381,f272]) ).

fof(f387,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f386]) ).

fof(f390,plain,
    ( $false
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f377,f298]) ).

fof(f391,plain,
    ~ spl0_7,
    inference(contradiction_clause,[status(thm)],[f390]) ).

fof(f392,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f383,f387,f391]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUM547+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n009.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 May 30 09:53:46 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 0.12/0.36  % Refutation found
% 0.12/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.58  % Elapsed time: 0.017835 seconds
% 0.24/0.58  % CPU time: 0.041667 seconds
% 0.24/0.58  % Memory used: 15.648 MB
%------------------------------------------------------------------------------