TSTP Solution File: NUM547+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM547+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   42 (  12 unt;   2 def)
%            Number of atoms       :  151 (  38 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  176 (  67   ~;  64   |;  34   &)
%                                         (  10 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :   50 (;  43   !;   7   ?)

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

fof(f57,definition,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aElementOf0(W1,szNzAzT0) )
     => ! [W2] :
          ( W2 = slbdtsldtrb0(W0,W1)
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( aSubsetOf0(W3,W0)
                  & sbrdtbr0(W3) = W1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f61,hypothesis,
    aElementOf0(xk,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f62,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & xk != sz00 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f63,hypothesis,
    ( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & slbdtsldtrb0(xS,xk) != slcrc0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f65,conjecture,
    ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f66,negated_conjecture,
    ~ ? [W0] : 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(f248,plain,
    ! [W0,W1] :
      ( ~ aSet0(W0)
      | ~ aElementOf0(W1,szNzAzT0)
      | ! [W2] :
          ( W2 = slbdtsldtrb0(W0,W1)
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( aSubsetOf0(W3,W0)
                  & sbrdtbr0(W3) = W1 ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f57]) ).

fof(f249,plain,
    ! [W0,W1] :
      ( ~ aSet0(W0)
      | ~ aElementOf0(W1,szNzAzT0)
      | ! [W2] :
          ( ( W2 != slbdtsldtrb0(W0,W1)
            | ( aSet0(W2)
              & ! [W3] :
                  ( ( ~ aElementOf0(W3,W2)
                    | ( aSubsetOf0(W3,W0)
                      & sbrdtbr0(W3) = W1 ) )
                  & ( aElementOf0(W3,W2)
                    | ~ aSubsetOf0(W3,W0)
                    | sbrdtbr0(W3) != W1 ) ) ) )
          & ( W2 = slbdtsldtrb0(W0,W1)
            | ~ aSet0(W2)
            | ? [W3] :
                ( ( ~ aElementOf0(W3,W2)
                  | ~ aSubsetOf0(W3,W0)
                  | sbrdtbr0(W3) != W1 )
                & ( aElementOf0(W3,W2)
                  | ( aSubsetOf0(W3,W0)
                    & sbrdtbr0(W3) = W1 ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f248]) ).

fof(f250,plain,
    ! [W0,W1] :
      ( ~ aSet0(W0)
      | ~ aElementOf0(W1,szNzAzT0)
      | ( ! [W2] :
            ( W2 != slbdtsldtrb0(W0,W1)
            | ( aSet0(W2)
              & ! [W3] :
                  ( ~ aElementOf0(W3,W2)
                  | ( aSubsetOf0(W3,W0)
                    & sbrdtbr0(W3) = W1 ) )
              & ! [W3] :
                  ( aElementOf0(W3,W2)
                  | ~ aSubsetOf0(W3,W0)
                  | sbrdtbr0(W3) != W1 ) ) )
        & ! [W2] :
            ( W2 = slbdtsldtrb0(W0,W1)
            | ~ aSet0(W2)
            | ? [W3] :
                ( ( ~ aElementOf0(W3,W2)
                  | ~ aSubsetOf0(W3,W0)
                  | sbrdtbr0(W3) != W1 )
                & ( aElementOf0(W3,W2)
                  | ( aSubsetOf0(W3,W0)
                    & sbrdtbr0(W3) = W1 ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f249]) ).

fof(f251,plain,
    ! [W0,W1] :
      ( ~ aSet0(W0)
      | ~ aElementOf0(W1,szNzAzT0)
      | ( ! [W2] :
            ( W2 != slbdtsldtrb0(W0,W1)
            | ( aSet0(W2)
              & ! [W3] :
                  ( ~ aElementOf0(W3,W2)
                  | ( aSubsetOf0(W3,W0)
                    & sbrdtbr0(W3) = W1 ) )
              & ! [W3] :
                  ( aElementOf0(W3,W2)
                  | ~ aSubsetOf0(W3,W0)
                  | sbrdtbr0(W3) != W1 ) ) )
        & ! [W2] :
            ( W2 = slbdtsldtrb0(W0,W1)
            | ~ aSet0(W2)
            | ( ( ~ aElementOf0(sk0_10(W2,W1,W0),W2)
                | ~ aSubsetOf0(sk0_10(W2,W1,W0),W0)
                | sbrdtbr0(sk0_10(W2,W1,W0)) != W1 )
              & ( aElementOf0(sk0_10(W2,W1,W0),W2)
                | ( aSubsetOf0(sk0_10(W2,W1,W0),W0)
                  & sbrdtbr0(sk0_10(W2,W1,W0)) = W1 ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f250]) ).

fof(f252,plain,
    ! [X0,X1,X2] :
      ( ~ aSet0(X0)
      | ~ aElementOf0(X1,szNzAzT0)
      | X2 != slbdtsldtrb0(X0,X1)
      | aSet0(X2) ),
    inference(cnf_transformation,[status(esa)],[f251]) ).

fof(f265,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnf_transformation,[status(esa)],[f61]) ).

fof(f266,plain,
    aSet0(xS),
    inference(cnf_transformation,[status(esa)],[f62]) ).

fof(f270,plain,
    slbdtsldtrb0(xS,xk) != slcrc0,
    inference(cnf_transformation,[status(esa)],[f63]) ).

fof(f272,plain,
    ! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)),
    inference(pre_NNF_transformation,[status(esa)],[f66]) ).

fof(f273,plain,
    ! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[status(esa)],[f272]) ).

fof(f303,plain,
    ! [X0,X1] :
      ( ~ aSet0(X0)
      | ~ aElementOf0(X1,szNzAzT0)
      | aSet0(slbdtsldtrb0(X0,X1)) ),
    inference(destructive_equality_resolution,[status(esa)],[f252]) ).

fof(f325,plain,
    ( spl0_3
  <=> aSet0(xS) ),
    introduced(split_symbol_definition) ).

fof(f327,plain,
    ( ~ aSet0(xS)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f325]) ).

fof(f333,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f327,f266]) ).

fof(f334,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f333]) ).

fof(f368,plain,
    ( spl0_11
  <=> slbdtsldtrb0(xS,xk) = slcrc0 ),
    introduced(split_symbol_definition) ).

fof(f369,plain,
    ( slbdtsldtrb0(xS,xk) = slcrc0
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f368]) ).

fof(f371,plain,
    ( spl0_12
  <=> aSet0(slbdtsldtrb0(xS,xk)) ),
    introduced(split_symbol_definition) ).

fof(f373,plain,
    ( ~ aSet0(slbdtsldtrb0(xS,xk))
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f371]) ).

fof(f374,plain,
    ( slbdtsldtrb0(xS,xk) = slcrc0
    | ~ aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(resolution,[status(thm)],[f83,f273]) ).

fof(f375,plain,
    ( spl0_11
    | ~ spl0_12 ),
    inference(split_clause,[status(thm)],[f374,f368,f371]) ).

fof(f382,plain,
    ( spl0_13
  <=> aElementOf0(xk,szNzAzT0) ),
    introduced(split_symbol_definition) ).

fof(f384,plain,
    ( ~ aElementOf0(xk,szNzAzT0)
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f382]) ).

fof(f385,plain,
    ( ~ aSet0(xS)
    | ~ aElementOf0(xk,szNzAzT0)
    | spl0_12 ),
    inference(resolution,[status(thm)],[f373,f303]) ).

fof(f386,plain,
    ( ~ spl0_3
    | ~ spl0_13
    | spl0_12 ),
    inference(split_clause,[status(thm)],[f385,f325,f382,f371]) ).

fof(f387,plain,
    ( $false
    | spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f384,f265]) ).

fof(f388,plain,
    spl0_13,
    inference(contradiction_clause,[status(thm)],[f387]) ).

fof(f389,plain,
    ( $false
    | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f369,f270]) ).

fof(f390,plain,
    ~ spl0_11,
    inference(contradiction_clause,[status(thm)],[f389]) ).

fof(f391,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f334,f375,f386,f388,f390]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUM547+1 : 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 : n003.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 10:01:53 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
% 0.12/0.38  % Elapsed time: 0.028439 seconds
% 0.12/0.38  % CPU time: 0.045412 seconds
% 0.12/0.38  % Memory used: 15.408 MB
%------------------------------------------------------------------------------