TSTP Solution File: RNG121+4 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : RNG121+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n001.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 12:32:58 EDT 2023

% Result   : Theorem 0.06s 0.28s
% Output   : CNFRefutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   39 (   8 unt;   0 def)
%            Number of atoms       :  221 (  51 equ)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives :  251 (  69   ~;  69   |;  99   &)
%                                         (  10 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   8 con; 0-2 aty)
%            Number of variables   :   88 (;  60   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f39,hypothesis,
    ( aElement0(xa)
    & aElement0(xb) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f42,hypothesis,
    ( aSet0(xI)
    & ! [W0] :
        ( aElementOf0(W0,xI)
       => ( ! [W1] :
              ( aElementOf0(W1,xI)
             => aElementOf0(sdtpldt0(W0,W1),xI) )
          & ! [W1] :
              ( aElement0(W1)
             => aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
    & aIdeal0(xI)
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xa))
      <=> ? [W1] :
            ( aElement0(W1)
            & sdtasdt0(xa,W1) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xb))
      <=> ? [W1] :
            ( aElement0(W1)
            & sdtasdt0(xb,W1) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,xI)
      <=> ? [W1,W2] :
            ( aElementOf0(W1,slsdtgt0(xa))
            & aElementOf0(W2,slsdtgt0(xb))
            & sdtpldt0(W1,W2) = W0 ) )
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f43,hypothesis,
    ( ? [W0] :
        ( aElement0(W0)
        & sdtasdt0(xa,W0) = sz00 )
    & aElementOf0(sz00,slsdtgt0(xa))
    & ? [W0] :
        ( aElement0(W0)
        & sdtasdt0(xa,W0) = xa )
    & aElementOf0(xa,slsdtgt0(xa))
    & ? [W0] :
        ( aElement0(W0)
        & sdtasdt0(xb,W0) = sz00 )
    & aElementOf0(sz00,slsdtgt0(xb))
    & ? [W0] :
        ( aElement0(W0)
        & sdtasdt0(xb,W0) = xb )
    & aElementOf0(xb,slsdtgt0(xb)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f53,conjecture,
    ( ? [W0,W1] :
        ( aElementOf0(W0,slsdtgt0(xa))
        & aElementOf0(W1,slsdtgt0(xb))
        & sdtpldt0(W0,W1) = xb )
    | ? [W0,W1] :
        ( aElementOf0(W0,slsdtgt0(xa))
        & aElementOf0(W1,slsdtgt0(xb))
        & sdtpldt0(W0,W1) = xb )
    | aElementOf0(xb,xI) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f54,negated_conjecture,
    ~ ( ? [W0,W1] :
          ( aElementOf0(W0,slsdtgt0(xa))
          & aElementOf0(W1,slsdtgt0(xb))
          & sdtpldt0(W0,W1) = xb )
      | ? [W0,W1] :
          ( aElementOf0(W0,slsdtgt0(xa))
          & aElementOf0(W1,slsdtgt0(xb))
          & sdtpldt0(W0,W1) = xb )
      | aElementOf0(xb,xI) ),
    inference(negated_conjecture,[status(cth)],[f53]) ).

fof(f70,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f72,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | X0 = sdtpldt0(sz00,X0) ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f208,plain,
    aElement0(xb),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f228,plain,
    ( aSet0(xI)
    & ! [W0] :
        ( ~ aElementOf0(W0,xI)
        | ( ! [W1] :
              ( ~ aElementOf0(W1,xI)
              | aElementOf0(sdtpldt0(W0,W1),xI) )
          & ! [W1] :
              ( ~ aElement0(W1)
              | aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
    & aIdeal0(xI)
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xa))
      <=> ? [W1] :
            ( aElement0(W1)
            & sdtasdt0(xa,W1) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xb))
      <=> ? [W1] :
            ( aElement0(W1)
            & sdtasdt0(xb,W1) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,xI)
      <=> ? [W1,W2] :
            ( aElementOf0(W1,slsdtgt0(xa))
            & aElementOf0(W2,slsdtgt0(xb))
            & sdtpldt0(W1,W2) = W0 ) )
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    inference(pre_NNF_transformation,[status(esa)],[f42]) ).

fof(f229,plain,
    ( aSet0(xI)
    & ! [W0] :
        ( ~ aElementOf0(W0,xI)
        | ( ! [W1] :
              ( ~ aElementOf0(W1,xI)
              | aElementOf0(sdtpldt0(W0,W1),xI) )
          & ! [W1] :
              ( ~ aElement0(W1)
              | aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
    & aIdeal0(xI)
    & ! [W0] :
        ( ( ~ aElementOf0(W0,slsdtgt0(xa))
          | ? [W1] :
              ( aElement0(W1)
              & sdtasdt0(xa,W1) = W0 ) )
        & ( aElementOf0(W0,slsdtgt0(xa))
          | ! [W1] :
              ( ~ aElement0(W1)
              | sdtasdt0(xa,W1) != W0 ) ) )
    & ! [W0] :
        ( ( ~ aElementOf0(W0,slsdtgt0(xb))
          | ? [W1] :
              ( aElement0(W1)
              & sdtasdt0(xb,W1) = W0 ) )
        & ( aElementOf0(W0,slsdtgt0(xb))
          | ! [W1] :
              ( ~ aElement0(W1)
              | sdtasdt0(xb,W1) != W0 ) ) )
    & ! [W0] :
        ( ( ~ aElementOf0(W0,xI)
          | ? [W1,W2] :
              ( aElementOf0(W1,slsdtgt0(xa))
              & aElementOf0(W2,slsdtgt0(xb))
              & sdtpldt0(W1,W2) = W0 ) )
        & ( aElementOf0(W0,xI)
          | ! [W1,W2] :
              ( ~ aElementOf0(W1,slsdtgt0(xa))
              | ~ aElementOf0(W2,slsdtgt0(xb))
              | sdtpldt0(W1,W2) != W0 ) ) )
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    inference(NNF_transformation,[status(esa)],[f228]) ).

fof(f230,plain,
    ( aSet0(xI)
    & ! [W0] :
        ( ~ aElementOf0(W0,xI)
        | ( ! [W1] :
              ( ~ aElementOf0(W1,xI)
              | aElementOf0(sdtpldt0(W0,W1),xI) )
          & ! [W1] :
              ( ~ aElement0(W1)
              | aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
    & aIdeal0(xI)
    & ! [W0] :
        ( ~ aElementOf0(W0,slsdtgt0(xa))
        | ? [W1] :
            ( aElement0(W1)
            & sdtasdt0(xa,W1) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xa))
        | ! [W1] :
            ( ~ aElement0(W1)
            | sdtasdt0(xa,W1) != W0 ) )
    & ! [W0] :
        ( ~ aElementOf0(W0,slsdtgt0(xb))
        | ? [W1] :
            ( aElement0(W1)
            & sdtasdt0(xb,W1) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xb))
        | ! [W1] :
            ( ~ aElement0(W1)
            | sdtasdt0(xb,W1) != W0 ) )
    & ! [W0] :
        ( ~ aElementOf0(W0,xI)
        | ? [W1,W2] :
            ( aElementOf0(W1,slsdtgt0(xa))
            & aElementOf0(W2,slsdtgt0(xb))
            & sdtpldt0(W1,W2) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,xI)
        | ! [W1,W2] :
            ( ~ aElementOf0(W1,slsdtgt0(xa))
            | ~ aElementOf0(W2,slsdtgt0(xb))
            | sdtpldt0(W1,W2) != W0 ) )
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    inference(miniscoping,[status(esa)],[f229]) ).

fof(f231,plain,
    ( aSet0(xI)
    & ! [W0] :
        ( ~ aElementOf0(W0,xI)
        | ( ! [W1] :
              ( ~ aElementOf0(W1,xI)
              | aElementOf0(sdtpldt0(W0,W1),xI) )
          & ! [W1] :
              ( ~ aElement0(W1)
              | aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
    & aIdeal0(xI)
    & ! [W0] :
        ( ~ aElementOf0(W0,slsdtgt0(xa))
        | ( aElement0(sk0_23(W0))
          & sdtasdt0(xa,sk0_23(W0)) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xa))
        | ! [W1] :
            ( ~ aElement0(W1)
            | sdtasdt0(xa,W1) != W0 ) )
    & ! [W0] :
        ( ~ aElementOf0(W0,slsdtgt0(xb))
        | ( aElement0(sk0_24(W0))
          & sdtasdt0(xb,sk0_24(W0)) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xb))
        | ! [W1] :
            ( ~ aElement0(W1)
            | sdtasdt0(xb,W1) != W0 ) )
    & ! [W0] :
        ( ~ aElementOf0(W0,xI)
        | ( aElementOf0(sk0_25(W0),slsdtgt0(xa))
          & aElementOf0(sk0_26(W0),slsdtgt0(xb))
          & sdtpldt0(sk0_25(W0),sk0_26(W0)) = W0 ) )
    & ! [W0] :
        ( aElementOf0(W0,xI)
        | ! [W1,W2] :
            ( ~ aElementOf0(W1,slsdtgt0(xa))
            | ~ aElementOf0(W2,slsdtgt0(xb))
            | sdtpldt0(W1,W2) != W0 ) )
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    inference(skolemization,[status(esa)],[f230]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( aElementOf0(X0,slsdtgt0(xa))
      | ~ aElement0(X1)
      | sdtasdt0(xa,X1) != X0 ),
    inference(cnf_transformation,[status(esa)],[f231]) ).

fof(f247,plain,
    ( aElement0(sk0_27)
    & sdtasdt0(xa,sk0_27) = sz00
    & aElementOf0(sz00,slsdtgt0(xa))
    & aElement0(sk0_28)
    & sdtasdt0(xa,sk0_28) = xa
    & aElementOf0(xa,slsdtgt0(xa))
    & aElement0(sk0_29)
    & sdtasdt0(xb,sk0_29) = sz00
    & aElementOf0(sz00,slsdtgt0(xb))
    & aElement0(sk0_30)
    & sdtasdt0(xb,sk0_30) = xb
    & aElementOf0(xb,slsdtgt0(xb)) ),
    inference(skolemization,[status(esa)],[f43]) ).

fof(f248,plain,
    aElement0(sk0_27),
    inference(cnf_transformation,[status(esa)],[f247]) ).

fof(f249,plain,
    sdtasdt0(xa,sk0_27) = sz00,
    inference(cnf_transformation,[status(esa)],[f247]) ).

fof(f259,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(cnf_transformation,[status(esa)],[f247]) ).

fof(f310,plain,
    ( ! [W0,W1] :
        ( ~ aElementOf0(W0,slsdtgt0(xa))
        | ~ aElementOf0(W1,slsdtgt0(xb))
        | sdtpldt0(W0,W1) != xb )
    & ! [W0,W1] :
        ( ~ aElementOf0(W0,slsdtgt0(xa))
        | ~ aElementOf0(W1,slsdtgt0(xb))
        | sdtpldt0(W0,W1) != xb )
    & ~ aElementOf0(xb,xI) ),
    inference(pre_NNF_transformation,[status(esa)],[f54]) ).

fof(f311,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X0,slsdtgt0(xa))
      | ~ aElementOf0(X1,slsdtgt0(xb))
      | sdtpldt0(X0,X1) != xb ),
    inference(cnf_transformation,[status(esa)],[f310]) ).

fof(f394,plain,
    ! [X0] :
      ( aElementOf0(sdtasdt0(xa,X0),slsdtgt0(xa))
      | ~ aElement0(X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f238]) ).

fof(f401,plain,
    ( spl0_11
  <=> aElement0(xb) ),
    introduced(split_symbol_definition) ).

fof(f403,plain,
    ( ~ aElement0(xb)
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f401]) ).

fof(f412,plain,
    ( spl0_14
  <=> aElementOf0(sz00,slsdtgt0(xa)) ),
    introduced(split_symbol_definition) ).

fof(f415,plain,
    ( spl0_15
  <=> aElementOf0(xb,slsdtgt0(xb)) ),
    introduced(split_symbol_definition) ).

fof(f417,plain,
    ( ~ aElementOf0(xb,slsdtgt0(xb))
    | spl0_15 ),
    inference(component_clause,[status(thm)],[f415]) ).

fof(f418,plain,
    ( ~ aElement0(xb)
    | ~ aElementOf0(sz00,slsdtgt0(xa))
    | ~ aElementOf0(xb,slsdtgt0(xb)) ),
    inference(resolution,[status(thm)],[f72,f311]) ).

fof(f419,plain,
    ( ~ spl0_11
    | ~ spl0_14
    | ~ spl0_15 ),
    inference(split_clause,[status(thm)],[f418,f401,f412,f415]) ).

fof(f420,plain,
    ( $false
    | spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f417,f259]) ).

fof(f421,plain,
    spl0_15,
    inference(contradiction_clause,[status(thm)],[f420]) ).

fof(f474,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f403,f208]) ).

fof(f475,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f474]) ).

fof(f530,plain,
    ( spl0_36
  <=> aElement0(sk0_27) ),
    introduced(split_symbol_definition) ).

fof(f532,plain,
    ( ~ aElement0(sk0_27)
    | spl0_36 ),
    inference(component_clause,[status(thm)],[f530]) ).

fof(f533,plain,
    ( aElementOf0(sz00,slsdtgt0(xa))
    | ~ aElement0(sk0_27) ),
    inference(paramodulation,[status(thm)],[f249,f394]) ).

fof(f534,plain,
    ( spl0_14
    | ~ spl0_36 ),
    inference(split_clause,[status(thm)],[f533,f412,f530]) ).

fof(f575,plain,
    ( $false
    | spl0_36 ),
    inference(forward_subsumption_resolution,[status(thm)],[f532,f248]) ).

fof(f576,plain,
    spl0_36,
    inference(contradiction_clause,[status(thm)],[f575]) ).

fof(f577,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f419,f421,f475,f534,f576]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.06  % Problem  : RNG121+4 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25  % Computer : n001.cluster.edu
% 0.06/0.25  % Model    : x86_64 x86_64
% 0.06/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25  % Memory   : 8042.1875MB
% 0.06/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25  % CPULimit : 300
% 0.06/0.25  % WCLimit  : 300
% 0.06/0.25  % DateTime : Tue May 30 11:07:15 EDT 2023
% 0.06/0.25  % CPUTime  : 
% 0.06/0.27  % Drodi V3.5.1
% 0.06/0.28  % Refutation found
% 0.06/0.28  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.28  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.49  % Elapsed time: 0.023297 seconds
% 0.10/0.49  % CPU time: 0.026516 seconds
% 0.10/0.49  % Memory used: 4.133 MB
%------------------------------------------------------------------------------