TSTP Solution File: RNG099+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : RNG099+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n012.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 12:32:53 EDT 2023

% Result   : Theorem 0.17s 0.33s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   80 (  22 unt;   0 def)
%            Number of atoms       :  192 (   3 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  177 (  65   ~;  62   |;  28   &)
%                                         (  11 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   19 (  17 usr;  12 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :   38 (;  36   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aElement0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,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)
    & aSet0(xJ)
    & ! [W0] :
        ( aElementOf0(W0,xJ)
       => ( ! [W1] :
              ( aElementOf0(W1,xJ)
             => aElementOf0(sdtpldt0(W0,W1),xJ) )
          & ! [W1] :
              ( aElement0(W1)
             => aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
    & aIdeal0(xJ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,hypothesis,
    ( aElement0(xx)
    & aElement0(xy) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f31,hypothesis,
    ( aElementOf0(xa,xI)
    & aElementOf0(xb,xJ)
    & sdtpldt0(xa,xb) = sz10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,hypothesis,
    xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f33,hypothesis,
    aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f34,hypothesis,
    aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f35,conjecture,
    ? [W0] :
      ( aElement0(W0)
      & ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
        | sdteqdtlpzmzozddtrp0(W0,xx,xI) )
      & ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
        | sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f36,negated_conjecture,
    ~ ? [W0] :
        ( aElement0(W0)
        & ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
          | sdteqdtlpzmzozddtrp0(W0,xx,xI) )
        & ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
          | sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
    inference(negated_conjecture,[status(cth)],[f35]) ).

fof(f40,plain,
    aElement0(sz00),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f44,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | aElement0(sdtpldt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | aElement0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f46,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | aElement0(sdtasdt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | aElement0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f80,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ! [W1] :
          ( ~ aElementOf0(W1,W0)
          | aElement0(W1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ~ aSet0(X0)
      | ~ aElementOf0(X1,X0)
      | aElement0(X1) ),
    inference(cnf_transformation,[status(esa)],[f80]) ).

fof(f130,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)
    & aSet0(xJ)
    & ! [W0] :
        ( ~ aElementOf0(W0,xJ)
        | ( ! [W1] :
              ( ~ aElementOf0(W1,xJ)
              | aElementOf0(sdtpldt0(W0,W1),xJ) )
          & ! [W1] :
              ( ~ aElement0(W1)
              | aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
    & aIdeal0(xJ) ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f131,plain,
    aSet0(xI),
    inference(cnf_transformation,[status(esa)],[f130]) ).

fof(f135,plain,
    aSet0(xJ),
    inference(cnf_transformation,[status(esa)],[f130]) ).

fof(f145,plain,
    aElement0(xx),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f146,plain,
    aElement0(xy),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f147,plain,
    aElementOf0(xa,xI),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f148,plain,
    aElementOf0(xb,xJ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f150,plain,
    xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f151,plain,
    aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f152,plain,
    aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f153,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ( ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
        & ~ sdteqdtlpzmzozddtrp0(W0,xx,xI) )
      | ( ~ aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
        & ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f36]) ).

fof(f154,plain,
    ! [W0] :
      ( pd0_2(W0)
     => ( ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
        & ~ sdteqdtlpzmzozddtrp0(W0,xx,xI) ) ),
    introduced(predicate_definition,[f153]) ).

fof(f155,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | pd0_2(W0)
      | ( ~ aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)
        & ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
    inference(formula_renaming,[status(thm)],[f153,f154]) ).

fof(f156,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | pd0_2(X0)
      | ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) ),
    inference(cnf_transformation,[status(esa)],[f155]) ).

fof(f167,plain,
    ! [W0] :
      ( ~ pd0_2(W0)
      | ( ~ aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)
        & ~ sdteqdtlpzmzozddtrp0(W0,xx,xI) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f154]) ).

fof(f168,plain,
    ! [X0] :
      ( ~ pd0_2(X0)
      | ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) ),
    inference(cnf_transformation,[status(esa)],[f167]) ).

fof(f181,plain,
    ( spl0_1
  <=> aElement0(xy) ),
    introduced(split_symbol_definition) ).

fof(f183,plain,
    ( ~ aElement0(xy)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f181]) ).

fof(f192,plain,
    ( spl0_4
  <=> aElement0(xx) ),
    introduced(split_symbol_definition) ).

fof(f194,plain,
    ( ~ aElement0(xx)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f192]) ).

fof(f202,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f194,f145]) ).

fof(f203,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f202]) ).

fof(f206,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f183,f146]) ).

fof(f207,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f206]) ).

fof(f211,plain,
    ( spl0_6
  <=> aElement0(xa) ),
    introduced(split_symbol_definition) ).

fof(f214,plain,
    ( spl0_7
  <=> aElement0(xb) ),
    introduced(split_symbol_definition) ).

fof(f279,plain,
    ( spl0_22
  <=> aSet0(xJ) ),
    introduced(split_symbol_definition) ).

fof(f281,plain,
    ( ~ aSet0(xJ)
    | spl0_22 ),
    inference(component_clause,[status(thm)],[f279]) ).

fof(f282,plain,
    ( ~ aSet0(xJ)
    | aElement0(xb) ),
    inference(resolution,[status(thm)],[f81,f148]) ).

fof(f283,plain,
    ( ~ spl0_22
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f282,f279,f214]) ).

fof(f284,plain,
    ( spl0_23
  <=> aSet0(xI) ),
    introduced(split_symbol_definition) ).

fof(f286,plain,
    ( ~ aSet0(xI)
    | spl0_23 ),
    inference(component_clause,[status(thm)],[f284]) ).

fof(f287,plain,
    ( ~ aSet0(xI)
    | aElement0(xa) ),
    inference(resolution,[status(thm)],[f81,f147]) ).

fof(f288,plain,
    ( ~ spl0_23
    | spl0_6 ),
    inference(split_clause,[status(thm)],[f287,f284,f211]) ).

fof(f311,plain,
    ( $false
    | spl0_23 ),
    inference(forward_subsumption_resolution,[status(thm)],[f286,f131]) ).

fof(f312,plain,
    spl0_23,
    inference(contradiction_clause,[status(thm)],[f311]) ).

fof(f313,plain,
    ( $false
    | spl0_22 ),
    inference(forward_subsumption_resolution,[status(thm)],[f281,f135]) ).

fof(f314,plain,
    spl0_22,
    inference(contradiction_clause,[status(thm)],[f313]) ).

fof(f349,plain,
    ~ pd0_2(xw),
    inference(resolution,[status(thm)],[f151,f168]) ).

fof(f350,plain,
    ( spl0_34
  <=> aElement0(xw) ),
    introduced(split_symbol_definition) ).

fof(f363,plain,
    ( spl0_37
  <=> pd0_2(xw) ),
    introduced(split_symbol_definition) ).

fof(f364,plain,
    ( pd0_2(xw)
    | ~ spl0_37 ),
    inference(component_clause,[status(thm)],[f363]) ).

fof(f366,plain,
    ( ~ aElement0(xw)
    | pd0_2(xw) ),
    inference(resolution,[status(thm)],[f152,f156]) ).

fof(f367,plain,
    ( ~ spl0_34
    | spl0_37 ),
    inference(split_clause,[status(thm)],[f366,f350,f363]) ).

fof(f404,plain,
    ( spl0_46
  <=> aElement0(sdtasdt0(xy,xa)) ),
    introduced(split_symbol_definition) ).

fof(f406,plain,
    ( ~ aElement0(sdtasdt0(xy,xa))
    | spl0_46 ),
    inference(component_clause,[status(thm)],[f404]) ).

fof(f407,plain,
    ( spl0_47
  <=> aElement0(sdtasdt0(xx,xb)) ),
    introduced(split_symbol_definition) ).

fof(f409,plain,
    ( ~ aElement0(sdtasdt0(xx,xb))
    | spl0_47 ),
    inference(component_clause,[status(thm)],[f407]) ).

fof(f422,plain,
    ( ~ aElement0(sdtasdt0(xy,xa))
    | ~ aElement0(sdtasdt0(xx,xb))
    | aElement0(xw) ),
    inference(paramodulation,[status(thm)],[f150,f45]) ).

fof(f423,plain,
    ( ~ spl0_46
    | ~ spl0_47
    | spl0_34 ),
    inference(split_clause,[status(thm)],[f422,f404,f407,f350]) ).

fof(f424,plain,
    ( $false
    | ~ spl0_37 ),
    inference(forward_subsumption_resolution,[status(thm)],[f364,f349]) ).

fof(f425,plain,
    ~ spl0_37,
    inference(contradiction_clause,[status(thm)],[f424]) ).

fof(f445,plain,
    ( spl0_51
  <=> aElement0(sz00) ),
    introduced(split_symbol_definition) ).

fof(f447,plain,
    ( ~ aElement0(sz00)
    | spl0_51 ),
    inference(component_clause,[status(thm)],[f445]) ).

fof(f462,plain,
    ( $false
    | spl0_51 ),
    inference(forward_subsumption_resolution,[status(thm)],[f447,f40]) ).

fof(f463,plain,
    spl0_51,
    inference(contradiction_clause,[status(thm)],[f462]) ).

fof(f617,plain,
    ( ~ aElement0(xy)
    | ~ aElement0(xa)
    | spl0_46 ),
    inference(resolution,[status(thm)],[f406,f47]) ).

fof(f618,plain,
    ( ~ spl0_1
    | ~ spl0_6
    | spl0_46 ),
    inference(split_clause,[status(thm)],[f617,f181,f211,f404]) ).

fof(f629,plain,
    ( ~ aElement0(xx)
    | ~ aElement0(xb)
    | spl0_47 ),
    inference(resolution,[status(thm)],[f409,f47]) ).

fof(f630,plain,
    ( ~ spl0_4
    | ~ spl0_7
    | spl0_47 ),
    inference(split_clause,[status(thm)],[f629,f192,f214,f407]) ).

fof(f631,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f203,f207,f283,f288,f312,f314,f367,f423,f425,f463,f618,f630]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : RNG099+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.31  % Computer : n012.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 300
% 0.12/0.31  % DateTime : Tue May 30 10:32:25 EDT 2023
% 0.12/0.31  % CPUTime  : 
% 0.17/0.32  % Drodi V3.5.1
% 0.17/0.33  % Refutation found
% 0.17/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.55  % Elapsed time: 0.024040 seconds
% 0.17/0.55  % CPU time: 0.067929 seconds
% 0.17/0.55  % Memory used: 19.101 MB
%------------------------------------------------------------------------------