TSTP Solution File: RNG118+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : RNG118+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 : Tue Apr 30 20:38:03 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   87 (  12 unt;   2 def)
%            Number of atoms       :  351 (  73 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  418 ( 154   ~; 163   |;  76   &)
%                                         (  16 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   17 (  15 usr;  11 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   5 con; 0-3 aty)
%            Number of variables   :  109 (  85   !;  24   ?)

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

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

fof(f24,definition,
    ! [W0] :
      ( aIdeal0(W0)
    <=> ( aSet0(W0)
        & ! [W1] :
            ( aElementOf0(W1,W0)
           => ( ! [W2] :
                  ( aElementOf0(W2,W0)
                 => aElementOf0(sdtpldt0(W1,W2),W0) )
              & ! [W2] :
                  ( aElement0(W2)
                 => aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1)
        & W1 != sz00 )
     => ? [W2,W3] :
          ( aElement0(W2)
          & aElement0(W3)
          & W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
          & ( W3 != sz00
           => iLess0(sbrdtbr0(W3),sbrdtbr0(W1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,definition,
    ! [W0] :
      ( aElement0(W0)
     => ! [W1] :
          ( W1 = slsdtgt0(W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
              <=> ? [W3] :
                    ( aElement0(W3)
                    & sdtasdt0(W0,W3) = W2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f42,hypothesis,
    ( aIdeal0(xI)
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f43,hypothesis,
    ( aElementOf0(sz00,slsdtgt0(xa))
    & aElementOf0(xa,slsdtgt0(xa))
    & aElementOf0(sz00,slsdtgt0(xb))
    & aElementOf0(xb,slsdtgt0(xb)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f45,hypothesis,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [W0] :
        ( ( aElementOf0(W0,xI)
          & W0 != sz00 )
       => ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f50,conjecture,
    ? [W0,W1] :
      ( aElement0(W0)
      & aElement0(W1)
      & xb = sdtpldt0(sdtasdt0(W0,xu),W1)
      & ( W1 = sz00
        | iLess0(sbrdtbr0(W1),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f51,negated_conjecture,
    ~ ? [W0,W1] :
        ( aElement0(W0)
        & aElement0(W1)
        & xb = sdtpldt0(sdtasdt0(W0,xu),W1)
        & ( W1 = sz00
          | iLess0(sbrdtbr0(W1),sbrdtbr0(xu)) ) ),
    inference(negated_conjecture,[status(cth)],[f50]) ).

fof(f55,plain,
    aElement0(sz00),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f95,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ! [W1] :
          ( ~ aElementOf0(W1,W0)
          | aElement0(W1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ~ aSet0(X0)
      | ~ aElementOf0(X1,X0)
      | aElement0(X1) ),
    inference(cnf_transformation,[status(esa)],[f95]) ).

fof(f125,plain,
    ! [W0] :
      ( aIdeal0(W0)
    <=> ( aSet0(W0)
        & ! [W1] :
            ( ~ aElementOf0(W1,W0)
            | ( ! [W2] :
                  ( ~ aElementOf0(W2,W0)
                  | aElementOf0(sdtpldt0(W1,W2),W0) )
              & ! [W2] :
                  ( ~ aElement0(W2)
                  | aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f24]) ).

fof(f126,plain,
    ! [W0] :
      ( ( ~ aIdeal0(W0)
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ( ! [W2] :
                    ( ~ aElementOf0(W2,W0)
                    | aElementOf0(sdtpldt0(W1,W2),W0) )
                & ! [W2] :
                    ( ~ aElement0(W2)
                    | aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
      & ( aIdeal0(W0)
        | ~ aSet0(W0)
        | ? [W1] :
            ( aElementOf0(W1,W0)
            & ( ? [W2] :
                  ( aElementOf0(W2,W0)
                  & ~ aElementOf0(sdtpldt0(W1,W2),W0) )
              | ? [W2] :
                  ( aElement0(W2)
                  & ~ aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f125]) ).

fof(f127,plain,
    ( ! [W0] :
        ( ~ aIdeal0(W0)
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ( ! [W2] :
                    ( ~ aElementOf0(W2,W0)
                    | aElementOf0(sdtpldt0(W1,W2),W0) )
                & ! [W2] :
                    ( ~ aElement0(W2)
                    | aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
    & ! [W0] :
        ( aIdeal0(W0)
        | ~ aSet0(W0)
        | ? [W1] :
            ( aElementOf0(W1,W0)
            & ( ? [W2] :
                  ( aElementOf0(W2,W0)
                  & ~ aElementOf0(sdtpldt0(W1,W2),W0) )
              | ? [W2] :
                  ( aElement0(W2)
                  & ~ aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f126]) ).

fof(f128,plain,
    ( ! [W0] :
        ( ~ aIdeal0(W0)
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ( ! [W2] :
                    ( ~ aElementOf0(W2,W0)
                    | aElementOf0(sdtpldt0(W1,W2),W0) )
                & ! [W2] :
                    ( ~ aElement0(W2)
                    | aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
    & ! [W0] :
        ( aIdeal0(W0)
        | ~ aSet0(W0)
        | ( aElementOf0(sk0_8(W0),W0)
          & ( ( aElementOf0(sk0_9(W0),W0)
              & ~ aElementOf0(sdtpldt0(sk0_8(W0),sk0_9(W0)),W0) )
            | ( aElement0(sk0_10(W0))
              & ~ aElementOf0(sdtasdt0(sk0_10(W0),sk0_8(W0)),W0) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f127]) ).

fof(f129,plain,
    ! [X0] :
      ( ~ aIdeal0(X0)
      | aSet0(X0) ),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f158,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | W1 = sz00
      | ? [W2,W3] :
          ( aElement0(W2)
          & aElement0(W3)
          & W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
          & ( W3 = sz00
            | iLess0(sbrdtbr0(W3),sbrdtbr0(W1)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f32]) ).

fof(f159,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | W1 = sz00
      | ? [W3] :
          ( ? [W2] :
              ( aElement0(W2)
              & aElement0(W3)
              & W0 = sdtpldt0(sdtasdt0(W2,W1),W3) )
          & ( W3 = sz00
            | iLess0(sbrdtbr0(W3),sbrdtbr0(W1)) ) ) ),
    inference(miniscoping,[status(esa)],[f158]) ).

fof(f160,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | W1 = sz00
      | ( aElement0(sk0_14(W1,W0))
        & aElement0(sk0_13(W1,W0))
        & W0 = sdtpldt0(sdtasdt0(sk0_14(W1,W0),W1),sk0_13(W1,W0))
        & ( sk0_13(W1,W0) = sz00
          | iLess0(sbrdtbr0(sk0_13(W1,W0)),sbrdtbr0(W1)) ) ) ),
    inference(skolemization,[status(esa)],[f159]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | X1 = sz00
      | aElement0(sk0_14(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f160]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | X1 = sz00
      | aElement0(sk0_13(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f160]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | X1 = sz00
      | X0 = sdtpldt0(sdtasdt0(sk0_14(X1,X0),X1),sk0_13(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f160]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | X1 = sz00
      | sk0_13(X1,X0) = sz00
      | iLess0(sbrdtbr0(sk0_13(X1,X0)),sbrdtbr0(X1)) ),
    inference(cnf_transformation,[status(esa)],[f160]) ).

fof(f191,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ! [W1] :
          ( W1 = slsdtgt0(W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
              <=> ? [W3] :
                    ( aElement0(W3)
                    & sdtasdt0(W0,W3) = W2 ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f192,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ! [W1] :
          ( ( W1 != slsdtgt0(W0)
            | ( aSet0(W1)
              & ! [W2] :
                  ( ( ~ aElementOf0(W2,W1)
                    | ? [W3] :
                        ( aElement0(W3)
                        & sdtasdt0(W0,W3) = W2 ) )
                  & ( aElementOf0(W2,W1)
                    | ! [W3] :
                        ( ~ aElement0(W3)
                        | sdtasdt0(W0,W3) != W2 ) ) ) ) )
          & ( W1 = slsdtgt0(W0)
            | ~ aSet0(W1)
            | ? [W2] :
                ( ( ~ aElementOf0(W2,W1)
                  | ! [W3] :
                      ( ~ aElement0(W3)
                      | sdtasdt0(W0,W3) != W2 ) )
                & ( aElementOf0(W2,W1)
                  | ? [W3] :
                      ( aElement0(W3)
                      & sdtasdt0(W0,W3) = W2 ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f191]) ).

fof(f193,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ( ! [W1] :
            ( W1 != slsdtgt0(W0)
            | ( aSet0(W1)
              & ! [W2] :
                  ( ~ aElementOf0(W2,W1)
                  | ? [W3] :
                      ( aElement0(W3)
                      & sdtasdt0(W0,W3) = W2 ) )
              & ! [W2] :
                  ( aElementOf0(W2,W1)
                  | ! [W3] :
                      ( ~ aElement0(W3)
                      | sdtasdt0(W0,W3) != W2 ) ) ) )
        & ! [W1] :
            ( W1 = slsdtgt0(W0)
            | ~ aSet0(W1)
            | ? [W2] :
                ( ( ~ aElementOf0(W2,W1)
                  | ! [W3] :
                      ( ~ aElement0(W3)
                      | sdtasdt0(W0,W3) != W2 ) )
                & ( aElementOf0(W2,W1)
                  | ? [W3] :
                      ( aElement0(W3)
                      & sdtasdt0(W0,W3) = W2 ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f192]) ).

fof(f194,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ( ! [W1] :
            ( W1 != slsdtgt0(W0)
            | ( aSet0(W1)
              & ! [W2] :
                  ( ~ aElementOf0(W2,W1)
                  | ( aElement0(sk0_17(W2,W1,W0))
                    & sdtasdt0(W0,sk0_17(W2,W1,W0)) = W2 ) )
              & ! [W2] :
                  ( aElementOf0(W2,W1)
                  | ! [W3] :
                      ( ~ aElement0(W3)
                      | sdtasdt0(W0,W3) != W2 ) ) ) )
        & ! [W1] :
            ( W1 = slsdtgt0(W0)
            | ~ aSet0(W1)
            | ( ( ~ aElementOf0(sk0_18(W1,W0),W1)
                | ! [W3] :
                    ( ~ aElement0(W3)
                    | sdtasdt0(W0,W3) != sk0_18(W1,W0) ) )
              & ( aElementOf0(sk0_18(W1,W0),W1)
                | ( aElement0(sk0_19(W1,W0))
                  & sdtasdt0(W0,sk0_19(W1,W0)) = sk0_18(W1,W0) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f193]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | X1 != slsdtgt0(X0)
      | aSet0(X1) ),
    inference(cnf_transformation,[status(esa)],[f194]) ).

fof(f205,plain,
    aElement0(xb),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f208,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f213,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f217,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [W0] :
        ( ~ aElementOf0(W0,xI)
        | W0 = sz00
        | ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f218,plain,
    aElementOf0(xu,xI),
    inference(cnf_transformation,[status(esa)],[f217]) ).

fof(f219,plain,
    xu != sz00,
    inference(cnf_transformation,[status(esa)],[f217]) ).

fof(f229,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | xb != sdtpldt0(sdtasdt0(W0,xu),W1)
      | ( W1 != sz00
        & ~ iLess0(sbrdtbr0(W1),sbrdtbr0(xu)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f51]) ).

fof(f230,plain,
    ! [W1] :
      ( ! [W0] :
          ( ~ aElement0(W0)
          | ~ aElement0(W1)
          | xb != sdtpldt0(sdtasdt0(W0,xu),W1) )
      | ( W1 != sz00
        & ~ iLess0(sbrdtbr0(W1),sbrdtbr0(xu)) ) ),
    inference(miniscoping,[status(esa)],[f229]) ).

fof(f231,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | xb != sdtpldt0(sdtasdt0(X0,xu),X1)
      | X1 != sz00 ),
    inference(cnf_transformation,[status(esa)],[f230]) ).

fof(f232,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | xb != sdtpldt0(sdtasdt0(X0,xu),X1)
      | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ),
    inference(cnf_transformation,[status(esa)],[f230]) ).

fof(f268,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | aSet0(slsdtgt0(X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f195]) ).

fof(f272,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ~ aElement0(sz00)
      | xb != sdtpldt0(sdtasdt0(X0,xu),sz00) ),
    inference(destructive_equality_resolution,[status(esa)],[f231]) ).

fof(f274,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | xb != sdtpldt0(sdtasdt0(X0,xu),sz00) ),
    inference(backward_subsumption_resolution,[status(thm)],[f272,f55]) ).

fof(f275,plain,
    aSet0(xI),
    inference(resolution,[status(thm)],[f129,f208]) ).

fof(f305,plain,
    ( spl0_10
  <=> aElement0(xu) ),
    introduced(split_symbol_definition) ).

fof(f308,plain,
    ( spl0_11
  <=> xu = sz00 ),
    introduced(split_symbol_definition) ).

fof(f309,plain,
    ( xu = sz00
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f308]) ).

fof(f323,plain,
    ( spl0_14
  <=> aSet0(xI) ),
    introduced(split_symbol_definition) ).

fof(f325,plain,
    ( ~ aSet0(xI)
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f323]) ).

fof(f326,plain,
    ( ~ aSet0(xI)
    | aElement0(xu) ),
    inference(resolution,[status(thm)],[f96,f218]) ).

fof(f327,plain,
    ( ~ spl0_14
    | spl0_10 ),
    inference(split_clause,[status(thm)],[f326,f323,f305]) ).

fof(f328,plain,
    ( spl0_15
  <=> aSet0(slsdtgt0(xb)) ),
    introduced(split_symbol_definition) ).

fof(f330,plain,
    ( ~ aSet0(slsdtgt0(xb))
    | spl0_15 ),
    inference(component_clause,[status(thm)],[f328]) ).

fof(f331,plain,
    ( spl0_16
  <=> aElement0(xb) ),
    introduced(split_symbol_definition) ).

fof(f334,plain,
    ( ~ aSet0(slsdtgt0(xb))
    | aElement0(xb) ),
    inference(resolution,[status(thm)],[f96,f213]) ).

fof(f335,plain,
    ( ~ spl0_15
    | spl0_16 ),
    inference(split_clause,[status(thm)],[f334,f328,f331]) ).

fof(f340,plain,
    ( $false
    | spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f325,f275]) ).

fof(f341,plain,
    spl0_14,
    inference(contradiction_clause,[status(thm)],[f340]) ).

fof(f343,plain,
    ( ~ aElement0(xb)
    | spl0_15 ),
    inference(resolution,[status(thm)],[f330,f268]) ).

fof(f344,plain,
    ( $false
    | spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f343,f205]) ).

fof(f345,plain,
    spl0_15,
    inference(contradiction_clause,[status(thm)],[f344]) ).

fof(f687,plain,
    ( spl0_45
  <=> aElement0(sk0_14(xu,xb)) ),
    introduced(split_symbol_definition) ).

fof(f689,plain,
    ( ~ aElement0(sk0_14(xu,xb))
    | spl0_45 ),
    inference(component_clause,[status(thm)],[f687]) ).

fof(f690,plain,
    ( spl0_46
  <=> aElement0(sk0_13(xu,xb)) ),
    introduced(split_symbol_definition) ).

fof(f692,plain,
    ( ~ aElement0(sk0_13(xu,xb))
    | spl0_46 ),
    inference(component_clause,[status(thm)],[f690]) ).

fof(f693,plain,
    ( spl0_47
  <=> iLess0(sbrdtbr0(sk0_13(xu,xb)),sbrdtbr0(xu)) ),
    introduced(split_symbol_definition) ).

fof(f695,plain,
    ( ~ iLess0(sbrdtbr0(sk0_13(xu,xb)),sbrdtbr0(xu))
    | spl0_47 ),
    inference(component_clause,[status(thm)],[f693]) ).

fof(f696,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xu)
    | xu = sz00
    | ~ aElement0(sk0_14(xu,xb))
    | ~ aElement0(sk0_13(xu,xb))
    | ~ iLess0(sbrdtbr0(sk0_13(xu,xb)),sbrdtbr0(xu)) ),
    inference(resolution,[status(thm)],[f163,f232]) ).

fof(f697,plain,
    ( ~ spl0_16
    | ~ spl0_10
    | spl0_11
    | ~ spl0_45
    | ~ spl0_46
    | ~ spl0_47 ),
    inference(split_clause,[status(thm)],[f696,f331,f305,f308,f687,f690,f693]) ).

fof(f698,plain,
    ( $false
    | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f309,f219]) ).

fof(f699,plain,
    ~ spl0_11,
    inference(contradiction_clause,[status(thm)],[f698]) ).

fof(f700,plain,
    ( spl0_48
  <=> sk0_13(xu,xb) = sz00 ),
    introduced(split_symbol_definition) ).

fof(f701,plain,
    ( sk0_13(xu,xb) = sz00
    | ~ spl0_48 ),
    inference(component_clause,[status(thm)],[f700]) ).

fof(f703,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xu)
    | xu = sz00
    | sk0_13(xu,xb) = sz00
    | spl0_47 ),
    inference(resolution,[status(thm)],[f695,f164]) ).

fof(f704,plain,
    ( ~ spl0_16
    | ~ spl0_10
    | spl0_11
    | spl0_48
    | spl0_47 ),
    inference(split_clause,[status(thm)],[f703,f331,f305,f308,f700,f693]) ).

fof(f705,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xu)
    | xu = sz00
    | spl0_46 ),
    inference(resolution,[status(thm)],[f692,f162]) ).

fof(f706,plain,
    ( ~ spl0_16
    | ~ spl0_10
    | spl0_11
    | spl0_46 ),
    inference(split_clause,[status(thm)],[f705,f331,f305,f308,f690]) ).

fof(f707,plain,
    ( spl0_49
  <=> xb = sdtpldt0(sdtasdt0(sk0_14(xu,xb),xu),sz00) ),
    introduced(split_symbol_definition) ).

fof(f708,plain,
    ( xb = sdtpldt0(sdtasdt0(sk0_14(xu,xb),xu),sz00)
    | ~ spl0_49 ),
    inference(component_clause,[status(thm)],[f707]) ).

fof(f710,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xu)
    | xu = sz00
    | xb = sdtpldt0(sdtasdt0(sk0_14(xu,xb),xu),sz00)
    | ~ spl0_48 ),
    inference(paramodulation,[status(thm)],[f701,f163]) ).

fof(f711,plain,
    ( ~ spl0_16
    | ~ spl0_10
    | spl0_11
    | spl0_49
    | ~ spl0_48 ),
    inference(split_clause,[status(thm)],[f710,f331,f305,f308,f707,f700]) ).

fof(f719,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xu)
    | xu = sz00
    | spl0_45 ),
    inference(resolution,[status(thm)],[f689,f161]) ).

fof(f720,plain,
    ( ~ spl0_16
    | ~ spl0_10
    | spl0_11
    | spl0_45 ),
    inference(split_clause,[status(thm)],[f719,f331,f305,f308,f687]) ).

fof(f728,plain,
    ( ~ aElement0(sk0_14(xu,xb))
    | ~ spl0_49 ),
    inference(resolution,[status(thm)],[f708,f274]) ).

fof(f729,plain,
    ( ~ spl0_45
    | ~ spl0_49 ),
    inference(split_clause,[status(thm)],[f728,f687,f707]) ).

fof(f768,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f327,f335,f341,f345,f697,f699,f704,f706,f711,f720,f729]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : RNG118+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 22:43:17 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.14/0.40  % Refutation found
% 0.14/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.42  % Elapsed time: 0.066267 seconds
% 0.21/0.42  % CPU time: 0.381864 seconds
% 0.21/0.42  % Total memory used: 65.785 MB
% 0.21/0.42  % Net memory used: 65.627 MB
%------------------------------------------------------------------------------