TSTP Solution File: RNG048+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : RNG048+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n022.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 : Fri May  3 02:57:24 EDT 2024

% Result   : Theorem 17.64s 3.20s
% Output   : CNFRefutation 17.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  146 (  16 unt;   0 def)
%            Number of atoms       :  519 ( 192 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  644 ( 271   ~; 290   |;  50   &)
%                                         (   3 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-2 aty)
%            Number of variables   :  201 (   0 sgn 115   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sz00 != szszuzczcdt0(X0)
        & aNaturalNumber0(szszuzczcdt0(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).

fof(f7,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => iLess0(X0,szszuzczcdt0(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).

fof(f9,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => aScalar0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).

fof(f20,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => sdtlseqdt0(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).

fof(f26,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => ( ( sdtlseqdt0(sz0z00,X1)
          & sdtlseqdt0(sz0z00,X0) )
       => ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
          & sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).

fof(f27,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).

fof(f30,axiom,
    ! [X0] :
      ( aVector0(X0)
     => aNaturalNumber0(aDimensionOf0(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aVector0(X0) )
     => aScalar0(sdtlbdtrb0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).

fof(f32,axiom,
    ! [X0] :
      ( aVector0(X0)
     => ( sz00 != aDimensionOf0(X0)
       => ! [X1] :
            ( sziznziztdt0(X0) = X1
          <=> ( ! [X2] :
                  ( aNaturalNumber0(X2)
                 => sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
              & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
              & aVector0(X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefInit) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( ( sz00 != aDimensionOf0(X1)
          & aDimensionOf0(X0) = aDimensionOf0(X1) )
       => aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEqInit) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( aDimensionOf0(X0) = aDimensionOf0(X1)
       => aScalar0(sdtasasdt0(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( ( sz00 = aDimensionOf0(X1)
          & aDimensionOf0(X0) = aDimensionOf0(X1) )
       => sz0z00 = sdtasasdt0(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( ( sz00 != aDimensionOf0(X1)
          & aDimensionOf0(X0) = aDimensionOf0(X1) )
       => sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPN) ).

fof(f37,conjecture,
    ! [X0] :
      ( aVector0(X0)
     => ( ! [X1] :
            ( aVector0(X1)
           => ( iLess0(aDimensionOf0(X1),aDimensionOf0(X0))
             => sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ) )
       => sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f38,negated_conjecture,
    ~ ! [X0] :
        ( aVector0(X0)
       => ( ! [X1] :
              ( aVector0(X1)
             => ( iLess0(aDimensionOf0(X1),aDimensionOf0(X0))
               => sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ) )
         => sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ) ),
    inference(negated_conjecture,[],[f37]) ).

fof(f44,plain,
    ! [X0] :
      ( ( sz00 != szszuzczcdt0(X0)
        & aNaturalNumber0(szszuzczcdt0(X0)) )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f49,plain,
    ! [X0] :
      ( iLess0(X0,szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f52]) ).

fof(f66,plain,
    ! [X0] :
      ( sdtlseqdt0(X0,X0)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
        & sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) )
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
        & sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) )
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f77]) ).

fof(f79,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f82,plain,
    ! [X0] :
      ( aNaturalNumber0(aDimensionOf0(X0))
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( aScalar0(sdtlbdtrb0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( aScalar0(sdtlbdtrb0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f83]) ).

fof(f85,plain,
    ! [X0] :
      ( ! [X1] :
          ( sziznziztdt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
                | ~ aNaturalNumber0(X2) )
            & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
            & aVector0(X1) ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f86,plain,
    ! [X0] :
      ( ! [X1] :
          ( sziznziztdt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
                | ~ aNaturalNumber0(X2) )
            & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
            & aVector0(X1) ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f85]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f87]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f89]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f91]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f93]) ).

fof(f95,plain,
    ? [X0] :
      ( ~ sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
      & ! [X1] :
          ( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
          | ~ iLess0(aDimensionOf0(X1),aDimensionOf0(X0))
          | ~ aVector0(X1) )
      & aVector0(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f96,plain,
    ? [X0] :
      ( ~ sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
      & ! [X1] :
          ( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
          | ~ iLess0(aDimensionOf0(X1),aDimensionOf0(X0))
          | ~ aVector0(X1) )
      & aVector0(X0) ),
    inference(flattening,[],[f95]) ).

fof(f99,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sziznziztdt0(X0) = X1
            | ? [X2] :
                ( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
                & aNaturalNumber0(X2) )
            | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
            | ~ aVector0(X1) )
          & ( ( ! [X2] :
                  ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
                  | ~ aNaturalNumber0(X2) )
              & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
              & aVector0(X1) )
            | sziznziztdt0(X0) != X1 ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(nnf_transformation,[],[f86]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sziznziztdt0(X0) = X1
            | ? [X2] :
                ( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
                & aNaturalNumber0(X2) )
            | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
            | ~ aVector0(X1) )
          & ( ( ! [X2] :
                  ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
                  | ~ aNaturalNumber0(X2) )
              & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
              & aVector0(X1) )
            | sziznziztdt0(X0) != X1 ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f99]) ).

fof(f101,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sziznziztdt0(X0) = X1
            | ? [X2] :
                ( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
                & aNaturalNumber0(X2) )
            | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
            | ~ aVector0(X1) )
          & ( ( ! [X3] :
                  ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
                  | ~ aNaturalNumber0(X3) )
              & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
              & aVector0(X1) )
            | sziznziztdt0(X0) != X1 ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(rectify,[],[f100]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
          & aNaturalNumber0(X2) )
     => ( sdtlbdtrb0(X1,sK1(X0,X1)) != sdtlbdtrb0(X0,sK1(X0,X1))
        & aNaturalNumber0(sK1(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sziznziztdt0(X0) = X1
            | ( sdtlbdtrb0(X1,sK1(X0,X1)) != sdtlbdtrb0(X0,sK1(X0,X1))
              & aNaturalNumber0(sK1(X0,X1)) )
            | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
            | ~ aVector0(X1) )
          & ( ( ! [X3] :
                  ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
                  | ~ aNaturalNumber0(X3) )
              & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
              & aVector0(X1) )
            | sziznziztdt0(X0) != X1 ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f101,f102]) ).

fof(f104,plain,
    ( ? [X0] :
        ( ~ sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
        & ! [X1] :
            ( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
            | ~ iLess0(aDimensionOf0(X1),aDimensionOf0(X0))
            | ~ aVector0(X1) )
        & aVector0(X0) )
   => ( ~ sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2))
      & ! [X1] :
          ( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
          | ~ iLess0(aDimensionOf0(X1),aDimensionOf0(sK2))
          | ~ aVector0(X1) )
      & aVector0(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f105,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2))
    & ! [X1] :
        ( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
        | ~ iLess0(aDimensionOf0(X1),aDimensionOf0(sK2))
        | ~ aVector0(X1) )
    & aVector0(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f96,f104]) ).

fof(f107,plain,
    ! [X0] :
      ( aNaturalNumber0(szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f112,plain,
    ! [X0] :
      ( iLess0(X0,szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f113,plain,
    aScalar0(sz0z00),
    inference(cnf_transformation,[],[f9]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f135,plain,
    ! [X0] :
      ( sdtlseqdt0(X0,X0)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f143,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f145,plain,
    ! [X0] :
      ( aNaturalNumber0(aDimensionOf0(X0))
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( aScalar0(sdtlbdtrb0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( aVector0(X1)
      | sziznziztdt0(X0) != X1
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
      | sziznziztdt0(X0) != X1
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f149,plain,
    ! [X3,X0,X1] :
      ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
      | ~ aNaturalNumber0(X3)
      | sziznziztdt0(X0) != X1
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f156,plain,
    aVector0(sK2),
    inference(cnf_transformation,[],[f105]) ).

fof(f157,plain,
    ! [X1] :
      ( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
      | ~ iLess0(aDimensionOf0(X1),aDimensionOf0(sK2))
      | ~ aVector0(X1) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f158,plain,
    ~ sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2)),
    inference(cnf_transformation,[],[f105]) ).

fof(f159,plain,
    ! [X3,X0] :
      ( sdtlbdtrb0(X0,X3) = sdtlbdtrb0(sziznziztdt0(X0),X3)
      | ~ aNaturalNumber0(X3)
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(equality_resolution,[],[f149]) ).

fof(f160,plain,
    ! [X0] :
      ( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0)))
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(equality_resolution,[],[f148]) ).

fof(f161,plain,
    ! [X0] :
      ( aVector0(sziznziztdt0(X0))
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(equality_resolution,[],[f147]) ).

cnf(c_51,plain,
    ( ~ aNaturalNumber0(X0)
    | aNaturalNumber0(szszuzczcdt0(X0)) ),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_55,plain,
    ( ~ aNaturalNumber0(X0)
    | iLess0(X0,szszuzczcdt0(X0)) ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_56,plain,
    aScalar0(sz0z00),
    inference(cnf_transformation,[],[f113]) ).

cnf(c_58,plain,
    ( ~ aScalar0(X0)
    | ~ aScalar0(X1)
    | aScalar0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f115]) ).

cnf(c_78,plain,
    ( ~ aScalar0(X0)
    | sdtlseqdt0(X0,X0) ),
    inference(cnf_transformation,[],[f135]) ).

cnf(c_85,plain,
    ( ~ sdtlseqdt0(sz0z00,X0)
    | ~ sdtlseqdt0(sz0z00,X1)
    | ~ aScalar0(X0)
    | ~ aScalar0(X1)
    | sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_86,plain,
    ( ~ aScalar0(X0)
    | sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_88,plain,
    ( ~ aVector0(X0)
    | aNaturalNumber0(aDimensionOf0(X0)) ),
    inference(cnf_transformation,[],[f145]) ).

cnf(c_89,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aVector0(X1)
    | aScalar0(sdtlbdtrb0(X1,X0)) ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_92,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aVector0(X1)
    | sdtlbdtrb0(sziznziztdt0(X1),X0) = sdtlbdtrb0(X1,X0)
    | aDimensionOf0(X1) = sz00 ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_93,plain,
    ( ~ aVector0(X0)
    | szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) = aDimensionOf0(X0)
    | aDimensionOf0(X0) = sz00 ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_94,plain,
    ( ~ aVector0(X0)
    | aDimensionOf0(X0) = sz00
    | aVector0(sziznziztdt0(X0)) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_95,plain,
    ( aDimensionOf0(X0) != aDimensionOf0(X1)
    | ~ aVector0(X0)
    | ~ aVector0(X1)
    | aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
    | aDimensionOf0(X1) = sz00 ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_96,plain,
    ( aDimensionOf0(X0) != aDimensionOf0(X1)
    | ~ aVector0(X0)
    | ~ aVector0(X1)
    | aScalar0(sdtasasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_97,plain,
    ( aDimensionOf0(X0) != aDimensionOf0(X1)
    | aDimensionOf0(X1) != sz00
    | ~ aVector0(X0)
    | ~ aVector0(X1)
    | sdtasasdt0(X0,X1) = sz0z00 ),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_98,plain,
    ( aDimensionOf0(X0) != aDimensionOf0(X1)
    | ~ aVector0(X0)
    | ~ aVector0(X1)
    | sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) = sdtasasdt0(X0,X1)
    | aDimensionOf0(X1) = sz00 ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_99,negated_conjecture,
    ~ sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2)),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_100,negated_conjecture,
    ( ~ iLess0(aDimensionOf0(X0),aDimensionOf0(sK2))
    | ~ aVector0(X0)
    | sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_101,negated_conjecture,
    aVector0(sK2),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_103,plain,
    ( ~ aScalar0(sz0z00)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_524,plain,
    ( szszuzczcdt0(X0) != aDimensionOf0(sK2)
    | aDimensionOf0(X1) != X0
    | ~ aNaturalNumber0(X0)
    | ~ aVector0(X1)
    | sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_100]) ).

cnf(c_525,plain,
    ( szszuzczcdt0(aDimensionOf0(X0)) != aDimensionOf0(sK2)
    | ~ aNaturalNumber0(aDimensionOf0(X0))
    | ~ aVector0(X0)
    | sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
    inference(unflattening,[status(thm)],[c_524]) ).

cnf(c_527,plain,
    ( szszuzczcdt0(aDimensionOf0(X0)) != aDimensionOf0(sK2)
    | ~ aVector0(X0)
    | sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_525,c_88,c_525]) ).

cnf(c_912,plain,
    ( szszuzczcdt0(aDimensionOf0(X0_14)) != aDimensionOf0(sK2)
    | ~ aVector0(X0_14)
    | sdtlseqdt0(sz0z00,sdtasasdt0(X0_14,X0_14)) ),
    inference(subtyping,[status(esa)],[c_527]) ).

cnf(c_914,negated_conjecture,
    aVector0(sK2),
    inference(subtyping,[status(esa)],[c_101]) ).

cnf(c_916,plain,
    ( aDimensionOf0(X0_14) != aDimensionOf0(X1_14)
    | ~ aVector0(X0_14)
    | ~ aVector0(X1_14)
    | sdtpldt0(sdtasasdt0(sziznziztdt0(X0_14),sziznziztdt0(X1_14)),sdtasdt0(sdtlbdtrb0(X0_14,aDimensionOf0(X0_14)),sdtlbdtrb0(X1_14,aDimensionOf0(X1_14)))) = sdtasasdt0(X0_14,X1_14)
    | aDimensionOf0(X1_14) = sz00 ),
    inference(subtyping,[status(esa)],[c_98]) ).

cnf(c_917,plain,
    ( aDimensionOf0(X0_14) != aDimensionOf0(X1_14)
    | aDimensionOf0(X1_14) != sz00
    | ~ aVector0(X0_14)
    | ~ aVector0(X1_14)
    | sdtasasdt0(X0_14,X1_14) = sz0z00 ),
    inference(subtyping,[status(esa)],[c_97]) ).

cnf(c_918,plain,
    ( aDimensionOf0(X0_14) != aDimensionOf0(X1_14)
    | ~ aVector0(X0_14)
    | ~ aVector0(X1_14)
    | aScalar0(sdtasasdt0(X0_14,X1_14)) ),
    inference(subtyping,[status(esa)],[c_96]) ).

cnf(c_919,plain,
    ( aDimensionOf0(X0_14) != aDimensionOf0(X1_14)
    | ~ aVector0(X0_14)
    | ~ aVector0(X1_14)
    | aDimensionOf0(sziznziztdt0(X0_14)) = aDimensionOf0(sziznziztdt0(X1_14))
    | aDimensionOf0(X1_14) = sz00 ),
    inference(subtyping,[status(esa)],[c_95]) ).

cnf(c_920,plain,
    ( ~ aVector0(X0_14)
    | aDimensionOf0(X0_14) = sz00
    | aVector0(sziznziztdt0(X0_14)) ),
    inference(subtyping,[status(esa)],[c_94]) ).

cnf(c_921,plain,
    ( ~ aVector0(X0_14)
    | szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0_14))) = aDimensionOf0(X0_14)
    | aDimensionOf0(X0_14) = sz00 ),
    inference(subtyping,[status(esa)],[c_93]) ).

cnf(c_922,plain,
    ( ~ aNaturalNumber0(X0_13)
    | ~ aVector0(X0_14)
    | sdtlbdtrb0(sziznziztdt0(X0_14),X0_13) = sdtlbdtrb0(X0_14,X0_13)
    | aDimensionOf0(X0_14) = sz00 ),
    inference(subtyping,[status(esa)],[c_92]) ).

cnf(c_925,plain,
    ( ~ aNaturalNumber0(X0_13)
    | ~ aVector0(X0_14)
    | aScalar0(sdtlbdtrb0(X0_14,X0_13)) ),
    inference(subtyping,[status(esa)],[c_89]) ).

cnf(c_926,plain,
    ( ~ aVector0(X0_14)
    | aNaturalNumber0(aDimensionOf0(X0_14)) ),
    inference(subtyping,[status(esa)],[c_88]) ).

cnf(c_928,plain,
    ( ~ aScalar0(X0_15)
    | sdtlseqdt0(sz0z00,sdtasdt0(X0_15,X0_15)) ),
    inference(subtyping,[status(esa)],[c_86]) ).

cnf(c_929,plain,
    ( ~ sdtlseqdt0(sz0z00,X0_15)
    | ~ sdtlseqdt0(sz0z00,X1_15)
    | ~ aScalar0(X0_15)
    | ~ aScalar0(X1_15)
    | sdtlseqdt0(sz0z00,sdtpldt0(X0_15,X1_15)) ),
    inference(subtyping,[status(esa)],[c_85]) ).

cnf(c_955,plain,
    ( ~ aScalar0(X0_15)
    | ~ aScalar0(X1_15)
    | aScalar0(sdtasdt0(X0_15,X1_15)) ),
    inference(subtyping,[status(esa)],[c_58]) ).

cnf(c_961,plain,
    ( ~ aNaturalNumber0(X0_13)
    | aNaturalNumber0(szszuzczcdt0(X0_13)) ),
    inference(subtyping,[status(esa)],[c_51]) ).

cnf(c_971,plain,
    X0_14 = X0_14,
    theory(equality) ).

cnf(c_972,plain,
    X0_15 = X0_15,
    theory(equality) ).

cnf(c_975,plain,
    ( X0_15 != X1_15
    | X2_15 != X1_15
    | X2_15 = X0_15 ),
    theory(equality) ).

cnf(c_982,plain,
    ( X0_15 != X1_15
    | X2_15 != X3_15
    | ~ sdtlseqdt0(X1_15,X3_15)
    | sdtlseqdt0(X0_15,X2_15) ),
    theory(equality) ).

cnf(c_983,plain,
    ( X0_14 != X1_14
    | aDimensionOf0(X0_14) = aDimensionOf0(X1_14) ),
    theory(equality) ).

cnf(c_986,plain,
    ( X0_14 != X1_14
    | X2_14 != X3_14
    | sdtasasdt0(X0_14,X2_14) = sdtasasdt0(X1_14,X3_14) ),
    theory(equality) ).

cnf(c_991,plain,
    ( sK2 != sK2
    | aDimensionOf0(sK2) = aDimensionOf0(sK2) ),
    inference(instantiation,[status(thm)],[c_983]) ).

cnf(c_993,plain,
    ( sK2 != sK2
    | sdtasasdt0(sK2,sK2) = sdtasasdt0(sK2,sK2) ),
    inference(instantiation,[status(thm)],[c_986]) ).

cnf(c_996,plain,
    sK2 = sK2,
    inference(instantiation,[status(thm)],[c_971]) ).

cnf(c_997,plain,
    sz0z00 = sz0z00,
    inference(instantiation,[status(thm)],[c_972]) ).

cnf(c_999,plain,
    ( aDimensionOf0(sK2) != aDimensionOf0(sK2)
    | ~ aVector0(sK2)
    | sdtpldt0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))) = sdtasasdt0(sK2,sK2)
    | aDimensionOf0(sK2) = sz00 ),
    inference(instantiation,[status(thm)],[c_916]) ).

cnf(c_1000,plain,
    ( aDimensionOf0(sK2) != aDimensionOf0(sK2)
    | aDimensionOf0(sK2) != sz00
    | ~ aVector0(sK2)
    | sdtasasdt0(sK2,sK2) = sz0z00 ),
    inference(instantiation,[status(thm)],[c_917]) ).

cnf(c_1002,plain,
    ( aDimensionOf0(sK2) != aDimensionOf0(sK2)
    | ~ aVector0(sK2)
    | aDimensionOf0(sziznziztdt0(sK2)) = aDimensionOf0(sziznziztdt0(sK2))
    | aDimensionOf0(sK2) = sz00 ),
    inference(instantiation,[status(thm)],[c_919]) ).

cnf(c_1003,plain,
    ( ~ aVector0(sK2)
    | aDimensionOf0(sK2) = sz00
    | aVector0(sziznziztdt0(sK2)) ),
    inference(instantiation,[status(thm)],[c_920]) ).

cnf(c_1004,plain,
    ( ~ aVector0(sK2)
    | szszuzczcdt0(aDimensionOf0(sziznziztdt0(sK2))) = aDimensionOf0(sK2)
    | aDimensionOf0(sK2) = sz00 ),
    inference(instantiation,[status(thm)],[c_921]) ).

cnf(c_1009,plain,
    ( ~ aVector0(sK2)
    | aNaturalNumber0(aDimensionOf0(sK2)) ),
    inference(instantiation,[status(thm)],[c_926]) ).

cnf(c_1930,plain,
    ( sdtasasdt0(sK2,sK2) != X0_15
    | sz0z00 != X1_15
    | ~ sdtlseqdt0(X1_15,X0_15)
    | sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2)) ),
    inference(instantiation,[status(thm)],[c_982]) ).

cnf(c_1931,plain,
    ( sdtasasdt0(sK2,sK2) != sz0z00
    | sz0z00 != sz0z00
    | ~ sdtlseqdt0(sz0z00,sz0z00)
    | sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2)) ),
    inference(instantiation,[status(thm)],[c_1930]) ).

cnf(c_1952,plain,
    ( sdtasasdt0(sK2,sK2) != X0_15
    | X1_15 != X0_15
    | sdtasasdt0(sK2,sK2) = X1_15 ),
    inference(instantiation,[status(thm)],[c_975]) ).

cnf(c_1995,plain,
    ( sdtasasdt0(sK2,sK2) != sdtasasdt0(X0_14,X1_14)
    | X0_15 != sdtasasdt0(X0_14,X1_14)
    | sdtasasdt0(sK2,sK2) = X0_15 ),
    inference(instantiation,[status(thm)],[c_1952]) ).

cnf(c_2185,plain,
    ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sK2))) != aDimensionOf0(sK2)
    | ~ aVector0(sziznziztdt0(sK2))
    | sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2))) ),
    inference(instantiation,[status(thm)],[c_912]) ).

cnf(c_2195,plain,
    ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0_14),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(X0_14,aDimensionOf0(X0_14)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))) != sdtasasdt0(X0_14,sK2)
    | sdtasasdt0(sK2,sK2) != sdtasasdt0(X0_14,sK2)
    | sdtasasdt0(sK2,sK2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0_14),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(X0_14,aDimensionOf0(X0_14)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))) ),
    inference(instantiation,[status(thm)],[c_1995]) ).

cnf(c_2196,plain,
    ( sdtpldt0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))) != sdtasasdt0(sK2,sK2)
    | sdtasasdt0(sK2,sK2) != sdtasasdt0(sK2,sK2)
    | sdtasasdt0(sK2,sK2) = sdtpldt0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))) ),
    inference(instantiation,[status(thm)],[c_2195]) ).

cnf(c_2344,plain,
    ( sdtasasdt0(sK2,sK2) != sdtpldt0(sdtasasdt0(sziznziztdt0(X0_14),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(X0_14,aDimensionOf0(X0_14)),sdtlbdtrb0(sK2,aDimensionOf0(sK2))))
    | sz0z00 != X0_15
    | ~ sdtlseqdt0(X0_15,sdtpldt0(sdtasasdt0(sziznziztdt0(X0_14),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(X0_14,aDimensionOf0(X0_14)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))))
    | sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2)) ),
    inference(instantiation,[status(thm)],[c_1930]) ).

cnf(c_2345,plain,
    ( sdtasasdt0(sK2,sK2) != sdtpldt0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2))))
    | sz0z00 != sz0z00
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))))
    | sdtlseqdt0(sz0z00,sdtasasdt0(sK2,sK2)) ),
    inference(instantiation,[status(thm)],[c_2344]) ).

cnf(c_2855,plain,
    ( aDimensionOf0(sziznziztdt0(sK2)) != aDimensionOf0(sziznziztdt0(sK2))
    | ~ aVector0(sziznziztdt0(sK2))
    | aScalar0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2))) ),
    inference(instantiation,[status(thm)],[c_918]) ).

cnf(c_5729,plain,
    ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sK2))) = aDimensionOf0(sK2)
    | aDimensionOf0(sK2) = sz00 ),
    inference(superposition,[status(thm)],[c_914,c_921]) ).

cnf(c_5749,plain,
    szszuzczcdt0(aDimensionOf0(sziznziztdt0(sK2))) = aDimensionOf0(sK2),
    inference(global_subsumption_just,[status(thm)],[c_5729,c_101,c_56,c_99,c_103,c_991,c_996,c_997,c_1000,c_1004,c_1931]) ).

cnf(c_5753,plain,
    ( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(sK2)))
    | aNaturalNumber0(aDimensionOf0(sK2)) ),
    inference(superposition,[status(thm)],[c_5749,c_961]) ).

cnf(c_5755,plain,
    aNaturalNumber0(aDimensionOf0(sK2)),
    inference(global_subsumption_just,[status(thm)],[c_5753,c_101,c_1009]) ).

cnf(c_6172,plain,
    ( ~ aNaturalNumber0(X0_13)
    | sdtlbdtrb0(sziznziztdt0(sK2),X0_13) = sdtlbdtrb0(sK2,X0_13)
    | aDimensionOf0(sK2) = sz00 ),
    inference(superposition,[status(thm)],[c_914,c_922]) ).

cnf(c_6506,plain,
    ( sdtlbdtrb0(sziznziztdt0(sK2),X0_13) = sdtlbdtrb0(sK2,X0_13)
    | ~ aNaturalNumber0(X0_13) ),
    inference(global_subsumption_just,[status(thm)],[c_6172,c_101,c_56,c_99,c_103,c_991,c_996,c_997,c_1000,c_1931,c_6172]) ).

cnf(c_6507,plain,
    ( ~ aNaturalNumber0(X0_13)
    | sdtlbdtrb0(sziznziztdt0(sK2),X0_13) = sdtlbdtrb0(sK2,X0_13) ),
    inference(renaming,[status(thm)],[c_6506]) ).

cnf(c_6513,plain,
    sdtlbdtrb0(sziznziztdt0(sK2),aDimensionOf0(sK2)) = sdtlbdtrb0(sK2,aDimensionOf0(sK2)),
    inference(superposition,[status(thm)],[c_5755,c_6507]) ).

cnf(c_6620,plain,
    ( ~ aNaturalNumber0(aDimensionOf0(sK2))
    | ~ aVector0(sziznziztdt0(sK2))
    | aScalar0(sdtlbdtrb0(sK2,aDimensionOf0(sK2))) ),
    inference(superposition,[status(thm)],[c_6513,c_925]) ).

cnf(c_7281,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(X0_14,aDimensionOf0(X0_14)),sdtlbdtrb0(sK2,aDimensionOf0(sK2))))
    | ~ aScalar0(sdtasdt0(sdtlbdtrb0(X0_14,aDimensionOf0(X0_14)),sdtlbdtrb0(sK2,aDimensionOf0(sK2))))
    | ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(X0_14),sziznziztdt0(sK2)))
    | ~ aScalar0(sdtasasdt0(sziznziztdt0(X0_14),sziznziztdt0(sK2)))
    | sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(X0_14),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(X0_14,aDimensionOf0(X0_14)),sdtlbdtrb0(sK2,aDimensionOf0(sK2))))) ),
    inference(instantiation,[status(thm)],[c_929]) ).

cnf(c_7282,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2))))
    | ~ aScalar0(sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2))))
    | ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
    | ~ aScalar0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)))
    | sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(sziznziztdt0(sK2),sziznziztdt0(sK2)),sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2))))) ),
    inference(instantiation,[status(thm)],[c_7281]) ).

cnf(c_9481,plain,
    ( ~ aScalar0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)))
    | aScalar0(sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))) ),
    inference(instantiation,[status(thm)],[c_955]) ).

cnf(c_87763,plain,
    ( ~ aScalar0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)))
    | sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(sK2,aDimensionOf0(sK2)),sdtlbdtrb0(sK2,aDimensionOf0(sK2)))) ),
    inference(instantiation,[status(thm)],[c_928]) ).

cnf(c_87764,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_87763,c_9481,c_7282,c_6620,c_2855,c_2345,c_2196,c_2185,c_1931,c_1009,c_1004,c_1003,c_1002,c_1000,c_999,c_997,c_996,c_993,c_991,c_103,c_99,c_56,c_101]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : RNG048+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May  2 21:19:12 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.64/3.20  % SZS status Started for theBenchmark.p
% 17.64/3.20  % SZS status Theorem for theBenchmark.p
% 17.64/3.20  
% 17.64/3.20  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.64/3.20  
% 17.64/3.20  ------  iProver source info
% 17.64/3.20  
% 17.64/3.20  git: date: 2024-05-02 19:28:25 +0000
% 17.64/3.20  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.64/3.20  git: non_committed_changes: false
% 17.64/3.20  
% 17.64/3.20  ------ Parsing...
% 17.64/3.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 17.64/3.20  
% 17.64/3.20  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 17.64/3.20  
% 17.64/3.20  ------ Preprocessing... gs_s  sp: 4 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 17.64/3.20  
% 17.64/3.20  ------ Preprocessing... sf_s  rm: 4 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 17.64/3.20  ------ Proving...
% 17.64/3.20  ------ Problem Properties 
% 17.64/3.20  
% 17.64/3.20  
% 17.64/3.20  clauses                                 55
% 17.64/3.20  conjectures                             2
% 17.64/3.20  EPR                                     10
% 17.64/3.20  Horn                                    43
% 17.64/3.20  unary                                   5
% 17.64/3.20  binary                                  16
% 17.64/3.20  lits                                    184
% 17.64/3.20  lits eq                                 50
% 17.64/3.20  fd_pure                                 0
% 17.64/3.20  fd_pseudo                               0
% 17.64/3.20  fd_cond                                 1
% 17.64/3.20  fd_pseudo_cond                          5
% 17.64/3.20  AC symbols                              0
% 17.64/3.20  
% 17.64/3.20  ------ Input Options Time Limit: Unbounded
% 17.64/3.20  
% 17.64/3.20  
% 17.64/3.20  ------ 
% 17.64/3.20  Current options:
% 17.64/3.20  ------ 
% 17.64/3.20  
% 17.64/3.20  
% 17.64/3.20  
% 17.64/3.20  
% 17.64/3.20  ------ Proving...
% 17.64/3.20  
% 17.64/3.20  
% 17.64/3.20  % SZS status Theorem for theBenchmark.p
% 17.64/3.20  
% 17.64/3.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.64/3.21  
% 17.64/3.21  
%------------------------------------------------------------------------------