TSTP Solution File: RNG050+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : RNG050+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% 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  : 600s
% DateTime : Mon Jul 18 20:35:52 EDT 2022

% Result   : Theorem 1.83s 2.05s
% Output   : CNFRefutation 1.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   38 (  15 unt;   0 def)
%            Number of atoms       :   84 (  39 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   86 (  40   ~;  34   |;   3   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn   9   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mSZeroSc,axiom,
    aScalar0(sz0z00) ).

fof(mLERef,axiom,
    ! [W0] :
      ( aScalar0(W0)
     => sdtlseqdt0(W0,W0) ) ).

fof(mDefSPZ,axiom,
    ! [W0,W1] :
      ( ( aVector0(W0)
        & aVector0(W1) )
     => ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
          & aDimensionOf0(W1) = sz00 )
       => sdtasasdt0(W0,W1) = sz0z00 ) ) ).

fof(m__1542,hypothesis,
    aVector0(xs) ).

fof(m__,conjecture,
    ( ( aDimensionOf0(xs) != sz00
     => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
   => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ).

fof(subgoal_0,plain,
    ( ( aDimensionOf0(xs) != sz00
     => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
   => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ( ( aDimensionOf0(xs) != sz00
       => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
     => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
    & ( aDimensionOf0(xs) = sz00
      | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    aVector0(xs),
    inference(canonicalize,[],[m__1542]) ).

fof(normalize_0_3,plain,
    ! [W0,W1] :
      ( aDimensionOf0(W0) != aDimensionOf0(W1)
      | aDimensionOf0(W1) != sz00
      | ~ aVector0(W0)
      | ~ aVector0(W1)
      | sdtasasdt0(W0,W1) = sz0z00 ),
    inference(canonicalize,[],[mDefSPZ]) ).

fof(normalize_0_4,plain,
    ! [W0,W1] :
      ( aDimensionOf0(W0) != aDimensionOf0(W1)
      | aDimensionOf0(W1) != sz00
      | ~ aVector0(W0)
      | ~ aVector0(W1)
      | sdtasasdt0(W0,W1) = sz0z00 ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ( aDimensionOf0(xs) = sz00
    | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_6,plain,
    aDimensionOf0(xs) = sz00,
    inference(simplify,[],[normalize_0_5,normalize_0_1]) ).

fof(normalize_0_7,plain,
    aScalar0(sz0z00),
    inference(canonicalize,[],[mSZeroSc]) ).

fof(normalize_0_8,plain,
    ! [W0] :
      ( ~ aScalar0(W0)
      | sdtlseqdt0(W0,W0) ),
    inference(canonicalize,[],[mLERef]) ).

fof(normalize_0_9,plain,
    ! [W0] :
      ( ~ aScalar0(W0)
      | sdtlseqdt0(W0,W0) ),
    inference(specialize,[],[normalize_0_8]) ).

cnf(refute_0_0,plain,
    ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    aVector0(xs),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_2,plain,
    ( aDimensionOf0(W0) != aDimensionOf0(W1)
    | aDimensionOf0(W1) != sz00
    | ~ aVector0(W0)
    | ~ aVector0(W1)
    | sdtasasdt0(W0,W1) = sz0z00 ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
    ( aDimensionOf0(W0) != sz00
    | aDimensionOf0(W1) != sz00
    | aDimensionOf0(W0) = aDimensionOf0(W1) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(aDimensionOf0(W0),aDimensionOf0(W1)) ),[1],$fot(sz00)]]) ).

cnf(refute_0_4,plain,
    ( aDimensionOf0(W0) != sz00
    | aDimensionOf0(W1) != sz00
    | ~ aVector0(W0)
    | ~ aVector0(W1)
    | sdtasasdt0(W0,W1) = sz0z00 ),
    inference(resolve,[$cnf( $equal(aDimensionOf0(W0),aDimensionOf0(W1)) )],[refute_0_3,refute_0_2]) ).

cnf(refute_0_5,plain,
    ( aDimensionOf0(xs) != sz00
    | ~ aVector0(xs)
    | sdtasasdt0(xs,xs) = sz0z00 ),
    inference(subst,[],[refute_0_4:[bind(W0,$fot(xs)),bind(W1,$fot(xs))]]) ).

cnf(refute_0_6,plain,
    ( aDimensionOf0(xs) != sz00
    | sdtasasdt0(xs,xs) = sz0z00 ),
    inference(resolve,[$cnf( aVector0(xs) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    aDimensionOf0(xs) = sz00,
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_8,plain,
    ( aDimensionOf0(xs) != sz00
    | sz00 != sz00
    | aDimensionOf0(xs) = sz00 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(aDimensionOf0(xs),sz00) ),[0],$fot(sz00)]]) ).

cnf(refute_0_9,plain,
    ( sz00 != sz00
    | aDimensionOf0(xs) = sz00 ),
    inference(resolve,[$cnf( $equal(aDimensionOf0(xs),sz00) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( sz00 != sz00
    | sdtasasdt0(xs,xs) = sz0z00 ),
    inference(resolve,[$cnf( $equal(aDimensionOf0(xs),sz00) )],[refute_0_9,refute_0_6]) ).

cnf(refute_0_11,plain,
    sz00 = sz00,
    introduced(tautology,[refl,[$fot(sz00)]]) ).

cnf(refute_0_12,plain,
    sdtasasdt0(xs,xs) = sz0z00,
    inference(resolve,[$cnf( $equal(sz00,sz00) )],[refute_0_11,refute_0_10]) ).

cnf(refute_0_13,plain,
    ( sdtasasdt0(xs,xs) != sz0z00
    | ~ sdtlseqdt0(sz0z00,sz0z00)
    | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    introduced(tautology,[equality,[$cnf( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),[1],$fot(sz0z00)]]) ).

cnf(refute_0_14,plain,
    ( ~ sdtlseqdt0(sz0z00,sz0z00)
    | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(resolve,[$cnf( $equal(sdtasasdt0(xs,xs),sz0z00) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ~ sdtlseqdt0(sz0z00,sz0z00),
    inference(resolve,[$cnf( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )],[refute_0_14,refute_0_0]) ).

cnf(refute_0_16,plain,
    aScalar0(sz0z00),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_17,plain,
    ( ~ aScalar0(W0)
    | sdtlseqdt0(W0,W0) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_18,plain,
    ( ~ aScalar0(sz0z00)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(subst,[],[refute_0_17:[bind(W0,$fot(sz0z00))]]) ).

cnf(refute_0_19,plain,
    sdtlseqdt0(sz0z00,sz0z00),
    inference(resolve,[$cnf( aScalar0(sz0z00) )],[refute_0_16,refute_0_18]) ).

cnf(refute_0_20,plain,
    $false,
    inference(resolve,[$cnf( sdtlseqdt0(sz0z00,sz0z00) )],[refute_0_19,refute_0_15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG050+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon May 30 15:38:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.83/2.05  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.83/2.05  
% 1.83/2.05  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.83/2.05  
%------------------------------------------------------------------------------