TSTP Solution File: RNG047+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : RNG047+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 12:32:42 EDT 2023

% Result   : Theorem 0.14s 0.36s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   67 (  12 unt;   1 def)
%            Number of atoms       :  187 (  78 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  197 (  77   ~;  85   |;  19   &)
%                                         (  10 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   12 (  10 usr;   9 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (;  34   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
       => W0 = W1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,axiom,
    ! [W0] :
      ( aVector0(W0)
     => aNaturalNumber0(aDimensionOf0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,definition,
    ! [W0] :
      ( aVector0(W0)
     => ( aDimensionOf0(W0) != sz00
       => ! [W1] :
            ( W1 = sziznziztdt0(W0)
          <=> ( aVector0(W1)
              & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
              & ! [W2] :
                  ( aNaturalNumber0(W2)
                 => sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f33,hypothesis,
    ( aVector0(xs)
    & aVector0(xt) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f34,hypothesis,
    ( aDimensionOf0(xs) = aDimensionOf0(xt)
    & aDimensionOf0(xt) != sz00 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f35,conjecture,
    aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f36,negated_conjecture,
    aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
    inference(negated_conjecture,[status(cth)],[f35]) ).

fof(f48,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | szszuzczcdt0(W0) != szszuzczcdt0(W1)
      | W0 = W1 ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | szszuzczcdt0(X0) != szszuzczcdt0(X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f112,plain,
    ! [W0] :
      ( ~ aVector0(W0)
      | aNaturalNumber0(aDimensionOf0(W0)) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f113,plain,
    ! [X0] :
      ( ~ aVector0(X0)
      | aNaturalNumber0(aDimensionOf0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f112]) ).

fof(f116,plain,
    ! [W0] :
      ( ~ aVector0(W0)
      | aDimensionOf0(W0) = sz00
      | ! [W1] :
          ( W1 = sziznziztdt0(W0)
        <=> ( aVector0(W1)
            & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
            & ! [W2] :
                ( ~ aNaturalNumber0(W2)
                | sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f32]) ).

fof(f117,plain,
    ! [W0] :
      ( ~ aVector0(W0)
      | aDimensionOf0(W0) = sz00
      | ! [W1] :
          ( ( W1 != sziznziztdt0(W0)
            | ( aVector0(W1)
              & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
              & ! [W2] :
                  ( ~ aNaturalNumber0(W2)
                  | sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) )
          & ( W1 = sziznziztdt0(W0)
            | ~ aVector0(W1)
            | szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
            | ? [W2] :
                ( aNaturalNumber0(W2)
                & sdtlbdtrb0(W1,W2) != sdtlbdtrb0(W0,W2) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f116]) ).

fof(f118,plain,
    ! [W0] :
      ( ~ aVector0(W0)
      | aDimensionOf0(W0) = sz00
      | ( ! [W1] :
            ( W1 != sziznziztdt0(W0)
            | ( aVector0(W1)
              & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
              & ! [W2] :
                  ( ~ aNaturalNumber0(W2)
                  | sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) )
        & ! [W1] :
            ( W1 = sziznziztdt0(W0)
            | ~ aVector0(W1)
            | szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
            | ? [W2] :
                ( aNaturalNumber0(W2)
                & sdtlbdtrb0(W1,W2) != sdtlbdtrb0(W0,W2) ) ) ) ),
    inference(miniscoping,[status(esa)],[f117]) ).

fof(f119,plain,
    ! [W0] :
      ( ~ aVector0(W0)
      | aDimensionOf0(W0) = sz00
      | ( ! [W1] :
            ( W1 != sziznziztdt0(W0)
            | ( aVector0(W1)
              & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
              & ! [W2] :
                  ( ~ aNaturalNumber0(W2)
                  | sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) ) ) )
        & ! [W1] :
            ( W1 = sziznziztdt0(W0)
            | ~ aVector0(W1)
            | szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
            | ( aNaturalNumber0(sk0_1(W1,W0))
              & sdtlbdtrb0(W1,sk0_1(W1,W0)) != sdtlbdtrb0(W0,sk0_1(W1,W0)) ) ) ) ),
    inference(skolemization,[status(esa)],[f118]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ~ aVector0(X0)
      | aDimensionOf0(X0) = sz00
      | X1 != sziznziztdt0(X0)
      | aVector0(X1) ),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ aVector0(X0)
      | aDimensionOf0(X0) = sz00
      | X1 != sziznziztdt0(X0)
      | szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0) ),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f125,plain,
    aVector0(xs),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f126,plain,
    aVector0(xt),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f127,plain,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f128,plain,
    aDimensionOf0(xt) != sz00,
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f129,plain,
    aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f145,plain,
    ! [X0] :
      ( ~ aVector0(X0)
      | aDimensionOf0(X0) = sz00
      | aVector0(sziznziztdt0(X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f120]) ).

fof(f146,plain,
    ! [X0] :
      ( ~ aVector0(X0)
      | aDimensionOf0(X0) = sz00
      | szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) = aDimensionOf0(X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f121]) ).

fof(f148,plain,
    aDimensionOf0(xs) != sz00,
    inference(forward_demodulation,[status(thm)],[f127,f128]) ).

fof(f149,plain,
    ( spl0_4
  <=> aDimensionOf0(xt) = sz00 ),
    introduced(split_symbol_definition) ).

fof(f150,plain,
    ( aDimensionOf0(xt) = sz00
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f149]) ).

fof(f152,plain,
    ( spl0_5
  <=> aVector0(sziznziztdt0(xt)) ),
    introduced(split_symbol_definition) ).

fof(f153,plain,
    ( aVector0(sziznziztdt0(xt))
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f152]) ).

fof(f155,plain,
    ( aDimensionOf0(xt) = sz00
    | aVector0(sziznziztdt0(xt)) ),
    inference(resolution,[status(thm)],[f145,f126]) ).

fof(f156,plain,
    ( spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f155,f149,f152]) ).

fof(f157,plain,
    ( spl0_6
  <=> aDimensionOf0(xs) = sz00 ),
    introduced(split_symbol_definition) ).

fof(f158,plain,
    ( aDimensionOf0(xs) = sz00
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f157]) ).

fof(f160,plain,
    ( spl0_7
  <=> aVector0(sziznziztdt0(xs)) ),
    introduced(split_symbol_definition) ).

fof(f161,plain,
    ( aVector0(sziznziztdt0(xs))
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f160]) ).

fof(f163,plain,
    ( aDimensionOf0(xs) = sz00
    | aVector0(sziznziztdt0(xs)) ),
    inference(resolution,[status(thm)],[f145,f125]) ).

fof(f164,plain,
    ( spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f163,f157,f160]) ).

fof(f165,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f158,f148]) ).

fof(f166,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f165]) ).

fof(f167,plain,
    ( aDimensionOf0(xs) = sz00
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f127,f150]) ).

fof(f168,plain,
    ( $false
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f167,f148]) ).

fof(f169,plain,
    ~ spl0_4,
    inference(contradiction_clause,[status(thm)],[f168]) ).

fof(f221,plain,
    ( spl0_19
  <=> szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) ),
    introduced(split_symbol_definition) ).

fof(f222,plain,
    ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
    | ~ spl0_19 ),
    inference(component_clause,[status(thm)],[f221]) ).

fof(f224,plain,
    ( aDimensionOf0(xt) = sz00
    | szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) ),
    inference(resolution,[status(thm)],[f146,f126]) ).

fof(f225,plain,
    ( spl0_4
    | spl0_19 ),
    inference(split_clause,[status(thm)],[f224,f149,f221]) ).

fof(f226,plain,
    ( spl0_20
  <=> szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ),
    introduced(split_symbol_definition) ).

fof(f227,plain,
    ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
    | ~ spl0_20 ),
    inference(component_clause,[status(thm)],[f226]) ).

fof(f229,plain,
    ( aDimensionOf0(xs) = sz00
    | szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ),
    inference(resolution,[status(thm)],[f146,f125]) ).

fof(f230,plain,
    ( spl0_6
    | spl0_20 ),
    inference(split_clause,[status(thm)],[f229,f157,f226]) ).

fof(f282,plain,
    ( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f113,f153]) ).

fof(f284,plain,
    ( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f113,f161]) ).

fof(f327,plain,
    ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xs)
    | ~ spl0_19 ),
    inference(forward_demodulation,[status(thm)],[f127,f222]) ).

fof(f494,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != szszuzczcdt0(X0)
      | aDimensionOf0(sziznziztdt0(xs)) = X0
      | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f49,f284]) ).

fof(f495,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | aDimensionOf0(xs) != szszuzczcdt0(X0)
      | aDimensionOf0(sziznziztdt0(xs)) = X0
      | ~ spl0_20
      | ~ spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f227,f494]) ).

fof(f606,plain,
    ( spl0_55
  <=> aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ),
    introduced(split_symbol_definition) ).

fof(f608,plain,
    ( aDimensionOf0(xs) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt)))
    | spl0_55 ),
    inference(component_clause,[status(thm)],[f606]) ).

fof(f609,plain,
    ( spl0_56
  <=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ),
    introduced(split_symbol_definition) ).

fof(f610,plain,
    ( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
    | ~ spl0_56 ),
    inference(component_clause,[status(thm)],[f609]) ).

fof(f612,plain,
    ( aDimensionOf0(xs) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt)))
    | aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
    | ~ spl0_20
    | ~ spl0_7
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f495,f282]) ).

fof(f613,plain,
    ( ~ spl0_55
    | spl0_56
    | ~ spl0_20
    | ~ spl0_7
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f612,f606,f609,f226,f160,f152]) ).

fof(f619,plain,
    ( aDimensionOf0(xs) != aDimensionOf0(xs)
    | ~ spl0_19
    | spl0_55 ),
    inference(forward_demodulation,[status(thm)],[f327,f608]) ).

fof(f620,plain,
    ( $false
    | ~ spl0_19
    | spl0_55 ),
    inference(trivial_equality_resolution,[status(esa)],[f619]) ).

fof(f621,plain,
    ( ~ spl0_19
    | spl0_55 ),
    inference(contradiction_clause,[status(thm)],[f620]) ).

fof(f626,plain,
    ( $false
    | ~ spl0_56 ),
    inference(forward_subsumption_resolution,[status(thm)],[f610,f129]) ).

fof(f627,plain,
    ~ spl0_56,
    inference(contradiction_clause,[status(thm)],[f626]) ).

fof(f628,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f156,f164,f166,f169,f225,f230,f613,f621,f627]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : RNG047+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n029.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue May 30 10:51:37 EDT 2023
% 0.09/0.31  % CPUTime  : 
% 0.14/0.31  % Drodi V3.5.1
% 0.14/0.36  % Refutation found
% 0.14/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.38  % Elapsed time: 0.072188 seconds
% 0.14/0.38  % CPU time: 0.183373 seconds
% 0.14/0.38  % Memory used: 31.568 MB
%------------------------------------------------------------------------------