TSTP Solution File: RNG081+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 20:37:55 EDT 2024

% Result   : Theorem 0.18s 0.48s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  119 (  30 unt;   0 def)
%            Number of atoms       :  457 ( 161 equ)
%            Maximal formula atoms :   40 (   3 avg)
%            Number of connectives :  452 ( 114   ~; 111   |; 198   &)
%                                         (  14 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   53 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   20 (  18 usr;  15 prp; 0-2 aty)
%            Number of functors    :   26 (  26 usr;  18 con; 0-2 aty)
%            Number of variables   :   98 (  42   !;  56   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( aNaturalNumber0(szszuzczcdt0(W0))
        & szszuzczcdt0(W0) != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f12,axiom,
    ! [W0] :
      ( aScalar0(W0)
     => aScalar0(smndt0(W0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [W0] :
      ( aScalar0(W0)
     => ( sdtpldt0(W0,sz0z00) = W0
        & sdtpldt0(sz0z00,W0) = W0
        & sdtasdt0(W0,sz0z00) = sz0z00
        & sdtasdt0(sz0z00,W0) = sz0z00
        & sdtpldt0(W0,smndt0(W0)) = sz0z00
        & sdtpldt0(smndt0(W0),W0) = sz0z00
        & smndt0(smndt0(W0)) = W0
        & smndt0(sz0z00) = sz0z00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [W0] :
      ( aScalar0(W0)
     => sdtlseqdt0(W0,W0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,axiom,
    ! [W0,W1] :
      ( ( aVector0(W0)
        & aNaturalNumber0(W1) )
     => aScalar0(sdtlbdtrb0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f35,axiom,
    ! [W0,W1] :
      ( ( aVector0(W0)
        & aVector0(W1) )
     => ( ( aDimensionOf0(W0) = aDimensionOf0(W1)
          & aDimensionOf0(W1) = sz00 )
       => sdtasasdt0(W0,W1) = sz0z00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f38,hypothesis,
    ( aVector0(xs)
    & aVector0(xt) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f40,hypothesis,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f41,conjecture,
    ( ( aDimensionOf0(xs) != sz00
     => ? [W0] :
          ( aVector0(W0)
          & szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
          & ! [W1] :
              ( aNaturalNumber0(W1)
             => sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
          & W0 = sziznziztdt0(xs)
          & ? [W1] :
              ( aVector0(W1)
              & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
              & ! [W2] :
                  ( aNaturalNumber0(W2)
                 => sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
              & W1 = sziznziztdt0(xt)
              & ? [W2] :
                  ( aScalar0(W2)
                  & W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
                  & ? [W3] :
                      ( aScalar0(W3)
                      & W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
                      & ? [W4] :
                          ( aScalar0(W4)
                          & W4 = sdtasasdt0(W0,W0)
                          & ? [W5] :
                              ( aScalar0(W5)
                              & W5 = sdtasasdt0(W1,W1)
                              & ? [W6] :
                                  ( aScalar0(W6)
                                  & W6 = sdtasasdt0(W0,W1)
                                  & ? [W7] :
                                      ( aScalar0(W7)
                                      & W7 = sdtasdt0(W2,W2)
                                      & ? [W8] :
                                          ( aScalar0(W8)
                                          & W8 = sdtasdt0(W3,W3)
                                          & ? [W9] :
                                              ( aScalar0(W9)
                                              & W9 = sdtasdt0(W2,W3)
                                              & ? [W10] :
                                                  ( aScalar0(W10)
                                                  & W10 = sdtasdt0(W4,W8)
                                                  & ? [W11] :
                                                      ( aScalar0(W11)
                                                      & W11 = sdtasdt0(W6,W9)
                                                      & ? [W12] :
                                                          ( aScalar0(W12)
                                                          & W12 = sdtasdt0(W7,W5)
                                                          & ? [W13] :
                                                              ( aScalar0(W13)
                                                              & W13 = sdtasdt0(W10,W12)
                                                              & sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
                                                              & sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
                                                              & sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
                                                              & sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
   => sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f42,negated_conjecture,
    ~ ( ( aDimensionOf0(xs) != sz00
       => ? [W0] :
            ( aVector0(W0)
            & szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
            & ! [W1] :
                ( aNaturalNumber0(W1)
               => sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
            & W0 = sziznziztdt0(xs)
            & ? [W1] :
                ( aVector0(W1)
                & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
                & ! [W2] :
                    ( aNaturalNumber0(W2)
                   => sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
                & W1 = sziznziztdt0(xt)
                & ? [W2] :
                    ( aScalar0(W2)
                    & W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
                    & ? [W3] :
                        ( aScalar0(W3)
                        & W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
                        & ? [W4] :
                            ( aScalar0(W4)
                            & W4 = sdtasasdt0(W0,W0)
                            & ? [W5] :
                                ( aScalar0(W5)
                                & W5 = sdtasasdt0(W1,W1)
                                & ? [W6] :
                                    ( aScalar0(W6)
                                    & W6 = sdtasasdt0(W0,W1)
                                    & ? [W7] :
                                        ( aScalar0(W7)
                                        & W7 = sdtasdt0(W2,W2)
                                        & ? [W8] :
                                            ( aScalar0(W8)
                                            & W8 = sdtasdt0(W3,W3)
                                            & ? [W9] :
                                                ( aScalar0(W9)
                                                & W9 = sdtasdt0(W2,W3)
                                                & ? [W10] :
                                                    ( aScalar0(W10)
                                                    & W10 = sdtasdt0(W4,W8)
                                                    & ? [W11] :
                                                        ( aScalar0(W11)
                                                        & W11 = sdtasdt0(W6,W9)
                                                        & ? [W12] :
                                                            ( aScalar0(W12)
                                                            & W12 = sdtasdt0(W7,W5)
                                                            & ? [W13] :
                                                                ( aScalar0(W13)
                                                                & W13 = sdtasdt0(W10,W12)
                                                                & sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
                                                                & sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
                                                                & sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
                                                                & sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
     => sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(negated_conjecture,[status(cth)],[f41]) ).

fof(f46,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f47,plain,
    ! [W0] :
      ( ~ aNaturalNumber0(W0)
      | ( aNaturalNumber0(szszuzczcdt0(W0))
        & szszuzczcdt0(W0) != sz00 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f48,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | aNaturalNumber0(szszuzczcdt0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f63,plain,
    aScalar0(sz0z00),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f68,plain,
    ! [W0] :
      ( ~ aScalar0(W0)
      | aScalar0(smndt0(W0)) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ aScalar0(X0)
      | aScalar0(smndt0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f70,plain,
    ! [W0] :
      ( ~ aScalar0(W0)
      | ( sdtpldt0(W0,sz0z00) = W0
        & sdtpldt0(sz0z00,W0) = W0
        & sdtasdt0(W0,sz0z00) = sz0z00
        & sdtasdt0(sz0z00,W0) = sz0z00
        & sdtpldt0(W0,smndt0(W0)) = sz0z00
        & sdtpldt0(smndt0(W0),W0) = sz0z00
        & smndt0(smndt0(W0)) = W0
        & smndt0(sz0z00) = sz0z00 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f73,plain,
    ! [X0] :
      ( ~ aScalar0(X0)
      | sdtasdt0(X0,sz0z00) = sz0z00 ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f96,plain,
    ! [W0] :
      ( ~ aScalar0(W0)
      | sdtlseqdt0(W0,W0) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f97,plain,
    ! [X0] :
      ( ~ aScalar0(X0)
      | sdtlseqdt0(X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f96]) ).

fof(f120,plain,
    ! [W0,W1] :
      ( ~ aVector0(W0)
      | ~ aNaturalNumber0(W1)
      | aScalar0(sdtlbdtrb0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f31]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ aVector0(X0)
      | ~ aNaturalNumber0(X1)
      | aScalar0(sdtlbdtrb0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f120]) ).

fof(f135,plain,
    ! [W0,W1] :
      ( ~ aVector0(W0)
      | ~ aVector0(W1)
      | aDimensionOf0(W0) != aDimensionOf0(W1)
      | aDimensionOf0(W1) != sz00
      | sdtasasdt0(W0,W1) = sz0z00 ),
    inference(pre_NNF_transformation,[status(esa)],[f35]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( ~ aVector0(X0)
      | ~ aVector0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | aDimensionOf0(X1) != sz00
      | sdtasasdt0(X0,X1) = sz0z00 ),
    inference(cnf_transformation,[status(esa)],[f135]) ).

fof(f141,plain,
    aVector0(xs),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f142,plain,
    aVector0(xt),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f145,plain,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f146,plain,
    ( ( aDimensionOf0(xs) = sz00
      | ? [W0] :
          ( aVector0(W0)
          & szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
          & ! [W1] :
              ( ~ aNaturalNumber0(W1)
              | sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
          & W0 = sziznziztdt0(xs)
          & ? [W1] :
              ( aVector0(W1)
              & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
              & ! [W2] :
                  ( ~ aNaturalNumber0(W2)
                  | sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
              & W1 = sziznziztdt0(xt)
              & ? [W2] :
                  ( aScalar0(W2)
                  & W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
                  & ? [W3] :
                      ( aScalar0(W3)
                      & W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
                      & ? [W4] :
                          ( aScalar0(W4)
                          & W4 = sdtasasdt0(W0,W0)
                          & ? [W5] :
                              ( aScalar0(W5)
                              & W5 = sdtasasdt0(W1,W1)
                              & ? [W6] :
                                  ( aScalar0(W6)
                                  & W6 = sdtasasdt0(W0,W1)
                                  & ? [W7] :
                                      ( aScalar0(W7)
                                      & W7 = sdtasdt0(W2,W2)
                                      & ? [W8] :
                                          ( aScalar0(W8)
                                          & W8 = sdtasdt0(W3,W3)
                                          & ? [W9] :
                                              ( aScalar0(W9)
                                              & W9 = sdtasdt0(W2,W3)
                                              & ? [W10] :
                                                  ( aScalar0(W10)
                                                  & W10 = sdtasdt0(W4,W8)
                                                  & ? [W11] :
                                                      ( aScalar0(W11)
                                                      & W11 = sdtasdt0(W6,W9)
                                                      & ? [W12] :
                                                          ( aScalar0(W12)
                                                          & W12 = sdtasdt0(W7,W5)
                                                          & ? [W13] :
                                                              ( aScalar0(W13)
                                                              & W13 = sdtasdt0(W10,W12)
                                                              & sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
                                                              & sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
                                                              & sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
                                                              & sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    & ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(pre_NNF_transformation,[status(esa)],[f42]) ).

fof(f147,plain,
    ( ( aDimensionOf0(xs) = sz00
      | ? [W0] :
          ( aVector0(W0)
          & szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs)
          & ! [W1] :
              ( ~ aNaturalNumber0(W1)
              | sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) )
          & W0 = sziznziztdt0(xs)
          & ? [W1] :
              ( aVector0(W1)
              & szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt)
              & ! [W2] :
                  ( ~ aNaturalNumber0(W2)
                  | sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) )
              & W1 = sziznziztdt0(xt)
              & ? [W2] :
                  ( aScalar0(W2)
                  & W2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
                  & ? [W3] :
                      ( aScalar0(W3)
                      & W3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
                      & ? [W4] :
                          ( aScalar0(W4)
                          & W4 = sdtasasdt0(W0,W0)
                          & ? [W5] :
                              ( aScalar0(W5)
                              & W5 = sdtasasdt0(W1,W1)
                              & ? [W6] :
                                  ( aScalar0(W6)
                                  & W6 = sdtasasdt0(W0,W1)
                                  & ? [W7] :
                                      ( aScalar0(W7)
                                      & W7 = sdtasdt0(W2,W2)
                                      & ? [W8] :
                                          ( aScalar0(W8)
                                          & W8 = sdtasdt0(W3,W3)
                                          & ? [W9] :
                                              ( aScalar0(W9)
                                              & W9 = sdtasdt0(W2,W3)
                                              & ? [W10] :
                                                  ( aScalar0(W10)
                                                  & W10 = sdtasdt0(W4,W8)
                                                  & ? [W11] :
                                                      ( aScalar0(W11)
                                                      & W11 = sdtasdt0(W6,W9)
                                                      & ? [W12] :
                                                          ( aScalar0(W12)
                                                          & W12 = sdtasdt0(W7,W5)
                                                          & ? [W13] :
                                                              ( aScalar0(W13)
                                                              & W13 = sdtasdt0(W10,W12) )
                                                          & sdtlseqdt0(sdtasdt0(W6,W6),sdtasdt0(W4,W5))
                                                          & sdtlseqdt0(sdtpldt0(W11,W11),sdtpldt0(W10,W12))
                                                          & sdtlseqdt0(sdtasdt0(sdtpldt0(W6,W9),sdtpldt0(W6,W9)),sdtasdt0(sdtpldt0(W4,W7),sdtpldt0(W5,W8)))
                                                          & sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    & ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(miniscoping,[status(esa)],[f146]) ).

fof(f148,plain,
    ( ( aDimensionOf0(xs) = sz00
      | ( aVector0(sk0_2)
        & szszuzczcdt0(aDimensionOf0(sk0_2)) = aDimensionOf0(xs)
        & ! [W1] :
            ( ~ aNaturalNumber0(W1)
            | sdtlbdtrb0(sk0_2,W1) = sdtlbdtrb0(xs,W1) )
        & sk0_2 = sziznziztdt0(xs)
        & aVector0(sk0_3)
        & szszuzczcdt0(aDimensionOf0(sk0_3)) = aDimensionOf0(xt)
        & ! [W2] :
            ( ~ aNaturalNumber0(W2)
            | sdtlbdtrb0(sk0_3,W2) = sdtlbdtrb0(xt,W2) )
        & sk0_3 = sziznziztdt0(xt)
        & aScalar0(sk0_4)
        & sk0_4 = sdtlbdtrb0(xs,aDimensionOf0(xs))
        & aScalar0(sk0_5)
        & sk0_5 = sdtlbdtrb0(xt,aDimensionOf0(xt))
        & aScalar0(sk0_6)
        & sk0_6 = sdtasasdt0(sk0_2,sk0_2)
        & aScalar0(sk0_7)
        & sk0_7 = sdtasasdt0(sk0_3,sk0_3)
        & aScalar0(sk0_8)
        & sk0_8 = sdtasasdt0(sk0_2,sk0_3)
        & aScalar0(sk0_9)
        & sk0_9 = sdtasdt0(sk0_4,sk0_4)
        & aScalar0(sk0_10)
        & sk0_10 = sdtasdt0(sk0_5,sk0_5)
        & aScalar0(sk0_11)
        & sk0_11 = sdtasdt0(sk0_4,sk0_5)
        & aScalar0(sk0_12)
        & sk0_12 = sdtasdt0(sk0_6,sk0_10)
        & aScalar0(sk0_13)
        & sk0_13 = sdtasdt0(sk0_8,sk0_11)
        & aScalar0(sk0_14)
        & sk0_14 = sdtasdt0(sk0_9,sk0_7)
        & aScalar0(sk0_15)
        & sk0_15 = sdtasdt0(sk0_12,sk0_14)
        & sdtlseqdt0(sdtasdt0(sk0_8,sk0_8),sdtasdt0(sk0_6,sk0_7))
        & sdtlseqdt0(sdtpldt0(sk0_13,sk0_13),sdtpldt0(sk0_12,sk0_14))
        & sdtlseqdt0(sdtasdt0(sdtpldt0(sk0_8,sk0_11),sdtpldt0(sk0_8,sk0_11)),sdtasdt0(sdtpldt0(sk0_6,sk0_9),sdtpldt0(sk0_7,sk0_10)))
        & sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) )
    & ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(skolemization,[status(esa)],[f147]) ).

fof(f184,plain,
    ( aDimensionOf0(xs) = sz00
    | sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(cnf_transformation,[status(esa)],[f148]) ).

fof(f185,plain,
    ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(cnf_transformation,[status(esa)],[f148]) ).

fof(f201,plain,
    ( spl0_4
  <=> aDimensionOf0(xs) = sz00 ),
    introduced(split_symbol_definition) ).

fof(f202,plain,
    ( aDimensionOf0(xs) = sz00
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f201]) ).

fof(f344,plain,
    ( spl0_40
  <=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    introduced(split_symbol_definition) ).

fof(f345,plain,
    ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    | ~ spl0_40 ),
    inference(component_clause,[status(thm)],[f344]) ).

fof(f347,plain,
    ( spl0_4
    | spl0_40 ),
    inference(split_clause,[status(thm)],[f184,f201,f344]) ).

fof(f351,plain,
    aNaturalNumber0(szszuzczcdt0(sz00)),
    inference(resolution,[status(thm)],[f48,f46]) ).

fof(f370,plain,
    sdtlseqdt0(sz0z00,sz0z00),
    inference(resolution,[status(thm)],[f63,f97]) ).

fof(f469,plain,
    ( sz00 = aDimensionOf0(xt)
    | ~ spl0_4 ),
    inference(backward_demodulation,[status(thm)],[f202,f145]) ).

fof(f696,plain,
    sdtasdt0(sz0z00,sz0z00) = sz0z00,
    inference(resolution,[status(thm)],[f73,f63]) ).

fof(f948,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | aScalar0(sdtlbdtrb0(xt,X0)) ),
    inference(resolution,[status(thm)],[f121,f142]) ).

fof(f949,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | aScalar0(sdtlbdtrb0(xs,X0)) ),
    inference(resolution,[status(thm)],[f121,f141]) ).

fof(f956,plain,
    aScalar0(sdtlbdtrb0(xt,szszuzczcdt0(sz00))),
    inference(resolution,[status(thm)],[f948,f351]) ).

fof(f957,plain,
    aScalar0(sdtlbdtrb0(xt,sz00)),
    inference(resolution,[status(thm)],[f948,f46]) ).

fof(f971,plain,
    aScalar0(smndt0(sdtlbdtrb0(xt,sz00))),
    inference(resolution,[status(thm)],[f957,f69]) ).

fof(f977,plain,
    sdtlseqdt0(sdtlbdtrb0(xt,sz00),sdtlbdtrb0(xt,sz00)),
    inference(resolution,[status(thm)],[f957,f97]) ).

fof(f986,plain,
    aScalar0(sdtlbdtrb0(xs,szszuzczcdt0(sz00))),
    inference(resolution,[status(thm)],[f949,f351]) ).

fof(f987,plain,
    aScalar0(sdtlbdtrb0(xs,sz00)),
    inference(resolution,[status(thm)],[f949,f46]) ).

fof(f1001,plain,
    aScalar0(smndt0(sdtlbdtrb0(xs,sz00))),
    inference(resolution,[status(thm)],[f987,f69]) ).

fof(f1007,plain,
    sdtlseqdt0(sdtlbdtrb0(xs,sz00),sdtlbdtrb0(xs,sz00)),
    inference(resolution,[status(thm)],[f987,f97]) ).

fof(f1019,plain,
    ( spl0_117
  <=> sz0z00 = sdtasasdt0(xs,xs) ),
    introduced(split_symbol_definition) ).

fof(f1020,plain,
    ( sz0z00 = sdtasasdt0(xs,xs)
    | ~ spl0_117 ),
    inference(component_clause,[status(thm)],[f1019]) ).

fof(f1030,plain,
    ( spl0_120
  <=> sz0z00 = sdtasasdt0(xt,xt) ),
    introduced(split_symbol_definition) ).

fof(f1031,plain,
    ( sz0z00 = sdtasasdt0(xt,xt)
    | ~ spl0_120 ),
    inference(component_clause,[status(thm)],[f1030]) ).

fof(f1350,plain,
    ( $false
    | ~ spl0_40 ),
    inference(forward_subsumption_resolution,[status(thm)],[f345,f185]) ).

fof(f1351,plain,
    ~ spl0_40,
    inference(contradiction_clause,[status(thm)],[f1350]) ).

fof(f1599,plain,
    ( spl0_145
  <=> aDimensionOf0(xt) = sz00 ),
    introduced(split_symbol_definition) ).

fof(f1601,plain,
    ( aDimensionOf0(xt) != sz00
    | spl0_145 ),
    inference(component_clause,[status(thm)],[f1599]) ).

fof(f1805,plain,
    ( spl0_182
  <=> aScalar0(sdtlbdtrb0(xt,sz00)) ),
    introduced(split_symbol_definition) ).

fof(f1807,plain,
    ( ~ aScalar0(sdtlbdtrb0(xt,sz00))
    | spl0_182 ),
    inference(component_clause,[status(thm)],[f1805]) ).

fof(f1828,plain,
    ( spl0_187
  <=> sdtlseqdt0(sdtlbdtrb0(xt,sz00),sdtlbdtrb0(xt,sz00)) ),
    introduced(split_symbol_definition) ).

fof(f1830,plain,
    ( ~ sdtlseqdt0(sdtlbdtrb0(xt,sz00),sdtlbdtrb0(xt,sz00))
    | spl0_187 ),
    inference(component_clause,[status(thm)],[f1828]) ).

fof(f1836,plain,
    ( $false
    | spl0_182 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1807,f957]) ).

fof(f1837,plain,
    spl0_182,
    inference(contradiction_clause,[status(thm)],[f1836]) ).

fof(f1838,plain,
    ( $false
    | spl0_187 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1830,f977]) ).

fof(f1839,plain,
    spl0_187,
    inference(contradiction_clause,[status(thm)],[f1838]) ).

fof(f1877,plain,
    ( spl0_191
  <=> aScalar0(sdtlbdtrb0(xs,sz00)) ),
    introduced(split_symbol_definition) ).

fof(f1879,plain,
    ( ~ aScalar0(sdtlbdtrb0(xs,sz00))
    | spl0_191 ),
    inference(component_clause,[status(thm)],[f1877]) ).

fof(f1900,plain,
    ( spl0_196
  <=> sdtlseqdt0(sdtlbdtrb0(xs,sz00),sdtlbdtrb0(xs,sz00)) ),
    introduced(split_symbol_definition) ).

fof(f1902,plain,
    ( ~ sdtlseqdt0(sdtlbdtrb0(xs,sz00),sdtlbdtrb0(xs,sz00))
    | spl0_196 ),
    inference(component_clause,[status(thm)],[f1900]) ).

fof(f1908,plain,
    ( $false
    | spl0_191 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1879,f987]) ).

fof(f1909,plain,
    spl0_191,
    inference(contradiction_clause,[status(thm)],[f1908]) ).

fof(f1910,plain,
    ( $false
    | spl0_196 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1902,f1007]) ).

fof(f1911,plain,
    spl0_196,
    inference(contradiction_clause,[status(thm)],[f1910]) ).

fof(f2141,plain,
    ( spl0_235
  <=> aScalar0(sdtlbdtrb0(xt,szszuzczcdt0(sz00))) ),
    introduced(split_symbol_definition) ).

fof(f2143,plain,
    ( ~ aScalar0(sdtlbdtrb0(xt,szszuzczcdt0(sz00)))
    | spl0_235 ),
    inference(component_clause,[status(thm)],[f2141]) ).

fof(f2189,plain,
    ( $false
    | spl0_235 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2143,f956]) ).

fof(f2190,plain,
    spl0_235,
    inference(contradiction_clause,[status(thm)],[f2189]) ).

fof(f2191,plain,
    ( spl0_245
  <=> aScalar0(sdtlbdtrb0(xs,szszuzczcdt0(sz00))) ),
    introduced(split_symbol_definition) ).

fof(f2193,plain,
    ( ~ aScalar0(sdtlbdtrb0(xs,szszuzczcdt0(sz00)))
    | spl0_245 ),
    inference(component_clause,[status(thm)],[f2191]) ).

fof(f2239,plain,
    ( $false
    | spl0_245 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2193,f986]) ).

fof(f2240,plain,
    spl0_245,
    inference(contradiction_clause,[status(thm)],[f2239]) ).

fof(f2241,plain,
    ( spl0_255
  <=> aScalar0(smndt0(sdtlbdtrb0(xt,sz00))) ),
    introduced(split_symbol_definition) ).

fof(f2243,plain,
    ( ~ aScalar0(smndt0(sdtlbdtrb0(xt,sz00)))
    | spl0_255 ),
    inference(component_clause,[status(thm)],[f2241]) ).

fof(f2289,plain,
    ( $false
    | spl0_255 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2243,f971]) ).

fof(f2290,plain,
    spl0_255,
    inference(contradiction_clause,[status(thm)],[f2289]) ).

fof(f2291,plain,
    ( spl0_265
  <=> aScalar0(smndt0(sdtlbdtrb0(xs,sz00))) ),
    introduced(split_symbol_definition) ).

fof(f2293,plain,
    ( ~ aScalar0(smndt0(sdtlbdtrb0(xs,sz00)))
    | spl0_265 ),
    inference(component_clause,[status(thm)],[f2291]) ).

fof(f2339,plain,
    ( $false
    | spl0_265 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2293,f1001]) ).

fof(f2340,plain,
    spl0_265,
    inference(contradiction_clause,[status(thm)],[f2339]) ).

fof(f2736,plain,
    ! [X0] :
      ( ~ aVector0(X0)
      | aDimensionOf0(xt) != aDimensionOf0(X0)
      | aDimensionOf0(X0) != sz00
      | sdtasasdt0(xt,X0) = sz0z00 ),
    inference(resolution,[status(thm)],[f136,f142]) ).

fof(f2737,plain,
    ! [X0] :
      ( ~ aVector0(X0)
      | sz00 != aDimensionOf0(X0)
      | aDimensionOf0(X0) != sz00
      | sdtasasdt0(xt,X0) = sz0z00
      | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f469,f2736]) ).

fof(f2738,plain,
    ! [X0] :
      ( ~ aVector0(X0)
      | sz00 != aDimensionOf0(X0)
      | sdtasasdt0(xt,X0) = sz0z00
      | ~ spl0_4 ),
    inference(duplicate_literals_removal,[status(esa)],[f2737]) ).

fof(f2739,plain,
    ! [X0] :
      ( ~ aVector0(X0)
      | aDimensionOf0(xs) != aDimensionOf0(X0)
      | aDimensionOf0(X0) != sz00
      | sdtasasdt0(xs,X0) = sz0z00 ),
    inference(resolution,[status(thm)],[f136,f141]) ).

fof(f2740,plain,
    ! [X0] :
      ( ~ aVector0(X0)
      | sz00 != aDimensionOf0(X0)
      | aDimensionOf0(X0) != sz00
      | sdtasasdt0(xs,X0) = sz0z00
      | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f202,f2739]) ).

fof(f2741,plain,
    ! [X0] :
      ( ~ aVector0(X0)
      | sz00 != aDimensionOf0(X0)
      | sdtasasdt0(xs,X0) = sz0z00
      | ~ spl0_4 ),
    inference(duplicate_literals_removal,[status(esa)],[f2740]) ).

fof(f3391,plain,
    ( sz00 != sz00
    | ~ spl0_4
    | spl0_145 ),
    inference(forward_demodulation,[status(thm)],[f469,f1601]) ).

fof(f3392,plain,
    ( $false
    | ~ spl0_4
    | spl0_145 ),
    inference(trivial_equality_resolution,[status(esa)],[f3391]) ).

fof(f3393,plain,
    ( ~ spl0_4
    | spl0_145 ),
    inference(contradiction_clause,[status(thm)],[f3392]) ).

fof(f3513,plain,
    ( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
    | ~ spl0_120 ),
    inference(backward_demodulation,[status(thm)],[f1031,f185]) ).

fof(f3564,plain,
    ( spl0_359
  <=> sz0z00 = sdtasasdt0(xs,xt) ),
    introduced(split_symbol_definition) ).

fof(f3565,plain,
    ( sz0z00 = sdtasasdt0(xs,xt)
    | ~ spl0_359 ),
    inference(component_clause,[status(thm)],[f3564]) ).

fof(f3626,plain,
    ( ~ sdtlseqdt0(sdtasdt0(sz0z00,sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
    | ~ spl0_359
    | ~ spl0_120 ),
    inference(forward_demodulation,[status(thm)],[f3565,f3513]) ).

fof(f3627,plain,
    ( ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
    | ~ spl0_359
    | ~ spl0_120 ),
    inference(forward_demodulation,[status(thm)],[f3565,f3626]) ).

fof(f3628,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
    | ~ spl0_359
    | ~ spl0_120 ),
    inference(forward_demodulation,[status(thm)],[f696,f3627]) ).

fof(f3629,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtasdt0(sz0z00,sz0z00))
    | ~ spl0_117
    | ~ spl0_359
    | ~ spl0_120 ),
    inference(forward_demodulation,[status(thm)],[f1020,f3628]) ).

fof(f3630,plain,
    ( ~ sdtlseqdt0(sz0z00,sz0z00)
    | ~ spl0_117
    | ~ spl0_359
    | ~ spl0_120 ),
    inference(forward_demodulation,[status(thm)],[f696,f3629]) ).

fof(f3631,plain,
    ( $false
    | ~ spl0_117
    | ~ spl0_359
    | ~ spl0_120 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3630,f370]) ).

fof(f3632,plain,
    ( ~ spl0_117
    | ~ spl0_359
    | ~ spl0_120 ),
    inference(contradiction_clause,[status(thm)],[f3631]) ).

fof(f3726,plain,
    ( sz00 != aDimensionOf0(xt)
    | sdtasasdt0(xt,xt) = sz0z00
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f2738,f142]) ).

fof(f3727,plain,
    ( ~ spl0_145
    | spl0_120
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f3726,f1599,f1030,f201]) ).

fof(f3730,plain,
    ( sz00 != aDimensionOf0(xt)
    | sdtasasdt0(xs,xt) = sz0z00
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f2741,f142]) ).

fof(f3731,plain,
    ( ~ spl0_145
    | spl0_359
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f3730,f1599,f3564,f201]) ).

fof(f3732,plain,
    ( sz00 != aDimensionOf0(xs)
    | sdtasasdt0(xs,xs) = sz0z00
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f2741,f141]) ).

fof(f3733,plain,
    ( ~ spl0_4
    | spl0_117 ),
    inference(split_clause,[status(thm)],[f3732,f201,f1019]) ).

fof(f3734,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f347,f1351,f1837,f1839,f1909,f1911,f2190,f2240,f2290,f2340,f3393,f3632,f3727,f3731,f3733]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem  : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35  % Computer : n010.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Mon Apr 29 22:08:35 EDT 2024
% 0.12/0.35  % CPUTime  : 
% 0.12/0.36  % Drodi V3.6.0
% 0.18/0.48  % Refutation found
% 0.18/0.48  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.48  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.49  % Elapsed time: 0.137972 seconds
% 0.18/0.49  % CPU time: 0.974478 seconds
% 0.18/0.49  % Total memory used: 77.965 MB
% 0.18/0.49  % Net memory used: 77.187 MB
%------------------------------------------------------------------------------