TSTP Solution File: RNG081+2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.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 02:57:33 EDT 2024

% Result   : Theorem 3.97s 1.11s
% Output   : CNFRefutation 3.97s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).

fof(f13,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => ( sz0z00 = smndt0(sz0z00)
        & smndt0(smndt0(X0)) = X0
        & sz0z00 = sdtpldt0(smndt0(X0),X0)
        & sz0z00 = sdtpldt0(X0,smndt0(X0))
        & sz0z00 = sdtasdt0(sz0z00,X0)
        & sz0z00 = sdtasdt0(X0,sz0z00)
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).

fof(f27,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( aDimensionOf0(X0) = aDimensionOf0(X1)
       => aScalar0(sdtasasdt0(X0,X1)) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).

fof(f38,axiom,
    ( aVector0(xt)
    & aVector0(xs) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).

fof(f40,axiom,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).

fof(f41,conjecture,
    ( ( sz00 != aDimensionOf0(xs)
     => ? [X0] :
          ( ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( ? [X6] :
                                  ( ? [X7] :
                                      ( ? [X8] :
                                          ( ? [X9] :
                                              ( ? [X10] :
                                                  ( ? [X11] :
                                                      ( ? [X12] :
                                                          ( ? [X13] :
                                                              ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
                                                              & sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
                                                              & sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
                                                              & sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
                                                              & sdtasdt0(X10,X12) = X13
                                                              & aScalar0(X13) )
                                                          & sdtasdt0(X7,X5) = X12
                                                          & aScalar0(X12) )
                                                      & sdtasdt0(X6,X9) = X11
                                                      & aScalar0(X11) )
                                                  & sdtasdt0(X4,X8) = X10
                                                  & aScalar0(X10) )
                                              & sdtasdt0(X2,X3) = X9
                                              & aScalar0(X9) )
                                          & sdtasdt0(X3,X3) = X8
                                          & aScalar0(X8) )
                                      & sdtasdt0(X2,X2) = X7
                                      & aScalar0(X7) )
                                  & sdtasasdt0(X0,X1) = X6
                                  & aScalar0(X6) )
                              & sdtasasdt0(X1,X1) = X5
                              & aScalar0(X5) )
                          & sdtasasdt0(X0,X0) = X4
                          & aScalar0(X4) )
                      & sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
                      & aScalar0(X3) )
                  & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
                  & aScalar0(X2) )
              & sziznziztdt0(xt) = X1
              & ! [X2] :
                  ( aNaturalNumber0(X2)
                 => sdtlbdtrb0(X1,X2) = sdtlbdtrb0(xt,X2) )
              & szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
              & aVector0(X1) )
          & sziznziztdt0(xs) = X0
          & ! [X1] :
              ( aNaturalNumber0(X1)
             => sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
          & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
          & aVector0(X0) ) )
   => sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f42,negated_conjecture,
    ~ ( ( sz00 != aDimensionOf0(xs)
       => ? [X0] :
            ( ? [X1] :
                ( ? [X2] :
                    ( ? [X3] :
                        ( ? [X4] :
                            ( ? [X5] :
                                ( ? [X6] :
                                    ( ? [X7] :
                                        ( ? [X8] :
                                            ( ? [X9] :
                                                ( ? [X10] :
                                                    ( ? [X11] :
                                                        ( ? [X12] :
                                                            ( ? [X13] :
                                                                ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
                                                                & sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
                                                                & sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
                                                                & sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
                                                                & sdtasdt0(X10,X12) = X13
                                                                & aScalar0(X13) )
                                                            & sdtasdt0(X7,X5) = X12
                                                            & aScalar0(X12) )
                                                        & sdtasdt0(X6,X9) = X11
                                                        & aScalar0(X11) )
                                                    & sdtasdt0(X4,X8) = X10
                                                    & aScalar0(X10) )
                                                & sdtasdt0(X2,X3) = X9
                                                & aScalar0(X9) )
                                            & sdtasdt0(X3,X3) = X8
                                            & aScalar0(X8) )
                                        & sdtasdt0(X2,X2) = X7
                                        & aScalar0(X7) )
                                    & sdtasasdt0(X0,X1) = X6
                                    & aScalar0(X6) )
                                & sdtasasdt0(X1,X1) = X5
                                & aScalar0(X5) )
                            & sdtasasdt0(X0,X0) = X4
                            & aScalar0(X4) )
                        & sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
                        & aScalar0(X3) )
                    & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
                    & aScalar0(X2) )
                & sziznziztdt0(xt) = X1
                & ! [X2] :
                    ( aNaturalNumber0(X2)
                   => sdtlbdtrb0(X1,X2) = sdtlbdtrb0(xt,X2) )
                & szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
                & aVector0(X1) )
            & sziznziztdt0(xs) = X0
            & ! [X1] :
                ( aNaturalNumber0(X1)
               => sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
            & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
            & aVector0(X0) ) )
     => sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(negated_conjecture,[],[f41]) ).

fof(f48,plain,
    ~ ( ( sz00 != aDimensionOf0(xs)
       => ? [X0] :
            ( ? [X1] :
                ( ? [X2] :
                    ( ? [X3] :
                        ( ? [X4] :
                            ( ? [X5] :
                                ( ? [X6] :
                                    ( ? [X7] :
                                        ( ? [X8] :
                                            ( ? [X9] :
                                                ( ? [X10] :
                                                    ( ? [X11] :
                                                        ( ? [X12] :
                                                            ( ? [X13] :
                                                                ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
                                                                & sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
                                                                & sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
                                                                & sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
                                                                & sdtasdt0(X10,X12) = X13
                                                                & aScalar0(X13) )
                                                            & sdtasdt0(X7,X5) = X12
                                                            & aScalar0(X12) )
                                                        & sdtasdt0(X6,X9) = X11
                                                        & aScalar0(X11) )
                                                    & sdtasdt0(X4,X8) = X10
                                                    & aScalar0(X10) )
                                                & sdtasdt0(X2,X3) = X9
                                                & aScalar0(X9) )
                                            & sdtasdt0(X3,X3) = X8
                                            & aScalar0(X8) )
                                        & sdtasdt0(X2,X2) = X7
                                        & aScalar0(X7) )
                                    & sdtasasdt0(X0,X1) = X6
                                    & aScalar0(X6) )
                                & sdtasasdt0(X1,X1) = X5
                                & aScalar0(X5) )
                            & sdtasasdt0(X0,X0) = X4
                            & aScalar0(X4) )
                        & sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
                        & aScalar0(X3) )
                    & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
                    & aScalar0(X2) )
                & sziznziztdt0(xt) = X1
                & ! [X14] :
                    ( aNaturalNumber0(X14)
                   => sdtlbdtrb0(X1,X14) = sdtlbdtrb0(xt,X14) )
                & szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
                & aVector0(X1) )
            & sziznziztdt0(xs) = X0
            & ! [X15] :
                ( aNaturalNumber0(X15)
               => sdtlbdtrb0(X0,X15) = sdtlbdtrb0(xs,X15) )
            & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
            & aVector0(X0) ) )
     => sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(rectify,[],[f42]) ).

fof(f60,plain,
    ! [X0] :
      ( ( sz0z00 = smndt0(sz0z00)
        & smndt0(smndt0(X0)) = X0
        & sz0z00 = sdtpldt0(smndt0(X0),X0)
        & sz0z00 = sdtpldt0(X0,smndt0(X0))
        & sz0z00 = sdtasdt0(sz0z00,X0)
        & sz0z00 = sdtasdt0(X0,sz0z00)
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 )
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f84,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f94]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f96]) ).

fof(f103,plain,
    ( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    & ( ? [X0] :
          ( ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( ? [X6] :
                                  ( ? [X7] :
                                      ( ? [X8] :
                                          ( ? [X9] :
                                              ( ? [X10] :
                                                  ( ? [X11] :
                                                      ( ? [X12] :
                                                          ( ? [X13] :
                                                              ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
                                                              & sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
                                                              & sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
                                                              & sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
                                                              & sdtasdt0(X10,X12) = X13
                                                              & aScalar0(X13) )
                                                          & sdtasdt0(X7,X5) = X12
                                                          & aScalar0(X12) )
                                                      & sdtasdt0(X6,X9) = X11
                                                      & aScalar0(X11) )
                                                  & sdtasdt0(X4,X8) = X10
                                                  & aScalar0(X10) )
                                              & sdtasdt0(X2,X3) = X9
                                              & aScalar0(X9) )
                                          & sdtasdt0(X3,X3) = X8
                                          & aScalar0(X8) )
                                      & sdtasdt0(X2,X2) = X7
                                      & aScalar0(X7) )
                                  & sdtasasdt0(X0,X1) = X6
                                  & aScalar0(X6) )
                              & sdtasasdt0(X1,X1) = X5
                              & aScalar0(X5) )
                          & sdtasasdt0(X0,X0) = X4
                          & aScalar0(X4) )
                      & sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
                      & aScalar0(X3) )
                  & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
                  & aScalar0(X2) )
              & sziznziztdt0(xt) = X1
              & ! [X14] :
                  ( sdtlbdtrb0(X1,X14) = sdtlbdtrb0(xt,X14)
                  | ~ aNaturalNumber0(X14) )
              & szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
              & aVector0(X1) )
          & sziznziztdt0(xs) = X0
          & ! [X15] :
              ( sdtlbdtrb0(X0,X15) = sdtlbdtrb0(xs,X15)
              | ~ aNaturalNumber0(X15) )
          & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
          & aVector0(X0) )
      | sz00 = aDimensionOf0(xs) ) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f104,plain,
    ! [X8,X5,X7,X4,X9,X6,X10,X11] :
      ( ? [X12] :
          ( ? [X13] :
              ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
              & sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
              & sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
              & sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
              & sdtasdt0(X10,X12) = X13
              & aScalar0(X13) )
          & sdtasdt0(X7,X5) = X12
          & aScalar0(X12) )
      | ~ sP0(X8,X5,X7,X4,X9,X6,X10,X11) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f105,plain,
    ! [X6,X4,X7,X5,X8,X3,X2] :
      ( ? [X9] :
          ( ? [X10] :
              ( ? [X11] :
                  ( sP0(X8,X5,X7,X4,X9,X6,X10,X11)
                  & sdtasdt0(X6,X9) = X11
                  & aScalar0(X11) )
              & sdtasdt0(X4,X8) = X10
              & aScalar0(X10) )
          & sdtasdt0(X2,X3) = X9
          & aScalar0(X9) )
      | ~ sP1(X6,X4,X7,X5,X8,X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f106,plain,
    ! [X2,X3,X5,X4,X1,X0] :
      ( ? [X6] :
          ( ? [X7] :
              ( ? [X8] :
                  ( sP1(X6,X4,X7,X5,X8,X3,X2)
                  & sdtasdt0(X3,X3) = X8
                  & aScalar0(X8) )
              & sdtasdt0(X2,X2) = X7
              & aScalar0(X7) )
          & sdtasasdt0(X0,X1) = X6
          & aScalar0(X6) )
      | ~ sP2(X2,X3,X5,X4,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f107,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( sP2(X2,X3,X5,X4,X1,X0)
                  & sdtasasdt0(X1,X1) = X5
                  & aScalar0(X5) )
              & sdtasasdt0(X0,X0) = X4
              & aScalar0(X4) )
          & sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
          & aScalar0(X3) )
      | ~ sP3(X0,X1,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f108,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( sP3(X0,X1,X2)
              & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
              & aScalar0(X2) )
          & sziznziztdt0(xt) = X1
          & ! [X14] :
              ( sdtlbdtrb0(X1,X14) = sdtlbdtrb0(xt,X14)
              | ~ aNaturalNumber0(X14) )
          & szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
          & aVector0(X1) )
      | ~ sP4(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f109,plain,
    ( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    & ( ? [X0] :
          ( sP4(X0)
          & sziznziztdt0(xs) = X0
          & ! [X15] :
              ( sdtlbdtrb0(X0,X15) = sdtlbdtrb0(xs,X15)
              | ~ aNaturalNumber0(X15) )
          & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
          & aVector0(X0) )
      | sz00 = aDimensionOf0(xs) ) ),
    inference(definition_folding,[],[f103,f108,f107,f106,f105,f104]) ).

fof(f117,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( sP3(X0,X1,X2)
              & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
              & aScalar0(X2) )
          & sziznziztdt0(xt) = X1
          & ! [X14] :
              ( sdtlbdtrb0(X1,X14) = sdtlbdtrb0(xt,X14)
              | ~ aNaturalNumber0(X14) )
          & szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
          & aVector0(X1) )
      | ~ sP4(X0) ),
    inference(nnf_transformation,[],[f108]) ).

fof(f118,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( sP3(X0,X1,X2)
              & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
              & aScalar0(X2) )
          & sziznziztdt0(xt) = X1
          & ! [X3] :
              ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(xt,X3)
              | ~ aNaturalNumber0(X3) )
          & szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
          & aVector0(X1) )
      | ~ sP4(X0) ),
    inference(rectify,[],[f117]) ).

fof(f119,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( sP3(X0,X1,X2)
              & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
              & aScalar0(X2) )
          & sziznziztdt0(xt) = X1
          & ! [X3] :
              ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(xt,X3)
              | ~ aNaturalNumber0(X3) )
          & szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
          & aVector0(X1) )
     => ( ? [X2] :
            ( sP3(X0,sK7(X0),X2)
            & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
            & aScalar0(X2) )
        & sziznziztdt0(xt) = sK7(X0)
        & ! [X3] :
            ( sdtlbdtrb0(xt,X3) = sdtlbdtrb0(sK7(X0),X3)
            | ~ aNaturalNumber0(X3) )
        & aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sK7(X0)))
        & aVector0(sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ! [X0] :
      ( ? [X2] :
          ( sP3(X0,sK7(X0),X2)
          & sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
          & aScalar0(X2) )
     => ( sP3(X0,sK7(X0),sK8(X0))
        & sdtlbdtrb0(xs,aDimensionOf0(xs)) = sK8(X0)
        & aScalar0(sK8(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f121,plain,
    ! [X0] :
      ( ( sP3(X0,sK7(X0),sK8(X0))
        & sdtlbdtrb0(xs,aDimensionOf0(xs)) = sK8(X0)
        & aScalar0(sK8(X0))
        & sziznziztdt0(xt) = sK7(X0)
        & ! [X3] :
            ( sdtlbdtrb0(xt,X3) = sdtlbdtrb0(sK7(X0),X3)
            | ~ aNaturalNumber0(X3) )
        & aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sK7(X0)))
        & aVector0(sK7(X0)) )
      | ~ sP4(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f118,f120,f119]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( sP2(X2,X3,X5,X4,X1,X0)
                  & sdtasasdt0(X1,X1) = X5
                  & aScalar0(X5) )
              & sdtasasdt0(X0,X0) = X4
              & aScalar0(X4) )
          & sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
          & aScalar0(X3) )
      | ~ sP3(X0,X1,X2) ),
    inference(nnf_transformation,[],[f107]) ).

fof(f123,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( sP2(X2,X3,X5,X4,X1,X0)
                  & sdtasasdt0(X1,X1) = X5
                  & aScalar0(X5) )
              & sdtasasdt0(X0,X0) = X4
              & aScalar0(X4) )
          & sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
          & aScalar0(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( sP2(X2,sK9(X0,X1,X2),X5,X4,X1,X0)
                & sdtasasdt0(X1,X1) = X5
                & aScalar0(X5) )
            & sdtasasdt0(X0,X0) = X4
            & aScalar0(X4) )
        & sdtlbdtrb0(xt,aDimensionOf0(xt)) = sK9(X0,X1,X2)
        & aScalar0(sK9(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( sP2(X2,sK9(X0,X1,X2),X5,X4,X1,X0)
              & sdtasasdt0(X1,X1) = X5
              & aScalar0(X5) )
          & sdtasasdt0(X0,X0) = X4
          & aScalar0(X4) )
     => ( ? [X5] :
            ( sP2(X2,sK9(X0,X1,X2),X5,sK10(X0,X1,X2),X1,X0)
            & sdtasasdt0(X1,X1) = X5
            & aScalar0(X5) )
        & sdtasasdt0(X0,X0) = sK10(X0,X1,X2)
        & aScalar0(sK10(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( sP2(X2,sK9(X0,X1,X2),X5,sK10(X0,X1,X2),X1,X0)
          & sdtasasdt0(X1,X1) = X5
          & aScalar0(X5) )
     => ( sP2(X2,sK9(X0,X1,X2),sK11(X0,X1,X2),sK10(X0,X1,X2),X1,X0)
        & sdtasasdt0(X1,X1) = sK11(X0,X1,X2)
        & aScalar0(sK11(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f126,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X2,sK9(X0,X1,X2),sK11(X0,X1,X2),sK10(X0,X1,X2),X1,X0)
        & sdtasasdt0(X1,X1) = sK11(X0,X1,X2)
        & aScalar0(sK11(X0,X1,X2))
        & sdtasasdt0(X0,X0) = sK10(X0,X1,X2)
        & aScalar0(sK10(X0,X1,X2))
        & sdtlbdtrb0(xt,aDimensionOf0(xt)) = sK9(X0,X1,X2)
        & aScalar0(sK9(X0,X1,X2)) )
      | ~ sP3(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f122,f125,f124,f123]) ).

fof(f127,plain,
    ! [X2,X3,X5,X4,X1,X0] :
      ( ? [X6] :
          ( ? [X7] :
              ( ? [X8] :
                  ( sP1(X6,X4,X7,X5,X8,X3,X2)
                  & sdtasdt0(X3,X3) = X8
                  & aScalar0(X8) )
              & sdtasdt0(X2,X2) = X7
              & aScalar0(X7) )
          & sdtasasdt0(X0,X1) = X6
          & aScalar0(X6) )
      | ~ sP2(X2,X3,X5,X4,X1,X0) ),
    inference(nnf_transformation,[],[f106]) ).

fof(f128,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ? [X6] :
          ( ? [X7] :
              ( ? [X8] :
                  ( sP1(X6,X3,X7,X2,X8,X1,X0)
                  & sdtasdt0(X1,X1) = X8
                  & aScalar0(X8) )
              & sdtasdt0(X0,X0) = X7
              & aScalar0(X7) )
          & sdtasasdt0(X5,X4) = X6
          & aScalar0(X6) )
      | ~ sP2(X0,X1,X2,X3,X4,X5) ),
    inference(rectify,[],[f127]) ).

fof(f129,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ? [X6] :
          ( ? [X7] :
              ( ? [X8] :
                  ( sP1(X6,X3,X7,X2,X8,X1,X0)
                  & sdtasdt0(X1,X1) = X8
                  & aScalar0(X8) )
              & sdtasdt0(X0,X0) = X7
              & aScalar0(X7) )
          & sdtasasdt0(X5,X4) = X6
          & aScalar0(X6) )
     => ( ? [X7] :
            ( ? [X8] :
                ( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,X7,X2,X8,X1,X0)
                & sdtasdt0(X1,X1) = X8
                & aScalar0(X8) )
            & sdtasdt0(X0,X0) = X7
            & aScalar0(X7) )
        & sdtasasdt0(X5,X4) = sK12(X0,X1,X2,X3,X4,X5)
        & aScalar0(sK12(X0,X1,X2,X3,X4,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ? [X7] :
          ( ? [X8] :
              ( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,X7,X2,X8,X1,X0)
              & sdtasdt0(X1,X1) = X8
              & aScalar0(X8) )
          & sdtasdt0(X0,X0) = X7
          & aScalar0(X7) )
     => ( ? [X8] :
            ( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,X8,X1,X0)
            & sdtasdt0(X1,X1) = X8
            & aScalar0(X8) )
        & sdtasdt0(X0,X0) = sK13(X0,X1,X2,X3,X4,X5)
        & aScalar0(sK13(X0,X1,X2,X3,X4,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f131,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ? [X8] :
          ( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,X8,X1,X0)
          & sdtasdt0(X1,X1) = X8
          & aScalar0(X8) )
     => ( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,sK14(X0,X1,X2,X3,X4,X5),X1,X0)
        & sdtasdt0(X1,X1) = sK14(X0,X1,X2,X3,X4,X5)
        & aScalar0(sK14(X0,X1,X2,X3,X4,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,sK14(X0,X1,X2,X3,X4,X5),X1,X0)
        & sdtasdt0(X1,X1) = sK14(X0,X1,X2,X3,X4,X5)
        & aScalar0(sK14(X0,X1,X2,X3,X4,X5))
        & sdtasdt0(X0,X0) = sK13(X0,X1,X2,X3,X4,X5)
        & aScalar0(sK13(X0,X1,X2,X3,X4,X5))
        & sdtasasdt0(X5,X4) = sK12(X0,X1,X2,X3,X4,X5)
        & aScalar0(sK12(X0,X1,X2,X3,X4,X5)) )
      | ~ sP2(X0,X1,X2,X3,X4,X5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f128,f131,f130,f129]) ).

fof(f133,plain,
    ! [X6,X4,X7,X5,X8,X3,X2] :
      ( ? [X9] :
          ( ? [X10] :
              ( ? [X11] :
                  ( sP0(X8,X5,X7,X4,X9,X6,X10,X11)
                  & sdtasdt0(X6,X9) = X11
                  & aScalar0(X11) )
              & sdtasdt0(X4,X8) = X10
              & aScalar0(X10) )
          & sdtasdt0(X2,X3) = X9
          & aScalar0(X9) )
      | ~ sP1(X6,X4,X7,X5,X8,X3,X2) ),
    inference(nnf_transformation,[],[f105]) ).

fof(f134,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ? [X7] :
          ( ? [X8] :
              ( ? [X9] :
                  ( sP0(X4,X3,X2,X1,X7,X0,X8,X9)
                  & sdtasdt0(X0,X7) = X9
                  & aScalar0(X9) )
              & sdtasdt0(X1,X4) = X8
              & aScalar0(X8) )
          & sdtasdt0(X6,X5) = X7
          & aScalar0(X7) )
      | ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
    inference(rectify,[],[f133]) ).

fof(f135,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ? [X7] :
          ( ? [X8] :
              ( ? [X9] :
                  ( sP0(X4,X3,X2,X1,X7,X0,X8,X9)
                  & sdtasdt0(X0,X7) = X9
                  & aScalar0(X9) )
              & sdtasdt0(X1,X4) = X8
              & aScalar0(X8) )
          & sdtasdt0(X6,X5) = X7
          & aScalar0(X7) )
     => ( ? [X8] :
            ( ? [X9] :
                ( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,X8,X9)
                & sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = X9
                & aScalar0(X9) )
            & sdtasdt0(X1,X4) = X8
            & aScalar0(X8) )
        & sdtasdt0(X6,X5) = sK15(X0,X1,X2,X3,X4,X5,X6)
        & aScalar0(sK15(X0,X1,X2,X3,X4,X5,X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ? [X8] :
          ( ? [X9] :
              ( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,X8,X9)
              & sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = X9
              & aScalar0(X9) )
          & sdtasdt0(X1,X4) = X8
          & aScalar0(X8) )
     => ( ? [X9] :
            ( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),X9)
            & sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = X9
            & aScalar0(X9) )
        & sdtasdt0(X1,X4) = sK16(X0,X1,X2,X3,X4,X5,X6)
        & aScalar0(sK16(X0,X1,X2,X3,X4,X5,X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ? [X9] :
          ( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),X9)
          & sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = X9
          & aScalar0(X9) )
     => ( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),sK17(X0,X1,X2,X3,X4,X5,X6))
        & sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = sK17(X0,X1,X2,X3,X4,X5,X6)
        & aScalar0(sK17(X0,X1,X2,X3,X4,X5,X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f138,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),sK17(X0,X1,X2,X3,X4,X5,X6))
        & sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = sK17(X0,X1,X2,X3,X4,X5,X6)
        & aScalar0(sK17(X0,X1,X2,X3,X4,X5,X6))
        & sdtasdt0(X1,X4) = sK16(X0,X1,X2,X3,X4,X5,X6)
        & aScalar0(sK16(X0,X1,X2,X3,X4,X5,X6))
        & sdtasdt0(X6,X5) = sK15(X0,X1,X2,X3,X4,X5,X6)
        & aScalar0(sK15(X0,X1,X2,X3,X4,X5,X6)) )
      | ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f134,f137,f136,f135]) ).

fof(f139,plain,
    ! [X8,X5,X7,X4,X9,X6,X10,X11] :
      ( ? [X12] :
          ( ? [X13] :
              ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
              & sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
              & sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
              & sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
              & sdtasdt0(X10,X12) = X13
              & aScalar0(X13) )
          & sdtasdt0(X7,X5) = X12
          & aScalar0(X12) )
      | ~ sP0(X8,X5,X7,X4,X9,X6,X10,X11) ),
    inference(nnf_transformation,[],[f104]) ).

fof(f140,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ? [X8] :
          ( ? [X9] :
              ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
              & sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
              & sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,X8))
              & sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
              & sdtasdt0(X6,X8) = X9
              & aScalar0(X9) )
          & sdtasdt0(X2,X1) = X8
          & aScalar0(X8) )
      | ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(rectify,[],[f139]) ).

fof(f141,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ? [X8] :
          ( ? [X9] :
              ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
              & sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
              & sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,X8))
              & sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
              & sdtasdt0(X6,X8) = X9
              & aScalar0(X9) )
          & sdtasdt0(X2,X1) = X8
          & aScalar0(X8) )
     => ( ? [X9] :
            ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
            & sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
            & sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)))
            & sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
            & sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = X9
            & aScalar0(X9) )
        & sdtasdt0(X2,X1) = sK18(X0,X1,X2,X3,X4,X5,X6,X7)
        & aScalar0(sK18(X0,X1,X2,X3,X4,X5,X6,X7)) ) ),
    introduced(choice_axiom,[]) ).

fof(f142,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ? [X9] :
          ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
          & sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
          & sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)))
          & sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
          & sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = X9
          & aScalar0(X9) )
     => ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
        & sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
        & sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)))
        & sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
        & sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = sK19(X0,X1,X2,X3,X4,X5,X6,X7)
        & aScalar0(sK19(X0,X1,X2,X3,X4,X5,X6,X7)) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
        & sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
        & sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)))
        & sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
        & sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = sK19(X0,X1,X2,X3,X4,X5,X6,X7)
        & aScalar0(sK19(X0,X1,X2,X3,X4,X5,X6,X7))
        & sdtasdt0(X2,X1) = sK18(X0,X1,X2,X3,X4,X5,X6,X7)
        & aScalar0(sK18(X0,X1,X2,X3,X4,X5,X6,X7)) )
      | ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f140,f142,f141]) ).

fof(f144,plain,
    ( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    & ( ? [X0] :
          ( sP4(X0)
          & sziznziztdt0(xs) = X0
          & ! [X1] :
              ( sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1)
              | ~ aNaturalNumber0(X1) )
          & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
          & aVector0(X0) )
      | sz00 = aDimensionOf0(xs) ) ),
    inference(rectify,[],[f109]) ).

fof(f145,plain,
    ( ? [X0] :
        ( sP4(X0)
        & sziznziztdt0(xs) = X0
        & ! [X1] :
            ( sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1)
            | ~ aNaturalNumber0(X1) )
        & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
        & aVector0(X0) )
   => ( sP4(sK20)
      & sziznziztdt0(xs) = sK20
      & ! [X1] :
          ( sdtlbdtrb0(xs,X1) = sdtlbdtrb0(sK20,X1)
          | ~ aNaturalNumber0(X1) )
      & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sK20))
      & aVector0(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    & ( ( sP4(sK20)
        & sziznziztdt0(xs) = sK20
        & ! [X1] :
            ( sdtlbdtrb0(xs,X1) = sdtlbdtrb0(sK20,X1)
            | ~ aNaturalNumber0(X1) )
        & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sK20))
        & aVector0(sK20) )
      | sz00 = aDimensionOf0(xs) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f144,f145]) ).

fof(f154,plain,
    aScalar0(sz0z00),
    inference(cnf_transformation,[],[f9]) ).

fof(f161,plain,
    ! [X0] :
      ( sz0z00 = sdtasdt0(sz0z00,X0)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f184,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f194,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f198,plain,
    aVector0(xs),
    inference(cnf_transformation,[],[f38]) ).

fof(f199,plain,
    aVector0(xt),
    inference(cnf_transformation,[],[f38]) ).

fof(f201,plain,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    inference(cnf_transformation,[],[f40]) ).

fof(f208,plain,
    ! [X0] :
      ( sP3(X0,sK7(X0),sK8(X0))
      | ~ sP4(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f215,plain,
    ! [X2,X0,X1] :
      ( sP2(X2,sK9(X0,X1,X2),sK11(X0,X1,X2),sK10(X0,X1,X2),X1,X0)
      | ~ sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f222,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,sK14(X0,X1,X2,X3,X4,X5),X1,X0)
      | ~ sP2(X0,X1,X2,X3,X4,X5) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f229,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),sK17(X0,X1,X2,X3,X4,X5,X6))
      | ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f233,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = sK19(X0,X1,X2,X3,X4,X5,X6,X7)
      | ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f237,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
      | ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f242,plain,
    ( sP4(sK20)
    | sz00 = aDimensionOf0(xs) ),
    inference(cnf_transformation,[],[f146]) ).

fof(f243,plain,
    ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_56,plain,
    aScalar0(sz0z00),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_64,plain,
    ( ~ aScalar0(X0)
    | sdtasdt0(sz0z00,X0) = sz0z00 ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_86,plain,
    ( ~ aScalar0(X0)
    | sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_96,plain,
    ( aDimensionOf0(X0) != aDimensionOf0(X1)
    | ~ aVector0(X0)
    | ~ aVector0(X1)
    | aScalar0(sdtasasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f194]) ).

cnf(c_97,plain,
    ( aDimensionOf0(X0) != aDimensionOf0(X1)
    | aDimensionOf0(X1) != sz00
    | ~ aVector0(X0)
    | ~ aVector0(X1)
    | sdtasasdt0(X0,X1) = sz0z00 ),
    inference(cnf_transformation,[],[f195]) ).

cnf(c_100,plain,
    aVector0(xt),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_101,plain,
    aVector0(xs),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_103,plain,
    aDimensionOf0(xt) = aDimensionOf0(xs),
    inference(cnf_transformation,[],[f201]) ).

cnf(c_104,plain,
    ( ~ sP4(X0)
    | sP3(X0,sK7(X0),sK8(X0)) ),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_111,plain,
    ( ~ sP3(X0,X1,X2)
    | sP2(X2,sK9(X0,X1,X2),sK11(X0,X1,X2),sK10(X0,X1,X2),X1,X0) ),
    inference(cnf_transformation,[],[f215]) ).

cnf(c_118,plain,
    ( ~ sP2(X0,X1,X2,X3,X4,X5)
    | sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,sK14(X0,X1,X2,X3,X4,X5),X1,X0) ),
    inference(cnf_transformation,[],[f222]) ).

cnf(c_125,plain,
    ( ~ sP1(X0,X1,X2,X3,X4,X5,X6)
    | sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),sK17(X0,X1,X2,X3,X4,X5,X6)) ),
    inference(cnf_transformation,[],[f229]) ).

cnf(c_132,plain,
    ( ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7)
    | sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(cnf_transformation,[],[f237]) ).

cnf(c_136,plain,
    ( ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7)
    | sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = sK19(X0,X1,X2,X3,X4,X5,X6,X7) ),
    inference(cnf_transformation,[],[f233]) ).

cnf(c_140,negated_conjecture,
    ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(cnf_transformation,[],[f243]) ).

cnf(c_141,negated_conjecture,
    ( aDimensionOf0(xs) = sz00
    | sP4(sK20) ),
    inference(cnf_transformation,[],[f242]) ).

cnf(c_246,plain,
    ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7),
    inference(global_subsumption_just,[status(thm)],[c_136,c_140,c_132]) ).

cnf(c_262,plain,
    ~ sP1(X0,X1,X2,X3,X4,X5,X6),
    inference(backward_subsumption_resolution,[status(thm)],[c_125,c_246]) ).

cnf(c_266,plain,
    ~ sP2(X0,X1,X2,X3,X4,X5),
    inference(backward_subsumption_resolution,[status(thm)],[c_118,c_262]) ).

cnf(c_270,plain,
    ~ sP3(X0,X1,X2),
    inference(backward_subsumption_resolution,[status(thm)],[c_111,c_266]) ).

cnf(c_274,plain,
    ~ sP4(X0),
    inference(backward_subsumption_resolution,[status(thm)],[c_104,c_270]) ).

cnf(c_278,plain,
    aDimensionOf0(xs) = sz00,
    inference(backward_subsumption_resolution,[status(thm)],[c_141,c_274]) ).

cnf(c_641,plain,
    aDimensionOf0(xt) = sz00,
    inference(light_normalisation,[status(thm)],[c_103,c_278]) ).

cnf(c_1782,plain,
    sdtasasdt0(xs,xt) = sP3_iProver_def,
    definition ).

cnf(c_1783,plain,
    sdtasdt0(sP3_iProver_def,sP3_iProver_def) = sP4_iProver_def,
    definition ).

cnf(c_1784,plain,
    sdtasasdt0(xs,xs) = sP5_iProver_def,
    definition ).

cnf(c_1785,plain,
    sdtasasdt0(xt,xt) = sP6_iProver_def,
    definition ).

cnf(c_1786,plain,
    sdtasdt0(sP5_iProver_def,sP6_iProver_def) = sP7_iProver_def,
    definition ).

cnf(c_1787,negated_conjecture,
    ~ sdtlseqdt0(sP4_iProver_def,sP7_iProver_def),
    inference(demodulation,[status(thm)],[c_140,c_1785,c_1784,c_1786,c_1782,c_1783]) ).

cnf(c_2885,plain,
    sdtasdt0(sz0z00,sz0z00) = sz0z00,
    inference(superposition,[status(thm)],[c_56,c_64]) ).

cnf(c_2890,plain,
    ( ~ aScalar0(sz0z00)
    | sdtlseqdt0(sz0z00,sz0z00) ),
    inference(superposition,[status(thm)],[c_2885,c_86]) ).

cnf(c_2891,plain,
    sdtlseqdt0(sz0z00,sz0z00),
    inference(forward_subsumption_resolution,[status(thm)],[c_2890,c_56]) ).

cnf(c_3789,plain,
    ( aDimensionOf0(X0) != sz00
    | ~ aVector0(X0)
    | ~ aVector0(xs)
    | aScalar0(sdtasasdt0(xs,X0)) ),
    inference(superposition,[status(thm)],[c_278,c_96]) ).

cnf(c_3793,plain,
    ( ~ aVector0(X0)
    | aScalar0(sdtasasdt0(X0,X0)) ),
    inference(equality_resolution,[status(thm)],[c_96]) ).

cnf(c_3808,plain,
    ( aDimensionOf0(X0) != sz00
    | ~ aVector0(X0)
    | aScalar0(sdtasasdt0(xs,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3789,c_101]) ).

cnf(c_3881,plain,
    ( ~ aVector0(xt)
    | aScalar0(sP6_iProver_def) ),
    inference(superposition,[status(thm)],[c_1785,c_3793]) ).

cnf(c_3906,plain,
    aScalar0(sP6_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_3881,c_100]) ).

cnf(c_4040,plain,
    sdtasdt0(sz0z00,sP6_iProver_def) = sz0z00,
    inference(superposition,[status(thm)],[c_3906,c_64]) ).

cnf(c_4362,plain,
    ( ~ aVector0(xt)
    | aScalar0(sdtasasdt0(xs,xt)) ),
    inference(superposition,[status(thm)],[c_641,c_3808]) ).

cnf(c_4363,plain,
    ( ~ aVector0(xt)
    | aScalar0(sP3_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_4362,c_1782]) ).

cnf(c_4364,plain,
    aScalar0(sP3_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_4363,c_100]) ).

cnf(c_4773,plain,
    sdtasdt0(sz0z00,sP3_iProver_def) = sz0z00,
    inference(superposition,[status(thm)],[c_4364,c_64]) ).

cnf(c_5511,plain,
    ( aDimensionOf0(X0) != sz00
    | ~ aVector0(X0)
    | ~ aVector0(xs)
    | sdtasasdt0(xs,X0) = sz0z00 ),
    inference(superposition,[status(thm)],[c_278,c_97]) ).

cnf(c_5513,plain,
    ( aDimensionOf0(X0) != sz00
    | aDimensionOf0(xs) != sz00
    | ~ aVector0(X0)
    | ~ aVector0(xs)
    | sdtasasdt0(X0,xs) = sz0z00 ),
    inference(superposition,[status(thm)],[c_278,c_97]) ).

cnf(c_5523,plain,
    ( aDimensionOf0(X0) != sz00
    | ~ aVector0(X0)
    | sdtasasdt0(xs,X0) = sz0z00 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5511,c_101]) ).

cnf(c_5531,plain,
    ( aDimensionOf0(X0) != sz00
    | ~ aVector0(X0)
    | sdtasasdt0(X0,xs) = sz0z00 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5513,c_101,c_278]) ).

cnf(c_5746,plain,
    ( ~ aVector0(xs)
    | sdtasasdt0(xs,xs) = sz0z00 ),
    inference(superposition,[status(thm)],[c_278,c_5531]) ).

cnf(c_5749,plain,
    ( ~ aVector0(xs)
    | sz0z00 = sP5_iProver_def ),
    inference(light_normalisation,[status(thm)],[c_5746,c_1784]) ).

cnf(c_5750,plain,
    sz0z00 = sP5_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_5749,c_101]) ).

cnf(c_5768,plain,
    sdtasdt0(sP5_iProver_def,sP6_iProver_def) = sP5_iProver_def,
    inference(demodulation,[status(thm)],[c_4040,c_5750]) ).

cnf(c_5853,plain,
    sP5_iProver_def = sP7_iProver_def,
    inference(light_normalisation,[status(thm)],[c_5768,c_1786]) ).

cnf(c_5857,plain,
    ~ sdtlseqdt0(sP4_iProver_def,sP5_iProver_def),
    inference(demodulation,[status(thm)],[c_1787,c_5853]) ).

cnf(c_5898,plain,
    ( aDimensionOf0(X0) != sz00
    | ~ aVector0(X0)
    | sdtasasdt0(xs,X0) = sP5_iProver_def ),
    inference(light_normalisation,[status(thm)],[c_5523,c_5750]) ).

cnf(c_5906,plain,
    ( ~ aVector0(xt)
    | sdtasasdt0(xs,xt) = sP5_iProver_def ),
    inference(superposition,[status(thm)],[c_641,c_5898]) ).

cnf(c_5907,plain,
    ( ~ aVector0(xt)
    | sP3_iProver_def = sP5_iProver_def ),
    inference(light_normalisation,[status(thm)],[c_5906,c_1782]) ).

cnf(c_5908,plain,
    sP3_iProver_def = sP5_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_5907,c_100]) ).

cnf(c_5910,plain,
    ~ sdtlseqdt0(sP4_iProver_def,sP3_iProver_def),
    inference(demodulation,[status(thm)],[c_5857,c_5908]) ).

cnf(c_5963,plain,
    sz0z00 = sP3_iProver_def,
    inference(light_normalisation,[status(thm)],[c_5750,c_5908]) ).

cnf(c_6175,plain,
    $false,
    inference(smt_impl_just,[status(thm)],[c_5963,c_5910,c_4773,c_2891,c_1783]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n026.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Thu May  2 21:42:51 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.97/1.11  % SZS status Started for theBenchmark.p
% 3.97/1.11  % SZS status Theorem for theBenchmark.p
% 3.97/1.11  
% 3.97/1.11  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.97/1.11  
% 3.97/1.11  ------  iProver source info
% 3.97/1.11  
% 3.97/1.11  git: date: 2024-05-02 19:28:25 +0000
% 3.97/1.11  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.97/1.11  git: non_committed_changes: false
% 3.97/1.11  
% 3.97/1.11  ------ Parsing...
% 3.97/1.11  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.97/1.11  
% 3.97/1.11  ------ Preprocessing... sup_sim: 2  sf_s  rm: 6 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 3.97/1.11  
% 3.97/1.11  ------ Preprocessing... gs_s  sp: 4 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.97/1.11  
% 3.97/1.11  ------ Preprocessing... sf_s  rm: 4 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.97/1.11  ------ Proving...
% 3.97/1.11  ------ Problem Properties 
% 3.97/1.11  
% 3.97/1.11  
% 3.97/1.11  clauses                                 64
% 3.97/1.11  conjectures                             1
% 3.97/1.11  EPR                                     12
% 3.97/1.11  Horn                                    52
% 3.97/1.11  unary                                   13
% 3.97/1.11  binary                                  17
% 3.97/1.11  lits                                    196
% 3.97/1.11  lits eq                                 58
% 3.97/1.11  fd_pure                                 0
% 3.97/1.11  fd_pseudo                               0
% 3.97/1.11  fd_cond                                 1
% 3.97/1.11  fd_pseudo_cond                          5
% 3.97/1.11  AC symbols                              0
% 3.97/1.11  
% 3.97/1.11  ------ Schedule dynamic 5 is on 
% 3.97/1.11  
% 3.97/1.11  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.97/1.11  
% 3.97/1.11  
% 3.97/1.11  ------ 
% 3.97/1.11  Current options:
% 3.97/1.11  ------ 
% 3.97/1.11  
% 3.97/1.11  
% 3.97/1.11  
% 3.97/1.11  
% 3.97/1.11  ------ Proving...
% 3.97/1.11  
% 3.97/1.11  
% 3.97/1.11  % SZS status Theorem for theBenchmark.p
% 3.97/1.11  
% 3.97/1.11  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.97/1.11  
% 3.97/1.12  
%------------------------------------------------------------------------------