TSTP Solution File: RNG081+2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n027.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 Sep 20 03:18:18 EDT 2022

% Result   : Theorem 0.19s 0.42s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   74
% Syntax   : Number of formulae    :  163 (  37 unt;  16 typ;   0 def)
%            Number of atoms       : 1779 ( 861 equ)
%            Maximal formula atoms :   80 (  12 avg)
%            Number of connectives : 2446 ( 943   ~; 772   |; 551   &)
%                                         ( 130 <=>;  50  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   55 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :  129 ( 129 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  12   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  10 usr;   2 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-2 aty)
%            Number of variables   :  276 ( 195   !;  56   ?; 276   :)

% Comments : 
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(sdtasdt0_type,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(sdtasasdt0_type,type,
    sdtasasdt0: ( $i * $i ) > $i ).

tff(xt_type,type,
    xt: $i ).

tff(xs_type,type,
    xs: $i ).

tff(sz0z00_type,type,
    sz0z00: $i ).

tff(smndt0_type,type,
    smndt0: $i > $i ).

tff(sdtpldt0_type,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(aScalar0_type,type,
    aScalar0: $i > $o ).

tff(aDimensionOf0_type,type,
    aDimensionOf0: $i > $i ).

tff(aVector0_type,type,
    aVector0: $i > $o ).

tff(sz00_type,type,
    sz00: $i ).

tff(sdtlbdtrb0_type,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(sziznziztdt0_type,type,
    sziznziztdt0: $i > $i ).

tff(aNaturalNumber0_type,type,
    aNaturalNumber0: $i > $o ).

tff(szszuzczcdt0_type,type,
    szszuzczcdt0: $i > $i ).

tff(1,plain,
    ^ [W0: $i] :
      refl(
        ( ( ~ 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 ) ) )
      <=> ( ~ 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(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [W0: $i] :
        ( ~ 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 ) ) )
  <=> ! [W0: $i] :
        ( ~ 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(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [W0: $i] :
      rewrite(
        ( ( ~ 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 ) ) )
      <=> ( ~ 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(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [W0: $i] :
        ( ~ 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 ) ) )
  <=> ! [W0: $i] :
        ( ~ 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(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ( ! [W0: $i] :
        ( ~ 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 ) ) )
  <=> ! [W0: $i] :
        ( ~ 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(rewrite,[status(thm)],]) ).

tff(6,plain,
    ^ [W0: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              trans(
                monotonicity(
                  trans(
                    monotonicity(
                      trans(
                        monotonicity(
                          trans(
                            monotonicity(
                              rewrite(
                                ( ( ( sdtpldt0(W0,sz0z00) = W0 )
                                  & ( sdtpldt0(sz0z00,W0) = W0 )
                                  & ( sdtasdt0(W0,sz0z00) = sz0z00 ) )
                              <=> ( ( sdtpldt0(W0,sz0z00) = W0 )
                                  & ( sdtpldt0(sz0z00,W0) = W0 )
                                  & ( sdtasdt0(W0,sz0z00) = sz0z00 ) ) )),
                              ( ( ( sdtpldt0(W0,sz0z00) = W0 )
                                & ( sdtpldt0(sz0z00,W0) = W0 )
                                & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                                & ( sdtasdt0(sz0z00,W0) = sz0z00 ) )
                            <=> ( ( sdtpldt0(W0,sz0z00) = W0 )
                                & ( sdtpldt0(sz0z00,W0) = W0 )
                                & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                                & ( sdtasdt0(sz0z00,W0) = sz0z00 ) ) )),
                            rewrite(
                              ( ( ( sdtpldt0(W0,sz0z00) = W0 )
                                & ( sdtpldt0(sz0z00,W0) = W0 )
                                & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                                & ( sdtasdt0(sz0z00,W0) = sz0z00 ) )
                            <=> ( ( sdtpldt0(W0,sz0z00) = W0 )
                                & ( sdtpldt0(sz0z00,W0) = W0 )
                                & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                                & ( sdtasdt0(sz0z00,W0) = sz0z00 ) ) )),
                            ( ( ( sdtpldt0(W0,sz0z00) = W0 )
                              & ( sdtpldt0(sz0z00,W0) = W0 )
                              & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                              & ( sdtasdt0(sz0z00,W0) = sz0z00 ) )
                          <=> ( ( sdtpldt0(W0,sz0z00) = W0 )
                              & ( sdtpldt0(sz0z00,W0) = W0 )
                              & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                              & ( sdtasdt0(sz0z00,W0) = sz0z00 ) ) )),
                          ( ( ( sdtpldt0(W0,sz0z00) = W0 )
                            & ( sdtpldt0(sz0z00,W0) = W0 )
                            & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                            & ( sdtasdt0(sz0z00,W0) = sz0z00 )
                            & ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) )
                        <=> ( ( sdtpldt0(W0,sz0z00) = W0 )
                            & ( sdtpldt0(sz0z00,W0) = W0 )
                            & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                            & ( sdtasdt0(sz0z00,W0) = sz0z00 )
                            & ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) ) )),
                        rewrite(
                          ( ( ( sdtpldt0(W0,sz0z00) = W0 )
                            & ( sdtpldt0(sz0z00,W0) = W0 )
                            & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                            & ( sdtasdt0(sz0z00,W0) = sz0z00 )
                            & ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) )
                        <=> ( ( sdtpldt0(W0,sz0z00) = W0 )
                            & ( sdtpldt0(sz0z00,W0) = W0 )
                            & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                            & ( sdtasdt0(sz0z00,W0) = sz0z00 )
                            & ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) ) )),
                        ( ( ( sdtpldt0(W0,sz0z00) = W0 )
                          & ( sdtpldt0(sz0z00,W0) = W0 )
                          & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                          & ( sdtasdt0(sz0z00,W0) = sz0z00 )
                          & ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) )
                      <=> ( ( sdtpldt0(W0,sz0z00) = W0 )
                          & ( sdtpldt0(sz0z00,W0) = W0 )
                          & ( sdtasdt0(W0,sz0z00) = sz0z00 )
                          & ( sdtasdt0(sz0z00,W0) = sz0z00 )
                          & ( sdtpldt0(W0,smndt0(W0)) = sz0z00 ) ) )),
                      ( ( ( 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 ) )
                    <=> ( ( 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 ) ) )),
                    rewrite(
                      ( ( ( 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 ) )
                    <=> ( ( 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 ) ) )),
                    ( ( ( 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 ) )
                  <=> ( ( 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 ) ) )),
                  ( ( ( 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 ) )
                <=> ( ( 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 ) ) )),
                rewrite(
                  ( ( ( 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 ) )
                <=> ( ( 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 ) ) )),
                ( ( ( 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 ) )
              <=> ( ( 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 ) ) )),
              ( ( ( 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 ) )
            <=> ( ( 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 ) ) )),
            rewrite(
              ( ( ( 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 ) )
            <=> ( ( 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 ) ) )),
            ( ( ( 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 ) )
          <=> ( ( 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 ) ) )),
          ( ( 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 ) ) )
        <=> ( 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 ) ) ) )),
        rewrite(
          ( ( 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 ) ) )
        <=> ( ~ 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 ) ) ) )),
        ( ( 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 ) ) )
      <=> ( ~ 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(bind,[status(th)],]) ).

tff(7,plain,
    ( ! [W0: $i] :
        ( 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 ) ) )
  <=> ! [W0: $i] :
        ( ~ 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(quant_intro,[status(thm)],[6]) ).

tff(8,axiom,
    ! [W0: $i] :
      ( 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/sandbox2/benchmark/theBenchmark.p',mScZero) ).

tff(9,plain,
    ! [W0: $i] :
      ( ~ 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(modus_ponens,[status(thm)],[8,7]) ).

tff(10,plain,
    ! [W0: $i] :
      ( ~ 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(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ! [W0: $i] :
      ( ~ 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(skolemize,[status(sab)],[10]) ).

tff(12,plain,
    ! [W0: $i] :
      ( ~ 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(modus_ponens,[status(thm)],[11,4]) ).

tff(13,plain,
    ! [W0: $i] :
      ( ~ 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(modus_ponens,[status(thm)],[12,2]) ).

tff(14,plain,
    ( aScalar0(sz0z00)
  <=> aScalar0(sz0z00) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).

tff(16,plain,
    aScalar0(sz0z00),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ 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 ) ) )
      | ~ aScalar0(sz0z00)
      | ~ ( ( smndt0(sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
          | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
          | ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ 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 ) ) )
      | ~ aScalar0(sz0z00)
      | ~ ( ( smndt0(sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
          | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
          | ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ( ~ aScalar0(sz0z00)
      | ~ ( ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
          | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
          | ( smndt0(smndt0(sz0z00)) != sz0z00 )
          | ( smndt0(sz0z00) != sz0z00 ) ) )
  <=> ( ~ aScalar0(sz0z00)
      | ~ ( ( smndt0(sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
          | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
          | ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ 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 ) ) )
      | ~ aScalar0(sz0z00)
      | ~ ( ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
          | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
          | ( smndt0(smndt0(sz0z00)) != sz0z00 )
          | ( smndt0(sz0z00) != sz0z00 ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ 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 ) ) )
      | ~ aScalar0(sz0z00)
      | ~ ( ( smndt0(sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
          | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
          | ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ) ),
    inference(monotonicity,[status(thm)],[18]) ).

tff(20,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ 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 ) ) )
      | ~ aScalar0(sz0z00)
      | ~ ( ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
          | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
          | ( smndt0(smndt0(sz0z00)) != sz0z00 )
          | ( smndt0(sz0z00) != sz0z00 ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ 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 ) ) )
      | ~ aScalar0(sz0z00)
      | ~ ( ( smndt0(sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
          | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
          | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
          | ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ) ),
    inference(transitivity,[status(thm)],[19,17]) ).

tff(21,plain,
    ( ~ ! [W0: $i] :
          ( ~ 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 ) ) )
    | ~ aScalar0(sz0z00)
    | ~ ( ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
        | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
        | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
        | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
        | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
        | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
        | ( smndt0(smndt0(sz0z00)) != sz0z00 )
        | ( smndt0(sz0z00) != sz0z00 ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(22,plain,
    ( ~ ! [W0: $i] :
          ( ~ 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 ) ) )
    | ~ aScalar0(sz0z00)
    | ~ ( ( smndt0(sz0z00) != sz0z00 )
        | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
        | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
        | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
        | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
        | ( smndt0(smndt0(sz0z00)) != sz0z00 ) ) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ~ ( ( smndt0(sz0z00) != sz0z00 )
      | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
      | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
      | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
      | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
      | ( smndt0(smndt0(sz0z00)) != sz0z00 ) ),
    inference(unit_resolution,[status(thm)],[22,16,13]) ).

tff(24,plain,
    ( ( smndt0(sz0z00) != sz0z00 )
    | ( sdtpldt0(sz0z00,sz0z00) != sz0z00 )
    | ( sdtasdt0(sz0z00,sz0z00) != sz0z00 )
    | ( sdtpldt0(sz0z00,smndt0(sz0z00)) != sz0z00 )
    | ( sdtpldt0(smndt0(sz0z00),sz0z00) != sz0z00 )
    | ( smndt0(smndt0(sz0z00)) != sz0z00 )
    | ( sdtasdt0(sz0z00,sz0z00) = sz0z00 ) ),
    inference(tautology,[status(thm)],]) ).

tff(25,plain,
    sdtasdt0(sz0z00,sz0z00) = sz0z00,
    inference(unit_resolution,[status(thm)],[24,23]) ).

tff(26,plain,
    ( ( aDimensionOf0(xs) = aDimensionOf0(xt) )
  <=> ( aDimensionOf0(xs) = aDimensionOf0(xt) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,axiom,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).

tff(28,plain,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    aDimensionOf0(xt) = aDimensionOf0(xs),
    inference(symmetry,[status(thm)],[28]) ).

tff(30,plain,
    ( aVector0(xt)
  <=> aVector0(xt) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,axiom,
    ( aVector0(xs)
    & aVector0(xt) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).

tff(32,plain,
    aVector0(xt),
    inference(and_elim,[status(thm)],[31]) ).

tff(33,plain,
    aVector0(xt),
    inference(modus_ponens,[status(thm)],[32,30]) ).

tff(34,plain,
    ( aVector0(xs)
  <=> aVector0(xs) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    aVector0(xs),
    inference(and_elim,[status(thm)],[31]) ).

tff(36,plain,
    aVector0(xs),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ^ [W0: $i,W1: $i] :
      refl(
        ( ( ( sdtasasdt0(W0,W1) = sz0z00 )
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
          | ~ aVector0(W0) )
      <=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
          | ~ aVector0(W0) ) )),
    inference(bind,[status(th)],]) ).

tff(38,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( sdtasasdt0(W0,W1) = sz0z00 )
        | ~ aVector0(W1)
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
        | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
        | ~ aVector0(W0) )
  <=> ! [W0: $i,W1: $i] :
        ( ( sdtasasdt0(W0,W1) = sz0z00 )
        | ~ aVector0(W1)
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
        | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
        | ~ aVector0(W0) ) ),
    inference(quant_intro,[status(thm)],[37]) ).

tff(39,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( aVector0(W0)
                  & aVector0(W1) )
              <=> ~ ( ~ aVector0(W1)
                    | ~ aVector0(W0) ) )),
              ( ~ ( aVector0(W0)
                  & aVector0(W1) )
            <=> ~ ~ ( ~ aVector0(W1)
                    | ~ aVector0(W0) ) )),
            rewrite(
              ( ~ ~ ( ~ aVector0(W1)
                    | ~ aVector0(W0) )
            <=> ( ~ aVector0(W1)
                | ~ aVector0(W0) ) )),
            ( ~ ( aVector0(W0)
                & aVector0(W1) )
          <=> ( ~ aVector0(W1)
              | ~ aVector0(W0) ) )),
          trans(
            monotonicity(
              rewrite(
                ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                  & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) )
              <=> ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
                    | ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
              ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                  & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) )
            <=> ~ ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
                    | ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
            rewrite(
              ( ~ ~ ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
                    | ( aDimensionOf0(W1) != aDimensionOf0(xs) ) )
            <=> ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
                | ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
            ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) )
          <=> ( ( aDimensionOf0(W0) != aDimensionOf0(W1) )
              | ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
          ( ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ ( aVector0(W0)
                & aVector0(W1) )
            | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )
        <=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ aVector0(W1)
            | ~ aVector0(W0)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ( aDimensionOf0(W1) != aDimensionOf0(xs) ) ) )),
        rewrite(
          ( ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ aVector0(W1)
            | ~ aVector0(W0)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ( aDimensionOf0(W1) != aDimensionOf0(xs) ) )
        <=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
            | ~ aVector0(W0) ) )),
        ( ( ( sdtasasdt0(W0,W1) = sz0z00 )
          | ~ ( aVector0(W0)
              & aVector0(W1) )
          | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
              & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )
      <=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
          | ~ aVector0(W0) ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( sdtasasdt0(W0,W1) = sz0z00 )
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
            & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( sdtasasdt0(W0,W1) = sz0z00 )
        | ~ aVector0(W1)
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
        | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
        | ~ aVector0(W0) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = sz00 ) )
          <=> ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )),
          ( ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ ( aVector0(W0)
                & aVector0(W1) )
            | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = sz00 ) ) )
        <=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ ( aVector0(W0)
                & aVector0(W1) )
            | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ) )),
        rewrite(
          ( ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ ( aVector0(W0)
                & aVector0(W1) )
            | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) )
        <=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ ( aVector0(W0)
                & aVector0(W1) )
            | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ) )),
        ( ( ( sdtasasdt0(W0,W1) = sz0z00 )
          | ~ ( aVector0(W0)
              & aVector0(W1) )
          | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
              & ( aDimensionOf0(W1) = sz00 ) ) )
      <=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
          | ~ ( aVector0(W0)
              & aVector0(W1) )
          | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
              & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(42,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( sdtasasdt0(W0,W1) = sz0z00 )
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
            & ( aDimensionOf0(W1) = sz00 ) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( sdtasasdt0(W0,W1) = sz0z00 )
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
            & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ) ),
    inference(quant_intro,[status(thm)],[41]) ).

tff(43,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( sdtasasdt0(W0,W1) = sz0z00 )
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
            & ( aDimensionOf0(W1) = sz00 ) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( sdtasasdt0(W0,W1) = sz0z00 )
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
            & ( aDimensionOf0(W1) = sz00 ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = sz00 ) )
             => ( sdtasasdt0(W0,W1) = sz0z00 ) )
          <=> ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                  & ( aDimensionOf0(W1) = sz00 ) )
              | ( sdtasasdt0(W0,W1) = sz0z00 ) ) )),
          ( ( ( aVector0(W0)
              & aVector0(W1) )
           => ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = sz00 ) )
             => ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
        <=> ( ( aVector0(W0)
              & aVector0(W1) )
           => ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                  & ( aDimensionOf0(W1) = sz00 ) )
              | ( sdtasasdt0(W0,W1) = sz0z00 ) ) ) )),
        rewrite(
          ( ( ( aVector0(W0)
              & aVector0(W1) )
           => ( ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                  & ( aDimensionOf0(W1) = sz00 ) )
              | ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
        <=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ ( aVector0(W0)
                & aVector0(W1) )
            | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
                & ( aDimensionOf0(W1) = sz00 ) ) ) )),
        ( ( ( aVector0(W0)
            & aVector0(W1) )
         => ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
              & ( aDimensionOf0(W1) = sz00 ) )
           => ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
      <=> ( ( sdtasasdt0(W0,W1) = sz0z00 )
          | ~ ( aVector0(W0)
              & aVector0(W1) )
          | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
              & ( aDimensionOf0(W1) = sz00 ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(45,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( aVector0(W0)
          & aVector0(W1) )
       => ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
            & ( aDimensionOf0(W1) = sz00 ) )
         => ( sdtasasdt0(W0,W1) = sz0z00 ) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( sdtasasdt0(W0,W1) = sz0z00 )
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
            & ( aDimensionOf0(W1) = sz00 ) ) ) ),
    inference(quant_intro,[status(thm)],[44]) ).

tff(46,axiom,
    ! [W0: $i,W1: $i] :
      ( ( aVector0(W0)
        & aVector0(W1) )
     => ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
          & ( aDimensionOf0(W1) = sz00 ) )
       => ( sdtasasdt0(W0,W1) = sz0z00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).

tff(47,plain,
    ! [W0: $i,W1: $i] :
      ( ( sdtasasdt0(W0,W1) = sz0z00 )
      | ~ ( aVector0(W0)
          & aVector0(W1) )
      | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
          & ( aDimensionOf0(W1) = sz00 ) ) ),
    inference(modus_ponens,[status(thm)],[46,45]) ).

tff(48,plain,
    ! [W0: $i,W1: $i] :
      ( ( sdtasasdt0(W0,W1) = sz0z00 )
      | ~ ( aVector0(W0)
          & aVector0(W1) )
      | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
          & ( aDimensionOf0(W1) = sz00 ) ) ),
    inference(modus_ponens,[status(thm)],[47,43]) ).

tff(49,plain,
    ! [W0: $i,W1: $i] :
      ( ( sdtasasdt0(W0,W1) = sz0z00 )
      | ~ ( aVector0(W0)
          & aVector0(W1) )
      | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
          & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ),
    inference(modus_ponens,[status(thm)],[48,42]) ).

tff(50,plain,
    ! [W0: $i,W1: $i] :
      ( ( sdtasasdt0(W0,W1) = sz0z00 )
      | ~ ( aVector0(W0)
          & aVector0(W1) )
      | ~ ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
          & ( aDimensionOf0(W1) = aDimensionOf0(xs) ) ) ),
    inference(skolemize,[status(sab)],[49]) ).

tff(51,plain,
    ! [W0: $i,W1: $i] :
      ( ( sdtasasdt0(W0,W1) = sz0z00 )
      | ~ aVector0(W1)
      | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
      | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
      | ~ aVector0(W0) ),
    inference(modus_ponens,[status(thm)],[50,40]) ).

tff(52,plain,
    ! [W0: $i,W1: $i] :
      ( ( sdtasasdt0(W0,W1) = sz0z00 )
      | ~ aVector0(W1)
      | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
      | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
      | ~ aVector0(W0) ),
    inference(modus_ponens,[status(thm)],[51,38]) ).

tff(53,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
            | ~ aVector0(W0) )
      | ~ aVector0(xt)
      | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
      | ~ aVector0(xs)
      | ( sdtasasdt0(xs,xt) = sz0z00 )
      | ( aDimensionOf0(xt) != aDimensionOf0(xs) ) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
            | ~ aVector0(W0) )
      | ~ aVector0(xt)
      | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
      | ~ aVector0(xs)
      | ( sdtasasdt0(xs,xt) = sz0z00 )
      | ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ( ( ( sdtasasdt0(xs,xt) = sz0z00 )
      | ~ aVector0(xt)
      | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
      | ( aDimensionOf0(xt) != aDimensionOf0(xs) )
      | ~ aVector0(xs) )
  <=> ( ~ aVector0(xt)
      | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
      | ~ aVector0(xs)
      | ( sdtasasdt0(xs,xt) = sz0z00 )
      | ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
            | ~ aVector0(W0) )
      | ( sdtasasdt0(xs,xt) = sz0z00 )
      | ~ aVector0(xt)
      | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
      | ( aDimensionOf0(xt) != aDimensionOf0(xs) )
      | ~ aVector0(xs) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
            | ~ aVector0(W0) )
      | ~ aVector0(xt)
      | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
      | ~ aVector0(xs)
      | ( sdtasasdt0(xs,xt) = sz0z00 )
      | ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
    inference(monotonicity,[status(thm)],[54]) ).

tff(56,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
            | ~ aVector0(W0) )
      | ( sdtasasdt0(xs,xt) = sz0z00 )
      | ~ aVector0(xt)
      | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
      | ( aDimensionOf0(xt) != aDimensionOf0(xs) )
      | ~ aVector0(xs) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( ( sdtasasdt0(W0,W1) = sz0z00 )
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
            | ~ aVector0(W0) )
      | ~ aVector0(xt)
      | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
      | ~ aVector0(xs)
      | ( sdtasasdt0(xs,xt) = sz0z00 )
      | ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ) ),
    inference(transitivity,[status(thm)],[55,53]) ).

tff(57,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( ( sdtasasdt0(W0,W1) = sz0z00 )
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
          | ~ aVector0(W0) )
    | ( sdtasasdt0(xs,xt) = sz0z00 )
    | ~ aVector0(xt)
    | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
    | ( aDimensionOf0(xt) != aDimensionOf0(xs) )
    | ~ aVector0(xs) ),
    inference(quant_inst,[status(thm)],]) ).

tff(58,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( ( sdtasasdt0(W0,W1) = sz0z00 )
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ( aDimensionOf0(W1) != aDimensionOf0(xs) )
          | ~ aVector0(W0) )
    | ~ aVector0(xt)
    | ( aDimensionOf0(xs) != aDimensionOf0(xt) )
    | ~ aVector0(xs)
    | ( sdtasasdt0(xs,xt) = sz0z00 )
    | ( aDimensionOf0(xt) != aDimensionOf0(xs) ) ),
    inference(modus_ponens,[status(thm)],[57,56]) ).

tff(59,plain,
    sdtasasdt0(xs,xt) = sz0z00,
    inference(unit_resolution,[status(thm)],[58,52,36,33,28,29]) ).

tff(60,plain,
    sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)) = sdtasdt0(sz0z00,sz0z00),
    inference(monotonicity,[status(thm)],[59,59]) ).

tff(61,plain,
    sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)) = sz0z00,
    inference(transitivity,[status(thm)],[60,25]) ).

tff(62,plain,
    ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
  <=> sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(monotonicity,[status(thm)],[61]) ).

tff(63,plain,
    ( sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
  <=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(symmetry,[status(thm)],[62]) ).

tff(64,plain,
    ^ [W0: $i] :
      refl(
        ( ( ~ aVector0(W0)
          | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
      <=> ( ~ aVector0(W0)
          | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )),
    inference(bind,[status(th)],]) ).

tff(65,plain,
    ( ! [W0: $i] :
        ( ~ aVector0(W0)
        | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
  <=> ! [W0: $i] :
        ( ~ aVector0(W0)
        | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
    inference(quant_intro,[status(thm)],[64]) ).

tff(66,plain,
    ( ! [W0: $i] :
        ( ~ aVector0(W0)
        | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
  <=> ! [W0: $i] :
        ( ~ aVector0(W0)
        | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,plain,
    ^ [W0: $i] :
      rewrite(
        ( ( aVector0(W0)
         => sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
      <=> ( ~ aVector0(W0)
          | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) )),
    inference(bind,[status(th)],]) ).

tff(68,plain,
    ( ! [W0: $i] :
        ( aVector0(W0)
       => sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
  <=> ! [W0: $i] :
        ( ~ aVector0(W0)
        | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ) ),
    inference(quant_intro,[status(thm)],[67]) ).

tff(69,axiom,
    ! [W0: $i] :
      ( aVector0(W0)
     => sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).

tff(70,plain,
    ! [W0: $i] :
      ( ~ aVector0(W0)
      | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
    inference(modus_ponens,[status(thm)],[69,68]) ).

tff(71,plain,
    ! [W0: $i] :
      ( ~ aVector0(W0)
      | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
    inference(modus_ponens,[status(thm)],[70,66]) ).

tff(72,plain,
    ! [W0: $i] :
      ( ~ aVector0(W0)
      | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
    inference(skolemize,[status(sab)],[71]) ).

tff(73,plain,
    ! [W0: $i] :
      ( ~ aVector0(W0)
      | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) ),
    inference(modus_ponens,[status(thm)],[72,65]) ).

tff(74,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aVector0(W0)
            | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
      | ~ aVector0(xt)
      | sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aVector0(W0)
            | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
      | ~ aVector0(xt)
      | sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(75,plain,
    ( ~ ! [W0: $i] :
          ( ~ aVector0(W0)
          | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
    | ~ aVector0(xt)
    | sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(76,plain,
    ( ~ ! [W0: $i] :
          ( ~ aVector0(W0)
          | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
    | ~ aVector0(xt)
    | sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
    inference(modus_ponens,[status(thm)],[75,74]) ).

tff(77,plain,
    sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)),
    inference(unit_resolution,[status(thm)],[76,73,33]) ).

tff(78,plain,
    ^ [W0: $i,W1: $i] :
      refl(
        ( ( aScalar0(sdtasasdt0(W0,W1))
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ~ aVector0(W0) )
      <=> ( aScalar0(sdtasasdt0(W0,W1))
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ~ aVector0(W0) ) )),
    inference(bind,[status(th)],]) ).

tff(79,plain,
    ( ! [W0: $i,W1: $i] :
        ( aScalar0(sdtasasdt0(W0,W1))
        | ~ aVector0(W1)
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
        | ~ aVector0(W0) )
  <=> ! [W0: $i,W1: $i] :
        ( aScalar0(sdtasasdt0(W0,W1))
        | ~ aVector0(W1)
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
        | ~ aVector0(W0) ) ),
    inference(quant_intro,[status(thm)],[78]) ).

tff(80,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( aVector0(W0)
                  & aVector0(W1) )
              <=> ~ ( ~ aVector0(W1)
                    | ~ aVector0(W0) ) )),
              ( ~ ( aVector0(W0)
                  & aVector0(W1) )
            <=> ~ ~ ( ~ aVector0(W1)
                    | ~ aVector0(W0) ) )),
            rewrite(
              ( ~ ~ ( ~ aVector0(W1)
                    | ~ aVector0(W0) )
            <=> ( ~ aVector0(W1)
                | ~ aVector0(W0) ) )),
            ( ~ ( aVector0(W0)
                & aVector0(W1) )
          <=> ( ~ aVector0(W1)
              | ~ aVector0(W0) ) )),
          ( ( aScalar0(sdtasasdt0(W0,W1))
            | ~ ( aVector0(W0)
                & aVector0(W1) )
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
        <=> ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ~ aVector0(W0)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
        rewrite(
          ( ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ~ aVector0(W0)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
        <=> ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) ) )),
        ( ( aScalar0(sdtasasdt0(W0,W1))
          | ~ ( aVector0(W0)
              & aVector0(W1) )
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
      <=> ( aScalar0(sdtasasdt0(W0,W1))
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ~ aVector0(W0) ) )),
    inference(bind,[status(th)],]) ).

tff(81,plain,
    ( ! [W0: $i,W1: $i] :
        ( aScalar0(sdtasasdt0(W0,W1))
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
  <=> ! [W0: $i,W1: $i] :
        ( aScalar0(sdtasasdt0(W0,W1))
        | ~ aVector0(W1)
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
        | ~ aVector0(W0) ) ),
    inference(quant_intro,[status(thm)],[80]) ).

tff(82,plain,
    ( ! [W0: $i,W1: $i] :
        ( aScalar0(sdtasasdt0(W0,W1))
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) )
  <=> ! [W0: $i,W1: $i] :
        ( aScalar0(sdtasasdt0(W0,W1))
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(83,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
             => aScalar0(sdtasasdt0(W0,W1)) )
          <=> ( aScalar0(sdtasasdt0(W0,W1))
              | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
          ( ( ( aVector0(W0)
              & aVector0(W1) )
           => ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
             => aScalar0(sdtasasdt0(W0,W1)) ) )
        <=> ( ( aVector0(W0)
              & aVector0(W1) )
           => ( aScalar0(sdtasasdt0(W0,W1))
              | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) ) )),
        rewrite(
          ( ( ( aVector0(W0)
              & aVector0(W1) )
           => ( aScalar0(sdtasasdt0(W0,W1))
              | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )
        <=> ( aScalar0(sdtasasdt0(W0,W1))
            | ~ ( aVector0(W0)
                & aVector0(W1) )
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
        ( ( ( aVector0(W0)
            & aVector0(W1) )
         => ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
           => aScalar0(sdtasasdt0(W0,W1)) ) )
      <=> ( aScalar0(sdtasasdt0(W0,W1))
          | ~ ( aVector0(W0)
              & aVector0(W1) )
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) )),
    inference(bind,[status(th)],]) ).

tff(84,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( aVector0(W0)
          & aVector0(W1) )
       => ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
         => aScalar0(sdtasasdt0(W0,W1)) ) )
  <=> ! [W0: $i,W1: $i] :
        ( aScalar0(sdtasasdt0(W0,W1))
        | ~ ( aVector0(W0)
            & aVector0(W1) )
        | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ) ),
    inference(quant_intro,[status(thm)],[83]) ).

tff(85,axiom,
    ! [W0: $i,W1: $i] :
      ( ( aVector0(W0)
        & aVector0(W1) )
     => ( ( aDimensionOf0(W0) = aDimensionOf0(W1) )
       => aScalar0(sdtasasdt0(W0,W1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).

tff(86,plain,
    ! [W0: $i,W1: $i] :
      ( aScalar0(sdtasasdt0(W0,W1))
      | ~ ( aVector0(W0)
          & aVector0(W1) )
      | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
    inference(modus_ponens,[status(thm)],[85,84]) ).

tff(87,plain,
    ! [W0: $i,W1: $i] :
      ( aScalar0(sdtasasdt0(W0,W1))
      | ~ ( aVector0(W0)
          & aVector0(W1) )
      | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
    inference(modus_ponens,[status(thm)],[86,82]) ).

tff(88,plain,
    ! [W0: $i,W1: $i] :
      ( aScalar0(sdtasasdt0(W0,W1))
      | ~ ( aVector0(W0)
          & aVector0(W1) )
      | ( aDimensionOf0(W0) != aDimensionOf0(W1) ) ),
    inference(skolemize,[status(sab)],[87]) ).

tff(89,plain,
    ! [W0: $i,W1: $i] :
      ( aScalar0(sdtasasdt0(W0,W1))
      | ~ aVector0(W1)
      | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
      | ~ aVector0(W0) ),
    inference(modus_ponens,[status(thm)],[88,81]) ).

tff(90,plain,
    ! [W0: $i,W1: $i] :
      ( aScalar0(sdtasasdt0(W0,W1))
      | ~ aVector0(W1)
      | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
      | ~ aVector0(W0) ),
    inference(modus_ponens,[status(thm)],[89,79]) ).

tff(91,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(92,plain,
    ( ( aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs)
      | $false
      | ~ aVector0(xs) )
  <=> ( aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(93,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(94,plain,
    ( ( aDimensionOf0(xs) = aDimensionOf0(xs) )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(95,plain,
    ( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[94]) ).

tff(96,plain,
    ( ( aDimensionOf0(xs) != aDimensionOf0(xs) )
  <=> $false ),
    inference(transitivity,[status(thm)],[95,93]) ).

tff(97,plain,
    ( ( aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs)
      | ( aDimensionOf0(xs) != aDimensionOf0(xs) )
      | ~ aVector0(xs) )
  <=> ( aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs)
      | $false
      | ~ aVector0(xs) ) ),
    inference(monotonicity,[status(thm)],[96]) ).

tff(98,plain,
    ( ( aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs)
      | ( aDimensionOf0(xs) != aDimensionOf0(xs) )
      | ~ aVector0(xs) )
  <=> ( aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs) ) ),
    inference(transitivity,[status(thm)],[97,92]) ).

tff(99,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs)
      | ( aDimensionOf0(xs) != aDimensionOf0(xs) )
      | ~ aVector0(xs) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs) ) ),
    inference(monotonicity,[status(thm)],[98]) ).

tff(100,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs)
      | ( aDimensionOf0(xs) != aDimensionOf0(xs) )
      | ~ aVector0(xs) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xs,xs))
      | ~ aVector0(xs) ) ),
    inference(transitivity,[status(thm)],[99,91]) ).

tff(101,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( aScalar0(sdtasasdt0(W0,W1))
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ~ aVector0(W0) )
    | aScalar0(sdtasasdt0(xs,xs))
    | ~ aVector0(xs)
    | ( aDimensionOf0(xs) != aDimensionOf0(xs) )
    | ~ aVector0(xs) ),
    inference(quant_inst,[status(thm)],]) ).

tff(102,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( aScalar0(sdtasasdt0(W0,W1))
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ~ aVector0(W0) )
    | aScalar0(sdtasasdt0(xs,xs))
    | ~ aVector0(xs) ),
    inference(modus_ponens,[status(thm)],[101,100]) ).

tff(103,plain,
    aScalar0(sdtasasdt0(xs,xs)),
    inference(unit_resolution,[status(thm)],[102,90,36]) ).

tff(104,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aVector0(W0)
            | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
      | ~ aVector0(xs)
      | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aVector0(W0)
            | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
      | ~ aVector0(xs)
      | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(105,plain,
    ( ~ ! [W0: $i] :
          ( ~ aVector0(W0)
          | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
    | ~ aVector0(xs)
    | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(106,plain,
    ( ~ ! [W0: $i] :
          ( ~ aVector0(W0)
          | sdtlseqdt0(sz0z00,sdtasasdt0(W0,W0)) )
    | ~ aVector0(xs)
    | sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(modus_ponens,[status(thm)],[105,104]) ).

tff(107,plain,
    sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
    inference(unit_resolution,[status(thm)],[106,73,36]) ).

tff(108,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(109,plain,
    ( ( aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt)
      | $false
      | ~ aVector0(xt) )
  <=> ( aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(110,plain,
    ( ( aDimensionOf0(xt) = aDimensionOf0(xt) )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(111,plain,
    ( ( aDimensionOf0(xt) != aDimensionOf0(xt) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[110]) ).

tff(112,plain,
    ( ( aDimensionOf0(xt) != aDimensionOf0(xt) )
  <=> $false ),
    inference(transitivity,[status(thm)],[111,93]) ).

tff(113,plain,
    ( ( aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt)
      | ( aDimensionOf0(xt) != aDimensionOf0(xt) )
      | ~ aVector0(xt) )
  <=> ( aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt)
      | $false
      | ~ aVector0(xt) ) ),
    inference(monotonicity,[status(thm)],[112]) ).

tff(114,plain,
    ( ( aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt)
      | ( aDimensionOf0(xt) != aDimensionOf0(xt) )
      | ~ aVector0(xt) )
  <=> ( aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt) ) ),
    inference(transitivity,[status(thm)],[113,109]) ).

tff(115,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt)
      | ( aDimensionOf0(xt) != aDimensionOf0(xt) )
      | ~ aVector0(xt) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt) ) ),
    inference(monotonicity,[status(thm)],[114]) ).

tff(116,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt)
      | ( aDimensionOf0(xt) != aDimensionOf0(xt) )
      | ~ aVector0(xt) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( aScalar0(sdtasasdt0(W0,W1))
            | ~ aVector0(W1)
            | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
            | ~ aVector0(W0) )
      | aScalar0(sdtasasdt0(xt,xt))
      | ~ aVector0(xt) ) ),
    inference(transitivity,[status(thm)],[115,108]) ).

tff(117,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( aScalar0(sdtasasdt0(W0,W1))
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ~ aVector0(W0) )
    | aScalar0(sdtasasdt0(xt,xt))
    | ~ aVector0(xt)
    | ( aDimensionOf0(xt) != aDimensionOf0(xt) )
    | ~ aVector0(xt) ),
    inference(quant_inst,[status(thm)],]) ).

tff(118,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( aScalar0(sdtasasdt0(W0,W1))
          | ~ aVector0(W1)
          | ( aDimensionOf0(W0) != aDimensionOf0(W1) )
          | ~ aVector0(W0) )
    | aScalar0(sdtasasdt0(xt,xt))
    | ~ aVector0(xt) ),
    inference(modus_ponens,[status(thm)],[117,116]) ).

tff(119,plain,
    aScalar0(sdtasasdt0(xt,xt)),
    inference(unit_resolution,[status(thm)],[118,90,33]) ).

tff(120,plain,
    ^ [W0: $i,W1: $i] :
      refl(
        ( ( ~ aScalar0(W1)
          | ~ aScalar0(W0)
          | ~ sdtlseqdt0(sz0z00,W0)
          | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
              | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
          | ~ sdtlseqdt0(sz0z00,W1) )
      <=> ( ~ aScalar0(W1)
          | ~ aScalar0(W0)
          | ~ sdtlseqdt0(sz0z00,W0)
          | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
              | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
          | ~ sdtlseqdt0(sz0z00,W1) ) )),
    inference(bind,[status(th)],]) ).

tff(121,plain,
    ( ! [W0: $i,W1: $i] :
        ( ~ aScalar0(W1)
        | ~ aScalar0(W0)
        | ~ sdtlseqdt0(sz0z00,W0)
        | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
            | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
        | ~ sdtlseqdt0(sz0z00,W1) )
  <=> ! [W0: $i,W1: $i] :
        ( ~ aScalar0(W1)
        | ~ aScalar0(W0)
        | ~ sdtlseqdt0(sz0z00,W0)
        | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
            | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
        | ~ sdtlseqdt0(sz0z00,W1) ) ),
    inference(quant_intro,[status(thm)],[120]) ).

tff(122,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
              & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
          <=> ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) )),
          trans(
            monotonicity(
              rewrite(
                ( ( aScalar0(W0)
                  & aScalar0(W1) )
              <=> ~ ( ~ aScalar0(W1)
                    | ~ aScalar0(W0) ) )),
              ( ~ ( aScalar0(W0)
                  & aScalar0(W1) )
            <=> ~ ~ ( ~ aScalar0(W1)
                    | ~ aScalar0(W0) ) )),
            rewrite(
              ( ~ ~ ( ~ aScalar0(W1)
                    | ~ aScalar0(W0) )
            <=> ( ~ aScalar0(W1)
                | ~ aScalar0(W0) ) )),
            ( ~ ( aScalar0(W0)
                & aScalar0(W1) )
          <=> ( ~ aScalar0(W1)
              | ~ aScalar0(W0) ) )),
          trans(
            monotonicity(
              rewrite(
                ( ( sdtlseqdt0(sz0z00,W0)
                  & sdtlseqdt0(sz0z00,W1) )
              <=> ~ ( ~ sdtlseqdt0(sz0z00,W0)
                    | ~ sdtlseqdt0(sz0z00,W1) ) )),
              ( ~ ( sdtlseqdt0(sz0z00,W0)
                  & sdtlseqdt0(sz0z00,W1) )
            <=> ~ ~ ( ~ sdtlseqdt0(sz0z00,W0)
                    | ~ sdtlseqdt0(sz0z00,W1) ) )),
            rewrite(
              ( ~ ~ ( ~ sdtlseqdt0(sz0z00,W0)
                    | ~ sdtlseqdt0(sz0z00,W1) )
            <=> ( ~ sdtlseqdt0(sz0z00,W0)
                | ~ sdtlseqdt0(sz0z00,W1) ) )),
            ( ~ ( sdtlseqdt0(sz0z00,W0)
                & sdtlseqdt0(sz0z00,W1) )
          <=> ( ~ sdtlseqdt0(sz0z00,W0)
              | ~ sdtlseqdt0(sz0z00,W1) ) )),
          ( ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
              & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
            | ~ ( aScalar0(W0)
                & aScalar0(W1) )
            | ~ ( sdtlseqdt0(sz0z00,W0)
                & sdtlseqdt0(sz0z00,W1) ) )
        <=> ( ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
            | ~ aScalar0(W1)
            | ~ aScalar0(W0)
            | ~ sdtlseqdt0(sz0z00,W0)
            | ~ sdtlseqdt0(sz0z00,W1) ) )),
        rewrite(
          ( ( ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
            | ~ aScalar0(W1)
            | ~ aScalar0(W0)
            | ~ sdtlseqdt0(sz0z00,W0)
            | ~ sdtlseqdt0(sz0z00,W1) )
        <=> ( ~ aScalar0(W1)
            | ~ aScalar0(W0)
            | ~ sdtlseqdt0(sz0z00,W0)
            | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
            | ~ sdtlseqdt0(sz0z00,W1) ) )),
        ( ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
            & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
          | ~ ( aScalar0(W0)
              & aScalar0(W1) )
          | ~ ( sdtlseqdt0(sz0z00,W0)
              & sdtlseqdt0(sz0z00,W1) ) )
      <=> ( ~ aScalar0(W1)
          | ~ aScalar0(W0)
          | ~ sdtlseqdt0(sz0z00,W0)
          | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
              | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
          | ~ sdtlseqdt0(sz0z00,W1) ) )),
    inference(bind,[status(th)],]) ).

tff(123,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
          & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
        | ~ ( aScalar0(W0)
            & aScalar0(W1) )
        | ~ ( sdtlseqdt0(sz0z00,W0)
            & sdtlseqdt0(sz0z00,W1) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ~ aScalar0(W1)
        | ~ aScalar0(W0)
        | ~ sdtlseqdt0(sz0z00,W0)
        | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
            | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
        | ~ sdtlseqdt0(sz0z00,W1) ) ),
    inference(quant_intro,[status(thm)],[122]) ).

tff(124,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
          & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
        | ~ ( aScalar0(W0)
            & aScalar0(W1) )
        | ~ ( sdtlseqdt0(sz0z00,W0)
            & sdtlseqdt0(sz0z00,W1) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
          & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
        | ~ ( aScalar0(W0)
            & aScalar0(W1) )
        | ~ ( sdtlseqdt0(sz0z00,W0)
            & sdtlseqdt0(sz0z00,W1) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(125,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ( sdtlseqdt0(sz0z00,W0)
                & sdtlseqdt0(sz0z00,W1) )
             => ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) )
          <=> ( ~ ( sdtlseqdt0(sz0z00,W0)
                  & sdtlseqdt0(sz0z00,W1) )
              | ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )),
          ( ( ( aScalar0(W0)
              & aScalar0(W1) )
           => ( ( sdtlseqdt0(sz0z00,W0)
                & sdtlseqdt0(sz0z00,W1) )
             => ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
        <=> ( ( aScalar0(W0)
              & aScalar0(W1) )
           => ( ~ ( sdtlseqdt0(sz0z00,W0)
                  & sdtlseqdt0(sz0z00,W1) )
              | ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ) )),
        rewrite(
          ( ( ( aScalar0(W0)
              & aScalar0(W1) )
           => ( ~ ( sdtlseqdt0(sz0z00,W0)
                  & sdtlseqdt0(sz0z00,W1) )
              | ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
        <=> ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
              & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
            | ~ ( aScalar0(W0)
                & aScalar0(W1) )
            | ~ ( sdtlseqdt0(sz0z00,W0)
                & sdtlseqdt0(sz0z00,W1) ) ) )),
        ( ( ( aScalar0(W0)
            & aScalar0(W1) )
         => ( ( sdtlseqdt0(sz0z00,W0)
              & sdtlseqdt0(sz0z00,W1) )
           => ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
              & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
      <=> ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
            & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
          | ~ ( aScalar0(W0)
              & aScalar0(W1) )
          | ~ ( sdtlseqdt0(sz0z00,W0)
              & sdtlseqdt0(sz0z00,W1) ) ) )),
    inference(bind,[status(th)],]) ).

tff(126,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( aScalar0(W0)
          & aScalar0(W1) )
       => ( ( sdtlseqdt0(sz0z00,W0)
            & sdtlseqdt0(sz0z00,W1) )
         => ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
            & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
          & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
        | ~ ( aScalar0(W0)
            & aScalar0(W1) )
        | ~ ( sdtlseqdt0(sz0z00,W0)
            & sdtlseqdt0(sz0z00,W1) ) ) ),
    inference(quant_intro,[status(thm)],[125]) ).

tff(127,axiom,
    ! [W0: $i,W1: $i] :
      ( ( aScalar0(W0)
        & aScalar0(W1) )
     => ( ( sdtlseqdt0(sz0z00,W0)
          & sdtlseqdt0(sz0z00,W1) )
       => ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
          & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).

tff(128,plain,
    ! [W0: $i,W1: $i] :
      ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
        & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
      | ~ ( aScalar0(W0)
          & aScalar0(W1) )
      | ~ ( sdtlseqdt0(sz0z00,W0)
          & sdtlseqdt0(sz0z00,W1) ) ),
    inference(modus_ponens,[status(thm)],[127,126]) ).

tff(129,plain,
    ! [W0: $i,W1: $i] :
      ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
        & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
      | ~ ( aScalar0(W0)
          & aScalar0(W1) )
      | ~ ( sdtlseqdt0(sz0z00,W0)
          & sdtlseqdt0(sz0z00,W1) ) ),
    inference(modus_ponens,[status(thm)],[128,124]) ).

tff(130,plain,
    ! [W0: $i,W1: $i] :
      ( ( sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
        & sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
      | ~ ( aScalar0(W0)
          & aScalar0(W1) )
      | ~ ( sdtlseqdt0(sz0z00,W0)
          & sdtlseqdt0(sz0z00,W1) ) ),
    inference(skolemize,[status(sab)],[129]) ).

tff(131,plain,
    ! [W0: $i,W1: $i] :
      ( ~ aScalar0(W1)
      | ~ aScalar0(W0)
      | ~ sdtlseqdt0(sz0z00,W0)
      | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
          | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
      | ~ sdtlseqdt0(sz0z00,W1) ),
    inference(modus_ponens,[status(thm)],[130,123]) ).

tff(132,plain,
    ! [W0: $i,W1: $i] :
      ( ~ aScalar0(W1)
      | ~ aScalar0(W0)
      | ~ sdtlseqdt0(sz0z00,W0)
      | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
          | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
      | ~ sdtlseqdt0(sz0z00,W1) ),
    inference(modus_ponens,[status(thm)],[131,121]) ).

tff(133,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( ~ aScalar0(W1)
            | ~ aScalar0(W0)
            | ~ sdtlseqdt0(sz0z00,W0)
            | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
            | ~ sdtlseqdt0(sz0z00,W1) )
      | ~ aScalar0(sdtasasdt0(xt,xt))
      | ~ aScalar0(sdtasasdt0(xs,xs))
      | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
      | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
          | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
      | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( ~ aScalar0(W1)
            | ~ aScalar0(W0)
            | ~ sdtlseqdt0(sz0z00,W0)
            | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
                | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
            | ~ sdtlseqdt0(sz0z00,W1) )
      | ~ aScalar0(sdtasasdt0(xt,xt))
      | ~ aScalar0(sdtasasdt0(xs,xs))
      | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
      | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
          | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
      | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(134,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( ~ aScalar0(W1)
          | ~ aScalar0(W0)
          | ~ sdtlseqdt0(sz0z00,W0)
          | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
              | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
          | ~ sdtlseqdt0(sz0z00,W1) )
    | ~ aScalar0(sdtasasdt0(xt,xt))
    | ~ aScalar0(sdtasasdt0(xs,xs))
    | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
    | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
        | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
    | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(135,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( ~ aScalar0(W1)
          | ~ aScalar0(W0)
          | ~ sdtlseqdt0(sz0z00,W0)
          | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(W0,W1))
              | ~ sdtlseqdt0(sz0z00,sdtasdt0(W0,W1)) )
          | ~ sdtlseqdt0(sz0z00,W1) )
    | ~ aScalar0(sdtasasdt0(xt,xt))
    | ~ aScalar0(sdtasasdt0(xs,xs))
    | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
    | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
        | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
    | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
    inference(modus_ponens,[status(thm)],[134,133]) ).

tff(136,plain,
    ( ~ aScalar0(sdtasasdt0(xt,xt))
    | ~ aScalar0(sdtasasdt0(xs,xs))
    | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
    | ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
        | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
    | ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt)) ),
    inference(unit_resolution,[status(thm)],[135,132]) ).

tff(137,plain,
    ~ ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
      | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(unit_resolution,[status(thm)],[136,119,107,103,77]) ).

tff(138,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    | ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
    | sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
    inference(tautology,[status(thm)],]) ).

tff(139,plain,
    sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(unit_resolution,[status(thm)],[138,137]) ).

tff(140,plain,
    sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(modus_ponens,[status(thm)],[139,63]) ).

tff(141,plain,
    ( ~ 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(rewrite,[status(thm)],]) ).

tff(142,plain,
    ( ~ ( ( ( aDimensionOf0(xs) != sz00 )
         => ? [W0: $i] :
              ( aVector0(W0)
              & ( szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs) )
              & ! [W1: $i] :
                  ( aNaturalNumber0(W1)
                 => ( sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) ) )
              & ( W0 = sziznziztdt0(xs) )
              & ? [W1: $i] :
                  ( aVector0(W1)
                  & ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt) )
                  & ! [W2: $i] :
                      ( aNaturalNumber0(W2)
                     => ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) )
                  & ( W1 = sziznziztdt0(xt) )
                  & ? [W2: $i] :
                      ( aScalar0(W2)
                      & ( W2 = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
                      & ? [W3: $i] :
                          ( aScalar0(W3)
                          & ( W3 = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
                          & ? [W4: $i] :
                              ( aScalar0(W4)
                              & ( W4 = sdtasasdt0(W0,W0) )
                              & ? [W5: $i] :
                                  ( aScalar0(W5)
                                  & ( W5 = sdtasasdt0(W1,W1) )
                                  & ? [W6: $i] :
                                      ( aScalar0(W6)
                                      & ( W6 = sdtasasdt0(W0,W1) )
                                      & ? [W7: $i] :
                                          ( aScalar0(W7)
                                          & ( W7 = sdtasdt0(W2,W2) )
                                          & ? [W8: $i] :
                                              ( aScalar0(W8)
                                              & ( W8 = sdtasdt0(W3,W3) )
                                              & ? [W9: $i] :
                                                  ( aScalar0(W9)
                                                  & ( W9 = sdtasdt0(W2,W3) )
                                                  & ? [W10: $i] :
                                                      ( aScalar0(W10)
                                                      & ( W10 = sdtasdt0(W4,W8) )
                                                      & ? [W11: $i] :
                                                          ( aScalar0(W11)
                                                          & ( W11 = sdtasdt0(W6,W9) )
                                                          & ? [W12: $i] :
                                                              ( aScalar0(W12)
                                                              & ( W12 = sdtasdt0(W7,W5) )
                                                              & ? [W13: $i] :
                                                                  ( 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))) )
  <=> ~ ( ~ ( ( aDimensionOf0(xs) = sz00 )
            | ? [W0: $i] :
                ( aVector0(W0)
                & ( szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs) )
                & ! [W1: $i] :
                    ( ~ aNaturalNumber0(W1)
                    | ( sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) ) )
                & ( W0 = sziznziztdt0(xs) )
                & ? [W1: $i] :
                    ( aVector0(W1)
                    & ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt) )
                    & ! [W2: $i] :
                        ( ~ aNaturalNumber0(W2)
                        | ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) )
                    & ( W1 = sziznziztdt0(xt) )
                    & ? [W2: $i] :
                        ( aScalar0(W2)
                        & ( W2 = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
                        & ? [W3: $i] :
                            ( aScalar0(W3)
                            & ( W3 = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
                            & ? [W4: $i] :
                                ( aScalar0(W4)
                                & ( W4 = sdtasasdt0(W0,W0) )
                                & ? [W5: $i] :
                                    ( aScalar0(W5)
                                    & ( W5 = sdtasasdt0(W1,W1) )
                                    & ? [W6: $i] :
                                        ( aScalar0(W6)
                                        & ( W6 = sdtasasdt0(W0,W1) )
                                        & ? [W7: $i] :
                                            ( aScalar0(W7)
                                            & ( W7 = sdtasdt0(W2,W2) )
                                            & ? [W8: $i] :
                                                ( aScalar0(W8)
                                                & ( W8 = sdtasdt0(W3,W3) )
                                                & ? [W9: $i] :
                                                    ( aScalar0(W9)
                                                    & ( W9 = sdtasdt0(W2,W3) )
                                                    & ? [W10: $i] :
                                                        ( aScalar0(W10)
                                                        & ( W10 = sdtasdt0(W4,W8) )
                                                        & ? [W11: $i] :
                                                            ( aScalar0(W11)
                                                            & ( W11 = sdtasdt0(W6,W9) )
                                                            & ? [W12: $i] :
                                                                ( aScalar0(W12)
                                                                & ( W12 = sdtasdt0(W7,W5) )
                                                                & ? [W13: $i] :
                                                                    ( 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(rewrite,[status(thm)],]) ).

tff(143,axiom,
    ~ ( ( ( aDimensionOf0(xs) != sz00 )
       => ? [W0: $i] :
            ( aVector0(W0)
            & ( szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs) )
            & ! [W1: $i] :
                ( aNaturalNumber0(W1)
               => ( sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) ) )
            & ( W0 = sziznziztdt0(xs) )
            & ? [W1: $i] :
                ( aVector0(W1)
                & ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt) )
                & ! [W2: $i] :
                    ( aNaturalNumber0(W2)
                   => ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) )
                & ( W1 = sziznziztdt0(xt) )
                & ? [W2: $i] :
                    ( aScalar0(W2)
                    & ( W2 = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
                    & ? [W3: $i] :
                        ( aScalar0(W3)
                        & ( W3 = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
                        & ? [W4: $i] :
                            ( aScalar0(W4)
                            & ( W4 = sdtasasdt0(W0,W0) )
                            & ? [W5: $i] :
                                ( aScalar0(W5)
                                & ( W5 = sdtasasdt0(W1,W1) )
                                & ? [W6: $i] :
                                    ( aScalar0(W6)
                                    & ( W6 = sdtasasdt0(W0,W1) )
                                    & ? [W7: $i] :
                                        ( aScalar0(W7)
                                        & ( W7 = sdtasdt0(W2,W2) )
                                        & ? [W8: $i] :
                                            ( aScalar0(W8)
                                            & ( W8 = sdtasdt0(W3,W3) )
                                            & ? [W9: $i] :
                                                ( aScalar0(W9)
                                                & ( W9 = sdtasdt0(W2,W3) )
                                                & ? [W10: $i] :
                                                    ( aScalar0(W10)
                                                    & ( W10 = sdtasdt0(W4,W8) )
                                                    & ? [W11: $i] :
                                                        ( aScalar0(W11)
                                                        & ( W11 = sdtasdt0(W6,W9) )
                                                        & ? [W12: $i] :
                                                            ( aScalar0(W12)
                                                            & ( W12 = sdtasdt0(W7,W5) )
                                                            & ? [W13: $i] :
                                                                ( 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/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(144,plain,
    ~ ( ~ ( ( aDimensionOf0(xs) = sz00 )
          | ? [W0: $i] :
              ( aVector0(W0)
              & ( szszuzczcdt0(aDimensionOf0(W0)) = aDimensionOf0(xs) )
              & ! [W1: $i] :
                  ( ~ aNaturalNumber0(W1)
                  | ( sdtlbdtrb0(W0,W1) = sdtlbdtrb0(xs,W1) ) )
              & ( W0 = sziznziztdt0(xs) )
              & ? [W1: $i] :
                  ( aVector0(W1)
                  & ( szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(xt) )
                  & ! [W2: $i] :
                      ( ~ aNaturalNumber0(W2)
                      | ( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(xt,W2) ) )
                  & ( W1 = sziznziztdt0(xt) )
                  & ? [W2: $i] :
                      ( aScalar0(W2)
                      & ( W2 = sdtlbdtrb0(xs,aDimensionOf0(xs)) )
                      & ? [W3: $i] :
                          ( aScalar0(W3)
                          & ( W3 = sdtlbdtrb0(xt,aDimensionOf0(xt)) )
                          & ? [W4: $i] :
                              ( aScalar0(W4)
                              & ( W4 = sdtasasdt0(W0,W0) )
                              & ? [W5: $i] :
                                  ( aScalar0(W5)
                                  & ( W5 = sdtasasdt0(W1,W1) )
                                  & ? [W6: $i] :
                                      ( aScalar0(W6)
                                      & ( W6 = sdtasasdt0(W0,W1) )
                                      & ? [W7: $i] :
                                          ( aScalar0(W7)
                                          & ( W7 = sdtasdt0(W2,W2) )
                                          & ? [W8: $i] :
                                              ( aScalar0(W8)
                                              & ( W8 = sdtasdt0(W3,W3) )
                                              & ? [W9: $i] :
                                                  ( aScalar0(W9)
                                                  & ( W9 = sdtasdt0(W2,W3) )
                                                  & ? [W10: $i] :
                                                      ( aScalar0(W10)
                                                      & ( W10 = sdtasdt0(W4,W8) )
                                                      & ? [W11: $i] :
                                                          ( aScalar0(W11)
                                                          & ( W11 = sdtasdt0(W6,W9) )
                                                          & ? [W12: $i] :
                                                              ( aScalar0(W12)
                                                              & ( W12 = sdtasdt0(W7,W5) )
                                                              & ? [W13: $i] :
                                                                  ( 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(modus_ponens,[status(thm)],[143,142]) ).

tff(145,plain,
    ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(or_elim,[status(thm)],[144]) ).

tff(146,plain,
    ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
    inference(modus_ponens,[status(thm)],[145,141]) ).

tff(147,plain,
    $false,
    inference(unit_resolution,[status(thm)],[146,140]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Sep  2 22:35:35 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35  Usage: tptp [options] [-file:]file
% 0.19/0.35    -h, -?       prints this message.
% 0.19/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.19/0.35    -m, -model   generate model.
% 0.19/0.35    -p, -proof   generate proof.
% 0.19/0.35    -c, -core    generate unsat core of named formulas.
% 0.19/0.35    -st, -statistics display statistics.
% 0.19/0.35    -t:timeout   set timeout (in second).
% 0.19/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.19/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35    -<param>:<value> configuration parameter and value.
% 0.19/0.35    -o:<output-file> file to place output in.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------