TSTP Solution File: RNG083+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : RNG083+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.c6ADvbKh6T true

% Computer : n025.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 : Thu Aug 31 14:06:46 EDT 2023

% Result   : Theorem 19.97s 3.48s
% Output   : Refutation 19.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   67
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  370 ( 128 unt;   7 typ;   0 def)
%            Number of atoms       :  866 ( 269 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives : 3007 ( 465   ~; 434   |;  19   &;2039   @)
%                                         (   0 <=>;  12  =>;  38  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  316 (   0   ^; 316   !;   0   ?; 316   :)

% Comments : 
%------------------------------------------------------------------------------
thf(smndt0_type,type,
    smndt0: $i > $i ).

thf(sdtasdt0_type,type,
    sdtasdt0: $i > $i > $i ).

thf(aElement0_type,type,
    aElement0: $i > $o ).

thf(sz10_type,type,
    sz10: $i ).

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

thf(sdtpldt0_type,type,
    sdtpldt0: $i > $i > $i ).

thf(xx_type,type,
    xx: $i ).

thf(mMulMnOne,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
          = ( smndt0 @ W0 ) )
        & ( ( smndt0 @ W0 )
          = ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) ) ).

thf(zip_derived_cl19,plain,
    ! [X0: $i] :
      ( ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mMulMnOne]) ).

thf(mMulUnit,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( ( ( sdtasdt0 @ W0 @ sz10 )
          = W0 )
        & ( W0
          = ( sdtasdt0 @ sz10 @ W0 ) ) ) ) ).

thf(zip_derived_cl15,plain,
    ! [X0: $i] :
      ( ( X0
        = ( sdtasdt0 @ sz10 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mMulUnit]) ).

thf(mMulAsso,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 )
        & ( aElement0 @ W2 ) )
     => ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
        = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ).

thf(zip_derived_cl13,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ X2 )
        = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mMulAsso]) ).

thf(zip_derived_cl129,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ sz10 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ sz10 @ ( sdtasdt0 @ X0 @ X1 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl15,zip_derived_cl13]) ).

thf(mSortsC_01,axiom,
    aElement0 @ sz10 ).

thf(zip_derived_cl2,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl138,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ sz10 @ ( sdtasdt0 @ X0 @ X1 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl129,zip_derived_cl2]) ).

thf(zip_derived_cl139,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ sz10 @ ( sdtasdt0 @ X0 @ X1 ) ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl138]) ).

thf(zip_derived_cl222,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
      | ~ ( aElement0 @ ( smndt0 @ sz10 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl19,zip_derived_cl139]) ).

thf(zip_derived_cl231,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ ( smndt0 @ sz10 ) )
      | ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl222]) ).

thf(zip_derived_cl288,plain,
    ( ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl231]) ).

thf(zip_derived_cl19_001,plain,
    ! [X0: $i] :
      ( ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mMulMnOne]) ).

thf(zip_derived_cl13_002,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ X2 )
        = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mMulAsso]) ).

thf(zip_derived_cl124,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ ( sdtasdt0 @ X1 @ X0 ) )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ ( smndt0 @ sz10 ) )
      | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
        = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl19,zip_derived_cl13]) ).

thf(mSortsB_02,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 ) )
     => ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ).

thf(zip_derived_cl5,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( aElement0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

thf(zip_derived_cl324,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
        = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) )
      | ~ ( aElement0 @ ( smndt0 @ sz10 ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl124,zip_derived_cl5]) ).

thf(zip_derived_cl325,plain,
    ( ! [X0: $i,X1: $i] :
        ( ~ ( aElement0 @ X0 )
        | ~ ( aElement0 @ X1 )
        | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
          = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) )
   <= ! [X0: $i,X1: $i] :
        ( ~ ( aElement0 @ X0 )
        | ~ ( aElement0 @ X1 )
        | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
          = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl324]) ).

thf(zip_derived_cl344,plain,
    ( ! [X0: $i] :
        ( ~ ( aElement0 @ sz10 )
        | ~ ( aElement0 @ sz10 )
        | ~ ( aElement0 @ X0 )
        | ( ( smndt0 @ ( sdtasdt0 @ X0 @ sz10 ) )
          = ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) )
   <= ( ! [X0: $i] :
          ( ( ( smndt0 @ X0 )
            = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
          | ~ ( aElement0 @ X0 ) )
      & ! [X0: $i,X1: $i] :
          ( ~ ( aElement0 @ X0 )
          | ~ ( aElement0 @ X1 )
          | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
            = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl288,zip_derived_cl325]) ).

thf(zip_derived_cl2_003,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl2_004,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl351,plain,
    ( ! [X0: $i] :
        ( ~ ( aElement0 @ X0 )
        | ( ( smndt0 @ ( sdtasdt0 @ X0 @ sz10 ) )
          = ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) )
   <= ( ! [X0: $i] :
          ( ( ( smndt0 @ X0 )
            = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
          | ~ ( aElement0 @ X0 ) )
      & ! [X0: $i,X1: $i] :
          ( ~ ( aElement0 @ X0 )
          | ~ ( aElement0 @ X1 )
          | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
            = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl344,zip_derived_cl2,zip_derived_cl2]) ).

thf(mSortsU,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( aElement0 @ ( smndt0 @ W0 ) ) ) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( smndt0 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mSortsU]) ).

thf(zip_derived_cl289,plain,
    ( ~ ( aElement0 @ ( smndt0 @ sz10 ) )
   <= ~ ( aElement0 @ ( smndt0 @ sz10 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl231]) ).

thf(zip_derived_cl366,plain,
    ( ~ ( aElement0 @ sz10 )
   <= ~ ( aElement0 @ ( smndt0 @ sz10 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl289]) ).

thf(zip_derived_cl2_005,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf('0',plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(demod,[status(thm)],[zip_derived_cl366,zip_derived_cl2]) ).

thf('1',plain,
    ( ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) )
    | ~ ( aElement0 @ ( smndt0 @ sz10 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl231]) ).

thf('2',plain,
    ! [X0: $i] :
      ( ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference('sat_resolution*',[status(thm)],['0','1']) ).

thf('3',plain,
    ( ! [X0: $i,X1: $i] :
        ( ~ ( aElement0 @ X0 )
        | ~ ( aElement0 @ X1 )
        | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
          = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) )
    | ~ ( aElement0 @ ( smndt0 @ sz10 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl324]) ).

thf('4',plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
        = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) ),
    inference('sat_resolution*',[status(thm)],['0','3']) ).

thf(zip_derived_cl406,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( smndt0 @ ( sdtasdt0 @ X0 @ sz10 ) )
        = ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl351,'2','4']) ).

thf(mAMDistr,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 )
        & ( aElement0 @ W2 ) )
     => ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
          = ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) ).

thf(zip_derived_cl16,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAMDistr]) ).

thf(zip_derived_cl413,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ ( smndt0 @ sz10 ) )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ ( sdtpldt0 @ ( smndt0 @ sz10 ) @ X1 ) )
        = ( sdtpldt0 @ ( smndt0 @ ( sdtasdt0 @ X0 @ sz10 ) ) @ ( sdtasdt0 @ X0 @ X1 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl406,zip_derived_cl16]) ).

thf(zip_derived_cl426,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtasdt0 @ X0 @ ( sdtpldt0 @ ( smndt0 @ sz10 ) @ X1 ) )
        = ( sdtpldt0 @ ( smndt0 @ ( sdtasdt0 @ X0 @ sz10 ) ) @ ( sdtasdt0 @ X0 @ X1 ) ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ ( smndt0 @ sz10 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl413]) ).

thf(zip_derived_cl406_006,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( smndt0 @ ( sdtasdt0 @ X0 @ sz10 ) )
        = ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl351,'2','4']) ).

thf(zip_derived_cl288_007,plain,
    ( ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl231]) ).

thf('5',plain,
    ! [X0: $i] :
      ( ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference('sat_resolution*',[status(thm)],['0','1']) ).

thf(zip_derived_cl370,plain,
    ! [X0: $i] :
      ( ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl288,'5']) ).

thf(zip_derived_cl1904,plain,
    ( ~ ( aElement0 @ sz10 )
    | ( ( smndt0 @ sz10 )
      = ( smndt0 @ ( sdtasdt0 @ sz10 @ sz10 ) ) )
    | ~ ( aElement0 @ sz10 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl406,zip_derived_cl370]) ).

thf(zip_derived_cl2_008,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl2_009,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl1907,plain,
    ( ( smndt0 @ sz10 )
    = ( smndt0 @ ( sdtasdt0 @ sz10 @ sz10 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1904,zip_derived_cl2,zip_derived_cl2]) ).

thf(zip_derived_cl3_010,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( smndt0 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mSortsU]) ).

thf(zip_derived_cl1934,plain,
    ( ( aElement0 @ ( smndt0 @ sz10 ) )
    | ~ ( aElement0 @ ( sdtasdt0 @ sz10 @ sz10 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1907,zip_derived_cl3]) ).

thf(zip_derived_cl2125,plain,
    ( ( aElement0 @ ( smndt0 @ sz10 ) )
   <= ( aElement0 @ ( smndt0 @ sz10 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1934]) ).

thf('6',plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference('sat_resolution*',[status(thm)],['0']) ).

thf(zip_derived_cl2126,plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2125,'6']) ).

thf(zip_derived_cl22356,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtasdt0 @ X0 @ ( sdtpldt0 @ ( smndt0 @ sz10 ) @ X1 ) )
        = ( sdtpldt0 @ ( smndt0 @ ( sdtasdt0 @ X0 @ sz10 ) ) @ ( sdtasdt0 @ X0 @ X1 ) ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl426,zip_derived_cl2126]) ).

thf(mAddInvr,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
          = sz00 )
        & ( sz00
          = ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) ) ).

thf(zip_derived_cl11,plain,
    ! [X0: $i] :
      ( ( sz00
        = ( sdtpldt0 @ ( smndt0 @ X0 ) @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddInvr]) ).

thf(zip_derived_cl22377,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ sz10 )
      | ( sz00
        = ( sdtasdt0 @ X0 @ ( sdtpldt0 @ ( smndt0 @ sz10 ) @ sz10 ) ) )
      | ~ ( aElement0 @ ( sdtasdt0 @ X0 @ sz10 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl22356,zip_derived_cl11]) ).

thf(zip_derived_cl2_011,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(mAddZero,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( ( ( sdtpldt0 @ W0 @ sz00 )
          = W0 )
        & ( W0
          = ( sdtpldt0 @ sz00 @ W0 ) ) ) ) ).

thf(zip_derived_cl9,plain,
    ! [X0: $i] :
      ( ( X0
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddZero]) ).

thf(zip_derived_cl14,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ X0 @ sz10 )
        = X0 )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mMulUnit]) ).

thf(zip_derived_cl17,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ X0 @ X2 ) @ X1 )
        = ( sdtpldt0 @ ( sdtasdt0 @ X0 @ X1 ) @ ( sdtasdt0 @ X2 @ X1 ) ) ) ),
    inference(cnf,[status(esa)],[mAMDistr]) ).

thf(zip_derived_cl249,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ sz10 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ X0 ) @ sz10 )
        = ( sdtpldt0 @ ( sdtasdt0 @ X1 @ sz10 ) @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl17]) ).

thf(zip_derived_cl2_012,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl265,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ X0 ) @ sz10 )
        = ( sdtpldt0 @ ( sdtasdt0 @ X1 @ sz10 ) @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl249,zip_derived_cl2]) ).

thf(zip_derived_cl266,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ X0 ) @ sz10 )
        = ( sdtpldt0 @ ( sdtasdt0 @ X1 @ sz10 ) @ X0 ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl265]) ).

thf(zip_derived_cl13985,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ X0 @ sz10 )
        = ( sdtpldt0 @ ( sdtasdt0 @ sz00 @ sz10 ) @ X0 ) )
      | ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl266]) ).

thf(zip_derived_cl10,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ ( smndt0 @ X0 ) )
        = sz00 )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddInvr]) ).

thf(zip_derived_cl9_013,plain,
    ! [X0: $i] :
      ( ( X0
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddZero]) ).

thf(zip_derived_cl24,plain,
    ( ~ ( aElement0 @ sz00 )
    | ( ( smndt0 @ sz00 )
      = sz00 )
    | ~ ( aElement0 @ ( smndt0 @ sz00 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl9]) ).

thf(mSortsC,axiom,
    aElement0 @ sz00 ).

thf(zip_derived_cl1,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl25,plain,
    ( ( ( smndt0 @ sz00 )
      = sz00 )
    | ~ ( aElement0 @ ( smndt0 @ sz00 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl24,zip_derived_cl1]) ).

thf(zip_derived_cl27,plain,
    ( ( ( smndt0 @ sz00 )
      = sz00 )
   <= ( ( smndt0 @ sz00 )
      = sz00 ) ),
    inference(split,[status(esa)],[zip_derived_cl25]) ).

thf(zip_derived_cl3_014,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( smndt0 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mSortsU]) ).

thf(zip_derived_cl26,plain,
    ( ~ ( aElement0 @ ( smndt0 @ sz00 ) )
   <= ~ ( aElement0 @ ( smndt0 @ sz00 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl25]) ).

thf(zip_derived_cl29,plain,
    ( ~ ( aElement0 @ sz00 )
   <= ~ ( aElement0 @ ( smndt0 @ sz00 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl26]) ).

thf(zip_derived_cl1_015,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf('7',plain,
    aElement0 @ ( smndt0 @ sz00 ),
    inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl1]) ).

thf('8',plain,
    ( ( ( smndt0 @ sz00 )
      = sz00 )
    | ~ ( aElement0 @ ( smndt0 @ sz00 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl25]) ).

thf('9',plain,
    ( ( smndt0 @ sz00 )
    = sz00 ),
    inference('sat_resolution*',[status(thm)],['7','8']) ).

thf(zip_derived_cl32,plain,
    ( ( smndt0 @ sz00 )
    = sz00 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl27,'9']) ).

thf(zip_derived_cl288_016,plain,
    ( ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl231]) ).

thf(zip_derived_cl297,plain,
    ( ( ( sz00
        = ( sdtasdt0 @ sz10 @ sz00 ) )
      | ~ ( aElement0 @ sz00 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl32,zip_derived_cl288]) ).

thf(zip_derived_cl1_017,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl298,plain,
    ( ( sz00
      = ( sdtasdt0 @ sz10 @ sz00 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl297,zip_derived_cl1]) ).

thf(mMulComm,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 ) )
     => ( ( sdtasdt0 @ W0 @ W1 )
        = ( sdtasdt0 @ W1 @ W0 ) ) ) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(zip_derived_cl307,plain,
    ( ( ~ ( aElement0 @ sz10 )
      | ~ ( aElement0 @ sz00 )
      | ( sz00
        = ( sdtasdt0 @ sz00 @ sz10 ) ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl298,zip_derived_cl12]) ).

thf(zip_derived_cl2_018,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl1_019,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl316,plain,
    ( ( sz00
      = ( sdtasdt0 @ sz00 @ sz10 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl307,zip_derived_cl2,zip_derived_cl1]) ).

thf('10',plain,
    ! [X0: $i] :
      ( ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference('sat_resolution*',[status(thm)],['0','1']) ).

thf(zip_derived_cl369,plain,
    ( sz00
    = ( sdtasdt0 @ sz00 @ sz10 ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl316,'10']) ).

thf(zip_derived_cl1_020,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl14036,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ X0 @ sz10 )
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl13985,zip_derived_cl369,zip_derived_cl1]) ).

thf(zip_derived_cl14037,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ X0 @ sz10 )
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl14036]) ).

thf(zip_derived_cl298_021,plain,
    ( ( sz00
      = ( sdtasdt0 @ sz10 @ sz00 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl297,zip_derived_cl1]) ).

thf(zip_derived_cl16_022,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAMDistr]) ).

thf(zip_derived_cl312,plain,
    ( ! [X0: $i] :
        ( ~ ( aElement0 @ sz00 )
        | ~ ( aElement0 @ sz10 )
        | ~ ( aElement0 @ X0 )
        | ( ( sdtasdt0 @ sz10 @ ( sdtpldt0 @ sz00 @ X0 ) )
          = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz10 @ X0 ) ) ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl298,zip_derived_cl16]) ).

thf(zip_derived_cl1_023,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2_024,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl321,plain,
    ( ! [X0: $i] :
        ( ~ ( aElement0 @ X0 )
        | ( ( sdtasdt0 @ sz10 @ ( sdtpldt0 @ sz00 @ X0 ) )
          = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz10 @ X0 ) ) ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl312,zip_derived_cl1,zip_derived_cl2]) ).

thf('11',plain,
    ! [X0: $i] :
      ( ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference('sat_resolution*',[status(thm)],['0','1']) ).

thf(zip_derived_cl600,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz10 @ ( sdtpldt0 @ sz00 @ X0 ) )
        = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz10 @ X0 ) ) ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl321,'11']) ).

thf(zip_derived_cl14_025,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ X0 @ sz10 )
        = X0 )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mMulUnit]) ).

thf(zip_derived_cl16_026,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAMDistr]) ).

thf(zip_derived_cl181,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ sz10 )
      | ( ( sdtasdt0 @ X0 @ ( sdtpldt0 @ X1 @ sz10 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ X0 @ X1 ) @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl16]) ).

thf(zip_derived_cl2_027,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl195,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ X0 @ ( sdtpldt0 @ X1 @ sz10 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ X0 @ X1 ) @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl181,zip_derived_cl2]) ).

thf(zip_derived_cl196,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtasdt0 @ X0 @ ( sdtpldt0 @ X1 @ sz10 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ X0 @ X1 ) @ X0 ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl195]) ).

thf(zip_derived_cl7912,plain,
    ( ~ ( aElement0 @ sz10 )
    | ( ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz10 @ sz10 ) )
      = ( sdtpldt0 @ ( sdtasdt0 @ sz10 @ sz00 ) @ sz10 ) )
    | ~ ( aElement0 @ sz00 )
    | ~ ( aElement0 @ sz10 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl600,zip_derived_cl196]) ).

thf(zip_derived_cl2_028,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl298_029,plain,
    ( ( sz00
      = ( sdtasdt0 @ sz10 @ sz00 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl297,zip_derived_cl1]) ).

thf(zip_derived_cl139_030,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ sz10 @ ( sdtasdt0 @ X0 @ X1 ) ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl138]) ).

thf(zip_derived_cl309,plain,
    ( ( ( sz00
        = ( sdtasdt0 @ sz10 @ sz00 ) )
      | ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ sz10 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl298,zip_derived_cl139]) ).

thf(zip_derived_cl1_031,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2_032,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl318,plain,
    ( ( sz00
      = ( sdtasdt0 @ sz10 @ sz00 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl309,zip_derived_cl1,zip_derived_cl2]) ).

thf('12',plain,
    ! [X0: $i] :
      ( ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference('sat_resolution*',[status(thm)],['0','1']) ).

thf(zip_derived_cl387,plain,
    ( sz00
    = ( sdtasdt0 @ sz10 @ sz00 ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl318,'12']) ).

thf(zip_derived_cl1_033,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2_034,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl7953,plain,
    ( ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz10 @ sz10 ) )
    = ( sdtpldt0 @ sz00 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl7912,zip_derived_cl2,zip_derived_cl387,zip_derived_cl1,zip_derived_cl2]) ).

thf(zip_derived_cl14408,plain,
    ( ~ ( aElement0 @ ( sdtasdt0 @ sz10 @ sz10 ) )
    | ( ( sdtasdt0 @ ( sdtasdt0 @ sz10 @ sz10 ) @ sz10 )
      = ( sdtpldt0 @ sz00 @ sz10 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl14037,zip_derived_cl7953]) ).

thf(zip_derived_cl9_035,plain,
    ! [X0: $i] :
      ( ( X0
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddZero]) ).

thf(zip_derived_cl15_036,plain,
    ! [X0: $i] :
      ( ( X0
        = ( sdtasdt0 @ sz10 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mMulUnit]) ).

thf(zip_derived_cl16_037,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAMDistr]) ).

thf(zip_derived_cl183,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ sz10 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz10 @ ( sdtpldt0 @ X1 @ X0 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ sz10 @ X1 ) @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl15,zip_derived_cl16]) ).

thf(zip_derived_cl2_038,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl198,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz10 @ ( sdtpldt0 @ X1 @ X0 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ sz10 @ X1 ) @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl183,zip_derived_cl2]) ).

thf(zip_derived_cl199,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtasdt0 @ sz10 @ ( sdtpldt0 @ X1 @ X0 ) )
        = ( sdtpldt0 @ ( sdtasdt0 @ sz10 @ X1 ) @ X0 ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl198]) ).

thf(zip_derived_cl8435,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz10 @ X0 )
        = ( sdtpldt0 @ ( sdtasdt0 @ sz10 @ sz00 ) @ X0 ) )
      | ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl199]) ).

thf(zip_derived_cl387_039,plain,
    ( sz00
    = ( sdtasdt0 @ sz10 @ sz00 ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl318,'12']) ).

thf(zip_derived_cl1_040,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl8479,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz10 @ X0 )
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8435,zip_derived_cl387,zip_derived_cl1]) ).

thf(zip_derived_cl8480,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ sz10 @ X0 )
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8479]) ).

thf(zip_derived_cl7953_041,plain,
    ( ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz10 @ sz10 ) )
    = ( sdtpldt0 @ sz00 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl7912,zip_derived_cl2,zip_derived_cl387,zip_derived_cl1,zip_derived_cl2]) ).

thf(zip_derived_cl11_042,plain,
    ! [X0: $i] :
      ( ( sz00
        = ( sdtpldt0 @ ( smndt0 @ X0 ) @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddInvr]) ).

thf(zip_derived_cl10_043,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ ( smndt0 @ X0 ) )
        = sz00 )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddInvr]) ).

thf(mAddAsso,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 )
        & ( aElement0 @ W2 ) )
     => ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
        = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) ).

thf(zip_derived_cl7,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAddAsso]) ).

thf(zip_derived_cl155,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ ( smndt0 @ X1 ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ ( smndt0 @ X1 ) @ X0 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl7]) ).

thf(zip_derived_cl165,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ ( smndt0 @ X1 ) @ X0 ) ) )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ ( smndt0 @ X1 ) )
      | ~ ( aElement0 @ X1 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl155]) ).

thf(zip_derived_cl3_044,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( smndt0 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mSortsU]) ).

thf(zip_derived_cl3684,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ ( smndt0 @ X1 ) @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl165,zip_derived_cl3]) ).

thf(zip_derived_cl3704,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ X0 @ sz00 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl3684]) ).

thf(zip_derived_cl3715,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ X0 @ sz00 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3704]) ).

thf(mSortsB,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 ) )
     => ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) ).

thf(zip_derived_cl4,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( aElement0 @ ( sdtpldt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB]) ).

thf(zip_derived_cl3727,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ sz00 )
      | ( aElement0 @ ( sdtpldt0 @ sz00 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3715,zip_derived_cl4]) ).

thf(zip_derived_cl1_045,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl3752,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ( aElement0 @ ( sdtpldt0 @ sz00 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3727,zip_derived_cl1]) ).

thf(zip_derived_cl3753,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3752]) ).

thf(zip_derived_cl8376,plain,
    ( ( aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ) )
    | ~ ( aElement0 @ ( sdtasdt0 @ sz10 @ sz10 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl7953,zip_derived_cl3753]) ).

thf(zip_derived_cl11405,plain,
    ( ( aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ) )
   <= ( aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl8376]) ).

thf(zip_derived_cl4_046,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( aElement0 @ ( sdtpldt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB]) ).

thf(zip_derived_cl3715_047,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ X0 @ sz00 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3704]) ).

thf(zip_derived_cl298_048,plain,
    ( ( sz00
      = ( sdtasdt0 @ sz10 @ sz00 ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl297,zip_derived_cl1]) ).

thf(zip_derived_cl17_049,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ X0 @ X2 ) @ X1 )
        = ( sdtpldt0 @ ( sdtasdt0 @ X0 @ X1 ) @ ( sdtasdt0 @ X2 @ X1 ) ) ) ),
    inference(cnf,[status(esa)],[mAMDistr]) ).

thf(zip_derived_cl308,plain,
    ( ! [X0: $i] :
        ( ~ ( aElement0 @ sz10 )
        | ~ ( aElement0 @ sz00 )
        | ~ ( aElement0 @ X0 )
        | ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ X0 ) @ sz00 )
          = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ X0 @ sz00 ) ) ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl298,zip_derived_cl17]) ).

thf(zip_derived_cl2_050,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl1_051,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl317,plain,
    ( ! [X0: $i] :
        ( ~ ( aElement0 @ X0 )
        | ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ X0 ) @ sz00 )
          = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ X0 @ sz00 ) ) ) )
   <= ! [X0: $i] :
        ( ( ( smndt0 @ X0 )
          = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
        | ~ ( aElement0 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl308,zip_derived_cl2,zip_derived_cl1]) ).

thf('13',plain,
    ! [X0: $i] :
      ( ( ( smndt0 @ X0 )
        = ( sdtasdt0 @ sz10 @ ( smndt0 @ X0 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference('sat_resolution*',[status(thm)],['0','1']) ).

thf(zip_derived_cl462,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ X0 ) @ sz00 )
        = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ X0 @ sz00 ) ) ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl317,'13']) ).

thf(zip_derived_cl3736,plain,
    ( ~ ( aElement0 @ sz10 )
    | ~ ( aElement0 @ sz00 )
    | ( ( sdtasdt0 @ ( sdtpldt0 @ sz00 @ sz10 ) @ sz00 )
      = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3715,zip_derived_cl462]) ).

thf(zip_derived_cl2_052,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl1_053,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl8,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ sz00 )
        = X0 )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddZero]) ).

thf(zip_derived_cl462_054,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ X0 ) @ sz00 )
        = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ X0 @ sz00 ) ) ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl317,'13']) ).

thf(zip_derived_cl474,plain,
    ( ~ ( aElement0 @ sz10 )
    | ~ ( aElement0 @ sz00 )
    | ( ( sdtasdt0 @ sz10 @ sz00 )
      = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl8,zip_derived_cl462]) ).

thf(zip_derived_cl2_055,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl1_056,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl387_057,plain,
    ( sz00
    = ( sdtasdt0 @ sz10 @ sz00 ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl318,'12']) ).

thf(zip_derived_cl480,plain,
    ( sz00
    = ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl474,zip_derived_cl2,zip_derived_cl1,zip_derived_cl387]) ).

thf(zip_derived_cl9_058,plain,
    ! [X0: $i] :
      ( ( X0
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddZero]) ).

thf(zip_derived_cl1961,plain,
    ( ( ( sdtasdt0 @ sz00 @ sz00 )
      = sz00 )
    | ~ ( aElement0 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl480,zip_derived_cl9]) ).

thf(zip_derived_cl2141,plain,
    ( ( ( sdtasdt0 @ sz00 @ sz00 )
      = sz00 )
   <= ( ( sdtasdt0 @ sz00 @ sz00 )
      = sz00 ) ),
    inference(split,[status(esa)],[zip_derived_cl1961]) ).

thf(zip_derived_cl5_059,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( aElement0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

thf(zip_derived_cl2140,plain,
    ( ~ ( aElement0 @ ( sdtasdt0 @ sz00 @ sz00 ) )
   <= ~ ( aElement0 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1961]) ).

thf(zip_derived_cl2143,plain,
    ( ( ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ sz00 ) )
   <= ~ ( aElement0 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl2140]) ).

thf(zip_derived_cl1_060,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl1_061,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf('14',plain,
    aElement0 @ ( sdtasdt0 @ sz00 @ sz00 ),
    inference(demod,[status(thm)],[zip_derived_cl2143,zip_derived_cl1,zip_derived_cl1]) ).

thf('15',plain,
    ( ( ( sdtasdt0 @ sz00 @ sz00 )
      = sz00 )
    | ~ ( aElement0 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1961]) ).

thf('16',plain,
    ( ( sdtasdt0 @ sz00 @ sz00 )
    = sz00 ),
    inference('sat_resolution*',[status(thm)],['14','15']) ).

thf(zip_derived_cl2293,plain,
    ( ( sdtasdt0 @ sz00 @ sz00 )
    = sz00 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2141,'16']) ).

thf(zip_derived_cl32_062,plain,
    ( ( smndt0 @ sz00 )
    = sz00 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl27,'9']) ).

thf(zip_derived_cl10_063,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ ( smndt0 @ X0 ) )
        = sz00 )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddInvr]) ).

thf(zip_derived_cl34,plain,
    ( ( ( sdtpldt0 @ sz00 @ sz00 )
      = sz00 )
    | ~ ( aElement0 @ sz00 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl32,zip_derived_cl10]) ).

thf(zip_derived_cl1_064,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl36,plain,
    ( ( sdtpldt0 @ sz00 @ sz00 )
    = sz00 ),
    inference(demod,[status(thm)],[zip_derived_cl34,zip_derived_cl1]) ).

thf(zip_derived_cl3765,plain,
    ( ( sdtasdt0 @ ( sdtpldt0 @ sz00 @ sz10 ) @ sz00 )
    = sz00 ),
    inference(demod,[status(thm)],[zip_derived_cl3736,zip_derived_cl2,zip_derived_cl1,zip_derived_cl2293,zip_derived_cl36]) ).

thf(zip_derived_cl13_065,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ X2 )
        = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mMulAsso]) ).

thf(zip_derived_cl12_066,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(zip_derived_cl120,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X2 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ ( sdtasdt0 @ X2 @ X1 ) )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ X2 @ ( sdtasdt0 @ X1 @ X0 ) )
        = ( sdtasdt0 @ X0 @ ( sdtasdt0 @ X2 @ X1 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl13,zip_derived_cl12]) ).

thf(zip_derived_cl143,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( sdtasdt0 @ X2 @ ( sdtasdt0 @ X1 @ X0 ) )
        = ( sdtasdt0 @ X0 @ ( sdtasdt0 @ X2 @ X1 ) ) )
      | ~ ( aElement0 @ ( sdtasdt0 @ X2 @ X1 ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl120]) ).

thf(zip_derived_cl5_067,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( aElement0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

thf(zip_derived_cl2634,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X2 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtasdt0 @ X2 @ ( sdtasdt0 @ X1 @ X0 ) )
        = ( sdtasdt0 @ X0 @ ( sdtasdt0 @ X2 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl143,zip_derived_cl5]) ).

thf(zip_derived_cl2293_068,plain,
    ( ( sdtasdt0 @ sz00 @ sz00 )
    = sz00 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2141,'16']) ).

thf(zip_derived_cl13_069,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtasdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ X2 )
        = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mMulAsso]) ).

thf(zip_derived_cl2301,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz00 @ X0 )
        = ( sdtasdt0 @ sz00 @ ( sdtasdt0 @ sz00 @ X0 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2293,zip_derived_cl13]) ).

thf(zip_derived_cl1_070,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl1_071,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2316,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz00 @ X0 )
        = ( sdtasdt0 @ sz00 @ ( sdtasdt0 @ sz00 @ X0 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2301,zip_derived_cl1,zip_derived_cl1]) ).

thf(zip_derived_cl2708,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz00 @ X0 )
        = ( sdtasdt0 @ X0 @ ( sdtasdt0 @ sz00 @ sz00 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2634,zip_derived_cl2316]) ).

thf(zip_derived_cl1_072,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl1_073,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2293_074,plain,
    ( ( sdtasdt0 @ sz00 @ sz00 )
    = sz00 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2141,'16']) ).

thf(zip_derived_cl2948,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz00 @ X0 )
        = ( sdtasdt0 @ X0 @ sz00 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2708,zip_derived_cl1,zip_derived_cl1,zip_derived_cl2293]) ).

thf(zip_derived_cl2949,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ sz00 @ X0 )
        = ( sdtasdt0 @ X0 @ sz00 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2948]) ).

thf(zip_derived_cl3813,plain,
    ( ( ( sdtasdt0 @ sz00 @ ( sdtpldt0 @ sz00 @ sz10 ) )
      = sz00 )
    | ~ ( aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3765,zip_derived_cl2949]) ).

thf(zip_derived_cl3931,plain,
    ( ~ ( aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ) )
   <= ~ ( aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ) ) ),
    inference(split,[status(esa)],[zip_derived_cl3813]) ).

thf(zip_derived_cl3976,plain,
    ( ( ~ ( aElement0 @ sz10 )
      | ~ ( aElement0 @ sz00 ) )
   <= ~ ( aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl3931]) ).

thf(zip_derived_cl2_075,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl1_076,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf('17',plain,
    aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ),
    inference(demod,[status(thm)],[zip_derived_cl3976,zip_derived_cl2,zip_derived_cl1]) ).

thf('18',plain,
    aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ),
    inference('sat_resolution*',[status(thm)],['17']) ).

thf(zip_derived_cl11407,plain,
    aElement0 @ ( sdtpldt0 @ sz00 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl11405,'18']) ).

thf(zip_derived_cl11409,plain,
    ( ~ ( aElement0 @ sz10 )
    | ( aElement0 @ ( sdtasdt0 @ sz10 @ sz10 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl8480,zip_derived_cl11407]) ).

thf(zip_derived_cl2_077,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl11411,plain,
    aElement0 @ ( sdtasdt0 @ sz10 @ sz10 ),
    inference(demod,[status(thm)],[zip_derived_cl11409,zip_derived_cl2]) ).

thf(zip_derived_cl14476,plain,
    ( ( sdtasdt0 @ ( sdtasdt0 @ sz10 @ sz10 ) @ sz10 )
    = ( sdtpldt0 @ sz00 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl14408,zip_derived_cl11411]) ).

thf(zip_derived_cl14037_078,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ X0 @ sz10 )
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl14036]) ).

thf(zip_derived_cl8480_079,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ sz10 @ X0 )
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8479]) ).

thf(zip_derived_cl14398,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( ( sdtasdt0 @ sz10 @ X0 )
        = ( sdtasdt0 @ X0 @ sz10 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl14037,zip_derived_cl8480]) ).

thf(zip_derived_cl14468,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ sz10 @ X0 )
        = ( sdtasdt0 @ X0 @ sz10 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl14398]) ).

thf(zip_derived_cl15_080,plain,
    ! [X0: $i] :
      ( ( X0
        = ( sdtasdt0 @ sz10 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mMulUnit]) ).

thf(zip_derived_cl15221,plain,
    ( ~ ( aElement0 @ sz10 )
    | ( sz10
      = ( sdtasdt0 @ sz10 @ sz10 ) )
    | ~ ( aElement0 @ sz10 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl14468,zip_derived_cl15]) ).

thf(zip_derived_cl2_081,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl2_082,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl15404,plain,
    ( sz10
    = ( sdtasdt0 @ sz10 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl15221,zip_derived_cl2,zip_derived_cl2]) ).

thf(zip_derived_cl15404_083,plain,
    ( sz10
    = ( sdtasdt0 @ sz10 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl15221,zip_derived_cl2,zip_derived_cl2]) ).

thf(zip_derived_cl17750,plain,
    ( sz10
    = ( sdtpldt0 @ sz00 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl14476,zip_derived_cl15404,zip_derived_cl15404]) ).

thf(zip_derived_cl10_084,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ ( smndt0 @ X0 ) )
        = sz00 )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddInvr]) ).

thf(zip_derived_cl7_085,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAddAsso]) ).

thf(zip_derived_cl151,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ ( sdtpldt0 @ X1 @ X0 ) )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ ( smndt0 @ ( sdtpldt0 @ X1 @ X0 ) ) )
      | ( sz00
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ ( smndt0 @ ( sdtpldt0 @ X1 @ X0 ) ) ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl7]) ).

thf(zip_derived_cl4_086,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( aElement0 @ ( sdtpldt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB]) ).

thf(zip_derived_cl3281,plain,
    ! [X0: $i,X1: $i] :
      ( ( sz00
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ ( smndt0 @ ( sdtpldt0 @ X1 @ X0 ) ) ) ) )
      | ~ ( aElement0 @ ( smndt0 @ ( sdtpldt0 @ X1 @ X0 ) ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl151,zip_derived_cl4]) ).

thf(zip_derived_cl17767,plain,
    ( ( sz00
      = ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ ( smndt0 @ sz10 ) ) ) )
    | ~ ( aElement0 @ ( smndt0 @ sz10 ) )
    | ~ ( aElement0 @ sz00 )
    | ~ ( aElement0 @ sz10 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl17750,zip_derived_cl3281]) ).

thf(zip_derived_cl2126_087,plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2125,'6']) ).

thf(zip_derived_cl1_088,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2_089,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl17790,plain,
    ( sz00
    = ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ ( smndt0 @ sz10 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl17767,zip_derived_cl2126,zip_derived_cl1,zip_derived_cl2]) ).

thf(zip_derived_cl9_090,plain,
    ! [X0: $i] :
      ( ( X0
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddZero]) ).

thf(zip_derived_cl7_091,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAddAsso]) ).

thf(zip_derived_cl156,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ X0 @ X1 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl7]) ).

thf(zip_derived_cl1_092,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl166,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ X0 @ X1 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl156,zip_derived_cl1]) ).

thf(zip_derived_cl167,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ X0 @ X1 ) ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl166]) ).

thf(zip_derived_cl19114,plain,
    ( ( ( sdtpldt0 @ sz10 @ ( smndt0 @ sz10 ) )
      = sz00 )
    | ~ ( aElement0 @ ( smndt0 @ sz10 ) )
    | ~ ( aElement0 @ sz10 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl17790,zip_derived_cl167]) ).

thf(zip_derived_cl2126_093,plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2125,'6']) ).

thf(zip_derived_cl2_094,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl19137,plain,
    ( ( sdtpldt0 @ sz10 @ ( smndt0 @ sz10 ) )
    = sz00 ),
    inference(demod,[status(thm)],[zip_derived_cl19114,zip_derived_cl2126,zip_derived_cl2]) ).

thf(zip_derived_cl11_095,plain,
    ! [X0: $i] :
      ( ( sz00
        = ( sdtpldt0 @ ( smndt0 @ X0 ) @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddInvr]) ).

thf(zip_derived_cl7_096,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAddAsso]) ).

thf(zip_derived_cl158,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ ( smndt0 @ X1 ) )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ ( smndt0 @ X1 ) @ ( sdtpldt0 @ X1 @ X0 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl7]) ).

thf(zip_derived_cl169,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ ( smndt0 @ X1 ) @ ( sdtpldt0 @ X1 @ X0 ) ) )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ ( smndt0 @ X1 ) )
      | ~ ( aElement0 @ X1 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl158]) ).

thf(zip_derived_cl3_097,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( smndt0 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mSortsU]) ).

thf(zip_derived_cl3984,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ ( smndt0 @ X1 ) @ ( sdtpldt0 @ X1 @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl169,zip_derived_cl3]) ).

thf(zip_derived_cl19150,plain,
    ( ~ ( aElement0 @ sz10 )
    | ~ ( aElement0 @ ( smndt0 @ sz10 ) )
    | ( ( sdtpldt0 @ sz00 @ ( smndt0 @ sz10 ) )
      = ( sdtpldt0 @ ( smndt0 @ sz10 ) @ sz00 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl19137,zip_derived_cl3984]) ).

thf(zip_derived_cl2_098,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl2126_099,plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2125,'6']) ).

thf(zip_derived_cl19173,plain,
    ( ( sdtpldt0 @ sz00 @ ( smndt0 @ sz10 ) )
    = ( sdtpldt0 @ ( smndt0 @ sz10 ) @ sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl19150,zip_derived_cl2,zip_derived_cl2126]) ).

thf(zip_derived_cl19173_100,plain,
    ( ( sdtpldt0 @ sz00 @ ( smndt0 @ sz10 ) )
    = ( sdtpldt0 @ ( smndt0 @ sz10 ) @ sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl19150,zip_derived_cl2,zip_derived_cl2126]) ).

thf(zip_derived_cl8_101,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ sz00 )
        = X0 )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mAddZero]) ).

thf(zip_derived_cl19510,plain,
    ( ( ( sdtpldt0 @ sz00 @ ( smndt0 @ sz10 ) )
      = ( smndt0 @ sz10 ) )
    | ~ ( aElement0 @ ( smndt0 @ sz10 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl19173,zip_derived_cl8]) ).

thf(zip_derived_cl2126_102,plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2125,'6']) ).

thf(zip_derived_cl19535,plain,
    ( ( sdtpldt0 @ sz00 @ ( smndt0 @ sz10 ) )
    = ( smndt0 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl19510,zip_derived_cl2126]) ).

thf(zip_derived_cl19544,plain,
    ( ( smndt0 @ sz10 )
    = ( sdtpldt0 @ ( smndt0 @ sz10 ) @ sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl19173,zip_derived_cl19535]) ).

thf(zip_derived_cl3984_103,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ ( smndt0 @ X1 ) @ ( sdtpldt0 @ X1 @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl169,zip_derived_cl3]) ).

thf(zip_derived_cl19887,plain,
    ( ~ ( aElement0 @ ( smndt0 @ sz10 ) )
    | ~ ( aElement0 @ sz00 )
    | ( ( sdtpldt0 @ sz00 @ sz00 )
      = ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) @ ( smndt0 @ sz10 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl19544,zip_derived_cl3984]) ).

thf(zip_derived_cl2126_104,plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2125,'6']) ).

thf(zip_derived_cl1_105,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl36_106,plain,
    ( ( sdtpldt0 @ sz00 @ sz00 )
    = sz00 ),
    inference(demod,[status(thm)],[zip_derived_cl34,zip_derived_cl1]) ).

thf(zip_derived_cl19914,plain,
    ( sz00
    = ( sdtpldt0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) @ ( smndt0 @ sz10 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl19887,zip_derived_cl2126,zip_derived_cl1,zip_derived_cl36]) ).

thf(mAddComm,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 ) )
     => ( ( sdtpldt0 @ W0 @ W1 )
        = ( sdtpldt0 @ W1 @ W0 ) ) ) ).

thf(zip_derived_cl6,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mAddComm]) ).

thf(zip_derived_cl20419,plain,
    ( ~ ( aElement0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
    | ~ ( aElement0 @ ( smndt0 @ sz10 ) )
    | ( sz00
      = ( sdtpldt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl19914,zip_derived_cl6]) ).

thf(zip_derived_cl18,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ X0 )
        = ( smndt0 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(cnf,[status(esa)],[mMulMnOne]) ).

thf(zip_derived_cl8480_107,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ sz10 @ X0 )
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8479]) ).

thf(zip_derived_cl4_108,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( aElement0 @ ( sdtpldt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB]) ).

thf(zip_derived_cl8516,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ sz00 )
      | ~ ( aElement0 @ X0 )
      | ( aElement0 @ ( sdtasdt0 @ sz10 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl8480,zip_derived_cl4]) ).

thf(zip_derived_cl1_109,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl8562,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ( aElement0 @ ( sdtasdt0 @ sz10 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl8516,zip_derived_cl1]) ).

thf(zip_derived_cl8563,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( sdtasdt0 @ sz10 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8562]) ).

thf(zip_derived_cl325_110,plain,
    ( ! [X0: $i,X1: $i] :
        ( ~ ( aElement0 @ X0 )
        | ~ ( aElement0 @ X1 )
        | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
          = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) )
   <= ! [X0: $i,X1: $i] :
        ( ~ ( aElement0 @ X0 )
        | ~ ( aElement0 @ X1 )
        | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
          = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl324]) ).

thf(zip_derived_cl5_111,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( aElement0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

thf(zip_derived_cl327,plain,
    ( ! [X0: $i,X1: $i] :
        ( ~ ( aElement0 @ X1 )
        | ~ ( aElement0 @ X0 )
        | ~ ( aElement0 @ X1 )
        | ~ ( aElement0 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) )
        | ( aElement0 @ ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) ) ) )
   <= ! [X0: $i,X1: $i] :
        ( ~ ( aElement0 @ X0 )
        | ~ ( aElement0 @ X1 )
        | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
          = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl325,zip_derived_cl5]) ).

thf(zip_derived_cl353,plain,
    ( ! [X0: $i,X1: $i] :
        ( ( aElement0 @ ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) ) )
        | ~ ( aElement0 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) )
        | ~ ( aElement0 @ X0 )
        | ~ ( aElement0 @ X1 ) )
   <= ! [X0: $i,X1: $i] :
        ( ~ ( aElement0 @ X0 )
        | ~ ( aElement0 @ X1 )
        | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
          = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl327]) ).

thf('19',plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) )
        = ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) ) ) ),
    inference('sat_resolution*',[status(thm)],['0','3']) ).

thf(zip_derived_cl495,plain,
    ! [X0: $i,X1: $i] :
      ( ( aElement0 @ ( smndt0 @ ( sdtasdt0 @ X1 @ X0 ) ) )
      | ~ ( aElement0 @ ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl353,'19']) ).

thf(zip_derived_cl9185,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ ( smndt0 @ sz10 ) )
      | ( aElement0 @ ( smndt0 @ ( sdtasdt0 @ X0 @ sz10 ) ) )
      | ~ ( aElement0 @ sz10 )
      | ~ ( aElement0 @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl8563,zip_derived_cl495]) ).

thf(zip_derived_cl2126_112,plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2125,'6']) ).

thf(zip_derived_cl2_113,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl9234,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( smndt0 @ ( sdtasdt0 @ X0 @ sz10 ) ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl9185,zip_derived_cl2126,zip_derived_cl2]) ).

thf(zip_derived_cl10344,plain,
    ( ~ ( aElement0 @ sz10 )
    | ( aElement0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
    | ~ ( aElement0 @ ( smndt0 @ sz10 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl18,zip_derived_cl9234]) ).

thf(zip_derived_cl2_114,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl2126_115,plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2125,'6']) ).

thf(zip_derived_cl10358,plain,
    aElement0 @ ( smndt0 @ ( smndt0 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl10344,zip_derived_cl2,zip_derived_cl2126]) ).

thf(zip_derived_cl2126_116,plain,
    aElement0 @ ( smndt0 @ sz10 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl2125,'6']) ).

thf(zip_derived_cl20443,plain,
    ( sz00
    = ( sdtpldt0 @ ( smndt0 @ sz10 ) @ ( smndt0 @ ( smndt0 @ sz10 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl20419,zip_derived_cl10358,zip_derived_cl2126]) ).

thf(zip_derived_cl3684_117,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ ( smndt0 @ X1 ) @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl165,zip_derived_cl3]) ).

thf(zip_derived_cl20483,plain,
    ( ~ ( aElement0 @ sz10 )
    | ~ ( aElement0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
    | ( ( sdtpldt0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
      = ( sdtpldt0 @ sz10 @ sz00 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl20443,zip_derived_cl3684]) ).

thf(zip_derived_cl2_118,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl10358_119,plain,
    aElement0 @ ( smndt0 @ ( smndt0 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl10344,zip_derived_cl2,zip_derived_cl2126]) ).

thf(zip_derived_cl20504,plain,
    ( ( sdtpldt0 @ sz00 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
    = ( sdtpldt0 @ sz10 @ sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl20483,zip_derived_cl2,zip_derived_cl10358]) ).

thf(zip_derived_cl167_120,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ X0 @ X1 ) ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl166]) ).

thf(zip_derived_cl20554,plain,
    ( ( ( sdtpldt0 @ sz10 @ sz00 )
      = ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ sz00 ) ) )
    | ~ ( aElement0 @ ( smndt0 @ ( smndt0 @ sz10 ) ) )
    | ~ ( aElement0 @ sz00 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl20504,zip_derived_cl167]) ).

thf(zip_derived_cl10358_121,plain,
    aElement0 @ ( smndt0 @ ( smndt0 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl10344,zip_derived_cl2,zip_derived_cl2126]) ).

thf(zip_derived_cl1_122,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl20577,plain,
    ( ( sdtpldt0 @ sz10 @ sz00 )
    = ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ sz00 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl20554,zip_derived_cl10358,zip_derived_cl1]) ).

thf(zip_derived_cl7_123,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ( ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAddAsso]) ).

thf(zip_derived_cl6_124,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mAddComm]) ).

thf(zip_derived_cl147,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X2 )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ ( sdtpldt0 @ X2 @ X1 ) )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtpldt0 @ X2 @ ( sdtpldt0 @ X1 @ X0 ) )
        = ( sdtpldt0 @ X0 @ ( sdtpldt0 @ X2 @ X1 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl6]) ).

thf(zip_derived_cl172,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( sdtpldt0 @ X2 @ ( sdtpldt0 @ X1 @ X0 ) )
        = ( sdtpldt0 @ X0 @ ( sdtpldt0 @ X2 @ X1 ) ) )
      | ~ ( aElement0 @ ( sdtpldt0 @ X2 @ X1 ) )
      | ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X2 )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl147]) ).

thf(zip_derived_cl4_125,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( aElement0 @ ( sdtpldt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB]) ).

thf(zip_derived_cl5370,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X2 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtpldt0 @ X2 @ ( sdtpldt0 @ X1 @ X0 ) )
        = ( sdtpldt0 @ X0 @ ( sdtpldt0 @ X2 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl172,zip_derived_cl4]) ).

thf(zip_derived_cl20675,plain,
    ( ~ ( aElement0 @ sz00 )
    | ~ ( aElement0 @ sz00 )
    | ~ ( aElement0 @ sz10 )
    | ( ( sdtpldt0 @ sz10 @ sz00 )
      = ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz00 @ sz10 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl20577,zip_derived_cl5370]) ).

thf(zip_derived_cl1_126,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl1_127,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2_128,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl17750_129,plain,
    ( sz10
    = ( sdtpldt0 @ sz00 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl14476,zip_derived_cl15404,zip_derived_cl15404]) ).

thf(zip_derived_cl17750_130,plain,
    ( sz10
    = ( sdtpldt0 @ sz00 @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl14476,zip_derived_cl15404,zip_derived_cl15404]) ).

thf(zip_derived_cl20711,plain,
    ( ( sdtpldt0 @ sz10 @ sz00 )
    = sz10 ),
    inference(demod,[status(thm)],[zip_derived_cl20675,zip_derived_cl1,zip_derived_cl1,zip_derived_cl2,zip_derived_cl17750,zip_derived_cl17750]) ).

thf(zip_derived_cl3984_131,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X1 )
      | ~ ( aElement0 @ X0 )
      | ( ( sdtpldt0 @ sz00 @ X0 )
        = ( sdtpldt0 @ ( smndt0 @ X1 ) @ ( sdtpldt0 @ X1 @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl169,zip_derived_cl3]) ).

thf(zip_derived_cl20731,plain,
    ( ~ ( aElement0 @ sz10 )
    | ~ ( aElement0 @ sz00 )
    | ( ( sdtpldt0 @ sz00 @ sz00 )
      = ( sdtpldt0 @ ( smndt0 @ sz10 ) @ sz10 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl20711,zip_derived_cl3984]) ).

thf(zip_derived_cl2_132,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl1_133,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl36_134,plain,
    ( ( sdtpldt0 @ sz00 @ sz00 )
    = sz00 ),
    inference(demod,[status(thm)],[zip_derived_cl34,zip_derived_cl1]) ).

thf(zip_derived_cl20760,plain,
    ( sz00
    = ( sdtpldt0 @ ( smndt0 @ sz10 ) @ sz10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl20731,zip_derived_cl2,zip_derived_cl1,zip_derived_cl36]) ).

thf(zip_derived_cl22628,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( sz00
        = ( sdtasdt0 @ X0 @ sz00 ) )
      | ~ ( aElement0 @ ( sdtasdt0 @ X0 @ sz10 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl22377,zip_derived_cl2,zip_derived_cl20760]) ).

thf(zip_derived_cl12_135,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(zip_derived_cl8563_136,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( sdtasdt0 @ sz10 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8562]) ).

thf(zip_derived_cl9187,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ sz10 )
      | ( aElement0 @ ( sdtasdt0 @ X0 @ sz10 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl12,zip_derived_cl8563]) ).

thf(zip_derived_cl2_137,plain,
    aElement0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl9215,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ( aElement0 @ ( sdtasdt0 @ X0 @ sz10 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl9187,zip_derived_cl2]) ).

thf(zip_derived_cl9216,plain,
    ! [X0: $i] :
      ( ( aElement0 @ ( sdtasdt0 @ X0 @ sz10 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl9215]) ).

thf(zip_derived_cl22642,plain,
    ! [X0: $i] :
      ( ( sz00
        = ( sdtasdt0 @ X0 @ sz00 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl22628,zip_derived_cl9216]) ).

thf(zip_derived_cl12_138,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(zip_derived_cl22644,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ sz00 )
      | ( sz00
        = ( sdtasdt0 @ sz00 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl22642,zip_derived_cl12]) ).

thf(zip_derived_cl1_139,plain,
    aElement0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl22757,plain,
    ! [X0: $i] :
      ( ~ ( aElement0 @ X0 )
      | ~ ( aElement0 @ X0 )
      | ( sz00
        = ( sdtasdt0 @ sz00 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl22644,zip_derived_cl1]) ).

thf(zip_derived_cl22758,plain,
    ! [X0: $i] :
      ( ( sz00
        = ( sdtasdt0 @ sz00 @ X0 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl22757]) ).

thf(m__,conjecture,
    ( ( ( sdtasdt0 @ xx @ sz00 )
      = sz00 )
    & ( sz00
      = ( sdtasdt0 @ sz00 @ xx ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ( ( sdtasdt0 @ xx @ sz00 )
        = sz00 )
      & ( sz00
        = ( sdtasdt0 @ sz00 @ xx ) ) ),
    inference('cnf.neg',[status(esa)],[m__]) ).

thf(zip_derived_cl21,plain,
    ( ( ( sdtasdt0 @ xx @ sz00 )
     != sz00 )
    | ( sz00
     != ( sdtasdt0 @ sz00 @ xx ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl23,plain,
    ( ( sz00
     != ( sdtasdt0 @ sz00 @ xx ) )
   <= ( sz00
     != ( sdtasdt0 @ sz00 @ xx ) ) ),
    inference(split,[status(esa)],[zip_derived_cl21]) ).

thf(zip_derived_cl22642_140,plain,
    ! [X0: $i] :
      ( ( sz00
        = ( sdtasdt0 @ X0 @ sz00 ) )
      | ~ ( aElement0 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl22628,zip_derived_cl9216]) ).

thf(zip_derived_cl22,plain,
    ( ( ( sdtasdt0 @ xx @ sz00 )
     != sz00 )
   <= ( ( sdtasdt0 @ xx @ sz00 )
     != sz00 ) ),
    inference(split,[status(esa)],[zip_derived_cl21]) ).

thf(zip_derived_cl22754,plain,
    ( ( ~ ( aElement0 @ xx )
      | ( sz00 != sz00 ) )
   <= ( ( sdtasdt0 @ xx @ sz00 )
     != sz00 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl22642,zip_derived_cl22]) ).

thf(m__468,axiom,
    aElement0 @ xx ).

thf(zip_derived_cl20,plain,
    aElement0 @ xx,
    inference(cnf,[status(esa)],[m__468]) ).

thf(zip_derived_cl22915,plain,
    ( ( sz00 != sz00 )
   <= ( ( sdtasdt0 @ xx @ sz00 )
     != sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl22754,zip_derived_cl20]) ).

thf('20',plain,
    ( ( sdtasdt0 @ xx @ sz00 )
    = sz00 ),
    inference(simplify,[status(thm)],[zip_derived_cl22915]) ).

thf('21',plain,
    ( ( sz00
     != ( sdtasdt0 @ sz00 @ xx ) )
    | ( ( sdtasdt0 @ xx @ sz00 )
     != sz00 ) ),
    inference(split,[status(esa)],[zip_derived_cl21]) ).

thf('22',plain,
    ( sz00
   != ( sdtasdt0 @ sz00 @ xx ) ),
    inference('sat_resolution*',[status(thm)],['20','21']) ).

thf(zip_derived_cl22920,plain,
    ( sz00
   != ( sdtasdt0 @ sz00 @ xx ) ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl23,'22']) ).

thf(zip_derived_cl23339,plain,
    ( ~ ( aElement0 @ xx )
    | ( sz00 != sz00 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl22758,zip_derived_cl22920]) ).

thf(zip_derived_cl20_141,plain,
    aElement0 @ xx,
    inference(cnf,[status(esa)],[m__468]) ).

thf(zip_derived_cl23518,plain,
    sz00 != sz00,
    inference(demod,[status(thm)],[zip_derived_cl23339,zip_derived_cl20]) ).

thf(zip_derived_cl23519,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl23518]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG083+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.c6ADvbKh6T true
% 0.14/0.34  % Computer : n025.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun Aug 27 03:23:23 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  % Running portfolio for 300 s
% 0.14/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.35  % Running in FO mode
% 0.21/0.64  % Total configuration time : 435
% 0.21/0.64  % Estimated wc time : 1092
% 0.21/0.64  % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.70  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.70  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.79  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 19.97/3.48  % Solved by fo/fo1_av.sh.
% 19.97/3.48  % done 1026 iterations in 2.717s
% 19.97/3.48  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 19.97/3.48  % SZS output start Refutation
% See solution above
% 19.97/3.49  
% 19.97/3.49  
% 19.97/3.49  % Terminating...
% 19.97/3.56  % Runner terminated.
% 19.97/3.57  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------